Spatial Electric Load Forecasting Second Edition, Revised and Expanded
H. Lee Willis ABB Inc. Raleigh, North Carolina
M A R C E L
MARCEL DEKKER, INC. D E K K E R
NEW YORK • BASEL
ISBN: 0-8247-0840-7 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812. CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Web http ://www.dekker. com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA
POWER ENGINEERING Series Editor
H. Lee Willis ABB Inc. Raleigh, North Carolina
1. Power Distribution Planning Reference Book, H. Lee Willis 2. Transmission Network Protection: Theory and Practice, Y. G. Paithankar 3. Electrical Insulation in Power Systems, N. H. Malik, A. A. AI-Arainy, and M. I. Qureshi 4. Electrical Power Equipment Maintenance and Testing, Paul Gill 5. Protective Relaying: Principles and Applications, Second Edition, J. Lewis Blackburn 6. Understanding Electric Utilities and De-Regulation, Lorrin Philipson and H. Lee Willis 7. Electrical Power Cable Engineering, William A. Thue 8. Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, James A. Momoh and Mohamed E. EI-Hawary 9. Insulation Coordination for Power Systems, Andrew R. Hileman 10. Distributed Power Generation: Planning and Evaluation, H. Lee Willis and Walter G. Scott 11. Electric Power System Applications of Optimization, James A. Momoh 12. Aging Power Delivery Infrastructures, H. Lee Willis, Gregory V. Welch, and Randall R. Schrieber 13. Restructured Electrical Power Systems: Operation, Trading, and Volatility, Mohammad Shahidehpour and Muwaffaq Alomoush 14. Electric Power Distribution Reliability, Richard E. Brown 15. Computer-Aided Power System Analysis, Ramasamy Natarajan 16. Power System Analysis: Short-Circuit Load Flow and Harmonics, J. C. Das 17. Power Transformers: Principles and Applications, John J. Winders, Jr. 18. Spatial Electric Load Forecasting: Second Edition, Revised and Expanded, H. Lee Willis
ADDITIONAL VOLUMES IN PREPARATION
Dielectrics in Electric Fields, Gorur G. Raju
Series Introduction A critical function contributing to the success of any enterprise is its ability to dependably forecast the volume and character of its future business. Good forecasts permit a company to keep capacity margins and inventory lean, delay spending until the last moment, but still satisfy customer needs. For a power delivery utility, forecasts of its future business volume must describe both how much power its customers will need and where that power must be delivered, so that the utility can make arrangements to convey the amounts required to the locations where it will be needed. The power delivery utility needs a spatial electric load forecast, a projection of future electric demand that identifies both how much power will be needed and where that future electric demand will be located. The updates and additions included in this second edition of Spatial Electric Load Forecasting reflect the larger changes that have transformed the electric power industry in the last ten years. First, this edition has grown by 63%. Modern power delivery utilities operate with narrower capacity and financial margins and are held to higher performance standards than in the past. This means that they need both more accurate and more comprehensively detailed processes, including forecasts, which must be applied with much more focus and far less tolerance for error. Simply put, the job of running an electric delivery utility has become much more difficult, and this is reflected in all aspects of its work, including its forecasting. Second, while this book includes updated and expanded treatment of technical theory, it focuses much more on practical application, particularly in near- and medium-term time frames. Modern utilities must put added emphasis
iv
Series Introduction
on short-term improvement and maintaining good performance in the near term as they build for the future. Finally, this book is more accessible, with expanded introductory-level material and new tutorial and self-study chapters, reflecting the growing need throughout the power industry to develop new experts as an aging workforce of planners and engineers retires. As both the author of this book and the editor of the Power Engineering Series, I am proud to include Spatial Electric Load Forecasting: Second Edition, Revised and Expanded, among this important group of books. Like all books in Marcel Dekker, Inc.'s Power Engineering Series, this book discusses modern power technology in a context of proven, practical applications. It is useful as a reference book as well as for self-study and advanced classroom use. Marcel Dekker, Inc.'s Power Engineering Series includes books that cover the entire field of power engineering, in all of its specialties and sub-genres, all aimed at providing practicing power engineers with the knowledge and techniques they need to meet the electric industry's challenges in the 21st century. H. Lee Willis
Preface This second edition of Spatial Electric Load Forecasting is both a reference and a tutorial guide on forecasting of electric load for power delivery system planning. Like the first edition, it provides nearly 450 pages of detailed discussion on forecasting and forecasting methods. But in addition, this revised edition provides nearly 300 new pages emphasizing practical application - how planners can evaluate their forecasting needs, what methods they should select for which situations, where they can find required data, and how to apply both data and method to best support the planning process. Spatial electric load forecasting is as critical a first step in transmission and distribution (T&D) planning as it has ever been. As was always the case, the efficiency, economy, and reliability of modern power systems depend not only on how well the equipment is selected, sized, and engineered, but on how well it is sited - put in the optimal locations with respect to area needs. A spatial load forecast addresses the where aspect of T&D planning, by studying load growth on a coordinated locational basis throughout the system. Where will demand grow? How much will consumer demand change at this location? The spatial load forecast answers these and other questions about future demand in a way that supports effective T&D planning. This -where, or spatial, dimension is what sets spatial load forecasting apart from other types of energy forecasting. The three-dimensional nature of spatial forecasting (predicting load growth as a function of the two X-Y dimensions in space, plus the traditional forecasting dimension of time) makes it particularly challenging. It also means that many of the "rules" encountered, and tradeoffs
vi
Preface
made in accommodating them, will run counter to traditional "projection in time" paradigms. In addition, in the last decade the needs for and application of spatial forecasting have expanded beyond the traditional least-cost planning venue. Modern utilities as pushing their systems to achieve higher utilization rates (higher ratios of peak demand served to total installed capacity) in order to improve investment efficiency, while making firm commitments to high reliability levels. Spatial forecasting is now important as a basis for reliability and reliability-based planning, too, and new methodology has been developed to accommodate this need. This second edition was written to serve the needs of modern electric power delivery planners. It reflects the changing nature of the industry in myriad ways, but three changes seem most significant: This edition includes greatly expanded discussion of applications. The original edition was aimed primarily at experienced planners and focused mostly on theory and methodology. By the author's survey, when first published, the average owner of that edition had over 15 years of experience in T&D planning. A similar survey in the last year indicated the average user of the book now has less than three years experience as a planner. To meet this need, Chapters 18 through 22, comprising nearly 200 pages, cover in detail the nuances of forecasting in urban, suburban, and rural areas. They focus on the characteristics that can be expected when forecasting in rapidly developing nations, in urban areas with a lot of redevelopment, or in a variety of common types of unusual forecasting contexts which planners may encounter. These chapters not only address forecasting but discuss some of the best practices related to using a forecast and interfacing it with the planning functions that follow it. Weather adjustment of load data and normalization of forecasts to standard design conditions is the subject of 74 pages of new material (Chapters 5 and 6). Measured by page count, the book has changed from a 1% focus on weather adjustment in the first edition to a 9% focus in the second edition. This meets a dramatically growing need in the utility industry. As more utilities push their system utilization rates upward, the risk associated with extreme weather must be a real consideration in their planning. Many of the large interruption events that plagued utilities in the past decade were caused at least in part by incorrect anticipation of peak demands tied to extreme weather. The term "utility customer" has been replaced with "energy consumer." In a de-regulated industry it is often difficult to determine who is whose customer - the homeowner is the ESCo's customer, who in turn is the Distco's customer. To clear up any ambiguity in the use of the word
Preface
vii
customer and because it seems a more apt description of the energy user's role, the term "consumer" is used throughout to identify the households and businesses that are actually using the power. The book is organized into three sections, or groups of chapters, which deal respectively with background and basics, methodology, and application. Chapters 1 - 8 discuss the requirements for and characteristics of spatial forecasts and provide tutorials on a number of basic and background issues associated with modern forecasting and planning. Chapter 1 begins this group of chapters with a tutorial on T&D systems, T&D planning, and spatial electric load forecasting, for those unfamiliar with the field. It is a good stand-alone overview but will prove somewhat redundant to experienced forecasters and planners. Chapter 2 looks at the basis underlying electric load, including the reasons why consumers need power (end uses) and the characteristics of the appliances, devices, and machines that translate end-use demand into electric demand. It provides a foundation for planners who want to understand load and reliability needs at the most rudimentary level, which is often necessary in particularly challenging forecast situations. Chapter 3 takes what might be termed the opposite view of electric load from Chapter 2. Here, electric demand is viewed from the perspective of the power system, regardless of its causes and consumer profiles. The characteristics of electric demand, including temporal behavior and particularly coincidence of load as a function of consumer group size, are examined in a comprehensive manner. Chapter 4 merges the themes of Chapters 2 and 3 and develops them into various types of load models, each appropriate to different types of demand or consumer analysis situations. The chapter looks at quantitative formats, and various types of end-use representations, that analyze and model load as a function of time. Some of this detail is needed as a foundation for Chapters 5 and 6. Chapter 5 is the first of two chapters on weather, its impact on load, and the issues and methods that planners must deal with in the forecasting and planning process. It is basically a tutorial on weather as viewed by the load forecaster and delivery planner, and on how this relationship can be modeled for forecasting purposes. Chapter 6 builds on Chapter 5, looking at extreme weather and the electric peaks it causes. What is extreme weather? How does a utility analyze and characterize it? Most important, how do planners identify an "extreme enough" weather target for planning? The chapter reviews several methods of increasing complexity and quality to address this last question. Chapter 7 is the first to take up the spatial aspect of electric load growth in detail. It focuses on spatial growth behavior - on how electric load growth
viii
Preface
"looks" as a ftmction of location and how it spreads or diffuses over wider areas as cities and towns grow. It develops and explores the consequences of the fundamental rule of spatial load growth - the hierarchical "S" curve growth characteristic. Chapter 8 looks at what qualities are most importance in a good load forecast. In particular, it explores the meaning of "accuracy" in the spatial format, when an error can include merely getting the location wrong, even if the amount of load growth and its timing was forecast correctly. Accuracy and error behavior in a spatial context often seem counterintuitive to the uninitiated. Once understood, however, the concepts are simple, even if the mathematics behind them are not. Chapters 9 through 16 constitute the second part of the book and cover forecasting methods including basic approaches, data usage and algorithms, and procedures. These chapters are largely taken from the first edition, but have been updated as appropriate. Chapter 15, on hybrid algorithms, is new, covering methods that had not been developed when the first edition was published. Chapter 9, on trending methods, covers methods that forecast future load growth by working with historical load values themselves. Extrapolation of past area load growth trends using polynomial curve fitting (by regression) is the classic trending method and the technique most people think of first when they face spatial forecasting problems. But as the chapter makes clear, there are a host of innovative and worthwhile improvements on that basic method, and there are several entirely different trending approaches worth considering. Chapter 10 addresses methods that forecast spatial load growth by modeling the root causes of load growth, rather than just trending historical load measurements themselves. This chapter introduces the basic definitions and concepts, which are developed in subsequent chapters Chapter 11 covers an actual simulation-based forecast in a step-by-step manner, where every computation and data manipulation is done manually, rather than by computer. Actually performing a simulation forecast manually would be prohibitively expensive for most utilities, but it proves quite illuminating as a learning example and gives a very thorough example for anyone needing to learn the simulation technique. Chapters 12, 13, and 14 constitute a three-chapter discussion of simulation algorithms and how they are rendered as computer programs. These chapters cover, respectively, the overall organization of data flow, functions, and the division of the forecasting process in major program modules; the various computational engines that are used in each of the major modules of a simulation program, and their variations; and a number of "tricks" or advanced features that address special situations or accelerate analytical speed and accuracy. These chapters go beyond the understanding of methodology required by most forecasters, but include the detail needed by those who are writing or tailoring algorithms.
Preface
ix
Chapter 15 covers a relatively new category of forecasting algorithm in which elements of trending and simulation are melded together to obtain (at least hopefully) advantages over either of the two approaches alone. The chapter introduces an information-usage perspective for evaluating what forecast methods do with their data, after which it looks at three hybrid algorithms, each a very different mix of features taken from the trending and simulation worlds. Chapter 16 addresses two challenging areas of modeling consumer demand in space and time. The first involves using a simulation method to forecast demand for not only electric energy, but gas and fuel oil too. Such forecasts are very useful in "converged" planning by gas and electric utilities. The second area of advanced modeling seeks to analyze demand for power quality, and how that varies with location, time, and consumer class. Chapters 17 through 22 constitute the final section of the book, addressing practical application. Chapter 17 presents a comprehensive "level playing field" evaluation of major forecasting methods including a look at 19 specific forecast programs and methods, examples of trending, simulation, and hybrid approaches. It presents and then applies by example case study a method to evaluate forecast needs and select the most appropriate forecasting method for any electric utility situation. Chapter 18 introduces the concept of development dimensionality, a measure of how local-area load growth interacts with growth in those areas around it, and how the complexity or "dimension" of this process increases over time. In some sense this chapter can be viewed as an advanced discussion of load growth behavior and the "S" curve growth characteristics covered in Chapter 7. However, the focus here is on practical application, on understanding this dimensionality and how it impacts the approaches planners must use in various types of forecast situations. Chapter 19 looks in detail at load growth caused by urban "redevelopment," which occurs whenever existing land use in an area of a city is replaced by some (usually higher density) type of new development. Such growth is responsible for 25% of all load growth. The chapter begins with a quantitative look at redevelopment and its characteristics. It classifies redevelopment into five categories and discusses nine methods of redevelopment forecasting, and their advantages and disadvantages. Chapter 20 discusses spatial forecasting in developing economies, particularly where forecasters must predict the load in rural provinces previously without electric power but scheduled for "electrification." Forecasting methods and procedures appropriate to these situations are discussed. A forecast of such an area is used as an example and method, data, and results analyzed in detail. Chapter 21 is an accumulation of observations and advice on how to maximize forecast accuracy and minimize effort expended in practical spatial forecasting. Although its focus is on simulation methods, it will be of use to anyone trying to get the most out of any forecasting method, simulation or
x
Preface
trending. Its first two sections, on application and calibration, are meant to be of use to planners regardless of the particular program or approach they are using. The remaining two sections address how to work around or "live with" limitations and features common to several specific spatial simulation programs in wide use. Chapter 22 wraps up the book with a summary of forecast priorities and a presentation of recommendations and pitfalls. Together with Chapter 1, it provides a good managerial-level tutorial on spatial forecasting, its priorities, and the chief concerns that both management and technician must keep in mind to do the job right. I wish to thank my many colleagues and co-workers who have provided so much assistance and advice on this book, in particular, Drs. Richard Brown and Andrew Hanson and David Farmer, Randy Schrieber, and Greg Welch for their valuable assistance and good-natured skepticism and encouragement. I also owe a debt of gratitude to Mike Engel of Midwest Energy, David Helwig of Commonwealth Edison, and Jim Bouford of National Grid for their advice and suggestions. In addition, as always, Rita Lazazzaro, Lila Harris, and Russell Dekker of Marcel Dekker, Inc., have done an outstanding job of providing encouragement and support. H. Lee Willis
Contents
Series Introduction Preface 1
Spatial Electric Load Forecasting 1.1 1.2 1.3 1.4
2
Hi v 1
Spatial Load Forecasting T&D Planning Requirements for a T&D Load Forecast Summary References
1 4 25 35 35
Consumer Demand for Power and Reliability
37
2.1 2.2 2.3 2.4 2.5
37 38 49 65 70 71
The Two Qs: Quality and Quantity of Power Electric Consumer Demand for Quantity of Power Electric Consumer Demand for Quality of Power Two-Q Analysis: Quantity and Quality versus Cost Conclusion and Summary References
XI
xii
3
4
Contents
Coincidence and Load Behavior
73
3.1 3.2 3.3 3.4
73 74 85 94 94
Introduction Peak Load, Diversity, and Load Curve Behavior Measuring and Modeling Load Curves Summary References
Load Curve and End-Use Modeling 4.1 4.2 4.3 4.4 4.5
End-Use Analysis of Electric Load The Basic "Curve Adder" End-Use Model Advanced End-Use Models Application of End-Use Models Computer Implemented End-Use Load Curve Model References
95 95 102 109 112 121 126
Weather and Electric Load 5.1 Introduction 5.2 Weather and Its Measurement 5.3 Weather's Variation with Time and Place 5.4 Weather and Its Impact on Electric Demand References
129 129 131 137 147 165
Weather Design Criteria and Forecast Normalization 6.1 Introduction 6.2 Extreme Weather 6.3 Standardized Weather "Design Criteria" 6.4 Analyzing Weather's Impact on Demand Curve Shape 6.5 Risk-Based Determination of Weather Criteria 6.6 Example: Risk-Based Weather-Related Demand Target Analysis 6.7 How Often Will a Utility See "Weather-Related Events?" 6.8 Summary and Guidelines References
167 167 169 174 180 185 194 197 200 202
Contents
xiii
7
Spatial Load Growth Behavior
203
7.1 7.2 7.3 7.4
203 204 211 228 229
8
9
Introduction Spatial Distribution of Electric Load Small Area Load Growth Behavior Summary References
Spatial Forecast Accuracy and Error Measures
231
8.1 8.2 8.3 8.4
231 232 245 257 259
Introduction Spatial Error: Mistakes in Location Spatial Frequency Perspective on Error Impact Conclusions and Guidelines References
Trending Methods 9.1 9.2 9.3 9.4 9.5
Introduction Trending Using Polynomial Curve Fit Improvements to Regression-Based Curve Fitting Methods Other Trending Methods Summary References
10 Simulation Method: Basic Concepts 10.1 10.2 10.3 10.4 10.5
Introduction Simulation of Electric Load Growth Land-Use Growth: Cause and Effect Quantitative Models of Land-Use Interaction Summary of Key Concept References
11 A Detailed Look at the Simulation Method 11.1 Introduction
261 261 262 273 -293 300 301
303 303 304 314 321 324 324 325 325
xiv
Contents 11.2 Springfield 11.3 The Forecast 11.4 Critique and Commentary on Manual Simulation References
12 Basics of Computerized Simulation 12.1 12.2 12.3 12.4 12.5
Introduction Overall Structure and Common Features Small Area Spatial Module Top-Down Structure Summary and Conclusion References and Bibliography
13 Analytical Building Blocks for Spatial Simulation 13.1 13.2 13.3 13.4
Introduction Land-Use Input-Output Matrix Model Activity Center Gravity Models Consumer-Class Spatial Allocation Using Preference Matching References and Bibliography
14 Advanced Elements of Computerized Simulation 14.1 14.2 14.3 14.4 14.5
Introduction Simulation Program Structure and Function Fast Methods for Spatial Simulation Growth Viewed as a Frequency Domain Process Summary References
15 Hybrid Trending-Simulation Methods 15.1 15.2 15.3 15.4
Introduction Using Information in a Spatial Forecast Land-Use Classified Multivariate Trending (LCMT) Extended Template Matching (ETM)
326 330 369 372
373 373 374 382 391 393 394
397 397 397 405 410 418
421 421 421 436 441 444 445
447 447 448 451 455
Contents
xv
15.5 SUSAN - A Simulation-Driven Trending Method 15.6 Summary and Guidelines References
16 Advanced Demand Methods: Multi-Fuel and Reliability Models 16.1 16.2 16.3 16.4
462 474 475
477
Introduction Simultaneous Modeling of Multiple Energy Types Spatial Value-Based Analysis Conclusion References
477 478 494 504 505
17 Comparison and Selection of Spatial Forecast Methods
507
17.1 17.2 17.3 17.4 17.5 17.6
Introduction Classification of Spatial Forecast Methods Comparison Test of Nineteen Spatial Forecast Methods Data and Data Sources Selecting a Forecast Method Example Selection of a Spatial Forecast Method by a Utility References
18 Development Dimensionality: Urban, Rural and Agrarian Areas 18.1 18.2 18.3 18.4 18.5
Introduction Regional Types and Development Dimension Forecasting Load Growth in Rural Regions Forecasting Load Growth in Agrarian Regions Summary and Guidelines Reference
19 Metropolitan Growth and Urban Redevelopment 19.1 19.2 19.3 19.4
Introduction Redevelopment Is the Process of Urban Growth Representing Redevelopment in Spatial Forecasts Eight Simulation Approaches to Redevelopment Forecasting
507 508 513 533 540 548 565
569 569 571 577 586 590 590 591 591 592 603 606
xvi
Contents 19.5 Recommendations for Modeling Redevelopment Influences 19.6 Summary References
20 Spatial Load Forecasting in Developing Economies 20.1 20.2 20.3 20.4 20.5
Introduction Modeling Load Growth Due to Latent Demand Example Latent Demand Forecast New-City Load Growth Summary and Guidelines
21 Using Spatial Forecasting Methods Well 21.1 21.2 21.3 21.4 21.5 21.6
Introduction Forecast Application Calibration of a Spatial Forecast Model Tricks and Advice for Using Simulation Programs Well Partial-Region Forecast Situations Forecasts That Require Special Methodology References
22 Recommendations and Guidelines 22.1 22.2 22.3 22.4 22.5 Index
Introduction Spatial Forecasting Priorities Recommendations for Successful Forecasting Pitfalls to Avoid How Good Is Good Spatial Forecasting?
626 629 630
631 631 634 643 660 670
673 673 674 680 695 700 709 716 717 717 717 720 730 736 739
1 Spatial Electric Load Forecasting 1.1 SPATIAL LOAD FORECASTING In order to plan the efficient operation and economical capital expansion of an electric power delivery system, the system owner must be able to anticipate the need for power delivery - how much power must be delivered, and where and when it will be needed. Such information is provided by a spatial load forecast, a prediction of future electric demand that includes location (where) as one of its chief elements, in addition to magnitude (how much) and temporal (when) characteristics. Figure 1.1 shows the spatial nature of electric load growth over time, in this case the anticipated growth of electric demand in a metropolitan area in the central United States. Over a twenty-year period, the total electric demand in this city is expected to increase by nearly fifty percent. Growth is expected to affect numerous existing areas of the system - those where load already exists — where the present demand is expected to increase substantially. Facilities in these areas can be expected to be much more heavily loaded in the future, and may need enhancement or redesign to greater capacity. The growth also includes considerable spread of electric demand into currently vacant areas, where no electric demand exists. Here, the utility must schedule additions of equipment and facilities to meet the demand as it develops.
Chapter 1
2011 WINTER PEAK 3442MVA
1991 WINTER PEAK 2310 MVA
Ten miles
Figure 1.1 Maps of peak annual demand for electricity in a major American city, showing the expected growth in demand during a 20-year period as determined using a comprehensive simulation-based method. Growth in some parts of the urban core increases considerably, but in addition, electric load spreads into currently vacant areas as new suburbs are built to accommodate an expanded population.
In addition, a forecast as shown in Figure 1.1 identifies areas where no electric load growth is expected - information quite useful to the utility planner, for it indicates those areas where no new facilities will be needed. In other areas, electric demand may decrease over time, due to numerous causes, particularly the deliberate and planned actions that the utility or the energy consumers on its system may take to reduce energy consumption - demand side management (DSM). Spatial analysis of how these reductions might impact future transmission and distribution (T&D) requirements is a useful feature of electric utility planning, and can be accommodated by some types of spatial forecasting methods. In addition, competitive market assessment and open access planning of electric systems require spatial analysis of the market - the electric demand, and how it will react to changes in price and availability of electric power and its competing energy sources, such as gas and solar power.
Spatial Electric Load Forecasting
3
Small Area Forecasting A very wide variety of methods exist to forecast electric demand growth on a spatial basis. In all of these, geographic location of load growth is accomplished by dividing the utility service territory into many small areas, as shown in Figure 1.2. These might be irregularly shaped areas of varying size, as for example, the service areas of substations or feeders in the system, or they might be square areas defined by a grid. Any technique that forecasts load by extrapolating recent growth trends on a feeder - or substation area- basis is a small area forecasting method (although perhaps not a very accurate one) that works on irregularly shaped and sized areas. The spatial forecasts shown in Figure 1.1 were accomplished by dividing the region studied into 60,000 square areas, each 1/4 mile wide (40 acres). Some spatial forecast methods work with square areas as small as 2.5 acres (1/16 mile wide), analyzing as many as 3,000,000 at one time. Regardless, all spatial forecasts work on a small area basis, but as will be discussed later in this book, not all small area forecasts are spatial forecasts. A spatial forecast involves the coordinated forecast of all small areas in a region, using a consistent and coherent set of assumptions and characteristic factors. Many small area forecast methods, particularly trending, do not, strictly speaking, accomplish this coordination.
Equipment areas
N
llnifnvm ttr
Figure 1.2 Spatial load forecasts are accomplished by dividing the service territory into small areas, either irregularly shaped areas, perhaps associated with equipment service areas, or elements of a uniform grid.
4
Chapter 1
1.2 T&D PLANNING Electric power delivery is among the most capital intensive of businesses. The required transmission and distribution (T&D) facilities need rights-of-way and substation sites, power equipment for transmission, distribution, protection and control, and extensive construction labor, all involving considerable expense. Arrangements for new or expanded facilities normally require several years, meaning that a power delivery utility usually must plan at least five years ahead. For a variety of reasons, most utilities wants to evaluate the wisdom and value of their investments over a portion - roughly the first half - of their service lifetimes, meaning that long-range planning needs to look out another ten to fifteen years into the future. Thus, power delivery utilities need to plan, in various ways, over a period as far as fifteen or twenty years into the future. Planning is a decision-making process that seeks to identify the best schedule of future resource commitments and actions to achieve the utility's goals. Ordinarily, these goals include financial considerations — minimizing cost and maximizing profit - along with service quality and reliability standards, as well as other criteria, including environmental impact, public image, and future flexibility. Generally, the objective of the T&D planning process is to determine an orderly and economical expansion of equipment and facilities to meet the utility's future electric demand with an acceptable level of reliability. This involves determining the sizes, locations, interconnections, and timing of future additions to transmission, substation, and distribution facilities, and perhaps a compatible program of "nontraditional distributed resource" commitments as well - such things as demand-side management, distributed generation and storage, and automation. Such planning is a difficult task, compounded by recent trends of tightening design margins, lengthening equipment lead times, and increasing regulatory scrutiny. Traditional T&D Planning Traditionally, T&D planning was a standards-based planning process. An electric utility's Engineering Department set certain standards for equipment type, characteristics, loading, and usage, as well as standards for voltage drop, power factor, utilization, contingency margin, and other operating parameters for the system (see Willis, 1998, Chapters 4 and 5). Planners then attempted to develop a plan that met all standards and criteria and had the lowest possible cost. "Lowest cost" was rigorously defined by decree/agreement with state regulatory authorities. It usually meant that all costs were considered, and that the utility attempted to minimize the total revenue requirements needed to serve
Spatial Electric Load Forecasting
TRANSMISSION SYSTEM PLANNING 5 - 25 yrs.
t SUBSTATION SYSTEM PLANNING 3 - 20 yrs.
t FEEDER SYSTEM PLANNING 1 - 1 5 yrs.
Figure 1.3 The traditional T&D planning process in a vertically integrated electric utility. The spatial load forecast is the first step, driving the rest of the planning process.
Transco
LDC or DistCo LOAD FORECAST 1-25 yrs. ahead
TRANSMISSION SYSTEM PLANNING 5-25 yrs.
ESCo
CONTRACTS 1-25 yrs. ahead
SUBSTATION SYSTEM PLANNING 3 -20 vrs. k
/
'
r ^ FEEDER SYSTEM PLANNING 1-15 yrs.
Figure 1.4 The T&D planning process in a de-regulated power industry. "Planning" (the study of the future, assessment of needs and options, selection of strategy and development of tactics to achieve it) is now part of three organizations. These include one or more electric service companies (ESCos), the local distribution company, which may be a pure wire company (Distco) or have an interest in selling energy, too (LDC - local distribution company), and the transmission owner-operator (Transco or regional transmission authority). Communications between all (crossing the dotted lines) are heavily regulated and formalized. Both the ESCos and delivery companies have an interest in spatial forecasting.
Chapter 1
its consumers' demand. Minimizing revenue requirements meant that the utility considered operating and financing costs as well as initial capital costs in deciding if one option was less expensive than another. Figure 1.3 shows the traditional T&D planning process as it was often represented, consisting of transmission, substation, and distribution-level planning. The exact organization and emphasis of these individual planning steps would vary from one utility to another. Regardless, a key element of the overall planning was the load forecast, the first step. That defined the capabilities the future system needed to possess. If the forecast was poorly or inappropriately done, then subsequent steps were directed at planning for future loads different than would develop, and the entire planning process was at risk. Table 1.1 shows typical traditional lead times required to plan, permit, and put into place facilities at various levels of an electric T&D system. Conditions and requirements varied from one situation to another, but the values shown are illustrative. Larger, high voltage equipment requires longer lead times. Smaller equipment at the lower voltage levels can be installed with a shorter lead time. Modern T&D Planning T&D planning at the beginning of the 21st century is decidedly different from traditional T&D planning, in both operating environment and planning focus. To begin, most of the power production and bulk transmission in the power industry has been de-regulated. It is under federal regulatory control, and regulated in a way that fosters competition and provides minimal protection for business risk, but a great deal of reliability protection and a certain amount of price protection for energy consumers. De-regulation has brought about disaggregation of power delivery systems, and a change in the entities planning "their parts" of the utility industry, as shown in Figure 1.4. Somewhere in the chain of power flow from generator to consumer, a dividing line has been drawn between the wholesale grid and the energy delivery systems, and perhaps between the energy delivery and the retail marketer(s). The de-regulated electric power landscape provides a bewildering array of slightly different ways of organizing the local electric industry. Readers needing more detail may wish to consult a reference on the industry's structure (e.g., Philipson and Willis, 1999). Under de-regulation, transmission is owned by a Transco (transmission company) and operated by an ISO (independent system operator) or RTO (regional transmission operator). Distribution is owned by a Distco or an LDC (local distribution company). For purposes of this discussion, four entities will be identified as composing the "power industry," only three of which are discussed here:
Spatial Electric Load Forecasting
7
Genco - the various companies that own and operate generation, sell power into the competitive wholesale grid and provide related services (load following, etc). They are not a concern here and are listed only for completeness. Trans Co - the owner(s) and/or operator of the bulk power transmission system in the region. "Bulk power transmission" is defined here as transmission connected to generators, but not to consumers (except very large industries that buy power on the competitive market). Strictly speaking, Transco means the transmission owner, but it will be used here to refer to whoever is making the plotting the future of and the decisions about expansion and investment in the bulk power transportation system for the region. DistCo or Local Distribution Company (LDC) - the company that operates the wires down to and including the connection to the end energy consumers. A "DistCo" owns and operates the wires, providing the service of connectivity and power delivery, but sells no power (it merely moves power for ESCos). A local distribution company (LDC) provides this service, and sells the power itself. Energy service companies (ESCos) retail power, buying it at the wholesale level and selling it to retail consumers, and paying transmission and local delivery charges to the Transco and Distco, respectively, to have it delivered. This disaggregation of ownership and operation, with the slightly different perspectives it brings to each entity, and the formalized, regulated communication between them, is the first major difference in a "modern" power industry. The T&D system is no longer owned and operated by a single company which can plan it "as a piece" and make compromises between or commitments from T to D and vice versa, as it sees fit. Modern planning of transmission and distribution is done separately, with only limited communication between planning staffs. Often, regulatory requirements put up a "firewall" between the different organizations, setting tight limits and regulations on what information must be and cannot be shared and how and when these organizations will communicate with one another, and how they must do it. The dividing line between "T" and "D" varies quite greatly from one state jurisdiction to another, a remarkable fact considering that the power systems are (or were) rather similar regardless of location. Just where this line is drawn has a great deal to do with the nature of planning in a region. Table 1.1 shows the dividing line between T and D for several states in the U.S., at the time this was written. Dividing lines and their interpretation will change over time. Generally,
8
Chapter 1
the "D" or distribution utility (often called the delivery utility) owns all facilities from the energy consumer's meter box up to and including the switches on the high side of the transformers that accept power at the "T" voltage from the transmission utility. A second difference between traditional and modern T&D planning is that many states have moved toward performance-based regulation of utilities. Performance-based rates usually mean that the utility's earnings are tied to the reliability of service it gives its consumers. The issues are much too complicated and vary too much from one state to another to cover in detail here. However, many utilities have a very real incentive to focus on achieving certain reliability targets. Beyond this, electric delivery utilities are seeing much more financial pressure to cut costs than they saw traditionally. Traditionally, a utility had a regulatory obligation to consider alternatives and select the least-cost options in every case. But it was permitted a great deal of discretion in how it defined the standards and criteria that set limits on how far it could trim costs, and in how it planned its system expansion and spending. Capital dollars went into the "rate base" and earned the permitted profit margin. So in a way, a utility had an incentive to keep justifiable spending as high as possible so that the rate base, and hence the base on which it earned money, would grow. Modern power delivery utilities are still subject to the same regulatory paradigm, but they have a host of new financial pressure points that control their planning priorities so they often need to spend far less than would have been justifiable under the traditional paradigm. First, many can no longer assume that
Table 1.1 Regulatory "Dividing Line" between T and D* State
Level
Florida
35 kV
Wisconsin
50 kV
Maine
99 kV
Texas
138kV
Pennsylvania
138kV
Illinois
138 kV
* Some of the data here is based on proposed regulations and may be superceded.
Spatial Electric Load Forecasting
9
all "justifiable costs" will be passed into their rate base and therefore earn them a profit. Many utilities are under rate freezes: if costs rise, they must cut back somewhere because they cannot pass the cost on to their consumers. A few are luckier, their rates will increase, but no matter what they need or could justify, their spending cannot grow beyond a certain rate. And a few utilities are under mandated rate reductions: their spending has to go down, period. But beyond this, there is a further set of self-imposed financial constraints. Executive management at many utilities has determined that they cannot accept the risk, lack of financial leverage, and other consequences that high capital spending brings. This is because they feels their companies must improve their stockholder performance. As one utility executive said, "I will not put my company in financial jeopardy to keep our power system out of jeopardy." Many utilities have cut capital spending by 30 - 40% below traditional levels. Thus, modern utility planners face a variety of new pressures in charting their system's expansion to handle future demands. These are summarized in Table 1.2. The utility must do more with less. The "more" includes achieving specific levels reliability as measured by regulatory-defined formula or rules in the actual performance of the system. "The "less" includes less information: delivery planners can obtain all the information they used to from transmission and retail sources.
Table 1.2 Added Considerations for Modern T&D Planners Pressure Dis-aggregated T&D
Focus on reliability
Rate freezes/reductions
Reductions in capital
Consequence Power delivery planning is now "stand alone." It must produce explicit requests for wholesale delivery "feed points" into its locale delivery system. Delivery planners must consider bulk delivery and formalize their plans and requests, much like T&D utilities used to formalize generation plans. The utility must achieve certain levels of overall consumerlevel reliability or suffer certain financial and political consequences. Planners must plan a system that can deliver the required reliability. Often, the manner in which projects and spending are justified to regulators has changed, requiring more detail and a wider span of consideration. Reductions in operating cost often dictate reductions in planning staffs and support resources. Regulators and upper management alike have told planners they most "do much more with much less." There is 30 to 40% less capital to spend.
10
Chapter 1
Planning Consequences of De-Regulation Perhaps the largest shift away from traditional utility procedures in the new "do more with less" environment has been a strong move toward higher utilization rates for all system equipment. Traditionally, utilities loaded substation transformers to about 66% of capacity during normal operation - planning standards dictated that a transformer was "overloaded" if its forecast peak demand exceeded 66% of its normal load rating. Today that utilization rate hovers right at 80% for the industry, with some utilities actually operating at 90% or above. The increase in utilization rate was a direct result of financial pressures - an increase from 66% to 80% loading means that a transformer can serve 21% more load. Put another way, the money spent on that transformer will support 21% more revenue "flowing through it." Similarly, a host of other traditional standards and criteria have been "loosened" in an attempt to push the system harder and get more for less. This increase in equipment and system utilization rates and other associated changes in criteria has had a beneficial financial impact - spending at nearly every electric utility went down during the 1990s. But it often had undesirable effects on reliability, some of which were of a type that could not be assessed by traditional planning methods.1 In many cases the increases in utilization rates were not the direct cause of reliability problems, but were blamed for them. Power systems can operate reliably at very high (near 100%) peak utilization rates, but traditional standard-based planning methods and tools cannot engineer them so such performance is assured. An intense focus on reliability is the second important consequence of the modern paradigm. Some utilities have developed innovative programs to identify the causes of poor reliability, prioritize those causes and identify cures, and rank and select those curves that are most cost effective. However, a good many have bogged down trying to apply traditional planning methods to this new paradigm: they spend extensive effort measuring reliability and developing extensive "data mines" related to equipment reliability and service problems, but do very little that is effective in managing reliability with the resulting data. The key to success with regard to reliability (among those utilities that appear to be succeeding) is the move to a reliability-based planning paradigm. In this, traditional standards are made somewhat flexible: where a substation can be operated reliably at high utilization, that option is selected; where that would inhibit reliability, another option is taken. Results, in particular the expected reliability of the future system, rather than standards, control the planning process. In consequence T&D system planning puts less emphasis on capacity margin and far more on configuration, switching and "operability." 1
See Willis et al (2001) for more details.
Spatial Electric Load Forecasting
11
Short-Range Planning and Its Forecasting Needs Short-range planning is that part of the planning process that assures lead time requirements will be meet. Short-range planning's purpose is to identify if something needs to be started now, or if the utility can defer action for another year. When action is needed (i.e., when the lead time has been reached), shortrange planning must identify, justify, authorize and schedule the required facilities or equipment. Thus, short-range planning must look into the future at least as far ahead as the lead time to assure that facilities of sufficient capability and location will be available when needed. Thus, if the lead time on substations is five years, then the T&D planner must plan at least five years ahead to assure that any new additions are ready when needed. For example, if it takes five years to permit, order equipment, construct, test and commission a new substation, then there is no reason to start that process more than five years ahead. But it must be started five years prior to need or it will not be available when required. Good or bad, the utility has to commit to construction or no construction at the lead time; waiting any longer means that it selects a "do nothing" or "wait another year" option by default. Lead times vary from level to level of a power system. Table 1.3 gives a rough idea of the lead time required by level of the power system, although they vary depending on region, utility, and regulatory environment.
Table 1.3 Typical Lead Times for T&D System Equipment Additions in an Electric Power System.
Level
Years Ahead
Nuclear generation (> 250 MVA) 10 Small generation (< 250 MVA) 4 Transmission (138 kV and above) 10 Transmission switching stations 7 Sub-transmission (34kV - 13 8kV) 6 Distribution substations 4 Control centers or dispatch centers 3 Primary three-phase feeders 3 Single-phase laterals 1 Distributed generation 1 Customer-site specific reliability equip. % 1 Service transformers and secondary A
Chapter 1
12
Short-range planning is action specific and project oriented Short-range planning is project-oriented, as shown in Figure 1.4. The initial short-range planning/forecasting process seeks only to identify where problems exist and by when additions or changes must be made to solve them. This initiates individual projects aimed at solving each problem, each project taking on a life of its own, as it were, to be completed in order to solve its designated problem. At many utilities these projects are not limited to planning in the purest sense (development and evaluation of feasible alternatives, leading to selection of the preferred option) but include actual detailed engineering, perhaps including design, and always generally leading to an authorization for construction. Short-range planning is action directed - it is intended to lead to specific actions (or a decision not to take them).
Load forecast for the lead time year(s)
Existing system & planned additions thru lead time
Short Range Planning Process,
Identified area capacity shortfalls
Figure 1.5 The short-range planning process consists of an initial planning phase in which the capability of existing facilities is compared to short-term (lead time) needs. Where capacity falls short of need, projects are initiated to determine how to best correct the situation. The load forecast is primarily an input to the short-range planning process - i.e., it is used to compare with existing capacity to determine if and where projects need to be initiated.
Spatial Electric Load Forecasting
13
For short-range planning and its subsequent project development, the most important aspects of forecasting are accuracy in predicting the timing of future load growth - when it will reach levels that require something to be done to enhance system capability. Timing is truly critical at this stage for determining when these projects must be started (often involving commitment of considerable capital expense). There is a lead time, and if the timing is poorly estimated this might be missed. Thus, the most important role of the load forecast in supporting the shortrange planning is to sound a reliable alarm about when the present facilities will first be insufficient. Figure 1.6 illustrates the basic concept: the short-range forecast is a trigger which sets in motion the project(s) required to keep capability sufficient to deal with future load. Clearly, a second priority is identification of how much load growth should be anticipated, but this is not quite as important: once the project is triggered, it can focus as much attention as needed on trying to identify how much load will develop.
100
Peak Load 50 MVA
5 10 Years into the Future
15
Figure 1.6 Three projections of load growth for an area of 30 square miles agree on the eventual "build out" peak load but differ in the rate of growth. Existing facilities will be intolerably overloaded when the peak load reaches 57 MVA, and a new substation must be added, costing $6,500,000. A year's delay in this expense means a present worth savings of $500,000, but delaying a year too long means poor reliability and consumer dissatisfaction. Therefore, accuracy in predicting timing of growth - in knowing which of these three forecasts is most likely to be correct - is critical to good planning.
14
Chapter 1
Long-Range Planning and Forecasting Needs Long-range planning looks beyond the lead time in order to assure that the shortrange decisions provide lasting value. Unlike short-range planning, long-range planning is not concerned with ensuring that the system additions are made hi time to meet needs. It is done to assure that those additions have lasting investment and performance value. For example, planner's might have decided to meet the needs forecast load growth in an area of the system by adding a new 50 MVA substation five years from now. However, if continued growth is expected after that, it might require expansion only a few years later, at a considerable additional cost. It might be more economical to install a larger facility initially, or to design the substation so it can be quickly upgraded at low cost when needed. Beyond that, if growth in the area is expected to continue, it might be best to build the substation at a location other than what is optimum from only the five-year ahead perspective, perhaps locating it closer to the expected center of long-term load growth. Each of these questions requires looking at the substation in the period after it is installed and operating — beyond the lead time required to build it. To make certain they leave no "if only we had . . . " regrets, the substation's planners must study it over a period that begins on the day it goes into service and includes a reasonable portion of its lifetime — at least the first ten to fifteen years. (Such a ten- to fifteen-year period represents a majority of the substation's present worth on the day it is put in service. To meet this need, the load forecast must provide a projection of load growth for ten or more years beyond the lead time. Table 1.4 gives typical long-range planning periods for T&D equipment.
Table 1.4 Typical Long-Range Periods For T&D System Equipment Planning In An Electric Power System. Level
Years Ahead
Large generation (> 250 MVA) Small generation (< 250 MVA) Transmission/switching (138 kV and above) Sub-transmission (34kV - 138kV) Distribution substations Distribution feeders Renewable generation Distributed generation Customer site - specific reliability equipment
30 20 25 20 20 15 20 7 4
Spatial Electric Load Forecasting
15
The Long-Range Plan To study facilities or other options in detail over the period five to twenty-five years ahead, the utility's planners must have a good idea of the conditions under which that equipment will function. In other words, they need a long-range plan to provide a backdrop against which they can evaluate the value of their shortrange projects. This plan must lay out the economics (e.g., value of losses) and operating criteria that will apply in the future. It must specify the load and reliability needs that the system will have to meet (long-range demand forecast), and the locations of this new demand. Finally, it must specify how the T&D planners expect to handle that load growth - what other new facilities will be installed in the long run to accommodate the future pattern of load growth. Going back to the example substation discussed above, a great deal of its value to the utility will depend on what other new substations will or will not be built nearby during its lifetime. The purpose of long-range planning is to provide assessment of the wisdom, or optimality if one prefers, of the short-range decisions — those commitments that have to be made now. Its value is the improvement in investment value bang-for-the-buck, return on assets, lifetime utilization or however measured — that this evaluation will provide. Long-range planning should be judged by how it contributes to improving the utilization (value) of existing facilities and the long-term value of new investments in the system. For this reason, long-range planning does not lead to a set of projects as does short-range planning. In fact, the long-range planning process does not lead directly to any actions, nor will it ever "authorize" any projects. Its only "product" is the long-range plan itself: the material needed and foundation for that long-range assessment of short-range decisions. Development and maintenance of the long-range plan is the major goal of the long-range planning process: a continuously updated long-range vision of needs and plans that provides a basis for evaluation, and guidelines and direction to short-range planning. This is shown in Figure 1.7. The long-range plan is used to judge the effectiveness of all short-range commitments. As an example, consider the substation required to be built in five years, discussed earlier in this chapter. Perhaps the long-range plan shows that while load growth in the area will continue, it will be handled in the long run by other new substations, to be added later. In such a case, the substation need be built only in its initial configuration and any plans to expand it or build it to a larger size initially can be considered to have a low priority compared to cutting initial cost as much as possible. The long-range plan needs only detail sufficient to permit resolution of questions such as that, to study the economics and "fit" of short-range decisions against the systems long-range trends and needs. Effort to provide detail and precision of sites, routes, and exact equipment description beyond this is wasted
16
Chapter 1
Spatial Load Forecast
Existing System & Committed Additions
Long-Range Planning Process
for evaluation of possible short range projects
possible revision of plan Long-Range Plan
Figure 1.7 The long-range planning process, where the major goal is the maintenance of a long-range plan that identifies needs and development of the system, so that short-range decisions can be judged against long-range goals. Here, the load forecast is a part of the plan, and there is no "project oriented" part of the activities.
100
Peak Load 50
MVA
5
10
15
Years into the Future Figure 1.8 Long-range planning requirements are less concerned with "when" and more sensitive to "how much will eventually develop." The three forecasts shown here, all for the same substation area discussed in Figure 1.4, lead to the conclusion that the new substation is needed in five years, but differ in their projections of the long-term load. They would lead to far different conclusions about how short-range commitments can match long-range needs, and probably to a different decision about what to do in the short run as well as the long run.
Spatial Electric Load Forecasting
17
wasted (Tram et al., 1983). As a result, long-range T&D planning requirements for a spatial load forecast are oriented less toward the "when" aspect (as was short-range planning) and more toward the "what" and "how much," as shown in Figure 1.8. For long-range planning, knowing what will eventually be needed is more important than knowing exactly when. Long-range plans can be moved forward or back in time as needed, but what hurts is if the overall plan is moving toward the wrong "picture" of future needs, calling for too much or too little, or just enough, but in the wrong locations. Thus, timing is not a priority in a long-range plan, because most of the elements of a long-range plan do not have to be built anytime soon. By definition, its timeframe is beyond the lead time. Consider a new substation specified for construction by the long-range plan for eleven years from the present. Given the five-year lead time required, the utility has another six years before it must commit to that substation's construction. In the meantime conditions or expectations may change. Thus, no action must be taken anytime soon. The substation and other elements exist in the plan only to show the planners how they will meet long-term needs, so that they know what is and is not expected of the substation and other equipment that must be committed now. Temporal Resolution Requirements Temporal resolution is the when of the forecast, the degree of detail on timing of future growth in a forecast. (See Figure 1.9). Most forecasts have a temporal resolution of one year - they forecast future load growth in a series of one-year increments. This is true even if they generate hourly load curves, seasonal peaks, or other time-related "details." Those details are based on one-year "snapshots" of growth generated by the forecasts. Daily load curves, and seasonal peaks, for example, are based upon projections of conditions in that year. One-year resolution is generally sufficient for T&D planning (given that those "details" are supplied, because planning is done on an annual basis. Generally, as a planning study moves into the long-range time period, it will skip selected years, spacing out the time between "snapshots" of the future. A typical forecast, and the planning based on it, therefore includes a base year (calibrated study of present load), a forecast for years 1, 2, 3, 4, 5 ahead (shortrange period), and a forecast for years 7, 9, 12, 15, and 20 years ahead, for longrange analysis. This satisfies both short- and long-range planning needs Spatial Resolution Requirements Spatial resolution is the where of a load forecast. Conceptually, spatial or geographic resolution is the "area size" that the forecast uses to locate load and growth. A forecast that identifies load on an acre basis has more resolution than
Chapter 1
18 20 years ahead 15 years ahead 12 years ahead I 9 years ahead 7 years ahead | 5 years ahead | 4 years ahead | 3 years ahead | 2 years ahead | 1 year ahead I Base year data
Figure 1.9 Both planning and forecasting are usually done with a temporal resolution of one year - forecast "snapshots" of peak conditions in future years. T&D planning involves examining expansion needs for a series of future years in both the short- and long-range periods. The load forecast must accommodate these needs, providing forecasts - maps of projected load density throughout the service territory - for the years to be planned.
one that locates load and growth only to within square miles. The spatial resolution required in planning varies from level to level of a power system, being roughly proportional to the capacity of the power equipment involved. A typical distribution substation (primary voltage 12.47 kV) might serve an area of 25 square miles. A distribution feeder serves a much smaller area, perhaps only 4 square miles. In every sense, feeder planning will be more sensitive to detail about where load is located than the substation planning. How this sensitivity to spatial detail varies with level of the system will be discussed in Chapter 8. But qualitatively, levels of the system composed of larger equipment serving larger service areas can be planned with lower resolution spatial resolution, while levels composed of smaller, lower voltage equipment generally require more detail about where load is located.
19
Spatial Electric Load Forecasting Table 1.5 Typical Service Area Sizes For T&D System Equipment In An Electric Power System And Spatial Resolution Needed To Model Their Loads. Service area - mi.2
Level Large generation (> 150 MVA) Small generation (< 150 MVA) Transmission (138 kV and above) Sub-transmission (34kV - 138kV) Distribution substations Primary three-phase feeders Single-phase laterals Service transformers and secondary Distributed generation (« 50 kW)
entire system 50 100 50 30 5 .25 .01 .01
Resolution - mi.2 entire system 4 9 4 2 .5 .02 consumer consumer
Entire System
M
M
01
o> o
e
[
53
0>
£ 5
-
•^
8 B [-] 1 LN
"r"""~~ffl~7Jrini
ll 1 irll Btf Dlliln li Substations
Transmission
-i
o» o
u u Major equipment
Dis tribution
K.
ft 0
Spatial Resolution - acres
Generation
0
5
10 15 Years Ahead
20
25
Figure 1.10 Planning period and spatial resolution for various levels of the power system are inversely related. Forecasts for "large equipment" levels of the system must be done farther into the future, but require lower spatial resolution than lower voltage/size levels of the distribution system.
20
Chapter 1
Table 1.5 gives typical service area sizes for various levels of the power system, along with resolution requirements (area size to which load levels must be studied on an individual basis to assure adequate planning of the level). These differences in service area sizes by level of the power system mean that, while larger equipment levels require planning farther into the future as was shown earlier in Tables 1.3 and 1.4, the geographic detail required is less. Thus, load forecasting requirements farther into the future generally require less spatial resolution than short-range forecasts, as shown in Figure 1.10. Uncertainty and Multi-Scenario Planning Planning and forecasting always face uncertainty about future developments. Will the economy continue to expand so that load growth will develop as forecasted? Will a possible new factory (employment center) develop as rumored, causing a large and as yet unforecasted increment of growth? Will the bond election approve the bonds for a port facility (which would boost growth and increase load growth)? Situations like these confront nearly every planner. Those of most concern to the distribution planner are factors that will increase growth and change its location. In the presence of uncertainty about the future, utility planners face a dilemma. They do not want to commit to investment that may not be needed. However, they cannot ignore the fact that the development could happen, and that they must commit soon if they are to fit within the lead time so they have the facilities in place if the growth does occur. Given the reality of lead times, planners must sometimes commit without certainty that the events they are planning for will, in fact, come to pass. A clearly desirable goal of the planning process is to minimize the risk due to uncertainty. Ideally, plans can be developed to confront any, or at least the most likely, eventualities, as illustrated in Figure 1.11. Multiple long-range plans, all stemming from the same short-range decisions (decisions that must be made because of lead times) cover the various possible events. This type of planning, called multi-scenario planning, involves explicit enumeration of plans to cover the various likely outcomes of future events. One of the worst mistakes that can be made in T&D planning, integrated or otherwise, is to try to circumvent the need for multi-scenario planning by using "average" or "probabilistic forecasts." Generally, this approach leads to plans that combine poor performance with high cost. As an example, the forecast maps in Figure 1.12 show forecasts of spatial distribution of load for a large city. Shown at the top are maps of load in 1994 and as projected for twenty years later. The difference in these maps represents the task ahead of the T&D planners - they must design a system to deliver an additional 1,132 MW, in the geographic pattern shown.
Spatial Electric Load Forecasting
21 Neither
Event A
Event B
Time period during vhich commitments must be made now Present
+ 4 gears
Events A andB
+ 8 years
+12 years
Figure 1.11 Multi-scenario planning uses several long-range plans to evaluate the shortrange commitments, assuring that the single short-range decision that is being made fits the various long-range situations that might develop. This shows the scenario variations for the case involving two possible future events.
At the bottom of Figure 1.12 are two alternate forecasts that include a possible new "theme park and national historical center" built at either of two possible sites. Given voter approval (unpredictable) and certain approvals and incentives from state officials (likely, but not certain), the theme park/resort developer would build at one of the two sites. The park itself would create only 11.3 MW, of new load (it has some on-site generation to serve its 25 MW peak load). But it would generate 12,000 new jobs and bring other new industries to the area, causing tremendous secondary and tertiary growth, and leading to an average annual growth rate of about 1% more than in the base forecast during the decade following its opening. Thus, the theme park means an additional 260 MW of growth on top of the already healthy expansion of this city. The maps in Figure 1.12 show where and how much growth is expected under each of three scenarios: no park (considered 50% likely), site A (25%), or site B (25% likely). The spatial distribution of the secondary and tertiary growth will be very much a function of the new park location. Hence, the where aspect, as well as the how much, of the utility's T&D plan will change, too. Feeders, substations, and transmission will have to be relocated and re-sized to fit the scenario that develops. The planners need to study the T&D needs of each of the three growth scenarios and develop a plan to serve that amount and geographic pattern of load. Ideally, they will be able to develop a short-range plan that "branches"
Chapter 1
22
2O13 - Base Forecast 3442 MV •'•'.&><•
1993 2310 MV
Ten miles 2013 - Scenario A 3702 MV
2013 - Scenario B 3662 MV
B
Figure 1.12 The base T&D load forecast (upper right) for an American city is based on recent historical trends (same as in Figure 1.1). At the bottom, alternate forecasts including a "major theme park" at either one of two alternate sites are shown. Overall amount of growth differs for the two theme park scenarios because in scenario B a portion of the secondary and tertiary growth falls outside the utility's service territory.
Spatial Electric Load Forecasting
23
Expectation 3562 MV
Ten miles
Figure 1.13 The probability-weighted sum of the three forecasts in Figure 1.12. This is perhaps the worst forecast the T&D planners could use to develop their plans.
after the lead time to any of three different plans tailored to the three different patterns of load growth. Such planning is challenging, very much "advanced T&D Planning," but it can be done, and done well. Regardless, planners will never do it unless they have the forecasts and ability to study the situation One thing the planners must not do is form a single forecast map based on a probability-weighted sum of the various possible forecasts, an "expectation of load growth" map. Such a map is easy to produce. Figure 1.13 is the probability-weighted sum of the three forecast maps shown in Figure 1.12. While mathematically valid (from a certain perspective, at least) this forecast map will contribute nothing useful to the planning effort - it represents a future with 1/4 of a theme park at location A, 1/4 at location B and the other half somewhere else. That is one scenario that will never happen. Using an expectation-of-scenarios forecast map, as in Figure 1.13, for T&D planning leads to plans that spread resources too thinly over too much territory. In this case, it would lead the utility to plan additional T&D capacity to handle about half of the load difference represented by the theme park - capacity to serve about 140 MW of load - split between the south part of the system (site A) and the east (site B). No matter which scenario eventually develops, the system
24
Chapter 1
plan based on the "forecast" shown in Figure 1.13 will contain several major and potentially expensive flaws: 1) If the base case actually develops, then the planners have "wasted" resources capable of serving about 140 MW of capacity. 2) If scenario A develops, the planners have wasted the capacity additions they made in the eastern part of the system (capable of serving about 70 MW). In addition, near site A they have put facilities that fall short of the capacity needed there by 75%. 3) If scenario B develops, they have similarly wasted about 70 MW and put in place facilities that fall short of capacity requirements by 75%. Planning with the forecast shown in Figure 1.13 guarantees only that the T&D plan will be inappropriate no matter what happens. A much better way to handle uncertainty is to recognize that there -will be a need to change direction and to plan for that. This is the essence of the multi-scenario approach and the concept illustrated in Figure 1.11 and the forecasts in Figure 1.12. Supporting "Delaying Tactics" for Lead Times As mentioned above, the "nightmare scenario" for a power delivery planner is a multi-scenario situation where the development time for a possible new load is less than the lead time for the facilities required to serve it. In the example above, the theme park developer is going ahead with his plans for his park designing the rides, ordering equipment, etc. - while he negotiates to buy one of the two locations or put his theme park in another city. As a result, if and when he selects a site, he will proceed very rapidly. T&D planners can use various tactics to shorten their lead times in the same way. They, too, can make tentative plans, option sites, and order equipment in advance - identifying equipment they can use no matter which scenario develops (This is not easy to do. It is "advanced planning," but it can be done well). Modular substations are a modern option that makes a big difference in such situations. Of up to 100 MVA capacity, they can be ordered and installed within half a year, and, moved to another site later if the first site proves to be nonoptimal. No spatial forecast method can remove the uncertainty about the type of events depicted above. But it needs to support the process of identifying how sensitive plans will be to various highly-uncertain events and planning to mitigate the financial burden that uncertain creates. This means a critical need for a modern spatial forecast is representativeness - the ability to accurately render a "scenario" of what future growth would be under a specified set of conditions. This is the difference between mere "projection" of present trends, and real forecasting.
Spatial Electric Load Forecasting
25
1.3 REQUIREMENTS FOR A T&D LOAD FORECAST The foregoing discussion illuminated the single most important aspect of spatial load forecasting. It is the first step in determining future T&D system design, and largely determines its direction and quality. A forecast's every characteristic and its effectiveness must be assessed in terms of this purpose. Its goal is to provide the information needed for T&D planning in a way that fits the planning process. This means describing as accurately as possible the amount, timing, and locations of future load growth in a way suited to the short-range and long-range and multi-scenario planning needs of the power delivery planners. If the forecast leads the planner to make the correct decisions, then it has no error from a practical standpoint. If it leads the planner to the wrong decisions, then it is a poor forecast, regardless of what statistical evaluation of its ability to predict future load might say. Requirement 1: Forecast of Magnitude - the Amount of Demand and Energy The amount of future load is the primary forecast quantity in any load forecast, spatial or otherwise — specifically, the T&D planner needs to know how much peak demand must be met in order to determine the capacities of future facilities. Timing and location of this peak demand are important in order to determine the sites and routes and the schedule. T&D equipment must meet peak demands on a local basis, not just satisfy average demand. Therefore, a spatial forecast must project expected peak demands in each small area throughout the system. Without exception, the magnitude of power (either kW or MW of real load demand or kVA or MVA of total demand) is always forecast. Some spatial forecasts also project power factor, too. Requirement 2: Spatial Resolution and Analysis The need for information on the location of future load growth is what sets T&D planning needs apart from generation and system level planning requirements. It is also what distinguishes spatial load forecasting methods from system level forecasting used to project energy and demand for generation, rate, revenue, and financial planning. The amount of "where information" (spatial resolution) in a forecast must match the T&D planning needs. Locations of future load growth must be described with sufficient geographic precision to permit valid siting of future T&D equipment. There are a number of ways to provide locational detail, always with the small area method described earlier, but regardless of how this is done, it must provide the required spatial resolution. Reliable location of load to within ten square mile areas might be sufficient for a particular planning purpose. Then again, another might require location of future load to within 1/2 square mile (160 acre) areas.
26
Chapter 1
Analytical methods can determine the required spatial resolution based on T&D equipment characteristics and load densities as will be discussed in Chapter 5. While many planning applications require forecasts only for high growth areas where overloads, augmentation, or new construction is expected, in general, a forecast of the entire service area is recommended. Covering the entire service area with small area forecasts brings three advantages. First, it permits the multitude of small area forecasts to be summed and compared to statistics on the total system - a useful way to check accuracy and reasonableness. Second, a spatial forecast that covers the entire service territory is a step toward assuring that nothing is missed in the utility's T&D planning. Growth doesn't always occur where expected, as will be discussed in Chapter 4, and a system-wide small area forecast often catches trends before they become apparent. Finally, some of the best (most accurate, most flexible) spatial forecasting methods work only when projecting the growth of all small areas over a large region. Thus, the forecast usually will cover the entire service area even if only a portion is of interest, or if the service territory is quite vast, cover it with a series of separate, region-by-region forecasts. Modem computerized forecasting programs can handle truly prodigious numbers of small areas - up to 3,000,000 - sufficient usually to model growth at adequate resolution for distribution planning over an entire state if need be. Requirement 3: Timing and Temporal Detail Usually T&D planning consists of detailed, year-by-year expansion studies during the short-range period, and examination of selected years in the longrange period (with results interpolated for years in between). A typical set of planning periods might be 1,2, 3, 5, 7, 9, 12, 15, and 20 years ahead. This set of forecast years accommodates the short-range planning needs, which must distinguish growth from year to year during the lead time period) and long-range planning needs, which require less timing and more long-term vision on eventual development. To accommodate this need, a T&D forecast generally produces a series of spatial peak load forecasts, "snapshots" of the geographic pattern of peak electric load distribution for selected future years, as shown earlier in Figure 1.12. The actual forecast is produced as a series of iterations or "jumps," the forecasting method predicting growth in year- or multi-year increments. In addition, many T&D planning situations will require forecasting of seasonal peak loads for times of the year other than system peak. For example, a particular utility's system load might have the annual peak load in winter, but the summer peak might be significant enough to warrant study. Capability of equipment such as transformers is lower in summer due to the higher ambient
Spatial Electric Load Forecasting
27
temperature so that even if the summer loads are less than winter's, the time of highest equipment stress might actually be during summer. Beyond this, spatial forecasts may reveal that while the system as a whole has a peak in winter, certain areas peak in the summer. For this reason, projecting both summer and winter peak loads is common in spatial forecasting. Requirement 4: Weather Normalization of Forecasts The electric demand level in a power system is very sensitive to weather. Hot summer conditions give rise to high peak demands. Cold winter conditions increase the use of electric heating, also creating high demand levels. An important aspect of forecasting is to study this relationship and adjust all forecasts to a similar level of "assumed weather" - usually some level of rather extreme (worst summer in five years, worst summer in ten years) weather scenario. Generally, this requires extensive analysis of weather, and demand, and adjustment of all load histories used in forecasting to a standard set of weather conditions. Weather adjustment of data and proper normalization of forecasts is critical to effective planning for reliable future service. Load forecasting, specifically inappropriately done weather adjustment, played a key role in several major utility operating problems in the late 1990s. Weather, demand, weather adjustment and forecast normalization will be covered in detail in Chapters 5 and 6. Requirement 5: Representational Accuracy: Accurately Predicting Future Load Is Not The Primary Goal A critical factor in a good spatial forecasting method is representational accuracy, the ability to represent future load under specific future conditions. This is as important, and often more important, than "accuracy" alone (as measured by minimizing the error between a forecast and the loads that actually develop). A load forecast for T&D planning, spatial or otherwise, is not an attempt to most accurately forecast future load. While this may come as a surprise to those unfamiliar with T&D planning, it is not only reasonable but required. Forecasts designed to support good planning often contain biases meant to improve the planning process. An example of this is weather normalization. If the goal of a electric delivery planning forecast was to predict peak load as accurately as possible, weather normalization would adjust the forecast to average (most likely) annual peak day weather conditions. But forecasts are instead normalized to infrequent weather conditions such as "worst weather expected in ten years" (i.e., hottest summer, coldest winter). This is because the power system is not designed to "just get by" under average conditions, but instead to "get by" under the harshest
28
Chapter 1
conditions that can reasonably be expected. What is needed is a forecast of load under these extreme weather conditions. On average, such weather will develop rarely, and as a result, the forecast will not be as accurate as it could have been made. But that is not the point. Done in this way, it serves the planner's purpose. A forecast method must be judged against planning needs such as these, and not solely on the basis of statistics and error measures that evaluate its accuracy as judged by how well forecasts matched actual load growth. While such "error evaluation" is important, and useful in selecting, calibrating, and fine tuning a spatial forecast method, it is far less important than assuring that the forecast method is accurate in representing how load growth changes as assumptions about the future are changed. What is most important is if it can represent accurately load under conditions that are specified as part of the T&D planning scenario and criteria. This is a key element of a forecasting method. It is why some spatial methods (simulation) are heavily preferred as planning tools over other, simplerto-use forecasting techniques (trending). Trending methods provide very poor representational ability, while that is simulation's forte. Requirement 6: Consistency with the Corporate Forecast Almost all utilities maintain a division or group within the finance, revenue, rates, or corporate planning departments whose sole function is to forecast future sales and revenues, usually by application of comprehensive econometric models to marketing and historical sales data. Regardless of how this is performed, this activity produces the forecast of most interest to the company's executives - the forecast of future revenues on which budgeting and financial planning are based. All electric forecasts used for the utility's planning should be based upon, driven by, or appropriately made consistent with this corporate forecast. This does not mean they should match the corporate forecast MW to MW. There may be legitimate reasons why there should be a difference - coincidence of load and weather normalization being two typical adjustments needed. But there are several compelling reasons why all T&D planning forecasts should be made consistent with this corporate forecast. First, based on the spatial forecast and the subsequent steps in the planning process, the T&D planners will ask their executives to commit future revenues to T&D investment. The executives, while always reluctant to spend any more than necessary, do understand that "you have to spend money to make money." But they have a right to expect that the forecast that is telling them they must spend money is based on the same assumptions and growth as the forecast that tells them how much money they will have to spend. Is the planner's request for investment in the T&D system based on the same assumptions and "vision of
Spatial Electric Load Forecasting
29
the future" as the forecast that the executives are using to estimate future revenues, from which they plan the utility's business case? If not, the T&D planners have failed to do their job. Beyond this, the economists and analysts in the revenue forecasting group generally know what they are doing. Their forecasts of consumer count, sales, and peak load for the system are probably as accurate (from a representational standpoint) as anything the T&D planners could ever produce. Why re-do all that work? Finally, the corporate forecast contains the assumptions about future economy, demographics, major political and industrial events that have been approved or at least well-studied, and not opposed, as the "corporate" vision about the general trends of the future. Adjustments needed to keep "consistency" honest Given that all of this required consistency is built into the T&D planning forecast, the planners then need to make certain they have made the appropriate "adjustments" to it. Quite important is that they account for coincidence of area peaks and differences in weather normalization. All must be fully documented and justified, however. Weather normalization is a good example of the valid differences in the details that should exist between the T&D and corporate forecasts. A T&D planner's greatest worry, and the highest with regard to weather, is that weather will be extreme and cause higher loads and more stress on the system than forecast. Thus, a T&D planner wants to forecast high to accommodate this risk, but in a controlled, risk-mitigation manner. By contrast, the revenue forecaster's worst scenario is that weather will be milder than forecast and thus revenues will fall short of forecast (mild weather resulting in lower sales and hence lower revenue). Thus, very often the revenue forecast is normalized to "mildest weather in ten years" or something similar, not worst weather in ten years as T&D planning requires. Adjustments to correct for this difference are necessary and justifiable, but the T&D planners should be able to fully document and defend the adjustment factors used. Requirement 7: Analysis of Uncertainty and Sensitivity The ability to show how the forecast varies as assumptions about future conditions are changed - multi-scenario capability - is particularly useful in long-range planning, and essential in some planning situations. To some extent this is representational accuracy again. But there is a distinction - the forecast method must have the "levers and knobs" so the planner can represent the type of future scenario needed. Analysis of forecast sensitivity and uncertainty for spatial forecasting is quite different from that needed for traditional system-wide forecasting. Again, the "where" element adds an unusual dimension to possible error that makes most
30
Chapter 1
traditional definitions of error sensitivity unacceptable (see Willis and Northcote-Green, 1983, and Engel, 1992). For T&D planning, sensitivity analysis means paying special attention to possible changes in future conditions that might impact where growth will locate - such factors as transportation routes, land availability, zoning, taxation, and other aspects of urban culture that can vary from one locale to another. For example, a bond issue might be proposed to approve money for a new bridge and highway, which would alter commuting patterns in the region, and therefore change where future growth would concentrate. Such transportation expansion can have significant impact on the locations of load growth during the following decade. Some modern spatial forecast methods can forecast the impact of such a transportation addition with reasonable accuracy. However, they cannot forecast whether the voters will approve the expenditure. The best way to study such an unforecastable event is to examine how it would impact the utility plan. This requires forecasting load growth with and without taking the event into consideration. Such planning is called multi-scenario planning and is a cornerstone of modern T&D planning. This means attempting to develop a short-range plan which allows a sensible expansion to either of the potential long-range outcomes, whether load grows with or without the multi-scenario event being considered. Requirement 8: Consumer Classes The type of load (consumer class) is often an important factor in T&D planning, particularly in any study that involves consumer-side assessment, whether that is for reliability analysis, DSM planning, or marketing and retail level strategic planning. Traditionally, basic distinctions of consumer class - residential, commercial, industrial - have been used by distribution planners because they broadly identify the expected load density (kW/acre), load factor, equipment types, and power quality issues on an area basis. Spatial forecast methods based on forecasting consumer type and density have been used since the 1930s and computerized since the middle of the 1960s (see Engel, 1992). Many spatial forecast methods distinguish among sub-classes within residential (apartments, small homes, large homes), commercial (retail, offices by low-rise and hi-rise, institutional), and industrial (various classes and purposes), typically using between nine and twenty consumer classes. Usually, consumer-class based forecasts are done as a step toward some type of market-based or end-use analysis. Market studies may include assessment of what needs each consumer class might have for energy and/or energy services. Or, they might try to estimate by area of the system what response a retail marketer would get to various sales and marketing tactics. Generally, consumer class forecasting is a prelude - the mechanism of implementation - to any or all the three further forecast requirements listed below. Load curve shape, reliability need and value, and power factor and
31
Spatial Electric Load Forecasting
voltage sensitivity characteristics are all developed from consumer-class end-use models of usage, made once a consumer class or consumer category forecast has been done. Requirement 9: Load Curve Shapes and Seasonal Peak Loads Generation of annual load duration curves, along with peak day and off-peak day (seasonal) daily (hourly) load curves, is a required product for some of the finetuning done in modern T&D system planning. For this reason, production of peak day load curves, estimates of how daily load curve varies from season to season, and production of the annual load duration curve are all quite important. Forecast of hourly loads for the peak day - 24 hourly loads as shown in Figure 1.14 - is often needed or useful. Usually this is the coincident peak load curves for each area being forecast. This forecast permits the study of coincidence of peaks among areas - commercial areas may have a daily peak in mid-afternoon, while others such as residential areas peak in early evening. Hourly load curve forecasts for the peak day also permit analysis of the length of time demand is expected to be at or near peak. This can be important in planning situations where capacity margin is slim and equipment is "dynamically rated." Overloads of equipment such as transformers can often be tolerated if they last an hour or less, in which no significant damage or loss of life can be expected, but might be intolerable if the high loading lasts four hours or more.
8.0 6.0
g 4.0 1 I 2.0
12
12 Hour of the Day
12
Figure 1.14 Many spatial forecasts project peak day load curve shape, usually on an hourly basis, in order to determine time of peak (for coincidence studies) and length of peak (for loading and economy studies). The two curves here exemplify the differences that can occur. Curve A is a typical annual peak day residential area load curve for northern Florida, Curve B is a peak day curve for a residential area in New England.
32
Chapter 1
Load curves data covering longer periods than the peak day(s) is occasionally necessary. Annual energy (the area under the year-long 8760 hour load curve) is an important additional element of the forecast. It is useful in determining total sales to an area as well as being a necessary input in the economic sizing of equipment - a part of minimizing the system cost of losses. Knowledge of the general characteristics of the annual load curve shape - in particular its annual load and loss factors - is useful in computing these economic capacity targets and for estimating the cost of losses accurately. Very rarely will the power delivery planning needs require a spatial forecast for all 8760 hours in the year. For example, forecasts done for some demandside management (DSM) planning applications need hourly data for the peak day and some off-peak days (or longer) periods. This information is used both to identify when the peak occurs as well as assess to how long and how much exposure there is to various reliability or service problems. It is also needed for various types of retail level market planning, and for evaluations of the effectiveness of different DSM programs in reducing T&D costs. Generally, such long-period, hour-by-hour forecasts are not done by forecasting each 8760 hours individually. Instead, load curves for selected key days (e.g., weekends and weekdays for each of twelve months) are developed and then copied as needed, perhaps adding some weather variation, to assemble an 8760-hour load curve. Requirement 10: Reliability Planning and Engineering Needs The demand for reliability - basically how critical continuity of service is and how much each consumer is willing to pay to maintain it - varies from consumer class to consumer class. In some planning applications, a useful product of a spatial forecast is an identification of where premium-grade reliability will be needed in the future, and where consumers who place economy ahead of high reliability will be concentrated. Some spatial forecast methods can estimate the types of reliability needs of consumers in various areas of the system. Most of these accomplish this by forecasting type of customer on a small area basis and use an end-use model to identify key reliability needs. These capabilities will be discussed later. Requirement 11: Power Factor And Voltage Sensitivity Some planners want to forecast power factor of the demand. Generally this is done by: a) For short-range, assuming the same uncorrected power factor on each feeder in the future as at present
Spatial Electric Load Forecasting
33
b)For long-range planning, power factor is consumer-class specific (end-use) as is its voltage sensitivity (power, constant current, or impedance load). Relative Importance of Requirements Table 1.6 summarizes the spatial load forecast requirements discussed above, and assigns them a relative importance, which is solely based on the author's subjective judgement. The top three requirements - how much, where, when, are the raison de entree for the spatial forecast and have been arbitrarily assigned a "10" ranking. Other factors are by definition assigned something less than 10. 1.4 SUMMARY Spatial load forecasting involves predicting the future demand for electric power in a way that is compatible with the planned requirements for electric transmission and distribution (T&D) systems. Among its unique requirements is that it provide information on where future load will develop (the spatial element). As will be discussed in Chapter 8, the concept of error in a spatial forecast requires recognizing that the forecast can predict the amount of load growth correctly but still get its locations wrong, to the extent that the accuracy in
Table 1.6 "Product" Requirements for Spatial Electric Load Forecasts Rank 1 2 3 4 5 6 7 8 9
10 11
Requirement Forecast MW - how much Locational accuracy - where Temporal resolution - when Weather normalization - how Representational accuracy - why Consistency with corporate forecast Analysis of uncertainty - why and how Consumer class forecast - who Load curve shapes Reliability value/need Power factor/voltage sensitivity
Importance 10 10 10 9 8 7 7 6 5 5 4
34
Chapter 1 Table 1.7 Required Characteristics Of Spatial Load Forecasting Methods For The Electric Power Industry Characteristic
Percent of Applications
Forecast annual peak Forecast off-season peaks Forecast total annual energy Forecast some aspects of load curve shape (e.g., load factor, peak duration) Forecast peak day(s) hourly load curves Forecast hourly loads for more than peak days Forecast annual load duration curve Power factor (KW/KVAR) forecast Forecast reliability demand in some fashion Multiple scenario studies done in some manner
100% 66% 85%
Base forecasts updated - at least every five years - at least every three years - at least every year - at least twice a year
100% 66% 50% 5%
Forecast covers period - at least three years ahead - at least five years ahead - at least ten years ahead - at least twenty years ahead - beyond twenty years ahead
100% 100% 50% 20% 20%
Spatial forecast "controlled by" or adjusted so it will sum to the corporate forecast of system peak (coincidence adjustment may be made)
50%
Forecasts adjusted (normalized) to standard weather Weather adjustment done rigorously
80% 25%
Consumer class loads forecast in some manner End-use usage forecast on small area basis DSM impacts forecast on a small area basis Small area price elasticity of usage forecast
35% 5% <5% <5%
66% 50% 15% 10% 20% 15% 66%
Spatial Electric Load Forecasting
35
forecasting amount of load was worthless. Ultimately, every forecast must be judged by how well it supports the planning process in correctly identifying future T&D needs. Table 1.7 lists the characteristics summarized above and their implementation within the industry. These values are based on the author's experience and opinion and, while approximate, are indicative of general requirements in the power industry.
REFERENCES M. V. Engel, editor, Tutorial on Distribution Planning, IEEE Course Text EHO 361-6PWR, Institute of Electrical and Electronics Engineers, Hoes Lane, NJ, 1992. L. Philipson and H. L. Willis, Understanding Electric Utilities and De-Regulation, Marcel Dekker, New York, 1999. H. N. Tram et al., "Load Forecasting Data and Database Development for Distribution Planning," IEEE Trans, on Power Apparatus and Systems, November 1983, p. 3660. H. L. Willis, Power Distribution Planning Reference Book, Marcel Dekker, New York, 1998. H. L. Willis and J. E. D. Northcote-Green, "Spatial Load Forecasting - A Tutorial Review," Proceedings of the IEEE, February 1983, p. 232. H. L. Willis, G. V. Welch, and R. R. Schrieber, Aging Power Delivery Infrastructures, Marcel Dekker, New York, 2001.
2 Consumer Demand for Power and Reliability 2.1 THE TWO Qs: QUANTITY AND QUALITY OF POWER Electric consumers require power, whether delivered from the utility grid or generated locally by distributed sources, in order to help accomplish the uses for which they need energy. Their need for electric power, and the value they place upon its delivery to them, has two interrelated but fundamentally separate dimensions. These are the two Qs: Quantity, the amount of power needed, and Quality, the most important aspect of which is usually dependability of supply (reliability of power supply, or availability as it is often called). The relative importance of these two features varies from one consumer to another depending on their individual needs, but each consumer finds value in both the amount of power he obtains, and its availability as a constant, steady source that will be there whenever needed. This chapter discusses demand and use of electric power as seen from the consumer's standpoint: the utility's job is to satisfy consumer needs as fully as possible within reasonable cost constraints. Cost is very much an important aspect to consumers too, so both the utility and the consumer must temper their 37
38
Chapter 2
plans and desires with respect to power and reliability based on real world economics. Energy consumers do not get everything they want; only what they are willing to pay for. Utilities should not aim to provide flawless service, which would be prohibitively expensive, but instead aim to provide the highest level possible within economic constraints of the consumers' willingness to pay. This chapter begins, in section 2.2, with a discussion of consumer use of electricity and includes the quantity of electric demand as seen from an "enduse" perspective. It continues with how demand varies as a function of consumer type and end-use, and how power demand is represented in electric system studies using load curves and load duration curves. Section 2.3 then discusses reliability and availability as seen by the consumers and ways this can be characterized and studied. Section 2.4 briefly reviews Two-Q analysis and planning concepts and their application to consumer load analysis. Finally, section 2.5 provides a summary of key points. 2.2 ELECTRIC CONSUMER DEMAND FOR QUANTITY OF POWER No consumer wants to buy electric energy. Electricity is only an intermediate means to many end-uses. Consumers want the products it can help provide - a cool home in summer, hot water on demand, compressed air for manufacturing, cold beer in the 'fridge and football on color TV for the homeowner; computer control of the factory, heavy-duty compression of molds for manufacturing, and a host of other applications for commerce and industry.. These different goals and needs are called end-uses, and they span a wide range of applications. Some end-uses are unique to electric power (the author is not aware of any manufacturer of natural gas powered TVs, stereos, or computers). For many other end-uses, electricity is only one of several possible energy sources (water heating, home heating, cooking, or clothes drying). In many other end-uses, electricity is so convenient that it enjoys a virtual monopoly, even though there are alternatives, e.g., gasoline-powered refrigerators, and natural gas for interior lighting and for air conditioning. Each end-use is satisfied through the application of appliances or devices that convert electricity into the desired end product. For example, with lighting a wide range of illumination devices are used, including incandescent bulbs, fluorescent tubes, sodium vapor, high-pressure monochromatic gas-discharge tubes, and in special cases, lasers. Each type of lighting device has differences from the others that give it an appeal to some consumers or for certain types of applications. Regardless, each requires electric power to function, creating an electric load when it is activated. Similarly, for other end-uses, such as space heating, there are various types of appliances, each with advantages or disadvantages in initial cost, operating efficiency, reliability and maintenance, noise and vibration, or other aspects. Each produces an electric load when used to produce heat for a home or business.
Consumer Demand for Power and Reliability
39
Other utilities - 9% Industrial - 11%
Commercial -22%
Cooling - 50% Residential • 58% Lighting -17% Water Heat -12% Cooking - 9% Refrig. - 6% Other-6%
Figure 2.1 Electric peak demand of a utility in the southeastern United States broken down by consumer class and within the residential class, by contribution to peak for the major uses for which electricity is purchased at time of peak by the residential class.
Consumer Classes Different types of consumers purchase electricity. About half of all electric power is used in residences, which vary in the brands and types of appliances they own, and their daily activity patterns. Another fourth is consumed by commercial businesses, both large and small, that buy electricity, having some similar end-uses to residential consumers (heating and cooling, and illumination), but that have many needs unique to commercial functions (cash register/inventory systems, escalators, office machinery, neon store display lighting, parking lot lighting). Finally, industrial facilities and plants buy electricity to power processes such as pulp heating, compressor and conveyor motor power, and a variety of manufacturing applications. As a result, the load on an electric system is a composite of many consumer types and appliance applications. Figure 2.1 shows this breakdown of the peak electrical load for a typical power system by consumer class and end-use category within one class. Appliances Convert End-Uses into Electric Load The term load refers to the electrical demand of a device connected to and drawing power from the electric system in order to accomplish some task, e.g.,
40
Chapter 2
opening a garage door, or converting that power to some other form of energy, such as a light. Such devices are called appliances, whether they are a commonly regarded household item, e.g., a refrigerator, lamp, garage door opener, paper shredder, electric fence to keep cattle confined, etc. To the consumer, these appliances convert electricity into the end product. But the electric service planner can turn this relation around and view an appliance (e.g., a heat pump) as a device for transforming a demand for a particular end-use warm or cool air - into electrical load. Electrical loads are usually rated or measured by the amount of power they need, in units of real volt-amperes, called watts. Large loads are measured in kilowatts (thousands of watts) or megawatts (millions of watts). Power ratings of loads and T&D equipment refer to the device at a specific nominal voltage. Constant Power, Constant Current, and Constant Impedance Load Many electric appliances and devices have an electric load that varies as the supply voltage is varied. Generally, loads are grouped into three categories depending on how their demand varies as a function of voltage, as shown in Figure 2.2: constant power (demand is constant regardless of voltage), as a constant current (demand is proportional to voltage), or as a constant impedance (power is proportional to voltage squared). The load at a particular consumer or in a particular area might be a mixture of all three. There are situations in distribution engineering where it is quite important to model the voltage sensitivity of load correctly. Given a feeder with a 7.5% voltage drop from substation to feeder end, a constant impedance load will vary by up to 14.5% depending on where it is located on the feeder. The same constant impedance load that creates 1 kW of demand at the feeder head would produce only .855 kW at the feeder end. By contrast, a 1 kW constant power load will produce 1 kW of demand anywhere on the feeder. Incandescent lighting, resistive water heaters, and electric stoves and ranges and many other household loads are constant impedance loads. Induction motors, controlled power supplies, as well as loads downstream of any tap-changing transformer in a power system, appear to the power system as relatively constant power loads and are generally modeled in this manner.1 Very few loads are constant current, although a 50/50 mixture of power and impedance loads look very much alike and can be modeled as "constant current." Generally, when modeled in detail, loads are represented with a type and load at nominal (1.0 PU) voltage. Thus, a 1 kW constant power load is referred to as "1 kW, constant power" and a constant impedance load that produces 1 kW at 1.0 PU is referred to as a "1 kW, constant impedance load." From a practical
1
Only steady-state voltage sensitivity is important in distribution planning and is considered here. Planning generally does not consider transient voltage sensitivities.
Consumer Demand for Power and Reliability 1.10
41
Constant Impedance
Constant Current
1.05
1.00
Constant Power
.95
.90 .95
.96
.97
.98
.99
1.0
1.01
1.02
1.03
1.04
1.05
Voltage - PU Figure 2.2 Actual demand for power created by "1 kilowatt" of the three types of load, as a function of voltage supplied to them.
standpoint, it is not necessary to model constant current loads. However, the distinction between constant power and constant impedance loads is important.2 Since voltage drop on a feeder depends very much on the load, the manner of representing load is critical to computing voltage drop accurately. For example, a three-phase 12.47 kV line built with 336 MCM phase conductor (a typical suburban overhead distribution trunk) can serve a 10.72 MW constant impedance load at a distance of two miles, while staying just within "range A" 7.5% voltage drop limits. The "10.72 MW constant impedance load" will create a demand of only 9.36 MW due to the voltage drop (9.36 MW = (1 - .075)2 x 10.72 MW). Thus, the feeder stays within voltage criteria if serving a "10.72 MW constant impedance load." However, voltage drop rises to 8.59 volts, more than a volt beyond what the criteria permits, if the load is a 10.72 MW constant power load. The cost of writing and putting into place software to represent loads as constant power, constant impedance, or any mixture thereof in distribution engineering tools (load flows) is minor, but the cost of obtaining good data for such a model is not. Usually, the data is estimated, in one of two ways:
2
A 50%/50% mix of constant voltage and constant power loads represents a constant current load within 4% over the range .9 to 1.1 PU.
42
Chapter 2 1. All loads, except special ones, are designated as a default mixture of power and impedance loads. In the absence of measured results to the contrary, the recommended general rule of thumb is to use a 60%/40% constant power/constant impedance mixture for summer peak loads, and a 40%/60% split for winter peak loads. 2. The proportion of constant power and constant impedance loads at each location in the power system is estimated based on a spatial end-use appliance model.
The load of most individual consumers, and thus in any small area, is a mixture of types. Industrial areas are most typically closest to constant power loads (about 80/20 constant power/constant impedance). Residential areas with very strong summer-peaking loads usually have a 70/30 split of constant power/constant impedance load, while winter peaking residential areas, or those summer-peaking areas with low summer load densities per household (little air conditioning) tend to have a mix closer to 30/70 constant power/constant impedance loads. Commercial areas are usually about 50/50 or 60/40 constant power/constant impedance loads. In rural and residential areas of developing countries, and commercial areas in economically depressed regions, loads generally tend to be about 20/80 constant power/constant impedance. Load Curves and Load Curve Analysis The electric load created by any one end-use usually varies as a function of time. For example, in most households, demand for lighting is highest in the early evening, after sunset but before most of the household members have gone to bed. Lighting needs may be greater on weekends, when activity lasts later into the evening, and at times of the year when the sun sets earlier in the day. Some end-uses are quite seasonal. Air-conditioning demand generally occurs only in summer, being greatest during particularly hot periods and when family activity is at its peak, usually late afternoon or very early evening. Figure 2.3 shows how the demand for two products of electric power varies as a function of time. The result of this varying demand for the products of electricity application is a variation in the demand for power as a function of time. This is plotted as a load curve, illustrated in Figure 2.4. Typically, the values of most interest to the planners are the peak load (maximum amount of power that must be delivered). This defines, directly or indirectly, the capacity requirements for equipment; the minimum load and the time it occurs; the total energy, area under the curve that must be delivered during the period being analyzed; and the load value at the time of system peak load.
Consumer Demand for Power and Reliability
Mid
Noon Time of Day
Mid
Mid
43
Mid
Noon Time of Day
Figure 2.3 End-use demand. (Left) Average demand for BTU of cooling among houses in the author's neighborhood in Gary NC on a typical weekday in early June. Right, lighting lumens used by a retail store on a typical weekday in early June.
Summer and Winter Residential Peak Day Load Curves Summer
„
HOUR
Winter
HOUR
Figure 2.4 Electric demand for each class varies hourly and seasonally, as shown here, with a plot of average coincident load for residential users in central Florida.
Residential
Time of Day
Commercial
Time of Day
Industrial
Time of Day
Figure 2.5 Different consumer classes have different electrical demand characteristics, particularly with regard to how demand varies with time. Here are summer peak day load curves for the three major classes of consumer from the same utility system.
Chapter 2
44
200
Q
O 100
"K,
12
6
Noon Hour
6
12
Figure 2.6 Demand on an hourly basis (blocks) over 24 hours, and the actual load curve (solid black line) for a feeder segment serving 53 homes. Demand measurement averages load over each demand interval (in this case each hour) missing some of the detail of the actual load behavior. In this case the actual peak load (263 kW at 6 PM) was not seen by the demand measuring, which "split the peak," averaging load on an hourly basis and seeing a peak demand of only 246 kW, 7% lower. As will be discussed later in this chapter, an hourly demand period is too lengthy for this application.
Consumer Class Load Curves While all consumers differ in their electrical usage patterns, consumers within a particular class, such as residential, tend to have broadly similar load curve patterns. Those of different classes tend to be dissimilar in their demand for both quality and quantity and the time of day and year when their demand is highest. Therefore, most electric utilities distinguish load behavior on a classby-class basis, characterizing each class with a "typical daily load curve," showing the average or expected pattern of load usage for a consumer in that class on the peak day, as shown in Figure 2.5. These "consumer class load curves" describe how the demand varies as a function of time. While often an entire 8,760-hour record for the year is available, usually only key days perhaps one representative day per season - are used for studies. The most important points concerning the consumers' loads from the distribution planner's standpoint are: 1. Peak demand and its time and duration 2.
Demand at time of system peak
3.
Energy usage (total area under the annual load curve)
4.
Minimum demand, its time and duration
Consumer Demand for Power and Reliability
45
Details of Load Curve Measurement Demand and demand periods "Demand," as normally used in electric load analysis and engineering, is the average value of electric load over a period of time known as the demand interval. Very often, demand is measured on an hourly basis as shown in Figure 2.6, but it can be measured on any interval basis - seven seconds, one minute, 30 minutes, daily, and monthly. The average value of power during the demand interval is given by dividing the kilowatt-hours accumulated during the demand interval by the length of the interval. Demand intervals vary among power companies, but those commonly used in collecting data and billing consumers for "peak demand" are 15, 30, and 60 minutes. Load curves may be recorded, measured, or applied over some specific time. For example, a load curve might cover one day. If recorded on an hourly demand basis, the curve consists of 24 values, each the average demand during one of the 24 hours in the day, and the peak demand is the maximum hourly demand seen in that day. Load data is gathered and used on a monthly basis and on an annual basis. Load factor Load factor is the ratio of the average to the peak demand. The average load is the total energy used during the entire period (e.g., a day, a year) divided by the number of demand intervals in that period (e.g., 24 hours, 8,760 hours). The average is then divided by the maximum demand to obtain the load factor:
Load Factor
=
kWh/Hr Peak Demand kW
=
Average Demand kW
(2.1)
Peak Demand kW
KWh (kW Demand) x (Hr)
(2.2)
Load factor gives the extent to which the peak load is maintained during the period under study. A high load factor means the load is at or near peak a good portion of the time. Load Duration Curves A convenient way to study load behavior is to order the demand samples from greatest to smallest, rather than as a function of time, as in Figure 2.7. The two diagrams consist of the same 24 numbers, in a different order. Peak load, minimum load, and energy (area under the curve) are the same for both.
Chapter 2
46 Hourly Load Curve
Re-ordered as load duration curve
Hour of the Day
Hour of the Day
Figure 2.7 The hourly demand samples in a 24-hour load curve are reordered from greatest magnitude to least to form a daily load duration curve.
Load Duration Curve
100 80 60 40 20
2800
8760
Hours per Year
Figure 2.8 Annual load duration curve for a commercial site with a 90 kW peak demand, from an example DG reliability study case in Chapter 16. As shown here, in that analysis the demand exceeds 40 kW, the capacity of the smaller of two DG units installed at the site, 2,800 hours a year. During those 2,800 hours, adequate service can be obtained only if both units are operating.
Consumer Demand for Power and Reliability
47
Annual load duration curves Most often, load duration curves are produced on an annual basis, reordering all 8,760 hourly demands (or all 35,040 quarter hour demands if using 15-minute demand intervals) in the year from highest to lowest, to form a diagram like that in Figure 2.8. The load shown was above 26 kW (demand minimum) 8,760 hours in the year, never above 92 kW, but above 40 kW for 2,800 hours. Most often, load duration curves are produced on an annual basis, reordering all 8,760 hourly demands (or all 35,040 quarter hour demands if using 15minute demand intervals) in the year from highest to lowest, to form a diagram like that shown in Figure 2.8. The load shown was above 26 kW (demand minimum) for all 8,760 hours in the year. It was never above 92 kW, its peak, but was above 40 kW for 2,800 hours. Load duration curve behavior will vary as a function of the level of the system. The load duration curves for small groups of consumers will have a greater ratio of peak to minimum than similar curves for larger groups, due to coincidence of load effects (see Chapter 3). Those for very small groups (e.g., one or two consumers) will also have a pronounced "blockiness," consisting of plateaus — many hours of similar demand level (at least if the load data were sampled at a fast enough rate). The plateaus correspond to combinations of major appliance loads. The ultimate "plateau" load duration curve would be a load duration curve of a single appliance, for example a water heater that operated a total of 1,180 hours during the year. This appliance's load duration curve would show 1,180 hours at its full load, and 7,580 hours at no load, without any values in between, as shown in Figure 2.9.
o
>
4
(0
•a
9) 0)
3
O X
111 n o
2 I
2 | A
8760 Hours per Year
Figure 2.9 Solid line indicates the load duration curve for a typical 5 kW residential water heater. Compare to Figures 3.3 and 3.4. Dotted line shows the load duration curve that would result from a 2 kW water heater serving the same end-use demand.
Chapter 2
48
Spatial Patterns of Electric Demand An electric utility must not only produce or obtain the power required by its consumers, but also must deliver it to their locations. Electric consumers are scattered throughout the utility service territory, and thus the electric load can be thought of as distributed on a spatial basis as depicted in Figure 2.10. Just as load curves show how electric load varies as a function of time (and can help identify when certain amounts of power must be provided), so spatial load analysis helps identify -where load growth will be located and how much capacity will be needed in each locality. The electric demand in an electric utility service territory varies as a function of location depending on the number and types of consumers in each locality, as shown by the load map in Figure 2.10. Load densities in the heart of a large city can exceed 1 MW/acre, but usually average about 5 MW per square mile over the entire metropolitan area. In sparsely populated rural areas, farmsteads can be as far as 30 miles apart, and load density as low as 75 watts per square mile. Chapter 7 and Table 7.1 gives more details on typical load densities in various types of areas. Regardless of whether an area is urban, suburban, or rural, electric load is a function of the types of consumers, their number, their uses for electricity, and the appliances they employ. Other aspects of power system performance, including capability, cost, and reliability, can also be analyzed on a location basis, an often important aspect of siting for facilities, including DG.
" LcwJensRes. i Resifenlnl || Aptrtntnts
Ljl M
Med.W Hvykid.
Figure 2.10 (Left) Map showing types of consumer by location for a small city. (Right) Map of electric demand for this same city.
Consumer Demand for Power and Reliability
49
2.3 ELECTRIC CONSUMER DEMAND FOR QUALITY OF POWER As mentioned in this chapter's introduction, a central issue in consumer value of service analysis is matching availability and power quality against cost. T&D systems with near perfect availability and power quality can be built, but their high cost will mean electric prices the utility consumers may not want to pay, given the savings an even slightly less reliable system would bring. All types of utilities have an interest in achieving the correct balance of quality and price. The traditional, franchised monopoly utility, in its role as the "electric resource manager" for the consumers it serves, has a responsibility to build a system whose quality and cost balances its consumers' needs. A competitive retail distributor of power wants to find the best quality-price combination - only in that way will it gain a large market share. While it is possible to characterize various power quality problems in an engineering sense, characterizing them as interruptions, voltage sags, dips, surges, or harmonics the consumer perspective is somewhat different. Consumers are concerned with only two aspects of service quality: 1. They want power when they need it. 2. They want the power to do the job. If power is not available, neither, aspect is provided. However, if power is available, but quality is low, only the second is not provided. Assessing Value of Quality by Studying the Cost of a Lack of It In general, consumer value of reliability and service quality are studied by assessing the "cost" that something less than perfect reliability and service quality creates for consumers. Electricity provides a value, and interruptions or poor power quality decrease that value. This value reduction - cost - occurs for a variety of reasons. Some costs are difficult if not impossible to estimate: rescheduling of household activities or lack of desired entertainment when power fails;3 or flickering lights that make reading more difficult. But often, very exact dollar figures can be put on interruptions and poor power quality. Food spoiled due to lack of refrigeration; wages and other operating costs at an industrial plant during time without power; damage to product caused by the sudden cessation of power; lost data and "boot up" time for computers; equipment destroyed by harmonics; and so forth. Figure 2.11 shows two examples of such cost data. 3
No doubt, the cost of an hour-long interruption that began fifteen minutes from the end of a crucial televised sporting event, or the end of a "cliffhanger" movie, would be claimed to be great.
Chapter 2
50 20
sf 40,
15
o * 30
10
20!
o
'0
15 30 45 60 75 90 Interruption Duration - Minutes
0 10 20 30 Total Harmonic Voltage Distortion - %
Figure 2.11 Left, cost of a weekday interruption of service to a pipe rolling plant in the southeastern United States, as a function of interruption duration. An interruption of any length costs about $5,000 - lost wages and operating costs to unload material in process, bring machinery back to "starting" position and restart - and a nearly linear cost thereafter. At right, present worth of the loss of life caused by harmonics in a 500horsepower three-phase electric motor installed at that same industrial site, as a function of harmonic voltage distortion.
Value-Based Planning To be of any real value in utility planning, information of the value consumers put on quality must be usable in some analytical method that can determine the best way to balance quality against cost. Value-based planning (VBP) is such a method: it combines consumer-value data of the type shown in Figure 2.11 with data on the cost to design the T&D system to various levels of reliability and power quality, in order to identify the optimum balance. Figure 2.12 illustrates the central tenet of value-based planning. The cost incurred by the consumer due to various levels of reliability or quality, and the cost to build the system to various levels of reliability, are added to get the total cost of power delivered to the consumer as a function of quality.4 The minimum value is the optimum balance between consumer desire for reliability and aversion to cost. This approach can be applied for only reliability aspects, i.e., value-based reliability planning, or harmonics, or power quality overall. Generally, what makes sense is to apply it on the basis of whatever qualities (or lack of them) impact the consumer - interruptions, voltage surges, harmonics, etc., in which case it is comprehensive value-based quality of service planning.
4
Figure 2.12 illustrates the concept of VBP. In practice, the supply-side reliability curves often have discontinuities and significant non-linearities that make application difficult.
Consumer Demand for Power and Reliability Customer Vaue of Odrty
§
51
Utility Cost of ProvidngCldity
Sun of Costs
(A O O
o
Low
Low
Qjalily
He*
OdHy
ION Qelity
Figure 2.12 Concept of value-based planning. The consumer's cost due to poorer quality (left) and the cost of various power delivery designs with varying levels of quality (center) are computed over a wide range. When added together (right) they form the total cost of quality curve, which identifies the minimum cost reliability level (point A).
Cost of Interruptions The power quality issue that affects the most consumers, and which receives the most attention, is cessation of service, often termed "service reliability." Over a period of several years, almost all consumers served by any utility will experience at least one interruption of service. By contrast, a majority will never experience serious harmonics, voltage surge, or electrical noise problems. Therefore, among all types of power quality issues, interruption of service receives the most attention from both the consumers and the utility. A great deal more information is available about cost of interruptions than about cost of harmonics or voltage surges. Voltage Sags Cause Momentary Interruptions The continuity of power flow does not have to be completely interrupted to disrupt service: If voltage drops below the minimum necessary for satisfactory operation of an appliance, power has effectively been "interrupted" as illustrated in Figure 2.13. For this reason many consumers regard voltage dips and sags as momentary interruptions - from their perspective these are interruptions of the end-use service they desire, if not of voltage. Much of the electronic equipment manufactured in the United States, as well as in many other countries has been designed to meet or exceed the CBEMA
Chapter 2
52
Figure 2.13 Output of a 5.2-volt DC power supply used in a desktop computer (top) and the incoming AC line voltage (nominal 113 volts). A voltage sag to 66% of nominal causes power supply output to cease within three cycles.
200
£ 150 ra
I .2 100
50
1
10'
10"°
101
102
10J
104
105
106
10'
Time in Cycles
Figure 2.14 CBEMA curve of voltage deviation versus period of deviation, with the sag shown in Figure 2.13 plotted (black dot).
Consumer Demand for Power and Reliability
53
(Computer and Business Equipment Manufacturer's Association) recommended curves for power continuity, shown in Figure 2.14. If a disturbance's voltage deviation and duration characteristics are within the CBEMA envelope, then normal appliances should operate normally and satisfactorily. However, many appliances and devices in use will not meet this criterion at all. Others will fail to meet it under the prevailing ambient electrical conditions (i.e., line voltage, phase unbalance power factor and harmonics may be less than perfect). The manner of usage of an appliance also affects its voltage sag sensitivity. The voltage sag illustrated in Figure 2.13 falls just within the CBEMA curve, as shown in Figure 2.14. The manufacturer probably intended for the power supply to be able to withstand nearly twice as long a drop to 66% of nominal voltage before ceasing output. However, the computer in question had been upgraded with three times the standard factory memory, a second and larger hard drive, and optional graphics and sound cards, doubling its power usage and the load on the power supply. Such situations are common and this means that power systems that deliver voltage control within recommended CBEMA standards may still provide the occasional momentary interruption. For all these reasons, there are often many more "momentary interruptions" at a consumer site than purely technical evaluation based on equipment specifications and T&D engineering data would suggest. Momentary interruptions usually cause the majority of industrial and commercial interruption problems. In addition, they can lead to one of the most serious consumer dissatisfaction issues. Often utility monitoring and disturbance recording equipment does not "see" voltage disturbances unless they are complete cessation of voltage, or close to it. Many events that lie well outside the CBEMA curves and definitely lead to unsatisfactory equipment operation are not recorded or acknowledged. As a result, a consumer can complain that his power has been interrupted five or six times in the last month, and the utility will insist that its records show power flow was flawless. The utility's refusal to acknowledge the problem irks most consumers more than the power quality problem itself. Frequency and Duration of Interruptions Both Impact Cost Traditional power system reliability analysis concepts recognize that service interruptions have both frequency and duration (see Chapter 4). Frequency is the number of times during some period (usually a year) that power is interrupted. Duration is the amount of time power is out of service. Typical values for urban/suburban power system performance in North America are about 2 interruptions per year with about 100 to 120 minutes total duration. Both frequency and duration of interruption impact the value of electrical service to the consumer and must be appraised in any worthwhile study of consumer value of service. A number of reliability studies and value-based
54
Chapter 2
planning methods have tried to combine frequency and duration in one manner or another into "one dimension." A popular approach is to assume all interruptions are of some average length (e.g., 2.2 interruptions and 100 minutes is assumed to be 2.2 interruptions per year of 46 minutes each). Others have assumed a certain portion of interruptions are momentary and the rest of the duration is lumped into one "long" interruption (i.e., 1.4 interruptions of less than a minute, and one 99-minute interruption per year). Many other approaches have been tried (see References and Bibliography). But all such methods are at best an approximation, because frequency and duration impact different consumers in different ways. No single combination of the two aspects of reliability can fit the value structure of all consumers. Figure 2.15 shows four examples of the author's preferred method of assessing interruption cost, which is to view it as composed of two components, a fixed cost (Y intercept) caused when the interruption occurred, and a variable cost that increases as the interruption continues. As can be seen in Figure 2.15, consumer sensitivity to these two factors varies greatly. The four examples are:
1.
A pipe-rolling factory (upper left). After an interruption of any length, material in the process of manufacturing must be cleared from the welding and polishing machinery, all of which must be reset and the raw material feed set up to begin the process again. This takes about 1/2 hour and sets a minimum cost for an interruption. Duration longer than that is simply a linear function of the plant operating time (wages and rent, etc., allocated to that time). Prior to changes made by a reliability study, the "re-setting" of the machinery could not be done until power was restored (i.e., time during the interruption could not be put to use preparing to re-start once it was over). The dotted line shows the new cost function after modifications to machinery and procedure were made so that preparations could begin during the interruption.
2.
An insurance claims office (upper right) suffers loss of data equivalent to roughly one hour's processing when power fails. According to the site supervisor, an unexpected power interruption causes loss of about one hour's work as well as another estimated half hour lost due to the impact of any interruption on the staff. Thus, the fixed cost of each interruption is equivalent to about ninety minutes of work. After one-half hour of interruption, the supervisor's policy is to put the staff to work "on other stuff for a while," making cost impact lower (some productivity); thus, variable interruption cost goes down. The dotted line shows the cost impact
55
Consumer Demand for Power and Reliability
Insurance Claims Office
Pipe Rolling Plant
5
20
o
15
o o x *«•
10
~ o o
0
4 3
2
0
15 30 45 60 75 90 Interruption Duration - minutes
Chemical Process Plant
15 30 45 60 75 90 Interruption Duration - minutes
Residence
400
40
300
30
8 20
200
o
10
100
0
15 30 45 60 75 90 Interruption Duration - minutes
0
15 30 45 60 75 90 Interruption Duration - minutes
Figure 2.15 The author's recommended manner of assessing cost of interruptions includes evaluation of service interruptions on an event basis. Each interruption has a fixed cost (Y-intercept) and a variable cost, which increases as the interruption continues. Examples given here show the wide range of consumer cost characteristics that exist. The text gives details on the meaning of solid versus dotted lines and the reasons behind the curve shape for each consumer.
56
Chapter 2 of interruptions after installation of an uninterruptible power supply (UPS) on the computer system, which permits orderly shutdown in the event of an interruption. 3.
An acetate manufacturing and processing plant (lower left) has a very non-linear cost curve. Any interruption of service causes $38,000 in lost productivity and after-restoration set-up time. Cost rises slowly for about half an hour. At that point, molten feedstock and interim ingredients inside pipes and pumps begin to cool, requiring a daylong process of cleaning hardened stock from the system. The dotted line shows the plant's interruption cost after installation of a diesel generator, started whenever interruption time exceeds five minutes.
4.
Residential interruption cost function (lower right), estimated by the author from a number of sources including a survey of consumers made for a utility in the northeastern United States in 1992, shows roughly linear cost as a function of interruption duration, except for two interesting features. The first is the fixed cost equal to about eight minutes of interruption at the initial variable cost slope, which reflects "the cost to go around and re-set our digital clocks," along with similar inconvenience costs. Secondly, a jump in cost between 45 and 60 minutes, which reflect inconsistencies in human reaction to outage, time on questionnaires. The dotted line shows the relation the author uses in such analysis, which makes adjustments thought reasonable to account for these inconsistencies.
This recommended analytical approach, in which cost is represented as a function of duration on a per event basis, requires more information and more analytical effort than simpler "one-dimensional" methods, but the results are more credible. Interruption Cost Is Lower if Prior Notification Is Given Given sufficient time to prepare for an interruption of service, most of the momentary interruption cost (fixed) and a great deal of the variable cost can be eliminated by many consumers. Figure 2.16 shows the interruption cost figures from Figure 2.15 adjusted for "24-hour notification given." This is the cost for "scheduled outages." Cost of Interruption Varies by Consumer Class Cost of power interruption varies among all consumers, but there are marked distinctions among classes, even when cost is adjusted for "size" of load by computing all cost functions on a per kW basis. Generally, the residential class has the lowest interruption cost per kW and commercial the highest. Table 2.1
57
Consumer Demand for Power and Reliability Table 2.1 Typical Interruption Costs by Class for Three Utilities - Daytime, Weekday (dollars per kilowatt hour) Class Agricultural Residential Retail Commercial Other Commercial Industrial Municipal
1
2
3
3.80 4.50 27.20 34.00 7.50 16.60
4.30 5.30 32.90 27.40 11.20 22.00
7.50 9.10 44.80 52.10 13.90 44.00
Insurance Claims Office
Pipe Rolling Plant
20
§ 15
o X
~ 10 8 0
5 0
0
15 30 45 60 75 90 Interruption Duration - minutes
Chemical Process Plant
15 30 45 60 75 90 Interruption Duration - minutes
Residence
§ 300
8 20
u
10 0
15 30 45 60 75 90 Interruption Duration - minutes
'0
15 30 45 60 75 90 Interruption Duration - minutes
Figure 2.16 If an interruption of service is expected, consumers can take measures to reduce its impact and cost. Solid lines are the interruption costs (the solid lines from Figure 2.15). Dotted lines show how 24-hour notice reduces the cost impact in each case.
58
Chapter 2
gives the cost/kW of a one-hour interruption of service by consumer class, obtained using similar survey techniques for three utilities in the United States: 1. A small municipal system in the central plains, 2. An urban/suburban/rural system on the Pacific Coast 3. An urban system on the Atlantic coast.
Cost Varies from One Region to Another Interruption costs for apparently similar consumer classes can vary greatly depending on the particular region of the country or state in which they are located. There are many reasons for such differences. The substantial difference (47%) between industrial costs in utilities 1 and 3 shown in Table 2.1 is due to differences in the type of industries that predominate in each region. The differences between residential costs of the regions shown reflect different demographics and varying degrees of economic health in their respective regions. Cost Varies among Consumers within a Class The figures given for each consumer class in Table 2.1 represent an average of values within those classes as surveyed and studied in each utility service territory. Value of availability can vary a great deal among consumers within any class, both within a utility service territory and even among neighboring sites. Large variations are most common in the industrial class, where different needs can lead to wide variations in the cost of interruption, as shown in Table 2.2. Although documentation is sketchy, indications are the major differing factor is the cost of a momentary interruption - some consumers are very sensitive to any cessation of power flow, while others are impacted only by an interruption of power longer than a few minutes. Cost of Interruption Varies as a Function of Time of Use Cost of interruption will have a different impact depending on the time of use, usually being much higher during times of peak usage, as shown in Figure 2.19. However, when adjusted to a per-kilowatt basis, the cost of interruption can sometimes be higher during off-peak than during peak demand periods, as shown. There are two reasons. First, the data may not reflect actual value. A survey of 300 residential consumers for a utility in New England revealed that consumers put the highest value on an interruption during early evening (Figure 2.17). There could be inconsistencies in the values people put on interruptions (data plotted were obtained by survey).
59
Consumer Demand for Power and Reliability
Table 2.2 Interruption Costs by Industrial Sub-Class for One hour, Daytime, Weekday (dollars per kilowatt) Class
$/kW
Bulk plastics refining Cyanide plant Weaving (robotic loom) Weaving (mechanical loom Automobile recycling Packaging Catalog distribution center Cement factory
38 87 72 17 3 44 12 8
25 20 Q. 2 15
<5 I
10
° 5 *° (A O O
0
Mid.
Noon Time of Day
Mid.
Figure 2.17 Cost of a one-hour interruption as a function of when it occurs, as determined by surveys and interviews with 300 consumers of a utility in the northeastern United States, was determined on a three-hour period basis. A high proportion of households in this survey have school-age children at home and thus perhaps weighed interruption costs outside of school hours more than during school hours. However in general, most households rate interruption cost as higher in early morning and early evening.
60
Chapter 2
However, there is a second, and valid, reason for the higher cost per kilowatt off-peak: only essential equipment, such as burglar alarms, security lighting and refrigeration is operating - end-uses that have a high cost of interruption. While it is generally safe to assume that the cost of interruption is highest during peak, the same cannot be assumed about the cost per kilowatt. Recommended Method of Application of Consumer Interruption Cost Data A good analytical approach to value-based planning of power delivery includes assessment of consumer costs using functions that acknowledge both a fixed cost for any interruption, no matter how brief, and a variable cost as a function of duration. It should acknowledge the differences in value of service among the different consumer classes, and the time differences within those consumer classes. Ideally, reliability and service quality issues should be dealt with using a value-based reliability or power-quality planning method with consumer interruption cost data obtained through statistically valid and unbiased sampling of a utility's own consumers. Not with data taken from a reference book, report, or technical paper describing data on another utility system. However, in many cases for initial planning purposes the cost and time of data collection are not affordable. Figure 2.18 provides a set of costs of typical interruption curves that the author has found often match overall consumer values in a system. It is worth stressing that major differences can exist in seemingly similar utility systems, due to cultural and economic differences in the local consumer base. These are not represented as average or "best" for use in value-based planning studies, but they are illustrative of the type of cost functions usually found. They provide a guide for the preparation of approximate data from screening studies and initial survey data. Cost in Figure 2.18 is given in terms of "one hundred times nominal price." It is worth noting that in many surveys and studies of interruption cost, the cost per kW of interruption is on the order of magnitude one hundred times the normal price (rate) for a kWh. Generally, if a utility has low rates its consumers report a lower cost of interruption than if it has relatively higher rates. No reliable data about why this correlation exists has been forthcoming.5
5
It could be that value of continuity is worth more in those areas where rates are high (generally, more crowded urban areas). However, the author believes that a good part of this correlation occurs simply because in putting a value on interruptions, respondents to surveys and in focus groups base their thinking on the price they pay for electricity. Given that a typical residential consumer uses roughly 1,000 kWh/month, they may simply be valuing an interruption as about "one tenth of my monthly bill."
Consumer Demand for Power and Reliability Industrial
61
Commercial Retail
!200 High sensitivity
.S
o100 Low sensitivity
0
15 30 45 60 75 90 Interruption Duration - minutes
15 30 45 60 75 90 Interruption Duration - minutes
Commercial Non-Retail m 150
Residence
High sensitivity
-100
Low sensitivity
$ SO E
0
15 30 45 60 75 90 Interruption Duration - minutes
0
15 30 45 60 75 90 Interruption Duration - minutes
Figure 2.18 Typical interruption cost characteristics for consumer classes.
Cost of Surges and Harmonics Far less information is available on consumer costs of harmonics and voltage surges as compared to that available on the cost of interruptions. What data is made available in publications and most of the reported results and interpretations in the technical literature were obtained in very consumerspecific case studies, most done on a single-consumer basis. As a result there is very little information available on average of typical costs of voltage surge sensitivity and harmonics sensitivity. Few consumers suffer from voltage dip (voltage problems lasting minutes or hours), surge, harmonics, electrical noise, and similar problems. For this reason most studies of cause, effect, and curve are done on a single-consumer or specific area basis. Here, results reported in technical literature are the best guide.
62
Chapter 2
End-Use Modeling of Consumer Availability Needs The consumer-class, end-use basis for analysis of electric usage, discussed in more detail in Chapter 4, provides a reasonably good mechanism for study of the service reliability and power quality requirements of consumers, even if originally developed only for analysis of demand and DSM needs. Reliability and power quality requirements vary among consumers for a number of reasons, but two characteristics predominate analytical considerations: 1. End-usage patterns differ. The timing and dependence of consumers' need for lighting, cooling, compressor usage, hot water usage, machinery operation, etc., varies from one to another. 2.
Appliance usage differs. The appliances used to provide end-uses will vary in their sensitivity to power quality. For example, many fabric and hosiery manufacturing plants have very high interruption costs purely because the machinery used (robotic looms) is quite sensitive to interruption of power. Others (with older mechanical looms) put a much lower cost on interruptions.
End-use analysis can provide a very good basis for detailed study of power quality needs. For example, consider two of the more ubiquitous appliances in use in most consumer classes: the electric water heater and the personal computer. They represent opposite ends of the spectrum from the standpoint of both amount of power required and cost of interruption. A typical 50-gallon storage electric water heater has a connected load of between 3,000 and 6,000 watts, a standard PC a demand of between 50 and 150 watts. Although it is among the largest loads in most households, an electric water heater's ability to provide hot water is not impacted in the least by a one-minute interruption of power. In most cases a one-hour interruption does not reduce its ability to satisfy the end-use demands put on it.6 On the other hand, interruption of power to a computer, for even half a second, results in serious damage to the "product." Often there is little difference between the cost of a one-minute outage and a one-hour outage. It is possible to characterize the sensitivity of most end-uses in most consumer classes by using an end-use basis. This is in fact how detailed studies of industrial plants are done in order to establish the cost-of-interruption
6
Utility load control programs offer consumers a rebate in order to allow the utility to interrupt power flow to water heaters at its discretion. This rebate is clearly an acceptable value for the interruption, as the consumers voluntarily take it in exchange for the interruptions. In this and many other cases, economic data obtained from market research for DSM programs can be used as a starting point for value analysis of consumer reliability needs on a value-based planning basis.
63
Consumer Demand for Power and Reliability
statistics, which they use in VBP of plant facilities and in negotiations with the utility to provide upgrades in reliability to the plant. Following the recommended approach, this requires distinguishing between the fixed cost (cost of momentary interruption) and variable cost (usually linearized as discussed above) on an end-use basis. A standard end-use model used to study and forecast electric demand can be modified to provide interruption cost sensitivity analysis, which can result in "two-dimensional" appliance end-use models as illustrated in Figure 2.19. Generally, this approach works best if interruption costs are assigned to appliances rather than end-use categories. In commercial and industrial classes different types of appliances within one end-use can have wildly varying power reliability and service needs. This requires an "appliance sub-category" type of an end-use model. Modifications to an end-use simulation program to accommodate this approach are straightforward (see Chapter 4), and not only provide accurate representation of interruption cost sensitivity, but produce analysis of costs by time and, if combined with the right type of simulationbased spatial forecast algorithm, location, as shown in Figures 2.20 and 2.21.
Residential Electric Water Heater
Hour of the Day
Figure 2.19 The simulation method's end-use model (see Chapters 10 - 16) is modified to handle "two-dimensional" appliance curves, as shown here for a residential electric water heater. The electric demand curve is the same data used in a standard end-use model of electric demand. Interruption cost varies during the day, generally low prior to and during periods of low usage and highest prior to high periods of use (a sustained outage prior to the evening peak usage period would result in an inability to satisfy enduse demand).
64
Chapter 2
Residential Class 2
Noon Time of Day
Mid. less than S1 per kW
S1 to $2 perkW
Mid. $2 to $5
perkW
( $5moreperthan kW
Residential Class 2
Mid.
Noon Time of Day
Mid.
Figure 2.20 Result of a power quality evaluation, using an end-use model. Top: the daily load curve for single family homes segmented into four interruption-cost categories. High-cost end-uses in the home are predominantly digital appliances (alarm clocks, computers) and home entertainment and cooking. The bottom figure shows total interruption cost by hour of the day for a one-hour outage - compare to Figure 2.21.
Consumer Demand for Power and Reliability 1 Hcrdcspy
4 fhother
65 22-CFR-95 il'42'32 I
to
ttwe curecr to PR Hit t)ra rurober ken of the required feature. Relative
Reliability Value Darker shading indicates higher reliability demand
N :;:;
t *&&•! : : : JS>:;S§: mwSM:^:^fifff] >
'
Thro« mil»£
Lines indicate highways and roads
Figure 2.21 Map of average reliability needs computed on a 10-acre small area grid basis for a port city of population 130,000, using a combination of an end-use model and a spatial consumer simulation forecast method, of the type discussed in Chapters 10 - 16. Shading indicates general level of reliability need (based on a willingness-to-pay model of consumer value).
2.4 TWO-Q ANALYSIS: QUANTITY AND QUALITY VERSUS COST The amount of power used and the dependability of its availability for use are both key attributes in determining the value of the electric power to each consumer. The values attached to both quantity and quality by most consumers are linked, but each is somewhat independent of the value attached to the other. The "two-dimensional" load curve shown in Figure 2.19 is a two-Q load curve, giving demand as a function of time hi both Q dimensions. In order to demonstrate this, it is worth considering two nearly ubiquitous appliances, which happen to represent opposite extremes of valuation in each of these dimensions: the electric water heater and the personal computer. A typical residential storage water heater stores about 50 gallons of hot water and has a relatively large connected load compared to most household appliances: about 5,000 watts of heating element controlled by a thermostat. Its contribution to coincident peak hourly demand in most electric systems is about 1,500 watts. The average heater's thermostat has it operating about 30% of the time (1,500/5,000) during the peak hour.
Chapter 2
66
Despite its relatively high demand for quantity, this appliance has a very low requirement for supply quality. A momentary interruption of electric flow to this device - on the order of a minute or less - is literally undetectable to anyone using it at that moment. Interruptions of up to an hour usually create little if any disruption in the end-use the device provides, which is why direct load control of water heaters is an "economy discount" option offered by many utilities. Similarly, the water heater is not critically dependent on other aspects of power quality. It will tolerate, and in fact turn into productive heat, harmonics, spikes, and other "unwanted" contamination of its supply. By contrast, a typical home computer requires much less quantity, about 180 watts. But unlike the water heater, it is rendered useless during any interruption of its power supply. Just one second without power will make it cease operation. Battery backup power supplies, called un-interruptible power supplies, can be used to avoid this problem, but at an increase in the computer's initial and
High XJ
Space heating Water heater
.1 '3 cr 0)
o
Refrigerator
CL
c ro
Computer
3
o Low High
Low
Need for Continuity of Service Figure 2.22 Electrical appliances vary in the amount of electricity they demand, and the level of continuity of service they require to perform their function adequately. Scales shown here are qualitative. Typically quantitative scales based on the most applicable consumer values are used in both dimensions.
67
Consumer Demand for Power and Reliability
O)
if
peoi
High
Low
Energy
High
Low
Load
Figure 2.23 A Two-Q diagram of a consumer's needs can be interpreted in either of two dimensions to identify the total (area under the curve) and range of needs in either Q direction, producing Q profiles of the importance of demand, or reliability to his particular needs.
operating cost. In addition to its sensitivity to supply availability, a computer is also more sensitive to harmonics, voltage dips, and other power quality issues than a water heater. Figure 2.22 shows these two appliances and several other household energy uses plotted on a two-dimensional basis according to the relative importance of both quantity and quality. This Two-Q load plot is a type of two-dimensional demand and capability analysis that treats both Qs as equally important. Traditionally, "demand" has been viewed only as a requirement for quantity of power, but as can be seen the true value of electric service depends on both dimensions of delivery. Recognition of this fact has been the great driver in moving the electric industry toward "tiered rates," "premium rates," and other methods of pricing power not only by amount and time of use, but by reliability of delivery. Either or both dimensions in the plot can be interpreted as single-dimensional profiles for quantity or quality, as the case may be, providing useful information in the analysis of consumer needs and how to best meet them (Figure 2.23).
68
Chapter 2
Two-Q Planning and Engineering Two-Q analysis using these same two dimensions also applies to the design of utility power systems. This section will only summarize Two-Q planning and engineering so that its capabilities, and how load forecasting and analysis interacts with them, can be understood. The essence of Two-Q planning is to add cost as a third dimension, and then "optimize" either rigorously or through trial, error, and judgement, until the most effective cost to obtain both Q target levels is obtained. Figure 2.24 shows the "options" for development of an existing T&D system, in this case in a growing rural area of the southern United States, currently serving a peak load of about 2 MW/square mile with a SAIDI (System Average Interruption Duration Index) of 114 minutes (indicated by a dot). A series of design studies were used to form the manifold (surface) shown. It indicates what the cost/kW would be if peak load or reliability performance levels were changed from current levels. This manifold gives a rough idea of the cost of building and operating a modified version of the existing system. (Only a rough idea, because the manifold was interpolated from a total of eight design studies. Once this has been used as a rough guide in planning target designs, specific studies then hone the plan and selection of specific detailed design elements).
Figure 2.24 Three-dimensional Two-Q plot of a power system's capabilities, in which cost has been added as the third consideration. The manifold (surface) shown represents the best possible cost of a 138 kV/12.47kV system if re-designed and optimized for various combinations of amount of power and target reliability level in a well-managed and planned system. Dot indicates 2 MW density and 114 minutes SAIDI,
Consumer Demand for Power and Reliability
69
Figure 2.25 Left - the capabilities of a 25 kV distribution system are shown by a second manifold. Right — comparison of the two manifolds results in a Two-Q diagram that shows where each system approach is most cost effective. The results shown are from a real study, but one with a number of real-world constraints. As a result the manifold shape and results shown are not generalizable, although the approach is.
Figure 2.25 shows a second manifold plotted along with the first. This second manifold represents the costs and capabilities of using a 25 kV primary distribution system for some future construction, the 25 kV being used on a targeted basis in the area for large loads and for "express" service to areas where reliability is a challenge with 12.47 kV. The plot indicates that the 25 kV design paradigm offers lower costs at higher load densities and is more expensive at lower load levels. To the right is shown a diagram developed from this data, which shows which Two-Q situations are best-served by 12.47 kV or 25 kV systems. Inspection of the shapes of the manifolds in Figures 2.24 and 2.25 will indicate to the reader the importance of accurate load and reliability targets for planning. The slopes of each manifold are steep in places — small errors in estimating the demand for either Q will generate substantial displacements in the cost estimates used in planning. Thus good forecasts are important. Further, hhe distance between the manifolds is small in many places, and the angle of divergence from where they meet is small — thus small errors in estimating the demand for either Q will yield substantial mistakes in selecting the optimal approach. The reader should note that this sensitivity is not a characteristic of the Two-Q method - the figures above are merely illustrating the cost and decision-making realities of distribution planning, sensitivities that
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would be there regardless of the method used to engineering reliability and demand capability into the system. Therefore, the lesson for the forecaster is that accurate projections of future load levels are crucial, in achieving both good reliability and cost. While this concept is fairly obvious to any experienced T&D planner, the Two-Q approach can quantitatively measure, analyze, and help manage these issues. 2.5 CONCLUSION AND SUMMARY The whole purpose of electric utility systems is to meet the electric demands of individual households, businesses, and industrial facilities. Two useful mechanisms for evaluation of consumer requirements and planning for their provision are end-use analysis and Two-Q planning which provide a useful basis for the study and analysis of both quantity and quality. In addition to having a demand for electric energy, electric consumers value availability and quality of power too, seeking satisfactory levels of both the amount of power they can obtain and the availability of its supply. Each consumer determines what is satisfactory based on specific needs. An interruption that occurs when a consumer does not need power is of no concern. Harmonics or surges that make no impact on appliances are not considered of consequence. Among the most important points in consumer value analyses are: 1.
Interruption of service is the power quality problem that has the widest effect. A majority of electric consumers in most utility systems experience unexpected interruptions at least once a year.
2.
Voltage dips and sags create momentary interruptions for many consumers that are indistinguishable in impact on their needs with short-term interruptions of power flow.
3.
Analysis of consumer needs for power quality is generally done by looking at the cost which less than perfect quality creates, not the value that near-perfect quality provides. Thus, availability of power is usually studied by analyzing the cost incurred due to interruptions, and determining the costs created by those interruptions assesses harmonics.
4.
Power quality costs and values vary greatly depending on consumer class, time of day and week, region of the country, and individual characteristics.
5.
Price concerns often outweigh quality concerns. Throughout the late 1980s and early 1990s, several independent studies indicated that roughly "30%-40% of commercial and industrial consumers are willing to pay more for higher power quality," or something similar, a statistic that seems quite believable and realistic. This led to considerable focus on improving power system reliability and quality.
Consumer Demand for Power and Reliability
71
However, it is worth bearing in mind that these same studies indicate that 20-30% is quite content with the status quo, while the remaining 30-40% would be interested in trading some existing quality for lower cost.
REFERENCES P. F. Albrecht and H. E Campbell, "Reliability Analysis of Distribution Equipment Failure Data," EEI T&D Committee Meeting, January 20,1972. R. N. Allan et al., "A Reliability Test System for Educational Purposes - Basic Distribution System Data and Results," IEEE Transactions on Power Systems, Vol. 6, No. 2, May 1991, pp. 813-821. R. E. Brown and J. R. Ochoa, "Distribution System Reliability: Default Data and Model Validation," paper presented at the 1997 IEEE Power Engineering Society Summer Meeting, Berlin. EEI Transmission and Distribution Committee, "Guide for Reliability Measurement and Data Collection," October 1971, Edison Electric Institute, New York. W. F. Horton et al., "A Cost-Benefit Analysis in Feeder Reliability Studies," Transactions on Power Delivery, Vol. 4, No. 1, January 1989, pp. 446 - 451.
IEEE
Institute of Electrical and Electronics Engineers, Recommended Practice for Design of Reliable Industrial and Commercial Power Systems, The Institute of Electrical and Electronics Engineers, Inc., New York, 1990. A. D. Patton, "Determination and Analysis of Data for Reliability Studies," IEEE Transactions on Power Apparatus and Systems, PAS-87, January 1968. N. S. Rau, "Probabilistic Methods Applied to Value-Based Planning," IEEE Transactions on Power Systems, November 1994, pp. 4082 - 4088.
3 Coincidence and Load Behavior 3.1 INTRODUCTION This chapter discusses how electric load "looks" when measured and recorded at the distribution level. Load behavior at the distribution level is dominated by individual appliance characteristics and coincidence — the fact that all customers do not demand their peak use of electricity at precisely the same time. For this reason alone, accurate load studies on the distribution system require considerable care. In addition, proper measurement and modeling of distribution loads can be quite difficult for a variety of reasons related to how coincidence phenomena interact with load metering and numerical analysis methods. Successful analysis of load data at the distribution level requires procedures different from those than typically used at the system level. This chapter addresses the reasons why and the measurement and analytical methods needed to accurately represent and handle distribution load curve data. The discussion in this chapter is divided into two sections. In 3.2, coincident and non-coincident load curve behavior are discussed - the behavior of distribution load as it actually occurs on the distribution system. Section 3.3 then looks at load curve measurement, and shows how some popular measuring systems and analytical methods interact with coincident/non-coincident behavior to distort observed load curve measurement. Finally, section 3.4 summarizes the key points and develops some guidelines for accurate load curve monitoring. 73
Chapter 3
74
3.2 PEAK LOAD, DIVERSITY, AND LOAD CURVE BEHAVIOR
Almost all electric utilities and electric service companies represent the load of consumers on a class by class basis, using smooth, 24-hour peak day load curves like those shown in Figure 3.1. These curves are meant to represent the "average behavior" or demand characteristics of customers in each class. For example, the utility system whose data are used in Figure 3.1 has approximately 44,000 residential customers. Its analysts will take the total residential customer class load (peaking at about 290 MW) and divide it by 44,000 to obtain a 'typical residential load' curve for use in planning and engineering studies, a curve with a 24-hour shape identical to the total, but with a peak of 6.59 kW (1/44,000ms of 290 MW). This is common practice, and results in the "customer class" load curves used at nearly every utility. Actually, no residential customer in any utility's service territory has a load curve that looks anything like this averaged representation. Few concepts are as
Summer and Winter Residential Class Peak Day Load Curve Summer
Winter 300
5200
>200
2
12
6
12 HOUR
12
12
12 HOUR
6
Summer and Winter Residential Peak Day Customer Load Curves Summer
Winter
7 6 • 4 23
3 22 1 0
12
12 HOUR
12
12
12 HOUR
6
Figure 3.1 Utilities often represent the individual load curves of consumers with smooth, "coincident" load curves, as shown here for the residential load in a utility system in Florida. Top, summer and winter demand of the entire residential class in a southern US utility with 44,000 residential consumers. Bottom, representation of "individual" consumer load curves. Each is 1/44,000 of the total class demand.
75
Coincidence and Load Behavior
22 kW
One household
Hour Figure 3.2 Actual winter peak day load behavior for an individual household looks like this, dominated by high "needle peaks" caused by the joint operation of major appliances.
important as understanding why this is so, what actual load behavior looks like, and why the smooth representation is "correct" in many cases but not in many that apply to the distribution level. The load curve shown in Figure 3.2 is actually typical of what most residential customer load looks like over a 24-hour period. Every residential customer's daily load behavior looks something like this, with sharp "needle peaks" and erratic shifts in load as major appliances such as central heating, water heaters, washer-dryers, electric ranges, and other devices switch on and off. Appliance Duty Cycles The reason for the erratic "needle peak" load behavior shown in Figure 3.2 is that a majority of electric devices connected to a power system are controlled with what is often called a "bang-bang" control system. For example, a typical 50-gallon residential electric water heater holds 50 gallons of water, which it keeps warm by turning on its heating elements anytime the temperature of the water, as measured by its thermostat, dips below a certain minimum target value. Thus switched on, the heating elements then create a demand for power, which heats the water, and thereby the temperature begins to rise. When the water temperature has risen to where it meets the thermostat's high target temperature setting, the elements are turned off by that thermostat's relay. The on-and-off-
76
Chapter 3
75
170
Ti me
>
Figure 3.3 Top curve indicates the water temperature inside a 50-gallon water heater whose thermostat is set at 172 degrees over a period of an hour. The thermostat cycles the heater's 4 kW element on and off to maintain the water temperature near the 172 degree setting. Resulting load is shown on the bottom of the plot.
cycling of the demand, and the consequent impact on water temperature, is shown in Figure 3.3. The water heater cycles on and off in response to the thermostat - bang it is on until the water is hot enough, then bang it is off and remains so until the water is cold enough to cause the thermostat to cycle the elements back on. This bang-bang control of the water heater creates the actual demand curve of the water heater. Over a 24-hour period, it is a series of 4 kW demands, as shown in the top row of Figure 3.4. There is no "curve" in the sense of having a smooth variation in demand, or variation in demand level, beyond an up and down variation between 4 kW when the water heater is on, and 0 when it is not. Aggregation of Individual Demand Curves into Coincident Behavior Daily load curves for several residential water heaters are shown in Figure 3.4. Most of the time a water heater is off, and for a majority of the hours in the day it may operate for only a few minutes an hour, making up for thermal losses (heat gradually leaking out of the tank). Only when household activity causes a use of hot water will the water heater elements stay on for longer than a few minutes each hour. Then, the hot water use draws heated water out of the tank,
77
Coincidence and Load Behavior
B Cust.R1-37747QW F$b. 6,1994
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C Cust.R1-67548BU
Feb. 6, 1 994
Feb. 1, 1 994
S kU
S kU
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•o o
o _l
O _J
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Hour
Hour
D 10KU
Cust. R1-37747QWand Oust R1-67548BU Feb. 6,1994
Hour
Five water heaters
50 Water Heaters
25 kU
Hour
Hour
Figure 3.4 Curves A and B are water heater loads at neighboring houses on the same day (Feb. 6), displaying similar but not identical behavior. Curve C is the second household's water heater curve for Feb. 7, showing that random differences and slight shifts in usage cause different timing in that day's needle peaks. Curve D shows the sum of the two water heaters' curves for Feb. 6. For the most part, there is little likelihood that they are both on at the same time, but occasionally around peak time they are. Assembling 50 water heaters results in a smoother load curve, one where load peaks during peak periods of water heater usage ~ the average cycle time of the water heaters is longer (needle is wider) — meaning there is more likelihood that many overlap, and hence add to a high peak value.
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with it being replaced by cool water piped in to re-fill the tank, which lowers the temperature in the tank significantly, requiring the element to remain on for a long time thereafter to "manufacture" the replacement hot water. During that hour, its duty cycle — the percent of the time it is on — might be high, but the rest of the day it is quite low. Figure 3.4 shows several water heater loads, as well as plots representing the sum of the load for a number a number of water heaters over a 24-hour period. It illustrates several important points. First, all water heaters exhibit the same overall on-off behavior, but differ slightly as to the timing of the cycles. Second, if enough load curves are added together, their sum begins to look more like a smooth curve (similar to Figure 3.1) than the typical blocky individual device curve. Almost all the large loads in every residence operate in a manner similar to the water heaters discussed here. Air conditioners and heaters operate by control of thermostats. So do refrigerators and freezers and electric ranges. As a result, the household's total load curve (Figure 3.2) is the sum of a number of individual appliance on-off curves that each look something like those at the top of Figure 3.4. Duty Cycle Load of Air Conditioners and Heat Pumps Figure 3.5 shows the ambient (outside) temperature and the electric load of an air conditioner set to 68°F inside temperature over a 24-hour period. It illustrates a slightly more complex behavior and will help to examine appliance duty cycle performance in slightly more detail than the preceding section. Note that, like the water heater, the air conditioner unit shown here cycles on and off. As outside temperature increases, and the burden of removing heat from inside the house becomes greater, the AC unit stays on longer every time it turns on, and stays off for a shorter time. During the hottest period of the day, its duty cycle (percent of the time it is on during the hour) is above 90%. The particular unit shown in Figure 3.5 was selected for this house based on a 35 degree difference criteria ~ at 100% duty cycle it can maintain a 35°F difference between outside and inside. At the 100°F ambient temperate reached, it is providing a 32°F difference for the 68°F thermostat setting, near its maximum. Note also that here, unlike in the case of the water heater, the amount of load (the height of the load blocks when the unit is on) varies over the day. Connected load of the AC unit increases as the ambient temperature increases. The mechanical burden of an air conditioner or heat pump's compressor will be higher when the temperature gradient the unit is opposing is higher (due to the
Coincidence and Load Behavior
79
Figure 3.5 Daily cycle of THI (temperature-humidity-illumination index) and air conditioner load as it cycles between on and off under thermostatic control (see text). As THI rises throughout the morning, demand for cooling increases, and the air conditioner's duty cycle (% of time the unit is operating) increases, until at peak it is operating all but a few minutes in every hour.
nature of the system's closed cycle design causing higher internal pressures and hence more pumping load). When the pressure is higher, the electric motor must work harder, and hence draws more power (i.e., has a higher load). The net result is that an air conditioner's operating load increases as outside temperature gets warmer, and a heat pump's load increases as outside temperature gets colder. Thus, during the heat of mid-day, the air conditioner unit shown in Figure 3.5 not only stays on most of the time, but has a load about 10% higher than it would when ambient is cooler. Most air conditioner and heat pump units, and many other mechanical pumping loads, display this characteristic. Coincident Load Behavior Suppose one were to consider one hundred homes, for example one hundred houses served by the same segment of a distribution feeder. Every one of these homes is full of equipment that individually cycles on and off like appliances just described — water heaters, air conditioners, heaters, and refrigerators that all are controlled by thermostats. Thus, each household will have an individual daily load curve similar to the erratic, choppy daily load curve shown in Figure 3.2, although each will be slightly different, because each home has slightly different appliances and is occupied by people with slightly different schedules and usage preferences, and
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because the times that individual thermostats activate appliances are usually random, differing slightly throughout the day for each appliance. Thus, one particular household might peak at 22 kVA between 7:38 AM and 7:41 AM, while another peaks at 21 kVA between 7:53 AM and 8:06 AM, while another peaks at 23 kVA between 9:54 AM and 10:02 AM. These individual peak are not additive because they occur at different times. The individual peaks, all quite short, do not all occur simultaneously. They are non-coincident. As a result, when one adds two or more of these erratic household curves together, the load curve needles usually interleave, much as the overlapping teeth of two combs might interleave. As yet more customer load curves are added to the group, more and more "needles" interleave, with only an occasional situation where two are absolutely coincident and add together. The load curve representing the sum of a group of households begins to take on the appearance of a smoother curve, as shown in Figure 3.6, in exactly the same way and for the same reasons that the water heater load curves in Figure 3.4 did. By the time there are twenty-five homes in a group, a smooth pattern of load behavior begins to emerge from within the pattern of erratic load shifts, and by the time the loads for one hundred homes have been added together, the curve looks smooth and "well-behaved." This is the non-coincidence of peak loads. Individual household demand consists of load curves with erratic swings as major appliances switch on and off at the behest of their thermostats and other control devices. Distribution equipment that serves only one customer ~ service drops or a dedicated service transformer for example — sees a load like this. But distribution equipment that serves large numbers of customers — a distribution feeder for example — is looking at many households and hundreds of appliances at once. Individual appliance swings do not make a big impact. It is their sum, when many add together, that causes a noticeable peak for the feeder. This happens when many duty cycles overlap. Peak load per customer drops as more customers are added to a group. Each household has a brief, but very high, peak load — up to 22 kW in this example for a southern utility with heavy air-conditioning loads. These needle peaks seldom overlap, and under no conditions would all in a large group peak at exactly the same time.l As a result, the group peak occurs when the combination of the individual load curves is at a maximum, and this group peak load is usually substantially less than the sum of the individual peaks, as can be seen by studying Figure 3.6.
1
Except due to something called "cold load pickup," which occurs when all appliances have been without power during a long outage. As soon as service is restored, all appliances switch on immediately, creating a larger than normal demand.
81
Coincidence and Load Behavior
Two Homes
Five Homes
Hour
Hour
22kW
15kW
Figure 3.6 Daily load curves for groups of two, five, twenty, and one hundred homes in a large suburban area. Note vertical scale is in "load per customer" for each group. Peak load per customer decreases as the number of customers in the group becomes larger. This is coincidence of peak load.
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Chapter 3
This tendency of observed peak load per customer to drop as the size of the customer group being observed increases is termed coincidence and is measured by the coincidence factor, the fraction of its individual peak that each customer contributes to the group's peak. C = coincidence factor =
(observed peak for the group) I. (individual peaks)
(3.1)
Peak load per customer is generally a strictly decreasing value as a function of the number of customers in the group. Often, the value of C for large values is only .3 to .25. Thus, the coincidence factor, C, can be thought of as a function of the number of customers in a group, n: C(n)
=
observed peak load of a group of N customers Z (their individual peaks)
(3.2)
where n is the number of customers in the group, 1 < n < N = number of customers in the utility
C(n) has a value between 0 and 1 and varies with the number of customers in identical fashion to how the peak load varies, so that a curve showing C(n) and one showing peak load as a function of the number of customers are identical except for the vertical scale. Distribution engineers sometimes use the inverse of C to represent this same phenomenon. The diversity factor, D, measures how much higher the customer's individual peak is than its contribution to group peak. D = diversity factor
=
I/coincidence factor
(3.3)
The coincidence curve shown in Figure 3.7 is typical of residential peak load behavior in the United States ~ C(n) for large groups of customers is typically between .5 and .33, and may fall to as low as .2. Coincidence behavior varies greatly from one utility to another. Each utility should develop its own coincidence curve data based on studies of its own customer loads and system. Estimates of equipment loads are often based on load data from coincidence curves. Very often, T&D equipment sizes are determined by using such coincidence curves to convert load research data (or whatever data are available) to estimates of the equipment peak loads. For example, the "coincident peak"
83
Coincidence and Load Behavior
22 20
O
o> o CO
O 10 TJ
'o O
CO
5
10 100 1000 Number of Customers in the Group
10000
Figure 3.7 The peak load per customer drops as a function of the number of customers in a group.
60
30 0)
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10 100 1000 Number of Customers in the Group
10000
Figure 3.8 The peak period as a function of the number of customers in a group. Larger groups have longer peak periods.
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for a group of customers served by a feeder segment, transformer, or secondary line can be estimated from individual ("instantaneous") peak load data, as Group peak for n customers = C(n) x n x (average individual peak load)
(3.4)
Thus, the peak load for a transformer serving eight houses, each with an estimated individual peak load of 22 kW would be Transformer peak load = C ( 8 ) x 8 x 2 2 k W
(3.5)
Using a typical value of C(8), which is about .6, gives 106 kW as the estimated peak load for the transformer. Often, reliable estimates of the individual customer peak loads (the 22 kW figure in these examples) may not be available. In this example, that would mean the planner did not know the 22 kW value of individual peak load but instead had only the "contribution to peak" value of 7.9 kW/customer. The transformer load can still be estimated from the coincidence curve as: Transformer peak load = C(N)/C(8) x 8 x 7.9 kW where N>»8
(3.6)
Here, using .36 as C(N) gives the same 106 kW. Peak period lasts longer for larger groups of customers. The erratic, up and down load curve of a single customer may have a very high peak load, but that peak lasts only a few minutes at any one time, although it is reached (or nearly reached) several times a day. By contrast, the load curve for one hundred homes reaches its peak only once during a day but stays at or near peak much longer -- perhaps for over an hour. Figure 3.8 shows the peak load duration — the longest continuous period during the day when the peak load is at or within 5% of maximum ~ for various numbers of customers. Coincident load curve behavior can be viewed as the expectation of a single household's load What does the smooth, average residential customer curve, one computed from Figure 3.1 as described earlier, indicate? As stated, it is the average, coincident customer load curve, l/44,000th of the load from 44,000 households. While no customer within the entire utility service territory has an individual load curve that looks anything like this curve, the application of a smooth load curve computed in this way has two legitimate interpretations on a per customer basis:
Coincidence and Load Behavior
85
/. The curve is an individual customer's contribution to system load. On the average, each customer (of this class) adds this much load to the system. Add 10,000 new customers of this type, and the system load will increase by 10,000 times this smooth curve. 2. The curve is the expectation of an individual customer's load. Every customer in this class has a load that looks something like the erratic behavior shown on Figure 3.1, but each is slightly different and each differs slightly from day to day. The smooth curve gives the expectation, the probability-weighted value of load that one would expect a customer in this class, selected at random, to have at any one moment, as a function of time. The fact that the expectation is smooth while actual behavior is erratic is a result of the unpredicatable randomness of the timing of individual appliances. The behavior discussed above is infra-class coincidence. Commercial and industrial customers have similar behavior to that discussed above for residential loads, but the shape of their coincidence curves may be different. Qualitatively the phenomenon is the same, quantitatively it is usually quite different. One can also speak of coincidence between classes. Figure 3.1 showed average or typical coincident curves for residential, commercial, and industrial customer classes in a summer peaking utility in the southern United States. These various classes peak at different times of the day. Commercial load peaks in mid-afternoon, and residential load peaks in late afternoon or early evening. A substation or feeder serving a large number of customers of both types will not see a peak equal to the sum of the coincident residential and commercial peaks for the customers it serves. It will see a somewhat lower peak load, because these two classes of customer experience their peak load, as classes, at different times. Coincidence and its effects on planning will surface again and again throughout this book, and we will make reference to coincidence, and discuss its impact on planning when we discuss how to determine feeder and transformer capacity; what loads to use in feeder voltage drop and losses studies; how to site and size substations; which load curves are appropriate for certain special applications; and how to forecast load growth. Therefore, it is vital that the reader understand the concept and phenomenon of load coincidence, both within each customer class, and among the classes. 3.3 MEASURING AND MODELING LOAD CURVES The manner in which load curve data are collected, recorded, analyzed, and represented can produce a dramatic effect on what the resulting load curves look like, and the perceived values of peak load and coincidence. The apparent load curve shape can change depending on how the load data are measured and how periodically these measurements are recorded.
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Sampling rate and sampling method both have a big impact on what load curve data look like, how accurate they are, and how appropriate they are for various planning purposes. Sampling rate refers to the frequency of measurement ~ the number of times per hour that load data are recorded. Sampling method refers to exactly what quantity is measured — instantaneous load or total energy used during each period. Most load metering equipment measures the energy used during each period of measurement (called demand sampling). If the load is measured every 15 minutes, the equipment measures and records the total energy used during each 15-minute period, and the resulting 96-point load curve gives the energy used during each quarter hour of the day. Plotted, this forms a 24-hour demand curve. This method of recording is sampling by integration — the equipment integrates the area under the load curve during each period and stores this area, even if the actual load is varying up and down on a second-by-second basis. By contrast, discrete instantaneous sampling measures and records the actual load at the beginning of each period. Essentially, the equipment opens its eyes every so often, records whatever load it sees, and then goes to sleep until the beginning of the next period. Some load monitoring equipment uses this type of sampling. Discrete instantaneous sampling often results in erratically sampled data that dramatically misrepresent load curve behavior. The right side of Figure 3.9 shows a data curve for a single home, produced by a discrete instantaneous sampling technique applied on a 15-minute basis to the individual household data first shown in Figure 3.2. This "load curve" is hardly representative of individual, group, or average load behavior. It does not represent hourly load behavior in any reasonable manner. This data collection error cannot be corrected or counteracted with any type of subsequent data processing. What happened is that the very instant of measurement, which occurred once every 15 minutes, sometimes happened upon the very moment when a sharp load spike of short duration was at its peak. Other times, the sampling stumbled upon a moment when energy usage was low. This type of sampling would yield a good representation of the load behavior if the sampling were more rapid than the rapid shifts in the load curve. But sampling at a 15-minute interval is much too slow ~ the load curve can shoot back and forth from maximum to minimum several times within 15 minutes. As a result, it is just random luck where each period's sampling instant happens to fall with respect to the actual load curve behavior ~ and a portion of the sampled load curve data is essentially randomly selected data of no real consequence or value. Automatic load metering equipment seldom uses discrete instantaneous sampling. Almost all load recorders use demand sampling (period integration). However, many sources of load data do start with instantaneous discrete sampled data, particularly because human beings usually do use this approach when gathering data.
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Period integration
Discrete instantaneous
22 kW
22 kW
Hour
Hour
Figure 3.9 Load for a single household (the load curve in Figure 3.1) sampled on a fifteen-minute interval by both period integration (left) and discrete instantaneous sampling (right). Neither curve is fully representative of actual behavior, but the period integration is more accurate for most purposes. The discrete sampling is nearly worthless for planning and load study applications.
For example, data written down by a technician who reads a meter once an hour, or by a clerk who takes hourly load values off a strip chart by recording the reading at each hour crossing tic mark, have been sampled by this method. So, too, have data that have been pulled from a SCADA monitoring system on an hourly basis by programming a system macro to sample and record the power flow at each bus in the system at the top of each hour. In all such cases, the planner should be aware of the potential problem and correct for it, if possible. The technician taking hourly values off the strip chart can be instructed to estimate the average of the plotted value over the entire hour. The SCADA system should make several readings separated by several minutes and average them. To be entirely valid, load curve data gathered using discrete instantaneous sampling must satisfy the Nyquist criteria, which requires that the load be sampled and recorded at least twice as often as the fastest load shift occurring in the measured load.2 When measuring a single customer, whose load can shift up
2
The author has taken slight liberties with the interpretation of the Nyquist criteria (also called the sampling theorem), but from a practical .standpoint the description is more than sufficient to explain application to load curve measurement. A more theoretical presentation of load curve sampling rates can be found elsewhere (see Willis et al, 1985).
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and down completely within a few minutes, this means a sampling rate on the order of a minute or less must be used. If taken at one-minute intervals, such data are accurate, but even at 10-minute intervals, a rate often considered very fast for load research purposes, discrete sampling will produce very poor results when applied to individual or small groups of customers. As was discussed earlier, larger groups of customers have smoother and more well-behaved load curves. Thus, the problem discussed here is not as serious when the load being metered is for a feeder or substation as when the load being measured is for only a few customers, although it can still produce noticeable error at the feeder level. At the system level it seldom makes any difference. A telltale sign that discrete sampling data errors are present in load data is erratic load shifts in the resulting load curves, like those shown on the right side of Figure 3.9. However, lack of this indicator does not mean the data are valid. Hourly, half hour, or even 15-minute load research data gathered via discrete instantaneous sampling should be used only when absolutely necessary, and the planner should be alert for problems in the resulting load studies. Sampling by integration, by contrast, always produces results that are valid within its context of measurement. For example, hourly load data gathered by period integration for an individual customer will accurately reflect that customer's average energy usage on an hour by hour basis. Whether that sampling rate is sufficient for the study purposes is another matter, but the hourly data will be a valid representation of hourly behavior. Figure 3.10 shows the daily load curve for one household (that from Figure 3.1), demand sampled (period integration) at rates of quarter hour, half hour, one hour, and two hours. None give as accurate a representation of peak load and peak period as the original curve (which was sampled at one-minute intervals), but each is an accurate recording usage averaged to its temporal sampling rate. Such is not the case with discrete sampling, where the recorded values may be meaningless for any purpose if sampled at a rate below the Nyquist rate for the load behavior being measured. Figure 3.11's curve of peak load versus sampling rate bears a striking resemblance to the peak coincidence curve plotted in Figure 3.7, an interesting potential source of error, which will be discussed later in this chapter. As the sampling period of demand sampling is lengthened, the observed peak load drops, as shown in Figure 3.11. The sharp needle peaks are being averaged with all behavior over longer periods, reducing the measured "peak demand." This reduction in measured peak as a function of demand period is why most load analysts always use a time designation with respect to any demand measurement or peak load reference, as in "hourly demand reading" or "peak 15-minute demand."
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Coincidence and Load Behavior 22 kW
15 Min.
10 kW
22 kU
30 Min.
10 KW
Hour
Hour
Figure 3.10 Daily load shape for the household load curve in Figure 3.1 demand sampled (i.e., using period integration) on a 15, 30,60, and 120 minute basis.
22 20 0)
E o 3
O
10
_
CD Q) 0_
30 Length of Sampling Period - Minutes
60
Figure 3.11 Observed peak load is a function of time period of sampling for the single household's daily load curve, as a function of the sampling period. Only high sampling rates can see the needle peaks and thus correctly sample their full behavior.
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90 10 kW
10 kU 15 Min.
10 kW
Hour
Hour
Figure 3.12 Daily load shape for 100 homes demand sampled with a 1, 15, 30, and 60 minute period. Little error is introduced by using a one hour sampling rate as opposed to 1 minute, because the basic coincident load behavior of 100 households' load is inherently smooth, not erratic and full of needle peaks as in the single household case. Note vertical scale is the same in all four plots.
High Sampling Rates Are Needed When Sampling Small Groups Of Customers In Figure 3.12 sampling rate is again varied, this time for a load curve representing the sum of loads from 100 homes. The measured curve varies insignificantly as sampling rate is increased. The smooth, coincident load curve for a large group of customers does not need to be sampled at a high rate in order to be accurately recorded. High sampling rates are needed only when studying the non-coincident load behavior of small groups of customers. Figure 3.13 shows the measured peak load of this group of 100 homes as a function of the demand period used in measurement. Clearly, little error is introduced with sampled periods up to one hour in length. Again, high sampling rate is not needed when measuring aggregate load behavior for large groups of customers.
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22 20 o>
o to
O 10
TO 0> Q_
60
120
Length of Sampling Period - Minutes Figure 3.13 Measured per customer coincident peak load for a group of 100 homes, as a function of the sampling period used with period integration. For any sampling period less than 60 minutes, the measured peak load varies little, indicating that the load curve does not need to be sampled more often than hourly.
Comparison of the 60-minute sampled curves from Figures 3.12 and 3.14 shows that they are very similar. An individual customer curve, demand sampled at a slow rate, yields a good estimate of the coincident curve shape. In essence, measuring an individual customer's load at a lower rate with period integration gives a picture of that customer's contribution to overall coincident load behavior. Depending on the goals of the load measurement, this can be a positive or negative aspect of using the lower sampling rate. Determining the Required Sampling Rate Recall that the measured peak load versus sampling period curve for a single customer (Figure 3.11) bears a striking resemblance to the actual peak load versus number of customers coincidence curve (Figure 3.7). A good rule of thumb is: the demand sampling rate required to measure the load for a group of customers is that which gives the same measured coincident peak/customer when applied to an individual customer curve. For example, suppose it is desired to sample the load behavior of a group of five homes to determine peak loading, daily load curve shape, and so forth. Note that in Figure 3.8, C(5) = .8, giving a coincident load of .8 x 22 kW = 17.6 kW per household for a group of five homes.
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As Figure 3.11 shows, when applied to an individual household load curve, a sampling period in the range of 10 minutes (6 demand samples/hour) should give a peak of 18 kW. Therefore, one can conclude that a group of five homes needs to be sampled and analyzed at at least this rate to be represented accurately. Similarly, one can determine the smallest number of customers for which a particular sampling rate provides accurate data. Suppose that half hour data are to be used in a load research study. Figure 3.11 shows that this can be expected to record a peak load of 10.9 kW when applied to a single customer load curve. This is equivalent to a coincidence factor of 10.9 kW/22 kW or .49, which is equal to C(25). Thus, half hour data are accurate (in this utility) for studies of distribution loads and loading on any portion of the system serving 25 customers or more. It is not completely valid for studies on equipment serving smaller groups of customers. In a similar way, a plot of sampling period versus number of customers can be determined, as shown in Figure 3.14. This example is qualitatively generalizable but the values shown are not valid for systems other than the one used here — average individual household needle peak of 22 kW, coincident behavior as plotted here, and so forth, vary from one utility to another and often by area within utility systems. These data were taken from a utility system in the Gulf Coast region of the United States, and the results given are valid for that system. Quantitative results could be far different for systems with different customer types, load patterns, and coincidence behavior (see Electric Power Research Institute, 1990).
60 30 D) C CO
15L.S2 E i 'oT
% 'I w IU CO E, w o -in *-a en
5
10 100 1000 Number of Customers in the Group
10000
Figure 3.14 Rule-of-thumb plot of sampling period (for integrated sampling) versus number of customers in the group.
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Often, a planner does not have even a few samples of high resolution (very short sampling period) load data from which to make the type of analysis described above. In that case, the author recommends that the coincidence curve (Figure 3.7) and the peak versus sampling rate curve (Figure 3.11) be estimated as best as can be done from whatever data are available. For example, suppose only 15minute period load curve data are available. Added together in blocks of two and four periods, this gives 30-minute and 60-minute sampled curves, whose peak loads can be used to provide the peak versus sampling rate curve in the 30minute to 60-minute sampling period portion of the curve. Estimates of the absolute individual household peak load can often be derived from knowledge of the types and market penetrations of appliances or by the planner's judgment. These data give an estimated value for the Y intercept of the coincidence curve. Measured peaks on distribution equipment such as service transformers and feeder line segments provide detail on the peak loads of groups of customers of various sizes. Analysis of sampling period versus number of customers in the group can then be carried out as outlined earlier.
60 .• •
30
O)
.
if co E
CO
810 0> O
?fe 0) Q_ 1/V
1
5
10
100
1000
10000
Number of Customers in the Group Figure 3.15 Example of estimating the sampling rate versus peak load relation from incomplete data, as explained in the text. Dots represent actual data taken from the system and analyzed as described in text. The solid line indicates the relationship that can be determined exactly based on this available data; the dashed line shows the estimated portion. As a general rule, the curve passes through the origin of the point (1, 1), shown by the X, a fact useful in estimating the curve shape.
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The approximate nature of the number of customers versus sampling period relation is estimated from these data, as shown in Figure 3.15. While not of the quality of accurate, high-sample rate data, the resulting curve is the best available under the circumstances and can be used, with judgment, to make decisions about the legitimate uses of whatever load data are available. 3.4 SUMMARY Distribution load behavior is dominated by coincidence, the fact that peak loads do not occur simultaneously. Individual customer load curves are erratic, formed of fast, sharp shifts in power usage. As customers are combined in groups, as when the planner analyzes load for groups served by equipment such as service transformers, laterals, and feeders, the erratic load curves add together with the sharp peaks intermingling and forming a smoother curve. As a result, when comparing the load curves for different size groups of customers, as the number of customers increases, the group load curve becomes smoother, the peak load per customer decreases, and the duration of the peak increases. Also important is the manner in which the load curves are measured. Where possible, particularly when working with small groups of customers, data should be collected and analyzed using the period integration method, and the sampling period should be quite short, generally less than 15 minutes.
REFERENCES H. L. Willis, T. D. Vismor, and R. W. Powell, "Some Aspects of Sampling Load Curves on Distribution Systems," IEEE Transactions on Power Apparatus and Systems, November 1985, p. 3221. Electric Power Research Institute, DSM: Transmission and Distribution Impacts, Volumes 1 and 2, Palo Alto, CA, August 1990, EPRI Report CU-6924.
4 Load Curve and End-Use Modeling
4.1 END-USE ANALYSIS OF ELECTRIC LOAD The ability to distinguish and model the behavior of electric demand based on class of consumer and as a function of time is an important element in many electric load forecasting applications. A wide variety of methods have been developed, but none more successful or applicable to spatial load analysis than the consumer class end-use load model. Consumer class end-use models are ubiquitous in the power industry, and a single chapter cannot begin to cover all of the variations and all of the finer points involved Instead, this discussion will concentrate on the basic concepts and those points which the author feels are important to spatial load forecasting. End-use models represent a "bottom up" approach to load modeling. They distinguish electric usage by three levels of categorization: consumer classes, end-use classes within each consumer class, and appliance categories within each end-use. Generally, they work with coincident load curve data in order to analyze and forecast curve shape, and they can incorporate weather sensitive elements where applicable. The best are nearly indispensable load analysis tools and all serious forecasters should consider the use of this workhorse of temporal modeling.
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Electricity Is Purchased for End-Uses Electricity is always purchased by the consumer as an intermediate step towards some final, non-electrical product. No one wakes up in the morning saying "I want to consume 12 kWh today." Instead, they want the products electricity can produce when applied through the actions of various appliances ~ a cool home in summer, a warm one in winter, hot water on demand, vegetables kept fresh in the refrigerator, and 48 inches of dazzling color with stereo commentary during Monday night football. These different products of electric usage are called end-uses, and they span a wide range of applications over all aspects of our society and its economy. For some end-uses there is no viable alternative to electric power (the author is aware of no manufacturer of natural-gas powered televisions or computers). For others, there are alternatives but electricity is by and large the dominant energy source (there are gas-powered refrigerators, and natural gas can be used for illumination beyond its niche application for ornamental outdoor lighting). But for many important applications, electricity is just one of several possible energy sources — water heating, home heating, cooking, clothes drying, and many industrial applications can be done with natural gas, oil, or coal. Each end-use — the need for lighting is a good example ~ is satisfied through the application of electricity to appliances or devices that convert the electric power into the desired end product. For lighting, a wide range of illumination devices can be used, from incandescent bulbs, to fluorescent tubes, to sodium vapor and high-pressure monochromatic gas-discharge tubes, and even lasers. Each uses electric power to produce visible light. Each has differences from the others that give it an appeal to some consumers and perhaps substantial advantages in some applications. And each requires electric power to function, creating an electric load when it is activated. By studying both the need for the final product (i.e., illumination) and the types of devices used to convert electricity to the final product (e.g., light bulbs), one can determine a great deal about the character of electric usage, particularly with respect to its variation with time of day, day of week, and season of the year. Further, one can determine its variation with temperature, and possible changes in future electric demand as technology, population demographics, or societal needs and values change. This is end-use analysis. Load Behavior Can Be Distinguished by Consumer Class Generally, electric utilities track sales of their product by consumer class, or more specifically, rate class, because different rates are charged to different types and sizes of electric consumer, and sales are inventoried and tracked within
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19,000 GWhr
3,500 MW Peak
other other
Figure 4.1 Peak load and annual kWh sales broken down by basic consumer class for a municipal utility in the central United States.
each rate class, as shown in Figure 4.1. Many utilities charge a lower rate for usage of electricity in the home as compared to their rates for commercial or industrial applications (something called cross-subsidization). Rates are in a sense end-use based. Consumer class distinctions are nearly always used in end-use models because the basic uses of electricity and also the usage patterns vary greatly depending on the basic class of consumer (see Ceilings and Taylor, 1981). For example, while residential and commercial users of electricity both purchase a great deal of power for illumination purposes, commercial consumers use a predominance of fluorescent lighting while residential consumers use predominantly incandescent lighting. Commercial usage is high during normal business hours while residential lighting usage is highest in the early evenings. Distinction by class of consumer is an important element of end-use modeling. A class is any subset of consumers -whose distinction as a subset helps identify or track load behavior in a way that improves the effectiveness of the forecast. It is typical to study end-uses of electricity on a class-by-class basis, with classes defined so that they make important distinctions about usage. For example, commercial users might be segregated into retail and office classes, since these two applications differ substantially in both basic end-use needs (what they use electricity for) as well as the timing of their usage (retail generally
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stays open in the evenings, offices shut down after normal business hours). Similarly, the residential class might be split between homes in areas without gas distribution (thus they are more likely to be all-electric) and homes where natural gas delivery is available for alternatives to water heating and space heating. Therefore, while end-use models almost always start with the basic residential-commercial-industrial-other distinction of class, most use many more than three classes. Practical limitations place an upper limit on the number of classes that can be accurately and conveniently tracked, so most end-use models work with one or two dozen consumer classes, although successful models have been built using as few as four and as many as one hundred classes. What is important about the class definitions is that: 1) they make meaningful distinctions with regard to the load forecasting application, and 2) they are distinguishable based on available data. As an example, for analysis of usage in a seaside resort area, it might be useful to distinguish retail consumers of two classes: "retail establishments open all year" and "retail establishments open only for the tourist season." Such distinction could improve analysis by identifying seasonal versus annual users of electricity, and it might be possible to model usage in these two categories as functions of different parts of the local economy (seasonal load linked to tourism, annual users linked to other aspects) further improving the forecasting. The distinction of existing consumers into these two categories could be determined very simply from monthly billing data ~ seasonal consumers will have "zero kWh" bills for the winter months each year. Thus, this appears to be a good class definition: applicable to the forecaster's goals and distinguishable from available data. By contrast, while it might be useful in forecasting future load to distinguish residential consumer categories of "those who would spend extra to buy efficient appliances that conserve energy" and "those who will buy appliances based only on the lowest first cost," no reliable way of obtaining data to do so exists for most utilities. Similarly, just because a subclassification can be done based on available data does not mean it should be: one can group residential consumers into "those whose last names start with letters in the first half of the alphabet" and "those whose don't," but such distinctions have doubtful utility in forecasting load growth. Serendipitously, the consumer classes typically most useful in end-use modeling bear a very close match to the land-use classes used to distinguish locational growth and econometric patterns in the better types of spatial load forecasting models. Both start with the basic residential-commercial-industrialother classifications and make subclass distinctions within each. With only a little effort, spatial and end-use models can be structured so that their classifications are identical, and thus they can work in harmony.
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Load Curve and End-Use Modeling End Uses of Electricity
Within each consumer class, electric usage is distinguished by subdividing usage into end-use categories, as illustrated in Figure 4.2. As was the case with the definitions of consumer classes, the end-use categories are defined based on what is needed to improve the forecasting and analytical ability of the model for its particular application. An end-use model developed solely to analyze winter heating demand might make numerous distinctions of usage for space heating, but lump all other uses into an "other" category because detail is not particularly necessary there. Table 4.1 lists the end-use categories into which rural residential peak and energy sales for a municipal utility in the southwestern United States (same as plotted in Figure 4.1) were broken down in one end-use model developed by the author for both distribution planning and demand side management (DSM) planning. The categories shown are typical of a "full" breakdown of residential usage into categories, and similar detail is required in other consumer classes if the results are to be used in a comprehensive study.
11225GWhr
2310 MW
Water heat
Water heat
Cooling Domestic I and
omestic
Heating
Figure 4.2 Residential class from the municipal utility plotted in Figure 4.1 broken down into major end-use categories. The "domestic" category includes cooking and washing loads, entertainment (TV, stereo), and refrigerator loads.
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Table 4.1 End-Use Categories Distinguished for Residential Class Interior lighting Electric heating Water heater Freezer Washer-dryer Home entertainment
Exterior lighting Air conditioner Refrigerator Electric cooking Water well Other
Appliance Subcategories
Many end-use models make a further distinction within some or all of the enduse categories in each class, breaking the end-use load into subcategories based upon the appliances used to convert electricity into the end-use product. For example, electricity can be used to provide space heating in several ways: central resistive furnace, resistive-element circulating water, heat pump, high-efficiency heat pump, or dual fuel heat pump. Figure 4.3 illustrates a typical end-use appliance subcategory breakdown of this category.
100% of homes
Peak 440 MW
Energy 1,160 Gwhr
Figure 4.3 Residential class usage for heating. At left, breakdown of homeowners by type of appliance used to heat their homes. Middle chart shows contribution to system peak load, by appliance type, and rightmost chart shows annual kWh sales by appliance subcategory. Data are for the municipal utility data plotted in Figures 4.1 and 4.2.
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There are three reasons why appliance distinction is important in an end-use model used to forecast future peak and energy sales. The first is that the same end-use demand ("Keep the interior of my home at 68°F all through the winter.") will produce different electric demands depending on the type of appliance used. In the case cited here (home heating) the difference in appliance type can make over a two-to-one difference in the electric load created by the same household. For most applications, it is important to acknowledge such differences in conversion efficiency and to use them in the load analysis. Second, the mixture of appliance types used within a consumer base will change considerably over time, as appliances are replaced when they wear out. In most utility systems, the percentage of high efficiency heat pumps is increasing, and the application of resistive heat is declining — electric heating usage is becoming more efficient. A model broken down by appliance type has no problem tracking and even anticipating future changes in peak and energy usage due to continued shifts in appliance mixture. It can model today's usage as 28% heat pumps, 7% resistive heat, and tomorrow's as 32% heat pumps, 3% resistive, showing the difference in overall usage. Third, overall efficiency of appliances in any category changes slowly over time ~ major appliances are replaced only every ten years or so. An appliance subcategory model can represent such long-term trends by using two representations of an appliance such as a heat pump — normal and high efficiency, and varying their mixture over time to reflect the gradual shift toward higher efficiency. Load Curve Based End-Use Models Most end-use models work with load curves, most typically using coincident load curves as illustrated in Figure 4.4. Some early end-use models did not use temporal data of any type — some end-use models project peak load and energy usage by class, end-use, and appliance category without any distinction of demand as a function of time. However, since the 1980s end-use models based upon hourly, coincident load curves have been ubiquitous, for three reasons: 1. Ease of application. It takes very little additional effort to program an enduse model to handle 24 hours in a peak day than to handle just the peak hour. Hourly data are often available. 2. Load as a function of time is important. Consumer classes, end-uses, and appliance subcategory loads do not all peak at the same time nor have the same curve shape. Use of temporal modeling allows comparison of peak times and determination of coincidence (or lack of it) in category peaks.
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HOUR Space heating
Lighting
Water heating
Other
Figure 4.4 Four separate end-use category curves are shown plotted on top of one another (i.e., added together) to get one curve. This is a typical residential coincident peak day load curve for a utility in New England.
3. Curve shape is a useful clue in load research and analysis. Certain classes have identifiable curve shapes. Certain end-uses do, too. Therefore, uses of curve shape can improve the load analyst's ability to match characteristics to observed data and help explain load behavior. Temporal sampling rate and length of the period used to represent the load curves vary widely, depending on application. Hourly and quarter-hour sampling periods are most common. Some models represent only a single 24-hour period (usually the annual peak day) while others represent load behavior over many days, for example three days in each month (peak, average, and minimum). A few have used 8760 hour load curves (hourly for the entire year).
4.2 THE BASIC "CURVE ADDER" END-USE MODEL Figure 4.5 shows the basic structure of an end-use. The model distinguishes total system load as broken into a number of consumer classes, usually about a dozen. Within each consumer class, load is further broken into end-uses; within each end-use, into appliance curves. At the bottom of the model is a set of appliance load curves. In the example here, they will be represented as 24-hour, annual peak day coincident load curves. In practice the load curves could be of any temporal resolution and length required to do the job at hand.
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Figure 4.5 Overall structure of an end-use model, of the type necessary to provide a good foundation for effective load study and forecasting. The model is hierarchical and computes all the load curves except those on the bottom level of the model, which are input. Circles represent computations involving weighting factors (market penetrations, consumer counts, as appropriate -- see text). Only a small part of the overall model is shown. Squares represent load curve data on a per consumer basis (at the bottom) and as summed/weighted within classes, etc. Circles represent computations involving weighting factors (market penetration, consumer counts, etc., as appropriate - see text).
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The end-use model's structure consists of a hierarchical framework of weighting factors and pointers that designate the consumer classes, under which are end-use categories, under which are appliance subcategories. Only the appliance subcategories have load curve data associated with them. Each such load curve is the electric load over the peak day that is expected from a single appliance of this subcategory for an average consumer in this class. Figure 4.6 shows the four curves that might be included under "suburban residential heating." Also stored along with each appliance curve in the model is the market share of the appliance ~ the percent of consumers in this class that use this particular type of appliance for this particular end-use, as shown. To form an estimate of the total residential heating demand, the model sums all the residential appliance categories, weighted by their market share of the appliances. This forms an average consumer estimated heating curve — a weighted load curve sum representing a mythical consumer with a "cross section" of heating appliances ~ perhaps .2 high efficiency heat pump, .4 heat pump, and .4 resistive heater, representative of the total mix of the class. Similarly, within other end-use categories in this class, the various appliance types can be added together ~ in the interior lighting end-use, the curves for incandescent, fluorescent, e-lamps, and so forth can be summed into one lighting curve. In some end-use classes (well pumps, cooking) there may be only one load curve, indicating an average load curve of this end-use. Doing this for all end-uses in the class produces a full set of end-use load curves. Adding all these end-use curves together gives the coincident load curve for one average consumer of this class. This sum can then be multiplied by the total number of consumers in this class to obtain the total electric heating demand for the class. Other classes can be similarly computed, and all classes added together to obtain the entire system load.
Forecasting End-Use Load Changes Using Weighting Factor Trends Generally, to accommodate forecasting, end-use models have the capacity to store future values or trends in weighting factors and consumer count values at all levels of the model structure. Thus, while 28% of rural residential consumers use heat pumps today, this might drop to 18% in a decade, as most present heat pump owners opt to replace their unit when it wears out with a high efficiency heat pump (up from 11% today to perhaps 21% in ten years). Consumer counts might increase or decline and can similarly be trended in the model. Thus structured, it can "forecast" future usage by substituted future projected values for weighting factors, counts, etc., in all its computations.
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Load Curve and End-Use Modeling Heat Pump - SEER 9.2 Peak = 5.2 kW, 100 kWh 28% of class
Hi-eff. Heat Pump SEER 13.0 Peak = 4.85 kW, 92 kWh = 11% of class
Noon Time
Noon Time
Resistive Heat Peak = 8.9 kW, 164kWh 16% of class
Noon Time
Blower Motor only, non-electric Peak=.42kW, 8.5 kWh = 39% of class
Noon Time
Figure 4.6 Example of the appliance subcategory load curves at "the bottom" of the enduse model's structure. Here are the four load curves under the "space heating" end-use in the "rural residential single family home" consumer class, representing the coincident load curves for four different types of appliances, with the appropriate market penetration of each type in this class shown, so the proper weighted sum of the curves can be formed to represent a "typical" consumer's heating load. Percentage market penetrations here sum to 94% — apparently 6% of this class uses no electricity at all to heat their homes. The figures shown here match the "today" column in Table 4.2.
Variations in End-Use Model Structure The basic structure of the end-use model has been implemented in dozens of different applications, manually and particularly via computerization, going back into the early 1950s, and perhaps earlier. The author's first experience with such a model was a mainframe computer program which he helped write in FORTRAN to apply such a model at Houston Lighting and Power in the mid1970s. It was not considered a unique or innovative model at that time. If the load curve lengths are limited to less than about 100 periods (four days at hourly
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sampling or one day at quarter hour) this method can quite easily fit within an electronic spreadsheet template running on a small PC. Considerable variation has and will no doubt continue to exist in exactly how "curve adders" are implemented, due both to differences in the applications intended and to the personal preferences of those using them. Three significant areas of variation are worth comment: 1. Time period and sampling period. A few end-use models have represented less than a full day (perhaps only a ten-hour period around the peak); others represent all 8760 hours in a year. Some models have used two-hour periods (and are applied only to systems with broad, flat peak load periods), while some have used sampling rates as short as one minute in order to model noncoincident load curve behavior. Time period and sampling rate for a model depend entirely on the application's requirements. 2. Some end-use models lack the appliance subcategory level, particularly computerized models developed in the 1970s and early 1980s. Instead of modeling the various appliance types, an average load curve representing the existing appliance mix was entered for each end-use type. Changes in this curve shape over time were entered manually, having been calculated or estimated by some means outside the model. In the author's opinion, the appliance subcategory level ~ at least for major appliances ~ is what makes an end-use model especially useful as a forecasting tool. 3. Span and applicability. There is no need to limit an end-use model to the analysis of only electric load. Natural gas, fuel oil, and wood-burning energy applications can be modeled, too. This makes considerable sense for utilities that distribute both electricity and natural gas ~ such a model can study fuel switching, cross-elasticity and interdependence of energy sources. Application of an End-Use Model to Forecasting End-use models generally are applied to determine future curve shape, peak load, and energy usage that are expected to develop from expected future changes in appliance mixture, appliance technology and efficiency, consumer mix or demographics, and overall consumer count. The following examples illustrate typical applications: 1.
Change in appliance mixture. Usage for electric heating is expected to change within the rural residential class in the next decade as a new, efficient heat pump enters the market and other shifts in
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appliance mix take place. This results in the appliance mixture and heating load curves are shown in Table 4.2 and Figure 4.7. Even though one percent more of the class is expected to use electricity for heating ten years from now, and five percent more will use electricity as the primary heat source, both peak and energy usage decrease, due to the increase in efficiency of the overall mixture of appliances. Change in appliance technology. Suppose that a detailed study of federal guidelines on refrigerator energy efficiency, manufacturer's plans, and the present age distribution of refrigerators in a utility service territory establishes that the average refrigerator in a utility system will shift as shown in Table 4.3 over the next twenty years.
Table 4.2 Change in Appliance Market Share Over Next Ten Years Appliance
Peak - kW
Today
Ten Year;
18% 25% 9% 8% 35% 95%
Standard heat pump - 9.2 SEER Hi-eff. heat pump - 13 EER G.W. heat pump - 15 EER Resistive heating Non-electric fuel Total % using electricity
5.20 4.85 4.20 8.90 .42 in some form
Present Peak = 3.58kW/consumer Peak day energy - 67.7 kWh/cust.
Ten years Peak = 3.47kW/consumer Peak day energy - 65.9 kWh/cust.
Mid.
Noon Time
Mid.
Mid.
28% 11% 16% 39% 94%
Noon Time
Mid.
Figure 4.7 End-use heating curve for the rural residential SFH class for the present and ten years from now. Present curve is the weighted composite of the curves shown in Figure 4.6. "Ten years ahead" curve reflects the changes in market penetration of appliances given in Table 4.2.
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Table 4.3 Average Refrigerator Usage per Consumer Quantity Connected load Duty cycle @ peak Peak coinc. demand Annual energy Market penetration
Today
Twenty Years
500 W
280 W
.35
.45
175 W 1004kWh 103%
126 W 878 kWh 105%
This could be represented in the end-use model by creating two types of refrigerators, one with a load curve whose peak and energy match today's values of 175 W coincident peak and 1004 kWh annually, and one with values that match the projected future values of 126 W peak and 878 kWh. It is possible that the curve shape of the two is different (i.e., the future unit is not just a scaled down version of today's curve), since the duty cycle of the future unit is so much higher than today's units.1 To represent a gradual change in usage of these units over the next twenty years, market share between these two types can be varied in 5% increments from year to year, starting with a 100%-0% mix in the base year, to a 95%-5% in the next year, to 0%-100% in year twenty. This would implement a gradual, linear shift in appliance mixture. If known, a non-linear trend could be used just as easily. Maybe the 1 One way to increase the efficiency of nearly any cycled device is to arrange for it to use the same energy but at a higher duty cycle. The higher duty cycle means it goes through thermal transients caused by starting and stopping -- a major cause of inefficiency -- less often. In this case the new high-efficiency refrigerator has a compressor with a smaller net size, which will work about 10% more of the time, in addition to other changes. Consequently, the new refrigerator will not chill food put into it as fast, but it will use less energy overall. This means the future's refrigerator load curve will be flatter than the present's. Very likely, accurate data on that future load curve are not available. To obtain that curve for a forecasting study, a reasonable "assumption" would be to take the present refrigerator data curve and move its peak value "down" until it matches the new peak value of 126 W. Then, holding that peak constant, one can scale the curve so its minimum is such that the overall energy (area under the curve) matches the 878 kWh annual total. This would be a reasonable approximation, but only an approximation.
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change isn't 5% change each year, but a very gradual 1% year rate of acceptance initially, followed by an increasing rate of up to 10% market change in the final years. This or any other change can be represented with the proper trend modeling in the computer program. Note that the market penetration of refrigerators shown in Table 4.3 is more than 100%. This is typical throughout many areas of North America. Roughly 3% of residential consumers in this class (and 5% projected twenty years from now) have two refrigerators per household (beyond which roughly a third to a half may have a freezer in addition). 3.
Change in number of consumers. Today there are 19,000 rural residential consumers; in ten years there are expected to be 21,000. This can be reflected by changing the number of consumers used to multiply the completed residential curve to 21,000 instead of 16,000. In this case, it would mean that while peak heating load per consumer goes down from 3.58 kW/consumer to 3.47 kW/consumer, total contribution to system peak from this class's heating end-use will increase from 68 MW to 72.9 MW. Assuming the refrigerator trend in Table 4.3 is linear over the next twenty years, it would be half complete in ten years. Peak refrigerator load per household would thus shift from 1.03 x 175 = 180 W to 1.04 x (175 + 126)72 = 156 W, meaning total refrigerator load in this class would drop from 3.42 to 3.27 MW.
The above are offered only as examples. The real power of an end-use model is that it can represent the accumulated changes from dozens of simultaneous changes in factors like those illustrated here. Usually, those changes are developed by a forecasting department or as part of an overall econometric projection and as a set represent a future consumer "scenario."
4.3 ADVANCED END-USE MODELS The basic "curve adder" is a useful forecasting tool, but it has been called a "non-intelligent" model because it does nothing more than add together curves and trends input or developed from other models. Nevertheless, the author considers it a requirement for accurate and useful load forecasting for power system planning applications.
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Numerous "improved" end-use models have been developed to add "smarts" to the model, giving it greater accuracy or applicability. These generally fall into several categories which will be summarized here. Direct End-Use Consumption Models In this approach, end-uses are represented not by electric or gas demand curves as discussed above (Figure 4.6), but by curves that represent the end-use product demand in its raw units, such as gallons of hot water consumed on an hourly basis. These end-use product demand curves are then "interpreted" into electric or gas end-use curves by "appliance translators." Essentially, this adds another level to the structure of any computer program developed for an end-use model. "Appliance translator modules" replace the subcategory load curves in the basic model, and a single "end-use demand curve" sits below them in a model structure otherwise similar to Figure 4.5. There is only one end-use product demand curve in each end-use category, because it is assumed that demand for the end product is not a function of the energy source being used (a reasonable but not absolutely certain assumption). Generally, the "appliance translator" computation is more than just the application of a scaling factor to the end-use product curve, for it includes some time shifting and modification of the curve shape as well. For example, a translator to convert a "demand for hot water by hour" curve to an electric water heater load curve would use a factor to convert gallons of hot water to kWh, but it would also have to model a delay between the usage of hot water and when a water heater may activate, and it would need to model that the water heater will continue to demand electricity for perhaps an hour after a period of heavy usage. Thus it would have to modify the original curve shape. Appliance and Building Simulators A number of computer programs have been developed as "bootstrap" load simulators. These compute the electric load and daily peak load of individual consumers or groups of consumers with detailed data descriptions of the buildings, the appliances, the activity patterns, and the ambient weather (the last two on an hourly basis) as illustrated in Figure 4.8. The more comprehensive models represent a building in great detail, modeling the thermal losses through walls, ceiling, and roof, and even representing the circulation of air inside the building. They represent the impact of sunlight entering through windows, the effects of wind, humidity, and sunlight angle, and simulate the non-coincident operation and cycling of heating, cooling, and other appliances in great detail.
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Figure 4.8 A "bootstrap" simulator models the heating and cooling, water heating, and illumination needs of a building, and perhaps other loads as well, through a simulation of the building, the weather, water usage, and human activity patterns. Most involve very complicated numerical modeling and have a narrow range of application. In the author's experience, few are dependable, accurate models of actual load behavior.
Such models are quite involved, often requiring extensive numerical subroutines to represent the action of different appliances. Beyond this, they have to model the interaction of end-uses in their energy inventories. For example, incandescent light bulbs convert over 70% of the electric power they consume directly into heat, not light. Beyond that the light they produce is converted secondarily into heat when it eventually falls upon something. Thus, incandescent lights serve as space heater, whether desirable or not, aiding any space heating appliance, but placing an additional burden on air conditioning when needed. The author has participated in the development of one load simulator and has used a number of others. Overall, while the concept of "bootstrap" end-use simulation seems to be a sound idea, available computer programs can not live up to that promise. Generally, most bootstrap simulators work well only when applied to a narrow range of appliances and climate, usually that on which they were tested during development. For example, one popular simulator which the author has used on several planning studies was developed and first applied to load curve studies in the Boston area. It does quite well whenever applied to situations similar to the Boston area's climate, building, and appliance mix, but it fails miserably elsewhere. When applied to studies of a residential community in west Texas, it
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mis-estimated annual peak load by 15%, and perhaps worse, insisted that peak daily load occurred at 9 o'clock in the morning, an absurdity. No amount of changing of the input data or set-up within reasonable limits could force it to produce reasonable outputs. A different model had to be used, one which incidentally does not give good results when applied to the New England area. Thus, "bootstrap" simulators that estimate electric usage from raw data on buildings, consumers, appliances, and weather are generally very specialized and valid only within a narrow range. Such simulators should always be carefully calibrated against measured load data in the region being studied. If it cannot accurately "forecast" existing load behavior including the magnitude and time of the peak and daily minimum, and if it cannot predict both peak and off-peak day curve shapes when fed reasonable data on existing building types, appliances, weather, occupancy and activity patterns, etc., then what expectation is there that it can accurately forecast future loads? Whenever possible, the author prefers to produce forecasts using the "curve adder" type of end-use models which use measured load curve data by consumer class and appliance subcategory.
4.4 APPLICATION OF END-USE MODELS End-use models, at least those applied to system-wide modeling of electric load growth, are widely used in the electric utility industry. In the author's experience, most electric utilities in North America have an "end-use model" that "explains" their annual sales, breaking them among rate (consumer) classes and end-uses, and quite often utilizing appropriate appliance subcategory models. The majority of these models have peak day or annual load curve features, usually a combination of hourly models for certain peak days and an inferred annual energy (area under the curve) based on these curves. Computed load curves are used primarily for planning purposes and for assessment of the potential of peak shaving DSM methods (e.g., direct control of water heaters) to reduce system peak. End-use and appliance subcategory load curve data are obtained by actual measurement of (usually randomly selected) consumers in each class. Quality of these end-use models varies widely. Unfortunately, many have flaws that impact the accuracy of their results for system-wide, DSM, and spatial applications. Recommended procedure to avoid the most common pitfalls is: 1. Load curves should be measured with sufficient sampling rate and recorded using a statistically significant set of consumers. The number of consumers or appliances sampled must be sufficient that the coincidence plot (for the
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end-use or the appliance itself, not the consumer class as a whole) is well into the part of the curve where the slope is close to horizontal. This will depend on the coincidence behavior of the appliances, but in almost all cases requires at least 25 and perhaps as many as 50 actual recorded samples. Figure 4.9 shows the actual 24-hour data used to represent "highefficiency" heat pumps in the residential class. Note that this has the tell-tale pattern caused by "frequency folding" or "aliasing" that occurs when sampling rate is too slow to track the on-off cycling of the appliance being sampled (see Chapter 3). In this case, the utility sampled a total of 140 residences with "multi-channel" load recorders which recorded the whole house load and the load of four selected appliances inside, on an hourly basis. Out of these 140 homes, only nine had high-efficiency heat pumps. Thus, the load curve used shown in Figure 4.9 is based upon data sampled on only nine homes, a small enough number that coincident load curve shape will be a real problem. The data were sampled at an hourly rate. Heat pumps cycle on and off in less than one-half hour, meaning that even 15-minute sampling would be a bit too long to completely capture the data. Note that the actual data clearly have frequency folding effects in them, even though they were obtained with demand metered (period integrated data). Demand metered data integrated on a periodic window basis (every
(0
o>
Q.
Mid.
Noon Time
Mid.
Figure 4.9 High-efficiency heat pump load curve used by a utility was based upon too few consumers and sampled at too slow a sampling rate. It clearly shows effects of "frequency folding" (aliasing) yet was used nonetheless. Aliasing was caused primarily by the sampling period (hourly, when it should have been at no more than ten minutes) but augmented by the fact that only nine appliances were actually sampled.
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hour on the hour) are not always completely free of aliasing effects. The data shown in Figure 4.9 are simply not valid. As pointed out in Chapter 3, these data are useless for any load-curve related applications (the only valid measurement is the total energy used, or area under the curve). Lesson: Above all else, load curve data should always be examined to determine if they look reasonable and appropriate. The number of consumers metered in any study should be large enough to be out of the "high slope" area of coincidence curves, and sampling period should be no more than half the length of the average cycle period of the appliances being sampled. 2. The end-use model should "add up" to the observed system load. This may seem like an obvious point (the author thinks it is), but a surprising number of end-use models employed within the electric utility industry do not. In one case, a utility had developed a full end-use model of its system, which broke out all classes, all end-uses, and, where needed, all appliance subgroups. It was used for DSM studies and had been applied to determine the effectiveness of specific DSM programs — how much reduction per consumer was being obtained ~ in order to provide study results to the state utility commission. But the model overestimated most loads, and thus overestimated DSM impacts. For example, the model estimated peak water heater demand at 1.1 kW per household, and it was a reduction of this much (1.1 kW/household) upon which the efficiency of the utility's water heater load control program had been based and upon which it was justified to the utility commission. The particular water heater load curves used had not been sampled locally, but taken from a technical paper published by another utility.2 The data were not valid as applied ~ actual peak/household at this utility was only 600 W. Thus, each load controller was reducing peak by only a little more than half of what had been estimated. This particular end-use model was wildly overestimating water heater contribution to peak load in this utility's consumer base, and in fact it was overestimating a number of other end-uses in a similar manner. These errors would have been obvious had the model's loads ever been summed together 2
Water heater load curves sampled and tested prior to implementation of a water heater load control program at Detroit Edison. In the Detroit study, load curves were sampled correctly and the average water heater peak load was 1.1 kW per household in the Detroit area. The problem was that the data were not valid for the utility which had copied it for use on their system. Ground water there was much warmer (hence less energy was needed to raise it to proper temperature) and per capita hot water usage was less (hence less enduse demand).
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to obtain a "proper" weighted sum for the whole system, so they could be compared to actual observed system load behavior. In fact, that had never been done. When it was, it turned out that the model overestimated system peak by 40% and annual energy by 50%. This particular mistake ended up costing the utility dearly. Its load control program, justified on the basis of 1.1 kW reduction per water heater load controller, was delivering only a little over .6 kW/controller, at which level it was not cost-effective. Worse, when the errors were finally discovered, the bad publicity, as well as the financial penalties levied by the utility commission, were quite costly. Lesson: An end-use load model should always be compared to all actual measured peak and load curve data available. At the very least it must explain system peak, system minimum load, and their times of day and season of year. Ideally, it should accurately reflect load curve shape for all hours, too, not just those peak and minimum times.
End-Use Application to Spatial Forecasting End-use models can prove a useful tool in spatial load forecasting studies. When a land-use based simulation spatial model is used, application is fairly straightforward and there is little reason not to merge an end-use model with the spatial forecast model. The benefits far outweigh any slight additional effort required. (Land use simulation methods forecast spatial load growth on a consumer class by consumer class basis, and will be covered in much more detail in Chapters 10-16.) In order to merge spatial simulation and end-use analysis, the consumer class definitions used in both must be identical. This often adds some complexity to both the spatial and the end-use models, for the one set of consumer class definitions must cover all the distinctions needed in both spatial and end-use analysis. Thus, while a spatial model might be able to get by with twelve consumer classes for spatial forecasting, and an end-use model with nine classes for its application, the joint application requires them to work in concert with a total of sixteen classes. (An example will be given later in this section.) End-use models merged with a spatial model can associate end-uses and class behavior with location. This approach has a number of important applications, beginning with the ability to now apply the benefits of the end-use forecasting to spatial (distribution) forecasting, as well as more esoteric applications such as that shown in Figure 4.10.
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22-QCT-93 12-12-13 4 flnother ft»p 9B
JOuSHMl
REDUCTION IN PEAK LOAD SUMMER 2013 RES.ACA CONTROL 40% 21.3 MYA
N Three miles Shading indicates relative !o«d density. Lines show major roads and highways.
Figure 4.10 Computer-generated map of peak reduction expected from a 20% reduction in residential air conditioner loads (via direct load control) in a small city. The reduction is 21.5 MW but as the map shows it is concentrated in outlying areas (north of the highway). Older parts of the T&D system (south of the major east-west highway) are near capacity and could use a reduction in peak. This program does not provide that.
Example of Spatial End-Use Analysis Spatial end-use analysis is most convenient to apply whenever a computer program developed specifically for spatial end-use forecast can be used. However the principles can be applied as needed in "manual" studies, which require nothing more than a PC-based electronic spreadsheet, a good deal of data gathering, and a lot of hard work. The example given here will illustrate the principles and the need for spatial end-use analysis. Near the author's home (Gary, North Carolina) there are two distinct regions of zoning for residential construction, as illustrated in Figure 4.11. In incorporated cities and towns (those with sewers and water systems) homes can be built to any density approved by the local government. Typical density for new single family construction allows lots of about .5 acre, which works out to 1.33 homes per acre, after allowing for land used for streets, as well as municipally required greenspaces, easements, and restricted setback areas, or about 850 homes per square mile.
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Figure 4.11. Growing residential areas near Gary and Raleigh, NC (shaded) are limited to different housing densities depending on whether they are inside or outside of incorporated city boundaries (dark lines). Construction in rural areas is limited to about 310 houses per square mile, while in incorporated areas it typically runs about 850 homes per square mile. Differences in electric usage between the two areas (rural areas have no gas distribution) mean load density is very similar at 5.93 MW/sq. mi., but the areas present very different challenges to the distribution planner as discussed in the text, and thus must be modeled as separate classes in a combined spatial end-use model.
Gas distribution systems are ubiquitous in these incorporated areas, so that a majority of the new homes there use the (more economical) gas for heating, water heating, and cooking, as shown in Table 4.4. However, in non-incorporated areas — those with no water or sewer system available — homes must have an individual water well and septic tank, and both public safety and environmental concerns about the water table and aquifer purity have led to laws restricting development to no more than one home every 2 acres. Allowing for land devoted to roads, this means a limit of about 310 homes per square mile. Since gas distribution is virtually unknown in these outer suburbs, 95+% of homes built there are all electric. Table 4.4 gives the statistics on end-use appliance mix and load for these rural homes.
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Chapter 4 Table 4.4 Loads for New Construction, Rural and Suburban Residential Characteristic Houses per square mile % using resistive heat % electric heat pumps % using hi-eff. heat pumps % using non-electric % using AC or HP % using hi-eff. AC or HP % using electric WH % using electric cooking Peak load/cust. Win. coinc. kW Peak load/cust. Sum. coinc. kW Peak load/sq. mi. Win. MW Peak load/sq. mi. Sum. MW
Rural
Suburban
320 5 69 24 1 66 29 98 98 8.27 18.55
850 2 15 8 74 72 22 25 40 6.99 6.61
2.65 5.93
5.94 5.62
Interestingly, despite the differences in housing density and appliance mix, the annual peak loads of these two types of areas (winter peak in the rural areas, summer peak in the suburban areas) is almost identical at 5.93 MW/square mile (Table 4.4). Using electricity for home heating, peak load per household is much higher in rural areas, but the lower housing density results in much the same load density as in the suburban areas in summer. Without the detailed end-use analysis shown in Table 4.4, it would be easy to conclude that both types of areas could be lumped into one class for distribution planning studies — a single residential. After all, each consists of the same types of homes, and overall peak load per mile is identical. However, Table 4.5 shows the predicted peak load levels in another fifteen years. Continued trends toward higher usage of high-efficiency appliances are expected to continue. In addition, the price of electricity is projected to decrease (due to de-regulation, increased competitiveness, etc.), while the cost of retail natural gas is expected to rise slightly. As a result, electric heating will become more cost competitive and its market share in suburban areas is expected to increase by half again, from its present 25% to 37%.
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Table 4.5 Forecast Loads — 15 years Rural and Suburban Residential Characteristic Houses per square mile % using resistive heat % electric heat pumps % using hi-eff. heat pumps % using non-electric % using AC or HP % using hi-eff. AC or HP % using electric WH % using electric cooking Peak load/cust. Win. Coin. kW Peak load/cust. Sum. Coin. kW Peak load/sq. mi. Win. MW Peak load/sq. mi. Sum. MW
Rural 320 2 32 64 1 32 64
Suburban
98 8.02 18.21
850 1 8 28 60 40 56 25 40 6.80 8.20
2.57 5.83
5.78 6.97
98
10
I
8
• Suburban
le
Suburban Rural
•o re S 2
-5
5 10 15 Years into the Future
20
25
Figure 4.12 Projected annual peak load for a fully developed square mile of the rural (winter peak) and suburban residential development (peaking in summer through +5 years, then winter) discussed in the text and described in Tables 4.4 and 3.5. Although historically identical in peak load, the two types of residential areas will develop different load densities over time, presenting different design goals for the distribution planners.
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As a result of these changes in appliance efficiency and market shares, fifteen years from now substantial differences in the annual peak loads for these two types of residential areas are expected, as shown in Figure 4.12. By then both should be winter peaking. Peak in rural areas will have dropped slightly, from 5.93 to 5.83 MW per square mile, part of what looks like a long-term trend of about l/7th of a percent decrease per year. In the suburban areas, annual peak load will have increased by more than 17%, in what also appears to be a very long-term trend of about 1.5% growth annually in the winter peak per year. It will take roughly five years for the (initially lower) winter peak to grow to parity with the present summer peak, after which it grows at 1.5% annually with no end in sight. As will be discussed in Chapter 7, even in a rapidly growing area (RaleighCary has annual population growth of over 6%) the typical "S" characteristic of spatial growth means that a square mile of either type will take from five to eight years to build out to completion. Thus, predicted annual peak load for a square mile of currently undeveloped land of either type of consumer class, beginning to grow at the present, looks like that shown in Figure 4.13, substantially different trends calling for quite different expansion plans.
10
Suburban •= 6
Suburban Rural
E
§4
S 2 Q.
° -5
0
5
10
15
20
25
Years into the Future
Figure 4.13 Forecasts of annual peak load for a square mile of each of the two types of residential development plotted in Figure 4.12, assuming a typical "S" type development trend begins in each square mile in year zero. The resulting peak load curves for the two areas present very different expansion situations for the T&D planner.
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While both types of residential areas have roughly the same peak load per square mile today, in rural areas distribution equipment installed today will most likely never see higher loadings than during its first few years of service, and thus a design that is highly stressed today would perhaps be the most economical — loading will gradually decrease over equipment lifetimes. In suburban areas, the forecast trend (Figure 4.13) shows nearly linear growth for the foreseeable future. Equipment installed to meet only short-term peak requirements will be overwhelmed by load growth long before it reaches even a thirty-year lifetime. However, equipment sized to meet the eventual high load levels will remain "underloaded" for a good portion of its life. A far different plan is called for here than in the rural areas. This plan must include provisions to gradually add service transformers, upgrade equipment, and "split feeders" as load continues its long-term trend. If designed with this in mind at the outset, both short- and long-term economy can be achieved. Time-Tagged End-Use Models Houses and commercial buildings have a certain amount of "energy efficiency" built into them when originally constructed. Although many buildings are modified and upgraded over the years, there is in most utility systems an observable difference in the electric usage of residential and commercial buildings based on age. Homes in an area of town "build out" in the 1960s have slightly different densities and load patterns than homes in areas built in 2002. Only part this type of difference is due to inherent energy efficiency differences in the buildings themselves. Some of the difference is due to demographic variations between areas within a city. 4.5 COMPUTER-IMPLEMENTED END-USE LOAD CURVE MODEL This section briefly outlines a computer program for end-use load curve analysis, meant as an illustration of the overall design and necessary features to be included in software intended to merge with spatial load forecasting applications. Its characteristics are based on those of several published programs (see Gellings and Taylor, 1981; Broehl, 1981; and Willis and Rackliffe, 1994). Load Curves The program is dimensioned to handle load curves of up to 288 points. This provides the ability to store one day of load curve data sampled with five-minute demand periods, three days of 15-minute data, or twelve days (perhaps one day for each month of the year) if the load curves are measured using hourly demand periods. To keep things simple, all load curves must have the same sampling rate (i.e., there cannot be a mixture of sampling rates, some curves using 5-minute
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data, some 15-minute data, and some hourly data). The program can store up to 500 curves. Load curve data are somewhat separate from the structure of the end-use model itself. Curves are stored and manipulated in a "load curve submodule" as shown in Figure 4.14. After entry of data, load curves are normalized to peak = 1.0 for storage, i.e., the curves themselves are just a shape. In addition to up to 288 data points, each load curve has five addition values associated with it: • Name, a simple text string for identification purposes • Base year peak value, K, the maximum value in kW of the curve • Market share, S, the fraction of consumers in the class who have this appliance • Technology growth trend per year, q, the change in this curve's values anticipated due to technological advance • Market share growth rate per year, p, the change in market share within the class for this appliance All points in the normalized curve are multiplied by the K and S values for that curve to produce the curve's base year per consumer load curve values. All points in that base year curve are further multiplied times (1 + q) x (1 + p) if it is to represent per consumer load values t years ahead. Thus, the load curve submodule can produce a load curve on a per consumer basis for any future year, taking into account changes in technology and market share. That is the sole function of this submodule - it produces load curves computed for any future year as requested. Hierarchical Structure The consumer load module works on a hierarchical basis of classes, end-uses, and appliance subcategories. This structure is independent of the load curve data and load curve submodule in the sense that a table of pointers defines how the load curves are interpreted and how they are added together to form load curves for each end-use and consumer class. The consumer load module permits three levels of hierarchy to be defined by the user:
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Resid «3nhnnkiiV Suburb. - Avu Reskj ocnoois o. .u. .-u r^ •Rural
Lad Curve Sub-module
Figure 4.14 Overall structure of a computerized end-use model as described in the text. The model creates a hierarchical tree from pointers, permitting but not requiring three levels of pointers that control the addition of load curves: consumer classes, end-uses, and appliances. The bottom level elements of the hierarchy tree are assigned to load curves in the load curve submodule. The real structure of the model is contained in the arrows, which define how addition of load curves is accumulated, and the load curves. The ovals shown represent only interim additions of all the load curves below them in the hierarchy. The top level of ovals, representing the classes, consists of per capita load curves on a consumer class basis. Not all pointers are shown in this drawing.
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Consumer classes are defined on a global basis within the overall shell program (i.e., the same class definitions are used in all modules within the spatial load forecast program). Definitions of the end-uses and appliance subcategories within the end-use module are set up through a data table that must be input by the user. A class does not have to be broken up into end uses, but can be. An end-use category in a class does not have to be broken up into appliance subcategories, but can be. The result is that a user can create everything from a model using only consumer classes (a single load curve for every class) to a model consisting of full consumer class/end-use/appliance subcategory representation in all classes of consumer. Most important from a practical, ease-of-use standpoint, the program has the flexibility to handle a mixed combination of classes, end-uses, and/or subcategories, as illustrated in Figure 4.14. Where needed, the user can apply a full end-use subcategory representation, but classes for which such data are unavailable can be represented with only a single load curve. The consumer load module requires that one load curve be assigned to every "lowest element" in the load model hierarchy. Basically, every class, end-use, and appliance subcategory must have either: 1. A load curve assigned to it, or 2. Two elements of the next lower level assigned to it Thus, every "bottom" node in the tree structure in Figure 4.14 has a load curve assigned to it ~ some consumer classes will have but a single load curve assigned to them, others may have pointers to a dozen end-uses, from which flow pointers to many dozen appliance subcategories. Generally, an ability to handle two dozen consumer classes, and an average of a dozen end-uses per class is sufficient. Thus, an upper limit of 25 consumer classes and 300 end-use pointers is a reasonable expectation on operating program dimensions.
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Error Checking A feature that is quite desirable in an end-use load curve program is a comprehensive set of error-checking logic in both the load curve submodule and the class-end-use hierarchy definition tables, because mistakes in load curve models are more prevalent than might be expected, and data errors are very difficult to find through manual inspection. Errors in the set-up of end-use load curve models are among the leading causes of what could be termed "really embarrassing" forecasting errors.3 A superior error-checking routine would not only verify the completeness and proper range of all data entered, but check for violation of set-up rules about the content of the input data (e.g., one cannot assign just one end-use to a class, the minimum required is two). In addition, a really superior program would apply a set of knowledge-based rules (a miniexpert system) to examine the end-use data in an attempt to detect errors or poor set-up. Comparison of the input data with these rules is made to identify possible indicators of trouble, such as appliances in the same end-use category with wildly different load levels or curve shape assignments (e.g., one appliance uses MW of power, another kW) and other similar mistakes, or if market shares of all the different appliance types sum to more than 100%). This is all toward attempting to reduce errors in the module, which, in the author's experience, contributes to more than 75% of avoidable forecasting errors. Load Curve Adder Function The consumer load model functions as a curve adder, as discussed earlier in this chapter. When requested by the user (interactively) or the program shell (in the course of the forecast) to produce a load curve for a particular consumer class for a specific year, the consumer load module will consult the tree structure, gather together all end-use and appliance load curves under that class, adjust each with (1 + q) x (1 + p) to get the correct values for that curve t years ahead, and add all the appropriate curves together to form that consumer class's load curve. During a forecast for year t, the load curve submodule first computes an updated version of every load curve for year t, using each curve's market share and technology change adjustment factors q and p to adjust its values for the year, t. It then works upward through the tree defined by the hierarchical 3
Mistakes in setting up or entering data to an end-use load curve model usually do not cause the computer program written to implement it to halt or even to give obviously ridiculous results. Instead, they lead to a forecast that looks reasonable overall, but that is flawed internally. Very often such mistakes are not caught until much later (such as after a forecast has been filed with a regulatory agency or used in a rate case).
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structure, adding together the load curves into end-use sum load curves and class sum load curves as it works its way toward the top. For example, in Figure 4.18, it computes the sum of the load curves for all appliance categories under "residential heating" and adds them together to form a per load curve for "residential heating" of a per-member-of-this-class basis. Similarly, once load curves have been produced for the other end-use categories in the residential class, it adds them together to form a per consumer load curve that it assigned to the node "residential class." In a like manner, it then computes the curves for all other classes. This is all a "curve adder" program does. Its product is the set of per consumer load curves for each consumer class, computed as needed for any year in the future. Of course, in addition, the program needs graphics display, data editing, and other database and user interface features. But the major functional features are that it can produce the per-consumer load curves for any consumer class for any future year when called upon to do so, that it can accommodate varying levels of end-use detail from class to appliance subcategory, that it can handle five minute to hourly demand periods, and that it has extensive error checking. Despite the apparent complexity of this data model, memory requirements are slight. At the maximum dimensions the program uses 500 load curves of 288 points each, and slightly less than 650 possible pointers. Program and data fit easily within two megabytes.
REFERENCES J. H. Broehl, "An End-Use Approach to Demand Forecasting," IEEE Transactions on Power Apparatus and Systems, June 1981, p. 271. A. Capasso et al., "A Bottom Up Approach to Residential Load Modeling," IEEE Transactions on Power Systems, May 1994, p. 957. M. L. Chan et al., "Simulation-Based Load Synthesis Methodology for Evaluating LoadManagement Programs," IEEE Transactions on Power Apparatus and Systems, April 1981, p. 803. M. V. Engel et al., editors, Tutorial on Distribution Planning, IEEE Course Text EHO 361-6-PWR, Institute of Electrical and Electronics Engineers, Hoes Lane, NJ, 1992. C. W. Ceilings and R. W. Taylor, "Electric Load Curve Synthesis — A Computer Simulation of an Electric Utility Load Shape," IEEE Transactions on Power Apparatus and Systems, January 1981, p. 36.
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H. N. Tram et al., "Load Forecasting Data and Database Development for Distribution Planning," IEEE Transactions on Power Apparatus and Systems, November 1983, p. 3660. H. L. Willis and G. B. Rackliffe, Introduction to Integrated Resource T&D Planning, ABB Systems Control, Gary, NC, 1994.
5 Weather and Electric Load 5.1 INTRODUCTION This is the first of two chapters on how weather influences demand and the analytical and planning issues associated with that relationship. This chapter looks at weather and how it influences electric load and summarizes methods that can be used to identify a relationship that describes weather's impact on demand and energy usage. It might be characterized as "basic" material building toward the applications in Chapter 6. That chapter then looks at design weather criteria - how utility planners use their knowledge of weather in setting target loading levels for the system and in assuring the system can handle the loads created by extremely hot and cold weather. This chapter begins with a look at why planners need to study weather and its impact on electric load. Section 5.2 then looks at weather itself- what it is, how it is measured. Section 5.3 examines how weather varies with time and location, and how much of that behavior is predictable, and what "predictable" means in the context of T&D planning. Section 5.4 studies the relationship between demand for electricity and weather and the various aspects of interaction that planners need to address. Chapter 6 will build upon the foundation developed here, looking at how equations relating demand to weather measures can be determined. It will demonstrate their application to historical demand data to "wash away" differences due to the weather having been different during the times of the various load readings taken.
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Why Study Weather and Demand? The electric demand in most every electric utility system displays variations that have an obvious tie to season and weather. Demand is higher in summer and winter than at other times of the year. During periods of extremely hot weather, or very cold weather, demand is higher than when weather conditions are milder. The tie between weather and demand seems clear to most utility engineers, operators, and planners. "Weather sensitive demands" cause it - appliances and usage patterns that are (at least partly) influenced by weather conditions. During hotter weather, air conditioners have to run more often, thereby using more electric power. Similarly, during really cold spells, more electric power is used by residential, commercial, and industrial heating systems than during periods of mild weather. This chapter along with Chapter 6 address three highly intertwined analytical applications involving weather and electric demand forecasting: 1. Understanding of consumer needs and load patterns can come from analysis of weather sensitive demand. Study of weather and its impact on load can help utility planners and marketers better understand the variability of demand. It can provide indications of the composition of consumer demand - the most obvious example being how the market penetrations of appliances like air conditioning and chillers change over time. 2. Weather normalization of historical load readings involves adjusting load readings taken at different times (and therefore under different weather conditions) so they approximate the readings that would have been taken under identical weather conditions. Weather varies from year to year and month to month. As a result, demand readings meant to represent annual peak readings, for example, all taken at different times, are not directly comparable. These demand readings must be adjusted to a standard set of weather conditions if forecasters are to make a valid comparison of those readings to identify trends in consumer growth and usage patterns. 3. Demand forecasts done to standard weather design criteria involve producing forecasts of future demand that are adjusted to represent expected demand under some standard set of weather conditions. Generally, the forecasts will be produced to represent demands under the same "standard conditions" that represent "extreme enough" weather and demands for planning.
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Four Key Technical Steps Weather adjustment and normalization is complicated by the fact that there are invariably large amounts of weather and demand data involved, within which there is only a certain amount of relevant information, much of it somewhat "fuzzy." The fuzziness comes from the probabilistic nature of weather - in part weather behaves like a random process and cannot be forecast with numerical methods beyond characterizing its behavior as a probability distribution, or with non-numerical methods beyond the resultant fuzzy-logic classifications. Good weather adjustment and normalization involves four coordinated technical tasks: a) Analysis of weather itself for a particular utility system. How does it vary over the year? How does it vary spatially over the system? Are there micro-climate areas in the system distinct areas of substantially different weather? b) Identification of weather's influence on demand: What is the functional relationship between weather and demand, and how can that be used in a predictive approach for forecasting? c) Classification of extreme weather conditions - those that create really high loads that lead to periods of high stress on the power system - encountered. Just what is "extreme," how often does it occur, and how does a utility plan for those conditions? d) Determination of weather-related design criteria: What conditions of extreme weather should be set as the standard target for utility planning, and how does the utility set and implement these? This chapter addresses (a) and (b) above, in order and building from one to the other. Chapter 6 then addresses (c) and (d), using the results form this chapter throughout. 5.2 WEATHER AND ITS MEASUREMENT The Elements of Weather For purposes of electric demand analysis and forecasting, weather is usually considered to be composed of three elements: temperature, humidity, and sunlight (solar illumination) often abbreviated as T, H, and I. Two other weather components, wind and precipitation, are usually not included in demand
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Table 5.1 Components of Weather for Electric Demand Analysis Component
Metric
Impact on Demand
Temperature
Dry-bulb temperature in °C or °F
Electric demand is higher whenever temperature rises or falls from a base "most comfortable" level
Humidity
Per cent saturation
Temperature-dependent demand variations are more extreme if humidity is higher - moisture increases the heat retention capability of air
Illumination
Insolation in Sols Or gross energy in kWm 2
Demand is generally greater when insolation is high (sunlight = heat = air conditioning demand)
analysis, even if they are an important element in a utility's weather record keeping, and used in analysis of storms, system restoration strategies, ice-loading on lines, and other system reliability studies. Table 5.1 explains temperature, humidity, and illumination, gives their typical form of measurement (metric), and summarizes their impact on electric demand. As mentioned earlier, measures of wind, rain and snow are not normally used in "weather sensitivity" analysis for demand. There is no doubt all three have some impact on demand level. Rain reduces outdoor activities of humans, creating more lighting demand indoors. It often means reduced temperatures which correlate with demand reductions in air conditioning and increases in heating demand. Snow can close schools and change business activity patterns. However, normally such effects are of secondary or tertiary importance and are not included in "weather-demand" analysis. In fact, illumination is often not included as an independent variable in weather-demand analysis. There are several reasons, none of which is because illumination doesn't correlate with demand (it does). First, the majority of variation in illumination on an annual, seasonal, and even daily basis is due to natural periodicities that are completely predictable (sunrise and sunset, etc.).
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Variations in illumination from that expected pattern on a seasonal, daily or hourly basis, all due to changing cloud cover, make only a small impact on the overall pattern of sunlight.' Second, illumination correlates well with temperature. In fact, it is a major cause of increases in temperature because of its direct effect - bright sunlight raises ambient air temperature. Thus, a great deal of illumination's impact on electric demand is seen through its action on ambient air temperature (high outside air temperatures occur largely because of illumination). That being the case, quite naturally illumination correlates highly with temperature, and is often not used as a variable since temperature alone is a reasonably good proxy for it as well as temperature's effects on demand. Weather Indices Often Used in Electric Demand Analysis A number of indices, or measures based on combinations of weather components, are used in weather analysis for utility and other applications. Each attempts to aggregate the effects of temperature and other weather components into a single-valued measure of something, usually human comfort level, or to measure some aspect of weather useful in electric demand analysis. Temperature-Humidity Index (THI) Temperature and humidity are often combined into a single-valued index, THI (temperature-humidity index), which gives a measure of the comfort level as a function of both. Usually, when one encounters the term "THI" or THI index", the measure being discussed is: THI in degrees F = .4 (Td + Tw) + 15
(5.1)
where Td = dry bulb temperature, and Tw = wet bulb temperature At a THI value of 75 (as calculated with this formula) approximately 50% of persons say they are "comfortable" and 50% say they are "uncomfortable." By the time THI has risen to 79, 90% state they are "uncomfortable" and a THI of 71 will register comfortable with a similar portion. A THI of 95 (100 degrees at 100 per cent humidity) is seriously uncomfortable ~ virtually all persons are 1
Illumination on a very "dark, cloudy" day is still far more than on a cloudless night with a full moon. In addition, sunlight not reaching the ground still heats the air, making illumination's major contribution to demand in spite of the "darkness."
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uncomfortable at that level. Some may suffer some health risk or distress, under that condition. A confusing point: the index abbreviation, THI, contains the initials for Temperature, Humidity, and Illumination, leading some people to assume that it is a temperature, humidity, and illumination index. Further compounding the confusion is the fact that at least one major electric utility in the United States uses a "THI Index" that includes an adjustment for illumination or cloud cover, making it a legitimate temperature-humidity and illumination index: THI in degrees F = .4 (Td + Tw) + C/6 +15
(5.2)
where Td = dry bulb temperature, Tw = wet bulb temperature And C = cloud cover, in percent Full sun (zero cloud cover or haze) conditions can add up to 15 additional degrees Fahrenheit to the temperature-related comfort level perceived by the average person. It can also make a noticeable difference on the demand in a large metropolitan area, versus heavy overcast at the same temperature and humidity. However, in most cases of use, the "I" in THI refers to Index, not Illumination, as described here, and THI is a combined measure of the comfort level due to the combination of temperature and humidity, using equation 5.1. It is highly recommended that anyone working with a THI index check to make certain they know exactly what this particular index includes. But regardless, it is important to keep in mind that THI is a comfort-level index, based on how people feel. It weights equally an increase of one degree in either dry- or wet-bulb temperature. It is not a deterministic or engineering-based formula that will necessarily linearly relate to the work an air conditioner must do to cool air, the load increase that will be seen as THI increases, etc. However, THI is a qualitative match for demand impact of weather. And, it is a representative measure of discomfort, which is the basis for both how humans determine if an AC unit is doing its job and how they set their thermostats. Heat Index (HI) The heat index is another metric designed to measure how uncomfortable the combination of temperature and humidity "feels" to humans. It and its winter equivalent - wind chill ~ measure comfort level, but are supposed to be more "linear" in their relation to "temperature that is felt." Unlike THI, where the resulting numerical value is not really equivalent to temperature, a heat index is
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70
75
Temperature -c 80 85 90 95
64 65 66 67 68 69 70 70 71 71 72
69 70 72 73 74 75 76 77 78 79 80
73 75 77 78 79 81 82 85 86 88 91
Humidity 0 10 20 30 40 50 60 70 80 90 100
78 80 82 84 86 88 90 93 97 102 108
83 85 87 90 93 96 100 106 113 122 133
87 90 93 96 101 107 114 124 136 150
100
105
110
91 95 88 104 110 120 132 144
95 100 105 113 122 135 149
99 105 112 123 137 150
supposed to merely translate a combination of temperature and humidity to an equivalent of "how hot it feels" in terms of temperature alone. While there is a formula to compute heat index from temperature and humidity, the index is best expressed in tabular form, as shown in Table 5.2. The perspective embodied in this table is interesting: humidity basically multiplies the "impact" of higher temperatures. For example, at 20% humidity, the increase from 80 to 90 degrees Fahrenheit "feels" like an increase often degrees, while at 40% humidity that same increase feels like 14 degrees of difference. At 80% humidity, the increase in apparent temperature nearly doubles from 40%, to 27 degrees, and at 100% humidity it registers four times the increase at 20% humidity - a whopping 41 degrees of "felt" increase in temperature or discomfort level. Cooling degree hours or days Both THI and Heat Index are metrics aimed at measuring human discomfort, not any physical manifestation that is directly related to electric demand, as might be desired in forecasting. A somewhat better weather-based index for demand analysis and forecasting is cooling degree hours (CDH) or days (CDD). Cooling degrees are simply the degrees of difference between ambient (outside) temperature) and outside temperature that produces an ideal interior-building comfort level for humans - 65°F. This is slightly cooler than optimum comfort level for most people (around 70 to 72°F). However, CL as used here is the
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outside temperature at which the interior temperature of buildings is most comfortable without AC assistance. Heat from lights, equipment, and humans adds to interior temperature so that it remains several degrees above outside ambient. Thus, cooling degrees at hour h are: C(h) =T(h)-CL 0
ifT(h)>CL otherwise
(5.3)
where C(h) = the number of cooling degrees in hour h, T is the temperature in hour h, and CL is the optimum ambient outdoor comfort level for interior building temperature
Cooling degrees are given in degrees Fahrenheit or Centigrade - whichever is being used to measure T and CL. The number of cooling degree hours in any one day is calculated as the sum of the hourly differences: 24
CDH = Cooling degree hours (day) =
ZC(h)
(5.4)
h= 1
The number of cooling degree days (CDD) in a season or period of time is simply the number of cooling degree hours in the period divided by 24. Not surprisingly, cooling degree hours correlate reasonably well with weather-sensitive demand in most power systems. Air conditioner and chiller energy use is a fairly linear function of the temperature differential desired (see Chapter 3). For this reason, cooling degree hours and days are often used to measure the overall intensity of weather during a day, season, or year for electric demand purposes. Heating degree hours and days Heating degrees are those displacements of ambient temperature below, rather than above, 65° F. Heating degree hours (HDH) or days (HDD) are computed and applied identically to cooling degrees, except of course that heating degrees are computed as: H(h) =T(h)-CL ifT(h)
(5.5)
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5.3 WEATHER'S VARIATION WITH TIME AND PLACE Location and Climate Weather varies spatially (with location) and temporally (with time). The type of weather - which people normally take to mean the average and extreme temperatures, the expected amount and nature of precipitation, and their expected seasonal changes - varies a great deal depending on location. Some locales, such as Chicago, with summer temperatures that can exceed 103°F and winters that are quite cold, have relatively more intense weather and seasonal change, than others, such as Saratoga, California, where weather is relatively mild and relatively constant year-round. Mildness of a locale's weather is not a requisite for any lack of volatility in change with the seasons. There are areas with "extreme temperatures" that see comparatively little change from season to season despite the intense weather - deserts and some arctic regions being good examples. The expected or average weather behavior at a location is referred to as its climate. While in each area or location, weather conditions will vary from hour to hour, day to day, and year to year, the weather in each locale can be characterized by its long-term average conditions and behavior - its climate. Table 5.3 gives average annual weather conditions for several places, illustrating the differences in climate that can occur among different locations.
Table 5.3 Average Weather Conditions (Climate) for Several Regions Region Location Bangkok Buenos Aires Chicago Grossauheim, Germany Rome, Georgia Rome, Italy Santa Barbara, CA Saratoga, CA Saratoga, NY Paris, France Paris, Texas
Summer - °F 90% peak THI 92 83 84 83 90 83 75 74 84 80 94
Winter - °F 90% Wind-chill 43 24 13 15 25 38 40 42 11 20 27
Annual Precip. - in. 60 32 44 34 44 44 41 28 51 27 32
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Micro-climates Often, a significant difference in climate will exist among different sub-areas within a region - an electric utility's service territory. These significantly different sub-areas are called micro climates: isolated or small areas which have different average or typical weather conditions that can and usually do lead to far different electric demand characteristics. Usually, these micro climate areas are created by major geologic features, such as mountain ranges or coastlines, or by combinations of geologic features and differing wind patterns. The San Francisco Bay area is perhaps the best known example of a region sub-devided by microclimates. Weather there varies greatly among coastal areas, the city, Silicon Valley, and inland areas of a fairly small (100 by 100 mile) area centered on that bay. But as Figure 5.1 shows, other areas of the nation can have significant variations over relatively small distances.
Figure 5.1 Micro-climate zones in the region in and around Salt Lake City, developed by the author in only 30 minutes using data available from the Western Region Climate Center web site. Dashed lines show borders of zones. Figures are mean highest temperature during the summer. These are rather constant within each of the 94, 92 and 82 degree areas shown, whereas the 86 degree zone shown is really a gradual and nearly linear transition from the 92 to the 82 degree zone. This map would need further refinement before being used in load studies, but illustrates both the differences that exist, and the speed with which such maps can be made using data from the Internet.
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Temporal Variation of Weather At any one location, temperature, humidity and illumination vary temporally — over time. They change from minute to minute, hour to hour, day to day, and year to year. Many of these changes are linked to patterns or cycles of the seasons and the daily rotation of the earth. But within those large annual and daily cycles are changes in weather that are apparently random - very much at the whim of nature. Thus, at a particular location, say downtown Saratoga, New York, weather at 3 PM on June 1 of one year can be expected to be more similar to weather at that same date and time in other years, than it will be to the weather at 2 AM on April 4th, or 7AM on November 29th. But weather at 3 PM on June 1st in one year is not exactly the same as on every other June 1st. In fact, temperature, humidity, and illumination at that time will vary a great deal from year to year. Certain seasonal and diurnal (daily) patterns in weather are predictable, but a large measure of it varies, apparently at random. Predictable versus unpredictable aspects of weather Therefore, variation over time in the weather (temperature, humidity, illumination, precipitation) at any one location can be viewed as composed of two components, one a predictable element - the expected average behavior due to seasons and daily cycles - and the other an unpredictable element. Weather = [Predictable or expected part] ± [unpredictable (random) portion] For example, the predictable element of illumination can be calculated quite accurately years ahead, for any specific time and location on the earth, based on latitude, longitude, and the inclination of the sun for that location at that time. This is the light hitting the upper atmosphere above the ground location, light undistorted by cloud cover. But illumination reaching the ground at any location is also a function of the amount of overcast and haze, which cannot be "predicted" with anywhere near the same precision as gross, high-altitude illumination. While the expected cloud cover can be characterized as a probability distribution for any location and time of year (Figure 5.2), it cannot be predicted with complete confidence far in advance, or at some locations, even an hour in advance. Thus, illumination is a composite of a predictable element and a random aspect. A similar perspective applied to temperature and humidity (and precipitation if included) would view the predictable portion of each as its average or expected behavior based on a review of historical data on seasonal and daily cycles, and the unpredictable part of the probability distribution about its expected
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.25
.5 0
.75
1.00
Gross Solar Energy - kW/m2
Figure 5.2 Solar illumination, measured here as gross solar energy expected at a location in the southern U.S. at noon on June 22 (summer solstice), based on 40 years of weather data. Theoretical maximum solar energy at this site is close to 1 kW per square meter, but even on cloudless days atmospheric haze makes this value unattainable in any practical sense. Less than a third could be converted to electric power under the best of practical circumstances (see Willis and Scott, Chapter 9).
mean. The unpredictable element is the distribution of outcomes possible in this characterization, the predictable element the mean and standard deviation of that distribution, etc., and how they vary with season and time of day. This unpredictability is, for temperature and humidity, a plus or minus value depending on an "apparently random" process which can often be characterized but not predicted. However, the mean and the statistical characteristics of the unpredictable behavior (i.e., the overall probability distribution) of temperature, humidity, or weather, can be predicted in advance based on observation of past weather. Predictable Weather Behavior Seasons and days The characteristics of weather behavior over time are partly predictable based on annual and diurnal (daily) cycles. Annually, one expects winter, spring, summer, and fall, weather during each season to differ along established patterns (in terms of maximums, averages, and variabilities) of temperature, humidity, and illumination. Usually, summer is warmest, winter coolest, with T, H, and I all less extreme in spring and fall. Early spring often has a slightly higher volatility
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(greatest "unpredictable" element, or standard deviation in the distribution of possible weather). Similarly, one can "predict" certain patterns of weather on a daily basis. At any time of year (season), it is possible to characterize the average, or expected temperature, humidity, and illumination at a spot, and their variation over a day. It is usually coolest in early morning and warmest in late afternoon, the exact nature and length of the daily cycle varying somewhat by season of year. Any particular day is likely to deviate slightly from this expected behavior due to the partial randomness of weather, but like seasons, daily behavior can be characterized by an expected behavior. Longer-term predictable cycles There are observable and somewhat predictable longer-term cycles to weather variation in many parts of the world. These include: El Nino cycles. The multi-year (3 - 7) cycle of ocean heating and cooling, and its consequent impact on weather in North, Central, and South America, has received a good deal of attention in the popular press in recent years, and has been a subject of scientific study for much longer. There is a clearly a detectable physical cycle of changes in ocean temperatures which affects precipitation and heat storm intensity throughout the western hemisphere. The exact mechanism behind this cycle is not precisely known nor is it entirely predictable. However, there are models and forecasts which take into account this periodic cycle. The author's viewpoint is that enough data exist to produce forecasts which dependably alter, slightly, the distribution of expected temperature, humidity, and precipitation from year to year, based on this cycle, but this is not terribly pertinent to power system planning. Over time, weather still nets out to its overall variation, including extremes. Solar activity cycle. Observation during the last century and a half has shown that the sun goes through an 11-year cycle of surface storm and solar flare activity. During the most intense part of each cycle, electrical storms are more frequent and intense. There is some evidence that this "weather" affects terrestrial weather through indirect means: solar electromagnetic activity impacts upper atmosphere conditions which impact lower atmosphere, etc. This is not completely proven but theory, based on both detailed model and some observations supports its predictions. There may also be some cycle-related interaction with the size of the "ozone hole" over the South Pole.
Relative Frequency of Occurrence
O 3o>
T3 r* (D T
(J1
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Beyond these longer-term cycles, there is no reason to believe that there are not longer-term cycles in the weather, cycles that mankind has not yet confirmed due to the relatively short duration of its quantitative observation of earth's weather (only two centuries at best). Cycles of variation of up to 4000 years in duration among oceanic flows and chemical/biological content (PH, plankton count, etc.), along with significant interactions with weather, have been the basis of some theories of how the planetary meteorological system functions (see Hsu, 1988). Unpredictable Elements of Weather Beyond the predictable daily, seasonal, and longer-term cycles in weather, there is the "unpredictable" element to variation over time. Unpredictable as used here signifies that it cannot be forecast far (e.g., a year and often far less) in advance with any precision characterizing that forecast by its most expected value. Figures 5.3 and 5.4 show typical behavior ~ summer temperatures at locations in Texas and California, along with a fitted Weibulll distributions. Weibull distributions often fit observed weather variation patterns well.2 Although T, H, and I at every location will have an apparently random, unpredictable element to them, the amount of unpredictability or randomness varies depending on location and season. Temperature and humidity vary less from their expected or average day-to-day patterns in Los Gatos, CA than they do in Moline, WI. In many locales, temperature, humidity, wind, and precipitation are much more variable in spring (tornado, or storm, season) than they are in summer or winter. The amount of variation also varies from year to year, with some years being more "volatile" than others. Often, "extremely hot weather" occurs during a summer in which the average temperature is a bit higher than normal, when there may also be more variation than in a normal year. "Heat storms" occur as very high excursions from an already slightly higher than normal mean. However, in this same summer there may be "cool periods" that match those expected in normal years, even though the mean temperature is slightly higher than average. Is Weather a Stationary Process? (Is Climate Changing?) A subject of debate in many environmental and meteorological circles is if climate is stationary (unchanging over time) or if climate and weather are changing. Is global warming real?
2
See, for example, Distributed Power Generation - Planning and Evaluation, by H. Lee Willis and Walter J. Scott (Marcel Dekker, New York, 2001) for a discussion of Wiebul distributions as a model of ambient air speed at any location, and their application in the planning wind-powered electric generation systems.
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Clearly, over long periods of time, climate does change. There is indisputable geological evidence that several ice ages, and their reciprocals — "tropical ages" ~ have occurred just in the last 100 million years. But geological time scales are so far removed from practical day-to-day time scales that their associated climate changes seem irrelevant to a person's life and job, or an electric system expansion plan. Perhaps more relevant are the climate changes recorded in the human record. The Arabian peninsula, which today has a very dry desert climate, had in biblical times considerably milder weather, and far less desert. Then, the land of Sheba (today, western Oman) had a climate somewhat like modem-day southern California (Clapp, 1998). In even earlier times, rhinoceros and other "African" animals thrived there in a climate much like modern-day Kenya. Climate does change significantly over centuries and millennia. In fact, there is no geological evidence to support the view that climate doesn't change and that it isn't currently changing. In fact, there is reasonably convincing evidence that average temperatures over the entire planet have been rising very slightly for several decades. Most of the debate over global warming centers not over if global warming exists, but over its cause and its future: Will it get worse? Is mankind to blame? There are several different theories or explanations for global warming, some backed by computer models or scientific explanations and forecasts of global warming. Some lay the blame for the warming trend directly and entirely at mankind's door: A somewhat convincing correlation between the increase in fossil emissions and other man-made pollutants, and global warming, can be found in the record of the last century. However, numerous opinions exist as to meaning, if any, and the interpretation of this correlation.3 However, other scientific viewpoints raise doubt about whether mankind has anything at all to do with global warming - the planet Earth experienced much wider deviations in climate long before man existed, and this latest trend might be only a part of another such oscillation of climate. The author's opinion is that mankind alone has not caused global warming, but hydrocarbon emissions and overuse of land in areas might have triggered or accelerated a nascent trend or changing local patterns. Regardless, for both power system planners and demand forecasters the important points are: • Global warming is real. Based on historical record, and having no reason to expect a change, one can expect average temperatures at any location to go up, rather than down, in the future.
A similar correlation can be made between the number of human beings residing on the planet, and global warming; or the number of artificial satellites put in orbit, and global warming. Again, correlation does not imply cause.
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Weather and Electric Load 90.0 88.0 -
E
* .
84.0
o> •
82.0
1i
80.0
I «o ->
I
-
c
S
78.0 76.0 74.0
Year
Figure 5.5 Thirty year's of average highest daily one-hour temperatures, June 1 to Aug. 31, measured at a point in the Midwest US. Mean value is 82.587 °F. However, a trend based on a starting value of 82.25 degrees in 1971 plus .166 degree added per year (for a total one half degree rise over the 30 years) fits the data slightly better than just the mean value alone. The fact that this trend fits 30 years of data is not too significant, but it is representative of more comprehensive studies that show a definite trend of warming.
• Often, particularly in and around large cities, there is a local "warming effect" due to the city's impact on local climate, amounting to as much as one degree Fahrenheit over three to four decades. • Within the planning period used in most utilities (5 - 20 years) both global and local warming effects are minor. • A serious challenge is analysis of historical average expected temperature? One obtains a different estimate of next year's most expected temperature from such analysis depending on whether one assumes weather has been stable, or that temperature is slightly increasing (Figure 5.5). Weather Is Less Predictable Over Longer Forecast Periods Weather takes time to change. The reason, which is linked to its physical manifestation, means that temperature, humidity, illumination, precipitation, and wind have a higher short-term than long-term correlation with their own values. If temperatures in early afternoon are extremely high, then temperatures are more likely to be extremely high three hours later, in late afternoon.
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12
°
8
a 4
1
2
3
7
10
30 Days Ahead
1Year
Figure 5.6 Standard deviation of differences in peak daily one-hour temperature for various lead periods (today's peak one-hour temperature - yesterday's peak one hour temperature) and for other different lengths of separation.
But while a period of an hour or two will produce fairly good correlation, even a single day ahead is a long period from the standpoint of forecasting and correlation, or lack of it, in weather. Figure 5.6 shows the standard deviation of daily peak temperatures of days separated by from one to 365 days, averaged over three sites (all in the mid-west US), during a 30-year period 1970 - 1999. Data used is only for mid-year (June 1 through Sept. 15). The difference in peak daily temperature measured only a day apart has a standard deviation of 6.9 degrees, while one week's separation gives a difference of 10.3 degrees, not much less than what a full year provides (11.2 degrees). There is no substantial increase in correlation for periods more than one year ahead. For this reason, weather is more predictable a few hours or days ahead than weeks, months, or years ahead. In some cases, auto-regressive models (which predict weather based on the present and recent past values of weather) are used for short-term (operational) electric demand forecasting purposes. Such models do not work well more than a few hours or days in advance, indicating they are no more accurate than merely characterizing the expected probability distributions based on historical observation alone. The opinion among many mathematicians and weather forecasters is that weather is a chaotic process, meaning that it can not be forecast in detail no more than a few days or perhaps a week ahead, no matter how much effort is expended.
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5.4 WEATHER AND ITS IMPACT ON ELECTRIC DEMAND In nearly every area of the world, ambient temperature varies by time of day and time of year, reaching its highest point each day in the afternoon or early evening, and its highest levels of the year during those times of day in the summer. Qualitatively, the electric demand in many utility systems varies in a similar manner, daily hitting its highest value in late afternoon, and (in most utility systems) hitting its highest annual values during the summer. Very clearly, a correlation, if not a direct cause-and-effect relationship, exists between weather and demand for electric power. Figure 5.7 shows the relationship between temperature and electric demand in a large metropolitan area of the U.S. Quantitative investigation and analysis of this relationship between demand and weather is useful to a utility demand forecaster for three reasons: Weather adjustment. Records of peak loads may have been made under different weather conditions. "Correction" to standard weather conditions makes them more useful for tracking trends. End-use analysis. Study of the variability of demand can provide indications of the composition of consumer demand. Weather normalization of forecasts - formulae are needed to adjust forecasts to extreme weather, so the system will be reliable.
5000
4000
Q 3000
3 O
re
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20 30 40 50 60 70 80 90 100 Maximum Average Three- Hour Temperature During Day
Figure 5.7 Relationship used to represent peak daily system demand during summer as a function of weather in a large metropolitan power system.
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Correlation versus Cause Some elements of electric demand are clearly directly attributable to temperature, humidity, and illumination. Air conditioning and heating are the best examples. If temperature, humidity and illumination all happen to be at extreme values at 3 PM on a given Tuesday afternoon, electric demand will be very high, too, compared to an identical Tuesday where all three are closer to average. The reason is that air conditioning and heating demand is directly attributable to temperature and humidity and sunlight. There is a causal relationship. By contrast, demand varies in many other electric end-use categories in a way that correlates with weather, particularly temperature and illumination, without having a direct causal relationship. It is important to keep in mind that a correlation between weather and demand does not necessarily imply a causal relationship. Temperature, humidity, and illumination cause some of the observed variations in demand. But other elements of demand's variation over time may correlate with diurnal or seasonal weather variations without being caused by that change in weather. Commercial lighting is a good example of a daily cycle that correlates with weather and yet is not directly caused by it. In most office buildings, interior lighting is on only during the day, when temperature is also highest. Therefore a temporal correlation exists. But there is no cause: High temperatures do not cause commercial lighting demand. Commercial office and professional building lighting demand appears to correlate with temperature because both are linked to the same driving cause, but theirs is not a causal relationship Resort and tourist loads are an example of a seasonally varying load that similarly correlates with weather without having a direct causal relationship. For example, in Bar Harbor, Maine, demand is higher in summer than in winter. But the higher demand in summer is not due mainly to temperature, at least not in a direct sense. The resort hotels, restaurants and shops in Bar Harbor are open only during the "season" (roughly May through October). Nearly the whole industry closes during the winter, and many of the seasonal workers leave the region (thus even residential demand drops). In this case, demand and temperature have a common cause to their variation (the season), but one is not a direct function of the other. Very often, seasonal demand patterns contain a juxtaposition of both causal and non-causal correlated variations. As an example, daily household lighting demand curves are significantly different in winter than in summer, particularly at higher latitudes. This seasonal difference in demand pattern is partly due to seasonal changes in ambient sunlight (the sun rises later and sets earlier in winter, thus creating a longer period each day of lighting demand). But part of it
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is due to changes in daily activity patterns for both residences and businesses from season to season. Winter sees far less outdoor activity, and more school activity, and thus different household occupancy patterns, and different electric usage patterns, as a result. Thus, the change in electric demand for the end-use "illumination" is a function of both the actual changes in ambient (outside) illumination and the different seasonal activity patterns. Interpretation of "Causal" In some cases, the identification of "weather sensitivity" of demand as a causal function of weather is a matter of interpretation and preference, as with seasonal differences in water heating demand. Water heaters have to work harder (run for longer periods, using more energy) to heat cold water (e.g., 40°F) versus cool water (65°F). In cities and towns where public water is drawn from lakes or rivers, water heating demand will be noticeably higher in winter than in summer. The reason is that from winter to summer, temperature of lake or river water will increase as long-term changes in air temperature and solar illumination have their effect. As average daily temperatures increase in summer, and as the period of sunlight received each day increases, water gradually warms, until by early summer it is much warmer than it was in mid-winter. Consequently, water temperature is higher in summer, and heating demand is far less than it was in winter, for the same households.4 This seasonal variation can be viewed as either a seasonal variation that simply happens ("Water temperature goes up in summer and down in winter, period. Who cares why?") or as a weather-related variation, a function of THI, but with a very long time constant (moving average period). It is a legitimate weather-sensitive load variation. However a majority of utilities model it as a seasonal variation.5'6 An advantage is that perspective also easily encompasses non-weather-related changes in water heater demand due to such causes as different seasonal human activity patterns.
4
By contrast, in cities and towns where well water is used, particularly deep-well water of the type that high-volume municipal pumps usually draw, seasonal variation in water heater demand is far less. Ground water temperature fifty feet or more below ground varies only slightly throughout the year in most locations. 5 And frankly, a lot of utilities ignore the issue, electric water heater demands, or the variation in them, being below the level of detail in their demand analysis. 6 In addition, activity patterns involving water heating are different from one season to another - people bathe and wash clothes, etc., in different amounts and at different times of day in different seasons. However these changes are usually minor compared to the possible changes in seasonal demand due to water temperature variations.
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Humidity and Demand Temperature is only one of three weather factors that significantly impact electric demand. As mentioned earlier, the other two are humidity and solar illumination. In particular, humidity can have a significant effect on electric demand. Air conditioners and heaters must remove or add heat to the air being conditioned, and if the air is humid it has considerably more mass, and hence heat, to give or take heat energy, and thus requires more work on the part of heating and cooling equipment. Humidity can make a large difference in electric demand in the summer, but little in the winter. Cold air cannot hold nearly as much moisture as warm air, so in winter there is much less increase in thermal storage capacity of air as humidity increases. Figure 5.8 compares residential daily demand profiles for areas whose major difference is the humidity on the day of measurement. Note the per unit curve shapes. Humidity not only causes a higher overall burden (note the difference in the actual demand curves, in kW), but it also causes a fatter curve. Humid air retains a great deal more heat than dry air. Thus, temperature does not plunge as rapidly after sundown, and the air retains considerable heat all night long, requiring more work of AC units at night.
100% humidity
100% humidity
i \ 52% humidity \
(0 0)
a.
52% humidity
,.5 .* re 0)
a.
Mid.
Noon Time of Day
Mid.
Mid.
Noon Time of Day
Mid.
Figure 5.8 Daily coincident demand curves for homes in a "dry climate" (dashed line, 52% humidity and 100°F, southern Arizona on the day measured) and in a very "muggy climate" (solid line, 100% humidity and 100°F, Texas Gulf Coast on the day measured). At left, per household coincident demand curves in kW; at right, the same curves on a per unit basis - normalized to the same peak value — to best illustrate the difference in curve shape attributable mostly to humidity.
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The two areas represented in Figure 5.8 lie at nearly the same latitude and thus see the same diurnal solar inclination patterns. Sample data sets used to prepare the demand curves for each area were prepared from whole-house metered demand data recorded on a 15-minute basis, for 64 and 72 single-family homes, respectively, and were recorded on the same day in August 1990. Homes in each sample area are single story, roughly 2,200 square feet each, and built in 1982-1986 ~ as similar as practicably possible. Cloud cover in the two areas was similar (20-30%) on the days measured. For these reasons, this is one of the author's favorite data sets. Despite the impact that humidity has on demand, analysis of demand-weather interaction, as done at many utilities, sometimes does not include humidity. The reason is that humidity is rather constant (at least during seasonal extremes), or else it is quite highly correlated with temperature. For example, in the Texas Gulf Coast region plotted in Figure 5.8 humidity almost never dips below 90% during summer, and in the Arizona region plotted in the same figure, it seldom rises above 55% during warm periods. Therefore, demand analysis can disregard humidity as an independent variable, by assuming that it will remain at its maximum regional value, at least during those extreme situations which define design conditions. However, one should note that humidity varies regionally so that demand data from one region or microclimate cannot be imported to another for use there. Figure 5.8 amply demonstrates this point. Normalized End-Use Load Curve Weather Models Given care in collecting and analyzing data, weather analysis, adjustment and modeling can be done on an end-use basis, as illustrated in Figure 5.9. Here, data such as that shown in Figure 5.8 — metered demand curves for selected subsets of consumer classes — have been collected and analyzed both for peak and offpeak days. Something similar to the analysis in Figure 5.8 has been done from recorded data to establish AC demand behavior as a function of weather. This has been used to prepare AC appliance demand curves normalized to standard conditions (a "design day" with a peak temperature of 94°F). An additional curve has also been developed which represents "one degree Fahrenheit" ~ the additional increment of demand that would occur in a day where the peak temperature reached one degree higher. This permits the end-use model to add higher than design demands into the forecast so that contingency studies can be done if desired. Such end-use models are not difficult to develop. Basically, the same type of analysis is used on each class as on the system as a whole to determine weather sensitivity.
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1. A useful first step is to perform the type of analysis shown in Figure 5.8 on a class basis, using demand data for selected feeders or substations known to serve single classes of consumer. For example, peak day demands from five substations all serving only residential areas can be recorded, then added to form a "residential demand" for residential weather adjustment studies. 2. Not all seasonal variation is due to weather. During summer, parking lot lights in commercial areas (which consume a noticeable amount of power) are not turned on until as late as 9 PM in some latitudes. In winter those same lights may be on before 6 PM. Interior lighting patterns also vary from winter to summer. As mentioned earlier, ground water temperature varies from winter to summer by several degrees, so water heaters have farther to raise temperature, and water heater demand is thus higher in winter. 3. Appliance characteristics and market penetrations can be used to allocate weather sensitivity to the various appliance types within each class. Usually, for engineering purposes, one can assume that the per unit shape of the temperature sensitivity curve is the same as the per unit shape of the base appliance daily demand curve. Doubts about this can be resolved by applying a bootstrap building simulator to test hypothetical curve shapes. However, in general, if data are properly used, building simulators do not need to be used to determine historical weather sensitivities, because thermal loss factors for buildings are not weather sensitive. On the other hand, appliance output is a function of ambient temperature,7 and demand saturates at high temperatures because duty cycles reach 100% -- two factors modeled by the duty-cycle simulation that should be part of any good bootstrap simulator. The author recommends that weather normalization be a part of all demand analysis. Standard weather design conditions should be defined and applied to engineering, and demand data and base forecast values should be normalized to such conditions. Weather normalized end-use models (Figure 5.9) require a good deal of work in both data gathering and construction/verification but are worthwhile if detailed forecasts, DSM studies, or combined "integrated resource" planning are involved. 7
For example, the demand of a typical heat pump, when acting as a cooling unit, increases by 10% from 85°F to 100°F due to increases in the compressor back pressure caused by the worsening Carnot cycle of the heat pump loop.
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1 i 2
Mid.
Noon Time of Day
Mid.
Mid.
Noon Time of Day
Mid.
Figure 5.9 The coincident per-consumer appliance end-use curve at the left is for a normal AC appliance demand for a typical single-family home in the Texas Gulf Coast area plotted in Figure 5.8. This is normalized to a "standard design day" (94°F THI here). Effect of higher or lower temperatures can be simulated by adding or subtracting one on more copies of the "one degree more" demand curve at the right, as needed, up to the point where AC demands begin to saturate (thought to be 97°F THI in this system).
The Relationship Between Weather and Peak Demand All manner of weather adjustment and normalization methods have been developed, applied, and refined by the power industry. Most rely on regression analysis and allied statistical methods to establish a functional correlation between data variables, then use this function to determine demand as a function of weather for adjustment and prediction. Many weather-demand models use a "jackknife function" analysis, shown in Figure 5.10. This function has a minimum point, usually at a temperature slightly lower than comfortable room temperature (e.g., 65°F or 17°C). From that point, demand increases as temperature increases or decreases. Since in most systems recorded data give no indication that the slope in both directions is not linear, a straight line is used, as shown. Since in many utility systems recorded data give no strong indication that the slope of the function in both directions is not straight, a straight line is often used for both increasing and decreasing temperature, as shown in Figure 5.11. However, at extreme high temperatures the slope of demand versus temperature usually decreases at high temperatures, as shown in Figure 5.10. This is due to saturation of air conditioner duty cycles (see Chapter 3). Usually, residential and
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1000
800 ro Q O)
600
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400
c •c
•o ro o
200
It
ro 0) O. 0
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20 30 40 50 60 70 80 90 Maximum One Hour Temperature During Day
100
Figure 5.10 The simple weather-demand jackknife function. Shown are peak daily demand versus peak daily temperature for all Tuesdays in a year (several Tuesdays thought non-representative because they were holidays or similar special events were left out of the analysis). Only Tuesdays are used in order to reduce the effects that different weekday activity patterns may have on demand variation.
1000 800 (Q Q O)
600
Q
400
c
re o -J 200 ro Q)
a.
« 10
20 30 40 50 60 70 80 90 Maximum One Hour Temperature During Day
100
Figure 5.11 A refinement often used is to represent the high-temperature relationship as "bending" at some point in the high 90°F range, due to duty-cycle saturation of air conditioners. The transition in slope is almost certainly gradual, not sharp as shown here, but that is often not modeled.
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commercial air conditioners are sized to handle a 25 to 30°F inside-outside differential when working at full (100% duty cycle) output. As a result, at somewhere around 95 to 100°F, the installed base of AC units in most utility systems begins to reach 100% duty cycle and AC demand does not increase as ambient temperature increases beyond that point. Of course, AC units vary in condition and precise fit to their application (a few will be oversized because only a choice of larger- or smaller-than-needed was available among standard sizes). As a result, the actual transition to completely "saturated" AC demand temperature is gradual, the slope decreasing as temperature climbs above some point. In addition, one would expect that at some point all weather sensitive demand would become completely saturated and the demand versus temperature curve would be flat.8 A similar reduction in slope would be expected at low temperatures, but is rarely seen. There are at least two reasons. First, the heating equipment installed in commercial and residential buildings (both apartments and single-family homes) is usually greatly oversized (i.e., installed capacity is greater than needed for expected temperature differentials), so that it seldom "runs out of capacity" no matter how cold the weather becomes. In addition, in extremely cold weather people use portable heaters (similar "portable AC units" do not exist or are much more expensive), turn on electric ovens and leave their doors open, and activate other devices to generate extra heat in their homes, further increasing demand. Figure 5.12 shows a simple improvement that can be made over Figure 5.11 by using simple end-use analysis concepts, in this case the recognition that winter and summer peak times are different and thus the "weather demand" falls on top of different "base" (non-weather related) demand levels. In the system illustrated in these examples, daily peak demand occurs in early morning, in winter, and in early evening in the summer. Rather than use a true "jackknife function" where the two whiter and summer slopes meet at a common point, this analysis realizes that they in fact "meet" at different demand levels because the non-weather sensitive demand is different at their respective peak times. The analysis in Figure 5.12 results in a better understanding of weather behavior and a superior identification of weather variability with temperature.
1
Records in some parts of a few systems in extremely hot climes show that residential demand actually begins to drop when temperature reaches very extreme levels — 105°F. Opinion among utility analysts in these areas is that in such extreme conditions, residential AC units may fall 5 - 10°F behind minimum comfort levels. As a result homeowners "give up" and head to a mall (which generally have both over-designed chiller units and higher thermal inertia so its takes longer to heat up) or the beach, etc. This explanation has not been proven but seems possible.
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V
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20 30 40 50 60 70 80 90 Maximum One Hour Temperature During Day
100
Hour of the Day
Figure 5.12 Improved weather adjustment based on end-use analysis recognizes that weather-sensitive demand builds on top of different levels of "base" daily activity in winter and summer. Thus, the "starting point" for peak demand varies seasonally. Daily curves shown for winter (solid) and summer (dashed) at right indicate the slight difference in the base curves due to solar inclination or other seasonal changes.
Statistical Analysis to Identify Weather's Impact on Peak Demand Analysis of weather and demand data for demand forecasting purposes generally has one ultimate goal: to adjust historical demand readings (recorded peak demand values for each year) to standard weather conditions. This is done by: a. Developing a relationship (equation) between weather and peak demand, for each past year, seeking the best statistical fit possible for each year b. Using that equation to determine what the peak demand would have been in each year had the weather been the same in each year Nearly anywhere in the world, a determined utility demand forecaster can obtain the basic weather information needed to perform a basic weather-demand interaction analysis. Availability of raw data is seldom a problem. Hourly records of temperature and humidity, and in some cases illumination, are available in a majority of locations, in some cases going back more than ten decades. If there is any one general lament among forecasters about available weather data, it is that usually it does not have sufficient spatial resolution - in a very large metropolitan area there may be only four sites (downtown, two airports, one weather bureau location) with decades-long records available.
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General characteristics of the analysis This type of study is always historical, in that it involves only analysis of past weather, demands, and their characteristics and interactions. No prediction or extrapolation is involved in the analysis, nor will the results be used for prediction in the normal sense of the word. The analysis works on weather and demand data for some past period of time, be it a day, year, or usually several decades. For T&D planning purposes, the analytical focus is nearly always on explaining the peak hourly demand that occurred during a period (day, season, or year). Usually, annual peak is the key focus. The historical analysis will do so by looking at all peaks (daily peaks) in the record and trying to explain each as a function of weather at that time. The relationship, once identified, can then be used to explain extreme peaks as they relate to extreme weather and determine load duration curve shapes as will be discussed in Chapter 6. Almost invariably, only a causal mathematical relationship between weather and demand is sought — a relationship that represents demand as a function of weather up to and including the time of the peak demand, but not after it. In other words, demand can not be a function of weather that has yet to occur. This restriction to a causal relationship is made because a working assumption is that weather causes demand variations, and therefore weather that has not yet occurred cannot possibly affect present demand levels. Interestingly, a purely statistical analysis does not always bear this out. As an example, in one utility system in the western United States the highest correlation of weather, on the day of the peak, with daily peak demand was temperature at 10 PM that night. But peak occurred between 6 and 7 PM, hours earlier than that time, although analysis proved temperature at 10 PM had a slightly superior correlation to peak demand than temperature at 6 PM or any hourly temperature leading up to it.9 This situation and its not-too-convincing explanation illustrate one problem with weather analysis — correlation of weather data with itself. 9
The explanation developed for this vexing incongruity was only partly convincing although it passed muster from a statistical standpoint. The area in question often received mild winds during the day, which blew milder air in from the coast, miles away. These winds tended to die down at sunset. Air temperature at 6 PM was therefore often not a function of the amount of illumination received locally throughout the day. But the temperature at 10 PM in the evening (well after sundown) was a function of air temperature at sunset, when the winds tended to abate, and illumination throughout the day (long periods of sunlight heated the earth, which then kept the ambient air warmer at night). Demand at 6 PM was also partly a function of total illumination over the course of the day: By 6 PM the cumulative effect on demand was noticeable. Thus, demand at 6 PM correlated best with temperature four hours later.
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Regardless, planners should agree among themselves up front if they are going to restrict their analysis to developing only a causal relationship, or if a non-causal relationship will be acceptable. They should understand that their purpose and goals will be equally well served by either a causal or non-causal relationship, whichever has the best statistical fit. The weather-demand relationship, once identified, will be used to adjust past peak demand levels to normalized weather. Since this is a purely historical analysis, in every case, they will always know the weather on the peak day and thereafter, and can apply a non-causal relationship in their application. Weather at 10 PM on the day of the peak will be available to them even if the peak always occurred at 6 PM. This is the nature of a purely historical analysis. A multitude of possible weather variables Section 5.2 on weather focused on examples, graphs, and discussions that centered around peak one-hour temperatures. This variable was selected as illustrative of weather and its variation and behavior, in general. However, system planners and demand analysts should realize that there are many possible weather variables, besides just peak one-hour temperature, that should be explored during the process of finding a good relationship between weather and demand. In particular, often multi-hour averages, such as peak three-hour temperature, THI instead of temperature, and lagged temperature or THI readings (i.e., those taken a number of hours prior to peak) are most useful in explaining demand as a function of weather. Collinearity of data A challenge in the analysis of many types of time series, and weather in particular, is that there are so many choices for the variables to be used in a statistical analysis, and many of these are highly collinear (correlated among themselves). This is because weather variables interact with one another (e.g., intense illumination raises the temperature of air) and because one can choose "variables" that are merely lagged versions of one another (temperature at this hour, temperature an hour earlier). Table 5.4 shows the correlation of annual peak demand for a system in Texas, with a number of weather variables for the day of peak. Peak occurred at 6 PM. Four variables have correlations greater than 85% with peak demand: THI at the peak hour, wind chill at the peak hour, cooling degrees in the peak hour, and the temperature at 7 AM that morning.
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Table 5.4 Correlation of Selected Weather Variables with Peak Daily Electric Demand and With Each Other Weather Variable
Peak THI@ Demand MAX
Wind Chill
Dew CD Temp Temp Max Sky CD Pt. Hr @Max 7AM 3hr Cvr 7AM
THI@Max
0.88
1.00
Wind Chill
0.85
0.94
1.00
DewPt
0.78
0.88
0.74
1.00
CD pk hr
0.90
0.87
0.88
0.83
1.00
Max Temp
0.82
0.89
0.94
0.72
0.92
1.00
Temp 7AM
0.86
0.90
0.86
0.83
0.88
0.83
1.00
Max 3 hr °F
0.83
0.95
0.97
0.76
0.90
0.96
0.87
1.00
-0.13
-0.15
-0.24
0.06
-0.16
-0.28
-0.12
-0.25
0.83
0.71
0.92
0.70
-0.08
1.00
0.88
0.91
0.83
0.90
-0.29
0.73
Sky Cover 7 AM CD
0.81
0.82
0.77
0.84
CD 12-14
0.79
0.90
0.91
0.69
1.00
Solely on the basis of having four variables with correlation above 85%, an analyst might assume that a model based on all four would provide an outstandingly high accuracy in relating demand to weather. But that is not the case due to the collinearity — correlation among the variables. The highest correlation between any two variables in Table 5.4 is between THI at peak hour and wind chill at peak hour. The 94% correlation between the two means that either one provides just about all the information contained in both: use of both doesn't tell the forecaster much more than use of either one. In fact, nearly all of the weather variables, except overcast, correlate fairly well with one another: there is not a lot of information in this set of variables, even if it contains a lot of data. Regardless, a correlation analysis such as shown in Table 5.4 provides a good start for demand-weather analysis and is recommended. It determines what is the preferred variable for analysis (CD in this case) and warns the analyst of collinearity in the data if they exist. Usually, they do. Statistical modeling of peak demand as a function of weather Many utilities expend considerable effort on statistical analysis of weatherdemand interaction, leading to development of functional relationships (equations) that explain or "predict" peak demand based on weather variables.
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This is all based on analysis of weather and demand records of a multi-year period - usually the last five to ten years. The equations, once developed, are then used to adjust demand readings to normalize weather conditions (for comparison purposes) and to adjust forecasts to the standard weather design criteria. Regardless of the method selected, however, the use of only valid statistical analysis methods and the application of formulae developed from such rigorous analysis, is highly recommended. Shortcuts and heuristic rules tend to be too approximate to be useful in this type of application. There are pitfalls. The most common is to spend a great deal of time on very advanced statistical analysis, which produces little benefit over more basic approaches. It is possible to perform a statistical study of weather and demand far beyond what is necessary for planning, a study that provides intellectual challenge and exercises advanced techniques. But its results bring nothing to the planning process. It is best to keep one's eye on the ball, so to speak, and always ask: "Is this work improving the results of the planning process?" Analytical method This book is not a treatise on statistical analysis. A number of excellent references on statistical analysis and its applications are available (see References). Most studies apply step-wise regression to develop the numerical relationship between weather variables and peak demand. This method is preferred over other approaches due to the myriad of variables with high collinearity involved in the analysis. The equation(s) selected are those that provide the best (narrowest range) of error in explaining demand as a function of weather. An example is the formula developed from statistical weather-demand analysis for a small utility system in the Midwest: 4PM
Peak MW = a(y) + b(y) (Td(7AM)) - 7 + c(y)(Z(THI(h)-70)) 1PM
where Td(7AM) is the temperature in °F at 7AM for day d THI (h) is the THI (equation 5.1) at hour h and a(y), b(y), and c(y) are the coefficients sought for year y among the historical period being used, y e [first year, . . . , last year]
(5.6)
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This formula was developed for a utility system in the central United States, fit to the past ten years of weather and load history, based on 2 months of detailed data collection and statistical analysis by the utility's demand analysts. To obtain the best fit, they developed a formula using the same parameters, but different coefficients (values for a, b, and c) for each of the past ten years of data. One specific set of coefficients is determined by fitting the equation to 1992 data, another, for 1993, and so forth. Different coefficients are used for each year because number of consumers and economic/demographic factors vary from year to year. For example, different values of a, the y-axis intercept, essentially account for different amounts of base, non-weather sensitive load, due to such factors as consumer count. This equation with its year-specific coefficients was then used to adjust each year's peak demands to standard conditions. For each year, that year's coefficients are used as the equation is applied to solve for the peak demand that would have been seen under standard weather conditions. These standard conditions are the design criteria weather conditions - those conditions of temperature and THI, etc., which have been identified for use as "standard design conditions." Determining those values will be discussed in Chapter 6. 4PM
Adjusted Peak MW = a(y) + b(y) (TCd(7AM)) - 7 + c(y)(I(THIC(h)-70)) (5.7) 1PM
where TCd(7AM) is the design criteria temperature in °F at 7AM THIC(h) is the design criteria THI for hour h Note that the same parameter values (standard weather conditions) are used for every historical year, while the coefficients vary from year to year. The result is a set of weather-adjusted historical demands for each of the years used in the historical analysis. All are now on the same standard weather basis, as much as this process produces. Caveat. The author has seen some applications in which different equations are used, not just the same equation with different coefficients in each year. "Different equation" means that different parameters (base variables or their exponent) are used. As an example, the equation for 1998 might relate demand to temperature at 7 AM and cooling degree hours from 3 PM to 6 PM squared, while that for 1999 relates demand to cooling degrees from 6AM to 9AM and cooling degree hours from 3 PM to 6 PM (not squared). Mathematically and functionally, as far as the process of fitting equations and applying them to historical data is concerned, there is no real reason why different equations cannot be used.
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However, the author prefers to see the same equation used (with different coefficients) for each year. This is due to the need for consistency in defining extreme weather for the needs that will be described in Chapter 6. Once the equation(s) and coefficients are determined through the process discussed above, they are applied to the standard set of weather variables. Usually, these consist or two or three parameters such as temperature at 7 AM, cooling degree hours from 3 PM to 6 PM, etc. The specific values used (temperature at 7AM = 83 °F) are selected to weather "extreme enough" that it will be used as the target for design (Chapter 6 will discuss this in detail). Usually, the selection of the exact parameter values is based on a detailed statistical analysis of each: what value of temperature at 7AM is really one-year-in-ten? It is difficult to determine a set of only two or three parameter values that represent the same degree of "extreme" weather. To identify temperature at 7 AM, cooling degree hours from 3 PM to 6 PM, and perhaps one other variable such as solar illumination, so that they each represent the same one-in-ten year pattern takes care in coordinating them - do they all represent the same type of once-in-ten-year weather or is each a representation of one-in-ten year data that never occur together? Using different equations with different variables for different years increases the number of variables required to correct the data history. This larger set of variables creates more room for error. The requirement for different parameters among different years' equations means more must be studied and their extreme values selected. The potential for error (inconsistency) is increased. Worse, the sensitivity of the entire process is increased. If inconsistency exists among the values selected for a set of parameters used in the same way in every one of the yearly equations, then the error is consistently applied in each year. However, if some years use some parameters and others other parameters, the potential for inconsistency increases. Ruling day model In fact, the problem of consistency in identifying extreme weather is serious enough to create problems even when only two or three variables are involved. There are rare locations where one-in-ten temperature and one-in-ten humidity have never occurred simultaneously. Apparently the conditions that create each extreme are mutually exclusive. In many locations, extreme illumination and high humidity are partly exclusive (high humidity creates haze or comes from light cloud cover). For this reason, it is often best to abandon a purely statistical study of individual variables because they may produce an "over-extreme" set of weather variables. Instead, it is best to identify specific days - ruling days which will be used to represent each "one-in-N" weather scenario - all variables being taken from that scenario's day.
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Example Application The particular equation used in 5.6 and 5.7 was selected by a utility over several other candidate formulae purely because it rated better in terms of two statistical tests in relating peak demand to weather variables on a daily basis for the summer periods (June 1 - Aug. 31) of 1990 - 1999.10'11 Regardless of that statistical fit, one questionable aspect of that formula is the physical explanation for its terms. Certainly the meaning of the first term is clear and seems legitimate: temperature early in the day (7 AM) is an indicator of pre-existing conditions (i.e., a high value indicates this is the second day of a 'heat storm'). However, the squared term (THI(h)-70) is more difficult to relate to a physical basis. But why should a term like THI reduction hours that is normally linearly related to demand, be squared?12 The formula given below proved better in actual use: 6PM
Peak MW = a(y) + b(y) (Td(7AM)) - 72) + c(y) (2(THI(h) - 70)) (5.8) 3PM
This equation had a slightly worse overall fitting accuracy in seven of the ten historical years examined, with respect to its accuracy in explaining peak daily demand level based on daily weather for the entire set of days from June 1 to Aug. 31. However, it had two advantages. First, its physical explanation is made easier due its lack of a squared term, and to a lesser extent by the fact that it includes THI up to the peak time. (This equation's summation of THI cooling hours includes hours up to 6 PM. Typically, system peak occurs at 6 PM.) But second and more important, equation 5.8 proved more accurate in explaining the highest 15% of peak daily demands in each year during that period (R2 of .908 versus .867). While equation 5.8 is less accurate than 5.6 in
Specifically, peak day demand versus weather prior to and including that day, for weekdays from June 1 through September 15 of each year. 1 ' The measures used were R2, the coefficient of determination, which approximates the amount of variability in the data that is explained by the model. An R2 value of 0.90 means that the formulae being used "explain" 90% of the variation seen in the time series being "predicted" by the model (in this case MW). Also used is CP) a statistic which indicates the total mean square error for the regression model's fit to the data. 1 Based on detailed assessment of the equipment and processes involved, the relationship between temperature and energy usage, or THI and energy usage, can be established as roughly linear between temperature and demand is essentially a straight line (See Figures 5.10-5.12).
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Table 5.5 Peak Demand Weather Adjustment Equation Coefficients, Parameters, and Results for Application During the Sample Historical Period Study Year
1987 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Coefficients
A
B
C
4767 4767 4810 4863 4921 4978 5050 5117 5180 5239 5297 5360
65.0 65.0 65.6 66.3 67.1 67.9 68.9 69.8 70.6 71.4 72.2 73.1
25.0 25.0 25.2 25.5 25.8 26.1 26.5 26.8 27.2 27.5 27.8 28.1
Weather 7AM PMA
77.1
5.2 9.1 7.0 9.1 3.5 8.3 9.6 6.9 4.8 1.5 8.4
Demand - MW Actual By eq. Adjust 7234 7351 7622 7410 7876 7328 7947 8240 8162 7901 7957 8545
374.5 92.0 82.0 84.2 86.3 83.2 87.5 91.8 93.9 86.9 90.6 91.1
7258 7402 7474 7476 7758 7390 7940 8247 8218 7967 7920 8535
7747 7747 7817 7903 7998 8090 8207 8316 8417 8514 8608 8711
9000 -a 8500 c CO
E D O
x
8000 7500
CO CD
D- 7000 "co c c
87
88
89
90
91
92 Year
93
94
95
96
97
Figure 5.13 Actual and fitted demand histories, and adjusted (to ten year weather) peak demands for 1987 - 1997 (top, solid line). That adjusted trend shows a slightly lower actual demand growth rate than would have been extrapolated by trending the average of the unadjusted data (dashed line).
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relating peak daily demand to weather for all 92 days of each summer, it is more accurate when evaluated on only the 14 days which had the highest peak demands. Since the desired application is to apply the formula to adjust peak annual demands to extreme-weather peak conditions, it seemed better to use equation 5.8. Applying the Example Formula to Normalize Data Normalizing historical demand data means adjusting all of the peak and off-peak data to be used in the analysis to some appropriate, standard set of weather conditions. Table 5.5 shows ten years of data including: • Coefficients fitted to equation 5.8 for each year: A, B, and C • Actual (historical) parameter values for each year's peak day, as "Weather" » THI at 7AM, and the sum of the THI for the four hours 3 through 6 PM on the peak day • Actual (historical) peak one-hour demand for that year, in MW. • The equation's estimate of peak demand for that year, at the conditions shown for the year under "Weather" (difference with actual is fitting error for that point) • Adjusted peak demand (equation's estimate) of the peak demand that would have resulted at standard weather conditions Figure 5.13 shows the historical, fitted, and adjusted demand values plotted by year.
REFERENCES Nicholas Clapp, The Road to Ubar, Houghton Mifflin, New York, 1998. Howard Hsu, The Great Dying, Ballantine Books, New York, 1988. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall, New York, 1998. S. Kachigan, Multivariate Statistical Analysis: A Conceptual Introduction, Radius Press, New York, 1991.
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L. Ott and M. Longnecker, An Introduction to Statistical Methods and Data Analysis, Wadsworth, New York, 1999 H. L. Willis and W. G. Scott, Distributed Power Generation: Planning and Evaluation, Marcel Dekker, New York, 2001.
6 Weather-Design Criteria and Forecast Normalization 6.1 INTRODUCTION This is the second of two chapters on how weather influences demand and the analytical and planning issues associated with that relationship. It could also be characterized as "advanced weather-demand analysis" building on the "basic" material covered in Chapter 5. That chapter examined how weather influences electric load and looked at analytical methods to identify the relationship between weather and load, and use it to improve planning. This chapter looks at one aspect of weather in more detail - extreme weather, those conditions when it creates very high loads. It also examines weather's influence on electric demand from two other perspectives — that of the annual load duration curve and daily load curves. Both are necessary to build toward using the knowledge of weather and load in planning. Finally, the chapter addresses weather design criteria how utility planners use their knowledge of weather in setting target loading levels for the system and in assuring the system can handle the loads created by extremely hot and cold weather. It begins in section 6.2 with a look at "extreme weather" - what it is, how often it occurs, and how planners can study and access its impact. Section 6.3 then looks at weather design criteria and summarizes the basic approaches
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94 92 90 88 86 1971
1980
1990
2000
1990
2000
Year
1400 1200 . 1000 Q '
800 600 400 200
0 1971
1980
Year
Figure 6.1 Top, hottest peak daily temperature seen in each year from 1971 to 2000. Extremes in this measure often create peak demand conditions. Bottom, total cooling degree days from June 1 to Aug. 1 for the same years. What concerns the utility most are the extremes of both. Very high temperatures (above the dotted line in the top diagram) usually create record peak demand levels and high system stress. Very cool summers (below the dotted line in the diagram at the bottom) mean low revenues and a possible financial shortfall.
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utilities have used to set design criteria. Section 6.4 then looks at a particularly effective analytical method to select an appropriate weather design target and presents an example. Section 6.5 provides a summary of both Chapters 5 and 6, along with some guidelines on weather, weather adjustment, extreme weather, and design weather criteria. 6.2 EXTREME WEATHER What matters to the T&D planner are the extreme situations that might be created by future weather and the likelihood of seeing those extreme weather conditions. How often can the planner expect weather conditions that lead to really high, stressful levels of peak demand on the power system? How often can the utility expect really mild summers, with the extremely low revenues they bring? Figure 6.1 shows actual data from a system in the Midwest U.S., addressing both questions. Extreme values occur rarely, but over a long enough period of time they are essentially certain to occur. From any practical standpoint of T&D planning, it is impossible to "forecast" accurately the time and severity of extreme weather. The "forecasting period" of interest to T&D and financial planners is a function of the lead times for system equipment and additions, and is measured in years. While predicting weather a few hours or a day ahead is feasible, short lead times like that are important only to bulk power schedulers and T&D system dispatchers at a utility. As mentioned in Chapter 5, over a period of even one year ahead, it is impossible to forecast future weather beyond being able to project the probabilistic distribution of possible outcomes. As a result, "forecasting" extreme weather for T&D planning basically boils down to determining the expected characteristics of future weather based on analysis of historical weather variation Frequency of extreme weather One of the most useful ways to characterize weather for T&D planning is to look at how often the utility can expect to see weather conditions extreme enough to lead to really high demand levels. This "frequency analysis" will be used later in this chapter to derive risk-based definitions of weather design criteria for power systems. On many power systems, annual peak demands occur in summer, near the end of multi-day periods of very high temperature - what are often called "heat storms." In winter, a peak demand period can occur due to an intense cold snap, often brought on by the movement from the polar region of an area of intensely cold air (called, in the U.S., a "blue norther"). The more extreme the weather, the less often it occurs and the less often it can be expected in the future. As an example, Figure 6.2 shows frequency of
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occurrence of temperatures at a location in the Midwest United States. This is called a weather severity diagram. As shown, in this case a temperature of at least 91°F can be expected to be reached or exceeded every summer, while it is quite common to see temperature reach or exceed 96°F - on average every other year (one out of every two summers). A temperature of 99°F is reached only one out of every five summers, and 102°F is reached only on average once every ten years. This type of "once every X years" weather-severity plotting is a useful way of characterizing weather for forecasting and planning purposes, as will be discussed later in this chapter. As mentioned above, not just the peak temperature for an hour, but the entire seasonal weather behavior tends to vary in "extremeness" too (Figure 6.3). Simply put, some summers average out hotter than others, all summer long. During those, average temperatures are higher and temperature reaches any particular high level (e.g., 96°F) more often and/or for longer periods than in cooler summers. Figure 6.4 shows how extremes of temperature and cooling degree days were related (same data as used for Figures 6.1 through 6.3).
104 102
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100 98 96 94 92 90 88 86
Period Length, Years
Figure 6.2 Weather-severity plot showing frequency of occurrence of highest annual temperatures (for one hour) for the downtown of a city in the central United States. Horizontal axis is the average period over which one has to wait to see a summer that reaches or exceeds the plotted temperature on the vertical axis.
171
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86 84 82 80 78 76 74 72 1
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Figure 6.3 Weather severity plot, showing the frequency of occurrence of average daily peak summer temperatures, derived from the same data that led to Figures 6.1 and 6.2. Horizontal axis is the average period over which one has to wait to see a summer that reaches or exceeds the average peak daily temperature shown on the vertical axis. 1300 1200 1100 M >,
O
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700 600 500
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96 98 100 102 Highest One-Hour Temperature -°F
104
Figure 6.4 Not surprisingly, hot summers give rise to the highest recorded temperatures. Shown here are the total cooling degree days versus highest one-hour temperatures for the same data used in Figures 6.1 through 6.3.
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14- 1°4 O . 102 O^ 100 o f 98
ii 96
^1 94 92
2 55 fl> Q. Q. i_ E <»
go.
90 88 86
10 15 Period Length, Years
10 20 30 40 50 60 70 80 90 100 Maximum One Hour Temperature During Day
10
15
20
Hour of the Day
20
Period Length, Years Figure 6.5 Weather severity information (top) is translated via the weather to demand relationship determined from historical study (middle), into a peak demand frequency data set (bottom).
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Extreme Demand Frequency Computed from Extreme Weather Equations like 5.6 and 5.7 can be used to translate weather-severity diagrams such as were shown in Figure 6.2 and 6.3 into a diagram showing the frequency of expected peak demand levels. This is done by translating the weather conditions corresponding to various points on the curve into demand, using the equation for the most recent, or forecast, demand, as appropriate. Figure 6.5 shows this process, producing plots like Figure 6.6. The resulting data provides planners with information about the risk they face in weather-induced high loads. "Extremeness" of weather often changes with the seasons In most locations, quite noticeable changes in the expected weather occur with the change of seasons. The location's summer and winter each have definite patterns of high and low temperatures, precipitation, etc., which are expected. Spring and fall have milder weather and can be viewed as transitions between the two extreme seasons as the weather changes within its predictable annual cycle. Generally, the characteristics of the unpredictable element of weather behavior how extreme the weather is - changes with the seasons, too. For example, the
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Figure 6.6 "Load severity" diagram shows how often the utility can expect certain levels of maximum peak demand, as a function of the frequency of weather. Amount of load is measured in "per unit" of the expected mean summer peak load.
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year's summer might have been quite extreme - perhaps statistically that means it was "one out of twenty" or "one out of twenty-five" with respect to high temperatures. However, the following winter will not be any more, or less, likely to be mild (a 'hot' winter) or extreme (a one-in-twenty extreme winter) because of this. The "extremeness" of a summer's weather can change half-way through the season, so that the first half sees one-in-twenty weather and the latter half only average weather. However, significant shifts in the 'unpredictable' character of weather appear to occur more often and "predictably" when the seasons change. The author's viewpoint is that the overall character of weather for a particular season (how extreme it is) can change any time, but that it is most likely to change between summer and winter, or vice versa. Apparently, a change of season often triggers some process of "reinitialization" in the process (jet-stream height wind flow, etc.) that determines the extremeness of weather for the next season. Thus, a hot summer tends to stay a hot summer through its full duration, but that means nothing with respect to whether the following winter will be particularly harsh or not. Weather data analysis such as covered in Chapter 5, and here, can be used to evaluate this premise for the study area and provide some support for the application of this perspective in weather-demand studies. 6.3 STANDARDIZED WEATHER "DESIGN CRITERIA" Setting Design Weather Conditions Looking to the future, what type of weather conditions should the utility set for the peak demand conditions which its system is designed to serve? Should it plan its system to handle the peak loads associated with average weather conditions? Designing for average conditions means that weather (and hence, peak demand) will exceed design conditions, on average, every other year. Alternatively, should the utility set design weather conditions at the most extreme ever observed? Installing enough capacity to handle the peak demands generated by "the heat storm of the century" or the "worst cold snap seen every fifty years" would pretty much assure that weather-induced high demands never lead to equipment over-demands. However, it means that a good deal of money must be spent on equipment capacity that will be used rarely, if at all. Engineers and planners always want to have enough margin to cover any contingency. But distribution demand forecasters and planners need to realize that energy consumers won't relish paying high rates every month for one hundred years just so the system has the capacity for that one storm of the century. A balance needs to be sought between design targets set to provide reliability, and trimming of targets to affect an economy in planning.
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Table 6.1 Approaches to Weather Normalization of Electric Demand Forecasts Method
Summary
Philosophy and Perspective
No weather criteria
No weather analysis is done. No weather criteria is used.
Ignorance is bliss.
Arbitrary criteria
Set criteria at some level deemed "sufficiently infrequent enough."
Keep it simple,
"Never again" criteria
Set criteria to equal actual weather conditions that led to a system problem in the past
Reactionary
Reliability-based criteria Set criteria based on achieving Pro-active a satisfactory level of reliability when weather variation is considered
Thus, something above average conditions, but less than the most extreme weather ever observed, is best as a design goal. There are three basic approaches to determining the standard weather conditions to which the system will be designed. In addition, some utilities do not have a formally defined set of weather criteria - weather impact on load is not addressed in a formal sense, and the system is designed without regard to weather sensitivity in the planning process. All four of these approaches are summarized in Table 6.1. Method 1: No Weather Criteria Perhaps as much as 15% of the power industry plans without explicit regard for or consideration of weather and the impact it has on electric load. Most planners who take this approach say they are not actually ignoring the effects of weather on demand, but only assuming that by not assessing it explicitly or correcting for it in their historical demand analysis, their forecasts will "even out" to average conditions. Figure 6.7 illustrates the basic concept behind this thinking, which is that weather variations in annual historical loads will tend to cancel one another out, resulting in mean weather conditions in trending of demand growth and forecasts. To some extent, Figure 6.7 bears out the assumption that ignoring weather in trending analysis means that it averages out to the mean over time. However, in this case while the trend line (dashed line) split most of the weather variation the
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resulting extrapolation is far off the values produced by weather-adjusting the annual peak loads and then extrapolating. The error shown is representative of what occurs in many situations where this approach is taken. (The reader can examine Figure 5.13 (page 164), which shows a different set of peak load data, on which this same approach would produce similar levels of error, but due to over-, not under-forecasting load growth). In addition, it is worth noting that working with unadjusted weather data precludes effective use of higher-order polynomials in the historical trending. Figure 6.7 employs straight-line interpolation and extrapolation of the historical data. A second- or third-order equation, as often used (and recommended) for
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90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 Year
Figure 6.7 Ten-year history of annual peak demand (through 1999) unadjusted for weather (solid line) and extrapolated another ten years for the regional load in a metropolitan area of the southern United States. Dashed line shows trend line fitted to the uncorrected values, and extrapolated into the future - analysis and projection both assuming "weather averages out." Dotted line shows a similar extrapolation based on adjustment of weather conditions using the technique described in Chapter 5 (equation 5.5). Ten years into the future, the assumption that "weather averages out" results in a 220 MW deviation, 25% of the forecast load growth.
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trending distribution loads (see Chapter 9) would vastly increase the level of error in forecasting, as the greater degrees of freedom in the fitting equation would adjust to "explain" weather rather than strike an average through its variations. The "fitting" equations that result from application of second- or third-order polynomials to unadjusted demand data generally prove highly inaccurate in forecasting load growth, even a few years ahead Beyond the forecast error that this approach creates, perhaps its most damaging impact on planning is that it implicitly sets design demand levels at or near mean weather conditions. As mentioned earlier, this means design demands will be exceeded on average every other year. Such frequent likelihood that peak demands will exceed design conditions means the system is very likely to get into operating problems, perhaps severe problems, over time. Very few utilities that take this approach are unaware of the link between weather and demand, or that many other utilities adjust demand data through analysis and normalization as discussed here and in Chapter 5. In fact, a few have guidelines on their books that call for weather adjustment, but for various reasons that step is skipped, for expediency. And most utility planners who take this approach argue that they have had no problems in the past with demands exceeding planned system capability, so the approach must work. But in fact, examination of operating records at these utilities shows that in every case, actual loads have exceeded design levels by significant amounts, but that there were no severe problems because historically the systems were designed with very healthy capacity margins. It is precisely these utilities who get into serious trouble when they begin to cut back on capital spending and/or raise equipment utilization rates on their system. Basically, they do not have the forecasting and planning infrastructure in place to plan a system to tight margins. For several of the utilities that experienced notable blackouts in the summer of 1999 due to the intense heat that year's summer brought, lack of weather adjustment in forecasting was a contributing factor to their poor planning. Method 2: Arbitrary Conditions This approach can be considered the "traditional approach," in that it has been used by many utilities since the 1950s. With this approach, a "judgement call" is made on the frequency of over-demands that should be treated as "too extreme" to be considered as targets for system capability. Essentially this is an arbitrary decision, but it usually is made with due regard to historical weather behavior (including, perhaps, a great deal of study of weather patterns and their effect on demand) and serious consideration of the consequences of setting targets both too high or too low.
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In the late 1990s and early 'OOs, this was the most widely used method for determining weather design criteria for electric utilities in the United States. A majority of utilities taking this approach selected ten-year extreme weather and its associated demands as their design criterion standard weather. The resulting criterion is often referred to as a "90% criteria," "90/10" demand criteria," or "ten-year peak load criteria." Ten years is used most often for a number of reasons. First, many planners picked up the "one in ten years" value from generation planning procedures of the 70s and 80s, when ten years was a de facto industry standard for loss of load expectation (LOLE). In addition, to many planners, ten years seems like an appropriate period for extreme weather frequency. Ten years is a rather long time between expected events, but not so extreme as to be unreasonable. After all, even taking probabilities and randomness into account, "one in ten year weather" is certain to occur several times during one's career or lifetime. Finally, perhaps contributing to its widespread use, ten years was often a traditionally recommended approach, among many other places being cited in the first edition of this book. Overall, proper use of this approach creates few problems. Systems that are well-planned to this level of weather criteria tend to be robust enough to survive most weather-created extreme loads, even those more extreme than one-in-ten year levels. Yet their historical operating performance usually indicates that there were times when they were under high levels of stress from loads above their design criteria - a sign that unnecessarily large (and expensive) capacity margins have not been employed because their criteria is not too extreme. The basic problem can be considered one of fine tuning and compatibility. First, an arbitrary criteria means the utility cannot justify the value used, be it one-in-ten year or one-in-five year weather, because it is arbitrary. The risk due to using an arbitrary criterion cannot be justified against, and managed, with respect to other risks the utility is weighing and considering as it tries to trim budgets but maximize performance. Risk-based planning, which seek to measure or translate risk into dollars, and then mitigate that risk through optimization of design and operating procedures, is a recent trend in the power industry. Given the general level of success with the one-in-ten year criterion prior to the widespread use of this approach, it is not surprising that using arbitrary weather design criteria was a traditional favorite among electric utilities. Method 3: "Never Again" Criteria In some cases, after a particularly intense summer in which high demands led to operating problems and/or consumer interruptions and poor service, a utility's upper management will order its Engineering and Planning Departments to
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revise their weather criteria to match that summer's extreme weather. In essence, the utility has decided that the problems created by that year's extreme weather were severe enough that the utility will set its design criteria so it can handle those conditions the next time they occur. Utilities taking this approach are overreacting. The weather values they select as targets usually work out to be one-in-twenty year weather or even more extreme. One set of utility planning standards reviewed by the author used a value that was equivalent to once-in-55-year weather, although the utility had never performed analysis to determine how likely it was to occur again. Reliability is certainly bolstered by this approach, but capital and operating costs are higher than might be justifiable. In almost every case, when these criteria are examined based on their economic effectiveness in providing reliability, that reliability proves too costly by comparison to other ways the utility can "buy" similar levels of performance improvement. Method 4: Reliability-Based Selection of Weather Criterion In this approach, the added stress created by extreme weather is treated as a contingency with a probability distribution (i.e., one-in-ten year weather has a probability of 10%, one in twenty a probability of 5%, and so forth). Service problems created by extreme weather are treated as just one more probabilistic factor to be weighed into a rigorous analysis of the system's expected performance. The system is planned to a service reliability target or to a metric limit that corresponds to a certain "target" level of consumer service. Risk-based planning of a power system takes into account the probability of failures of individual units of equipment and groups of equipment due to independent but simultaneous failure, as well as common-mode failures. Advanced risk/reliability analysis approaches even consider the probability that the protection equipment fails, or works but not completely as it was planned and coordinated. To this approach, weather is added merely as another probability. Now, the load is represented as a probability distribution. On average, the peak demand will be so much (the mean value), but there is a probability distribution that describes how likely it is to be much higher. Given this likelihood, risk-based planning methods respond by incorporating just enough capacity and redundant configuration into the system plan, so the calculated expected "lights on" performance of the future system will meet a target "service reliability criterion." Generally, such planning methods assume that system equipment is operated at emergency levels during extreme stress periods (a one-in-ten year event is rare enough that, at least in the author's opinion, it qualifies as an "emergency"). But other causes of service problems - failures, mis-operation of equipment, etc., are also taken into account. The resulting system has not only an ability to tolerate
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those causes of service problems, but also the variations from weather that might occur, while taking into account that failures might occur during periods of extreme weather. There are two approaches used with risk-based weather criterion application. Dynamic weather risk planning. This approach can only be used when the subsequent planning is done entirely with risk-based planning and evaluation methods. The utility is using reliability-load flows and risk analysis, such as the ABB PAD (Performance Advantage - Distribution) program for distribution design. In this case, no weather criterion is set. Instead, a probability distribution of expected duration of peak demands (Figure 6.8) is used in the probabilistic reliability assessment of each planning decision. Risk-based criterion. Here, a risk-based analysis of weather is done to determine a weather design criterion, and this is used as the load target in what is otherwise a traditional (in this case, that means non-probabilistic) planning process. Section 6.5 will give a detailed example of this process and its result. Either of these approaches, if well executed, attains the planners' goal for riskbased planning: achieving the required level of service reliability while minimizing cost and balancing various conflicting design and service goals. The dynamic weather risk planning is superior only in that it permits more comprehensive differentiated reliability planning — planning different parts or locations of the system to different reliability targets. The rest of this chapter will focus on the use of extreme weather, design criterion, and the risk-based planning method (number 4) described above. However, first section 6.4 will look at a detail of weather-demand analysis needed for effective risk-based planning analysis. 6.4 ANALYZING WEATHER'S IMPACT ON DEMAND CURVE SHAPE Comprehensive risk-based planning of a power delivery system focuses a great deal of attention on economically achieving the capability to serve the expected levels of peak demand, but it also looks at the demand during the rest (off-peak periods) of the year. Loads are high and capability margins slimmest at peak, failures that lead to consumer interruptions can and do occur during off-peak times. For this reason, weather analysis for risk-based planning needs to look at the impact of weather on the load for the entire year. Often the best way to do this is to look at weather's impact on the annual load duration curve, as will be described here. Another way is to study the impact of weather on daily or longer load curve shapes (see Chapter 5, Figure 5.8 and accompanying discussion).
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Weather, extreme or otherwise, impacts more than just daily and annual peak demand levels. During a hot summer, temperatures are above typical (average) summer values most of the time. Thus demands are higher in general, not just during peak times. One way to capture all of the impact of weather on demand is to compare the demand duration curves for two different years' of weather. Figure 6.8 compares summer-season demand duration curves for a municipal (entirely urban and suburban) system in the southern U.S. These are a ten-year summer (based on cooling-degree days) compared to a demand duration curve for an average summer (one-in-two with regard to cooling degree days). The difference in peak demand is 10% (1002 vs. 920 MW). The difference in area (energy) under the curve is 7%.
Summer
Annual
Figure 6.8 Top, demand duration curves for l-in-20 and l-in-2 summers (June 1 Aug.31). Bottom, annual duration curves incorporating mean weather for the rest of the year with these two summers.
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Load duration curve comparisons, such as shown here, are very useful for several planning-related applications related to identifying and using weather design criteria. There are several ways that planners can approach the development of these curves. Generally, a purely analytic method does not work, in the sense of trying to "solve" for the entire curve shape an hour at a time based on historical data and weather. The mathematical problem involves too many hours of demand and weather data to be tractable. A good approach is to identify specific past years as representative of one-intwo, one-in five, one-in-ten, and other years from a weather severity standpoint, and then use their actual demand duration curve shapes, each scaled on a per unit basis to a common consumer-count basis. They can then be plotted in conjunction to form a diagram as shown in Figure 6.9. A detail in this approach is that the load duration curves must all be scaled to a common consumer base. Such scaling is required because the demand base (number of consumers in the system) has most likely been changing over time. For example, the year selected for use as the "one-in-two" curve might be 2000, when the system had 235,000 consumers, while that picked for use as the "onein-ten" year might be 1994, when there were only 218,000 consumers. A valid comparison will adjust both to a common consumer-count basis.
1000
850
Hours
Figure 6.9 Upper left corner of the resulting plot of multiple demand duration curves, each representing a different set of weather conditions for a summer (see text for description of method). Shown is the upper corner of annual load duration curves (1 to 200 hours, all summer hours). These curves represent 1 in 20 and 1 in 10 year highs, average load, and 1 in 10 and 1 in 20 year low load curves.
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Figure 6.10 Upper left comer of the resulting plot of multiple demand duration curves, each representing a different set of weather conditions for a summer (see text for description of method). Shown are curves for 1 in 20 and 1 in 10 years, average, 1 in 10 low, and 1 in 20 low, for the periods 1 to 200 hours per year.
An expected demand duration curve can now be developed by interpreting/translating the set of adjusted load duration curves into a probabilistic load duration curve, as depicted in Figure 6.10. Basically, the set of curves is treated as a probability distribution. One-in-ten weather's load duration curve becomes the 10% likely curve, and so forth for all curves. The expectation of hours at any one level, in any year, is merely the expectation of the curve above that load level (probability times load level). As shown in Figure 6.11, the expected hours at any one demand level, taking weather into account, are computed simply as the expectation across the set of demand-duration-curve-based probabilities at that demand level. As a final step, this probabilistic demand duration curve can be "normalized" to a particular "extremeness of weather," for example, putting its vertical scale values on a per-unit scale with the peak demand associated with mean weather assigned a value of 1.00 (Figure 6.12). The demand duration curve can now be used as a template, scaled as needed to a forecast done using "mean weather" demand levels. It then gives the probability of extreme loads for future planning based on that forecast. This will be given later in this chapter.
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Figure 6.11 Expected number of hours at a particular demand level for the normalized base (final year of the historical analysis) can now be computed as the expectation of the probability distribution at that demand level. Here, the expected hours at or above 925 MW is the composite of the area above the dotted line, roughly 10% for 20 hours and 5% for 40 hours. More comprehensive assessment computes it as a total of 4.4 hours/year expected to be operating at 925 MW or above.
Figure 6.12 Normalization to per unit scale permits the weather-sensitive load duration curve to be applied to planning of future years by scaling as appropriate.
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6.5 RISK-BASED DETERMINATION OF WEATHER CRITERIA Risk-Based Planning Risk-based planning involves measuring and managing risk. Risk is measured by determining, in a suitable way, the likelihood of various outcomes or states (e.g., consumers in service and no equipment over rated loads). Management of that risk is then accomplished by designing the system so that a certain likelihood of success is maintained - a certain target is achieved. For a power delivery system, risk is usually defined as the probability that consumers are out of service, for any reason - lack of capacity because demand exceeds equipment capabilities, failure of one or more units of equipment, or failure of switching and/or protective coordination and control systems. This is essentially a service-reliability analysis of the system, although strictly speaking there is a small difference between a pure "risk-based" analysis and "reliability" analysis.1 A number of different analytical techniques, embodied in different computer programs, can used for risk-based planning and engineering. Each method uses some risk or reliability metric - numerical measure of success or failure - and has an analytical method to compute that metric based on the power system's equipment, configuration, and loading. Such analysis is always applied in a predictive manner - the analysis is applied to systems as they will be loaded and operated in the future, as well as to candidate designs that have not yet been built. It is used to evaluate alternative plans until the best plan (most economical, most flexible) that achieves certain level of risk has been identified. The author prefers to use the BEAR (Expected Energy at Risk) method developed by Dr. Richard Brown. Expected Energy At Risk (EEAR) Expected Energy At Risk (EEAR) is an engineering and planning measurement that estimates the percentage of consumer demand for electric power that is "at risk" of not being delivered due to weaknesses in the inherent topology or equipment capacities in a power system. EEAR is that portion of the annual 1
In the author's opinion there is a difference between reliability and risk analysis. Reliability analysis looks at the likelihood of consumer interruptions due to equipment failure and misoperation of protection. Risk analysis looks at the likelihood of consumer interruptions due to all reasons, but also considers a gray area near "total failure" times when equipment has not failed and connectivity is not necessarily broken, but service can only be maintained by accepting loading levels above equipment ratings (emergency loading levels).
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consumer demand (area under the load duration curve) that may not be made available to consumers because the power system cannot deliver it to them. The term is called Expected Energy At Risk because it is computed using probabilities of outcomes to determine the expected result for a power system assigned to serve a particular consumer demand. Usually, a power system fails to deliver power to its consumers for one of two reasons. Either it has inadequate capacity (insufficient equipment capacity) somewhere in the chain of equipment leading to the consumers, or a failure occurs somewhere in that chain, breaking the continuous flow of power to the consumers. Figure 6.13 shows a daily demand curve for a designated group of consumers that are being served by a particular substation. This substation has a nominal rating of 75 MVA (two transformers with normal/emergency ratings of 41.7/55.6 MVA, or 37.5/50 MW at 90% PF). Any time demand exceeds 75 MW, the portion of the curve above that limit is deemed to be "at risk" (shaded area) of not being served. Identifying this particular load as being "at risk" does not necessarily mean that it will be unserved. The utility may choose to leave the substation equipment in service even though it will be operating at emergency rating. Or it might implement some unplanned emergency action, such as transferring a portion of this load to yet another substation.
100 75
c 50
ra
o Q 25
Mid.
Noon Time of Day
Mid.
Figure 6.13 A daily (24-hour) demand curve for a substation with 75 MW rated emergency capacity. Peak demand reaches 83 MW, and energy needed (area under the curve) is 1400 MWH. Black area (that portion above 75 MW) comprises 29 MWH.
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What the designation "at risk" means is that the demand cannot be served within the rules laid down for operation of the system. In this case, were there no other problems, the utility would almost certainly accept overloads up to 112% of normal rating (e.g., to 83 MW, the peak load shown) as preferable to dropping the demand from service. But regardless, this load is identified as being at risk. In a way, it is. If anything else were wrong in the power system near this substation, such as an outage of a neighboring substation that necessitates this substation picking up additional loading, then this load would be at risk of not being served. Thus, by the rules, 2% (28/1400) of the energy in this daily load curve is computed as being at risk of being unserved because peak demand exceeds capacity. Energy is at risk if the demand exceeds the rating of the power system equipment. But there is also a chance that service to consumers will be interrupted during times when demand is below 75 MW, even far below 75 MW, because of failure of equipment in the substation. For the sake of simplicity for this example, assume that the substation's capacity is "all or nothing" - it is all available or all unavailable (even though there are two separate transformers) - with a probability of failure of 1%. Then 1% of the non-shaded area in Figure 1 is also "at risk." This is 1% of (1400 - 28) MWH, or 13.72 MWH, which is .98%. Therefore, in this example, the total expected energy at risk due to these two causes is 2.98%. Energy at risk also includes energy not expected to be served due to the failure of the power system equipment involved. In actual application, the computation of expected energy at risk uses a much more comprehensive analysis than described in this example. First, the EEAR analysis must look at demand over more than just one day. Typically the evaluation is done over the entire year, based on a load duration curve approach. Second, the analysis of failures and capacity for the substation in this example would consist of more than just an evaluation of capacity and failures for its two transformers. Breakers, disconnects, buses, and other equipment in the substation need to be analyzed, too, as would the lines leading into and out of the substation. All would normally be included in a complete analysis, with both their capacity limits and likelihoods of failure used to determine EEAR.
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In addition, the analysis would recognize that some equipment failures will not necessarily disable the substation's capability to meet demand. For example, a bus section may fail and the substation configuration might permit switching to isolate it while still serving all the demand, if the substation's configuration is capable of such switching and if sufficient capacity exists in the remaining equipment to handle all the demand. Then too, equipment emergency ratings need to be considered, since during an emergency equipment can be loaded above normal rating. The emergency rating of a 37.5 MW transformer might be 50 MW, meaning that during the outage of one transformer, the unit remaining in service could serve 50 MW, not 37.5 MW. Finally, HEAR analysis normally looks at the system, not just one substation in isolation, and would consider that during a failure, some of the substation's demand could be switched so it could be served from other nearby substations during a problem period. How much load could be transferred, and how many consumers would be out for how long before the transfer was completed, would be determined by the HEAR analysis. But the concept of EEAR is exactly as illustrated here. An analysis aggregates consumer demand level throughout a period, equipment capacities, configuration and switching options, and failure likelihoods and their consequences into an estimate of the portion of total energy that is "at risk" because sufficient capability within the operating rules is not expected to be available to meet demand. A good EEAR analysis can break down the risk into categories: energy at risk due to failures where no capacity is available, energy at risk due to overload beyond emergency ratings, and energy at risk due to loading beyond normal ratings. EEAR Targets: One One-Hundredth Percent at the Low-Side Substation and Three One-Hundredths Percent at the Consumer Generally, EEAR is evaluated at the low-side bus (feeder head) of distribution substations and at the consumer. Evaluation of eleven major utility systems has shown that systems perform well when they have EEAR values of: EEAR at the substation low-side bus < .01 percent EEAR at the consumer delivery point < .03 percent Experience has also shown that performance is not acceptable when values rise above these limits. Values of .01 and .03 percent correspond to 53 and 159 minutes annually. Since typical values of SAIDI average in the neighborhood of 120 minutes annually (at the consumer) with outages down to the substation lowside bus contributing about 1/3 of that, one can see that a portion of the "at risk load" is in fact delivered. Systems are often loaded, or kept in service, beyond their intended operating limits, by what might be called "heroic" steps.
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Comparison of EEAR to SAIFI and SAIDI SAIFI and SAIDI are two commonly reported indices used to measure the actual consumer service quality of a power system. SAIFI (System Average Interruption Frequency Index) measures the average number of times a consumer in the system had his power delivery interrupted. SAIDI (System Average Interruption Duration Index) measures the average duration (total time) that consumers were without service. Generally, consumers in the U.S. see a SAIFI of about 2.0 and a SAIDI of about 120-140 minutes annually. However, with no notable exceptions, service in the core of large cities is always better than the average SAIFI and SAIDI for the metropolitan area surrounding it. SAIFI and SAIDI differ from EEAR in several ways. First, SAIFI and SAIDI are indexes based on actual results, whereas EEAR is an estimate of expected results. SAIFI and SAIDI are computed after the fact, looking back on actual operating results in the previous year, by analyzing all the consumer interruptions that occurred in the utility's service territory (or the portion of that territory being studied). By contrast, EEAR looks ahead to what is expected in the future, based on expected outcomes of capacity and failure against expected consumer demand levels. Second, EEAR does not assess the way in which the power system is operated or the quality and quantity of utility resources applied during emergencies. A utility that manages its operations well, so that it recognizes failures immediately and responds quickly, will reduce its SAIDI compared to a utility whose operations are done in a less timely and responsive manner. In addition, decisions to overload equipment beyond planned emergency ratings during contingencies, or "heroic" efforts to switch the system to keep critical consumers on line under circumstances where they would normally not be served, can reduce SAIDI. EEAR does not consider these aspects of reliability. It evaluates only the system's potential to fall into situations that will challenge the utility Operations department with failures or overloads - i.e., situations where consumer service is "at risk." Many, perhaps most, of these situations will lead to interruption of consumer service, but EEAR analysis makes no assessment of operations quality and how it might make a difference. It evaluates only the system's inherent likelihood to "get into" situations where consumer demand is at risk of not being served. Finally, an EEAR analysis does not evaluate what might be simply called "luck." Nearly every utility system will see variations in SAIDI and SAIFI from year to year, even if an EEAR analysis shows that it has been engineered to the same EEAR level every year. In some years, a utility will simply see fewer failures, milder storms, or for whatever other reason, have fewer stressful events that lead to service interruptions. Other years, it may have more.
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That said, HEAR corresponds more closely to SAIDI than to SAIFI. SAIDI measures the portion of the year that consumers were out of service. EEAR predicts the portion of the consumer's demand in the year that is expected to be unserved. Qualitatively, both measure the amount of service that is not delivered. However, EEAR takes into account the level of demand - failures during peak periods "count more" than those occurring during off peak. SAIDI looks only at the time unserved - an hour out at peak is the same as an hour out during minimum demand periods. Still, they are related, and much more similar than EEAR and SAIFI. In a system that has a flat (constant) load curve, an EEAR of .01% would correspond to a SAIDI of 53 minutes - service being unavailable .01% of the time. Given that failures and limitations in the sub-transmission-substation part of most power systems account for about 30% to 40% of outages, one can estimate that in most power systems SAIDI due to other causes would be roughly one and one half (60/40) to two and one-thirds (70/30) times as much, or between another 80 to 123 minutes. In company with this additional time, the 53 minutes or .01% EEAR computed for the sub-transmission-substation part of a power system becomes roughly a total SAIDI of between 135 to 180 minutes, slightly worse than the national average. For this reason, the author considers an EEAR of .01% to be an upper threshold, below which EEAR for the subtransmission/substation system should be targeted. What Then, Is EEAR? EEAR is a planning and engineering evaluation tool, in that it evaluates the most relevant engineered aspects of a power systems design with respect to reliability of service: equipment and its capacity ratings, layout and configuration, and the level of demand that must be served. EEAR will be higher (i.e., a larger portion of the demanded energy will be at risk) if equipment capacity is insufficient to meet peak load levels, or if equipment has high failure rates because it is old or has not been sufficiently maintained. It will tend to be lower if there is a margin of equipment capacity over and above peak demand, if the system layout permits switching around major equipment failures, and if equipment has low expected failure rates because it is of robust design and in good condition. These factors are the issues that planning and engineering seeks to manage, by calling for sufficient capacity, proper configuration, and acceptable condition of equipment. By design, EEAR includes only the engineering-related aspects of power systems performance, and does not include assessment of operating issues of the type discussed above. It focuses only on engineering-related aspects of the power system. It provides a quantitative measure of how those engineering-related issues aggregate with regard to consumer service quality, thereby providing a tool that engineers and planners can use to assure that their candidate designs
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will provide proper consumer service quality. Engineers and planners can select system designs, equipment sizes, and make decisions regarding acceptable equipment conditions that keep EEAR below a target threshold, all with a goal of assuring that the system should be capable of being operated so that service quality meets consumer service needs. Ultimately, a utility wants to manage its operation and review its performance based on actual consumer performance indices like SAIDI and SAIFI, which report how well it does in total, measuring the impact of both the PlanningEngineering and its Operations. But for engineering and planning purposes, EEAR provides a tool that can be used to assess candidate designs and assure that, while economical, proposed future systems will be capable of providing good consumer service reliability.2 A Rose by Any Other Name The author prefers the EEAR over other indices in the reliability and risk engineering of a power system. It has given only good results (leading to systems that perform as expected) from this method. This is attributable to the very comprehensive nature of its computation and the rigorous manner in which the PAD computer program developed by R. Brown calculates the EEAR index for a particular combination of power system configuration, equipment, and load duration curve. In addition, since EEAR respects normal and emergency capacity and capability limits for equipment, it proves very realistic at evaluating situations where connectivity remains but the system runs out of capability, and their consequences. This is one chief advantage of this method over purely "failure rate" based analysis methods. A large portion of operating problems for power systems are not created by outright failures of connectivity (i.e., a line is out and no other path is available), but by the inadequacy of the remaining paths or equipment to serve the load. However, in principal, any other rigorous probabilistic method of evaluating and ranking a power system against a specific service-availability target could be used as the index/tool in the weather-design criteria described here. The method outlined below will work with any method that computes reliability or risk in a quantitative manner, so that that value can be compared to a target value being used to design the system. The only requirement for applicability is that the method recognize and respond in some meaningful way to normal and emergency ratings for equipment and lines.
For more details on EEAR and kits application, Brown, 2002.
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EEAR and Peak Loading The service reliability performance of a power delivery system is quite sensitive to the ratio of peak load to equipment capacity or system capability. Figure 6.14 shows EEAR computed for the substation discussed above (two 41.6 MVA transformers) when serving peak demands between 70 and 85 MVA. In all cases the evaluation used a load duration curve shape (63% annual load factor) as in Figure 6.8 bottom, and looked at the EEAR for the entire year, from all causes. The relationship between peak demand and rated capability shown in Figure 6.14 is quite non-linear, and typical with respect to EEAR or reliability evaluations of most locations in modern power systems. This particular substation has been designed to achieve an EEAR of .01% at a peak demand of 75 MW, its nominal rating. That is the utility's EEAR target for the low-side bus of its substations in the metropolitan area of its system. At a peak load of 80 MW (actually 79.9 MW) the calculated EEAR doubles, to .02%, and at 84 MW, the EEAR has reached .11%, eleven times the target EEAR. However, EEAR does not drop from its 75 MW level nearly as quickly when peak demand is reduced below that rating, as it rises when peak is raised above it. At 50 MW, it is .085, a drop of only 15%.
.100
.010
.001 50
55
60 65 70 75 Peak Demand - MW
80
85
Figure 6.14 EEAR for a two-transformer substation, nominally rated at 75 MW peak demand, when serving various levels of annual peak demand.
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The reason for this non-linearity of the EEAR-peak demand relationship is that demand above the substation rating is defined as "at risk" even when no equipment has failed. All demand below that rating is not at risk unless some equipment in the substation has failed (essentially reducing its rating). Thus, if loading is kept below 75 MW, then the EEAR for the substation is due only to possible failures. The EEAR value at 75 MW is .01% because the probability of various equipment failures, times the possible loading (demand), over the entire 8760 hours of the load duration curve, equals .01% of the energy (area under the curve). The substation has been designed to that target level. The computed EEAR .01% is a small amount. It represents a total energy at risk of: MWH at risk = 75 MW x .63 x 8760 x .01% = 41.4 MWH
(6.1)
One hour operating at 80 MW adds 5 MWH to the total energy at risk, raising the EEAR by 12%, to .0112%. However, when peak demand is 80 MW, the expected total duration of load above 75 MW, based on the load duration curve, comes to 44.91 MWH. Thus, EEAR at 80 MW is: EEAR (80 MW) = .01% + 44.917(80 x.63 x 8760) = .0202%
(6.2)
Similarly, as peak demand increases further, both the amount of demand and the amount of tune demand is over 75 MW increase. As a result EEAR escalates rapidly, becoming ten times the value at 75 MW, only a bit above 83 MW, or less than 11% above the nominal rating of the substation. By contrast, when peak demand drops below 75 MW, not much happens to the computed EEAR. It drops slightly for one reason. As the peak load drops, the amount of time that demand stays below the amount that one transformer can handle, increases slightly. As a result, the percent of load during the year that is at risk due to a single transformer failure drops slightly, and EEAR improves slightly. 7s the strongly non-linear EEAR-demand relationship realistic? The answer is yes, without a doubt it is a valid measure to use in T&D planning. Without a doubt, the utility would choose to leave the substation in service even if its equipment had to operate at slightly above its ratings due to demand being higher than anticipated. However, at these times, the normal amounts of margin for contingency are not available, and the system is under levels of stress, that even if not severe, are more than it is intended to encounter during noncontingency (equipment failure) conditions.
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One can calculate a similar probability-based value that looks at only outages due to equipment failures, one which does not classify demand above rated capacity as "at risk." Below 75 MW the computation and HEAR are basically the same. Above that limit, however, the failure-only reliability computation is much more linear. The problem with this perspective is that capacity in a power system does matter. Otherwise planners and utility management would not choose to spend money to provide sufficient capacity. Again, BEAR is a good tool precisely because it does look at both failure- and rating-induced system problems. 6.6 EXAMPLE: RISK-BASED WEATHER-RELATED DEMAND TARGET ANALYSIS Metropolitan Power and Light builds two-transformer substations, each with a pair of 41.7/55.6 MVA transformers, serving a total of eight 12.47 kV feeders (four each), as its standard substation. It sets normal/emergency ratings for all equipment and specifies minimum feeder transfer criteria between so that it achieves a target level of .01% EEAR (Expected Energy At Risk) at the low-side bus of every substation in its downtown operating district. The particular substation for this example was designed to achieve this EEAR at a peak demand of 75 MW and load duration curve shape shown in Figure 6.8. Table 6.2 gives EEAR (Expected Energy At Risk) values for this substation evaluated against selected levels of peak demand, all with the same annual demand factor of 63% and the same demand duration curve shape, just a higher peak load. The particular demand levels listed correspond to the peak demands for 1:20, 1:10,
Table 6.2 Computation of Expected EEAR Taking Variation of Weather and Its Impact on Annual Weather into Account Weather Scenario
Probability
1 in 20 1 in 10 1 in 5 1 in 2 1 in 5 1 in 10 1 in 20
5% 8% 18% 40% 18% 8% 5% 100%
%
Peak Temp °F
Peak Demand - MW
EEAR
104.5 103 100 95 93 92 91.5
83.7 82.9 79.9 75.0 72.9 71.8 71.3
0.108
(Yr)
0.090 0.020 0.010 0.010 0.010 0.010
Prob. x EEAR 0.0054 0.0068 0.0035 0.0040 0.0017 0.0007 0.0005 0.0226
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1:5, 1:2, 4:5, 9:10 and 19:20 weather, as calculated from 50 years of weather data for this system. The BEAR values shown correspond to those plotted in Figure 6.14 (same data). Table 6.2 shows that when all possible levels of extreme weather are taken into account, the expected BEAR is far above the target. It is .0226%, or two and a quarter times as high. In other words, when designed to achieve an BEAR of .01 against the "one-in-two" year demand value, the system has two and one quarter times the expected BEAR, because of expected variations in the weather and their impact on demand. Table 6.3 shows the expectation of BEAR when the substation has been redesigned so that it can handle a peak demand of 81.3 MW with a computed .01% BEAR. (81.3 MW was the peak demand level at which the substation produced an BEAR of .0226% in Table 6.2). The "trick" is to re-design the substation so that the load level that had a calculated BEAR equal to the probability-weighted average (.0226 in this example) can now be handled at the target value of .01%. Designed in this way, BEAR expected due to the weather variation and its impact on demand is very nearly at the target level of .01. Slight non-linearities in the various formulae used, and the approximate nature of the simplified calculation given here, result in the slight mismatch - the EEAR value is actually .0105%, still about 105% of the desired target. A second adjustment or iteration of this process (table not shown) settles on a 81.7 MW peak load, resulting in .01% calculated EEAR. This is "one in seven and one half years" (twice in fifteen years) weather. Table 6.3's computation is approximate in that it represented the probability distribution of weather occurrence with only seven "bands" rather than computing it using a much finer representation of the distribution, or with a
Table 6.3 Computation of Expected EEAR with the Substation Designed for "One in Seven" Year Weather Demand Levels Weather Probability Peak Peak EEAR Prob. x Scenario Temp °F Demand - MW (Yr) EEAR % Iin20 5% 104.5 83.7 0.021 0.001 1 linlO 8% 103 82.9 0.015 0.001 1 1 in 5 18% 100 79.9 0.010 0.0017 1 in 2 95 40% 75.0 0.009 0.0038 Iin5 18% 93 72.9 0.009 0.0016 1 in 10 92 8% 71.8 0.009 0.0007 Iin20 5% 91.5 0.0004 71.3 0.008 100% 0.0105
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rigorous mathematical formula for the distribution itself. However, it arrived at a useful result. Designing the system to one-in-seven or one-in-eight year weather will provide the targeted reliability desired, even allowing for the real possibility (about 13%) that demands in any year will exceed these target demand levels used in the planning. A peak temperature of 101.5 degrees Fahrenheit (that of the one in seven and one half year weather) becomes the basis of their design weather criteria. This can also be expressed in terms of per unit of mean weather peak demand - the target is 81.7/75, or 8.9% higher than demand produced in mean-weather years. Weather Design Criteria Will Invariably Be Above Mean Weather, Possibly Far Above It The weather design criteria calculated for this example was 8.9% above the loading level of mean weather. That particular value is not generalizable. Design weather targets can work out to be anywhere from 5% to 15% higher than mean weather, depending on a number of factors. However, design weather is nearly always significantly above demand at mean weather, due mainly to the nonlinearity of the peak demand versus BEAR relationship (Figure 6.14). However, non-linearities in the relationship between T, H, I and demand, and nonsymmetries in the probability distribution of expected weather also influence the design criteria's margin over mean-weather demand levels. If the probability distribution of expected weather is symmetrical, and if both the relationship between weather (T, H, and I) and demand, and that between EEAR (or other metric being used) and peak demand are both linear, then the design criteria would be mean-weather demand. This is very rarely the case. Design Criteria Can Be Tailored to Areas and Circumstances in the System A utility can, and probably should, develop and apply different weather design criteria to each distinctly different micro-climate region within its service territory. In general, these will all be based upon the same EEAR target, but the resulting criteria will vary depending on: the sensitivity of peak demand to weather, the extremeness of the weather, and the frequency distribution of that extreme weather. In addition, the utility can vary the EEAR that it uses as a design criteria by area, or for particular facilities or projects (a power quality park, a downtown area where continuity of service is judged to be of critical importance) where it wishes to put a special emphasis on reliability. Either of these "multi-criteria" approaches involves a bit more work, in that the criteria have to be determined individually for every individual situation, but otherwise it is straightforward.
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6.7 HOW OFTEN WILL A UTILITY SEE "WEATHER-RELATED EVENTS?" The relationship between operating reliability of a power delivery system and weather demand is very non-linear, whether measured by HEAR (Figure 6.14) or any other representative metric. It is important to understand the way that these weather-related reliability problems manifest themselves. In years where the weather is anything from extremely mild to average, reliability of the system is expected to be roughly the same. But when weather becomes extreme, reliability quickly deteriorates. What this means for the utility is that there will be very few — essentially no - "average years." Almost all of its reliability problems expected due to variation in weather will be clustered in a few "extreme weather years." There will be many good years, and a few "really bad years." For a more detailed example, return for a moment to the criteria-computation done above (Tables 6.2 and 6.3 and associated discussion). Table 6.2 computed an BEAR of .0226 - two and one quarter times the target - for the system when designed to "average weather." This does not mean that the utility will see two and one quarter times the reliability problem level it expects during every year. Study of the data in Table 6.2 reveals the following: In seven out of ten years (69% of years are expected to be average or milder, the bottom four columns of the table), reliability will be about as targeted In about one out of five years (row three from the top) reliability is expected to be twice as bad as targeted Over half of the total amount of reliability problems the utility can expect, and four-fifths of those above its target limit of .01%, occur in only the most extreme one-eighth (one-in-ten, one-in-twenty) of years. (The top two rows account for .0122 of the.0226 total calculated expected average EEAR ~ see the leftmost column in the table). Thus, the utility that designs its system to average weather will experience many satisfactory years, only to have an occasional "year from hell." What a utility gains when it sets reliability-based design criteria as explained above (Table 6.3), is that it minimizes the number of years in which it can expect severe problems. The portion of years that it can expect service quality to be "generally satisfactory" increases only slightly (from seven-in-ten to about eight in ten in the example). The portion of years in which reliability will be "twice as bad" as the target decreases significantly, from one-in-five to one-in-twenty. And the likelihood of "a year from hell" plunges, from about one out of every eight years to much less than one year out of twenty.
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The Same Weather-Design Criterion Should Apply to Both Normal and Emergency Criteria This clustering of reliability problems into a few years (summer in this case) calls into question the "dual" weather-design criteria approach used by several utilities. With this method, substations and lines are planned to two criteria: a normal loading criterion based on extreme weather and an emergency condition criterion that is based on assuming only average weather. The rationale given for this approach is that extreme weather is infrequent, and that contingencies are also infrequent, and the simultaneous occurrence of both is extremely rare and thus can be reasonably discounted in the planning. But as discussed above, reliability problems cluster into "very rare" summers. And during any entire summer season, extreme or otherwise, a utility will experience contingencies. To see the mistake that develops from this approach, assume that a utility has the weather and demand relationship used in the computation of weather criterion done earlier (Tables 6.2 and 6.3). Also assume that after comprehensive study, a 2 x 25 MVA transformer substation has been planned to serve a maximum peak demand of 50 MVA, this load corresponding to two-in-fifteen year criteria. Assuming a 90% power factor, this 50 MVA substation can serve: 45 MW = 50 MVA x 90% PF and, based on a 184% emergency (four hour) high-stress rating of one transformer, during an outage of one of its two units, it can handle a peak of: 41.4 MW = 25MVA x 90% x 184% Now, the consumer demand that creates 45 MW as measured under "two-infifteen" weather-based design criteria creates only: 41.32 MW = 45.9 MW/1.089 under average summer peak (one-in-two year) weather conditions. Milder weather means lower load levels. (The 1.089 ratio used is the same value developed in the example above while working with Tables 6.2 and 6.3.) Thus, the utility checks the substation and the expected consumer demand against its dual criteria; Criteria for normal operation (2-in-15 year) Expected two-in-fifteen year demand of 45 MW < 50 x 90% Criteria for emergency rating (l-in-2) year Expected one-in-two year demand of 41.3 MW < 25 x 90% x 184%
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Thus, the substation satisfies both criteria if next year's forecast predicts a peak demand of 41.3 MW at average weather conditions (the same load that registers 45 MW at two-in-fifteen year weather conditions). But, if either one of the two transformers fails while at peak demand levels during a two-in-fifteen year summer, the remaining unit must pick up not 184% of its normal rating, but 200%. 200% = 184% x 45MW / 41.3 MW The difference is substantial. The unit will be operating at roughly 9% over its emergency rating, at which level it is absorbing and trying to dissipate 18% (45/41.4)2 more heat build-up than rated for during emergencies. It is much more likely to fail, and it will certainly suffer a much higher loss of life. How likely is the utility to have a problem because of this situation? Were the planners right in saying that simultaneous hot weather and equipment failures were very unlikely to occur? One can determine this in a rather straightforward manner: Roughly twice every fifteen years peak loads will be at or above the designed extreme. Assume these peak periods of 45 MW last only a total of 200 hours or more during these two summers, and that each transformer has a .15% forced outage rate; then, this substation has an expected annual exposure of roughly: Expected peak hours with one transformer = 200 hr x .0015 x 2 transformers = .6hr For something that is expected only during two summers every fifteen years this does not seem like too much risk. But these criteria is being applied systemwide. Suppose the utility has five hundred substations. This means it can expect Total problems system wide = 500 x .6 hr = 300 hours in a two-in-fifteen summer In other words, during a summer with 200 "peak" hours, the utility will experience 300 "severe stress" hours (equipment operating above its emergency rating) somewhere in its system. Very likely this will lead to outages somewhere, sometime. The utility will not meet its operating reliability performance goals. In effect, planning a system using an extreme weather for normal loading criteria and an average weather for emergency criteria produces a design whose reliability is very close to that of a system that is just designed using average weather conditions for both. The "flaw" in the thinking behind the different normal and emergency criteria was in applying a probabilistic context in a contingency-based engineering
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method. Traditional utility engineering contingency analysis methods focus on individual units of equipment (i.e., if transformer E235 fails, what happens?). Applying risk-based probabilistic concepts on this individual-unit basis is valid only if one completes the "probabilistic" paradigm by weighting it by the number of such units in the system - by looking at the utility's total exposure. 6.8
SUMMARY AND GUIDELINES
Extreme Weather Extreme weather occurs infrequently, but creates high peak loads which can stress the power system beyond the limits its planner's intended, unless they anticipate the load levels that this weather can create. One important part of this is determining a reasonable "extreme-ness" for the weather used as the target in planning. There are a number of ways to do this, including one that bases the selection of weather-demand design criterion on reliability targets set for the system. Regardless, the nature of extreme weather, and the reliability characteristics of a typical power system, mean that typically a utility can expect to see from two to three times the reliability problems it would anticipate if it assumed that all weather would be average weather. In addition, the utility's planners must keep in mind that if they "under design" the system with respect to weather, the reliability problems inherent in their system do not manifest themselves over all years. Instead, they will cluster into a few "years from hell" among a majority of years when the system will perform adequately. In years with extreme weather, the system is quite likely to have ten times the number of events that challenge operators or lead to outages. The cumulative impact of such a prolonged period of reliability problems on consumer satisfaction and public and political confidence in the utility can be severe, and quite beyond what it would be if the problems were in fact spread evenly over all years. Design Criteria Determination The weather design criteria (8.9% above mean weather loads) found in section 6.5's example above is not generalizable to all utilities, but the method used to obtain it is. It produces sound "weather adjustment" of forecasts in the sense that their adjustment leads to planning that will achieve the target levels of service reliability. As mentioned above, the example was simplified so it would fit in the amount of space available here, and in order to remove extraneous elements to focus on the overall concept. Key elements of this approach are:
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1. A relatively long (multi-decade) history of weather data for the analysis base to determine the likelihood of various levels of extreme weather. Planners must evaluate extreme weather on the basis of factors that contribute to both peak demand and overall energy: a.
Peak - usually a multi-hour average of weather prior to the time of peak on the same day, and the temperature or cooling degree hours early in the day, contribute most to the value of the peak demand.
b.
Energy - usually total seasonal cooling degree hours, and/or average peak daily temperature or average temperature for the season, correlate best with the energy usage over the entire season.
Planners should endeavor to identify "extreme years" that are extreme in both categories (usually this is the case, at least to a reasonable extent). 2.
Development and use of an accurate equation(s) and analysis to relate peak demand, energy, and demand duration curves to weather, generally on the basis of a historical demand-weather analysis covering a much shorter (e.g., ten years) and more recent period than the entire weather history data period.
3.
Translation of extreme weather scenarios, using the results of steps (1) and (2) above, into a set of normalized load duration curves for the year.
4.
HEAR or similar analysis that ties service reliability levels (the result of the power system equipment being in service) to equipment design and demand levels.
5.
Evaluation and determination of the weather criteria target in terms of "one-in-N" year likelihood of occurrence, as explained above, but using more "slices" of the probability distribution, or an actual probability distribution based computation.
6.
Forecasts should then be produced that correspond to future demands under the identified weather conditions that give an expected reliability level as desired: a.
If trending methods are being used, historical demand data upon which they are based should be normalized to the design weather conditions (in the example case, all historical data would be adjusted to peak temperatures of "101.5°F"). These demands are then used for the trending.
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If simulation or hybrid spatial forecasting methods are used, the demand history or end-use demand models upon which the simulation is calibrated should be adjusted to a "101.5°F" day. Usually, the curve shapes for an actual "101.5°F" day are used, but adjusted to the normalized peak demand determined by the weather adjustment for temperature, (i.e., an equation such as 5.7 is used to determine the scale for peak demand of a demand curve shape taken from an actual "101.5°F" day).
Thus, regardless of what type of forecasting method is used, historical demand data need to be normalized to the weather design criteria. Although normalization to any standard provides all the adjustment needed to compare histories and track trends, forecasting for effective planning requires that load histories be adjusted to the -weather design criteria. Beyond the use of this method for determining and justifying a weatherdemand design criterion, a utility should: Apply this to determine area-specific criterion for various microclimate areas within the system. Vary the reliability target that leads to the weather criterion, when situations call for differentiated levels of reliability at various places in the system.
REFERENCES R. E. Brown, Electric Power Distribution Reliability, Marcel Dekker, New York, 2002. R. E. Brown, S. Gupta, R. D. Christi, S. S. Venkata, and R. D. Fletcher, "Automated Primary Distribution System Design: Reliability and Optimization," IEEE Trans. Power Delivery, Vol. 12, No. 2, pp. 1017-1022, April 1997. R. E. Brown, A. P. Hanson, H. L. Willis, F. A. Luedtke, and M. F. Born, "Assessing the Reliability of Distribution Systems," IEEE Computer Applications in Power, Vol. 14, No. 1, January 2001.
7 Spatial Load Growth Behavior
7.1 INTRODUCTION Every T&D plan is based on a load forecast, whether it is only a vague, informal idea in the mind of the planner, or a detailed projection produced by a computer program. The load forecast defines the "T&D planning problem," and, as the first step in the planning process, is in many ways the most important. A poor load forecast will mislead the planner, causing him to design the wrong type of system expansion plan. By contrast, a good forecast simplifies his job, showing the planner what needs to be done in the future expansion of the power delivery system facilities. This chapter discusses distribution load, how it grows, and how it "looks" when examined for T&D planning and engineering purposes. It is the first of two that will focus on the spatial aspects of load forecasting, as opposed to temporal (Chapter 2 - 4 ) and weather-related factors (Chapters 5 - 6). A thorough understanding of spatial behavior is critical not only to forecasting, but to planning in general: Know your enemy A point stressed in this chapter is that when viewed at the small area level, load growth trends can look substantially different than when viewed at the system level. The reasons this occurs, and the manner in which this phenomenon shapes the way T&D loads must be forecast, are among the most important concepts covered in this chapter.
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7.2 SPATIAL DISTRIBUTION OF ELECTRIC LOAD Load density varies from one location to another within an electric utility's service area, as shown in Figure 7.1. In sparsely populated rural areas the density of peak electric load may be less than 1 kVA per square mile, while in the downtown core of a large city it can exceed 1 MVA per acre. Where densities are high, local distribution capacity must also be high in order to meet the demand. Where densities are low, correspondingly less capacity is needed. Thus, in order to plan a power distribution system, the planner must locate his equipment in proportion to the local demands, concentrating large amounts of transmission, substation, and feeder capacity in the urban core of a large city, and distributing capacity sparsely in rural areas, where there is little load. To plan properly the locations and capacities of future equipment, and minimize their cost while still assuring they can do the job, a distribution planner needs information on the location and magnitudes of the future distribution loads ~ where and how much load will there be?
1992 LOAD DENSITY Shading indicates load level
Figure 7.1 Computer-generated map of peak electric load density for a medium-sized coastal city. Shading indicates relative load density at time of annual system peak load. This shows the pattern of spatial distribution common to most cities: high density in an urban core, dropping with distance out to the periphery, with wide tendrils of slightly higher load density extending outward along major transportation corridors.
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Table 7.1 Typical Load Densities for Different Types of Areas Type of Area Urban
Suburban
Rural
Construction Dense, high rise Low rise office/prof. Retail Residential - dense Retail Office/Ind. Park Residential Residential Agricultural - non irrigation Agricultural - irrigation
kVA/acre 600 - 3000 50 - 750 50 - 300 10-60 10-100 5-50 2-25 3-15 005- .1 25-3
Load Density Varies with Location, Mostly Because of Land Use Type Figure 7.1 illustrates how load density varies as a function of location within a power system. Analysis of load in terms of kW/acre or MW/square mile is a convenient way of relating it to local T&D capacity needs and is often used in power delivery planning. Load density is an important aspect of T&D planning, since the capacity and location requirements of T&D equipment depend on local load characteristics, not system averages. Typical ranges of values for urban, suburban, and developed rural areas are given in Table 7.1. The values shown are typical, but values specific to each particular system should be obtained by measurement. Growth Drives System Expansion Figure 7.2 (same as Figure 1.1) shows expected long-term expansion of peak demand in a city in the central United States. These two decades of growth will add 1,132 MW to the load the metropolitan power system will be expected to serve. During the intervening 20 years, additions and changes to the system must be made so that it can grow along with the load. The utility's expansion budget will be well spent only if the equipment is located, and locally sized properly, to match the evolving load pattern shown.
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1991 WINTER PEAK 2310MVA
2011 WINTER PEAK 3442MVA i'^ttS*-*
t>,*,:t :rr™ ». .:
N * "&' •= «y'iff;'<*:tf*
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1
'*$$$
Ten miles
A
B
C
D
Figure 7.2 Maps of peak annual demand for electricity in a major American city, showing the expected growth in demand during a 20 year period. Letters and arrows indicate points described in text below.
Comparison of the 1992 and 2012 load maps in Figure 7.2 reveals several characteristics of load growth as it affects T&D systems: 1. Previously vacant areas develop load. This is shown by point A. There are others (the entire northeast corner of the city). 2. Some vacant areas do not grow. Point B indicates one such point. There are many others shown also. 3. Load in some developed areas increases in load density. Point C shows the center of one area of existing-area load growth. 4. Load in some developed areas remains constant, or falls slightly due to increasing appliance efficiency in areas that otherwise remain unchanged. Points E and F indicate such areas.
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Small Area Analysis of Load The locational aspects of distribution load growth — the where of a forecast « is handled by dividing the utility service area (or the region being studied, if it is a subset of the utility's service area) into a number of small areas. The most popular modern technique used to define the small areas is a grid that divides the study region into square areas, with each square small area being perhaps a half or a quarter mile wide, as shown in Figure 7.3. Consumer and load data are collected for every small area and a forecasting method of one form or another projects the future load for each, providing a load forecast which is geographic in nature (Willis and Northcote-Green, 1983). Alternately, a forecast may be done on a polygon area basis, in which the small areas are of irregular shapes and sizes. The most popular polygon small area method is a forecast by equipment area basis, as shown in Figure 7.4. In this approach, the peak loads for feeders, substations, or transmission regions are forecast directly, for example, by extrapolating the last five years of recorded peak loads for each. Regardless of whether done on a substation, feeder, or collector node basis, these equipment-oriented forecasts are small area forecasts. The planner has simply let the system configuration define the small areas, the small areas being the service area of the feeder and substations whose load is being forecast (Menge, 1977). Equipment-Oriented Versus Grid-Based Methodology Forecasting by equipment area has two major advantages over the grid method. First, the forecast relates directly to the equipment being studied ~ a feeder-byfeeder forecast gives the planner a projected load for each feeder. At a glance, he can tell whether the forecasted load is above or below the feeder rating, and thus whether some corrective action (reinforcement, switching, etc.) may be needed in the future. Equipment-oriented forecasts are very good at alerting the planner to a possible problem. Such capacity-shortfall warnings are one of the key reasons forecasting is done, and the direct applicability of equipment-oriented forecasting to this need is perhaps its strongest advantage. Equally important to many planners, equipment-oriented forecasting usually requires less data than forecasting with a uniform grid approach. Almost every utility has records of past annual peak feeder and substation loads, readings the planner can usually find with little effort. By contrast, the spatial land-use and other data on a small area basis, required for grid-based methods, can require somewhat more time and effort for collection, mapping, and data management. This reason, alone, has made equipment-based methods and the algorithms most compatible with them popular with some utilities.
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Figure 7.3 A popular method of addressing the "where" aspect in a spatial load forecast is to segment the region studied with a grid of small areas (above). Location within the grid provides the locational information needed by the distribution planner.
EQUIPMENT FORECASTING AREAS Substations 5 miles
Figure 7.4 An alternative approach is to let the distribution equipment itself define the small areas, for example, forecasting by substation area.
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Unfortunately, equipment area based methods have shortcomings that severely limit their usefulness, limitations not shared by most grid-based methods. Foremost among these is poor spatial resolution. A feeder-by-feeder forecast gives no details about how the load is distributed within each feeder area. Without that detailed information, it is often impossible to properly plan reinforcements, switching changes, and new equipment to handle the overload. In general, forecasts done on an equipment basis at a particular level of the distribution system do not provide enough geographic resolution to solve planning problems at that level ~ feeder-oriented forecasts do not provide sufficient "where" information to permit accurate planning of feeder layout, routing, and capacities. Spatial resolution is one advantage of grid-based forecasts, for they generally cover a study region with from ten to one hundred times as many small areas as there are feeders. These smaller areas provide more detail about where the load is, generally enough locational information to support the feeder planning. But this improvement is not without its price. There are more small areas to analyze and forecast, and more data to collect, than in a feeder-by-feeder forecast. That means higher data costs and considerably more computer memory and solution time requirements. Data and data collection for grid forecasting methods are not nearly the problem that one might think at first glance. A considerable amount of research during the 1980s and 1990s established a number of methods for building grid data bases rapidly. In addition, land-use bases, geographic background maps, and numerous geographic processing systems have evolved to make preparation of such data almost automatic. In addition, up-to-date land-use and demographic data bases are generally available from municipal sources or third party companies at nominal cost. As a result, the data collection effort is seldom the deciding factor against using a grid-based method. The chief advantage of the grid-based approach is its compatibility with simulation-based forecasting algorithms, currently the most accurate distribution load forecasting methods. Many of these algorithms depend on the fact that all the small areas are the same size and shape — they can only be applied to grids. In addition, the author prefers grid-based forecasting methods precisely because they do not associate the load forecast directly with equipment. An equipment-oriented forecast may give a capacity alarm, alerting the planner to a potential problem, but it also focuses the planner's attention on individual units of equipment, so that he may not be able stand back and take a fresh look at the load pattern. For example, an equipment-oriented forecast which projects that Eastside substation's load will exceed its capacity can easily put the planner into a mindset that the solution to the problem lies with Eastside substation, when in
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fact the best solution is to transfer load onto neighboring substations, and reinforce one of those. The grid and equipment oriented small area approaches each have advantages that make them the preferred approach in some situations. The planner who understands the implications of each approach should not hesitate to pick the method he feels is best. There are forecasting methods in wide use that employ each approach, as we will see in Chapters 9 through 17. Small Area, Spatial, and Geographic Forecasts Before going further, it would be best to define three terms that are often misused. These are the terms small area, spatial, and geographic, as applied to electric load forecasts. Each has a slightly different meaning. A small area forecast is a forecast done on a small area basis for distribution planning. The service area is divided into areas sufficiently small to be of use for distribution studies and a forecast is produced for each small area. It does not matter what size the small areas are, or if they are defined by a grid or by the equipment. The result is called a small area forecast. A spatial forecast is a small area forecast in which the forecasting of all small areas is done on a common, coordinated basis. All spatial forecasts are small area forecasts, but some small area forecasts may not be spatial forecasts. As will be shown later, some small area forecast methods treat each small area as a separate entity, forecasting it without any regard for the forecasts produced for its neighbors and without using any of the information available for areas outside that one area. By contrast, spatial forecasts "look outside" each small area, often basing their prediction of the future load in each particular area on considerations and data that are part of a larger picture, and coordinating the forecasting of each individual small area so it is consistent with those of other areas. Comparison data in Chapter 17 will show that the improvement in quality brought about by a spatial approach can be dramatic. The difference between a spatial forecast and a small area forecast is one of technique or algorithm and consistency of application, not small area sizes or definitions. Geographic forecasts are forecasts which divide the service territory into areas too big for distribution planning needs. For example, a county-by-county forecast for all of Georgia or a forecast of the nine hundred plus regions inside the Bonneville Power Administration's delivery territory are forecasts used for transmission and generation operations studies, not distribution planning. Technically a geographic forecast is done on a "small area" basis, but the areas are so large that it is seldom referred to as a "small area forecast."
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7.3 SMALL AREA LOAD GROWTH BEHAVIOR Two Causes of Load Growth Peak demand and energy usage within a utility system (Figure 7.5) grow for only two reasons. All growth is due to one or a combination of both: 1. New consumer additions. Load will increase if more consumers are buying the utility's product. New construction and a net population in-migration to the area will add new consumers and increase peak load. With more people buying electricity, the peak load and annual energy sales will most likely increase. 2. New uses of electricity. Existing consumers may add new appliances (perhaps replacing gas heaters with electric) or replace existing equipment with improved devices that require more power. With every consumer buying more electricity, the peak load and annual energy sales will most likely increase. There are no other causes of load growth. Similarly, any decrease in electric demand is due to reductions in either or both of these two factors. Regardless of what happens to the load, or how one looks at load growth or decline, change in one or both of these two factors is what causes any increase or decrease in peak and energy usage. The bulk of load growth on most power systems is due to changes in the number of consumers. North American electric utilities that have seen high annual load growth (5% or more) have experienced large population increases. Houston in the 1970s, Austin in the 1980s, Branson, Missouri, and the upper Rio Grande valley in the 1990s, Wilmington, NC, and Las Vegas in the 2000s, all experienced annual increases in peak load of 5% or more for many years at a time, due almost exclusively to new consumers moving into the service territories. Load growth caused by new consumers who are locating in previously vacant areas is usually the focus of distribution planning, because this growth occurs where the planner has little if any distribution facilities. Such growth leads to new construction, and hence draws the planner's attention. But changes in usage among existing consumers are also important. Generally, increase in per capita consumption is spread widely over areas with existing facilities already in place, and the growth rate is slow. Often this is the most difficult type of growth to accommodate, because the planner has facilities in place that must be rearranged, reinforced, and upgraded. This presents a very difficult planning problem.
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Load in new areas
increase in density
Figure 7.5 Load growth occurs both as new loads in previously vacant areas and as increases in the density of existing loads, as shown here in a twenty-year projection of load growth for a portion of the utility area from Figure 7.1.
Load Growth at the Small Area Level When viewed at the small area basis, electric load growth in a power system appears different than when examined at the system level. This phenomenon is fundamental to distribution load studies, affecting all types of forecasting methods, whether grid-based or equipment-oriented, and regardless of algorithm. Consider the annual peak electric load of a utility serving a city of perhaps two million people, as shown in Figure 7.6. For simplicity's sake, assume that there have been no irregularities in historical load trends due to factors such as weather (i.e., unusually warm summers or cold winters), the economy (local recessions and booms), or utility boundary changes (the utility purchases a neighboring system and thus adds a great deal of load in one year). This leaves a smooth growth curve, a straight line that shows continuing annual load growth over a long period of time, as shown in Figure 7.6. When divided into quadrants, to give a slight idea of where the load is located, the city will still exhibit this smooth, continuous trend of growth in each quadrant. The total load and the exact load history of each quadrant will be slightly different from the others, but overall each will be a smooth, continuous trend as shown in Figure 7.7.
213
Spatial Load Growth Behavior HISTORICAL LOAD TREND
MAP of CITY
1960
1970
1980 VERB
1990
Figure 7.6 Annual peak load of a large example city, discussed here, over a fifty-year period is relatively smooth and continuous.
1950
Northwest
Northeast
VEflR
YEflR Southeast
2000
Southwest
1950
VEflR
2000
1950
VEflR
200
°
2000
Figure 7.7 Dividing the city into four quadrants and plotting the annual peak load in each results in a set of four growth curves, all fairly smooth and showing steady growth.
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Subdivide again, dividing each quadrant into sub-quadrants, and examine the "load history" of each small area once more, looking for some typical pattern of behavior. Again, the resulting behavior is pretty much as before. The typical subquadrant has a long-term load history that shows continuing growth over many years. If this subdivision is continued further, dividing each sub-quadrant into subsub-quadrants, sub-sub-subquadrants, and so forth, until the city is divided into several thousand small areas of only a square mile, something unusual happens to the smooth, continuous trend of growth. Each small area has a load history that looks something like that shown in Figure 7.8, an "S" curve, rather than a smooth, long-term steady growth pattern. The S curve represents a load history in which a brief period of very rapid growth accounts for nearly all of the longterm load growth. When analyzed on a small area basis, there will be tens of thousands of small areas, and every one will have a unique load growth history. Although every small area will vary somewhat, the typical, or average, growth pattern will follow what is known as an S curve ~ a long dormant period, followed by rapid growth that quickly reaches a saturation point, after which growth is minimal. The S curve, also called the Gompertz curve, is typical of small area, distribution-level
MAP of CITY
HISTORICAL LOAD TREND
10
20
VEflR
Figure 7.8 Example of the typical growth behavior of a mile-square small area within the city. Once divided into "small enough" areas, growth in any region will display this characteristic. The 640-acre area experiences almost no growth for many years; then a period of rapid growth which lasts only a decade or slightly more will "fill it in."
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load growth (EPRI, 1979). Each small area will differ slightly from the idealized, average behavior, but overall, the S curve shown in Figure 7.8 represents load growth behavior at the distribution level very well The S curve has three distinct phases, periods during the small area's history when fundamentally different growth dynamics are at work. Dormant period. The time "before growth", when no load growth occurs. The small area has no load and experiences no growth. Growth ramp. During this period growth occurs at a relatively rapid rate, because of new construction in the small area. Saturated period. The small area is "filled up" — fully developed. Load growth may continue, but at a very low level compared to that experienced during the growth ramp. What varies most among the thousands of small areas in a large utility service territory is the timing of their growth ramps. The smooth overall growth curve for the whole (Figure 7.6) occurs because there are always a few, but only a few, small areas in this rapid state of growth at any one time. Seen in aggregate — summed over several thousand small areas ~ the "S" curve behavior averages out from year to year, and the overall system load curve looks smooth and continuous because there are always roughly the same number of small areas in their rapid period of growth. This explanation should not surprise anyone who stops to think about how societal growth occurs. A typical city began as a small town, and grew outward as well as upward. As it expanded, most of its growth occurred on the periphery -- the suburbs. The average small area's "life history" is one of being nothing more than a vacant field until the city's periphery of development reaches it. Then, over a period of several years, urban expansion covers the small area with new homes, stores, industry, and offices, and in a few years the available land is filled ~ there was only so much room. Then, growth moves to other areas, leaving the small area in its saturated period. Growth patterns in rural areas are similar, merely occurring at lower density and sometimes over slightly longer S periods.
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Of course, the actual characteristics of growth are not quite this simple. Often growth leapfrogs some areas, only to backtrack later and fill in regions left dormant. Sometimes a second S growth ramp occurs many years later, as for example when an area that has been covered with single family homes for several decades is suddenly redeveloped into a high rise office park. However, the S curve behavior is sufficient to identify the overall dynamics of what happens at the distribution level. Examining this in detail leads to an understanding of three important characteristics of growth. 1. The typical S curve behavior becomes sharper as one subdivides the service territory into smaller and smaller areas. The average four square mile area in a city such as Denver or Houston will exhibit, or will have exhibited in the past, a definite but rather mild S curve behavior of load growth, with the growth ramp taking years to fill in. The average growth
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behavior at one square mile resolution will be sharper — a shorter growth ramp period. The average, typical load growth behavior will be sharper still at 160 acres (small areas 1/2 mile wide ), and so forth, as shown in Figure 7.9. The smaller the small areas become (the higher the spatial resolution) the more definite and sharper the S curve behavior, as shown in the figure. Carrying the subdivision to the extreme, one could imagine dividing a city into such small areas that each small area contained only one building. At this level of spatial resolution, growth would be characterized by the ultimate S curve, a step function. Although the timing would vary from one small area to the next, the basic life history of a small area of such size could be described very easily. For many years the area had no load. Then, usually within less than a year, construction started and finished (for example's sake, imagine that a house is built in the small area), and a significant load was established. For many years thereafter, the annual load peak of the small area varies only slightly — the house is there and no further construction occurs. 2. As the utility service territory is subdivided into smaller and smaller areas, the number of small areas that have no load and never will have any load increases. A city such as Phoenix or Atlanta will have no quadrants or subquadrants that are completely devoid of electric load. When viewed on a square mile basis (640-acre resolution) there will likely be very few "completely" vacant areas — a large park or two, etc. But when chopped up into acre parcels, a significant portion of the total number will be "vacant" as far as load is concerned, and will stay that way. Some of these vacant areas will be inside city, state, or federal parks, others will be wilderness areas, cemeteries or golf courses, and many will be merely "useless land" ~ areas on the sides of steep mountains and inside flood-prone areas — where construction is unlikely. Other vacant areas, such as highway and utility rights-of-way, airport runways, and industrial storage areas, are regions where load is light and no "significant" load will ever develop. Figure 7.10 shows the percentage of small areas that have no load, as a function of spatial resolution, for areas within the limits of a large city. 3. The amount of load growth that occurs within previously vacant areas increases as small area size is decreased. When viewed at low spatial resolution (i.e., on a relatively large-area basis) most of the growth in a city over a year or a decade will appear to occur in areas that already have some load in them. But if a city or rural region is viewed at higher spatial
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resolution, for example on a ten-acre basis, then a majority of new consumer growth over a decade occurs in areas that were vacant at the beginning of the period (Figure 7.11). Thus, the observable dynamics of load growth are heavily linked to the spatial resolution used in the load analysis, as illustrated in Figures 7.10 and 7.11. As spatial resolution is changed, the character of the observed load growth changes, purely due to the change in resolution. At low resolution (i.e., when using "large" small areas) load growth appears to occur mostly in areas that already have some load in them. Its behavior is a long-term, steady load growth trend, with few if any areas vacant (without some amount of load in them). Such steady, omnipresent growth is relatively easy to forecast. But if this same load growth is viewed at high resolution, most of the growth appears as sharp bursts of growth, lasting only a few years. Many small areas have no load, and the majority of load growth will occur in such vacant areas, yet not all vacant areas will develop load — some will stay vacant. This type of behavior is relatively difficult to trend because it occurs as brief, intense growth, often in areas with no prior data history from which to project future load. The reader must understand that the three phenomena discussed above occur only because the utility service territory is being divided into smaller areas. By asking for more spatial information (the "where" of the distribution planning need) the planner changes the perspective of the analysis, so that the very appearance of load growth behavior appears to change. High spatial resolution (very small area size) makes forecasting load a challenge, calling for forecasting methods unlike those used for "big area" forecasting at the system level. Causes of Load Growth and Their Relation to S-Curve Shape The two causes of load growth mentioned earlier — new consumers or expanding usage by existing consumers - are tied to different parts of the S curve, as shown in Figure 7.12. The growth ramp occurring over a short period of time is due to new consumers in the area. The slow, steady growth thereafter is due to increasing per capita usage by the consumers in the area. Regions "Fill Up" in a Discontinuous Manner Figure 7.13 shows another perspective on "S" curve growth behavior at the distribution level, and reveals another implication of this growth behavior. The figure shows growth of electric load in a region of about 24 square miles on the northeast perimeter of a very large, growing metropolitan area, over a 12-year period. Individual land areas within this region generally follow the "S" curve growth behavior pattern, with a growth ramp (period from 10% to 90% of
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eventual saturated load) of about three years at the % square mile resolution. As one would expect from the type of spatial coupling of S-curve growth behavior discussed above, the complete area has a much slower growth rate. Overall, the region has a growth ramp of about 15 years. The growth within this area was geographically discontinuous, with the timing of initiation of growth of the various parcels somewhat, but not completely, coupled, so they displayed a partially random pattern. While growth usually develops from the southwest (this area is on the northeast edge of the metropolitan area), the timing of just when a parcel of land begins to develop is somewhat random. Thus, growth does not develop as a smooth trend outward, but instead appears to be a semi-random process. Once load has filled up one parcel, it does not automatically proceed to the next in line, but may jump to another area nearby, but not adjacent. Therefore, early in the process of growth for this whole area, some parcels develop to saturation on its far edge early in the process. The most unpredictable aspect of small area load growth is the exact timing of parcel development.
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In contrast, experience and research has shown that the eventual load level in most small areas can be predicted fairly well, as can the expected duration of growth ramps. However, the exact tuning of growth appears to be somewhat random, at least as viewed from a priori information likely to be available to the planner. Implications for T&D expansion are clear. The system cannot be extended incrementally outward from the southeast as load grows. Instead, substation siting and feeder expansion must deal with delivering "full load density" to an increasing number of neighborhoods scattered over the entire region, that develop geographically into a higher overall density. This means that full feeder capability (maximum designed load and maximum designed distance) may be needed far sooner than predicted by the "gradually increasing density" concept. Such expansion is difficult to accomplish economically: feeders must be extended over much of this area early in the 12-year period, so the utility can serve the widely scattered pockets of high load density. Great capacity is not needed at that time, because the overall load is not high. However, a good portion of all the routes eventually needed is required early, in order to reach these disparate locations. An economic dilemma develops because the utility will eventually need a good deal of capacity in these routes when the load fills in the area, but planners do not want to incur the cost of building now for load levels not expected for 10-12 years. The challenge is to find a way to expand the system without building a majority of the routes early, or having to build many long routes with higher capacity than will be needed for years. Redevelopment and "S" Curves Chapter 19 will discuss the process of redevelopment and ways to model it in spatial forecast models. Approximately 25% of electric load growth in a metropolitan area occurs due to replacement of older buildings and land usage with high-density loads/more intense use of the land, and in some systems redevelopment accounts for most electric load growth. Figure 7.14 shows the concept of the redevelopment series, which will be discussed in much more detail in Chapter 19. Basically, the really high-density areas of development in a city developed through several stages of transition, each accompanied by an S-curve growth ramp. In between these transition periods, development and load growth were fairly stable. The archetype redevelopment concept is the replacement of old, low-rise offices and warehouses on the outskirts of a downtown area by new high-rise, as the metropolitan core expands outward as well as upward. But in fact there are many more examples. Redevelopment occurs throughout a metropolitan region, usually in areas where the average building age is 35 years or older, but occasionally in areas only about half that old (Figure 7.15).
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Time
Figure 7.14 Theoretical "S" curve small-area growth history over the very long term, showing how an area redevelops several times on its way from sparse unused land to urban core high-rise.
Figure 7.15 Annual peak load history in a section (640 acres) NNW of the intersection of US-59 and Loop 1-610 in Houston, that displays three S-curve transitions. This example will be discussed in more detail in Chapter 19.
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Redevelopment is mostly linked to cause 1 of the two causes of load growth new consumers. There are a number of different drivers behind redevelopment: Urban core growth occurs in downtown areas where space is at a premium and the city grows "up, not just out." Strategic initiatives involve deliberate efforts on the part of local, state or even federal government to change the character of a city by changing the land use of one (now important) part of it. Tactical load growth is localized, opportunistic growth, basically actions by land owners and developers to take advantage of the greater value parcels have. Redevelopment in kind occurs when homeowners and businessmen rebuild or upgrade existing buildings. Urban core, strategic, and tactical redevelopment all change the land use in a small area(s). Essentially they are part and parcel of the load growth cause 1, new consumer development. In a way they do cause new electric consumers (at least a new type, in higher density) to locate in a small area. Redevelopment in kind can be viewed more as cause 2, a change in usage. Redevelopment causes, behavior, and forecasting will be discussed in much greater detail in Chapter 19. The important point here is that it manifests itself as growth ramps within the basic S-curve behavior pattern described earlier. "Putting Out Fires" Is the Norm in T&D Expansion T&D planners often speak about "putting out fires" - having to develop plans and install equipment and facilities on a tight time schedule, starting at the last moment, without proper time to develop comprehensive plans or coordinate area development overall. A point illustrated here is that the load growth aspect of this situation is the norm: rapid growth that starts with little warning, fills in an area relatively quickly, and then moves elsewhere not only happens on a regular basis, but is the normal mechanism of growth. The "S Curve" growth characteristic, its tendency to be sharper in smaller areas, and the semi-random, discontinuous pattern of load development described above, are very general characteristics that affect all power systems. Load development in a small area almost always begins with little long-term warning, grows at a rapid rate to saturation, and then moves to other areas, usually near by, but often not immediately adjacent. This growth characteristic is the basic process that drives T&D expansion, equipment additions, and the planning and engineering process. T&D engineers will never change the nature of load growth and development. The recommended
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approach is to develop planning, engineering, and equipment procurement procedures that are compatible with this process. These include: a) Master plan development based on projected area development. As noted above, the eventual load density for any small area, and the overall pattern of development for a region, can be predicted with reasonable accuracy fairly far in advance. Thus, long-range plans optimized to the expected pattern of development can be developed. b) Use of modular system layouts for transmission, substations, feeders and service (low voltage) parts of the system, that permit modular expansion on an incremental parcel basis. Some types of layout are more expandable on a "fill in the parts" basis that others. In particular, the growing use of multi-branched rather than large-trunk feeder layouts is one reaction to this situation. Such feeders can be expanded on a short- range basis, to cover a growing area as needed, yet still fit into an optimized long-range plan. c)
Organization of the planning, engineering, and construction process with short lead times for implementation. Given that a long-range master plan exists for an area, the key to success is a short start-up and lead time for engineering of the details and project implementation, once development begins.
Short-Range and Long-Range Forecasting Chapter 1 briefly discussed the short- and long-range time periods, and the far different planning needs within each time frame, something that will be examined at length later in this book. Not surprisingly, the short- and long-range periods have drastically different forecasting needs. Recall that short-range planning is motivated by a need to reach a decision, to commit to a particular installation or type of construction. What is needed in this time frame is as much detail as possible on the location and magnitude of the load. Accuracy, as measured by the forecast's ability to predict the locations and amounts of future loads, is the only real commodity sought in the short-range forecast. But long-range planning needs are more complicated. Long-range planning is done in large measure to determine just how good the short-range plan will prove in the long run. No commitment need be made to substation and feeder plans ten or more years in the future. Therefore, several long-range plans can be kept accounting for uncertainties in both load growth and the utility's plans itself. Thus, a "long-range forecast" may consist of several different scenarios, or variations, on the pattern of future distribution loads, each a forecast in itself.
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Figure 7.16 Generally, a spatial load forecast produces a series of "load maps" representing annual peak load on a small area basis, or small area loads at time of annual (coincident) system peak load, for a selected set of future years.
The chief reason for the multi-forecast approach is that it is often impossible to predict some of the events that will shape the location of long-range distribution load growth. In such cases, the planner is advised to admit that these factors cannot be forecast, and to run several "what if studies, analyzing the implications of each event as it bears on the distribution plan. This is called multiple scenario forecasting. Timing of Forecasts In general, a planner does not produce a plan for every future year, but instead studies a series of significant future years, for example, two, five, ten, fifteen, twenty, and twenty-five years out. The forecast must mirror this same series, producing a "snapshot" of the future loads in each small area for each future year, as shown in Figure 7.16. Multiple Scenario Forecasting The locational aspect of electric load growth is often very sensitive to issues that simply cannot be predicted with any dependability. As an example, consider a new bridge that might be planned to span the lake shown to the northwest of the city in Figure 7.17, and the difference it would make in the developmental patterns of the surrounding region. That lake limits growth of the city toward the
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northwest. People have to drive around it to get to the other side, which is a considerable commute, making land on the other side unattractive as compared to other areas of the city. As shown in Figure 7.17, if the bridge is completed it will change the shape of the city's load growth, opening up new areas to development and drawing load growth away from other areas. The reader should make note of both of the bridge's impacts: it increases growth to the northeast, and it decreases growth in the eastern/southern portions of the system. But the construction of this new bridge might be the subject of a great deal of political controversy, opposed by both environmentalists concerned about the damage it could cause to wilderness areas, and by community groups who believe it will raise taxes. Modern simulation forecasting methods can accurately simulate the impact such a new bridge will make on load growth, forecasting both of the "with and without" patterns shown in Figure 7.17. But these and other forecasting methods cannot forecast whether the bridge will be built or not. A future event that causes a change in the amount or locations of growth is called a causal event. Very often, critical causal events such as the bridge discussed above simply cannot be predicted with any reliability (Willis and
No bridge
Bridge across lake
Figure 7.17 A portion of the area covered by the "base load map" in Figure 7.1, showing the addition of load growth over the next ten-year period under two different scenarios. At left, growth continues as it has in the past, with the lake to the northwest of the city standing as a barrier to growth in that direction. At right, a new bridge spans that lake, bringing areas on the other side of it into close proximity to downtown and drawing growth away from the southeast and east sides of the system.
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Tram, 1993). A decision to lower taxes in the inner core of a large city, in order to foster growth there and avoid "commercial flight" to the suburbs, is a similar case. Other situations might be a major new factory or large government facility, announced and planned, but still uncertain as to exact location and timing within the utility service territory. In such situations the planner may be better off admitting that he cannot accurately forecast the causal event(s), and do "what if planning to determine the possible outcomes of the event. By doing multiple-scenario forecasts that cover the variety of possible outcomes, the planner can alert himself to the consequences of such unpredictable events. At the very least, he can then watch these events with interest, against the day a decision must be made, knowing what impact they will have and having an idea how he will respond with changes in his plan. Hopefully though, he can rearrange those elements of his plan that are sensitive to the event, so as to minimize his risk, perhaps pushing particularly scenario-sensitive elements into the future and bringing forward other, less sensitive items. In the example shown in Figure 7.17, the net impact of the bridge is to shift growth from the east and south areas of the city to the area west of the lake. Either way, three new substations are needed by the year 2002. However, their locations differ depending on the outcome. If the bridge is completed load growth will move outward past the lake. One substation will be needed there and only two, not three, will be needed further in toward the city. The challenge facing the planner is to develop a short-range plan that doesn't risk too much in the event that one eventuality or the other occurs. He must develop a short-range plan that can economically "branch" toward either eventuality — a plan with recourse. Such planning is difficult, but not impossible. The role of multi-scenario forecasting is not to predict which outcome will develop (that is often impossible) but to show the planner what might happen and provide a foundation for analysis of risk among different scenarios. The multi-scenario approach, leading to the development of a plan with the required amount of recourse built into it, is the heart of modern distribution planning, and will be discussed more fully in forthcoming chapters. 7.4 SUMMARY Electric load growth behavior looks different depending on the spatial resolution used to analyze growth trends. The key points covered in this chapter are: • Load growth occurs due to only two causes: addition of new consumers and/or changes in per capita consumption. • At the distribution (small area) level, a load history looks like an S curve, characterized by a brief period of intense growth, followed by a
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saturation period of slower load growth. New consumers are mostly responsible for the sharp rise in the S curve. Per capita consumption defines its slow growth in the "saturated" period. • As spatial resolution is increased (small area size is decreased), the S curve behavior becomes sharper and more step-like. • As spatial resolution is increased (small area size is increased), the fraction of small areas that are entirely vacant increases. • As spatial resolution is increased (small area size is increased), the amount of load growth that occurs in previously vacant small areas increases. • Uncertainty in a spatial load forecast is handled by using multiple scenarios — forecasts representing different assumptions about future causal factors.
REFERENCES Electric Power Research Institute, "Research into Load Forecasting and Distribution Planning," Palo Alto, CA, Electric Power Research Institute, 1979, EPRI report EL1198. E. E. Menge et al., "Electrical Loads Can be Forecasted for Distribution Planning," in Proc. American Power Conf. (University of Illinois, Chicago, IL, Apr. 1977). H. L. Willis and J. E. D. Northcote-Green, Spatial Load Forecasting — A Tutorial Review, Proceedings of the IEEE, February 1983, p. 232. H. L. Willis and H. N. Tram, "Distribution Load Forecasting," Chapter 2 in IEEE Tutorial on Distribution Planning, Institute of Electrical and Electronics Engineers, Hoes Lane, NJ, Feb. 1993.
8 Spatial Forecast Accuracy and Error Measures 8.1 INTRODUCTION Many aspects of T&D system design involve siting and routing, which are functions of location and often critical to overall system efficiency. To determine how well a particular load forecast satisfies these T&D planning needs, it is necessary to determine how well it answers those "where?" requirements, as well as if it identifies the "how much?" needs required for capacity planning. Accuracy definitions and error evaluation methods common to system-level (non-spatial) forecasting are little help, because they address only the magnitudinal aspect, not the locational dimension. Spatial error measures, which simultaneously analyze both error in location and error in magnitude, are necessary to determine how well a forecast matches the T&D planning needs. This chapter discusses spatial forecasting accuracy, along with methods to evaluate spatial error (lack of accuracy in forecasting location) and techniques to determine the minimum amount of spatial accuracy required in a T&D plan. It begins with the concept of locational error — mistakes made in the forecasting of only the location, not the amount, of future load. The spatial pattern of errors — where and how errors are located with respect to one another and to the power system — is shown to be a critical factor in determining how much the errors in a forecast are likely to contribute to mistakes in the eventual plan.
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Evaluation of locational patterns requires error-measurement statistics quite different from more traditional analysis. The method introduced in this chapter is spatial frequency analysis (SFA), a mechanism for dealing simultaneously with both the locational and magnitudinal aspects of any quantity that varies spatially, such as electric load, forecast error, or distribution capacity itself. SFA can be used to compare different forecasting methods, and to compute the required small area size needed to assure that T&D planning requirements are met. In advanced applications, it can also be used to evaluation uncertainty and risk, and estimate the T&D capacity reductions made possible by conservation and load control (Willis and Tram, 1992). But more important than mathematical derivations, analytical method, or advanced applications is the concept of location error itself: that errors in forecast location alone can spoil a forecast's effectiveness, quite independently of whether it correctly forecasts the amounts of load and the T&D capacity required. For that reason this chapter concentrates on examples to illustrate spatial error and its relation to T&D planning requirements. 8.2 SPATIAL ERROR: MISTAKES IN LOCATION Suppose that a power system planner wanted to compare two spatial load forecasting methods to determine which is the best, "best" meaning most accurate for T&D planning. While ease-of-use, robustness, data needs, and flexibility are also important criteria in choosing a forecast method, accuracy is the foremost requirement. Relative accuracy identifies which method is "best." A natural way to compare two forecast methods, A and B, would be to apply both to a problem where the answer is known, for example to forecast 1993 small area loads from 1983 and earlier data, and then compare their results with the known, actual loads. One could perform a test like that outlined in Figure 8.1, a hindsight test in which the actual load as measured on the system is compared to loads that "forecasted" from the ten-year-old data to identify the errors that were made by each forecast method. Presumably, the method with the lowest level of error would be picked for all future forecasting work, under the assumption that its future performance would mirror the advantage it displayed in the test's conducted with historical data. Suppose that such a test procedure were applied to two grid-based forecast methods, each applied to the same 14 by 20 mile study region at a small area size of 160 acres (small areas 1/2 mile across), using data for the year 1983. After comparison to actual loads, their forecasts would give two "error maps" — grids of numbers representing the mismatch (+ or -) that each made in forecasting the actual 1993 load in each small area. These two error maps could be evaluated to determine which is best.
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How would one evaluate the level of error in such error maps? One possible way would be to compute a statistic such as AAV (average absolute value) or RMS (root mean square) of the grid values
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Figure 8.2 Maps showing the errors made by two hypothetical grid-based forecasting methods. Each is identical by normal statistical measures, yet they have far different impacts on distribution planning. Neither is a real-world scenario (not all errors would be exactly plus or minus 500 kVA/small area), but they illustrate the importance of spatial distribution of error, representing the two extremes possible in arranging the "where" of error.
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AAV, RMS, and similar statistics would prove to be of little use in evaluating T&D planning needs, because they do not respond to the where element of error or assess its potential impact on distribution planning, as illustrated in Figure 8.2. Shown are two "error maps," which for the sake of this example can be assumed to be the errors that resulted respectively from forecast methods A and B in the test outlined in Figure 8.1. Each grid map represents an area 20 by 14 miles, covered by a grid of square small areas 1/2 mile on a side (160 acres each), for a total of 1120 small areas. To make this example easy to understand, in each grid there are 560 over errors, represented by a plus sign (+), where load will be said to have been overforecast by exactly 1000 kVA per small area. Similarly, there are 560 under errors represented by a minus sign (-), where error was forecast low by 1000 kVA/small area. Such a forecast situation, where every small area was under- or overforecast by the same amount, is very unlikely to occur in the real world, but it simplifies this example so that the key point is easy to see. Both error maps, A and B, have the same mean error (zero), the same AAV (1,000) and the same RMS value (1000). As far as these and similar statistics are concerned, forecasts A and B are identical in error content and, thus, their suitability for planning as judged by this method. But suppose a distribution planner had used forecast method A as the basis of a distribution plan, with the forecast containing (unknown to him) the errors shown in map A. These errors would have led the planner to overbuild system capacity in the west part of his system by an average of 4 MVA/mile2, while underinvesting in new capacity throughout the east side of the system by a like amount. The impact of these errors would be very serious. Consider the impact of substation planning. The average substation in an urban area covers roughly ten square miles, or about 40 small areas of the size being considered here, so that the average error in planning substations on the east side of the system would be to underplan their capacity by 40 MVA per substation. There would be no nearby substations with sufficient capacity to supplement them when it became clear they were way under actual capacity needs, because all substations in the east part of the system would be similarly under capacity. In exactly the
1 Actually, faced with the lower forecast load growth, the planner would probably build fewer substations, each covering a wider area. But the error impact would be the same. The east side of the system would have about 16 MV A/square mile deficiency in capacity as built and there would be little ability to "fix" the problem economically at a later date, since the only substations which would have substantial capacity margins at that time to assist in the capacity shortfall would be too far away to do any good (those on the west side of the system).
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same way, the western part of the distribution system would have excess capacity ~ a waste of capacity and budget, because being so far away from the south part of the system, that capacity excess would do little good. Only those substations along the centerline of the service area would end up being planned for the correct capacity, the plusses and minuses within their service areas more or less canceling out so that the correct total is planned on a substation basis. Overall, for the majority of substations planned with this forecast the consequences of the errors would be severe and unrecoverable without major expense. It would not have mattered much exactly what type of plan was developed, it would have been seriously flawed with too much capacity built in the west end of the system, and too little in the east. By contrast, despite the identical levels of AAV and RMS, forecast B would lead to no such mistakes. Here, wherever there is an overforecast there is, nearby, an underforecast to cancel it out. Regardless of exactly how a planner might locate substations and divide up the utility territory into substation service areas, the number of pluses and minuses within a substation area of about 40 small areas would nearly always contain enough over- and underforecasts to cancel almost completely. The resulting plan would be much more sound than any derived from forecast method A. Forecast B may contain a good deal of error as evaluated by A A V and similar statistics, but its spatial pattern means these errors make little impact on planning. Note just how completely spatial error dominates the quality of the forecasts in this particular example. Even if the magnitude of every error in Map A were to be reduced by a factor often, to ± 100 kW, while those in B are held at their original ± 1000 kW values, the Map A error pattern would still be more likely to have a negative impact on the T&D plan than Map B. Figure 8.2 was created specifically to illustrate how spatial arrangement alone can influence the error's impact on planning. With all the small area errors of the same magnitude (+ or - 1000 kVA), and in equal amounts (560 of each per map), Maps A and B differ only in how their values are distributed spatially. In fact, they represent the two theoretical extremes of spatial error pattern, something that will be analyzed later in this chapter. Due to their differences in spatial pattern of error locations, one has a very serious impact, the other has almost no impact. The patterns of errors associated with actual load forecasts fall somewhere in between the two extremes illustrated in Figure 8.2 in terms of impact, generally having 'clumps' of positive and negative values, of varying values, interspersed over the map as shown in Figure 8.3. The region shown in Figure 8.3 is a three by five mile area in the western half of Houston, Texas. Forecast A was produced using a trending of historical load growth, forecasting 1980 peaks from 1971 to 1976 data (for a three-year-ahead forecast period) using multiple linear
Spatial Forecast Accuracy and Error Measures
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regression fitting to a cubic polynomial. Forecast A was produced by using a land-use based, 2-2-2 type simulation program, and Forecast C with a 2-3-2 simulation method. (Chapters 9 through 17 will discuss nomenclature and forecast methods like these in more detail). The point here is that all three maps have similar AAV, but very different patterns in relative location of error. Pattern C has the least overall spatial error. Turning back to the example in Figure 8.2, given a choice between the two forecast methods, a distribution planner would be wise to select method B, on the (not altogether assured) assumption that both forecast methods will probably behave in future applications as they did in the historical tests that generated the error maps, and thus method B will probably outperform method A in actual forecast applications. This example illustrated two critical concepts: • Magnitude-only statistical measures such as AAV and RMS do not completely evaluate a forecast method's potential for distribution planning. They can be misleading because they neglect errors that have a locational aspect.
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• The spatial pattern ~ the locational arrangement of small area errors with respect to one another — is a major determining factor in shaping the impact of forecast error on T&D planning. Thinking of Error In Terms of Location, Not Magnitude Since "where?" is such an important aspect of planning, it might be useful to evaluate mistakes in meeting planning requirements by measuring error in terms of distance (location) rather than magnitude (kVA). The distance error measure would be an indication of how far off the forecast method was in predicting where load would be. As an example, consider again forecast load map A in Figure 8.2. Suppose one were to pick up all the "+" errors and move them as a block 10 miles to the east, so they completely overlapped all the "-" signs. The errors would cancel out completely. One way to interpret this is that, to correct the locational errors in Forecast A, one has to move half of all the small area errors 10 miles, or that the average small area locational error is five miles. By contrast, in Forecast B one merely has to pick up each "+" and move it one-half mile (one small area) to the right, so it falls on a neighboring "-". Again, one only has to move half of the errors to gain corrrection, so the net "locational error" can be interpreted as one-half of one-half mile, or .25 mile. Comparing locational errors determined this way establishes clearly that A is much worse that B — 5 miles instead of .25 mile of average error, and gives a much truer indication of the relative merits of these forecasts than AAV, RMS, or other similar statistics based on their magnitude. By this "locational error" measure, Forecast A has twenty times as much error as Forecast B. Not only did measuring error in this manner expose an important distinction between the two forecasts, but it also provided a helpful, intuitive way to understand their usefulness for planning and their errors' likely impact on the resulting plans. Forecast B's distance error of .25 mile is short compared to a typical primary feeder's length. An experienced T&D planner would understand that a forecast that randomly mislocated most new loads by .25 mile would not be seriously unreliable for feeder planning purposes. Although such locational errors might lead to a few small errors, they would seldom be serious. By contrast, Forecast A's five miles of error would be serious. Five miles is beyond the thermal and even economic reach of most primary distribution voltages. A forecast method that randomly mislocated new consumer growth by five miles would be of little use for feeder planning, because, on average, it would predict load growth as occurring in the wrong feeder service areas. In fact, in urban and suburban regions many substation service areas are only about five
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miles across, so that a T&D planner could expect considerable impact on substation planning, too. Thinking of error in spatial terms ~ as possible mislocation of load — and measuring it in terms of distance, provides a useful insight into what is needed in a distribution forecast and how error affects the quality of planning. However, measuring error by distance alone is no more valid than measuring it in terms of magnitude alone. Except in hypothetical examples such as Figure 8.2 (where all the values of the pluses and minuses are equal) the pattern of error locations and their magnitudes are equally important. Ideally, a T&D forecasting error measure should combine magnitude and location into one evaluation that addresses the central matter ~ how badly will these errors impact the T&D plan? This is something that will be treated quantitatively later in this chapter. Nevertheless, thinking of error in terms of distance is a useful learning exercise, for it drives home the central point of this chapter: in T&D planning, \vhere is a central concern. Accuracy, and the potential for mistakes in a forecast or a plan, must always be judged within that context. Spatial Resolution Consider a ten-year-ahead forecast of a small utility service area as illustrated in Figure 8.4. The service area is not divided into any small areas, and the forecast focuses on projecting only total peak load (and perhaps total energy, consumers, and other usage factors). This is a global forecast.
N
T
500 MVA growing to 600 MVA in next ten years
Forecast over-estimates growth by 10%f or 10 MVA somewhere in here.
•Tventy-four miles Figure 8.4 A "global forecast" for the area encompassing a small utility system. This forecast locates growth no more specifically than "it is inside the study area," which does not provide sufficient locational information to help determine T&D facility siting to the extent needed. In this example, the forecast estimates error 10% high.
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Total forecast growth is 110 MVA against 100 MVA correct, for 1095 overall error
Vest side growth forecast as 55 MVA, or 1095 high
T
250 MVA growing to 300 MVA Tl
250 MVA growing to 300 MVA S
East side growth forecast as 55 MVA, or 1095 high
•Twenty-four miles
Figure 8.5 The forecast in Figure 8.4 divided into two sections, each 250 MVA growing to 300 MVA, and each 5 MVA overforecast, for 10% error in both. Overall error and AAV are both 10%, the same as in the global forecast (Figure 8.4).
As shown in Figure 8.4, this global forecast's error is 10%. The base year load is 500 MVA, the actual ten-year-ahead peak is 600 MVA, but the forecast projects a peak of 610 MVA, for a total of 110 MVA projected load growth, or 10% error on the high side.2 Whatever virtues this forecast has, good or bad, it is of little use for T&D planning, because it provides no information on location of future load. To provide a limited amount of locational information, the study territory can be divided into east and west portions, as shown in Figure 8.5. To keep things simple for this example, assume that the present load and the future load growth are divided equally among the two parts (in other words, each half has 250 MVA peak today, and will have 300 MVA peak ten years from now). Assume that the error is divided equally, too, with each half forecast to grow to 305 MVA. Thus, both halves are forecast high by 10%, as shown in Figure 8.5. The overall error in the forecast is 10%, and the average error (AAV) of the two-area forecast is also 10%.
2
In an actual forecasting situation the planner does not know the eventual, accurate peak load, nor the level of error in the forecast as used here, but in order to study the effects of error in this example, it is assumed to be known.
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Dividing the global forecast into two parts provided an opportunity to make a mistake that could not be made in the global forecast: an error in how (or where) the projected load growth is allocated among the two halves. For the sake of this example, suppose that only one such mistake is made. An 8 MVA industrial park is forecast to be in the west half of the system when in fact it develops eventually in the east side. This is shown in Figure 8.6, which is merely Figure 8.5 with this error "added." Note that such a mistake has nothing to do with predicting whether the industrial park will develop — in this case its eventual development is correctly forecast. A mistake is made only in forecasting its location. This mistake has no impact on the overall amount of load, and hence no impact on the global forecast error, which remains 10%. But this mistake adds 8 MVA that really will not be there to the west side of the system, and it subtracts 8 MVA from the forecast for the east. The west side of the system is now forecast to develop 63 MVA (against an actual of 50) and is thus 26% high. The east side of the system in Figure 8.6 is forecast to be 47 MVA (against an actual of 50 MVA) and is thus forecast 6% low. The average absolute percent error is 16%.
Total forecast growth is still 110 MVA against 100 MVA correct, for 10SS overall error
Vest side growth forecast as 63 MVA, or 2695 high
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250 MVA growing to 300 MVA
250 MVA growing to 300 MVA
\
/
East side growth forecast as 47 MVA. or 6% low
•Twenty-four miles Figure 5.6 A purely locational error, in this case 8 MVA mistakenly forecast in the west when it eventually develops on the east side of the system, has no impact on the overall error. However, this purely locational error increases "small area" error to an average absolute error value of 16%.
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The mistake in locating the 8 MVA industrial park increased the small area error, but not the overall error. The reader is encouraged to ponder this result. From a global standpoint, the forecast in Figure 8.6 is as accurate as that shown in Figure 8.4 - both have 10% error in projecting the total for the service area. Further, if the spatial resolution required for planning were met by only a global forecast (i.e., if the planner needed no locational information, as when forecasting only total system demand), then the difference in these two forecasts would be irrelevant. The increased level of error is only important if the planner needs, or measures, locational accuracy. Also worth noting is that despite the overall forecast being high by 10%, one of the two areas in Figure 8.6 is forecast low. This is a characteristic of spatial forecasts. Despite having a net error that is measurably over or under the correct amount, spatial forecasts tend to have both plus and minus forecast errors on a local basis. Dividing the utility service territory into only two areas does not provide much locational information, certainly not enough for most T&D planning applications. If one were to further subdivide each of the east-west halves in Figures 8.4, 8.5, or 8.6 to produce quadrants, it would provide an increase in the locational information contained in the forecast, but create a further opportunity to make mistakes in predicting the location of future loads. Subdividing each quadrant into subquadrants (for a total of 16 subquadrants) would provide even more locational information, but also add further opportunities for error, and so forth. In subdividing the service territory into a greater number of areas in search of more "where" information, the planner is asking the forecast to provide additional information ~ location of load with higher spatial precision — and error is almost certain to rise when judged against this higher expectation. This does not mean that the forecast is any worse than it was before, but only that the spatial resolution used has defined a higher level of information requirement. Figure 8.7 shows the error in an actual spatial load forecast evaluated at various resolutions, and is indicative of how small area error behaves in the "real world." The particular forecast used what was among the very best spatial forecasting methods available in 1980 (a 2-3-3 simulation, as will be discussed in Chapters 10 through 14), and while more advanced methods can improve slightly on its error levels across the board, the qualitative error-versus-spatial-resolution behavior shown is a characteristic of all spatial forecasts. High Error Levels Do Not Necessarily Mean a Forecast Is Useless It is common to see spatial forecasts that have AAV and RMS approaching or even exceeding 100%, yet they can prove useful for many T&D planning applications, even if one naturally would wish for lower error. In this regard the
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£50 **
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10
100 1000 SMALL AREA SIZE - Acres
10000
Figure 8.7 The error in a weather-normalized, spatial forecast of 1990 peak loads for greater metropolitan Houston, Texas, made in 1980 with a 2-3-3 type land-use/end-use simulation method, and evaluated against actual 1990 small area development in 1993. Small-area size used in the forecast was 25.6 acres (more than 325,000 square areas 1/5 of a mile to a side). AAV error at 25.6 acre resolution averaged 51.2%, but error at 103 acre resolution (found by adding small areas into blocks of four) was only 19%, and error at a square mile basis was about 7%. Overall error (global error) was 3.5%. Despite the apparently high level of error when evaluated at the forecast spatial resolution, the forecast was quite useable, as explained in the text.
examples discussed above (Figures 8.4 through 8.6) are typical. Consider the forecast whose error evaluation is plotted as AAV versus block size in Figure 8.7 This is a ten-year-ahead forecast done on a 25.6 acre basis (a total of 325,000 small areas 1/5 mile wide) using 1980 data, with a simulation-based forecast method that was named ELUFANT (see Willis and Aanstoos, 1979, and also descriptions in Chapters 11 through 14). Evaluated on a 25.6 acre small area basis against actual 1990 loads, the forecast has an AAV of 51%. When blocks of four adjacent small areas are added together (102.4 acre resolution, or areas 2/5 mile on a side) some of the local error cancels out because neighbors sometimes have plus and minus errors, and AAV falls to 19%.
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These two values, 51% at 25.6 acre resolution and 19% at 102.4 acres, mean that 49% of the load growth (100% minus 51%) was located by this forecast to within 1/5 mile of its true location, and 81% to within 2/5 mile of its correct location. The difference in these two values' difference, 81%-49% = 32%, is load growth located with an error somewhere in between 1/5 and 2/5 miles. Similarly, using the other points on the curve, one can assemble the following data about the forecasted load growth in that test: 49% of the load growth was forecast within 1/5 mile of its correct location. 32% was forecast somewhere between 1/5 and 2/5 mile from its correct location. 12% was forecast somewhere between 2/5 and 1/2 mile from its correct location. 3% was forecast somewhere between 1/2 and 1 mile from its correct location. 4% was forecast more than one mile from its correct location or was mis-forecast in total (global). This gives a weighted average of .33 mile, meaning that on average this forecast mis-locates the average amount of small area load growth by slightly more than one-third mile. Suppose that one had decided that the 51% error was just too much, and instead reduced the forecast resolution to 102.4 acre resolution by adding together blocks of four adjacent small areas, with 32% of the computed AAV canceling out, to give only a 19% AAV. With the lower error value, this might seem to be a much better forecast. However, in this case, one would have a forecast whose characteristics are: 81% of the load growth was forecast within 2/5 mile of its correct location. 12% was forecast somewhere between 2/5 and 1/2 mile from its correct location. 3% was forecast somewhere between 1/2 and 1 mile from its correct location. 4% was forecast more than one mile from its correct location. This gives a weighted average of .43 mile, or about a 33% increase in real error level. Thus, despite the much higher AAV in the original forecast, if left at its 25.6 acre resolution it provides considerably more information on where load growth was located. It is a better, more useable T&D planning load forecast.
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While this method of evaluating error is valid, it is not an easy method of measurement, nor does it directly relate to T&D planning needs. What is really needed is a way of combining distance and magnitude into one value, rather than several. That will be covered in the next section, but before going on to direct methods to evaluate spatial error, it is worth summarizing the important points so far: 1. The spatial pattern of errors — how they are located with respect to one another ~ determines much of the value of a forecast for distribution planning. 2. One cannot compare forecast accuracy and error if evaluated only at different levels of spatial resolution. A 25.6 acre resolution forecast with 51% AAV error may or may not be better than a 40 acre resolution forecast with 29% AAV error. One cannot tell. 3. Error as measured by statistics such as AAV and RMS will almost certainly increase as small area size is reduced. AAV and RMS values of error computed at high spatial resolution may exceed 50%, yet under the right circumstances the forecast may still be useful. How useful depends on how AAV changes as a function of resolution, and cannot be determined by evaluation of error at any one resolution (small area size).
8.3 SPATIAL FREQUENCY PERSPECTIVE ON ERROR IMPACT This section introduces an analytical tool and a conceptual perspective that can combine spatial pattern and magnitude of error into a single-valued error measure that relates directly to T&D planning needs. The tool to do so is based upon discrete signal processing, and the method itself is called spatial frequency analysis (SFA). The technical derivation of spatial frequency analysis is described well in several technical papers (see Willis and Aanstoos, 1979; and Willis, 1983). Although mathematically involved, the idea is quite simple: analyze a set of small area errors, such as those in Figure 8.2 or Figure 8.3, in a way that determines how the locations and magnitudes of error are likely to "damage" a T&D plan. Most important, however, is the concept itself: error, accuracy, and distribution planning needs can be analyzed from the spatial frequency perspective.
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-8
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Figure 8.8 Cross-sections through the small area error maps shown in Figure 8.2 reveal a difference in how fast they "oscillate" back and forth from positive to negative error as a function of distance.
Figure 8.8 shows cross-sections through the two error maps first shown in Figure 8.2, and exposes a measurable difference in the two patterns of error ~ they vary greatly in how fast error alternates from plus to minus as a function of distance. The quick oscillation of error back and forth from negative to positive as a function of distance in B means that impact is minimal, even if the magnitudes of the individual errors are quite high. Fast oscillation means that errors cancel out within a short distance and hence net to zero within any small region on the map. As was discussed earlier, in such a case, it is unlikely that the small area errors will accumulate to any substantial net over- or underforecast within any particular substation or feeder area, regardless of its exact shape. On the other hand, in Forecast A errors do not alternate back and forth rapidly enough for neighboring errors to cancel, even partially, over short distances, and would leave large areas of the map with a net over or under error, and therefore have a significant negative impact on planning. What matters is how fast the errors alternate, or oscillate, back and forth as a function of space. The faster the
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ocsillation ~ the shorter the distance over which cancellation occurs — the more likely that cancellation will occur within any equipment service territory and impact on that area will be zero. Figure 8.9 shows the two error cross-sections with sine waves imposed to show how their oscillations can be interpreted in terms of spatial frequency. Forecast A has a low spatial frequency, with a fundamental wavelength of ten miles (spatial frequency of. 1 cycle/mile) while Forecast B has a wavelength of one mile (spatial frequency of 1 cycle/mile). Here, both A and B have the same magnitude (height) of 1,000 kVA. SFA provides a way to measure spatial pattern (frequency) and magnitudinal error (height) simultaneously. Spatial frequencies may be a new concept to the reader, but they are as valid, and as useful in spatial analysis, as frequency in time is in temporal analysis. Spatial frequencies oscillate over distance rather than with time as is common in many more familiar applications of frequency analysis. In spatial analysis, high frequencies are those that change rapidly as a function of location, completing a wavelength over short distances, while low frequencies are those that change slowly, having a long wavelength.
A +1
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Figure 8.9 Cross-sections through Figure 8.2 A and B with sine waves imposed on them to show how each has a fundamentally different spatial frequency content.
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Application of frequency concepts and Fourier analysis to spatial analysis is only slightly more complicated than in temporal (time) analysis, for two reasons. First, spatial applications involve two dimensions (east-west, north-south) instead of one, as with time. Spatial sine waves can oscillate in both directions with a different frequency in each axis. For example, a spatial sine wave could have a frequency of (1, 2) cycles/mile, meaning it oscillates 1 cycle per mile east-west and at two cycles per mile north-south. Second, in spatial analysis there is no past, present, and future to give a "preferred direction" to the analysis, as there is with analysis in time. This means certain types of non-symmetrical functions and analysis that depend on causal relationships (i.e., event/? happens before event q and in fact may have caused it) do not have direct equivalents (or at least equivalents that make intuitive sense) in spatial analysis. But other than those two slight complications, frequency analysis applies to evaluation of small area error as a function of location in exactly the same manner as it applies to analysis of signals, events, and relationships in time. As is always the case with any temporal signal, any spatial signal (e.g., any set of values indexed by x,y) can be transformed into its spectra ~ its unique representation as a sum of various spatial frequencies. Any small area error map can be viewed as composed of a unique weighed sum of various 2-D spatial frequencies. Spatial Frequency Analysis The examples given earlier in this chapter have illustrated that error maps containing only high frequencies (Figure 8.2 B) make relatively less negative impact on T&D planning than those with significant lower frequency components (Figure 8.2 A). One can conclude that low frequency spatial error is damaging to planning, while adverse planning impacts will be minimal if the spatial frequency is high enough. How high is high? What frequency is enough that the error makes no or little impact on planning, i.e., how fast does error have to oscillate back and forth before it makes no impact on a T&D plan? As a first step in assessing this question, consider taking a particular configuration of the distribution system and "adding up" the small area errors within each substation service area to get the net forecast error for each substation. For example, one could add up the "+" and "-" errors in Figure 8.2 by substation area to determine the impact by substation area. Figure 8.9 shows this for two arbitrary sets of substation areas. While there is some quantitative difference in the results depending on which service area plan is used, either one clearly demonstrates that Figure 8.2 A will likely lead to poor planning, while B
Spatial Forecast Accuracy and Error Measures A - Plan 1
A - Plan 2
B - Plan 1
B - Plan 2
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Figure 8.9 Forecast A and B (from Figure 8.2) with their errors summed by substation area for two sets of specific substation service areas. Size of the resulting plus or minus sign gives an indication of the net error in estimating the load in each substation. Forecast B effectively sums to zero in all cases. Although only two specific sets of substation areas are shown here, the results are general - for any viable distribution substation plan.
should make little adverse impact. By similarly adding up errors on a feeder-area basis rather than a substation basis, we could estimate impact at the feeder level, and so forth for other levels of the system, too. Basically, this is a sound way to compare one forecast to another and even estimate how much they would contribute to mistakes in distribution planning. However, a planner might be concerned (and rightly, it turns out) that this procedure would be overly sensitive to the characteristics of the particular set of substation and feeder service area boundaries being used. In the future, the planner might change these substation boundaries or add a new substation, changing the configuration entirely and perhaps the sensitivity of the system. It would be preferable to obtain a measure that reflects the impact not on any one configuration, but instead on all possible arrangements of substation areas that might be studied in planning the future system. Such an error measure, sensitive to the general structure of a distribution substation design needs, rather than any specific plan, can be based on the probability of mutual substation service function, shown in Figure 8.10. This function, Ps(d), measures the probability that two locations at distance, d, apart
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S -5 vt 0.
2 3 4 5 Distance - miles
Figure 8.10 Ps(d) gives the probability that two randomly selected consumers a distance d apart are served by the same substation. It can be used to calculate a single valued error measure that relates directly to impact on the distribution system.
will be served by the same substation. Although specifics differ from system to system, this function's probability always decreases with increasing distance — two neighbors are very likely to be served by the same substation; two consumers separated by ten miles are not. Ps(d) can be determined for any T&D system through analysis of the existing system, and is no t a function of specific substation areas, but a function of overall design constraints defined by the equipment, local load density, and design criteria being used (see Willis and Aanstoos, 1979; and Willis, 1983). Ps(d) can be used to estimate the most likely impact of a set of small area errors on the substation planning for any particular location, x, y, in a grid map by applying it using a mathematical procedure called convolution. To compute the value of impact for the small area located at x,y, a symmetrical 2-D version of this function is centered at x,y, and the plus and minus error values of neighboring cells are added together, weighted by the value of the probability Ps(d) at each point, as illustrated in Figure 8.11. This procedure means that in calculating the impact at a small area, x,y, the value of small area error in that particular small area is weighted by 1.0, while errors in other small areas, near and far, are weighted by a decreasing function of distance. If there is a pattern of alternating plus and minus errors in the neighborhood (as in Figure 8.2 B), then the errors around x,y will tend to cancel one another out, and the computed impact will be low. On the other hand, whenever all the nearby errors are of one sign, no cancellation occurs and the computed value will be large.
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Figure 8.11 The Ps(d) function, applied to average the errors around each small area, resulting in a calculated impact for each measure of the overall substation level error impact there. This computation is performed for all small areas, resulting in an impact map containing only those errors that will contribute to poor distribution planning.
B •»»*»• • »+++ + » » » » • • —• • • » » + »++++* •** »+ + + +•» • — • - • • » »+++*• •— » +++
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AAV=8.8%
AAV=4.6%
Figure 8.12 Impact maps derived from the three error maps shown in Figure 8.3 by convolution with a Ps(d) function, in this case one determined from the 12.47 kV substation level of a large metropolitan system in the southern United States [4.1]. Although all three error maps (Figure 8.3) had similar AAV, their impact maps now show very dissimilar error values, indicating different levels of impact, with C lowest.
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When calculated in this manner for every small area in an error map, the result is a substation planning impact map, as illustrated in Figure 8.12. The impact map is the error map with those spatial frequencies that do not affect substation planning removed by convolution with Ps(d), which has acted as a spatial filter, leaving those spatial frequencies that impact distribution planning, but removing those that do not. This impact map has a valuable property ~ its average absolute value is a good estimate of the forecast error's adverse impact on planning at the substation level. Two or more forecast methods can be compared using this error measure, regardless of whether they have the same spatial resolution. Moreover, the convolved "impact map" shows where errors are most likely to damage the resulting system. Finally, the AAV of the impact map is a reasonably good approximation of the fraction of capacity problems that the errors will cause in the resulting distribution plan if based on the forecast ~ a 10% AAV means 10% of capacity will be mislocated seriously enough to be unusable. Application of the Ps(d) function to the error map can be interpreted as transforming that map of small area errors into a map of probable impact ~ or errors that will most likely matter enough to cause problems. Areas in the impact (post-convolution) map with plus or minus signs are areas where over- or undercapacity planning impact can be anticipated.3 The Ps(d) function is a filter that removes from the original pattern of small area errors those with high frequencies, leaving only those whose frequencies are low enough to do damage to the substation level planning of the particular system from which Ps(d) was derived. It considers location and magnitude of errors simultaneously, and is thus system specific, but not design specific. Similarly, it is possible to derive a filter function for feeders rather than substations, a function that measures the probability that two randomly selected locations separated by distance d are served by the same feeder, and repeat this process to obtain a feeder planning impact map and feeder impact error measure. This Pf(d) function is similar to the Pg(d) function but will have different values and spatial frequency sensitivity (it will have a higher "cutoff frequency). It can be used to determine error impact on feeder-level planning. The technique described above is called spatial frequency analysis (SFA). It is a signal-filtering operation and can be applied to any and all levels of a T&D system. A different filter profile function [Px(d)J, must be determined for each
3
Again, in actual forecasting situations the planner never knows the errors in the forecast so such analysis cannot be of direct use. However, for post-forecast evaluation and as a concept to help in the design and application of forecasting methods, this is a valuable method.
Spatial Forecast Accuracy and Error Measures
253
level of the system (transmission, subtransmission, substations, feeders, etc.) to be analyzed. The reader interested in this method, its derivation, and its application can find details in Willis (1983). A Load Forecast Error Measure Based on SFA Throughout the rest of this book, and in many other references which the reader is likely to encounter, small area load forecasting error will be measured in terms of impact as evaluated by the spatial frequency analysis method described above. Evaluation of the error in a forecast method hindsight test thus involves the following steps: 1. Use the method to forecast today's loads from historical data. Subtract forecast from actual loads to get the error map E = [e(x,y)] where x =1,X and y = 1,Y index the grid. 2. Derive a filter operator Pg(d) for the system by Monte Carlo testing of the system as described in Willis (1983) and Willis and Tram (1992).4 3. Convolve ?s(d) with E to form the impact map, I. 4. Interpret the resulting impact map, I, as a qualitative map showing where impact is most likely to occur. 5. Calculate the substation capacity impact measure, Us, which is given by: Us = AAV(E)/(sum of all load growth in E/X-Y)
4
(8.3)
The reader interested in performing this process is urged to consult the methodology in Willis, 1983. Deriving the Ps(d) function, although straightforward, has several subtleties that make it imperative to understand fully such things as the relationship between spatial degrees of freedom and joint probability distributions, etc., which are described in that reference.
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Us is a useful estimate of the amount of planned capacity which would be "mislocated enough to be useless" if a small area forecast containing (unknown to the planner) the errors in E had been used as the basis of a plan. Similarly, one can calculate impact maps and estimates for other levels of the system through the same procedure. Only the P(d) function will differ from one level to another. This gives: Ut (subtransmission impact) the probable impact on substation planning, as fraction of overall subtransmission capacity needs Us (substation impact) the probable impact on substation planning, as a fraction of overall substation capacity needs Uf (feeder impact) the probable impact on substation planning, as a fraction of overall feeder capacity needs Choosing the Appropriate Small Area Size What is the correct size for the small areas to be used in a forecast? That decision depends on the level of the planning being done ~ different levels of the distribution system have different resolution requirements. Feeder planning involves location and sizing of lower capacity equipment with smaller service areas than in substation planning. Therefore, feeder planning requires more "where" information than substation planning, and will need a smaller small area to provide that resolution. The minimum resolution (largest small area size for a study) is the largest small area size that gives sufficient locational detail for the planning needs. Rule of thumb: Small areas one-tenth the area of the average service area size of the equipment being planned will generally be sufficiently small to meet all planning purposes. But by using the spatial frequency analysis method discussed above, it is possible to solve for the required small area size ~ the largest small area that will do the job. The reader interested only in the results can skip this discussion and merely consult the table of recommended small area sizes at the end of this section. Selection of a small area size means that the forecast method, and any planning based on it, cannot "see" geographic load density changes to any finer resolution than that small area size (Tram et al., 1983). Finer detail in the "where" of load is forfeited when a particular small area size is used. Essentially, all load variations inside each small area are averaged over its area. This is an important aspect of distribution forecasting. By picking a small area size, one introduces a certain amount of spatial error into the analysis ~ details finer than that spatial size cannot be seen. If those details are not needed,
255
Spatial Forecast Accuracy and Error Measures
Actual Load by Land Parcel
1y rtlfhfii I
o -
o o _J n
rTTTH—i n-Tln—• 1 In n HI n
Loads as Modeled at .5 mile res.
1
1
1
1
1
1
1
Figure 8.13 Example of the detail that is not seen by the small area approach, shown here in cross-section for one row of a small area grid (top). A small area model represents the load inside each small area as uniform over its area (middle). This means errors are introduced into any subsequent load analysis (bottom). The smaller the small areas used, the higher the resulting frequency of these "quantization errors" and the less their impact.
then the small area size is appropriate for the application. If a lack of those details leads to planning mistakes, then the small area size is not sufficiently small. Consequently, a planner must choose a small enough small area size that this type of error will not adversely impact the planning. The finer details forfeited when a particular small area size is selected are spatial frequencies that are higher than the resolution can track, as illustrated in Figure 8.13. As was noted earlier, high enough spatial frequencies of error do not have much impact on planning. The suitable small area size is that which introduces errors whose frequencies are above those needed for planning. How high that threshold is depends on the particular type of planning application ~ transmission planning, substation planning, feeder planning, or something else.
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1.0
.8 ^ .6
•o ^.4 .2 0
.5
1.0 1.5 Frequency - cycles mile
2.0
Figure 8.14 Spectra of Ps(d) for the substation level (dotted line) and feeder level (solid line) of a 12.47 kV overhead distribution feeder system, showing how sensitive the planning of 12.47 kV substations is to spatial errors as a function of their frequency.
The required small area size can be found from the spatial spectra, ^s(w), of the Ps(d) function. ^s(w) is the two-dimensional Fourier transform of the Ps(d) function and is symmetric in the spatial frequency domain. Figure 8.14 shows a cross-section through the ^s(w) spectra for the Ps(d) function in Figure 8.10. The spectra shows what spatial frequencies the Ps(d) function "passes" to the impact map, i.e., those that do make an impact on substation planning. Every P(d) function, whether substation, feeder, or other, is a low-pass filter, with a cutoff frequency above which it will not pass appreciable amounts of spatial frequencies. This cutoff frequency is used to determine the required small area size. Using the ^s(w) function, the process of solving for the small area size is straightforward: 1.
Based on
2.
The required small area size is Spatial resolution = small area width = 1/2ws
(8.4)
Spatial Forecast Accuracy and Error Measures
257
In the example shown in Figure 8.14, the cutoff frequency for the Ps(d) filter is .63 cycle per mile. Therefore, the largest small area size for this application is 11(2 x .63) mile, or .79 mile across. This method of determining maximum "spatial sampling size" is based on a fundamental theorem of discrete signal processing, the sampling theorem, or Nyquist criterion, which states that samples (in this case, small areas) must be made at least twice as often as the highest spatial frequency that is important in the analysis. Often, a planner will choose a small area size slightly smaller than called for by the spatial frequency analysis method for the sake of convenience. One of the most common constraints on small area size is mapping and data availability. Many federal, state, county, and city maps in North America are laid out on a section basis, along survey grids of miles, quarter miles, etc. In Europe and other parts of the world, surveys are similarly tied to kilometer-based grids. Small area sizes that are compatible with whatever mapping format is already in place are the easiest to use. Therefore, small area sizes typically used in distribution load forecasts are 160, 40, and 10 acres (cells of 1/2, 1/4, and 1/8 mile per side, respectively), which fit within these mapping systems, or 1/4 and 1/16 square kilometer in metric system mapping situations. In the example given above, the minimum resolution might be determined to be .79 mile. However, by selection of half mile wide small areas, a small area size is selected that has at least that resolution and also fits within standard section (one mile) grid mapping lines, which is useful for mapping purposes. Alterations in the small area size selection given by the formula above are fine as long as the resulting small area size is smaller than the size specified by this method. Table 8.1 gives maximum small area sizes calculated in this manner for typical power distribution systems in North American. The author stresses that these are only representative of general needs. Systems vary greatly and any conscientious planner will apply the method described above to the system to determine its specific needs.
8.4 CONCLUSIONS AND GUIDELINES This chapter has covered several concepts that the T&D forecaster and planner must bear in mind in using any distribution load forecast: •
"Where" is a big factor in distribution planning. Accuracy, error, and applicability of forecasting methods depend greatly on how they address location of load growth.
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Table 8.1 Largest Small Area Sizes Appropriate for Typical System Study Needs (Width of the Square Grid Cells -- miles) T&D Voltage 138KV 69 kV 46 kV 35 kV 25 kV 13 kV 4kV
Transmission Planning 10.0 6.5 4.2 3.0
Substation Planning
Feeder Planning
Feeder Segm. Planning
2.2 1.9 1.4 .82 .59
.71 .50 .33 .12
.30 .22 .12 .06
The spatial pattern of error is a key determinant of forecast quality. While the magnitudes of the errors themselves are quite important, the spatial pattern can make a big difference in impact. Valid comparison of two forecasts cannot be done based on their average small area error levels alone, particularly if done at different spatial resolutions. A spatial load forecast may have an AAV of 50% or more at high resolution, but be useful nonetheless. Its value depends on the spatial pattern of errors and cannot be evaluated at any one resolution. The spatial frequency approach can be used to combine locational and magnitudinal errors into a single-valued measure that reflects negative impact contributed by forecast error. In general, forecasting needs for planning at or near the consumer level, such as feeder design, require higher spatial resolution than higher levels of the system, such as transmission planning.
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259
REFERENCES H. N. Tram et al., "Load Forecasting Data and Database Development for Distribution Planning," IEEE Trans, on Power Apparatus and Systems, November 1983, p. 3660. H. L. Willis, "Load Forecasting for Distribution Planning, Error and Impact on Design," IEEE Transactions on Power Apparatus and Systems, March 1983, p. 675. H. L. Willis and J. V. Aanstoos, "Some Unique Signal Processing Applications in Power System Planning," IEEE Transactions on Acoustics, Speech, and Signal Processing, December 1979, p. 685. H. L. Willis and H. N. Tram, "Distribution Load Forecasting," Chapter 2 in IEEE Tutorial on Distribution Planning, Institute of Electrical and Electronics Engineers, Hoes Lane, NJ, February 1992.
9 Trending Methods 9.1 INTRODUCTION A vast and intriguing variety of load forecasting methods have been applied to spatial electric load forecasting. Most are variations on one of two basic themes: trending, which involves extrapolating past load growth into the future, or simulation, which involves modeling the process of load growth itself. Although simulation is the newer, and generally more effective, of the two, no single forecasting technique is best for all applications, and trending methods are recommended in certain circumstances. Trending methods work with historical load data, extrapolating past load growth patterns into the future. The most common trending method, and the method most often thought of as representative of trending in general, is polynomial curve fitting, using multiple regression to fit a polynomial function to historical peak load data and then extrapolating that function into the future to provide the forecast. This basic approach has a number of failings when applied to spatial forecasting, and a wide variety of other methods have been applied to trend load for T&D forecasting, some involving modifications to the polynomial-regression approach, others using completely different approaches. This chapter explores trending methods, beginning with the basic multiple regression polynomial curve fit, and proceeding through a series of additions and
261
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improvements on that method, aimed at correcting its most obvious measurable shortcomings. A number of other trending approaches are discussed as well. A Comment on Computerization Almost exclusively, modern T&D load forecasting methods are computerized. A few of the simpler approaches can be applied by manual means, but computerization brings several benefits that are essential to the practical application of most spatial forecast methods. First, a computer is needed to maintain the data base, because there are so many small areas to analyze. Second, computerization allows the forecast calculations, often complicated and quite involved, to be carried out with accuracy, repeatability, consistency, and objectivity that would be difficult to duplicate by hand. Third, computerization results in much faster analysis. The discussion in this chapter concentrates on the load forecasting methods themselves, not on computer programs or the algorithmic details of how to implement these methods as computer programs as efficiently as possible. The distinction is important. For example, the most commonly applied trending algorithm — polynomial curve fit determined by multiple regression ~ has been implemented in scores of different computer programs, developed by utilities, EPRI, and various software vendors. All of these programs and many more trending methods use basically the same mathematics and data, and produce nearly identical results. Among these many trending programs, one or another may be more prone to detect errors in the input data, simpler to understand and operate, faster or more robust (insensitive to data error), or in some other way easier to use. These are qualities of the programming, not the basic forecast method itself, and are outside the scope of discussion given here. Computerization is addressed only as it impacts selection of a particular method, or vice versa. When a specific computer program is mentioned, it is used only to identify exactly an example of the algorithm being discussed.
9.2 TRENDING USING POLYNOMIAL CURVE FIT Trending encompasses a number of different forecasting methods that apply the same basic concept - predict future peak load based on extrapolation of past historical loads. Many mathematical procedures have been applied to perform this projection, but all share a fundamental concept; they base their forecast on historical load data alone, in contrast to simulation methods, which include a much broader spectrum of data (Figure 9.1).
263
Trending Methods 8
i FITTED TREND
•o CD
EXTRflPOLflTION
6 HISTORICAL READINGS
CD
< 4
ot1985
1990
1995
2000
2005
Year Figure 9.1 Trending methods project future load values by trending — extrapolating the long-term trend of past load values into the future, as illustrated here.
Most utility planners and forecasters are familiar with the concept of curve fitting — using multiple regression to fit a polynomial function to a series of data points, so that the equation can be used to project further values of the data series. Not surprisingly, this technique has been widely used as a distribution load forecasting method. Generally, it is applied on an equipment-area basis (see Figure 1.2) such as for substations or feeders. In general, the curve fit is applied to the annual peak load data. There are two reasons for this. First, annual peak load is the value most important to planning, since peak load most strongly impacts capacity requirements. Second, annual peak load data for facilities such as substations and feeders is usually fairly easy to obtain ~ most electric utilities maintain readings on maximum feeder, substation bank and major consumer loads on an annual basis. Consider a planner who has annual peak load data on each of his company's substations, going back for the past ten years. He wants to forecast future loads by trending -- finding a polynomial equation that fits each substation area's historical load data and then extrapolating that equation to project future load
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growth into the future. There are a wide number of polynomials that he could use for the curve fit, but among the most suitable for small area load forecasting is the four-term cubic equation,
L n ( t ) = a - H y t + d,,
(9.1)
= annual peak load estimate for substation n for year t where n indexes the substation areas, n = 1 to N areas. t indexes the year, beginning with t =1 for the first year of load history. a
n' ^n' cn' ^n are ^e coeffic]'ents of the particular polynomial for substation n.
The coefficients that fit this equation to a particular substation's load history can be determined using multiple regression applied to the substation's load history. For each substation, n, the technique can find a unique set of coefficients, an, bn, cn, dn. All the substations could share the same basic equation, but the coefficients will vary from one feeder to another, tailoring the equation to each particular substation's load history. Alternatively, a forecaster could apply a different equation to each substation: a cubic polynomial to one, a second order to another, a forth order to a third. In the case discussed here, multiple regression curve fitting would begin with a parameter matrix ten elements high (for the ten years of data) by four elements wide (for the four coefficients to be determined). If the same polynomial equation is being fitted to each substation area, then this matrix is constant for all, even though one would determine different coefficients for each substation. Each column in this matrix is filled with the values of its particular parameter. For example, the first column is filled with the values 1 through 10 (because there are ten years, t = 1 to 10) cubed, because the first parameter of the polynomial is a cubic term, t . The second column is filled with one through ten values, squared, since the second parameter is a squared term, and so forth.
265
Trending Methods
1 P =
8 27 64 125 216 343 512 729 1000
1 4 9 16 25 36 49 64 81 100
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1
Substation n's annual peak loads for the past ten years are placed into a matrix ten elements high by one column wide:
l n (D ln(2) ln(3) ln(4) ln(5) ln(6) ln(7) ln(8) ln(9)
The coefficients an, bn, cn, d^ that best fit the polynomial to the load history are determined by the matrix equation
= [PTP]
-l
P'L
(9.2)
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Once the actual values of the coefficients are determined, they can be used to project future load, merely by placing them in equation 9.1, and solving it for values of t greater than ten. Solving with a value of t = 11 gives the projected value for the year following the last historical data point, t = 12 gives the value for two years beyond, and so forth, producing a projection of the future loads year by year. Curve fitting does not necessarily need to use consecutive years of data, either. Going back to the original cubic equation, 9.1, suppose that of the ten years of past data, the third and fourth year for a particular substation are missing. Those can simply be left out of that substation's curve fit analysis. In this case, the L and P matrices must both be changed to have eight instead of ten rows. L becomes
ln(2) C(6)
V7) ln(8) ln(9)
Uio) and P becomes an 8 by 4 matrix, missing the two rows for years 3 and 4:
1 P=
8 125 216 343 512 729 1000
1 4 25 36 49 64 81 100
1 2 5 6 7 8 9 10
The other steps in the calculation remain precisely the same. In order to apply the curve fit to all N substations in a particular utility's service territory, it is only necessary to perform this calculation on each substation. A computer program to perform this procedure can be quite simple.
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Trending Methods What Polynomial Is Best?
In the example given above, a four-coefficient cubic equation was used, but multiple regression will work with any polynomial equation, as long as the number of data points (years of load history) exceeds the number of coefficients. For example, instead of the equation in the earlier example, the equation shown below could be used:
(9.3)
in which case five coefficients must be determined in the curve fitting, not four. The P matrix could change, becoming ten by five elements wide:
1 P—
8 27 64 125 216 343 512 729 1000
1 4 9 16 25 36 49 64 81 100
1 2 3 4 5 6 7 8 9 10
1
.5 .333 .25 .2 .166 .143 .125 .111 .1
The coefficient matrix, C, will have five elements, instead of four, but otherwise the matrix equation for the solution, and any computerized procedure, will be as outlined earlier. Any polynomial, with any number of coefficients, can be fit to the historical data, as long as the number of data points exceeds the number of coefficients. In all cases, matrix P has a number of rows corresponding to the number of years of historical data, and a number of columns corresponding to the number of coefficients. Regardless of the type or order of the polynomial, the multiple regression method determines the set of coefficients that minimizes the fitted equation's root mean square (RMS) error in fitting to the historical data points. The RMS error
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268
10
Fitted function
•o " CD
O _J
[•*— error squared 71
eo
0) Q.
6
X Historical data points
CO
Year Figure 9.2 Multiple regression curve fitting determines a function that passes through the data points, minimizing the sum of the squares of the error between the function and the data points.
is the sum of the squares of the errors between the equation and the data points, as shown in Figure 9.2. RMS tends to penalize large residuals (difference between fitted point and actual point) more than small ones, and thus forces any minimization method to find coefficients that may give many small errors but few large ones. For example, if the coefficients found for equation 9.3 are 3, 2, 1.5, 4, and 6, then
L(t) - 3t3 + 2t2 + L5t f 4 + 6/t
(9.4)
will pass through the data points with minimum RMS error. It is important for any user of polynomial curve fit to realize just what "minimum fitting error" means in this context. First, the error is minimized only within the context of the particular polynomial being curve fit — no other set of coefficients will do as well with this particular polynomial, but another polynomial, perhaps one with the term t4 substituted for 13, might give less fitting error.
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Trending Methods
In fact, fitting error can almost always be reduced by using a "bigger equation" ~ one with more coefficients. In general, the more coefficients, the less the fitting error. By choosing an equation whose number of coefficients equals the number of years of data, it is usually possible to reduce the fitting error to zero — the calculated curve will pass right through each data point. But minimizing error in this manner, by picking a "bigger equation," means nothing in terms of actual forecasting ability, as shown in Figure 9.3. Forecast accuracy is related to the equation's ability to closely predict future values, not pass through past ones. In actual forecasting situations, equations with more than four terms generally perform worse than third-order equations such as equation 9.1 (see Electric Power Research Institute, 1979; Meinke, 1979). Beyond this, the reader should note there is nothing particularly magic about the use of RMS as an error measure while fitting a polynomial function to historical data. The use of methods that minimize RMS is so widespread that many people are unaware that they have any choice in the matter. There are curve fitting methods that minimize the sum of the errors (the mean error, not the
HISTORICAL READINGS
H
ot
1985
199O
1996
2000
YERR
Figure 9.3 A fitted function's ability to pass close to historical data points is no guarantee that it will be more accurate than another curve that has a higher fitting error. A high-order equation (dotted line) fits the historical data shown much better than a thirdorder equation (solid line), but clearly provides a poorer forecast.
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root mean square error) or some error measure other than RMS.1 However, none of these is nearly as easy to compute as the standard regression method which minimizes RMS. Thus, they are seldom used. In the author's experience, methods that minimize RMS fitting error are most often used because they are easy to apply, not because RMS is inherently the error measure to minimize. Research into trending applications in distribution load forecasting has shown no clear-cut winner among equations ~ no equation works best in all situations. However, the cubic log equation shown earlier
L n (t) = an
+
b
+
cnr + dn
(9.5)
where / = log (t) has been shown to be slightly superior to others in general applications and is the author's recommendation for most applications.
How Many Years of Data? The examples given above used ten years of data, but in fact any number of years of historical load data can be used. The only absolute requirement is that the number of years of data equals or exceeds the number of coefficients in the polynomial. How many and which years of data should be used in a small area forecast? A considerable body of research has shown that when working with typical distribution data and cubic or cubic log polynomials and fitting to only historical data, the most recent six years of data give slightly better results than any other historical sample, including seven, eight, or more years of data. Figure 9.4 shows the results of the author's tests, using the cubic log polynomial (equation 9.5) to forecast five-year-ahead peak load for 50 substations. The number of historical data points used varied from 3 to 12 years. Error is minimized at 6 data points. This is typical of results obtained in many other tests (see, for example, Meinke, 1979). For some reason not fully explained by research to date, in nearly all tests, six years of data give better results than seven or more.
1
The author's favorite for many applications is an "R° " curve fit method that minimizes only the maximum residual — it solves for the polynomial coefficients that give the smallest possible value for the largest value of the residuals.
271
Trending Methods
50
30 o 20 UJ
10 01
2 3 4 5 6 7 8 9 10 11 12 Years of Historical Data
Figure 9.4 Average Absolute Variation (AAV) error on a substation basis in a ten-yearahead hindsight forecast of 50 substations, based on curve fitting a cubic log equation applied to a varying number of years of historical data.
Trending - Poor at High Resolution Spatial Forecasting The spatial forecast error associated with a multiple regression polynomial curve fit — and almost all trending methods for that matter — increases very rapidly as small area size is decreased. This is far beyond the increase in error that can be expected due to increase in spatial resolution as discussed in Chapter 8 (see Figure 8.7 and associated discussion). Trending methods generally do not do well when applied to small area forecasting, largely because they cannot handle the S curve growth behavior well. In general, extrapolation of historical trends, whether based on regression curve fit or some other method, works well whenever the character of the system being modeled remains constant throughout the period studied. Small area growth behavior, on the other hand, undergoes two transitions in behavior as was pointed out in Chapter 7 ~ a transition from "dormant" to "growing" and a transition from "growing" to "saturated," each associated with a major change in slope of the expected growth curve. Recall that the S curve behavior, with its step-ftmction-like changes in load growth trend, becomes more pronounced as small area size is decreased. At the substation level — when the system is divided into substation service areas — S
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curve behavior is noticeable but not dramatic, and trending works acceptably well if carefully applied. When applied to smaller areas, such as feeder areas, curve fitting often gives poor results (see Menge, 1977). Figure 9.5 shows how accuracy changes as small area size is decreased in the example first used in Figure 9.4. The same 50 substation utility area is forecast, but this time the forecast is also applied at the feeder level (233 feeders) and at 907 "collector" point areas ~ subregions within each feeder area. There is roughly a four-to-one ratio of area size between each level (i.e., there are roughly four feeders within each substation area) and error level increases roughly by half as resolution is increased in this manner, so that one can form a general rule of thumb — quartering the small area size will increase forecast error by fifty percent.
200
Col. Pt.
2S 150
> < 100 k.
Feeder
o UJ
50
Subs. 4 subs.
01
2 3 4 5 6 7 8 9 10 11 12 Years of Historical Data
Figure 9.5 Error increases rapidly as smaller areas are used in the forecast. Here, the same test as in Figure 9.4 (number of years of historical data versus five-year-ahead accuracy) is performed, again using the cubic log equation fitted by multiple regression, and again on the same 50 substation test area, but this time for a variety of area sizes, including groups of four substations, substations, feeders, and collector point (subfeeders) areas. Substation curve shown is the same data plotted in Figure 9.4. No matter how many years of data are available, forecast accuracy increases very rapidly as area size used is decreased. This seems to be a characteristic of all trending methods, regardless of type or application.
Trending Methods
273
9.3 IMPROVEMENTS TO REGRESSION-BASED CURVE FITTING METHODS Chapter 7 discussed the fact that as distribution load growth is examined in higher and higher spatial resolution, the typical growth behavior appears to be more and more a sharp S curve. S curve behavior is quite difficult to extrapolate, particularly in situations where the load history represents only the beginning of the S curve. This section addresses those problems and looks at ways to improve forecasts in spite of them. Many dozens of ways to "improve" trending have been developed and applied. This section will discuss only those the author has found particularly useful. Trending has a basic incompatibility regarding small area analysis, as was discussed in the earlier part of this chapter. In any form in which it can be applied, trending implicitly assumes that the character of the system being extrapolated remains the same. If the boundaries of a small area remain the same, if the load growth doesn't pass through one or more of the S curves transitions as it grows, then nothing changes in the character being extrapolated, and the trending method is valid and gives generally satisfactory results. But when the service areas, growth characteristics, or controlling factors change, as they often do at the small area level, trending encounters one or more of the three problems discussed in this section. Generally, it then gives poor results. The enhancements to the basic trending method covered here can improve performance in the face of these problems, but do not correct entirely for the poor accuracy that results. Improving S Curve Extrapolation with Horizon Year Load Data Figure 9.6 shows that a polynomial curve fit to historical data can yield quite different results, depending on exactly where in the S curve pattern of load growth the load history happens to lie. In many cases, the resulting forecasts obtained by applying curve fitting at the feeder level or below can be truly ridiculous, with negative loads. One way to reduce this type of over-extrapolation is to use what are called horizon year loads — estimated future load values put into the data set to be curve fit (i.e., treated like the historical data). Very simply, these are the planner's guess at the eventual load level — the value that load growth will eventually reach, in another fifteen or twenty years. Nothing else in the multiple regression method changes. In the computation, the horizon year loads are treated exactly like historical data, and the coefficients are determined and the fitted function applied precisely as outlined earlier.
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274
a: =»
Z
z en
VEflR
Figure 9.6 The S curve growth behavior usually found at the small area level can give a curve fit technique considerable problems, as shown here. Curve fitting gives different results depending on just how much of the S curve lies in the history and how much in the future. Extrapolations from three different points demonstrate the level of error that can result.
Suppose that a fifteen-year-ahead estimate is to be used as a horizon year load in equation 9.1. Fifteen years ahead is year 25 (since years 1-10 are the load history), so the P matrix becomes 7 / by 4 terms:
1
P =
1 4 9 16 25 36 49 64 81 100 15625 625
8 27 64 125 216 343 512 729 1000
1 2 3 4 5 6 7 8 9 10 25
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As before, substation n's peak loads for the past ten years are placed into a vector matrix, but an 11th element, the horizon year estimate, ln(25), is added:
ln(2) ln(3) ln(4) ln(5) ln(6) J
n(7) ln(8)
ln(9) ln(10 ln(25)
In almost all cases, regardless of the number of years of load history or the small area size used, the horizon year load value stabilizes the extrapolation, preventing it from behaving in the wild manner shown in Figure 9.6 (see Figure 9.7). Horizon year estimates improve forecast accuracy considerably, even if the estimates are not highly accurate. As shown in Figure 9.8, major variations in horizon year load estimate cause only slight changes in the short-term accuracy of the forecast. In fact, several tests have shown that even random values used as horizon year loads will lead to an improvement in short-term forecast accuracy. Figure 9.9 shows forecast accuracy in the same tests first plotted in Figure 9.5 but using horizon year estimates which are randomly selected from an even distribution within the range (minimum existing load, maximum existing load) for the level (substation, feeder) being forecast. The improvement in forecast accuracy with respect to Figure 9.5 is substantial, particularly considering that this was obtained using randomly selected horizon year loads. Long-range accuracy is not improved much by the horizon year loads, because long-range values depend mostly on the horizon-year estimates, which are random or based on judgment. However, since trending is seldom used for long range planning, this is not a serious limitation. Horizon year load estimates are recommended in all trending applications. In cases where the overall system load growth rate is high (above 3% annually) or the small area size is quite small, dual horizon year loads - loads of
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a. _i cr
VERB Figure 9.7 Horizon year loads improve the trending shown in Figure 9.6. Here the horizon year load estimate (square point at right) results in the three trends shown. Compare to Figure 9.6.
a n o
wi thout Horizon year load
LU Q_
VERB Figure 9.8 Wide variations in the horizon load estimate (here ± 30%) cause only slight changes in the short-range improvement gained by using the horizon estimate, meaning it is best to use horizon year estimates and simply guess if no better value is available.
277
Trending Methods Using one horizon year load at +20 years
200
150 Col. Pt. 100
S UJ
Feeder 50
Subs. 4 subs. 01
2 3 4 5 6 7 8 9 10 11 12 Years of Historical Data
Using two horizon loads (same value) at +20 and +22 years 200
150 Col. Pt. 100
i_
o Uj
Feeder 50
Subs. 4 subs.
01
2 3 4 5 6 7 8 9 10 11 12 Years of Historical Data
Figure 9.9 The test plotted in Figure 9.5, repeated using a horizon year load in year +20 (top). Horizon values were selected at random, as explained in the text, but still led to a substantial improvement in forecasting accuracy, particularly at higher spatial resolutions. When repeated using the same value in years +22 and +24 (broad lines), the two horizon values force a small additional improvement over the performance using only one horizon load (thin lines in the bottom plot are the same data as plotted for single horizon year load results in the top plot).
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the same value, separated by one year in between them (i.e., years +25 and +27) - can make a slightly greater improvement. Use of two horizon load points tends to weight its impact more, and cause the curve fit both to flatten and to stay flat in the load run, better mimicking the S curve behavior. In such situations, it has proved best to use one more year of historical data to balance the horizon year using seven rather than six years. Thus, for high growth or very small area situations, seven historical years of data, plus horizon year estimates for year 22 (fifteen years ahead) and year 24 (seventeen years ahead) is the recommended approach (Figure 9.9). In general, when the growth rate is high (about 3% annually), the author's rules of thumb are: Number of years of historical data to use is equal to four plus the order of the equation: seven years when using third order polynomials, six when using two, five when using a straight line. The number of horizon year loads (all of the same value and separated by one intervening year in between), is [order of the equation - 1]: use two when fitting a third order equation, none when fitting a straight line. Hierarchical Vacant Area Inference Curve Fitting One of the major problems with trending is that it cannot establish any trend in a "vacant area" where no load history exists. In vacant areas - those with no load and hence no load history - normal extrapolation methods yield only one result a flat projection whose value remains zero. Yet very often development will start in a vacant area and a significant load will develop rapidly (see Figure 9.10). All small areas with load in them were vacant at some time in the past. This particular problem is encountered often in grid-based approaches, but seldom in equipment-oriented forecasts. The reason is that in an equipmentoriented forecast there are usually no vacant areas. All parts of the service territory are assigned to a substation or feeder, even if that area is vacant. But in a grid-based forecast, often more than half the small areas in the analysis are vacant, each having no load history but having a distinct possibility of future growth. For this reason vacant area forecasting problems are mostly associated with grid-based forecasts. However, equipment-oriented forecasts have their own problems due to vacant areas, which will be covered later in this chapter. Horizon load estimates help little in this situation. They provide a clue, indicating that the load in a vacant area is expected to grow eventually. However, extrapolating an all-zero load history with a horizon year load alone results in a curve that starts growing immediately (in the first forecast year) and grows linearly toward the horizon year, as shown in Figure 9.11. The forecast is completely a function of the horizon year load, and very sensitive to its value.
279
Trending Methods
UJ
o. Z Z
VERB Figure 9.10 A small area with no load and no load history may still develop load in the future, but without the load history it cannot be trended with normal extrapolation techniques, even if it is suspected that load will develop eventually.
History YEAR
Figure 9.11 A horizon year load helps when forecasting vacant areas, but gives little clue about when load will start growing.
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Vacant Area Inference A partial cure for this problem is called vacant area inference (VAI). It is based on a simple idea, illustrated in Figure 9.12. In that diagram, one of four neighboring small areas has no load history, and therefore cannot be forecast directly. The other three small areas have a load history and can be trended. The steps in applying VAI are: 1. Apply trending, with a horizon year load, to forecast each of the three small areas that have a load history. 2. Add the load histories of all four small areas together. Since the vacant area has no load history, this is the same as adding the load histories of only those three that do. Note that this sum of their load histories is the load history of the entire block (all four). 3. Apply multiple regression to extrapolate the load history sum (this is the sum of the load histories of the entire block), using as the horizon year load value the sum of all four small area's horizon year loads. The resulting trend is the forecast load for the entire block. 4. Subtract from this "block forecast," the projections for each of the three small areas that were forecast in step 1. What remains is the projection for the cell with no load history. The VAI method results in a reasonable improvement in forecast accuracy over the basic trending method, when applied to forecasts where a significant amount of growth might occur in vacant areas. Equally important, the VAI concept can quite easily be worked into a computer program that automatically performs the above steps on all vacant cells in a small area grid. The method is a hierarchical top-down procedure, which begins with a forecast of the entire service territory, obtained by adding all the small area load histories and extrapolating their sum. The VAI method then breaks the small area data set into four quadrants, forecasting each by adding together the load histories in only that quadrant and extrapolating that summed trend. It then subdivides each quadrant by four and repeats the process, and so forth. If at any time the method encounters a quadrant or small area with an all-zero load history, it applies the four steps above to infer its load history. The method continues subdividing by quadrants until it reaches the small area level, at which point it stops. For more details see Willis and Northcote-Green (1982).
281
Trending Methods
Sum of all four horizon year loads.
r» o _i
9
r\
< o
^"'" YEAR
YEAR
,---•"
c> <
O <
J YEAR
Forecast of the block's total load history toward the sum of its four areas' horizon year loads.
-
I
_l ~~ ~
YEAR
Sum of the horizon year load estimates for the three small areas that have a load history. Sum of forecasts of the three areas with a non-zero load history. YEAR
Figure 9.12 Vacant area inference is most easily accomplished as shown here. The vacant area is trended in combination with a block of its neighbors that have load histories. The vacant area's forecast, corresponding to the shaded area above, is the difference between the two trends obtained by: (1) trending the block's load history toward the horizon year load estimates of the three areas that have a load history, and (2) trending it toward the sum of all four horizon year loads. The vacant area's forecast accuracy is thus quite sensitive to the quality of the horizon year estimates, but in all cases it is an improvement over not taking this approach.
Improving Feeder and Substation-Oriented Forecasts with Load Transfer Coupling (LTC) Most often, trending is applied to equipment-oriented areas, such as feeders or substations, not to the cells of a grid. In such cases vacant areas will not be a direct factor in the forecast, because generally there are no feeders or substations with an all-zero load history. Instead, forecasts done on an equipment-oriented basis are plagued by errors caused by load transfers within their load histories, which are related to vacant area forecasting, after a fashion. Figure 9.13 shows a simplified example: in the past seven years, the load in substation B's service area has been growing rapidly. Last year, 5 MVA was transferred from B to its neighbor A, in order to reduce load on B and keep it within capacity. The resulting change in the load histories is shown.
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282
t
YEAR
YEAR
Figure 9.13 A transfer of load from substation B to its neighbor (map at top of figure) is accomplished by switching the service in the area shown from feeders emanating out of substation B to feeders served by A, and is done in order to keep peak load at substation B within its capacity limit. This transfer impacts the load histories, increasing the load at A (left) and decreasing the load for B (right), changes which are intermingled with any load growth. Trending cannot distinguish the cause of any change in load -- it responds to the changes wrought by the load transfer, treating it as if that change should be extrapolated.
The load histories of many feeders and substations in most utility systems contain many such transfers, not just in the final year of the load histories as shown in Figure 9.13, but throughout their histories. This is particularly true of any new substation or feeder that is brought on line during the period of the load history. A new substation has a significant load from day one and it has no load history (so in a way it is analogous to "the vacant areas" discussed earlier. Yet that load did not simply spring into being on the day the substation was put into operation. Load was transferred to the new substation by re-switching loads from neighboring substations. As a result, both the new substation and the neighboring substations have significant switching shifts in their load histories. To compound this problem, there may be more than one transfer in the load history of any particular substation of feeder.
283
Trending Methods
Substation A
Substation B
TREND IF THE LOAD TRANSFER HAD NOT BEEN IN THE LOAD HISTORY
YEAR
YEAR TREND VITH THE LOAD TRANSFERS
YEAR
YEAR
Figure 9.14 A transfer of load from one substation to another will impact the load histories of the two substations involved, as in this example for the two substations shown in Figure 9.13. At the top, trending of the load histories (without any transfer) of two substations. At the bottom, a transfer from B to A is added in the last year of load history, which greatly alters the extrapolated trend.
Those switching changes, as well as those that occur between existing substations which are made to keep loads within capacity limits (i.e., as outlined in Figure 9.13) can cause significant error in a trending method that treats all change in peak load from year to year as due to the cause it is trying to extrapolate (i.e., growth). Figure 9.14 illustrates how the load transfers shown in Figure 9.13 change the results of a multiple regression curve fitting for the load histories of substations A and B. Generally, load transfers have an adverse impact similar to that shown, with its severity depending on a host of factors specific to each situation. To compound the problem, it is often very difficult for the distribution engineer or planner to obtain accurate, complete information on historical load transfers. In theory, records are maintained on every load switched, but in practice assembling the data requires a great deal of time. Very often the exact
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load transferred is not recorded, or if available those data are of little value. For example, a load switch may have been made in the spring, months before summer peak. Operations personnel may have recorded that they transferred 800 kVA between two feeders, based on a reading taken at the time. How much load does this represent at peak? 900 kVA? 1000 kVA? Any estimate is only that, an estimate. Before discussing how to cure this problem, it is worthwhile to consider a subtle but critical point ~ what do the load transfers mean from the standpoint of the forecast? Suppose that there were no load transfers among any of the substation load histories during the period when data were collected. If that were the case, then the service areas of all the substations would have been constant during the data history period. But a load transfer means that at least two substation service areas changed. The real problem caused by a load transfer is that the small areas being forecast are not static ~ they changed shape and area during the historical data period. This exposes one of extrapolation's major weaknesses ~ it cannot accurately reflect changes in the basic character of the "system" being trended. There are few changes more basic than changing the actual area associated with a small area, but that is what switching does. If the load histories are trended without any adjustment for or acknowledgment of such transfers, then the resulting forecast represents no specific set of area definitions, but instead refers to a diffuse, blurry, difficult-to-define future where (implicitly) transfers will continue to change as they had in the past (i.e., even more load will be transferred from B to A in the future). While this might be true, such transfers are a part of the solution to the T&D planning, not a part of the forecast. What the planner needs is a forecast of load by defined, specific areas. This raises the question: what service area definitions should be used, or does it matter? Since service areas have changed during the historical data period, should the service areas to be forecast be defined as those at the end of the period, at the beginning, or in the middle? The author recommends that the forecast be based on the service area definitions in the final year of the load history. The major reason is that recently built substations may not have existed in the earlier years of the history and therefore can not be trended unless this definition is used. Load Transfer Coupling Regression The basic multiple regression curve fitting method described in section 9.2 will usually overreact wildly to load transfers, in the manner illustrated in Figure 9.14
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285
even if horizon year loads are used. However, a modification, called load transfer coupling (LTC) regression, can substantially reduce errors. LTC can accommodate situations when the direction of the transfer (to or from the substation) is not known with certainty, and when no idea of the amount of the load transfer is available. This makes it practical. It is possible to solve the multiple regression curve fit (i.e., determine the coefficients) for two or more small areas simultaneously. Consider small areas n and m, corresponding to the two substations in Figure 9.14, each with a sevenyear load history and two horizon year loads. The cubic polynomial equation, Ln(t) = ant3 + bnt2+ cnt + dn could be individually applied to each in the manner that was described earlier 'in this chapter — solving first for one, then for the other. However, the two substations' curve fits can be solved simultaneously. To do so requires that the L and P matrices be set up to have seven years of load data and two horizon years for each of the two areas. P and L become as shown below, each being the matrix combination of the individual matrices that would have been used to solve for the coefficients separately.
1
n,m
1
8 4 27 9 64 16 125 25 216 36 343 49 10648 484 13824 576
1 2 3 4 5 6 7 22 24
0 1 1 1
1 4 9 27 64 16 125 25 216 36 343 49 10648 484 13824 576 1 8
0
1 2 3 4 5 6 7 22 24
1 1 1 1 1 1 1 1 1
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286
'„<'> yz>
n,m
lm(7) Kn
The regression is solved as before, using the same basic matrix equation as in equation 9.2: (9.6)
n,m
Cn m, the solution matrix containing the coefficients, is now 8 by 1, and contains the coefficients for both substation areas:
-ri,m
m m m m
Trending Methods
287
The coefficients an, bn, cn, dn and am, bm, cm, dm are identical to those that would have been obtained had the regression been solved separately for each area. The only change is that the simultaneous solution required roughly twice as much computer time as it would have taken to solve them separately. This is because a major part of the computation involves inverting and multiplying the P matrix, which in the simultaneous case is 18 by 8, four times as large as the 9 by 4 individual case. Thus, this simultaneous calculation for two cases takes roughly four times as long as the calculation of each of the individual cases, which means a net doubling of solution time. At twice the effort overall, it hardly makes sense to solve the two areas simultaneously, except that this new method permits the trending of the two load histories to be coupled, which permits the acknowledgment of transfers within the load histories of both and removal of some of the adverse forecast aspect of the transfers. An additional matrix, R, the coupling matrix, is required to implement this. R is square, and has dimensions 2 x (number of years of load history and horizon loads). R is inserted into equation 9.6, as C
n,m
=
[P RP] ' p
RL
nm
(9-7)
If R is equal to the identity matrix, i.e., if all its off-diagonal terms are zero and it has ones along its upper left to lower right diagonal, then it makes no impact on the resulting solution, and the coefficients obtained are identical to those found by equation 8.6. However, suppose that the off-diagonal terms at (7, 16) and (16, 7) are set to 1, as shown in Figure 9.15 (top). These two positions correspond to the "meeting places" of the column representing the seventh year of substation n's history and the row representing the seventh year of substation m's history, and vice versa. If this matrix, with its off-diagonal ones, is used in equation 9.7 the resulting projections of the two substation load histories are much less sensitive to the load transfer between the two substations. No longer is the computation's goal to pass the extrapolated curve through all the data points as closely as possible. For the first six years of load history, that remains the goal. But, for the seventh year, the curve fit's goal is to end up with residuals for substation n and m of equal magnitude, but opposite sign. Since the load transfer caused load changes of equal magnitude but opposite sign to the two load histories, this "trick" tends to make the trending ignore the load transfer, yet take the load growth occurring in the 7th year (that with the load transfer) into account. In practical applications, forecast error is reduced, with error caused by load transfers being reduced by as much as 90%.
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s u B 1
R
3 4 5 6 7 H H
Sub 1 Load History Sub 2 Load History Year Year 1 2 3 4 5 6 7 H H J 1 2 3 4 5 6 7 H H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 H H 1 2 3 4 5 6 7 H H
Sub 1 Load History Sub 2 Load History Year Year 1 2 3 4 5 6 7 H H I 1 2 3 4 5 6 7 H H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 5
6
7 H H 1
=
2
S U B
2
S U B 1
R
= S U B 2
Figure 9.15 Top, the R coupling matrix to identify a possible transfer between substations 1 and 2 in year 7, which removes most of the impact of the load transfers and leaves the forecast in terms of the original (years 1-6) substation service areas. Bottom, alternate formulation of the matrix that transforms the forecast into substation service areas as they are in the final historical data year, seven.
Trending Methods
289
In ignoring the load transfer in this way, the forecast accuracy is improved. Technically speaking, the service area definitions that are being forecast are actually those for years 1-6, not the final year. The resulting forecast would be great if the planner wanted forecasts of load for those substation areas, as would be the case if this load transfer (and its consequent change in substation boundaries) were temporary. That may be the case. If so, matrix R above is the proper one to use. But if the transfer is permanent and the planner wants to forecast the load within the latest service area definitions, then R must be modified as shown in the bottom of Figure 9.15. The curve fit now treats the load transfer as having occurred on a "temporary basis" for years 1 through 6, and produces a forecast that represents a projection by service areas as they were in year 7. With so many off-diagonal terms, the curve fit is not as tight as it was with only two offdiagonal terms, but the forecast is still substantially improved. LTC is a practical forecasting method because the user does need the amount or the direction of the load transfer (information that often is either unavailable or difficult to obtain). The technique can be implemented on more than two substations, to handle simultaneous transfers between three or more substations, by extending the P, L, and C matrices to represent three or more substations at once. Load transfers are then handled by filling in the R matrix with Is everywhere a load transfer between substations or feeders is suspected, possibly representing complicated load transfer scenarios between substations. Care must be taken not to put too many Is into the R matrix. If it becomes too full of Is, the regression accuracy tends to degrade. However, used with judgment and common sense, this method in combination with horizon year loads and fitting cubic or cubic log equations as described above is the author's recommendation as a basic trending method for feeder and substation load forecasting.2 A thorough discussion of how and why the LTC adjusts the trending to ignore the load transfers is beyond the scope of this chapter, but is available in a technical publication (see Willis et al., 1984). Making the LTC algorithm 'automatic" Load transfer coupling trending methods can substantially reduce error in practical forecasts — usually providing a reduction of 20% to 35% in error level as compared to the basic regression-based curve fit. To be of practical use, the 2
This does not mean it is the recommended forecasting method overall. Short- or longrange simulation methods are much more accurate, but also more expensive. Given that only a trending approach is considered affordable, LTC is the recommended method.
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method must be able to handle a large number of small areas at once. Implementation for large numbers of small areas brings two difficulties, one involving computerization, the other data set-up and user effort requirements. With respect to computer implementation, while potentially the P and L matrices can be dimensioned for as many small areas as needed, both matrix size and computation time increase as the square of the number of small areas analyzed simultaneously. The author has experienced computational difficulties (severe round-off error, overflows, etc.) with LTC when handling as few as forty small areas, and such problems occur frequently if LTC is set up to deal directly with 100 or more areas simultaneously. Sparse matrix methods can partly correct this situation, but they increase programming complexity considerably. Beyond the computerization problems, the user has to set up the R matrix ~ even if the computer program has been written to make entry of the data easy, the user must identify any and all transfers manually. This takes time, data, and judgment. Despite these objections, when first developed (1984) LTC was widely used in this manner. Usually limited to a computer program capacity of 25 small areas, it would be applied numerous times to cover a large system. However, the basic LTC method can be included in a procedure that automatically applies it to all small areas serially (i.e., one small area at a time), and that can potentially handle thousands of small areas if necessary. In order to function, this procedure needs one additional item of information about each small area ~ an X-Y location. Such geographic data on the location of small areas are a common requirement of many newer trending methods developed in the 1990s, as will be discussed later in this chapter. For substation area based forecasting this location can be the X-Y coordinates of the substation. For feeder area forecasts this can be an X-Y location at or near the center of the feeder service area.3 These locations can be estimated if precise data are not available - the automatic LTC procedure is quite insensitive to error in these locations, and errors of 1/4 to 1/2 mile make little if any difference in results. The automatic LTC procedure is quite simple, with a computer program to implement it operating in five steps: 1. The user inputs seven years of historical load data, plus a horizon year load, and the X-Y location for each small area. The procedure also requires two arbitrary threshold values, Q and Z, which will be described later.
3
Often this can be done automatically. If a computerized feeder graphic data base is available, a routine can be written to extract all nodes in each feeder and average their XY locations, producing a "center of nodes" for the feeder.
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291
2. For each small area, multiple regression (without LTC) is used to fit a cubic polynomial to the small area's historical peak data and horizon year load. The residuals (mismatch between historical data point and curve value) for each of the seven historical years are computed and stored. 3. The program proceeds through the list of small areas (the order is not important). For each small area, it will perform an LTC regression analysis on the small area and four of its neighbors, setting up the R matrix itself. a. It uses the X-Y data to find the four nearest neighbors to this small area. b. It compares the stored residuals for this small area to those of each of its neighbors. If the residual for a particular year in the small area and a neighbor: i. are of opposite sign, ii. have magnitude within Q of one another, and iii. exceed a threshold value, Z, then a "1" is entered in the appropriate location in the fivearea R matrix. c. The LTC regression is solved, obtaining a curve fit for each of the five small areas. The curve fitted to the small area is used to forecast its future load. Those computed for its neighbors are ignored. d. The procedure repeats a through c above until it has exhausted the list of small areas. The residual detection threshold values Q and Z must be determined by hindsight testing for the particular system being forecast. Generally, this procedure works well when Q is between 20% to 35% and Z is in the range of 7% to 20%. Although this procedure should not do quite as good a job at "finding" load transfers and setting up the R matrix as an experienced forecaster working with good data, few forecasters have the time, data, or tolerance to work through the
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Chapter 9
50 c
40
0)
o 0) Q.
L
30
20 10
2 3 4 5 6 7 8 9 Forecasting Period - Years Ahead
10
Figure 9.16 "Automatic" LTC reduces forecast error significantly compared to the basic regression curve fit method. Solid lines compare forecast results in a test on a rapidly growing metropolitan system in the southern United States (700 feeders, average annual system peak growth, 2.7%) using 1979-1985 data. Dashed lines compare basic and LTC for a slowly growing system in the northeastern United States (200 feeders, average annual system peak growth, .3%), using data from 1981-1987.
very tedious and error-prone task of setting up the R matrix well. As a result, in practice this method outperforms manual LTC in terms of accuracy, as well as convenience. Figure 9.16 compares the forecast accuracy of this method with respect to the basic cubic polynomial curve fitting to historical data. Computation time for this method is about fifty times that required for the basic curve fit method — this procedure performs the basic curve fit for each small area (step 2) and then repeats its analysis for each small area using an LTC method covering five substations (using matrices 25 times as large). This increase must be kept in perspective however ~ it is fifty times a very small amount. Computation time is still reasonable: solution time when implemented on a 1500 MHz PC is less than five seconds for a three hundred feeder forecast problem.
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293
9.4 OTHER TRENDING METHODS Multiple regression is not the only method of curve fitting that can be applied to small area load forecasting. Many other mathematical approaches have been applied, often with results as good as those provided by multiple regression curve fitting. Most techniques that try to improve on standard multiple regression curve fitting attempt to gain an improvement through one of two approaches, either by forcing all extrapolated curves to have something close to an S curve shape, or by using some other trend beyond just load history to help the extrapolation. One method of each type will be discussed here. Template Matching (TM) - A Pattern Recognition Method It is possible to restrict curve fitting methods to only functions (such as the Gompertz function) that have an S curve characteristic using various algebraic means in the curve-fitting steps. However, the "template matching" method is a unique S curve extrapolation method that functions without curve fitting or regression. It will serve as an example of a non-regression based method. Template matching is a pattern recognition based method, rather than regression based. It is very simple mathematically (in fact it can be implemented as a computer program with only 16 bit arithmetic using no multiplication or division operations) but it requires much longer load histories than regression based curve fitting methods ~ the longer the better. Rather than extrapolate load histories, TM tries to forecast a small area's load by comparing its recent load history to "long-past" histories of other small areas. Figure 9.17 illustrates the concept ~ small area A's recent load history (last 6 years) is similar to the six years of load history that occurred sixteen years ago in small area B. Therefore, it is assumed that small area A's load will grow during the next ten years in the same pattern that B's did over the past ten years. Small area B's load history is used as a growth trend "template." In actual operation, template matching is slightly more complicated than illustrated in Figure 9.17 (see Willis and Northcote-Green, 1984). As a first step in finding load histories that match, the method compares each small area's load history to those of all other small areas in order to find several sets of small areas (clusters) that are similar in growth character, all small areas in a particular cluster having similar load history shapes. Typically, the method identifies from six to nine clusters. Small areas in each cluster are not necessarily geographically close to one another, nor do they necessarily experience their sharp growth ramps of S curve growth at the same time, but they have similar S growth characteristics (ramp rate, height, statistical variance from a pure S curve shape), whether their growth ramp occurred recently or long ago.
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AREA B
AREA A
Past | Future YEAR
Figure 9.17 The template matching concept. Small area A's recent load history is found to match small area B's load history of many years ago. Small area B's load history is then used as the "template" for area A's forecast.
For each cluster, the method next develops an average curve shape, which is called the group template. By overlapping and comparing load histories, this group template can be extended in length to cover a longer period than the available load history — twenty-five-year-long templates are extracted from just twelve to fifteen years of load history. These are sufficient to extrapolate all small area load histories far into the future. Overall, accuracy is comparable to that of the best multiple regression methods, but not substantially better. Template matching works best when applied to small areas defined by a uniform grid ~ like many pattern recognition methods, in practice it works best when all the items being studied have a common factor that is identical, in this case area size. With some modification and complication, the method has been applied in the VAI concept, proving slightly more accurate than regression based VAI methods at forecasting future growth in vacant areas of the grid. Template matching gives forecast error that is comparable to regression based curve fitting. Compared to curve fit methods, it requires a much longer period of load history in order to be effective ~ ten to fifteen years at least, versus a maximum of seven for curve fitting. In exchange for this greater need, it
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has only two advantages over curve-fit methods. It is very robust — quite insensitive to missing or erroneous data values -- and it requires minimal computational resources. Its numerical simplicity made it quite popular beginning in the mid 1980s, when it was ideally suited to the limited capabilities of the first generation of personal computers, such as the original Apple. While it continues to be widely used on small PCs by many smaller utilities worldwide, the capability of modern PCs of even modest cost to handle large floating point matrix calculations makes its computational advantages of negligible advantage. However, TM provides a ripe area for use in hybrid algorithms, as will be discussed in Chapter 15. Multivariate Trending Many trending methods attempt to improve the forecasting of electric demand by extrapolating it in company with some other factors, such as consumer count, gas usage, or economic growth. The concept behind such multivariate trending, applied to two variates such as electric load and number of consumers, would be: a. Establish a meaningful relation between the variables being trended (e.g., electric load is related to number of consumers). b. Trend both variates subject to a mathematical constraint that links them using the relationship established. In this way the trend in each variate affects the trend in the other, and vice versa. Hopefully, the larger base of information (one has two historical trends and an identified relationship between the two variables, so the base of information is more than doubled) leads to a better forecast of each variate. Many electric forecasting methods have been developed with this approach. Hybrid Methods Some multivariate trending methods go much farther in using the multiple variates than just "trending," working with the data to the point that they employ some aspects of simulation. Two such examples are extended template matching (ETM) and land-use based multivariate trending (LUMT). These will be discussed in Chapter 15, which covers hybrid forecast methods. Geometric and Cluster-Based Curve-Fit Methods Multivariate methods notwithstanding, the chief advantage of most trending methods has traditionally been economy of usage: data, computer, and user requirements are all minimal. They work on an equipment rather than grid basis, which minimizes time spent on mapping. They require only historical peak data, which are nearly always easy to obtain. Their computational requirements
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(usually multiple regression curve fitting) can be satisfied by small computers and occasionally even hand-held calculators. They are automatic ~ put the data in, run the program, and get the results — requiring only the most limited involvement from the user. Trending's major disadvantage is performance. Forecast accuracy of traditional and multivariate trending methods is marginal, and becomes unacceptably poor when predicting load growth more than four years ahead, particularly if at a small area size small enough for substation and feeder planning (160 acres of smaller). Beyond that, they are unsuited to multi-scenario forecasting. Beginning in the mid to late 1980s, research and development on trending methods turned away from multivariate methods and concentrated on developing improved methods that preserved the traditional simplicity and economy of trending, while improving forecast accuracy, particularly in the short-range T&D planning period (1-5 years ahead), where multi-scenario capability is not a big priority. This led to a number of trending methods with substantially better forecast accuracy than regression-based curve fit. In fact, the best of these methods can match the forecasting accuracy of multivariate methods, but retain most if not all of the simplicity and economy of operation expected of trending methods. In general, these methods were developed with three goals in mind: •
Forecast load on an equipment-oriented small area basis.
•
Use only data that are universally available and easy to obtain.
• Keep computerization simple and the application "automatic." There have been a number of improved trending methods developed, many quite successful in attaining some or all of these goals and improving accuracy. Most of these seek to improve forecast ability by: Combining successful characteristics of existing trending methods such as using both regression curve fit and template matching. All of the standard trending methods — curve fit, LTC regression, clustering, template matching -- have computational needs well within the capability of even low-end modern PCs. Using all of these trending methods simultaneously imposes no practical problem. Using additional data sources which are easy to obtain. An example is information on the location of substations used by several "geometric" methods ~ which is universally available and quite easy to obtain.
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/ \ Figure 9.18 Based only on the location of substations, a method such as LTCCT trending will estimate service area sizes, which helps it distinguish different types (clusters) of small areas it has been asked to forecast. Shown here are a set of substation locations (squares) and the estimated service area sizes (thin lines) interpreted by simply assigning all points to the nearest substation.
Simple geometric analysis of equipment areas as shown in Figure 9.18 has become a common analytical building block in many trending methods, because it is easy to implement, requires readily available data, and provides improvement in forecast accuracy. The required input data are limited simply to the locations of all substations, in any convenient X-Y coordinate system. Analysis consists of estimating the relative sizes of the substation service areas, based only on these data. These estimated service area sizes are only approximate, and they are not useful as a forecast parameter in regression analysis or template matching. However, they do prove useful in helping various clustering algorithms group small areas into meaningful sets with different growth characteristics, and thus can lead to unproved forecasts. Typical of these newer trending methods is the LTCCT forecast method developed by the author and two colleagues (see Willis, Rackliffe, and Tram, 1992). LTCCT (load transfer coupled classified trending) combines geometric analysis, LTC regression, template matching, clustering, horizon year loads, and regression-based curve fitting in one algorithm. As computerized by the author, the method performs forecasts on a feeder basis, in six steps:
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1. Input data. These include: for each feeder, seven years of historical peak load data, and the name (or index number) and X-Y location of the substation to which the feeder is assigned. Based on the feeders assigned to each substation, the method computes the total number of feeders for each substation. Horizon year loads for feeders or substations are not input. 2. Estimate feeder area sizes. Substation area sizes are computed using a simple geometric analysis (Figure 9.19), and the area is allocated to all feeders assigned to the substation on an equal basis. If the service area for Eastside substation is estimated to be 15 square miles and it has six feeders assigned to it, then each is assigned 2.5 square miles of service area. 3. Remove load transfers. LTC regression is used to fit a cubic log polynomial to each feeder in the manner described earlier in section 6.3. The polynomial is then solved for its value in each of the historical years, and those values are substituted for the actual historical data values. The point here is to use LTC only to remove the effects of load transfers from the historical data. The curve fitted by LTC regression ignores most of the load transfer effects. Thus, its values are used as the "true" history of load growth for each feeder. 4. Cluster into sets based on characteristics. The feeders are clustered into sets using a K-means clustering algorithm. In the original algorithm on this method, the clustering was programmed to group feeders into exactly six sets. Since then, the author has determined that it is better to let the clustering algorithm determine the number of clusters itself. Clustering is done based on the amount of load growth from year 1 to 7 in the "corrected" historical load data, the estimated feeder area size, the amount of load transfers removed in step 3 (difference between history and corrected trend), and the number of feeders in the substation to which the feeder is attached. 5. Compare clusters based on the average characteristics of feeders in each. Among clusters whose feeders have higher than average load density (i.e., among those clusters whose average of [kVA load for the feeder in year 7]/[estimate feeder's area] is above the average for all feeders), the cluster with the lowest average growth rate is picked. The average load density (i.e., [kVA load for the feeder in year 7]/[estimate feeder's area]) in this cluster is defined as the "horizon year load density," H. Horizon year loads for all feeders (in all clusters) are now computed as Horizon year load for feeder n = H x (estimated area for feeder n) (9.8)
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The rationale for this step is that the cluster picked to compute H is composed of feeders with above average loadings, but little growth. Hence it probably consists of feeders near the final part of the S curve and close to a stable horizon year load. Thus, those feeders are used to compute H, which is then applied to all feeders. 6. Forecast future load for all feeders by fitting a cubic log polynomial to each feeder's "corrected" load history and horizon year load using multiple regression (LTC regression need not be used since the load histories have already been corrected for load transfers). The fitted curve to each feeder is extrapolated five years into the future to form a shortrange forecast. This LTCCT method requires only data that are easily available. It is fairly automatic in its use, and has substantially improved accuracy when compared to other trending methods, including the multivariate approach, as shown in Figure 9.19. Several other trending methods have been developed with similar "combinations" of regression, clustering, and template matching, and give similar performance improvements.
Basic curve fit
1-1
u
LTCCT method Multivariate Simulation
g
UJ
2 3 4 5 6 7 8 9 Forecasting Period - Years Ahead
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Figure 9.19 Relative accuracy of various trending methods in forecasting feeder-level capacity needs, as a function of years into the future, evaluated in a hindsight test case using data from a utility in the southern United States, 1985-1995. All methods suffer from exponentially increasing levels of forecast error as the forecast is extended further into the future, but the rate of error increase with time varies considerably.
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9.5 SUMMARY "Trending" encompasses those small area forecasting methods that forecast future load growth by extrapolating trends among historical data. The simplest trending methods work only with historical peak data, which gives them both advantages and disadvantages over other forecasting methods. Foremost among their advantages is a wonderful compatibility with equipment-oriented small area data and a great economy of application. A feeder-by-feeder projection of future loadings using trending requires only the records of each feeder's past annual load peaks, and these data are nearly always available. Beyond their simple data needs, typically the computation methods required to apply trending are simple to understand, straightforward to implement, and quite easy to use. Many are totally automatic ~ the user does nothing beyond preparing the input data, running the program, and reviewing the output. On the downside, the severest problem associated with trending methods is poor forecast accuracy when applied to high resolution small area studies. The improvement to polynomial curve fitting made possible with the VAI and LTC methods should not blind the user to the basic handicap of trending methods. Trending methods have a difficult time handling the sharp S curve behavior common at the distribution level, which leads to forecast inaccuracy. When applying trending for distribution forecasting, recommended procedures include: 1. For grid-based small area definitions, multiple regression curve fitting of a cubic or cubic log polynomial, constrained with the VAI analysis. 2. For equipment-oriented area definitions, multiple regression curve fitting a cubic or cubic log polynomial using the LTC approach. 3. Where system peak load growth is less than three percent annually, six years of historical data (the six most recent years) and one horizon year (fifteen years in the future) should be used. 4. Where system peak load growth is more than three percent annually, seven years of historical data (the seven most recent years) and two horizon years (fifteen years and seventeen years in the future) should be used.
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5. Trending should be applied to forecast no more than five years into the future and to areas no smaller than feeders, whether using the cells of a square grid or as determined by equipment.
REFERENCES Electric Power Research Institute, Research into Load Forecasting and Distribution Planning, Electric Power Research Institute, Palo Alto, CA, 1979, EPRI Rep, EL1198. J. R. Meinke, "Sensitivity Analysis of Small Area Load Forecasting Models," in Proc. 10th Annual Pittsburgh Modeling and Simulation Conf. (Instrument Society of America, Pittsburgh, PA, Apr. 1979). E. E. Menge et al., "Electrical Loads Can Be Forecasted for Distribution Planning," in Proc. American Power Conf. (University of Illinois, Chicago, IL, Apr. 1977). H. L. Willis and J. E. D. Northcote-Green, "A Hierarchical Recursive Method for Substantially Improving Trending of Small Area Load Forecasts," IEEE Transactions on Power Apparatus and Systems, June 1982, p. 1776. H. L. Willis and J. E. D. Northcote-Green, "Distribution Load Forecasting Based on Cluster Template Matching," IEEE Transactions on Power Apparatus and Systems, June 1984, p. 3082. H. L. Willis, R. W. Power, and H. N. Tram., "Load Transfer Coupling Regression Curve Fitting for Distribution Load Forecasting," IEEE Transactions on Power Apparatus and Systems, May 1984, p. 1070. H. L. Willis, G. B. Rackliffe, and H. N. Tram, "Short Range Load Forecasting for Distribution System Planning—An Improved Method for Extrapolating Feeder Load Growth," IEEE Transactions on Power Delivery, August 1992, p. 2008 V. F. Wilreker et al., "Spatially Regressive Small Area Electric Load Forecasting," in Proc. IEEE Joint Automatic Control Conference 1977 (San Francisco, CA).
10 Simulation Method: Basic Concepts 10.1 INTRODUCTION Simulation-based distribution load forecasting attempts to reproduce, or model, the process of load growth itself in order to forecast where, when, and how load will develop, as well as to identify some of the reasons behind its growth. In contrast to trending methods, simulation uses a completely different philosophy, requires more data, and works best in a very different context. It is best suited to high spatial resolution, long-range forecasting, and ideally matched to the needs of multi-scenario planning. Most important, when applied properly, it can be much more accurate than the best trending techniques. For these reasons, simulation has become the neplus ultra of T&D load forecasting. One of the most important qualities of simulation is that it works well when applied at high spatial resolution — when the study region is divided into very small small areas. Its accuracy as a function of spatial resolution is the exact opposite of trending's. While trending is most suited to "large area" forecasting and becomes quite inaccurate when applied to smaller and smaller areas, many simulation techniques will not function well or at all if the small areas are larger than a square mile and provide improved accuracy as spatial resolution is further increased (i.e., as small area size is further decreased) to 160 acres or 40 acres or even less. Surprisingly, some of the best simulation methods also become easier to apply and less sensitive to data error as small area size is reduced.
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One point about which there is no arguing, however, is that simulation methods require more data and more user involvement than trending methods. Their data base needs can seem voluminous, difficult to obtain, and more difficult still to verify and maintain, particularly as described in the step-by-step forecast narrative given in Chapter 11, in which all data are collected and processed manually. Actually, data collection is seldom a burden given the capabilities of modern computing systems. Land-use data bases, geo-coded population and business demographic data bases, satellite imagery, a host of other sources, and utility consumer information systems make assembling data for a computerized simulation method straightforward. In addition, a considerable body of research on both accuracy requirements and man-machine time and effort requirements have led to the development of data collection methods that are remarkably effective and accurate (Tram et al., 1983). In this chapter, the first of five on simulation, the basic concepts behind simulation and the way it is implemented are introduced. Chapter 11 will then "walk through" a simulation forecast step by step, looking in detail at the data collection, analysis, and interpretation of a realistic forecast problem. Chapters 1 2 - 1 4 discuss variations on the simulation method and computerization of simulation and simulation data bases.
10.2 SIMULATION OF ELECTRIC LOAD GROWTH De-Coupled Analysis of the Two Causes of Load Growth Simulation addresses the two causes of load growth by trying to model or duplicate their process, directly but separately. As was described in Chapter 7, section 3, electric load will grow (or decrease) for only two reasons: •
Change in the number of consumers buying electric power
•
Change in per capita consumption among consumers
If the electric demand in a power system increases from one year to the next, it is due to one or both of these causes. Simulation forecast methods model possible changes in consumers and possible changes in per capita consumption using separate but coordinated models of each. This is quite a contrast to the trending techniques discussed in
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Consumer Growth
Spatial Analysis Temporal Analysis
Per Capita Growth
Handled by spatial land- I not done use model not done
I Handled by | temporal | end-use model
Figure 10.1 Simulation applies separate models to the analysis of consumer count as a function of location and consumer per capita consumption of electricity as a function of time. It thus "de-couples" load growth analysis in two ways, by cause (consumers, per capita), and by dimension (spatial, temporal).
Chapter 9, which treated all changes in load as of the same cause (just a change in load, without explanation beyond the fact that it happened). There is a further distinction in almost all simulation methods. One part of the model handles all the spatial analysis, the other part all the temporal (hourly, seasonal) analysis. Consumer modeling is done on a spatial basis, tracking where and what types and how many consumers are located in each small area. The per capita analysis does not consider location, only variation in usage as a function of consumer type, end-use, and time of day, week, and year. Thus, simulation decouples not only the causes of load growth, but also the dimensions of the forecast, as shown in Figure 10.1. Land-Use Consumer Classes Simulation methods distinguish consumers by class. Both the modeling of consumers and the modeling of per capita usage are done on a consumer class basis using definitions of various residential, commercial, and industrial classes and subclasses, as was introduced in Chapter 3's discussion of end-use models. The consumer and per capita models are coordinated by using the same consumer classes in each.
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Classification of consumers by type allows both the consumer and per capita models to distinguish consumers by different types of behavior. Three basic important types of behavior can be distinguished: Rate classes. Classification of consumers into residential, commercial, large commercial, industrial, etc., is closely related to the rate classes used in the definition of consumer billing and buying data in utility consumer information systems. Thus, it is easy to interface simulation methods with utility consumer, rate, and load research data and to interpret the results directly to the Rate, Revenue, and Market Research functions in the utility. Per capita consumption classes. As presented in Chapter 3, residential, commercial, and industrial consumers differ in how much and why they buy electric power, in daily and seasonal load shapes, and in growth characteristics and patterns. Spatial location classes. Residential, commercial, and industrial consumers seek different types of locations within a city, town, or rural area, in patterns based on distinct differences in needs, values, and behavior, patterns which are predictable. The term "land-use" is often applied to simulation methods because this locational aspect of distinction is the most visible and striking of the three types of distinctions made by the class definitions. This last application is the basis for the spatial forecasting ability of simulation methods. Within any city or region, land is devoted to residential use (homes, apartments), commercial use (retail strip centers, shopping malls, professional buildings, office buildings and skyscrapers), industrial use (factories, warehouses, refineries, port and rail facilities), and municipal use (city buildings, waste treatment, utilities, parks, roads). Each of these classes has predictable patterns of what type of land they need in order to accomplish their function and explainable values about why they locate in certain places and not in others. Their locational needs and preferences can be utilized to forecast where new consumers will most likely locate in the future. For example, industrial development is very likely to develop alongside existing railroads (93% of all industrial development in the United States occurs within 1/4 mile of an existing railroad right-of-way). In addition, new industrial development usually occurs in close proximity to other existing industrial land use. These two criteria ~ a need to be near a railroad and near other industrial
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development — identify a very small portion of all land within a utility region as much more likely than average to see industrial growth. Addition of a number of other, sometimes subtler factors can further refine the analysis to where it is usually possible to forecast the locations of future industrial development with reasonable accuracy. By contrast to industrial, residential development has a tendency to stay away from railroads (noise, pollution) and industrial areas (poor esthetics, pollution). Residential development has its own list of preferences ~ close to good schools, convenient but not too close to a highway, near other residential areas — that can be used to further identify areas where residential development is most likely. In fact, every land-use class has identifiable, and different, locational requirements. No American would be terribly surprised to find tall buildings in the core of a large city, or a shopping mall at the suburban intersection of a highway and a major road. On the other hand, most people would be surprised to find low-density housing, large executive homes on one to two acre lots, being built at either location. It wouldn't make sense. Modern simulation methods project future consumer locations by utilizing quantitative, spatial models of such locational preference patterns on a class basis to forecast where different land uses will develop (Willis and Tram, 1992). They use a separate forecast of per capita electric usage, done on the same class definitions, to convert that projected geography of future land use to electric load on a small area basis. In so doing, they employ algorithms which are at times quite complex and even exotic in terms of their mathematics. But the overall concept is simple, as shown in Figure 10.2: forecast where future consumers will be, by class, based on land-use patterns, forecast how much electricity consumers will use and when by class, then combine the two forecasts to obtain a forecast of the where, what, and when of future electric load. Overall Framework of a Simulation Method The land-use based simulation concept can be applied on a grid or a polygon (irregularly shaped and sized small areas) basis. Usually, it is applied on a grid basis, which the author generally recommends. A grid basis assures uniform resolution of analysis everywhere. In addition, some of the high-speed algorithms used to reduce the computation time of the spatial analysis work only if applied to a uniform grid of small square areas. Simulation methods are generally iterative, in that they extend the forecast in a series of computational passes, transforming maps of consumers and models of per capita consumption from one year to another as shown in Figure 10.3. Forecasts covering many future years are done by repeating the process several times. An iteration may analyze growth over only a single year (i.e., 1997 to 1998) or may project the forecast ahead several years (1998 to 2001).
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Base year locations of customers
Base year per capita consumption
1. GLOBAL FORECAST Determine the increase in number of customers that will occur somewhere in the service territory.
S 2. SPATIAL FORECAST Determine where the new customers will locate (allocate them to small areas).
Hour
X 3. LOAD CURVE FORECAST Determine changes in per capita use of electricity by time of day.
Combine locations of customers and changes in usage to obtain the small area load forecast
Figure 10.2 Simulation methods project consumer locations and per capita consumption separately, then combine the two to produce the final small area forecast.
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Year 1 database
SIMULATION METHOD Translates year 1 database into year 2 representation
Year 2 database
Figure 10.3 Simulation is applied as shown, transforming its data base from a picture of consumers and consumption in year t to a projection of consumers and consumption in year t + p.
Step-function models Simulation methods have proven quite good at forecasting vacant area growth — in fact that is among their greatest strengths compared to other spatial forecasting methods. However, they are not particularly good at forecasting incremental growth on a small area basis — as in representing that development in a particular area will go from vacant to only 20% developed hi the first year of growth, then continue to reach 50% developed by the following year, reach 80% the year after that, and only achieve 100% in the fourth year. Instead, unless considerable effort is put into modification of the basic approach, simulation methods tend to forecast a transition from "vacant" to "fully developed" in one jump, or from one type of land-use (for example, old homes) to another (high rises replacing them) in that same period. Essentially, simulation methods forecast step functions in development, the ultimate S curve — with a single year transition, as shown in Figure 10.4 (Brooks and Northcote-Green, 1978).
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7 8 9 10 11 12 13 14 15 YEAR
Figure 10.4 Most simulation methods forecast growth as step functions in development (solid line). This matches small area growth characteristics as seen at very high spatial resolutions, but not growth characteristics as they appear at lower spatial resolutions (on a large area basis). Dashed line shows the average historical land-use development curve for the sixty-four 10 acre small areas that comprise the square mile around the author's home in the Raleigh-Durham-Cary region of North Carolina. Dotted line shows the development of the square mile as a whole, being smoother because not all of the 10 acre small areas within it go through their rapid growth ramp in the same year.
This is the reason why simulation works better at high spatial resolutions. Its forecast characteristics are compatible with the growth characteristics of electric load as they appear when modeled at high spatial resolution. As described in Chapter 7, the smaller the areas used in forecast analysis, the shorter the transition period of growth, and the sharper the S curve shape. Thus, many simulation methods are much more accurate when applied at very high resolution, where their characteristic of forecasting a vacant small area as growing from zero to 100% growth in one to two years is a good match for what actually occurs. S curve behavior this sharp occurs in the range of 2 to 10 acre spatial resolution. The way to accurately forecast the growth of a 640 acre (square mile) area with simulation of this type is to divide it into 256 small areas of 2.5 acres each and explicitly forecast each. By using high-speed algorithms that can only forecast transitions, it is possible to keep run time reasonable, so that such a high resolution forecast takes only about 5 to 10 times as long. This will be discussed further in section 14.3.
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Structure of Simulation Methods More than fifty different computerized methods, many quite different from one another, have been developed to apply the simulation approach. These vary from simple and approximate to quite involved numerical approaches. However, there are some common steps which must be accomplished one way or another in the forecasting of spatial consumer location: Global consumer counts. A spatial model must account for the overall total of each consumer class within the utility service territory as a whole. Generally, these "global totals" are an input to the simulation method. Most utilities have a forecasting group separate from T&D planning — usually called Rate and Revenue Forecasting or Corporate Forecasting ~ that studies and projects total system-wide consumer counts (see Chapter 1 section 3). The author strongly recommends that all electric forecasts used for electric system planning be based upon, driven by, or corrected to agree with this forecast in an appropriate manner, as described in section 1.3 (see Lazzari et al., 1965 and Willis and Gregg, 1979). Interaction of classes. The developments of the various land-use classes within a region are interrelated with respect to magnitude and location. The amount of housing in a region matches the amount of industrial activity ~ if there are more jobs there are more workers and hence more homes. Likewise, the amount and type of retail commercial development will match the amount and type of residential population, and so forth. These interrelationships have a limited amount of spatial interaction, too. If industrial employment on the east side of a large city is growing, residential growth will tend to be biased heavily toward the east side, too. In general, these locational aspects of land use impact development only on a broad scale — urban model concepts help locate growth to within three to five miles where it occurs, but no closer (this will be discussed in section 10.4). There are myriad methods to model the economic, regional, and demographic interactions of land-use classes. All are lumped into a category called "urban models." Many urban models are appropriate only for analyzing non-utility or non-spatial aspects of land-use development, but some work very well in the context of spatial load forecasting. One such method is the Lowry model, which represents all land-use development as a direct consequence of development of what is termed "basic industry" — industry that markets outside the region being studied
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Chapter 10 (Lowry, 1964). In the Lowry model concept, growth starts through the development of "basic industry" such as refineries, factories, manufacturing, and tourism, which create jobs, which create a need for housing (residential development), which creates a local market demand for the services and goods sold by retail commercial, and so forth.
Locational land-use patterns. Ultimately the spatial forecast must assign land-use development to specific small areas. While overall system-wide totals and urban model interactions establish a good basis for the forecast, it remains for the spatial details to be done based on the distinction of land-use class locational preference as described earlier in this chapter. The determination of exactly where each class is forecast to develop has been handled with a wide variety of approaches. These range from simple methods utilizing little more than the planner's judgement (as in the manual method discussed in Chapter 11) to highly specialized, computerized pattern recognition techniques that forecast land-use location automatically (as will be discussed in Chapters 12-16). But one way or another, a spatial forecast must ultimately assign consumer class growth to small areas. Whether judgment-based or automatic, it must acknowledge and try to reproduce the types of locational requirements and priorities, and model how they vary from one class to another, as discussed earlier in this chapter. Most simulation methods accomplish the three tasks described above with an identifiable step to accommodate each, with the steps usually arranged in a top down manner. A top down structure can be interpreted as starting with the overall total (whether input directly or forecast) and gradually adding spatial detail to the forecast until it is allocated to small areas. The forecast is done first as overall total(s) by class, then each total sum of growth for the service area is assigned broadly on a "large area basis" using urban model concepts, and finally the growth on a broad basis is assigned more specifically to discrete small areas using some sort of land-use analysis on a small area basis Alternatively, a bottom up approach can be used in which the growth of each small area is analyzed and the forecast works upward to an overall total, usually in a manner where it can adjust its calculations so it can reach a previously input global total (i.e., the "corporate" forecast). Chapter 12 discusses the variety of approaches used and their algorithms in more detail. Per capita consumption is usually forecast with some form of consumer-class daily load curve model, very often one employing end-use analysis as described in Chapter 4. Regardless of approach, the per capita consumption analysis must accommodate two aspects of load development on a consumer class basis:
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Forecast of demand per consumer and its coincidence with other classes. Both the actual peak per consumer as well as the contribution to peak (the two may occur at different times) need to be forecast. Future changes in the market share of various appliances, appliance efficiency, and usage patterns from year to year need to be included in the forecast. This can be done by "inputting" the class curves as previously output from a separate end-use analysis effort, or by end-use analysis within the simulation method itself (Canadian Electric Association, 1986). Thus, the structure of most simulation methods is something like that shown in Figure 10.5. Again, Chapter 12 will provide a more detailed look at the techniques applied in each of the steps, but in one manner or another, a simulation forecast method must address the type of analysis shown in each module in Figure 10.5.
Figure 10.5 Overall structure of a simulation method. In some manner every simulation method accomplishes the steps shown above, most using a process framework very much like this one.
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10.3 LAND-USE GROWTH: CAUSE AND EFFECT This section presents the central tenet of the Lowry model with a hypothetical example of industrially driven growth. A city, town, or rural region can be viewed as a "socio-economic machine," built by man to provide places for housing, places to work, places to shop for food, clothing, and services, and facilities that allow movement from one place to another. Cities and towns may differ dramatically in appearance and structure, but all provide for their population's residential, commercial, industrial, and transportation needs in functional proportion to one another. Urban models are representations of how these different functions interact. There are literally dozens of different approaches to modeling how a city, town, or agricultural region functions. Some are simple enough that they do not need to be computerized to be useful, whereas others involve quite complicated numerical analysis. To illustrate the concepts of urban growth and urban modeling, consider what would happen if a major automobile company were to decide to build a pickup truck factory in an isolated location, for example in the middle of Kansas one hundred miles from any city. Having decided for whatever strategic reasons to locate the factory in rural Kansas, the auto maker would probably start with a search for a specific site on which to build the factory. The site must have the attributes necessary for the factory: located on a road and near a major interstate highway so it is accessible, adjacent to a railroad so that raw materials can be shipped in and finished trucks can be shipped out, near a river if possible, so that cooling and process water is accessible and also permitting barge shipment of materials and finished trucks. Figure 10.6 shows the 350 acre site selected by the auto maker, which has all these attributes. In order to function, the pickup truck factory will need workers. Table 10.1 shows the number by category as a function of time, beginning with the first years of plant construction and start up, through to full operation. Once this factory is up to full production, it will employ a total of 4,470 employees. Since there are no nearby cities or towns, the workers will have to come from other regions, presumably attracted by the prospect of solid employment at this new factory. Assume for the sake of this example that the auto maker arranges to advertise the jobs and to help workers re-locate. These workers will need housing near the factory — remember the nearest city or town is a considerable commute away. Using averages based on nationwide statistics for manufacturing industries, the people in each of the employment categories are likely to want different types of housing in roughly the proportions shown in Table 10.2.
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Figure 10.6 The hypothetical factory site at an isolated location (shaded area).
Table 10.1 Expected Pickup Truck Factory Employment by Year Year
Employment Category Management Professional Skilled labor Unskilled labor TOTALS
8
8 40 250 300 598
20 180 1400 900 2500
30 240 3100 1100 4470
20
25
30 240 3100 1100 4470
30 240 3100 1100 4470
12
30 240 3100 1100 4470
Table 10.2 Percent of Housing by Employment Category Employment Category Management Professional Skilled labor Unskilled labor
Large Houses 50 10 2 0
Med-Sm. M.F.H. Houses (apts, twnhs) 45 82 70 25
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Using the data in Table 10.2, one predicts that the 4,470 workers listed in Table 10.2 will want a total of 39 executive homes, 2,656 medium sized homes, and 1,775 apartments. Using typical densities of housing type (this will be explained in detail in Chapter 11) this equates to 57 acres of executive homes, 830 acres of normal single family homes, and 291 acres of apartments, for a total of 1,178 acres (nearly two square miles) of housing. Assume for the sake of this example that a road network is built around the site, and that the 1,178 acres of homes are scattered about the factory at locations that both match "residential land-use needs and preferences" and are in reasonable proximity to the factory, as shown in Figure 10.7. Based on nationwide statistics for this type of industry, there will be 2.8 people in each worker's family (there are spouses and children, and the occasional parent or sibling living with the worker). This yields a total of 12,516 people living in these 1.173 acres of housing. These people need to eat, buy clothing, get their shoes repaired, and obtain the other necessities of life, as well as have access to entertainment and a few luxuries. They will not want to
Single family homes Mufti-famity homes
Figure 10.7 Map showing the location of the pickup truck factory, to which has been added 1,173 acres of housing, representing the residential land use associated with the homes that will be needed to house the 4,470 workers for the factory and their families.
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drive 100 miles or more to do so. They create a local market, and a cross section of stores, movie theaters, banks, restaurants, bars, TV repair shops, doctors offices, and other facilities will develop to serve them, as shown in Figure 10.8. There will also need to be schools to educate the children, and police and fire departments to protect all those homes, and a city hall to provide the necessary infrastructure to run these facilities. And of course, there will have to be an electric utility, too, to provide the electricity for the factory, as well as all those homes and stores. These stores, shops, entertainment places, schools, and municipal facilities create more jobs, but there is a ready supply of additional workers. Based on typical statistics for factories in North American, one can assume that of the 4,470 factory workers, 3,665 (82%) will be married, and of those 3,665 spouses, about 2,443 (two-thirds) will seek employment. However, the stores, shops, schools, and other municipal requirements just outlined create a total of nearly 5,000 jobs (more than one for every one of the original factory jobs!) for a net surplus of 1,400 jobs unfilled.
N
One Mile ttS* Single family homes Multi-family homes «n Commercial
Figure 10.8 Map showing the factory, the houses for the factory workers, and the locations of the commercial areas that develop in response to the market demand for goods and services created by the factory workers.
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This rapidly growing little community will need even more workers to fill these jobs. Again, using typical values: At 1.55 employees per family (Remember, both husband and wife work in some families), these 1,400 additional jobs mean a further 1,400/1.55 = 903 families to house, for an additional population of 2.8 x 903 families = 2,529 more people. Assuming these 903 families have a cross section of housing demands like the original 4,470 factory workers,1 one can calculate a need for a further 8 executive homes (12 acres), 537 normal homes (168 acres), and 358 apartments (59 acres). These additional 2,529 people create a further need for shops and entertainment, police, fire, and municipal services, generating yet another 868 jobs, requiring housing for yet another 560 families (1,569 people), requiring a further 7 acres of executive homes, 104 of normal homes, and 37 acres of apartments. And of course those people require even more stores and services, creating jobs for yet another 347 families. This cycle eventually converges to a total population (counting the original factory workers and their families) of slightly more than 19,000 people, requiring a total of 87 acres of executive homes, 1,270 acres of medium size homes, and 547 acres of apartments. Assuming that all the commercial needs and densities are similar to those in many small towns, the commercial and industrial services sector needed to support this community of 19,000 people will require 396 acres, making the total land use needs of this small community very nearly four square miles, not counting any parks, playgrounds, or other restricted land. Essentially, the pickup truck factory, if built in the middle of Kansas, would bring forth a small community around it, a "factory town" which would eventually look something like the community mapped in Figure 10.9. 1 Actually, this isn't a really good assumption. The cross section of incomes, and hence housing demands, for employees in these categories is likely to be far different than for the factory workers. However, to simplify things here, it is assumed the same net percentage of housing per person as with the factory.
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*1& Single family homes •~5&- Multi-family homes Commercial
Figure 10.9 The ultimate result of the factory, a small "factory town" with housing, commercial retail, commercial offices, schools, utilities, and everything else needed to support a population approaching 20,000. This community "earns its living" building pickup trucks — the factory is the driving force behind the entire community's economy.
Table 10.3 Total Land Use Generated by the Pickup Truck Factory in Acres Year Land Use Class Residential 1 Residential 2 Apartments/twnhses. Retail commercial Offices Hi-rise Industry Warehouses Municipal Factory Peak Community MVA
2
4
12 170 73 22 8 3 12 6 1 350
49 710 305 94 34 12 50 27 5 350
87 1,270 547 168 61 22 89 48 8 350
87 1,270 2547 168 61 22 89 48 8 350
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77
8
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87 87 1,270 1,270 547 547 168 168 61 61 22 22 89 89 48 48 8 8 350 350 77
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In a manner similar to the analysis carried out here, the intermediate years of factory startup, before all 4,470 workers were employed, could be analyzed to determine if and how fast the community would grow. The employment numbers from Table 10.1 on a year by year basis can be analyzed to yield the year by year land use totals shown in Table 10.3. Working with projections of electric demand provided by the factory (doubtless, the auto maker's architects and plant engineers can estimate the electric demand required by the factory quite accurately), and using typical per capita electric demand data from mid-North America, this information leads to the forecast of total load given in the last line of the table. A common shortcut often used in electric load forecasting is to convert a Lowry type model as discussed above to a geographic area basis, in which all factors are measured in acres (or hectares, or square kilometers) instead of in terms of population count. Taking the numbers from the example above, a factory of 350 acres caused a demand for: 57 acres of executive homes, or .163 acres per factory acre 830 acres of single family homes, or 2.37 acres per factory acre 291 acres of multi-family housing, or .83 acres per factory acre This means that on a per acre basis, the factory causes . 163 acres of executive homes per factory acre 2.37 acres of single family housing per factory acre .83 acres of multi-family housing per factory acre Similar ratios can be established by studying the relationship between other land use classes, as for example, the ratios of the land-use development listed in Table 10.3. The Lowry model can then be applied on an area basis, without application of direct population statistics. Little loss of accuracy or generality occurs with this simplification. Techniques to apply this concept will be covered in Chapters 13-15. A Workable Method for Consumer Forecasting The example given above showed the interaction of industrial, residential, and commercial development in a community and illustrated how their relationships can be related quantitatively and in a cause-and-effect manner. This example was realistic, but slightly simplified in the interests of keeping it short while still making the major points. In an actual forecasting situation, whether done on a population count or a geographic area basis, the ratios used (such as 2.8 persons per household, 1.55 workers per household, etc.) could be based on local, industry-specific data (usually available from state, county, or municipal planning departments), rather than generic data as used here.
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In addition, the actual analysis should be slightly more detailed. For example, in this example it was assumed that the employees in the retail commercial and industrial areas had the same per capita housing demands and market demands as the new factory workers. In fact, this is unlikely. Salaries at the factory are probably much higher than the average retail or service job, and the skilled workers for the factory will tend to have a different distribution of ages, family types, and spending habits than workers in retail and service industries. Thus, the additional housing and market demand created by the retail and services sector of the local community would have slightly different housing and market impacts per worker than the factory. To account for this local variation, industry-specific data for commercial and services businesses could be obtained to refine such an analysis, or generic data based on nationwide statistics could be used in the absence of anything better. However, the basic method presented above is sound, only the data and level of detail used would need to be refined to make it work well in actual forecasting situations. Locational Forecasting While not highlighted during the example above, it is worth noting that Figures 10.6-10.9 showed where the growth of residential, commercial, and industrial development was expected. The locational aspects of land use fall naturally out of such an analysis. Land-use locational preference patterns of the type discussed earlier can be used to derive realistic patterns of development. As discussed earlier, industrial development seeks sites with certain attributes, while residential development occurs in locations with quite different local attributes. In the real world, a forecaster would use knowledge of these needs and locational patterns to help determine where growth of each of the consumer/landuse types was most likely to occur. Application of such "pattern recognition" is a key factor in most simulation methods, as will be discussed in both Chapters 12 and 13. 10.4 QUANTITATIVE MODELS OF LAND-USE INTERACTION To a very great extent, the factory's impact on development around it would be independent of where it was built. Dropped into a vacant, isolated region such as used in the example above, its effects are easy to identify. However, if that factory were added to Atlanta, Syracuse, Denver, Calgary, San Juan, or any other city, the net result would be similar ~ 4,470 new jobs would be added to the local economy. This increase in the local economy would ripple through a chain of cause and effect similar to that outlined above, leading to a net growth of about 19,000 population, along with all the demands for new housing, commercial services, and other employment that go along with it.
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The development caused by the factory would be more difficult to discern against the backdrop of a city of several million people, a city with other factories and industries, and with other changes in employment occurring simultaneously. But it would still be there. A complicating factor would be that the new housing and commercial development caused by the factory would not necessarily happen in areas immediately adjacent to it, but would have to seek sites where appropriate vacant space was available, which might be farther away than in the example given. A further complication would be that if local unemployment was high, or if other mitigating circumstances intervened, some of the 4,470 jobs created by the factory might be absorbed by local unemployment. Determination of the net development impact would be more complicated, requiring a comprehensive analysis of those factors. However, in principle the train of development given in section 10.3 is a valid perspective on how and why land-use development occurs and one that works well for forecasting. The small community of 19,000 pictured above earned its living building pickup trucks. Only that segment of the local economy brought money into the community. The jobs in grocery stores, gasoline stations, shoe repair shops, bars, doctors offices, and other businesses that served the local community did nothing to add to that. Thus, the fortunes of this small town can be charted by tracking how it fares at its "occupation." If pickup trucks sell well and the factory expands, then the city will do well and expand. If the opposite occurs, then its fortunes will diminish. So it is with nearly any town or city. Its local economy is fueled by only a portion of the actual employment in the region, and a key factor in forecasting its future development is to understand what might happen to this basis of its economy. Large cities generally are a composite of many different basic industries ~ a city like Edmonton, or Boston, or St. Louis, or Buenos Aires "earns its living" from a host of local basic industries. By definition, these basic industries are any activity that produces items marketed outside the region ~ in other words an activity that brings money in from outside the region. In section 10.3's example, only the truck factory is basic industry. Double the factory's employment, the Lowry concept states, and the entire town will eventually double in size. Double the number of grocery stores, shops and movie theaters (none of which "market" outside the local economy) and nothing much would happen, except that eventually a few grocery stores, shops and theaters would go out of business - the town "earns its living" from the factory and its local population will only support so many stores. Moreover, whether a city is growing, shrinking, or just changing, its total structure will remain in proportion to the local "basic industrial" economy, in a manner qualitatively similar to that outlined in section 10.3, whatever the causes
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of that change. If a city is going to grow, all of its parts will grow in an interrelated, at least partially predictable, manner related to the local basic industry. Urban Models The concepts of urban modeling covered here can be applied to predict how a city will grow, and in what proportions its various classes of land use will respond to such stimuli as the construction of a new pickup truck factory or a large government research facility, or for that matter, how the loss of a steel mill or the closing of a military base will reduce the local community. This particular concept is useful, and has wide application, but there are situations where it needs modification or interpretation. This is particularly true of cities or regions where the major source of local "employment" is retirement or pension income. In communities like Sun City, Arizona, or Sarasota, Florida, a significant portion of the local economy is driven by the residential class (or a portion of it, anyway) which has in effect become a basic industry, bringing income in from outside the region via pensions, social security, and investment income. There are many different types of urban models. All work with a structure of relationships among different demographic segments in a community ~ rules and equations similar in spirit to those used in the example above even if different in detail. Not all urban models are useful for electric load forecasting. Many have been designed to study quite different aspects of urban growth and structure than those given here. But a good number have been applied to utility forecasting with good success, and the most advanced simulation-based small area forecasting programs utilize urban models or urban modeling concepts to control the land-use inventory totals. For example, the multivariate model used in EPRJ project RP-570 worked in conjunction with an urban model called EMPIRIC. Many modern simulation methods work with either Lowry models or modified forms of the Lowry industrial-growth-causes-residential-growth-causescommercial-growth model. These will be discussed in more detail in Chapters 12 to 14. Although some of these ideas can be applied manually, most urban models require a detailed, formally structured set of equations implemented by a computer ~ a computerized urban model. This is true of the Lowry model outlined above. When properly computerized and coupled with pattern recognition of land-use development to help locate the growth to specific small areas, it serves as a very powerful tool for forecasting the what, when, and particularly the where of future electric consumer growth.
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10.5 SUMMARY OF KEY CONCEPT A city, whether a megaopolis, a metropolitan area, or just a big town, is a mechanism mankind has developed for his use. All are composed of parts residential, commercial and industrial, along with transportation and support infrastructures - that are all mutually supporting and interrelated. If a city is going to grow, all of its parts will grow in an interrelated, at least partially predictable, manner related to the local basic industry. This applies to all cities, regions, and towns without any exception. Chapters 18 - 20 will explore this concept, in detail and with regard to several specific directions of analysis useful for planners. But overall, forecasters can use this concept, embodied in a quantitative analysis of its various implications, to forecast a new city's future, including spatial electric load. This is the central concept behind simulation forecasting methods, but more fundamentally, this is the most useful perspective from which to view growth of electric load. Forecasters who use this concept as a guide and who grow themselves to understand its mechanism will be better forecasters. REFERENCES C. L. Brooks and J. E. D. Northcote-Green, "A Stochastic Preference Technique for Allocation of Consumer Growth Using Small Area Modeling," in Proceedings of the American Power Conference, University of Illinois, Chicago, IL, 1978. Canadian Electric Association, Urban Distribution Load Forecasting, final report on CEA Project 079D186, Canadian Electric Association, 1986 A. Lazzari et al., "Computer Speeds Accurate Load Forecast at APS," Electric Light and Power, Feb. 1965, pp. 31-40. I. A. Lowry, A Model of Metropolis, The Rand Corporation, Santa Monica, CA, 1964. H. N. Tram et al., "Load Forecasting Data and Database Development for Distribution Planning," IEEE Trans, on PAS, November 1983, p. 3660. H. L. Willis and J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, May 1979, p. 48. H. L. Willis and H. N. Tram, "Distribution Load Forecasting," Chapter 2 in IEEE Tutorial on Distribution Planning, Institute of Electrical and Electronics Engineers, Hoes Lane, NJ, February 1992.
11 A Detailed Look at the Simulation Method 11.1 INTRODUCTION This chapter is structured much differently from previous chapters. It presents in narrative form, and almost painful detail, the story of a distribution planner who performs a complete simulation-based distribution load forecast manually. Manual application of the simulation approach is usually impractical, because data volume alone makes non-computerized studies much too time-consuming. Beyond that, a computer is really necessary to properly analyze and balance the myriad factors that a simulation might address while producing a forecast. This narrative is presented because the author knows of no better way to communicate the details of the simulation process, along with the subtleties involved in its application than to "walk through" a forecast, step by step. In addition, this presentation highlights the many dimensions of electric load and consumer growth in a thorough manner, making it a good lesson about how and why T&D grows as it does. While fictional, the example given here is realistic, based upon an actual forecast the author did manually, partly as a training exercise and partly as a production forecast, for a municipal utility in 1984. All simulation, whether manual or computerized, uses the basic approach introduced in Chapter 10 and described here, a deceptively simple concept that can yield absolutely stunning results when used appropriately. Thus, the forecast method described is a viable
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SPRINGFIELD LIGHT & POVER CO. Service Territory and Distribution Substations
Figure 11.1 Map of the fictitious city of Springfield and its electric system substations.
forecasting approach, albeit a very labor-intensive one. When applied to very small towns or cities, the effort required to use the procedure described here is not so great as to preclude practical application, but for large cities, application of simulation is unthinkable without some degree of computerization to speed the process. Thus, this chapter provides a "cookbook" for any planner who wishes to do a manual simulation, as well as a step-by-step explanation of the basic steps through which all computerized methods proceed. Chapters 1 2 - 1 6 discuss computerization and application of computerized methods for implementation of the simulation approach.
11.2 SPRINGFIELD The forecasting problem presented here concerns a small, growing city of slightly more than 125,000 population, shown in Figure 11.1. This fictitious city
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is named Springfield, simply because it is an attractive name, and because in the author's experience there are more Springfields in the United States than cities of any other name.1 Most of these other Springfields are medium-sized, pleasant communities, just as this little Utopian community is supposed to be. The distribution system consists of thirteen substations all serving 12.47 kV primary feeders. In addition, there is some old 4.16 kV distribution still in service out of Downtown and Riverside substations, equipment dating from nearly 60 years earlier, which the local utility, Springfield Light and Power (SL&P), would love to retire but cannot afford to replace. The distribution planner, Susan Gannon, has been with Springfield Light and Power's System Planning Department for ten years. It is her responsibility to update the company's long-range distribution budget and construction plan every three years, and it is time to undertake this project again. The first step in her new plan is a forecast of Springfield's distribution loads. She will do her forecasting for a selected set of future planning years ~ two, four, eight, twelve, twenty, and twenty-five years ahead. The final time period is beyond Susan's twenty-year planning horizon, but she has decided to produce a load projection five years beyond that time frame as a check on her forecast. A small inconsistency or inaccuracy in the twenty-year forecast will often become more readily apparent when viewed as part of a further five years of projection into the future. Growth and Growth Influences Taken as a whole, Springfield's peak electric load, which occurs in the summer, has been growing at an annual rate of nearly 3% over the past decade. Susan's colleagues in her company's Rate and Consumer Studies Department have projected that the summer peak load will continue to grow, but at a lower rate in the next decade. Summer peak load growth is expected to drop to between 2% and 2.5% annually, due to a conservation and load management program that Springfield Power and Light is promoting quite aggressively. During the last decade, the winter peak has been growing at over 4% annually, faster than the summer peak due to a shift away from oil and gas heating to electric heat. This trend has accelerated among the residential and small business classes since Springfield Light and Power began a program of promoting heat pump usage, offering cash incentives to home and store owners
1
The author has seen statistics that show "Greensberg" is the most popular community name in the United States. However, he has personally run into many more Springfields than Greensbergs.
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700
600 Summer 500
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L
-10
-5
5
10
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Figure 11.2 Actual (broad lines) and weather-corrected forecasts (thin lines) for winter and summer system peak load of the Springfield Light and Power system.
who install both extra insulation and a new, high efficiency heat pump.2 Rate and Consumer Studies predicts that the winter peak will continue to grow at between 4 and 5%, and will exceed the summer peak in year seven, as shown in Figure 11.2. Of much interest to Susan and her department is a new pickup truck factory that may be built in the Springfield area within the next two years. The newspapers are full of rumors and expectations that this economic plum will be built on a site just north of the city. Susan knows that the Springfield City Council is actively negotiating with Nippon-America Motors, a huge JapaneseAmerican conglomerate, to influence them to locate their new factory in the 2 It is not unusual to see a utility simultaneously taking measures to cut its summer peak while encouraging more usage in winter, or vice versa if it's a winter peaking utility. Springfield's program makes a lot of sense. Cutting the summer peak while increasing winter sales will improve the utilization of the power system — spreading equipment costs over more energy sales, and therefore benefiting both the utility and its customers. Ultimately, SL&P will become winter peaking, but that is preferred, too, because it buys power from Multi-State Omni Utilities, a big, summer-peaking utility downstate, which is quite willing to sell power at a discount during its off-peak season.
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Springfield area. The city government has increased the attractiveness of their town with a package of tax incentives, promises of all the necessary permits and licenses, and a year's worth of meetings and three-martini lunches with NipponAmerica executives — the new factory represents an additional four thousand new jobs for Springfield, and will mean a big boom for local business. At the mayor's urging, Springfield Light and Power has held several meetings with Nippon-America, offering very appealing electric rates for the new factory, rates subsidized by the municipality itself, ever eager to remove any barrier to this economic boon. As near as Susan and her colleagues can determine, Nippon-America hasn't made a decision, but the company seems serious. Rumor has it that they have identified a site, just north of town, that seems particularly suitable for their factory. That site has the required amount of space for the factory and is conveniently close to the rail, highway, and river transportation facilities required to get the materials in and the product out, as well as the various electric, water, and gas utilities necessary to supply a major factory. The factory itself is expected to have a peak load of 19 MVA, and will be served by 69 kV transmission to a substation owned by Nippon-America. But what concerns Susan and her colleagues in System Planning most is the secondary impact of the factory, the type of development covered in Chapter 10, section 3. Four thousand new jobs over the next five years mean a large population boom, for the factory is sure to attract workers from other areas of the nation, bringing about construction of new homes and businesses. Local contractors and businessmen are looking forward to the building boom of new subdivisions, stores, offices, movie theaters, bars, restaurants, and other establishments required to support four thousand families. Police, fire, and school officials are worrying about growth — four thousand new jobs mean several thousand new families to protect and new children to educate, all requiring expanded municipal facilities. This growth, caused directly by the factory, will be in addition to Springfield's normal growth, and will require electric power, much more than the factory's 19 MVA load, all of it the direct responsibility of Springfield Light and Power, to generate and distribute. In addition to the normal distribution expansion plan which would not include the factory (since it is considered less than 50% likely), Susan's management wants a plan showing their system's distribution expansion needs if Nippon-America does build its factory in Springfield. Will additional capacity be needed to serve all the new consumers? If so, what facilities will have to be built, and where and when? How much will they cost? When must construction be started, and when will various expenses be incurred? These are the same
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questions Susan answers in her normal distribution plan, but now she must do it for two scenarios of growth — with and without the factory. The pickup truck factory is not the only causal influence on the location of new load. A major bridge, crossing the Springfield River near the south edge of town, is scheduled for completion in the next two years. Vacant farmland, now twenty minutes from downtown, will soon be only a few minutes away, transformed into highly desirable home sites by the new bridge. This is the planning problem faced by Susan Gannon. Her first step is to produce a base forecast of Springfield's growth that accounts for the influence of the new bridge, then modify it to an alternate scenario that includes the growth influences of the pickup truck factory. Because trending is not ideally suited to handling this type of causal factor analysis, and because Susan believes simulation is inherently more accurate, she decides to use it to develop scenarios of growth for both cases. Having access to nothing more powerful than an electronic spreadsheet on her office PC, she is determined to plunge ahead and do the study manually anyway.
11.3 THE FORECAST Susan decides to use a straightforward manual simulation method, taken directly from this section of the book. Since simple categorizations like residential, commercial, and industrial are insufficient for making distinctions in electric load and growth characteristics to the level of accuracy she needs, she decides to use the land-use classifications given in Table 11.1.
Table 11.1 Land-Use Types for Manual Simulation Class Residential 1 Residential 2 Apartments/townhouses Retail commercial Offices High-rise Industry Warehouses Heavy industry Municipal
Definition homes on large lots, farmhouses single family homes (subdivisions) apartments, duplexes, row houses stores, shopping malls professional buildings tall buildings small shops, fabricating plants, etc. warehouses primary or transmission consumers city hall, schools, police, churches
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These, she knows, are the author's recommended simulation classifications for typical small and medium-sized cities in North America. The simulation approach Susan will take is called the "coloring book" method, because during the course of her study she will keep track of the locations of different classes of land use by marking on a map with various colored pencils. The steps in her forecast are: • •
• •
Forecast future load by class on a per consumer basis. Develop a forecast of how the total amount of each landuse class within her service area will increase from year to year. Determine where the increases in each class will locate, producing a map of future land use. Use her map of future land uses and her data on future per consumer class load to calculate the load increases in various areas of the system, as needed.
As summarized above, the "coloring book" approach may seem simpleminded and prone to error. And although it has several shortcomings when compared to computerized simulation, it can give very good results when applied in a careful, well-prepared manner, particularly on a small planning problem like Springfield's. Its only drawback is that it represents a tremendous amount of very tedious work, as Susan is about to discover. Step 1: Base Year Land Use Map Before forecasting where future consumers will be, Susan first needs to determine where her existing consumers are. The goal of this step is to produce a small area land use map of her system for the base year. It is quite simple, but laborious. Base map. Susan begins with a map of Springfield. This particular map happens to be Springfield Light and Power's transmission system map, 42 by 31 inches in size, with a scale of one inch equals half a mile. Susan is fortunate, for this map has all the qualities needed in a small area base map: 1. The map is to scale. 2. It is clear and easy to read. 3. It shows the major highways, roads, railroads and other landmarks in and around Springfield.
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4. It shows a good deal of the land outside her service area, allowing her to study the areas several miles outside her service territory, should that become important. 5. The study region (her entire service territory) is completely covered by this one map. 6. It shows the locations of all distribution substations in her system. 7. The scale of two inches to the mile means the 1/4 mile wide grid cells she plans to use will be exactly 1/2 inch wide. That is a very nice, convenient size for her analysis, and easy to mark on her map. 8. Replacement copies are and will no doubt continue to be cheap and easy to obtain. 9. It will fit on her desktop. Small area grid. Susan visits a local drafting supplies store and buys a sheet of clear plastic film, 36 inches wide and fifty inches long. In addition, she purchases a roll of tracing paper, thirty-six inches wide by two hundred feet long. She also gets two four-foot metal straight edges, a very good marking pen, and three sets of colored pencils.
Figure 11.3 The master small area map, a clear plastic overlay grid defining the small areas to be used in all subsequent forecast steps.
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Carefully, taking an entire afternoon, Susan inks a 1/2 inch grid across the plastic acetate film with a straight edge and permanent marking pen. This will be her master grid map, and she wants it to be accurate. She numbers the grid columns and rows along the top and bottom, and both sides, as shown in Figure 11.3. Once done, she tapes the map of Springfield to her desktop and lays the clear plastic grid down on top of it, taping it down firmly along the edges so that it, too, is secured to both her system map and the desktop ~ neither the system map nor the grid (or the desktop for that matter) is going to move for a long time to come. With the small area grid overlaid on the map, the exact location of all small areas as used in the forthcoming study is defined. The one-half inch wide small areas at a scale of one inch equals half a mile means her small areas are 40 acres each (1/4 mile wide). Susan marks the location of several key landmarks on the plastic overlay, so that if it somehow comes loose, she can fit it back again, exactly as before. Susan now cuts off fifty inches from the roll of tracing paper and lays it atop the plastic overlay, overlapping it on all sides and firmly taping each of its corners down to the desktop. She traces several key landmarks and all four corners of the grid onto the paper, so that if it is removed she can reposition it exactly if need be. Base land use coding. Susan now has the base map, the clear plastic overlay, and the tracing paper laid out on her desk. She intends to color the tracing paper overlay with the colored pencils, using a different color to indicate each of the land-use classes, completely filling in each small area according to its current types of land use. She will use the colors shown in Table 11.2 to indicate her land-use classes: Table 11.2 Colors Used to Indicate Land Use Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices High-rise Light & medium industry Warehouses Municipal Heavy industry Vacant-restricted Water
Color light green green dark green yellow orange
red gray brown orange black purple blue
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The alert reader will notice that Susan has added two classes of "land use" that were not in Table 11.1 to the classes she will color: vacant-restricted and water. Vacant-restricted land includes parks, wildlife preserves, military firing ranges, ball fields, airport runways, and other land on which load will never develop. Both research and experience have proved that the vacant restricted class is the single most important class for distribution planning ~ this is land where load can never develop, and thus of great impact to the distribution plan (Tram et al., 1983). It is also the first class Susan colors onto her map -- she wants to have the vacant land that never can develop load identified and marked first. She then intends to color in other land uses until she has a map of the present land use in Springfield. To do this step well, Susan must first establish some definitions that she will use throughout her work, definitions of exactly what she will define as the land that belongs to a shopping center, an individual home, or a factory. Among her rules are: In residential areas, the entire lot, the portion of any streets alongside the residential lot (from the property line to the center of the street) and any alleyway bordering the property will be considered part of the residential land use. Similarly, grassy areas around apartments and office buildings, plazas, sidewalks, and courtyards are part of the area of the adjoining land use. Parking lots associated with stores, apartments, offices, and other buildings are included in their building's land use. A shopping mall that covers five acres, surrounded by a twenty-seven acre parking lot, will be defined as thirty-two acres of retail commercial land use. Outdoor storage areas, such as those used to inventory concrete pipe outside a concrete conduit factory, or wrecked automobiles at a wrecking yard, will be considered vacant-restricted land with no load, and identified as such. Any minor load in those areas (lighting, etc.) will be assumed to be part of the load in the factory or wrecking yard office, respectively. Susan could have defined land use differently, for example classifying all parking lots, etc., as "parking lots" and coloring them a different color. The important point is that she is consistent with whatever rules she applies. Using the rules listed above (rather than separate "parking lot" colors, etc.) makes her job a bit easier, and what matters is that she is absolutely consistent.
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Diagram of land uses
As colored
Residential 2 Residential 1
Vacant (nothing)
Figure 11.4 Map showing the land use in a forty-acre small area (a square area 1/4 mile to a side), and the colors Susan puts on her map.
For each small area on her map, Susan intends to use the appropriate colors in the correct amounts, indicating the present land use in that small area. For example, she would color the cell shown in Figure 11.4 as indicated. Where will she get the information on the land use in each small area? She plans to use a combination of sources: 1. Her own knowledge. She's grown up in Springfield, and worked for ten years as a distribution planner for Springfield Light and Power. She feels that she knows the town just about as well as anyone could. 2. A set of aerial photographs covering the Springfield Light and Power service area. She borrowed these from her company's Land and Right of Way Department, which keeps a photobook containing 30 by 24 inch black and white aerial photos, scale of one inch equals one thousand feet, for studies of potential easement and property purchases. It is quite simple for her to find landmarks on her system map — streets, creeks, and major roads, etc. ~ to help identify the location of any particular small area on these aerial photos. 3. Zoning and land-use maps produced by the City of Springfield's Municipal Planning Department, showing the land uses and zoning for
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various blocks within the city. (Zoning data are the least useful of her three sources, because as in most American cities, so many variances are granted in Springfield that it is unreliable as an indicator of future growth. In addition, Susan has seen the zoning in her city change at the whim of City Council, which generally responds to the wishes of developers and those pushing for economic development). Originally, Susan had planned to use only her own knowledge of Springfield and its development when coloring the land use onto her map. She felt confident that she would know the city accurately, since Springfield was fairly small, she had lived there a number of years and she got around the city a good deal in the course of her work. However, even a cursory look at the aerial photos convinces her that her "expert knowledge" of the Springfield area is incomplete. She decides that she will need to depend on the photos and zoning data more than she had expected. She spends several hours studying the photographs, concentrating on areas of the city that she knows well. This preliminary work allows her to learn what various land uses look like in the photos. She learns a number of "tricks." Among them: Parking lots around a building are the biggest clue to its land use. Retail shopping will always have a big parking lot between the building and the street. Parking for offices tends to be smaller in proportion to the building, and located around or even behind the building. Factories generally have a relatively tiny parking lot located behind or to the side of the building. Warehouses are normally along railroad tracks, which are discernible because they appear as very straight, thin lines (much narrower than roads), and always have wide, circular arcs in any turn. Cemeteries are discernible from parks and undeveloped areas because of the network of very narrow roads running throughout. The height of a building can be discerned from the shadows it casts to the side, which she can see in the photos. She learns she must be careful, however. The photobook contains 165 separate photos, and they were taken at different times of day. However, by comparing shadows within any one photo, using something she knows well as a baseline, she can identify building height.
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:: Lo-densRes. iii! Residential HI! Apartments m Retail 19 Offices •
Hi-rise
= Lgt, Ind. = Med.lnd. •i Hvylnd.
SPRINGFIELD LIGHT & POWER CO. Service Territory and Distribution Substations
Figure 11.5 Susan's base year land-use map of the Springfield System. In addition to the land uses shown, Susan colored restricted (non-buildable) land.
The key to Susan's success, however, is that she depends on all the sources of data at her disposal. She first locates each small area in the aerial photos, studies the information in the photo, checks the zoning data, and then colors the cell on her map to correspond to the land uses she sees. By moving across the map in columns and rows, and organizing her effort carefully, she minimizes the time it takes to do this work. The entire map takes her only four and one half days to complete (Figure 11.5). Land use inventory. Once her map in finished, Susan carefully estimates the total number of small areas of each land-use class that she has colored to obtain a "land use inventory" of the Springfield Light and Power service territory. She counts partial small areas, too, trying to estimate accurately the breakdown of small areas with multiple land uses, such as that shown in Figure 11.4. She then multiplies her figures by 40 (there are forty acres in each small area) to convert the counts to acres, obtaining Table 11.3, Susan's base year class inventory.
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Chapter 11 Table 11.3 Base Year Land-Use Inventory Land-Use Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices High-rise Industry Warehouses Municipal Transmission level custs.
Areas
389.1 192.4 41.28 27.78 10.05 3.65 14.70
7.9 1.275 2.65
Acres 15564 7695 1651 1111
402 146 588 316 51 106
Step 2: Consumer Class Load Projections The purpose of this second step is to determine a per acre peak kVA for each land-use class, and make a projection of how these values will change over the twenty-five year study period. Susan will do so by first developing a set of per consumer peak loads for her base year, then converting them to per acre values, and finally projecting those values into the future. This is not a difficult process, but it takes care and attention to detail. Step 2a: Per consumer peak load by class. Like almost every utility, Springfield Light and Power meters only energy sales, not peak, for its residential and smaller commercial and industrial consumers. For these smaller consumers, Susan must estimate the load at time of peak. For the larger commercial and industrial users she has reliable metered demand data which she can use to make accurate assessments of their peak load. For the residential and small commercial/industrial peak estimation, she uses four sources of information: 1. Her judgment. Susan's been a distribution planner for a decade and has developed a fairly good sense of the loads and load behavior of her system. 2. Load research data from the Rate and Consumer Studies Department. A selected sample of 62 homes has been metered for demand behavior, as has a set of 37 representative small
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businesses. Although that work was done carefully, Susan knows that such data are often far from accurate for the application she has in mind (see Chapters 3 and 4). 3. Transformer load management (TLM) data. Springfield's TLM program uses an empirical formula to convert consumer billing kWh to peak load kVA estimates, so that it can predict if service transformers are overloaded and when they should be economically switched to a larger size. Susan can use this formula to calculate per consumer peak load from average billing statistics. 4. Feeder load data. Susan obtains readings of last year's summer and winter peak loads for several key feeders she has identified. These are feeders which serve mostly consumers of only one class, where she knows the type and number of consumers, as shown in Table 11.4. Susan plans to use this source of information, but she suspects that the TLM formula's estimates will be low, for several reasons. First, she understands that the TLM program is based on purely empirical "it seems to work well" formula, and she suspects that her TLM department has set their formula to the lowest estimator that will work in order to cut down on false alarms — situations where the TLM predicts a transformer is overloaded, but subsequent investigation shows that it is not. Second, she knows that "peak" to a transformer or a TLM program may mean the maximum average load over a two, three, or even four hour period » long enough to severely overheat the windings. She wants the peak hourly value, which might be higher than the peak over a longer period.
Table 11.4 Load Readings and Consumer Content for Selected Feeders Feeder Name Ridgeway 2 Eastside 4, branch 1 Northwest 2, branch 4 Eastside 3, branch 2 Riverside 4, branch 3
Number of Consumers by Class 8 1 7 class 2 (normal resid.) 240 class 3 (apt) 14 class 2, 32 class 3, 91 c!4 340 class 2, 23 class 5 56 classes 7 and 8
Summer PeakkVA 3,529 717.6 1,087 2,314 687.9
Winter Peak kVA 2,328 597.3 912.7 1,747 642.2
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Table 11.5 Per Consumer Summer Peak Load Data Values by Source in kVA/Consumer Diversified Contribution to System Peak
Class 1 2 3 4 5 6 7 8 9 10
Confidence:
Fdr data .5
Load Rsrch .15
TLM .15
4.41 4.32 2.99 10.23 36.74 15.24 9.33 78.20 -
5.21 4.85 3.17 10.47 37.25 15.60 9.20 83.20 -
4.17 3.99 2.78 8.52 36.80 . 12.93 8.95 75.60 -
Mtrd Dmd 1.0
320.00
5,120.00
Wtd Ave.
4.55 4.37 2.98 9.86 36.88 320.00 14.70 9.20 78.80 5,120.00
Of these four data sources, Susan has the most confidence in the feeder data, because the feeder load readings were metered accurately and she has precise counts of the consumers downstream from those points. She begins with that data, calculating each class's per consumer peak. For example, in Table 11.4, Ridgeway 2 feeder, which is purely residential class 2, yields values of 4.32 and 2.85 kVA respectively for summer and winter peak loads per consumer. Those values allow her to infer from the feeder loading on Eastside 3 that class 5 has summer and winter loadings of 36.74 kVA/consumer and 33.83 kVA/consumer. She writes out her estimates from the feeder data, the load research values, and the TLM program, as shown in Table 11.5. Weighting each source proportional to her confidence in it, she forms an average of the values weighted by her confidence in each source, obtaining the values in the last column of Table 11.5. In a similar manner she produces estimates for the winter loadings. She does not have complete confidence in any of these figures. Forecasting, particularly distribution forecasting, is an inexact science, although Susan is trying to be as exact as she can. Step 2b: Converting to per acre loads. Susan knows that later in her forecast she will be working on a geographic basis when counting consumers, land area, and the other factors involved, as she did with her base year map in Step 1. She wants to use acres as much as possible in her analysis, and therefore must translate her consumer loads into kVA/acre from kVA/consumer. Making this change will not add any error to her forecast, because somewhere in any distribution forecast the planner must convert land area from acres to number of consumers and/or vice versa. Every distribution load forecast contains an
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explicit or implicit consumers/acre density factor. Susan has just decided that she will do this explicitly, at the beginning of her simulation. There are a number of sound reasons for her decision. First, this is the traditional way distribution engineers and planners think about load — so many megawatts per square mile, or so many kilowatts per acre. Her intuition and judgment, based on a decade of experience, will apply more directly if she puts load data into this framework. More important, she is going to be counting land use on an acre basis while using her land use maps. It will be easier to convert her data to load, and check her figures quickly if she works with load on a per acre basis (remember, she will have a lot of figuring to do, all of it manual). In addition, much of the data she has or will obtain from the City of Springfield Zoning Department, as well as various state agencies are on an acre basis. Translating Between Consumer and Acre Bases Susan already knows the total number of acres of each land-use class (these are the totals on her map). In order to translate her data on a per consumer basis (Table 11.5) to a per acre basis, she needs to know the total number of consumers in each of her land-use classes. The Rate and Consumer Studies Department's Forecast of Electric Sales and Revenues, a thick volume published annually, is her starting place. It lists consumer counts by rate class. She has to break some of the rate classes into several subclasses so that they correspond with her classifications. For example, the single rate class "residential single family home" contains both larger homes on large lots (Residential 1) and medium-sized houses (Residential 2). To some extent Susan
Table 11.6 Consumers per Acre by Class Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices High-rise Industry Warehouses Municipal Hvy industry
Consumers + 10584 24524 10072 2444 684 88 824 316 41 5
Acres = Custs./acre 15564 7695 1651 1111 402 146 588 316 51 106
.68 3.2 6.1 2.2 1.7 .6 1.4 1 .8 .047
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has to rely on her own knowledge and that of her colleagues to do this, but she obtains useful statistics from City building permit and zoning data, discussions with builders and developers, and load research statistics. With a little thought and work, Susan obtains the consumer counts shown in Table 11.6, column 1. She uses these numbers, and the land-use acre inventory from the last column in Table 11.3, to determine the consumers/acre for each class ~ the final column in Table 11.6. She then uses those consumer/acre ratios to convert her summer per consumer kVA values (the final column in Table 11.5) to a per acre basis, obtaining the values shown in Table 11.7 (only summer values are shown). She performs an identical analysis for winter peak. With these numbers she can convert consumer-based figures to acre-based, and vice versa. Step 2c: Projecting per consumer peak data into the future. To complete this step, Susan needs to forecast these summer and winter peak kVA/acre figures into the future for the years she plans to study. Once again, she turns to the Rate and Consumer Studies Department's Forecast of Electric Sales and Revenues. The Rate and Consumer Studies department had used a consumer-class, end-use appliance subcategory load model (see Chapter 4) to project peak contribution and energy usage on a per consumer basis by rate class over the next twenty years. From the tables in their forecast report, Susan determines the expected percentage growth in per consumer peak by year, for each rate class. She applies these percentages to project her kVA/acre figures into the future, knowing as she does that this step is a big potential source of error. Rate and Consumer Studies' peak projections focus on contribution to system peak for each class (load at time of peak not necessarily peak daily load). Of course Susan does have an interest in peak contribution and system peak, but her abiding interest is in peak load by class, because many areas of her system (and
Table 11.7 Per Acre Summer Peak Load Density Conversion Class Residential 1 Residential 2 Aparrments/rwnhses Retail commercial Offices High-rise Industry Warehouses Municipal Hvy industry
kVA/cust x Custs./acre 4.55 4.37 2.98 9.86 36.88 320.0 14.7 9.2 78.8 5120.0
0.68 3.2 6.1 2.2 1.7 0.6 1.4 1.0 0.8 0.047
=
kV A/acre 3.09 13.98 18.18 21.69 62.69 192.00 20.58 9.20 63.04 240.64
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343
the equipment that will serve them) will see a local peak not at the time of system-coincident peak but at the time of local class peak. What she really needs is peak day hourly load curve shapes for each class. Those would give her both each class's load at time of system peak and peak load, if different. In fact, such data are available to Susan, but she prudently decides not to try to include it in her manual analysis. Rate and Consumer Studies used peak day load curve shape data in their end-use model, but didn't put that level of detail in their report. The raw data are available if Susan wants it. But while she has the resources and time to analyze and work with load curves on a consumer class basis now, she recognizes that without computerization she will not be able to work with composite class curves on a small area by small area basis later in her study. She takes a look at the hourly load curve data to give her a feel for the curve shapes, but decides to stick with her single peak-per-class figures. Thus, she has the figures shown in Tables 11.8 and 8.9. Later in her simulation process, she will have to verify and perhaps change these numbers, but for now they are good estimates. At this point that is all she needs ~ estimates that are starting points for her study. She will refine them later. Before continuing, Susan studies these numbers to make certain that they seem reasonable and that she understands what these future changes in per consumer (per acre) load mean to her plan. What intrigues her most is the relative growth of the summer and winter loads. She has known for several years that Springfield's load was forecast to become winter peaking, but these figures illustrate just what that means to her system. Specifically, she notes that: 1. Many commercial and industrial classes will remain summer peaking throughout most of the twenty-five-year study period, only switching to winter peaking in the last few years. 2. The residential class will become winter peaking in less than four years, and its winter peak will continue to grow much faster than summer's. Susan realizes that this means substations and feeders serving predominantly residential areas of the Springfield Light and Power system will become winter peaking in only two to three years, even though the system, as a whole, may not be winter peaking until another five years later. Residential parts of her system may need to be reinforced for this higher and faster growing winter peak much sooner than had been expected. Reasoning that if she had been unaware of this problem, others in the Engineering Division probably were also, she sends a short memo to her boss, summarizing the problem and suggesting that it be routed to the other department heads.
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Table 11.8 Diversified Summer Peak Load Densities by Class (kVA/acre) Consumer Class Residential 1 Residential 2 Apartments/Twn h ses Retail commercial Offices High-rise Industry Warehouses Municipal Heavy industry
Now
3.09 13.98 18.18 21.69 62.69 192.00 20.58 9.20 63.04 240.64
2
4
Year 8
12
20
25*
2.80 2.75 2.73 3.03 2.87 2.97 13.75 13.52 12.99 12.50 12.02 11.80 17.83 17.59 17.40 17.25 17.10 17.00 20.51 20.00 19.86 19.75 19.65 19.55 61.40 60.50 59.50 59.00 58.80 58.65 189.90 187.20 185.00 183.00 181.20 179.80 20.00 19.50 19.00 18.75 18.69 18.66 9.32 9.21 9.24 9.28 9.30 9.22 61.80 59.35 57.50 56.73 56.73 56.73 240.64 239.00 237.00 235.00 233.00 232.00
* Extrapolated from previous time period growth rates.
Table 11.9 Diversified Winter Peak Load Densities by Class (kVA/acre) Consumer Class Residential 1 Residential 2 Apartments/Twnhses Retail commercial Offices High-rise Industry Warehouses Municipal Heavy industry
Now
2.85 11.86 15.32 18.64 57.39 161.00 19.62 11.30 51.60 237.40
2
4
Year 8
12
20
25*
3.54 3.54 3.54 2.97 3.10 3.33 12.20 12.54 13.15 13.60 13.80 13.80 15.61 15.95 16.42 16.60 16.70 16.75 18.82 20.04 21.00 22.00 23.00 23.50 57.41 57.40 57.30 57.00 56.80 56.80 159.00 160.00 162.0 165.00 170.00 173.00 19.60 19.55 19.00 18.75 18.69 18.64 9.70 9.58 11.00 10.50 10.00 9.90 50.70 49.20 47.80 46.44 46.44 46.44 237.40 237.00 236.00 234.00 234.0 234.00
* Extrapolated from previous time period growth rates.
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A Detailed Look at the Simulation Method Step 3: Global Forecast of Consumer Growth
The purpose of this third step is to produce a count (in acres) for each land-use class throughout the twenty-five-year study period. For the base scenario, this is easy to obtain from Rate and Consumer Studies' report, which lists consumer counts by rate class by year for the service territory. Those are not on an acre basis, but they give Susan the growth rates she needs to calculate acres. Susan needs similar numbers for the factory scenario. Fortunately, Rate and Consumer Studies had been asked to provide management with a projection of the NipponAmerica factory's impact on revenues and has already completed its study using a method similar to that described in Chapter 10, section 3.
Table 11.10 Projected Number of Consumers by Land-Use class Rate Class
Land-use class
Now
8
12
20
25*
rural 10584 11395 12200 14001 15821 19934 22885 normal 24524 26772 28820 32854 37125 46777 53702 multi-family 10072 10788 11532 13146 14854 18716 21487 Gen. serv. retail 2444 2617 2798 3189 3604 4541 5213 802 1504 offices 684 740 915 1040 1310 Lrg. gn. srv. big, high-rise 88 105 141 204 97 123 178 Industrial small shops, etc. 824 951 1094 1789 890 1236 1558 361 412 674 warehouses 31 6 338 466 587 Municipal city, schools, etc. 41 44 47 54 61 77 88 Spec, contr. transmission custs 5 5.72 6.52 7.4 10.6 5.35 9..3 *Extrapolated from year 1 5 to 20 year trends. Residential
Table 11.11 Projected Consumer Counts Added by the Pickup Truck Factory Scenario Land-Use Class Residential
2
rural 8 normal 544 mult-fam. 445 Commercial retail 46 offices 14 High-rise 2 Industry small 17 warehouses 6 Municipal 1
Years After Construction Begins 4 8 12 20 33 2272 1860 207 58 7 70 27 4
59 4064 3337 369 104 13 125 48 6
59 4064 3337 369 104 13 125 48 6
59 4064 3337 369 104 13 125 48 6
25 59 4064 3337 369 104 13 125 48 6
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Convert consumer counts to acres. Using her statistics on consumer density (Table 11.7), Susan simply converts the consumer counts in the R&CS tables above to acres by dividing each consumer count by its appropriate consumers/acre value, obtaining Tables 11.12 A and B, below. (Note that Table 11.12 B is identical to Table 10.3 in Chapter 10's example.) These are Susan's "global totals," the consumer counts that will "drive" her forecast of spatial load growth. Assuming the R&CS Department's forecast is accurate, and her rate class disaggregations and load density analysis were correct, the SL&P service territory will have the future land use inventories given by the columns shown in Table 11.12. Her job through the rest of the simulation forecast process is to assign that global growth to specific small areas. Table 11.12 A. Projected Consumer Class Acres by Year ~ Base Scenario Land-Use class
12
Now
Residential 1 15564 Residential 2 7695 Apartments/Twnhses 1651 Retail commercial 1111 Offices 402 High rise 146 Industry 588 Warehouses 316 Municipal 51 Transmission level cons. 106
16757 8366 1768 1190 435 162 635 338 55 114
20
17941 20589 23266 29314 9006 10266 11601 14618 1891 2155 2435 3068 1272 1638 2064 1450 611 770 471 538 175 205 235 296 1112 679 781 882 587 361 412 466 76 96 59 68 122 139 157 198
25 33654 16782 3522 2369 884 340 1278 674 110 225
Table 11.12 B. Projected Additional Consumer Class Acres by Year ~ Factory Scenario Land-Use class
Now
Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices High rise Industry Warehouses Municipal Addtnl Transmission level cons.
2
4
8
12 170 73 22 8 3 12 6 1 2
49 710 305 94 34 12 50 27 5 4
12
20
25
87 1,270 547 168 61 22 89 48 8 7
87 1,270 2547 168 61 22 89 48 8 7
87 1,270 547 168 61 22 89 48 8 7
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Table 11.13 Comparison of System Peak Load* Projections (MVA)
Forecast Year 0 2 4 8 12 20 25
From Susan's Numbers Summer Winter 315 328 343 379 425 525 598
270 299 328 388 452 575 662
From R&CS's Forecast Summer Winter 315 328 344 380 427 528
270 298 325 388 452 574
System peak load with transmission losses removed.
Check by calculating future system loads. Before going on to the next step, Susan combines her peak load per acre data (Table 11.8) with the projected land-use totals (Table 11.12), in order to calculate the system peak load for her base year and for each of her future study years. For each future year, she multiplies the projected number of acres for each land-use class by that class's kVA/acre for that year, to obtain the total load for that class (for example, in year 2 for Class 1, 3.03 kVA/acre times 16757 acres = 50.77 MVA). She then adds all the land use's loads together by year to get the total system loads projected by her figures, as shown in Table 11.13. As a check, she compares these to Rate and Consumer Studies' projections of annual system peak. She is quite pleased with her results, which are within 1% in all cases. These are good results, but not extraordinary. It is advisable not to go on past this step if there is any significant mismatch. This match means that she has the overall totals adjusted correctly — in the rest of her simulation procedure, she will be assigning the correct total amounts of consumer load ("correct" in the sense that it is totally consistent with Rate and Consumer Studies' figures) to the small areas on her map.
Step 4: Base Year Calibration A laborious step now faces Susan — spatial calibration of her base year loads. The data shown in the top line of Table 11.13 indicate that her overall totals match the actual recorded system loads — her combination of land-use totals and
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peak KVA/acre sums to the same figures as the most recent actual system peak. But how does she know that her spatial allocation of load (her geographic distribution of land use) is correct? She must verify the accuracy of the spatial or small area base year data by making certain that they correctly explain her existing substation loads. To do so, Susan must convert the land-use colors in each small area of her colored land use map to load per small area using the per acre load density figures developed in Step 2. Then she must sum up the appropriate small areas in each substation area to get a "forecast" base year peak load for each substation, and compare those sums to actual recorded substation peak loads. Given that Susan has only a calculator, pencil, and paper, this will be a laborious step. Determined to complete it as quickly and efficiently as possible, she lays a second sheet of tracing paper atop her colored land use map. She has, from bottom to top: the system map, her plastic overlay grid, her colored land use map, and this new, blank sheet. She can see through this top sheet of tracing paper to the colors on the map below and the small area grid beneath that. For each small area, she examines the colors covering that cell, and converts them to load in the manner shown below, writing the load value in pencil on the top layer of paper, as shown below:
50S y e l l o w < r e t a i l > x 2 0 acres 3 21.69 kUfl/acre = 433.8 40$ green
0.0 kUR/acre = 0.0 TOTflL 657.5
This is a very straightforward procedure, but quite tedious. Susan works at it on and off for a week, filling in her time with other work (a T&D planner is never without other work). Ultimately, she fills in every small area on this top level of tracing paper over her map with its calculated small area load. Spatial calibration of base year data Before proceeding with her forecast, Susan must verify that this base year small area load map matches the actual spatial distribution of loads in her system. If it doesn't, she must adjust the load density values and/or land uses in her base model and recalculate her map, repeating this process until the map is accurate.
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For example, she might find that the grid estimates for substations serving predominantly residential areas are low, and those for predominantly commercial areas are high. In that case, she would raise the residential load density values, while cutting the commercial densities, and recalculate her map. But whatever is required, Susan knows that she cannot proceed with a forecast until her base year data match actual substation loads — if her base data cannot explain present substation peak loads, what expectation is there that a forecast built upon them will accurately predict future substation peak loads? Susan draws the boundaries of her substation service areas on the load grid sheet and adds up all the small area loads within each substation to obtain that substation's load value, which should correspond to its past summer peak. She writes down some statistics on each substation, including its actual load and its load as estimated by the grid, in Table 11.14, below.
Table 11.14 Substation Summer Peak Loads as Estimated from the Base Year Grid Substation Name Coal Hollow Cross River Douglas Downtown Eastside Georgia St. Mountainview Northwest Nottingham Opperman Ridgeway Riverside Western
Land-Use Composition
Load: Sum from Grid*
ind., municipal, apts. residential, retail residential high-rise, offices, apts. offices, comm, resid. residential, industrial residential, retail industrial, residential residential, industrial high-rise, retail, resid. residential industrial, warehouses residential
28.0 23.9 25.7 40.5 13.6 28.2 15.9 23.9 22.8 40.8 22.7 18.3 10.7 315.0
Load: Sum with Coin.2
29.1 24.8 26.7 42.0 14.1 29.3 16.5 24.8 23.7 42.4 23.6 19.0 11.1 327.1
Actual Load3
Percent Error
28.2 24.6 22.4 54.5 22.3 27.2 16.7 23.8 21.3 37.8 20.2 18.7
+3.2 +.01 +19.2 -22.7 -36.8 +7.3 -.01 +4.2 +11.3 +12.1 +16.9 +1.6 +19.4
327.1
1 This is the sum of all the small area loads in the substation service area. 2 This is the sum adjusted for non-coincidence of peak. 3 This is the summer peak load recorded at the substation.
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Susan adjusts all the small-area-derived substation loads upwards by 3.84% to account for non-coincidence of peaks, thereby obtaining the second column of numbers shown in Table 11.14. She does so because she is comparing her small area loads, which are models of coincident load at peak, to non-coincident substation peak readings. The 3.84% adjustment should correct for this, and it seems to, bringing her load up to the sum of the substation peaks. Susan knew that her total load would be pretty close to correct because she had previously checked that against the system totals, in Table 11.13 in Step 3. But she is quite disappointed at how poorly her "predicted" substation loads match actual readings ~ only two of her substations are even close to correct. Many are quite far off. Although it is possible that her land-use data are in error ~ that the colors and amounts of different land-use classes that she colored into each small area are wrong ~ Susan understands that this is usually not the case, that if recent aerial photos were used, the land-use data will be fairly correct. Most likely, the problem is that her load densities (Table 11.7) are wrong. A little examination of Table 11.14 shows that substations with large proportions of residential classes 1 and 2 have "predicted" substation peak loads that are high compared to the actual metered reading. The more residential, the greater the error. Judging from Western, Ridgeway, and Douglas substations, Susan determines that the residential load density appears to be about 19% high.3 The total system load is correct, so that if Susan simply decreases the residential load densities to correct this error, her total will decrease. The fact that residential is high while the total is correct means that something else is low. She studies Table 11.14 and discovers the following clues: 1. The two substations that are most correct, Cross River and Mountainview, have a mixture of residential and retail commercial. Perhaps retail commercial's density is low, offsetting residential's "high" error.
3
An accomplished engineer might wonder why Susan doesn't solve a set of simultaneous equations to obtain her load densities. After all, she has ten unknowns (her densities) and thirteen knowns (her substation loads), more than enough to obtain a good fit to the densities using standard statistical techniques. In practice this will not work because of colinearity in the composition of substation land uses ~ most substations, or at least enough of them, have similar proportions of residential to commercial land use, so that statistically they are merely repeats of the same information as far as the statistical fitting is concerned.
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2. Downtown substation's "predicted" load is very low, as is Eastside's. Neither has much retail commercial, but both have a large number of office (classes 5 and 6) load. Since the high-rise load she is using is based on metered data, she is fairly certain it is correct. That leaves offices (low-rise, class 5) as the culprit. Susan plays "data detective" for a while longer, but finds no other useful clues. She spends a few minutes making some calculations, and ultimately decides to decrease the residential (classes 1 and 2) load densities (as listed in her original calculation, in the last column Table 11.7) by 18% and increase the retail and office (classes 4 and 5) load densities by a huge 72%. These adjustments appear to be what it would take to correct the major errors in her substation loads, lowering the total residential load (classes 1 and 2) and increasing the total commercial and office load (classes 4 and 5) by exactly equal amounts, so that her system load total ~ which is correct as far as she is concerned « will stay the same. Using these revised values, Susan recalculates her load grid and again adds up small area loads by substation service area, spacing the job over five workdays so that the work doesn't become too tedious. This time, she obtains a much better fit between estimated and actual substation loads, as shown in Table 11.15. The mismatch shown is acceptable. The average absolute error in matching substation peak loads is 2.75% (slightly less than the annual system load growth rate of 3%), and the maximum disagreement is 5% ~ about one and one-half years worth of growth. In a rather crude way, this level of error can be interpreted as meaning that without further adjustment, this simulation's results would have a confidence range of about one to one and one-half years in predicting the timing of substation level growth. Susan would prefer that the error were less, but she comforts herself with the fact that this amount of error is less than half the amount that trending (her only other option) has when forecasting peak loads only two or three years into the future. She also knows that she will make further adjustments later. Susan has been unusually, perhaps unreasonably, lucky in this example. Calibration of small area and class peak/acre values is a very difficult task. Obtaining accurate matches as described here seldom if ever occurs after only two iterations ~ it can take four, five, or even six adjustments to reach a good solution to the peak kVA/acre factor. Beyond this, occasionally a match simply cannot be achieved, in which case the land use data must be re-examined to determine if they are incorrect. Particularly when land use has been coded manually, as in this example, a high level of consistency in definitions is difficult to achieve, and some variation in interpretation makes its way into the data base (see Tram et al., 1983).
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Table 11.15 Substation Summer Peak Loads After Adjustment of Load Densities Substation Name
Land-Use Composition
Coal Hollow Cross River Douglas Downtown Eastside Georgia St. Mountainview Northwest Nottingham Opperman Ridgeway Riverside Western
ind. municipal, apts. residential, retail residential high-rise, offices, apts. offices, comm., resid. residential, industrial residential, retail industrial, residential residential, industrial high-rise, retail, resid. residential industrial, warehouses residential
from
Load: Sum Grid
27.9 24.2 21.1 49.9 22.4 27.0 15.8 22.2 20.2 37.5 19.0 18.9
Load: Sum with Coin.
29.0 25.1 21.9 51.8 23.3 28.0 16.4 23.1 21.0 38.9 19.7 19.6
Actual Load
Percent Error
28.2 24.6 22.4 54.5 22.3 27.2 16.7 23.8 21.3 37.8 20.2 18.7
+2.8 +2.0 -2.2 -5.0 +4.5 +2.9 -1.8 -2.9 -1.4 +2.9 -2.5 +4.8
0.0
8.9
9.3
9.3
315.0
327.1
327.1
One reason Susan is willing to accept the mismatches in Table 11.15 is that she observes that the errors correspond to the pattern shown in Figure 11.6: the mismatches in load are inversely proportional to substation boundary circumference and tend to be plus and minus across substation boundaries. Her largest percent errors are in substations with the smallest service areas, a sign (but not absolute proof) that some of her mismatch is due to boundary location errors like those in Figure 11.7, which cannot be corrected without increasing the spatial resolution of her model (i.e., using smaller, and thus more, small areas to cover her service territory, which would greatly increase the amount of manual labor in her study). Boundary location errors are caused by the grid's inability to accurately track every detail in the substation boundaries. Such errors will be most pronounced in substations with smaller service areas (Downtown, Eastside, Riverside). For substations with larger service areas, boundary location errors tend to cancel out along the relatively longer substation service area boundaries. These types of error cause mostly plus-minus differences across a boundary, one substation over while its neighbor is under, as shown in Figure 11.6. Susan is satisfied that the
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353
-493kVA
Figure 11.6 Although the small area grid estimates are not perfect, there are plus and minus errors on different sides of nearly every substation boundary and that substations with larger service areas have lower errors.
Shaded Area shows subst. area modeled -by grid.
Figure 11.7 Substation boundary errors are due to the grid's inability to see the boundary accurately enough to track the service area precisely, as shown here.
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Table 11.16 Final Diversified Summer Peak Load Densities by Class (kVA/acre) Consumer Class Residential 1 Residential 2 Apartments/twnh ses Retail commercial Offices High-rise Industry Warehouses Municipal Heavy industry
Year Now
2.53 11.46 18.18 37.31 107.80 192.00 20.58 9.20 63.04 240.64
2
4
8
12
20
25*
2.29 2.24 2.48 2.44 2.35 2.25 9.86 9.67 11.28 11.09 10.65 10.25 17.83 17.59 17.40 17.25 17.10 17.0 35.28 34.40 34.16 33.97 33.80 33.63 105.60 104.80 102.30 101.50 101.10 100.90 189.90 187.20 185.00 183.00 181.20 179.80 20.00 19.50 19.00 18.75 18.69 18.66 9.21 9.24 9.28 9.32 9.30 9.22 61.80 59.35 57.50 56.73 56.73 56.73 240.64 239.00 237.00 235.00 233.00 232.00
Table 11.17 Final Diversified Winter Peak Load Densities by Class (kV A/acre) Consumer Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices High-rise Industry Warehouses Municipal Hvy industry
Now
2.31 9.60 15.32 32.81 101.00 161.00 19.62 11.3 51.60 237.40
2
4
Year 8
12
20
25*
2.41 2.87 2.87 2.87 2.51 2.70 9.88 10.16 10.65 11.02 11.18 11.18 15.61 15.95 16.42 16.60 16.70 16.75 33.12 35.27 36.96 38.72 40.48 41.36 101.00 101.00 100.80 100.30 99.97 99.97 159.00 160.00 162.00 165.00 170.00 173.00 19.60 19.55 19.00 18.75 18.69 18.64 11.00 10.50 10.00 9.90 9.70 9.58 50.70 49.20 47.80 46.44 46.44 46.44 237.30 237.00 236.00 234.00 234.00 234.00
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boundary location errors are the major reason for the error in her substation load
fit4
Her work led to a set of adjusted values for the kVA/acre assigned to each consumer class, which are shown in the "Now" column of Tables 11.16 (compare these to her original values in the same column in Table 11.8). She now applies the growth rates projected for the per capita changes in demand for each class, taken from the Rate and Consumer Studies report, to those "Now" column values to obtain forecast peak/acre values for each consumer class for the entire forecast period, as shown in the other columns of Table 11.16. (Another way to look at this is that Susan obtained Table 11.16 by applying her calibration adjustments in the preceding step to every column of Table 11.8.) This gives the final summer kVA/acre figures shown. She repeats the entire calibration process reviewed above for her winter peak figures (more labor!), obtaining an equally good match and yielding her final winter kVA/acre values, as shown in Table 11.17. So far, Susan has developed: a grid map for her base year with various colors showing the consumer locations by class; a set of kVA/acre peak load values by class for her base and future years; and a set of global totals and consumer counts in acres by class, which are all consistent with every data source she can obtain ~ Rate and Consumer Studies, recorded substation peak loads, etc. Her "model" of the present small area load behavior of her system matches all recorded system and substation load data, and is consistent with the Rate and Consumer Studies'forecast. This is the best she can do with her available data and resources. Step 5: Spatial Consumer Forecast Finally, after several weeks of accumulated drudgery, Susan has reached the one step in her manual simulation procedure that is undeniably fun. Her goal in this step is to produce a set of colored land use maps, similar to Susan's base year map, for the future study years — 2, 4, 8, 12, 20, and 25 years into the future. Susan will draft them by progressively moving into the future one study year at a time, beginning with two years into the future and moving to four, etc., in a series of iterations that build on one another. 4
If she had been doing this study with a good computerized simulation method, she could have used 10 acre small areas (1/4 the area of the 40 acre areas she is using) or even 2.5 acre small areas (1/16 the area), reducing this error substantially. However, this would have increased the number of small areas she had to calculate by four or sixteen times, making her study nearly impossible to do by hand.
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For each study year, she will literally color by class the expected land-use developments onto her map. In each study year, the amount of land use she adds in each class will be the incremental amount of land-use growth predicted by Table 11.12 A (base forecast) and the sum of Tables 11.12 A and B (the factory scenario forecast includes the base and the incremental factory amounts). First study year: year +2. Consulting her global forecast land-use figures (Table 11.12), Susan determines that from year 0 to year 2, the increases in land use inventory are as shown in Table 11.18. These changes in land use are forecast to occur somewhere in her system, but where is up to her. In this step she will decide. Dividing the acre counts by 40 acres per small area gives her the number of small areas that need to be colored onto her map for each class. Of course, she does not have to color all of any one small area just one color — she can add only five acres of one class to a vacant small area and leave the other thirty-five blank, or add ten acres each of four different classes, or fill in a few acres left vacant in otherwise already-filled small areas, as she chooses. But converting to small area units gives her an idea of how much area she'll have to add. Susan removes the sheet of tracing paper on which she had written her final set of base year grid loads (she saves it for future reference), and lays down a fresh sheet. She has on her desk, from bottom to top: the system map, the plastic overlay showing the small area grid, the first layer of tracing paper with the base year land uses colored on it, and her new, blank sheet. Susan will color the
Table 11.18 Increase in Land Use by Class, Years 0 to 2 Class
1 2 3 4 5 6 7 8 9 10
Residential 1 Residential 2 Apartments/twnh ses Retail commercial Offices High-rise Warehouses Industry Municipal Transmission level
Acres
1193
671 117 79 33 16 22 47 4 8
Areas
29.9 16.78 2.95 1.98
.83 .4 .55 1.18
.1 .2
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amounts of land use shown above onto this blank sheet, to forecast where new growth will occur. Before starting, Susan reviews a thick folder of newspaper clippings, memos, and magazine articles she has collected during the last year, information on expected growth in the Springfield Light and Power service territory. Many of the articles are about the new Nippon-America pickup truck factory. She sets those aside and studies the rest ~ an article on the expected impact of the new bridge (to be completed in about a year and a half) across the Springfield River, articles about a new shopping mall to be built near the intersection of 1-36 and US93, a new city park and softball field northeast of town, a new high-rise insurance company headquarters building to be constructed downtown (which will be 11 stories, quite tall for Springfield), and a new industrial park near the airport, as well as others. These give her a pretty good feel for the short-term growth trends in her service territory. Susan also has statistics on local building permit applications, obtained from the Springfield city government, and more useful yet, the platts (lot and street maps) of several major subdivisions planned by local developers, along with letters from those developers giving their schedules for completing and selling the new homes to be built at those sites. Susan reviews the platts carefully, but ignores the developer's predictions about timing ~ she's never met a developer who wasn't unduly optimistic about the completion and sales rates of the next batch of 100 homes, or 360 homes, or however many were planned. When she is satisfied that she has noted everything important in the news articles, Susan begins her job of coloring the year 2 land use additions onto her map. She starts by adding the new city park and ball field to her map, first outlining its boundaries on her top sheet of tracing paper, then coloring that area purple to designate that it's off limits to any further development. She adds several other "vacant restricted areas" which she knows or believes will be added in the next two years. She gets "vacant restricted" out of the way first because it reduces the amount of land she has to consider as a possibility for development in her subsequent steps. Now, Susan works through the other land-use classes, in order of decreasing price of land, so that the highest price land uses have "first choice." Therefore, she does high-rise (class 6) first, because that land use can almost always "outbid" other uses for a particular site. She does classes on her list — retail, offices, apartments, and so forth, in the order 6, 4, 5, 3, 10, 9, 2, 1, 7, 8. For each, she will add a total corresponding to the year 2 incremental additions listed in Table 11.18, coloring it on her map only where it can occur (i.e., in vacant, non-restricted land).
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For each class, she begins by adding any of the "announced development" mentioned in the articles, building permits, and platts she reviewed ~ all of that which she believes is reasonable. However, in every case this falls short of the totals listed in Table 11.18, leaving her with more to allocate. She determines how much of each class is left to add, and spreads that growth over the map where she thinks it will occur. Even though she may be adding several small areas' worth of growth (for example, she will add 79 acres, or a total of nearly two small areas, of retail commercial), she does not have to fill in all 40 acres of a vacant small area or put all of the additions near one another. She can space that 79 acres over 15 or more small areas if she wants to, adding two acres here, three there, etc., filling in nooks and crannies of empty space in otherwise developed small areas. For example, she colors 1193 acres, equal to 29.9 small areas, of class 1 (light green) onto the map, and 671 acres, or 16.78 small areas of class 2 (green), adding some residential to more than 125 different small areas. She puts most of the growth on the outskirts of town, filling in the vacant land in some of the more newly constructed subdivisions that she learned about in her articles. She colors in only about seven percent of her residential growth across the river on the other side of the new bridge. It will be a big influence, but it is not scheduled to be completed until the last six months of this two year time period. She feels it is premature to expect a big building boom in that area until after the bridge is finished. She decides that industrial growth will stay close to the present industrial areas west of downtown, gradually moving north into the vacant land along the river and near the railroad track. So, in this near term time period, she colors industrial growth in those vacant, available areas between the river and the railroad tracks, immediately north of the present industry. Susan's judgment is critical throughout this step. She is determining the locations for future development using only her judgment and knowledge of Springfield's growth, without the aid of any numerical pattern analysis available to those used a computerized simulation. But this is the best she can do manually. In addition, she is conscientious and has a grasp of growth trends. Over the preceding ten years, both in the course of her job and because of her professional interest in Springfield's growth, she has paid attention to the city's growth patterns. In addition, she has read two books, this one and Edge City, by Joel Garreau. Thus, she understands the simulation process she is applying and the way builders, city planners, and investors think and act with regard to land development. With such experience and study behind them, and careful preparation and attention to detail, most T&D planners can do a fairly good job in situations where the city is relatively small, like Springfield. Large cities and regions are another matter entirely, and will be discussed in Chapters 12 and 19.
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Redevelopment. Susan tackles one situation that is quite unusual for her, but very common to distribution planners in many older cities — redevelopment of existing developed areas. Not all new construction occurs in areas that were vacant prior to development. In fact, in some utility areas, the bulk of growth occurs as redevelopment of existing developed areas, as for example when several blocks of older homes are razed in order to put in an office park, or when an older area of townhouses is "gentrified" by tearing out older construction and adding newer more expensive housing. Chapter 19 discusses redevelopment modeling and forecasting in more detail. In Springfield's case, there is not a lot of new development (this is common in smaller cities and towns), but a new set of apartment buildings is scheduled to be built northeast of downtown, replacing 19 acres of homes built just after World War I, so old and run down that many have been condemned and none are worth preserving. After thinking about it, Susan handles this redevelopment by: 1. Coloring over the nineteen acres of residential class 2 (green) with dark green to indicate the redevelopment to apartments 2. Coloring in 19 more acres of class 2 (green) into available vacant land on the outskirts of town, to make up for the 19 acres she lost Coloring in the future growth is the fun part of the study, and Susan attacks it with relish, finishing her two-year growth map in one day of intense but satisfying work. She concludes by checking her completed map, making certain that the total amount of each class she added corresponds exactly with the growth called for in Table 11.18. By looking through her top sheet (the one she just colored) to the one below (the base year colored sheet), she can see the combined land use. She now converts the combined base year and two-year-ahead land uses to grid loads by laying a fresh sheet of tracing paper on top of these maps, and converting each small area's land use to load exactly as she did earlier when she computed base year loads in the calibration step. The only difference is that now she uses the two-year-ahead consumer class load densities (from Table 11.16) instead of the base year load densities, and she includes the base year land use and the land use she has just colored for year +2. When done computing a load for each small area and marking it on her top layer of tracing paper, she removes the two-yearahead summer load grid, carefully rolls it up, and saves it. She places another sheet of blank tracing paper atop her desk and in a similar manner produces a winter load map. When complete, she removes it and carefully rolls it up and saves it for later use. In addition to her progress so far, in this very labor intensive step Susan has gained a keen appreciation for the benefits of computerization.
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Next iteration: year +4. Susan puts another layer of tracing paper onto her desktop, above the two-year ahead land-use colored map. She repeats the entire process she just performed for the two-year-ahead time frame, but now adding the incremental land use inventory for year four (difference between two- and four-year-ahead time periods). This transforms her total colored map set (base year + year two + year four) to a four-year-ahead map. Once done, she calculates four-year-ahead summer and winter peak load grid maps from the land uses as she did for year two. Further iterations: years +8 through +25. Susan continues this iterative process, producing colored land-use maps and calculating summer and winter load grid maps for years eight, twelve, twenty and twenty-five. As she moves out into the future, she finds herself having less and less information (newspaper articles, developer's plans, etc.) about development in that time period. She has to rely more and more on her own judgment and a sense of where growth will occur. Her base scenario forecast is finished. Her year-20 land-use map is shown in Figure 11.8.
service rerritory Boundary :: Lo-dens Res. III! Residential Illl
Apartments
m
Retail
8
Offices
•
Hi-rise
=
Lgt. Ind.
=
Mad. Ind.
. Hvylnd.
SPRINGFIELD LIGHT & POVER CO Service Territory and Distribution Substations
Figure 11.8 Susan's 20-year-ahead (final actual forecast year) land-use map. Springfield has grown considerably during the period (compare to Figure 11.5).
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Factory Scenario In a manner similar to the one she used for the base scenario, Susan next produces a set of land-use maps and load grids for the "pickup truck" scenario. She begins by removing all of her colored land-use maps for the base scenario she just completed, except year two. What she has left on her desk is: the map of Springfield, her plastic grid, her base year colored land-use map, and the twoyear-ahead colored land-use map. Since construction of the factory would begin two years from now, the factory scenario is identical to her base scenario through that first time period.5 From there, she repeats the process of stepping to the future a study year at a time, coloring land use and calculating load grids as she did for the base scenario, except that now she uses incremental growth amounts for all classes that are the sum of Tables 11.12 A and B. For example, in her base scenario for year 4, she had an increase in class 2 of 640 acres (9006 minus 8366 acres), for a total of sixteen 40 acre small areas she had to color onto her map to account for the incremental class 2 development in year 4. In this factory scenario, she adds to that the factory-caused growth for 2 years after construction starts — another 170 acres - for a total of 810 acres, or 20.25 small areas' worth of land that she must color onto the map in this case. In locating this growth on her maps, she makes certain that growth corresponds closely to what she had just done for the base forecast, but she bears in mind that additional development caused by the factory will tend to cluster in the northern areas. (Workers moving to the region to work at the factory will want to live near their employment.) Note that Susan did not produce this scenario by simply adding the additional growth caused by the factory to the incremental land-use maps she had produced for the base scenario. For example, she could have pulled out her year 4 incremental land-use map and added the 170 acres of additional class 2 5 In actual fact, two-year-ahead growth might be different in this scenario because anticipation of the factory's development could alter the decisions of some local developers about where they locate new buildings, before the factory is built. However, Susan decides not to try to tackle this subtlety for three reasons. First, such anticipation will have only a small impact on growth patterns. Second, at the present time, with the factory not announced but rumored, it is having something of that same effect anyway, just because it might happen, impacting both base and factory scenarios in the same manner. Thus, its impact is already included in her forecasts. Third, while she realizes the second reason is partly rationalization, she also recognizes that analysis of growth influences due to "anticipated events" is among the trickiest of tasks in spatial load growth simulation, tackled by only the most advanced computerized simulation methods, and that she hasn't anywhere near the computational resources to attempt it.
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development, and done similarly for all classes. That shortcut would have saved her time, but would have been less accurate. The factory might alter where base land-use development goes, or, more likely, it and the growth it causes will "use up" some of the land she forecast for base development for another purpose (i.e., maybe because of the additional growth caused by the factory, office commercial will use land in year 4 that she had forecast as becoming residential in year 8 in the base scenario), making a real mess of her work. For these reasons, it is prudent for her to re-do the entire forecast, rather than take that shortcut. Susan has no problems producing the factory scenario, other than having to slog through a lot of manual work, and completes the alternative forecast in an orderly manner, producing land-use maps (Figure 11.9) and converting them to summer and winter peak load grids as she goes along, until she carries her scenario study through the twenty-fifth year as she did her base case.
SPRINGFIELD LIGHT & POWER CO Service Territory and Distribution Substations
Figure 11.9 The year-20 factory-scenario land-use map, with additional land use caused by the factory added to that expected from base sources of growth.
A Detailed Look at the Simulation Method Base Year-315 MVA
Base scenario Year 20 - 525 MVA
363
Base scenario, year 8 - 379 MVA
Factory scenario, year 20 - 552 MVA
Figure 11.10 Graphic displays of the summer peak load distributions for the base and factory scenarios. Not surprisingly, most of the factory's impact on growth is on the northern side of the city, since the factory is near the northern edge of the service territory.
Figure 11.10 shows computer-generated "gray scale" maps of selected parts of Susan's forecasts, in which each small area is shaded to represent its relative load density based on the calculated summer peak loads. Because she did not have a computer, and did not want to do this additional, laborious step manually, Susan never had such an illuminating display of her work. No doubt she would have loved this set of computer-generated maps. Forecast review. Susan looks over all her forecasts, including the 25-year forecast which is, legitimately, not really part of her planning. The growth patterns seem reasonable. The majority of Springfield's growth occurs to the Northeast, beyond Ridgeway and Mountainview substations. Over the long term
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(years 12-20), a significant portion of the growth moves out beyond US93, north of 1-36, where Springfield Light and Power has no significant distribution facilities and, worse, no subtransmission. Even though it's a great deal of work, Susan adds up her small area projections by substation area for three of her forecast years (4, 8, and 20 years ahead). In addition, she adds the amount of mismatch that she had in her original base year substation fit to the actual substation loads. For example, in her final fit to substation base year peaks (Table 11.15), Coal Hollow substation's load as represented by her small area loads was 800 kVA high. Therefore, she now adjusts not only her base year load for Coal Hollow, but every other year by that same amount, subtracting 800 kW to compensate for the boundary location error. Her results, given in Table 11.19, provide a good idea of where the future growth is located and how large it is relative to present system loads. She realizes that SL&P can, and no doubt will, change substation areas via switching and new construction during the next twenty-five years, to accommodate this growth. Still, this table tells her a lot about how the projected growth relates to
Table 11.19 Forecast Annual Substation Peak Loads--Maximum of Summer or Winter Peak Load (MVA) Substation Name
Peak Base year
Coal Hollow Cross River Douglas Downtown Eastside Georgia St. Mountainview Northwest Nottingham Rd Opperman Ridgeway Riverside Western Sum of substs. System peak Subst. peak coinci.
28.2 24.6 22.4 54.5 22.3 27.2 16.7 23.8 21.3 37.8 20.2 18.7 9.3 326.1 315. .963
Peak 4 years
Peak 8 years
28.5 23.9 23.8 56.9 25.9 27.6 25.8 23.4 25.0 42.5 26.5 18.6 12.4 360.8 343. .951
29.6 23.2 27.8 60.3 28.7 27.1 40.1 22.7 34.5 48.8 35.1 18.4 15.5 411.8 388. .942
Peak 20 years 28.2 22.9 37.2 67.8 29.5 26.7 111.5 22.7 92.5 65.2 62.2 18.6 18.3 603.3 575. .953
Percent Growth 0.00 -6.91 +66.1 +24.2 +32.2 -1.83 +568. -4.62 +334. +72.5 +208. -.005 +96.8 +84.4 +82.5 -1.04
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her present system ~ it communicates the projected load growth in terms of the existing system facilities. Susan immediately notes that SL&P is going to need several new substations in the areas now served by Mountainview, Ridgeway, and Nottingham Rd. This comes as no surprise. What is a slight surprise is that four substations — Cross River, Georgia St., Northwest, and Riverside — will see a decline in peak load. A little study shows her that this is because of her company's conservation and load management program. Those areas see roughly a 5% increase in consumers during the twenty-year period, but per consumer load drops by 8% due to improving appliance efficiencies and conservation efforts, for a slight net decrease over time. In fact, some strange things will happen on her system during the next few years, she realizes. Coal Hollow's peak load will grow for several years before reversing that trend and declining. This is due to positive consumer growth during the short-term, which stops when all available land in the area is filled. After that nothing but the gradual effects of conservation and load management occur in the substation, so the load gradually drops. Substation peak load coincidence will change, she notes. For the past decade, Springfield Light and Power's ratio of system peak6 to the sum of substation peaks has stayed right around .963. But her forecast shows that this ratio will drop to .942 in the next eight years, before rising to about .952 by the end of the study period. The reason for this trend is the change from winter to summer peak loads, the only "load curve related" item that she can analyze in her non-hourly analysis.7 SL&P is currently summer peaking ~ all substations peak at about the same time, and coincidence is fairly high at .963. But as SL&P makes the transition to winter peaking, some substations become winter peaking in year 4, others not until years 8 or 12. In that interim, when some substations are peaking in winter and others in summer, coincidence falls. By the final years of the forecast, however, most of the system has shifted to winter peaking, and coincidence rises slightly. Susan makes the correct interpretation about what has happened — her company's conservation, load management, and strategic load growth programs will have a bigger impact on lowering system peak than on lowering substation 6
Actually, the system peak figures used here are the SL&P system peak with the transmission losses removed. 7 The fact that coincidence changed due to the only "load curve related" item she can analyze ought to concern Susan. It is an indication that maybe other changes are taking place, changes she is not observing because she is not able to use hourly peak day load curve shape data in her analysis.
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peaks. Because of SL&P's demand side management program, system peak will grow at a slower rate than substation peak load (and slower than energy sales or consumer count). While such a slight difference in coincidence may not seem like much, the change from .963 to .942 means nearly 9 MVA more in distribution system needs relative to total system peak load, which is on the order of between one and two million dollars worth of capital equipment requirements.8 Susan prepares a memo to inform her department head about this immediately, so that the budget forecast can be changed to reflect this increase. This change concerns upper management, who of course would prefer to keep the budget as low as possible, but they respect Susan's work, and frankly it is not a total surprise (see Willis and Rackliffe, 1994). Susan schedules a meeting to show both the base and scenario forecasts to her colleagues in Rate and Consumer Studies, who agree that both make sense. Together, they spend some time looking at the load growth patterns. Among the things they discover: 1. Her forecast shows less growth across the river, where the new bridge leads, than they had expected. While her forecast predicts significant growth there, the newspaper articles she had read, and her discussions with developers, had led her to expect a rush. But much of the land on the other side of the new Halston Road bridge is flood prone and not developable. Not only that, a 2300-acre Federal Wilderness Reserve Area has used up much of the otherwise developable land further in from there and stands as a barrier to the expansion of the road system in the area. While there is room for new homes, some shopping centers, and perhaps a small office park or two, that's about all. 2. The factory scenario forecast yields one startling discovery. A good portion of the factory-caused load will be located outside the Springfield Light and Power service territory. The factory site is in the northern part of the SL&P service territory, and because much of the growth it causes will scatter in a wide radius around it, some of that growth will fall even farther north, in the area served by Multi-State Omni Utilities. Note in Figure 11.10 the factory scenario adds only 27 MVA to Springfield's peak load, but that as computed in Chapter 10, Table 10.3, the total load impact (minus the factory) is 58 MVA. 8
This increase in distribution cost is small compared to the forty to fifty million dollars SL&P can expect to see at the system generation level, due to the reductions its conservation and load management program will make.
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Her friends in the Rate and Consumer Studies department are surprised and, at first, reluctant to accept this prediction of only 27 MVA. Their own systemwide forecast had assumed that all the factory-caused growth would be inside the SL&P service area. Revenue, budget, and cash flow projections based on that assumption have already been given to SL&P's executive committee. Acting largely on the projected revenue stream, they offered Nippon-America a further 3% discount on power for their factory, reasoning that they would make up the difference with all these new consumers that R&CS had forecast. But after studying Susan's maps for more than an hour, they decide her forecast is accurate. They are grateful when Susan drafts a very diplomatic memo to her department head, advising of this problem, thanking R&CS for their data and help in her work, and giving them a good deal of undeserved credit for the discovery. Although Susan does not know it at the moment, this memo zips its way up the ladder through management quickly, accelerating as it goes, and reaches the desk of the Mayor of Springfield in less than three days. It is a major discovery and of key strategic importance, for it shows that the City is on the horns of a dilemma. Much like the electric department, the city revenue planners had assumed that almost all of the follow-on growth caused by the new factory would fall inside the municipal boundaries, and would thus contribute to the city coffers via an increased tax base. On that basis, they were offering Nippon-America tax incentives for its factory, a $500,000 extension of roads to the factory site for their sole use, and a package of other payments and discounts costing more than $3,000,000 over the next six years. The news that the increased tax base will not be as much as anticipated is unwelcome but grudgingly appreciated ~ a major financial headache has been identified early enough to solve it smoothly and without controversy. Further Forecasting Work So far, Susan has spent about twelve work weeks, spread over an eighteen week period, to complete her spatial forecast of Springfield's growth. She is proud of her forecast and the important contributions it's already made to her company's plans, and she is eager to get on with the distribution planning, the real reason she started this project. But before she can, Springfield Light and Power receives surprising news. Nippon-America has purchased a 235 acre parcel of land southeast of Springfield, for four million dollars. Apparently the site north of town was a ruse to divert public attention and land speculators away from the company's true intentions, while it bought the land it wanted at non-inflated prices.
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Factory south - 574 MVA
Factory north - 552 MVA
Figure 11.11 Twenty-year, summer-peak spatial forecasts with the factory at the southern site (left) compared to the original factory scenario with it at the northern site (right). The movement of the factory site from north to south had two major impacts. First, the additional growth it causes now clusters around the southeastern quadrant of the city. Second, a higher portion of the growth it causes falls within SL&P's service territory.
Although Nippon-America has yet to state publicly that it plans to build the factory, their commitment seems obvious considering they have just spent $4,000,000 on the site, and SL&P's President directs the Engineering Department to proceed under the assumption that the factory will be built at this new site. Susan is told the production of a forecast reflecting this new site is critical, and her executives make sure that she has plenty of help ~ her friends from R&CS are assigned to assist her in coloring and calculating the winter and summer load grids for a third scenario, one with the factory located at the southeast site. The new forecast is completed over a weekend (Figure 11.11). To the delight of R&CS and City Hall it shows nearly all the factory-caused growth within the SL&P service territory. Multi-State Omni Utilities gets almost nothing. Susan's third forecast scenario is accepted and approved as SL&P's base system planning forecast. The company commits to planning system expansion for the new factory and for the amount, densities, and locations of consumer load she has forecast. In recognition of her hard work and dedication, the importance of her work, and particularly the diplomacy and teamwork she displayed while working with R&CS department, Susan is promoted to supervisor of the Engineering Planning section. The first thing she does in her new position is to buy a computer, so that this type of work will never have to be done manually again.
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11.4 CRITIQUE AND COMMENTARY ON MANUAL SIMULATION How good was Susan's forecast? Manual (judgement-based) simulation has been used since the 1950s, with mixed results (see Kanouse and Reinhard, 1955; Lazzari, 1966; Scott, 1976). Chapter 17 presents the results of a comparison test of nearly nineteen forecast methods, one of which is exactly the method described here. As will be seen, this method's forecast accuracy is only average, but its costs are far above average (it is generally regarded as the most expensive spatial forecast method, because of its intense labor requirement). Most likely, Susan's forecast has accuracy superior to anything that trending could produce, but quite below the best that a comprehensive computerized simulation could give. An additional point to bear in mind is that Susan's case was somewhat unique, in that Springfield is almost perfectly suited to manual simulation.9 It is a small enough city that it is possible, even if difficult, to perform a simulation study manually. But much more important to Susan's success were the facts that the existing geography, land-use patterns, growth dynamics, and consumer energy consumption patterns in Springfield Light and Power's service territory were all straightforward and uncomplicated. Both her base and factory scenarios are qualitatively correct, although quantitatively her spatial placement of growth was slightly inaccurate. It is simply impossible for a human being to balance the multitude of factors that influence where and how growth develops and apply them consistently to hundreds or thousands of small areas required in a spatial forecast. In Susan's case, her most serious mistake is in undervaluing the influence of the major highway through her city (1-36). Underestimating its effect slightly, she forecast that Springfield would grow in a somewhat circular pattern, whereas a city or town dominated by a single major traffic corridor has its growth heavily biased to follow that highway, even in the presence of factory sites and other influences to the contrary, as shown in Figure 11.12.10 The major T&D planning consequence of this particular mistake is that too little load growth is forecast in the area east and southeast of the airport, particularly just north of 1-36, where the load density is underforecast by a considerable margin. Load growth there will eventually surprise SL&P ~ two additional feeders, an upgraded substation transformer out of a new substation to
9
Not surprising, because the author deliberately picked a real-world problem ideally suited to this method as the basis from which to prepare this presentation. 10 The author has the advantage of having observed the actual growth over nearly a decade following "the present" in this narrative, and thus knows that actual growth followed the pattern described here, and that it was forecast correctly by a 2-3-2 simulation program (to be discussed in Chapters 12 - 14) at the time.
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SPRINGFIELD LIGHT & POVER CO Service Territory and Distribution Substations
Figure 11.12 In forecasting new consumer development locations manually, Susan's thinking reflected an expectation of a circular pattern of growth only slightly distorted by the highways influence, the ellipse shown in a solid line above. In reality, the highway's influence on the growth of her town was stronger, and actual new land-use development was dominated by a pattern like that shown by the dashed line. Quantitative balance of forecast aspects like this is a practical impossibility manually.
be built about three miles northeast of the existing Nottingham substation, and a good deal of last-minute re-engineering will be required to meet the unexpectedly high load density in that area. Cost of this "mistake" will be about $85,000." In addition, Susan's simulation calls for a bit too much development to be dispersed throughout the northern and southern areas of her service territory (since her overall forecast total is fairly accurate, the load she didn't put near the airport has to be somewhere else, in this case scattered widely to the north and south). However, there are no serious consequences to this 11 An upgraded transformer, two feeders and their associated equipment cost a good deal more than $85,000. This is the marginal cost of the mistake, the additional cost of having to "patch" a plan already underway — to pay premium prices for quick delivery of equipment and overtime in order to hasten construction, etc. This and similar costs associated with "planning mistakes" will be discussed further in Chapters 17 and 21.
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Table 11.20 Complexities That Will "Defeat" the Judgment-Based Manual Simulation Method Used by Springfield Light and Power Type Complexity
Explanation Even with the factory scenario, Springfield was a relatively uncomplicated growth situation. Referring to methods to be discussed in Chapter 12, it would need a polycentric activity model with only two poles — downtown and the factory. More complicated service territories can require up to two dozen poles, quantitative assessment of which is difficult enough given a computer, and impossible manually.
"Commuting" Springfield was small enough that anyone who works on the east side of town would not think twice about buying a home on the west side if it was otherwise to their advantage. Therefore, a manual assessment of "areas likely to grow" based only on local attributes works well (qualitatively) for forecasting. But in a city such as Atlanta, where commuting times across the city at rush hour are over 90 minutes, congestion has a major spatial impact on growth, analysis of which is beyond the scope of routine manual study. Nearby city
Even though relatively small, had Springfield been within fifty miles of a major city (such as Denver) the influence of the larger urban area on Springfield's growth would have been significant, and difficult to assess quantitatively without a computer's assistance.
Geographic
Except for a few exceptions, all the land around Springfield was reachable without undue effort, and developable, if there was a reason. Growth of cities such as Vancouver, BC and regions such as central Maine is dominated by geographic complexities (steep terrain, significant water or mountainous barriers to straight line travel, multiple pockets of undevelopable land). Manual studies can successfully take this into account, but the effort to do so would double or triple their already high labor requirement.
Spatially varying usage patterns
Many large and a few small utility service territories are divided by natural weather behavior into "micro-climates" with quite different weather, and hence quite different weather-sensitive consumer loads. As a result, in the San Francisco Bay area, electric usage along the Pacific Coast is quite different than in Silicon Valley, or in the city itself for that matter. Electric usage must be distinguished by defining different classes of electrical behavior for what might be similar land use behavior in these different regions. This further adds to the labor required.
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aspect of her mistake — in a few cases over the following years, a new feeder or change planned in anticipation of that load growth will simply be delayed several years until it is needed. Had Springfield been a larger city, or placed so that its growth was complicated by any of a host of possible geographic, land use, or energy usage complexities that occur frequently in large cities and populated coastal regions, and occasionally elsewhere, the manual simulation method would have given much less satisfactory results. First, it would have been far less accurate. Second, it would have been much more frustrating to apply, to the extent that somewhere during her weeks of work, Susan would most likely have realized that something was wrong and given up. Table 11.20 lists a number of factors that manual simulation cannot assess well enough to forecast effectively. Methods to model these in more detail will be discussed in Chapter 12.
REFERENCES J. Garreau, Edge City, Doubleday, New York, 1991. E. L. Kanouse and L.W. Reinhard, "The Function of Land Use Surveys in Power System Planning," in Proceedings of the American Power Conference, 1955, University of Chicago Press, Chicago, IL, 1955. A. Lazzari, "Land Use Data Improves Load Forecast," Electrical World, June 1966. W. G. Scott, "Computer Model Forecasts Future Loads," Electrical World, Sept. 1976, p. 114. H. N. Tram, H. L. Willis, and J. E. D. Northcote-Green, "Load Forecasting Data and Database Development for Distribution Planning," IEEE Transactions on Power Apparatus and Systems, November 1983, p. 3660. H. L. Willis and G. B. Rackliffe, Introduction to Integrated Resource T&D Planning, ABB Systems Control, Gary, NC, 1994.
12 Basics of Computerized Simulation 12.1 INTRODUCTION This chapter is the first of three that discusses computerized application of spatial electric load forecasting. Simulation has a number of advantages accuracy and multi-scenario capability among them - that make it the preferred approach for many utilities. But the manual simulation methods as presented in Chapter 11, although applied on a limited basis in the 1950's through the early 1970s, involve prodigious amounts of labor, and are not particularly accurate due to the inconsistencies introduced by approximations and human judgment. Since the 1960s, dozens of computer programs have been developed to apply a wide variety of simulation approaches. The method seems tailor-made for computerization, particularly when memory limitations are not severe, something that has been the case even with PCs since the mid-1990s. Simulation applied as a computerized process is both more accurate, less costly, and more practical than manual simulation studies. In addition, once the basic simulation method is computerized, numerous embellishments and improvements in method can be added, taking advantage of the computer's ability to quickly apply numerical methods that would be far beyond what any person could apply manually. Despite the great variety of programs that have been developed, all computerized simulation methods share several common characteristics. This 373
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chapter gives an overview of how these most common features are used to produce a simulation process. In Chapter 13, several building blocks of simulation are presented - numerical methods. Chapter 14 then covers the structure and flow of computation for several types of simulation and covers a number of enhancements or advanced features that have proven themselves over time. A discussion of these and their application concludes the chapter. 12.2 OVERALL STRUCTURE AND COMMON FEATURES While a widely diverse range of computerized simulation approaches have been developed for spatial electric load forecasting, all share several common design and operating features. Generally, they share several characteristics: • All work on a small area basis, although there is no commonality about how small areas are defined: just about every possible approach is in use. • Most work in iterations, forecasting "jumps" in growth - usually annual jumps of growth. • All work with distinctions of consumer classes, or area classifications based on consumer type, allocating growth by class among the small areas • Most take or can apply a top-down allocation of overall (system-wide) growth. In a very real sense these are spatial allocators that geographically distribute a previously performed, non-spatial systemwide forecast. • A vast majority determine their spatial allocation priorities (where growth is allocated) based on a bottom-up analysis. • Global and local inventories of land-use mixes are maintained and used to control allocation and spatial pattern of load growth. • Allocation involves some sort of pattern recognition method. • Electric load is determined as a last, and computationally almost insignificant, step involving the "translation" of the small area consumer class forecast into electric load, using a table or an end-use model of some sort. Within these constraints, which might seem very limiting, a tremendously wide variety of computer programs have been created and applied. This range embodies a surprisingly large variety of approaches representing a diverse set of perspectives on how growth should be modeled. Many of the ideas used are straightforward and obvious, a few are innovative and some quite clever, and some are just plain bizarre.
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As mentioned in Chapter 11, most simulation methods use separate modules to analyze spatial consumer locations and temporal per capita consumption respectively, the functions of these two modules coordinated by the use of both a common set of consumer class definitions and a shell program that controls their interactions appropriately, as shown in Figure 12.1. The shell program provides all user interaction (Man Machine Interface), manages database and data exchange functions, and acts as the controller and coordinator of the functional modules. Generally, except for the merger of their results at the end of their respective analyses as shown in Figure 12.1, these separate modules have no common analytical framework or interaction, and therefore are very often two completely separate programs. Even within a single tightly integrated program, the per capita load analysis and the spatial consumer analysis are almost always completely separate sections of program code. Thus, these two processes can be considered separately, as they will be throughout this chapter. Historically, this modularity has led to a good deal of swapping of modules between simulation programs, combining the temporal model from one with the spatial module of another, to create a third simulation program combining their best features.
Year N Spatial Data
Year N Load Curve Data
n
V"
SHELL V
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TEMPORAL USAGE ALGORITHM
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Yearri Spatia /
y
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I =T| Year N+P ]1 1 Temporal
^ s
\
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Figure 12.1 Simulation programs generally include both spatial and temporal "sides" which work independently, their function coordinated by the use of a common set of classes and a shell program that merges their results into the final spatial forecast.
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Consumer Class Definitions Both the per capita usage and spatial consumer sides of the simulation process use the concept of consumer classes to help distinguish between different types of behavior within each side's context. As noted in Chapters 2, 3 and 4, per capita electrical usage differs substantially among different classes of consumers such as retail commercial, residential, and industrial. Both the basic end-use needs (what they use electricity for) as well as the timing of usage differ substantially among classes like retail and residential. Behavior can be analyzed more exactly and forecast more accurately if done on a class-by-class basis. Similarly, Chapters 7 and 10 discussed how spatial consumer patterns can be distinguished on a class-by-class basis, various land-use classes having far different needs for the type of local attributes they require — such things as proximity to a railroad, highway, quiet neighborhood, and so forth. Distinction by class is an important element of forecasting. As far as what should constitute a class, the definition given earlier in this book bears repeating. A class is any subset of consumers whose distinction as a subset helps identify or track load behavior in a way that improves the effectiveness of the forecast. Perhaps the most important aspect of simulation program selection and design is the identification of the consumer classes that will be used. This has a bearing on the application ~ some types of analysis cannot be done unless certain class definitions are used ~ and algorithm selection ~ some types of algorithm do not accurately accommodate certain types of class definitions. In order to assure consistent function and completeness, the same classes and class definitions must apply to both the spatial and temporal modules used in a simulation program. As a result, each of the two modules must deal with slightly more classes than needed just for its own requirements. For example, the distinction between homes with special energy conservation measures and those without is of dubious value in helping a spatial model forecast where future consumers will locate. But that distinction is quite important to some types of per capita consumption models, particularly end-use models applied to DSM (Demand Side Management) or IRP (Integrated Resource Planning) studies. Therefore, if that distinction is needed in the end-use model, then the spatial model must accommodate that distinction in the classes it models. It may not be possible, because of data or algorithm limitations, for the spatial model to discriminate between the two types of homes (i.e., the spatial model may not be able to "see" any difference between their locational patterns), but it must accommodate the usage of those two classes somehow.
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Table 12.1 Consumer Class Definitions Commonly Used in Simulation Methods Class Spatial Consumer Model Requirements Residential Agricultural Rural Single family - lo dens. Single family - normal Single family - high Multi-family housing Commercial Retail small Retail large Offices Hi-rise Municipal office & schools Industry Small industry Outdoor storage Warehouses Medium industry Heavy industry Municipal facilities Vacant Restricted - environmental Restricted - government Restricted - public Restricted - private Restricted - flood Provisional Unrestricted Load Modeling Requirements Residential Agricultural Rural Residential - new Multi-family housing Energy efficient* Commercial Retail Offices Hi-rise Schools Industry Small industry Warehouses Large industry Energy intense
Definition
farm houses non-farm homes outside urban/suburban areas single family homes on large lots single family homes —average density townhouses, rowhouses apartments, duplexes, rowhouses stores, strip centers shopping malls, centers professional buildings tall buildings Often distinguished/locational different small shops, fabricating buildings wrecking yards, etc. space is major requir. warehouses large facilities, site dependent very large, transmission consumers sewage treatment, utilities, etc. Wetlands, wildlife preserves Military, classified, test ranges parks, greenspaces Small airports, golf courses, racetracks Flood prone areas Developable but problems to overcome No known reason cannot be developed
farm houses and farm equipment loads far different usage than urban (no gas) single family homes apartments, duplexes, rowhouses may be subcategory of all above one class fits all (load is proportional to size) professional buildings, municipal offices tall buildings (load shape not same as offices) different load shape definite diurnal load cycle warehouses flat (multi work shift) load behavior some types of industry (air liquefaction)
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Regardless, the model must be able to handle the two classes. This can be done either by treating them as two identical classes and arranging for the spatial model to forecast each independently, or by having the program somehow merge them into one spatial "class" for its internal functions, while retaining the ability to recognize they are two with respect to the overall program's function. In a similar way, the per capita model may also have to deal with classes that mean nothing to it. For example, the spatial model may need to distinguish between single-family homes on large lots and single-family homes on small lots (in many large metropolitan areas these two classes have distinctively different locational patterns and thus expand in predictably different ways). To the per capita consumption model, both classes are nearly identical -- houses of the same type and electrical consumption. — only the amount of space around each house is different. However, the consumption model must accommodate these two (to it identical) classes within its realm because they must be distinguished by the spatial model. How this is done can vary from model to model. Some enduse models can deal with this situation by combining both classes into one "class" as far as its analysis is concerned. Most, however, treat them as two separate classes with identical end-use statistics and load curves. The point here isn't how it is dealt with but that the model has to deal with classes, which to it have no distinction or impact on its function. This is an important point with respect to both spatial and load modeling, because the ability to deal with classes that have no distinguishable differences to the algorithm varies greatly among the range of methods available for both spatial and temporal modeling. In particular, many pattern recognition and identification algorithms (e.g., the K-means clustering algorithm) along with the analytical frameworks built around them, produce valid results only if the statistical variance between any two classes is greater than the variance within any one class. Clearly this would not be the case if the algorithms were forced to handle two "classes" that were "identical" from its perspective. Table 12.1 shows class definitions commonly used in simulation methods, from both the spatial consumer and temporal usage analysis perspectives. Not all categories are necessary in all models, and often some can be combined in ways that will be discussed later in this chapter. Generally, these is an overall correspondence between the classifications needed by the spatial and temporal analysis, and a set of definitions common to both is not too difficult to obtain. Preference Mapping The determination of "where" — where consumer growth is forecast, where reduction or shrinkage in density is forecast, and where no change is expected ~ is usually determined from a small area map of "scores" which rate each small
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area with respect to the possibility of change. Exactly what the scores or preferences mean, how they are used, how they are computed, and how they are interpreted by program and user varies greatly among successful methods. But almost all simulation methods use the basic concept in two steps: • Compute for every small area a "score," rating it with respect to a hypothetical change that may occur. • Allocate the amount of change that is expected to occur on a global basis (system wide) to the highest scoring (or lowest scoring in some cases) small areas. Preference maps and their application will be discussed in much greater detail later in this chapter. Iterative Year to Year Forecasting The vast majority of simulation algorithms, both spatial and temporal modules, perform a "single stage" forecast in which they transform or "update" their database from a data description of consumers and load at the start (e.g., 1997) of some period of analysis to that at the end (2000), adding to the starting database the changes forecast to occur during that period (in this case three years of growth and change). This was illustrated in Figure 12.1, in which both the spatial and end-use models update their database separately in this manner. Many of the most popular spatial and temporal forecast algorithms modify the data they retain in memory (RAM) in place, basically writing over the current iteration's data set in the process of computing the data description of the next iteration. In-place computation is preferred in order to keep memory and computational time at a minimum. A full data representation for a single year can require up to 50 Mbytes in some types of approaches. Algorithms that retain an 'input' and 'output' data set resident in memory need twice this amount and also suffer much slower computation due to virtual memory swapping.1 For that reason, the shell program both manages a series of iterations to extend the forecast in stages into the future, and also copies and saves the database for the base year and at the end of each completed iteration of the forecast.
1
Many of the better algorithms for spatial simulation "jump around" their data space in the course of their computations, often in unpredictable ways, which can create considerable run-time bottlenecks on virtual memory systems.
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2000
Figure 12.2 Computerized simulation methods begin with a database representing the initial (present) year and forecast specific future years in a series of iterations, each iteration extending the forecast one or more years farther into the future. The forecast is produced as a series of steps, with the user being able to review data, modify or add data to represent changes in controlling factors or scenario variables, at the end of each step, the changes taking place in the next step.
A Per Capita Temporal Load Curve Module As discussed in Chapter 4, a consumer-class end-use model utilizing load curves by appliance subcategory is the recommended method of assessing and forecasting per capita usage. At the very least, a simulation method must have an ability to apply load curve shapes to each class and vary these computed shapes as needed for the future years (study periods). An acceptable method is to require these curves to be input for each class. Load curve shapes by class can be determined outside the simulation program and simply input by the user or transferred via a data interface from another program. Several popular spatial forecast simulation programs have used this approach, the most widely used probably being the Stochastic Load Forecast (SLF) program developed and marketed by Westinghouse Advanced Systems Technology Division in the 1980s.
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The basic consumer-class, end-use "curve adder" load model was covered in Chapter 4. The author strongly recommends this general type of approach as the best for the per capita electric load analysis "side" of a spatial electric forecast simulation. While not trivial, computerization of the process and structure shown in that chapter is straightforward. Three points with regard to computerization are worth noting: • As mentioned in Chapter 4, a per capita end-use model which employs appliance subcategories makes a far more satisfactory forecasting tool than a model with only end-use category level data analysis. • Programs to implement the end-use model should permit the user to apply different levels of end-use data to different classes and end-uses within classes. For example, the user should be allowed to set up the residential class model so that only the space heating end-use is represented with a set of appliance subcategory level data below it, with the rest of the residential end uses represented only with end-use level data. While such representation is less accurate that full subcategory data, perhaps the user does not have access to appliance level data for the other end-uses. A good program can work with variable levels of load curve representation ~ some classes might be represented as a single class load curve, others with a break down into end-use data and curves, and perhaps some of those end-uses with a mixture of enduse and appliance-subcategory data. See Chapter 4 for further details. • A program that stores a curve once for a basic type of device and uses pointers to everywhere it is used is preferable. For example, there might be eight or more residential consumer classes used in an advanced simulation method. All might have a "high-efficiency heat pump" appliance subcategory and many of these load curves might have the same normalized load curve shape (peak kVA for the "large home" class might be greater than that for "small home" but the per unit shape might be the same). Convenience is enhanced if the program allows the user to input one curve for "high efficiency residential heat pump" and copy or point to it in every instance needed.
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Even with these practical considerations included, neither the database nor the numerical methods required to apply a per capita end-use load model presents any real challenge with respect to modern hardware and software technologies. Therefore, this chapter will not dwell on computerization of this model (but see Chapter 4, section 5 for a discussion of overall program design). 12.3 SMALL AREA SPATIAL MODULE Between 80 to 95% of the data and computational effort in a spatial electric load simulation method is devoted to analysis of the locational aspects of the electric utility's consumers, their interactions with one another, and with the local geography. This locational analysis is what makes the spatial load forecast unique, and the mechanism it uses to address the T&D planning requirements with their need for "where?" information about future load growth. A very wide variety of approaches has been tried for this spatial module, more than a few of them quite successful. This section begins by looking at several features used in most spatial consumer forecasting algorithms, and then examines the layout of spatial models. Polygon or Grid-based Small Area Format Spatial simulation programs can be designed with either a polygon and/or a grid small area map format. This format defines the way small areas are identified in the program -- square or rectangular small areas in a grid format, or irregularly shaped areas of varying size and shape in a polygon format. Generally, the use of a grid format for small area definition will result in many more small areas than when a polygon basis is used, with a resulting increase in data storage and computation requirements. As an example, a mainframe based simulation-based program called ELUFANT, which the author helped develop for application in the early 1980's, modeled Houston Lighting and Power Company's service territory with a grid of 325,000 square areas, each 1/5 of a mile wide. A detailed polygon consumer class map for this same area would probably involve on the order of 10,000 to 20,000 polygons. Either a grid or polygon format can be made to work well for spatial electric load forecasting simulation, but both the designer and user of the program should understand that there are three related issues to be resolved in deciding upon the spatial mapping format and how it is used. The first concerns data and database. Small area data must be input, stored, and manipulated by the simulation program. Selection of a grid or polygon format greatly affects the program's ability to interface with various sources of data ~ grid-based programs can easily input and use grid-based data, and vice versa, but either base creates considerable problems for the user trying to input a data source in the other format. Several modern database technologies can
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accommodate both grid and polygon data formats simultaneously and seamlessly. Using grid or polygon format data or both as needed can be done easily, and information can be moved between the two formats without problem. Sources of data in either grid or polygon format can thus be input, displayed, and used as needed. Second, the type of spatial format largely "defines" how the user thinks of spatial relationships. A simulation program that accepts, displays, and manipulates data only in grid format leads the user to think only in terms of uniformly sized and shaped small areas. A polygon format does the opposite. This is more important than it first appears — users adapt their intuition to and apply a perspective flavored by the analytical tool they use. In this respect the author believes a grid format is preferable ~ it promotes a perspective and thought process coherent with high-resolution spatial analysis. Third, in every simulation method, some portion of the spatial analysis is computed on an individual small area basis. The grid format is strongly recommended for all analysis, regardless of how data is to be stored or displayed. If analysis is carried out on a polygon basis, the spatial resolution of both the computation applied and the data analyzed will vary as a function of location ~ the "where?" information considered in the forecast will be detailed where the polygons are small but less where they are larger.
One quarter mile
( t
N
Figure 12.3 Approximately l/4th of the undeveloped 400 acre tract shown here is prime industrial land, having all the locational attributes necessary. If analyzed as a single unit, either none or all of it would be identified as potential industrial land. Only a higher resolution analysis based on smaller areas within it can correctly distinguish internal variations in important spatial attributes.
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This turns out to have a detrimental effect on accuracy, due to the spatial variation inherent in most polygon format databases. Usually, the polygon size is inversely proportional to the amount of local land-use development, being a finegrained mosaic within the intensely developed urban core of a city, somewhat less specific in the suburbs, and mostly large polygons on the outskirts of the metropolitan area, where development is light and there are many sizeable parcels of vacant land. Yet it is precisely in the outskirts of the city that new consumer growth can be expected, and where the most detailed spatial analysis is needed. As shown in Figure 12.3, computation on a polygon basis might analyze a 400 acre tract of undeveloped land as a single unit, rather than with sufficient resolution to note that part of it is immediately adjacent to both a road, a river, and a railroad, and thus eminently suited to industrial development. Effective analysis requires that the polygon be broken into smaller units for this step. There are methods for "splintering" large polygons into smaller ones for analysis, methods which can overcome any inaccuracy caused by this situation.2 However, a grid-based format avoids such resolution problems altogether. A grid format assures that a uniform spatial resolution is applied throughout. If spatial resolution has been selected properly to assure that sufficient "where" information is included in the computations and data, then that satisfactory resolution will be applied throughout the service territory in all calculations of growth. Despite the greater number of small areas that result when using a grid format for the analysis, computation is generally faster than with a polygon basis. Later in this section, several high-speed "building blocks" for spatial simulation, which use image-processing and signal-based methods of analysis, will be presented. Their five to one hundred-fold computation-time advantage over direct computation depends on their application to a set of uniformly spaced points such as those in a grid. Such "trick" calculation methods cannot be applied to polygons. Stacks of Maps Depending on the spatial simulation algorithm, anywhere from ten to more than two hundred different spatial variables may need to be retained and computed as interim results in order to perform the simulation's computations. Most programs written for land-use simulation use the concept of a stack of maps, as shown in 2
One method is to connect each vertex to the middle of the segment across the polygon from it (the segment most perpendicular to a line from the vertex to the segment's centerpoint). These new segments define a set of smaller polygons within the original.
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Transmission Facilities -199 Distribution Facilities -1998 Sendee Facilities-199 Highways-Year 2005^ Highways-Year 199
^Customers-2008 ustomers-1995 —Customers-1993
Figure 12.4 To the user, most computerized simulation methods appear to work with a large set of overlapping "small area maps," even if data is stored in more compact form and only displayed as "maps" when requested by the user.
Figure 12.4.3 In many, the database and database manager are in fact programmed in this manner, with each "map" in the stack denoting a separate data variable. In others, data is retained in a different fashion internal to the program, but interpreted for the user as belonging to such a stack of maps. Regardless, many of these maps may be workspace maps, holding places for interim spatial results during the computation of the spatial forecast. As an example, a popular simulation program called SLF-2 (marketed by Westinghouse from 1984 to 1990) used a total of 65 maps, only 22 of which contained input data.
3
These minimum and maximum counts are respectively for the 'stochastic1 simulation method developed at Westinghouse AST in the early 1980s (see Brooks and NorthcoteGreen, 1978) which required ten, and a commercial spatial electric load forecasting program called FORESITE®, marketed by ABB Distribution Information Systems of ABB Inc., which requires up to 233 maps (Willis, Engel, Tram, 1995).
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Interaction of Spatial Resolution, Map Stacks, and Class Definitions Two very different approaches have been taken on how the spatial resolution, map stacks, and consumer class distinctions interact in the design of the simulation program, as illustrated in Figure 12.5. In many programs, a small area is modeled as being composed, at least potentially, of portions of all different land-use classes, and a specific map in the map stack is designated to store a count of the portion of each land use. For example, a specific 40 acre small area in the grid -- perhaps that located at X coordinate 123 and Y coordinate 56 -- might contain 10 acres of single family homes, 5 acres of park, 6 acres of school, 4 acres of retail commercial, and 15 acres vacant. To represent this, the numbers 10, 5, 6, 4, and 15 would be stored in element 123, 56 of each of the maps designated for family home, park, school, retail, commercial, and vacant land-use acre counts, respectively.
Multi-map Framework Monoclass Map Framework
Figure 12.5 Two different ways of storing land-use data to represent the same region. At left, a "multi-map" framework with each map reserved for specific land-use class, storing for every small area the amount of that particular class in that small area. At right, a "monoclass" framework permits each small area to have only one type of land use, with the map storing the land-use class assignment (class number) for each small area. Generally, the monoclass approach is implemented with a much higher spatial resolution (smaller area sizes) than the multi-map approach, as shown.
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The multi-map framework is almost exclusively confined to grid-based format, but is very widely used. It requires storage and analysis of a set of small area maps ~ one for every land-use class — but permits very accurate accounting of exactly what land uses are in each small area. By contrast, some simulation methods use a mono-class framework, with only a single land-use map, and force small areas to be represented as each only one land use ~ 100% single family residential, 100% retail commercial, or 100% something else. The attribute stored in this single land-use map for every small area is the class designator for its particular land use. This approach avoids having to store more than one map for the land-use data. Almost all polygonbased databases are mono-class. They achieve an acceptable level of spatial accuracy because the varying shapes and sizes of their polygons are arranged to correspond well to single-class land parcels. In addition, they are more parsimonious with respect to data storage than grid methods, because very often very small parcels of land ~ the odd acre of retail commercial within a 200 acre parcel of single family homes ~ is simply neglected and not coded. However, the mono-class framework is not limited to only polygon format databases - some grid-based programs use a monoclass land-use map, too. The single land-use map approach is made to work well by making the small area size quite small. This takes advantage of a "natural feature" inherent in how cities, towns, and rural regions arrange themselves. As shown in Figure 12.6, the average number of land-use types within each small area varies as a function of the spatial resolution of a grid. If a city such as Denver or Houston is divided with a grid of 160 acre small areas (1/2 mile wide), the roughly 24,000 small areas that result in the metropolitan area and its surrounding periphery will contain on average four types of land use.4 If divided into 40 acre small areas, each of the nearly 100,000 that now cover the region will contain on average only about two land-use types. As spatial resolution is increased further, to ten and even 2.5 acres (small acres 1/16 mile, or only 100 meters across) the average number of land-use types per small area drops to very close to 1.0. At low spatial resolutions, when small area grid size is in the region of a kilometer or quarter kilometer, or 160 to 40 acres, an accurate data representation requires that multiple land-use maps be used, because each small area will have significant features in many classes. But at high spatial resolution, the assumption that a small area is composed of only one class is valid, at least within the limits of reasonable approximation.
This assumes that land-use definitions like those in Table 12.1 are used and considers only parcels of one acre or more. Sub-acre individual isolated land-use parcels are neglected.
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10 100 1000 Spatial Resolution - small area size, acres
Figure 12.6 The average number of significant land-use classes (out of 16 used) in a small area, as a function of the spatial grid size used, based on data from Houston, TX, Phoenix, AR, and Portland, ME, circa 1990.
Recall that in Chapter 8 the required spatial resolution for T&D planning was determined to be in the neighborhood of 71 to 25 acres — small grid areas 1/3 to 1/5 mile across (see Table 8.1). To meet this need, the designer of a grid-based spatial forecast program has two choices. Spatial resolution can be kept near the limit defined by the T&D application requirements -- perhaps at 40 acres (small areas 1/4 mile wide). Covering the 6,000 square miles required for a city such as Houston or Denver would require about 100,000 such small areas. Each will have on average somewhere between two and four land uses within it, and therefore the program will have to store individual maps for perhaps sixteen land-use classes, for a total data space of 100,000 x 16 maps = 1,600,000 words of data. Alternately, if a spatial resolution of two and one half acres (small areas 1/16 mile wide) is selected, there will be about 1,500,000 areas with the vast majority having only one land-use class. A single mono-class map can be used, with 1,500,000 small areas and roughly the same total data storage requirements as the multi-map framework. A mono-class framework would have an advantage whenever many more class definitions were going to be used; the "multi-map" framework would be preferable if fewer classes were going to be stored or if resolution needed to be kept low for some reason. But usually data storage and data issues are not the sole factor to be considered in choosing between mono-class and multi-map frameworks — algorithm compatibility is a major factor, too. Most land-use based spatial load
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forecast approaches work best within one or the other framework. For example, the statistical comparisons of land-use composition among neighboring small areas, used in the EPRI Multivariate program and the Canadian Electric Association CEALUS land-use simulation programs, while mathematically different, work much better in a low-spatial resolution, multi-map framework (see References). Both approaches work best in situations where the average small area has three or more land-use types within it and will not function if there is only a single land-use type within each. Therefore, they are most applicable to forecasting at a spatial resolution in the 160 to 40 acre range, and they must have a multi-map database structure to support them In the opposite manner, the FORESITE™ simulation program which the author designed for ABB Systems Control Division in 1992 uses a statetransition algorithm that keys on the primary land-use type within each small area. This algorithm works well in a monoclass environment but gives errors in cases where significant amounts of two or more land-use classes co-exist in a small area. In FORESITE, land-use data is entered and stored in polygon format but the algorithm's analysis is performed at a 2.5 acre grid resolution (small areas 1/16 mile across) on up to five million small areas. A subsequent hybrid simulation program, SUSAN, developed by the author and Dr. Andrew Hanson for ABB Consulting in 1999, used irregularly-shaped mono-class areas that were "carved" to follow the contours of contiguous areas of single classes. The areas were consequently somewhat larger (and hence there were far fewer). SUSAN produced equivalent results with much faster computation speed (due in part to other "tricks" beyond this reduction in number of areas to be analyzed). Neither a mono-class nor multi-map framework is best for all situations. Both have similar data storage and computation requirements, and either can be efficiently interfaced with a polygon land-use data structure for data entry and display. The important point is for program designers and users to realize that small area size, map stack design, and algorithm behavior interact ~ all have to be considered in making two of the most basic decisions about simulation program design — what will the spatial resolution of the program be, and how will the consumer class data be treated? Forecast of Change Based on Preference Allocation The primary function of the spatial model is to forecast where changes in land use will occur during the study period. As most often pictured, this mission involves forecasting where currently vacant areas will give rise to new development, but it also encompasses redevelopment (an existing area of one type is razed and rebuilt as another) as well as reduction in land-use density (a developed area is abandoned or de-inhabited).
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Usually, the forecasting of location of future change is accomplished with some form of preference map computation in which a score, or preference value, is assigned to each small area (Figure 12.7). Growth or change is then assigned to those small areas with the highest scores. Simulation programs nearly always apply the preference allocation method on a class-by-class basis, developing different preference maps for each class. As a simple example, suppose that it has been determined by some means that 500 acres of new industrial land use will develop somewhere within the utility territory during the period being analyzed (e.g., from 1998 to 2004). To determine where this 500 acres will be located, a preference map rating every small area versus industrial development would be developed. The score might be highest where there was a railroad, in areas immediately adjacent to a river, and near other industrial development. Scores might be reduced if the land were too close to residential neighborhoods, or far from highways and transportation. The highest scoring, available 500 acres on the map would then be selected to be forecast to change to industrial, from their current class, whatever that may be.
Figure 12.7 A preference map computed for retail commercial development using a sixattribute pattern template as described in Chapter 13, section 4. Level of shading reflects the degree to which the small areas match the requirements of retail commercial land use — proximity of major roads, intersections, other commercial development, with a significant population within a surrounding area. Only small areas that are potentially developable have been evaluated in the analysis shown here.
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Generally, one of two approaches is taken in developing the preference map, both done on a class-by-class basis, with a different preference map for each class: Land-use preference. This traditional approach corresponds to that described in the paragraph above. It has been used in spatial electric load forecasting for at least two decades. The user inputs a list of criteria or attribute values for each land use. Preference for each small area is computed based on how well it matches that list of required attribute features. For example, heavy industry's pattern might say the score is higher if near a river, if near a railroad, if near other industry, if fairly near a highway, and lower if farther away from each. It might indicate that the score is low if near substantial residential, parks, or environmentally sensitive areas, or near highrise development. Based on similarity to past observations. Here, the preference map is developed by comparing each small area to the characteristics of small areas that made a similar transition sometime in the past. For example, historical analysis could study all small areas that developed into retail commercial development (from something else) during the period 1990 to 1992, identifying characteristics common to those that developed but different from those that didn't develop. These could then be applied to determine a score for each small area, a measure of how well it matches the characteristics common to past observed changes. Both probabilistic and pattern recognition approaches have been used. 12.4 TOP-DOWN STRUCTURE Figure 12.8 shows an overall structure similar to that used in all simulation approaches. Individual programs will differ only slightly from this overall road map of layout and functional modules. Simulation methods differ substantially in the details of how each module functions within its function; the structure shown is not representative of all computer programs that have been developed, but this diagram is as representative as any the author has seen. Like Figure 12.1, this structure has two separate modules, spatial-consumer and temporal-load curve, which work largely independently and in parallel, with their coupling coordinated through the use of common class definitions. This is basically a top-down structure, the forecast being driven from the global forecast (at the "top") and the spatial process one of allocating the global growth to small areas. The majority of spatial modules function in this top-down
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manner, in which growth is analyzed with increasing spatial resolution in a series of from three to five steps - beginning with a global analysis of growth and culminating with assignment of growth to small areas. This top-down approach is applied equally to polygon and/or grid-based small area formats and with either multi-map or mono-class frameworks. In some programs, the steps in the top-down analysis are discrete, with the program literally proceeding through them in a hierarchical fashion in which the spatial resolution of forecasted consumer change is increased from one step to the next. For example, the ELUFANT program (see Chapter 17's lists) used a first step that allocated its global totals to large areas (e.g., 5 by 5 mile blocks of small areas). In the next step, the growth assigned to each 5 by 5 mile block was re-allocated to one of 45 smaller (71 acre) areas within it. In some versions of ELUFANT this was followed by a third step that allocated growth assigned to the 8-acre areas within each sub-block (Willis & Gregg, 1980).
|SPAfiAL"MODULE"
Figure 12.8 The spatial consumer module nearly always proceeds in several steps of analysis that include a gradual increase in spatial resolution (see text).
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However, in many simulation programs the steps shown in Figure 12.8 represent a series of computations carried out with increasing spatial resolution, but are not a set of explicit allocations, re-allocations, and re-re-allocations of the growth from one step to the next. In such cases, the steps differ in what they examine and perhaps in the spatial resolution used in their analysis, and each builds part of the analytical results from which a single, final allocation of growth is performed. The top step examines only global (system-wide) growth influences, the next considers "wide area" influences (those such as commuting time and traffic corridors that affect the growth of hundreds of small areas), and a final step might look at the detailed surroundings of every small area, focusing on such factors as whether it is adjacent to a railroad, and only considering the square mile around each small area while performing this very high-resolution analysis. The numerical results from these different steps of spatial analysis are then combined into a single preference map that is used to allocate the global totals directly to small areas. This approach is easiest to picture, and understand, if growth analysis is viewed from the spatial frequency domain perspective. The successive steps summarized above represent modeling of effects in different spatial frequency bands. The top level is the DC (zero frequency) component of growth, the next the lower frequency effects, and the succeeding step the model of effects and factors in the higher frequency bands. (This perspective will be discussed further in Chapters 13-14.) The CEALUS simulation-based program developed for the Canadian Electric Association was the first major simulation program to use this approach (see References). 12.5 SUMMARY AND CONCLUSION Worldwide, perhaps fifty or more distinctly different computer programs have been developed and applied that apply some form of simulation. All work on a small area basis, with nearly every type of approach used. Table 12.2 summarizes the most important characteristics common to a majority of approaches. Within these common characteristics, a very wide range of approaches have been developed. Forecast quality has varied tremendously (more, in the author's subjective judgement, than the quality of the programs). Poor quality forecasts have been more the result of poor usage than poor programs. The quality of algorithms and of programs does vary widely. There have been some "stinkers" written, and there are a few programs that stand out as superior. But most programs that implement the basic simulation method can be made to produce accurate, representative forecasts.
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Table 12.2 Common Features of Spatial Electric Load Programs Involving Simulation Approaches to Forecast Computation 1. Small area approach to spatial information processing 2. Forecast is done as a series of annual "jumps" (iterations) 3. Consumer-class based format of area classification. 4. Top-down allocation of an overall global total. 5. Bottom-up spatial allocation prioritization 6. Land-use inventory used as controlling feature 7. Pattern recognition of spatial features 8. End-use or load curve/factor model to convert land use to load
REFERENCES AND BIBLIOGRAPHY R. J. Bennett, Spatial Time Series Analysis, London, Pion, 1979 C. L. Brooks and J. E. D. Northcote-Green, "A Stochastic-Preference Technique for Allocation of Consumer Growth Using Small Area Modeling," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabot, April 1988. M. V. Engel et al, editors, Tutorial on Distribution Planning, New York, Institute of Electrical and Electronics Engineers, 1992. J. Gregg et al, "Spatial Load Forecasting for System Planning," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. A. Lazzari, "Computer Speeds Accurate Load Forecast at APS," Electric Light and Power, Feb. 1965, pp. 31-40. I. S. Lowry, A Model of Metropolis, Santa Monica, The Rand Corp., 1964. R. W. Powell, "Advances in Distribution Planning Techniques," in Proceedings of the Congress on Electric Power Systems International, Bangkok, 1983.
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C. Ramasamy, "Simulation of Distribution Area Power Demand for the Large Metropolitan Area Including Bombay," in Proceedings of the African Electric Congress, Rabot, April 1988. Research into Load Forecasting and Distribution Planning, EL-1198, Palo Alto, Electric Power Research Institute, 1979. B. M. Sander, "Forecasting Residential Energy Demand: A Key to Distribution Planning," IEEE PES Summer Meeting, 1977, IEEE Paper A77642-2. W. G. Scott, "Computer Model Offers More Improved Load Forecasting," Energy International, Sept. 1974, p. 18. Urban Distribution Load Forecasting, final report on project 070D186, Canadian Electric Association, 1982. H. L. Willis and J. Aanstoos, "Some Unique Signal Processing Applications in Power Systems Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, Dec. 1979, p. 685. H. L. Willis and J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, p. 48, May 1979. H. L. Willis and T. W. Parks, "Fast Algorithms for Small Area Load Forecasting," IEEE Transactions on Power Apparatus and Systems, October, 1983, p. 342. H. L. Willis and T. D. Vismor, "Spatial Urban and Land-Use Analysis of the Ancient Cities of the Indus Valley", in Proceedings of the Fifteenth Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, 1984. H. L. Willis, M. V. Engel, and M. J. Buri, "Spatial Load Forecasting," IEEE Computer Applications in Power, April, 1995. H. L. Willis, J. Gregg, and Y. Chambers, "Small Area Electric Load Forecasting by Dual Spatial Frequency Modeling," in IEEE Proceedings of the Joint Automatic Control Conference, San Francisco, 1977.
13 Analytical Building Blocks for Spatial Simulation 13.1 INTRODUCTION This is the second chapter on computerized application of simulation for spatial electric load forecasting. Chapter 12 presented an overview of the common characteristics and overall approach used in most simulation. This chapter will delve into the details of several analytical methods that are used in most growth simulation. This chapter will present the three most often used analytical tools in the spatial consumer module of a spatial electric load forecast simulation program. These are the matrix implementation of land-use cause and effect, the polycentric activity center or "multi-urban pole" gravity model of aggregation in an urban area, and pattern recognition using class-based template matching. The structure and flow of computation for several types of simulation programs that use these building blocks will be explored in Chapter 14. 13.2 LAND-USE INPUT-OUTPUT MATRIX MODEL Consider the example discussed in Chapter 10, section 3, in which a pickup truck factory built in an isolated region leads to the development of a small town. In that example, a factory of 350 acres directly causes a need for 57 acres of executive homes (home on large lots), 830 acres of single family homes, and 291 acres of multi-family housing. It eventually leads to land use (including the secondary and tertiary growth stages discussed), as shown in Table 13.1.
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Table 13.1 Land Use Caused Directly and Indirectly by the Truck Factory
Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices Hi-rise Industry Warehouses Municipal Factory
Acres 87 1,270 547 168 61 22 89 48 18
One can create a vector of the acres caused by the factory, normalized to a per-acre-of-factory basis, by dividing those land-use totals by 350, to get
[ .25, 3.6, 1.6, .48, .17, .06, .25, .15, .05, 0 ] Multiplied by 350, this vector gives the growth associated with the example pickup truck factory. Multiplied by 500 instead of 350 acres, it gives the expected land-use impact due to a 500 acre rather than 350 acre factory, other things being equal. Suppose that eventually the pickup truck factory in the original example were to expand due to increased demand for its product, adding another 75 acres. Then 75 multiplied times the vector above gives an estimate of the land-use additions expected due to the factory expansion. The example in Chapter 10, section 3 looked at a factory added at a remote site. While that example used a classic of basic industry (heavy manufacturing), the reader must understand that basic industry is anything that markets to or brings money into a region from outside the regional boundaries. Basic industry in the Lowry sense can include all or portions of any land-use class. Even small cities like Decatur, IL, Raleigh, NC, Branson, MS, and Sarasota, FL have diverse local economies in which basic industry includes portions of many land-use categories such as heavy industry (e.g., truck manufacturing), light industry (e.g., furniture assembly), office commercial (banking and insurance), retail commercial (retail that caters to tourists), schools (major universities), and even residential (retirement pension income as will be discussed in Chapter 21). A large city usually has basic industry composed of many types, and composed of at least a small amount of every land-use type.
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Table 13.2 Land Use Caused by the Insurance Company Headquarters
Class Residential 1 Residential 2 Apartments/rwnhses Retail commercial Offices Hi-rise Industry Warehouses Municipal Factory
Acres 140 1,200 600 150 75 35 45 18 18 0
The "pickup-truck factory" example in Chapter 10, section 10.3 could just as well have talked about a corporate headquarters and claims processing center for a major insurance company, instead of a pickup truck factory. Suppose that a 50acre site containing four hi-rise office buildings had been built for the new headquarters "campus," to accommodate a total of 4,500 insurance company workers of various categories. It would have led to similar types of development, though slightly different in composition because the salary distribution, demographics, and consumer preferences of office workers will be somewhat different from those of factory workers and lead to slightly different land-use inventories, as indicated in Table 13.2. Dividing by 50 acres gives a vector of the per-acre impacts due to hi-rise office commercial basic industrial growth
[ 2.8, 24, 12., 3.0, .1.5, .1.7, .9, .36, .36, 0 ] Multiplied by 50, this gives the growth associated with a 50-acre insurance company "headquarters campus." Multiplied by 10 instead of 50, it gives the expected land-use impacts due to the expansion of another 10 acres of similar high-rise development. Similar land-use-caused-by-an-acre-of-basic-industrial-development vectors can be determined for the other land-use classes, which can be formed into a matrix covering all the land-use classes, as shown in Table 13.3. Multiplied by a vector of basic land-use growth that has only one non-zero entry ~ 350 acres of factory, this gives the growth associated with the pickup truck factory (i.e., the growth listed in Table 13.1). Similarly, a basic growth vector containing only the
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Table 13.3
Example Total Development Matrix
One \ Acre of N^ 1 Resid 1 2 Resid 2 3 Apart. 4 Retail 5 Offices 6 Hi-rise 7 Industry 8 War eh. 9 Muni. 10 Factory
1 .005 .01 .01 .14 .28 2.8 .10 .03 .25 .25
2 .03 .06 .06 1.2 2.4 24 .8 .2 2.0 3.6
Causes Land-Use Growth (Acres) 7 8 3 4 5 6 .02 .005 .002 .001 .001 0 .01 .005 .003 .003 .001 .03 .01 .005 .003 .003 .001 .03 .04 .02 .6 .15 ..08 .04 1.2 .30 .07 .09 .04 .15 3.0 12 1.5 .7 .9 .36 .11 .04 .014 .05 .45 .03 .11 .03 .015 .01 .003 .01 .25 .12 .07 .02 1.0 .05 48 .17 1.6 .06 .25 .15
9 0 .001 .001 .02 .04 .36 .003 .001 .02 .05
10 0 0 0 0 0 0 0 0 0 0
50-acre insurance company "headquarters campus" would produce a list of the growth caused by it and it alone (Table 13.2). A vector containing both 350 acres of factory and 50 acres of high-rise would produce a total land uses equal to the sum of Tables 13.2 and 13.3. In general, if one forms a vector, B, composed of the amount of expected basic industrial land-use increase, with elements bc where c is the land-use class, then multiplication of this vector times T gives the total expected land-use development, DT, caused by the basic industry:
DT
=
TxB
= Tx
(13.1)
and the vector, L, of the total land-use growth with elements lc, including all growth of basic industry, too, is:
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1, Iz 13 14
Is 16 17
Is 19 1,0
=
b, d, d2 b2 d3 b2 b2 d4 d5 + b2 d* b2 d7 b2 b2 ds d9 b2 b2 dio
= T x B + B = [T+I] x B
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(13.2)
Throughout the rest of this book, the vector of consumer-class changes as above will be referred to as a " DT vector" or " LT vector," as the case may be, and will correspond to the definitions given here. This approach is basically an "input output matrix of land-use development. Surprisingly (at least it has always surprised the author) this approach works acceptably well in many cases, despite the fact that employment density and a host of other variables vary considerably from one particular factory site to another, even though they are all modeled as similar because they are members of the same class. Equations 13.1 and 13.2 showed the basic concept, applied in acres on both the input and output: so many acres of basic growth lead to so many acres of total land-use development. Often it is desired to "drive" a forecast with a control total or growth trend that is not in units of area. In such a case the approach can be modified so that the units for the "input side" are measured in consumers, employment, payroll dollars, or any other measurable unit. For example, the T&D planners and forecasters may want to "drive" their spatial forecast with projections of employment provided by a federal, state, or municipal Department of Economic Development. Usually such forecasts are by employment sector, and basic industrial jobs can be separated out of the total employment with a reasonable amount of study. Direct-Cause Matrix Models As described above, equations 13.1 and 13.2 give the total land use that develops as a direct and indirect result of a new factory, insurance center, etc. The total growth caused by the pickup truck factory included the growth caused directly because of the factory (57 acres of executive homes, 830 acres of single family homes, 291 acres of multi-family housing, along with some industrial support land use, etc.), and secondary land-use growth ~ the retail and services related
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Table 13.4 Land Use Caused Directly by the Truck Factory Class Residential 1 Residential 2 Apartments/twnhses Retail commercial Offices Hi-rise Industry Warehouses Municipal Factory
Acres 57 1830 291
4 10
growth needed to support that directly caused residential development -- and the tertiary growth ~ the residential development required for the workers in those establishments, and so forth as was described in section 10.3. In some cases, computer application of input-output land-use matrices is structured so that matrix application gives only the land-use change caused directly within each of these stages of growth Using the pickup truck factory again, the land use caused only as a direct result of it is shown in Table 13.4 (compare to Table 13.1). A vector of land-use-directly-caused-per-acre-of-factory can be produced, as previously, by simply dividing the amounts in Table 13.4 above by 350 acres. Multiplying that vector times 50 acres gives the amount of land use directly caused by a 50 acre addition to the factory, and so forth. Similarly, by study and analysis, one can develop similar vectors of land-use-directly-caused-by-theaddition-of-one acre for each of the other land uses. For example, for single family homes, this would describe the expected addition of retail and commercial services required when one acre of new homes was added. Admittedly the elements in this vector would be very small - one acre of homes does cause the need for much in the way of retail development. But multiplied by 1,000 acres of growth, as it would be in a large city over the course of several years, it would describe the amount of retail expansion that could be expected to develop to serve that residential growth, and so forth. Developing vectors like this for all classes leads to a matrix T', similar to the T matrix developed several pages earlier, but a matrix which when applied to B, the vector of all basic industrial growth, gives only D u , the vector of total landuse growth directly caused by B, the growth in the first stage of the Lowry concept growth model.
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Multiplying DI by T gives a land-use vector, D2,, the list of "secondary" growth caused by the Dj growth ~ this growth is the retail commercial that develops in the second stage, in response to the market needs of the factory workers, etc. Similarly, D3, the mostly residential growth caused by the employment created by that retail commercial development, is computed by applying T' to D2. D4 is the further retail/services growth caused as a result of D3 and is computed by applying T' to D3, and so forth. Using this approach, the total land-use development L is
(13.3)
+D 4
and T~> (T')n as n-> large. In practice, T = (T1)6 with small error. Table 13.5 shows an example T' matrix. Small values have been set to zero to show the quite different nature of this matrix as compared to T in Table 13.3. Here, the rows for industrial and commercial development indicate that adding one acre of any of their land-use types directly causes mostly residential development, and vice versa. This corresponds to the behavior cited in the stages of growth as modeled by the "Lowry" concept discussed in Chapter 11. This approach is more complicated to apply than the single matrix computation using T (eqs. 13.1 and 13.2) but it can be applied to spatial analysis in a more meaningful and precise spatial manner. For example, as shown in Figure 13.1, suppose the 350-acre pickup truck factory from section 10.3 is built on the outskirts of a big city rather than in the isolated region used in Chapter 10.
Table 13.5 Example Direct Development Matrix
One \ Acre of \ 1 Resid 1 2 Resid 2 3 Apart. 4 Retail 5 Offices 6 Hi-rise 7 Industry 8 Wareh. 9 Muni. 10 Factory
1
.09 .19 1.9 .07 .02 .15
.16
Directly Causes 3 4 - .005 .01 .01 .07 .3 .7 1.4 14 7 .5 .25 .13 .08 1.1 .6 .05 2.4 .83 2
Land-Use Growth (Acres) 5 6 7 8 .002 .001 .001 .005 .003 .003 .005 .003 .003 .02 .01 .02 .05 .2 .5 .01 .004 _ .05 .03 .04 .01 .01 .03
9
10
.01 .02 .2 0 0 -
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Based on the factory characteristics, D t can be computed by applying T to a basic industrial vector composed only of a single element of 350 acres, representing the factor. The Dj growth caused directly by the factory (this is mostly housing for those who are employed at the factory) is tied directly to the factory's location — the factory workers will want to be in reasonable proximity to the place they work, but for a variety of reasons which will be discussed later, will tend to locate nearer rather than farther away from the city, as shown. The location of the secondary growth impacts, D2, is not highly dependent on the location of the factory, but rather on the locations of those homes that develop because of the factory. D2 growth is most likely to develop near those homes, not near the factory. For example, if for some reason the D[ growth had located outward from the factory, farther into the countryside and away from the city, then the demand for new retail commercial development, D2, would develop there. But Figure 13.1 shows a much more typical situation-the residential development caused by the factory occurs mostly in or near the existing city but on another quadrant of the periphery, in this case to the northwest of the factory site along the northern periphery of the metropolitan area. There is where the demand for the secondary growth D3 will be centered -- the retail commercial development needed to support these new homes is a function of the locations of these new homes, not the factory.
Residential growth caused by factory concentrated here
Commercial growth caused by new homes centered here
FACTORY
Existing developed areas of city Figure 13.1 The stages of growth as represented in a "Lowry model" may have different locational centers of influence, as shown here and discussed in the text.
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The secondary growth, DI, can be computed (D2 = T x D t ) and spatially tied to the locations of these new homes rather than the factory in a manner that acknowledges the fact that the secondary growth is not necessarily near or centered around the factory, and that considers its distributed nature, too (i.e., the houses of the factory workers are scattered throughout a wide region, perhaps in a very non-homogeneous manner). Similarly, the tertiary and further stages of growth can be applied and "tracked" spatially. This discussion is getting a little ahead of itself, because the method used to apply and "track" this growth influence on a spatial basis has not been introduced. But the important concept here is that the T' matrix allows the stages of growth to be spatially allocated on an individual basis, which increases forecast accuracy. 13.3 ACTIVITY CENTER GRAVITY MODELS Modern cities exist, and in fact can be quite congested, because residents, store owners, and business operators alike all want their homes and businesses as close as possible to as many other activities as possible. There are a host of reasons given ~ convenience, business opportunity, cultural improvement, mutual security, reduced transportation cost -- but the fact is that human use of land (and of electricity) is drawn into geographic concentrations which, at least if the past four thousand years of historical record are any indication, has no upper bound. If this pressure to concentrate did not exist, there would be no cities or towns ~ development and population would be dispersed evenly throughout the countryside. Whether the existence of cities is truly desirable from a quality of life standpoint, and whether it provides an efficient impetus for business and a more secure residential environment is immaterial ~ it happens. Many models of land-use development, not just those applied in electric load growth study -- use a "gravity model" to represent this observable tendency of land-use development to locate in close proximity to other developed land use. Figure 13.2 illustrates the concept, with what is sometimes called an urban pole. The center of a large city is modeled as having an influence that draws other land use to it. This influence is strongest in the very core (activity center) and like gravity decreases in strength as one moves away from the city center. The urban pole is interpreted and applied as a model of the preference that developing land uses will have in being close to the activity center ~ every business, every homeowner, would ideally like to be at the very center of activity. However, except in rare cases, they must compromise this preference with the fact that they cannot find land that suits their needs, or that they can afford, in close proximity to the center, and thus they are forced to pick some location slightly farther out, but still as close to the city as practical in their circumstances.
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Existing developed areas of city
Figure 13.2 A gravity model represents the influence of a city or factory on other land use as a decreasing function of distance from the activity center. The urban pole function shown here assigns a certain influence (the height of the function) to the activity center and models this influence as decreasing as one moves away from that location.
Strictly speaking, there are two separate modeling concepts involved. The first concept is the gravity model ~ influence is a decreasing function of distance, not necessarily decreasing proportional to the square of distance as does gravity, but decreasing in some manner, be it linear, exponential, or whatever. The second concept is the activity center ~ influence is concentrated, or can be modeled as concentrated, at the center of a city, town, or aggregated group of land uses. Activity centers are concentrations of residential, employment, cultural or municipal facilities that are significant in shaping the locations of surrounding land-use development. The gravity model is applied to represent their influence on other locations nearby and far away. As illustrated in Figure 13.2, the city center exerts an influence that is modeled as strongest at its center, decreasing to zero only far beyond its boundaries. For example, the direct impact of a new factory on the economy and population of a region will be most profound near its site and substantially less farther away, as has already been discussed. "Distance" in this regard usually means travel time by car, train, or mass transit, not straight-line distance. In many cases, however, the simplifying assumption that travel time between areas is proportional to straight-line distance can be used with good effect, particularly on small or medium size (less than 1,000,000 population) cities lacking dominant geographical barriers. Urban pole
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functions of the type shown in Figure 13.2 work very well in the vast majority of situations. Polycentric Activity Center Models Large cities often have more than one activity center and must be represented with more than one urban pole function. The ELUFANT program used to forecast electric load for T&D planning at Houston Light and Power in the 1980s was one of the first to use a polycentric activity model, representing the greater metropolitan Houston region with eleven discrete activity centers, each a separate urban pole function (Gregg et al). A city like Paris or greater Los Angeles can have upwards of two dozen centers. Generally, the center of the city (downtown) or the major population center in a rural region will be one activity center. Others will include large industrial areas, major office park concentrations, and so forth ~ every area that constitutes a large concentration of employment or commercial activity and occasionally other cultural or municipal centers such as a major university. Figure 13.3 illustrates a simple polycentric activity center model with three urban poles. It shows how the influence of the pole functions is additive, and indicates that their influence may need to be modeled even when the center is outside the utility service territory.
Downtown Outlying industrial park
Employment center not in study area
Figure 13.3 Heights and radii in a polycentric activity center model vary according to employment and commuting times at each location. Note that the influence of the various urban poles is additive and that a pole's influence may extend beyond the map area being studied, or from beyond the area being studied.
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Urban poles and gravity models have been used in myriad types of land-use, population, and demographic models. A number of different methods exist for determining the quantitative aspects of the urban pole functions -- exactly where they are located, their height, and the diameter of their influence. Many of these methods have been based on innovative and clever theories about urban development, population demographics, or transportation behavior (see References). Others simply define the urban poles practical experience backed by no theory, simply using a set of definitions that have worked well in the past. For electric load forecasting, the following "rules" generally provide good results: 1. An urban pole should be used for any activity center that is more than 10 minutes travel distance from any other and has more than ten percent of the region's employment within a ten-minute travel diameter. 2. Radius is generally based on the "45-minute rule." Transportation studies have repeatedly confirmed that 80% of all commuters take 45 minutes or less (each way) to commute, worldwide.1 Eighty percent of the area of a circle lies within 89.4% of its radius. Therefore, the recommended radius of each urban pole, given a linear profile is: Recommended radius for an urban pole = R^s /.894 where R45 is the estimated distance that can be traveled away from the activity center in 45 minutes. Forty-five minutes divided by .894 equals 50.33 minutes. Thus, urban pole radii can be set to the "distance traveled radially outward from this site in 50 minutes." This distance should be the forecaster's estimate (or statistic
1
This rule appears to apply well to cities and regions worldwide, regardless of whether the predominant mode of transportation is auto, train, bicycle, or foot. It also appears to be applicable regardless of historical age or culture: an analysis of the ancient Indus Valley civilization (circa 1000 BC) performed by the author (see Willis and Vismor, 1984) indicated the layout of its major cities, Mohenjo Daro and Harappa, was consistent with this rule, at least on a macro scale. A preliminary analysis of ancient Rome (200 AD) seems to indicate the same.
Analytical Building Blocks for Spatial Simulation based upon gathered data) of the average commuting distance that can be achieved in slightly over 50 minutes, not the worse case during rush hour, or the best. This rule works for all but a handful of truly massive metropolitan regions like New York, Paris, Cairo, and Mexico City, where a significant portion of employees may commute more than an hour each way between home and work location. In any such "gigapolis" the radii used in the urban poles needs to be increased to a more representative value. But many other large cities, such as Houston and Atlanta, can be modeled very accurately, at least for electric load growth purposes, using this rule. Often one cannot travel from downtown to the periphery of a large city such as Houston or Los Angeles in only 50 minutes, but a 50minute radius still works well as a model of gravity influence. Employment in large cities is spatially distributed (some jobs are near the outskirts of the city), and their spatial development can be explained using a 50minute urban pole radius. That is the point of the urban poles. 3. Linear functions of distance (e.g., urban poles as shown in Figures 13.10 and 13.11) seen to work well enough in small, large, and massive population regions, so that little substantial evidence has ever been developed to suggest that any other type of profile need be applied. 4. Urban poles are dimensionless. As applied, only relative values matter. The author always normalizes these functions to some standard maximum - the maximum value is 1.0. 5. Poles in a polycentric activity center model their maximum values proportional to employment in the activity center they represent. If downtown is the largest employment center with 60,000 jobs, it is defined as 1.0 height. An outlying office park with 35,000 jobs is assigned a height of 35/60 = .583.
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The polycentric activity model is the most widely used approach to this type of "large region travel time" analysis and can satisfactorily represent the spatial interactions of land uses in large and complex regions with diverse economies, such as Philadelphia-Redding-Allentown, Los Angeles, and the Dallas-IrvingArlington-Fort Worth metropolitan regions. 13.4 CONSUMER-CLASS SPATIAL ALLOCATION USING PREFERENCE MATCHING The third building block of simulation programs is pattern recognition of local small area attributes, used to identify a match between individual small areas and specific land-use classes. As mentioned here and in previous chapters, different land-use classes have different needs regarding the characteristics of the land they are using. Close proximity to a railroad is a plus for industrial land uses, but a very negative factor for residential development. Similarly, retail commercial finds it necessary to be immediately adjacent to a major traffic corridor, whereas industry finds the nearby flow of traffic (and thus consumers) unimportant and not worth the price, while residential development will shy away from major roads, viewing heavy traffic as a nuisance. Land uses vary in their needs. Small areas vary in attributes. Finding a match involves assessing each small area against the different land-use class requirements. One complication is that most of the attributes that distinguish land suitability among different land-use classes have nothing to do with the small areas themselves, but with what is around and in close proximity to each. Certainly some features of each small area are important: the terrain must be developable (i.e. a 60% slope is unacceptable) and be unrestricted, but by and large suitability of land for a particular land use depends on features nearby, not in the small area. Is it near a railroad and near other industrial development? Then it may be suitable for industrial development, itself. Is there already hi-rise development in an adjoining small area? If so, historical precedent shows hi-rise is more likely to develop there than in small areas farther away. Is it surrounded by a substantial amount of housing in the immediate neighborhood? Then residential development is highly likely. Thus, one of the first steps in land-use pattern recognition is to establish the values of a set of "proximity and surround factors" that measure these distinguishing attributes for all small areas, or at least all those that must be evaluated for any possibility of change. Many of these factors are important for several land-use classes (e.g., proximity to railroads affects both industrial and residential classes), so it is common to compute the entire set of factors in a step prior to the pattern recognition. Following that, a series of pattern recognition
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Table 13.6 Local, Proximity, and Surround Factors Factor
Importance
Local (attributes of the small area) Buildable terrain
Undevelopable unless one can build upon it.
Restricted
Undevelopable if law or public use precludes it.
Forested?
Tree lots are a plus in residential, but increase building cost for industrial and commercial.
Water available?
A area is unlikely to develop if municipal water is unavailable or water wells are precluded.
Zoning classification
A key in some regions but at other times useless.
Proximity factors Distance to nearest railroad
Positive for industrial, negative for residential, can be a factor in other classes, too.
Dist. to nearest major road
Key factor in retail and some other commercial development.
Distance to nearest highway
While major roads are important to many classes, distance to highway defines "major access"
Distance to nearest intersec.
A major intersection is big for retail/office parks
Distance to nearest school
Factor in residential development, doesn't seem to matter what type of school (elem., middle)
Distance to nearest hvy ind.
This more than the amount seems to affect both industrial and residential development concerns.
Distance to transit terminal
Important in regions with mass transit industrial and residential development concerns.
Distance to nearest water
Key in both industrial and preferable for resid.
Distance to nearest comm.
Useful discriminator for comm. & resid. classes
Surround factors Residential within 1/2 mile
Most significant factor in residential development
Residential within 3 miles
Defines the "market" for commercial. Amount of retail correlates well with this sum.
Commercial within 3 miles
Resid. wants to have shopping nearby. Retail will not locate if too much already in region.
Hi-rise within 1/2 mile
Key factor in all commercial development
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sweeps through the small area data field are made, one sweep for each land-use class, using a pattern recognition template defined to match that class's needs. Table 13.6 lists proximity and surround factors that are often encountered as part of electric load forecasting simulation. Not all are needed in every situation, but usually a large subset of those shown must be included. Local factors are attributes of the small area itself, mostly related to the land's suitability to be built upon in any manner. To have any possibility of development, a small area must have terrain that can be built upon. It must not be precluded from development by law, and water must be available. In addition, factors such as trees and the view can be important in some cases — homesites with trees and/or a spectacular view tend to develop first. Proximity factors measure influences that are mainly a function of distance, not amount of the causal feature. For example, to most industries it is important to be near an active railroad right-of-way, but the number of tracks nearby is irrelevant. The needs of most factories or warehouse centers can be met with a single rail line. Thus, the factor to measure is distance to the nearest railroad, not the number of railroads nearby. In a similar manner, whether a particular small area is adjacent to one, two, or three interstate highways, or alongside one, two, or three industrial plants, is almost irrelevant with respect to residential development suitability ~ the prospects of residential development in the immediate neighborhood are ruined if just one of either is within 1/4 to 1/8 mile. Surround factors measure influences that do depend mostly on the amount nearby. The most obvious factor is the amount of residential development within a 3 mile radius - this correlates well with commercial development. Major malls and heavy commercial development only occurs when a certain threshold of development has occurred in the areas around the site. Similarly, a measure of the amount of residential development in a 1/2 mile radius of a site correlates very well with likelihood of residential development at that site. Usually, these factors sum land use, not population ~ residential factors based on the number of acres of residential land use within 1/2 mile are quite as satisfactory as actual housing counts, and usually much easier to determine. Methods vary, but generally, local factors are measured in binary status (zero-one for yes-no), proximity factors are measured in terms of a score that is a function of distance, and surround factors are measured in units of area (acres, hectares, square kilometers). Local factors are generally interpreted or provided as input data. The map stack (Figure 13.4) will contain a workspace map for each proximity and surround factor ~ a small area grid or polygon map as the case may be, which will retain the computed proximity and surround factors. Proximity factors can be computed using any of several methods (see References). In general, the program code works from the spatial data on the causal factor (e.g., a map of railroads) working outward from the locations of the
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item and assigning computed distance to all small areas within a set distance (if a railroad is not within 1/2 mile, it has no effect on development, so assignment need only be made to small areas within 1/2 mile of known railroads. As computed, proximity factor maps usually assign a score to small areas that is inversely related to distance from the railroad, highway, or whatever causal factor is being considered, as shown in Figure 13.4. Usually simulation programs are written to accept a wide variety of profile shapes, two of which are shown.. Computation of surround factors can be computationally intensive. The most straightforward (not nearly the quickest) way to calculate the values of the factor map is to use a program loop that "spirals outward" from each small area, examining all neighboring small areas out to some maximum search distance, adding together (and perhaps using a weighting based on the distance) the causal variable (e.g., residential development) found in each. This sum is then assigned as the surround factor value for that small area, and the program moves to the next small area and repeats the entire computation, doing so for all small areas until the factor has been computed for all small areas. In essence, this is the spatial convolution of the causal factor (e.g., residential development) with a circularly symmetric operator, two of which are shown in Figure 13.5. Use of a "pancake function" is equivalent to simply adding together all values in the causal variable map within a certain radius. Most simulation programs allow the user to specify a weighting function of distance with regard to the summation — e.g., residential two miles away is less important than that nearby, as shown in the bottom of Figure 13.5. Calculation of proximity and surround factors is numerically intensive. Careful attention to the details of logic flow, and efficient programming, are required to produce software that can compute these factors in a reasonable time period. Very quick, "trick" methods for computing both proximity and surround factors will be discussed later. Usually, proximity and surround factors are computed for all small areas, even when it is possible to determine a priori that some are not developable and therefore need no calculation: the program logic required to apply such tests and vary computation of factors takes longer than the computations themselves (such determination is not as straightforward as it might first seem). Preference Map Determination Using Pattern Templates For each land-use class, a template of factor coefficients can be used to assemble the computed factors into a preference map for that land-use class. The coefficients measure the degree to which a factor is positive or negative with respect to the particular land use's needs or its observed locational behavior.
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Distance
'Distance
Figure 13.4 Computed map for road proximity using an inverse function of distance (topmost of the two profile functions shown at the right). It assigns an arbitrary maximum value to small areas with a major road in them and lesser values to those farther away, out to a distance beyond which influence is zero. The bottom profile on the right is a "close but not too close" factor profile, used for influence of major roads on certain classes of residential and commercial — for example many apartment developments are near but not immediately adjacent to major streets and roads. It assigns a negative value to small areas with a road in them and a maximum to those close by but not actually alongside the road.
/ /
/ / /
/
/
7
/
/ r f
/
/
/ / / / I
Figure 13.5 A surround factor may integrate the amount of a particular factor (e.g., acres of housing) about each small area using a "pancake function" (top) in which the sum within a radius is computed for each small area, or it may use a radial function of distance (bottom) which assigns a higher weight to nearby values than to those far away.
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A wide variety of pattern recognition methods have been applied to spatial electric load forecasting. None has proven demonstrably better in practice than simply forming a linear combination of the proximity and surround factors. One of the first production applications to use this approach was the ELUFANT program developed at Houston Lighting and Power (see Willis and Aanstoss, 1979). It will be used an example. This program began the pattern recognition by computing the proximity and surround factors listed in Table 13.7. All proximity factors used an inverse linear profile (bottom of Figure 13.5). All surround factors used a "pancake function (Figure 13.5, top). Computation of each was normalized to maximum and minimum possible values of 1.00 and 0.0 and stored in a workspace map. Then, for each land-use class the program computed a pattern match score by forming a linear combination of these factor maps, using a different set of weighting coefficients for each class. Table 13.8 lists coefficients for three classes, giving an indication of the values used and the variation among classes.
Table 13.7 Proximity and Surround Factors Used in ELUFANT Program Factor
Description
Value
1
Railroad proximity factor
1.0 at a railroad decreasing to 0 at .04 mile
2
Near highway factor
1.0 at a highway decreasing to 0 at .04 mile
3
Highway proximity factor
1.0 at a highway, decreasing to 0 at 3.5 mi.
4
Industrial proximity factor
1.0 at an industry, decreasing to 0 at .6 mi.
5
Hi-rise proximity factor
1.0 at a hi-rise decreasing to 0 at .5 mile
6
Water proximity factor
1.0 if nearby or at water, to 0 at .2 mile
7
Trees - local factor
1.0 if trees in the small area, 0 otherwise
8
Major intersection proximity
1.0 at an inters. ,decreasing to 0 at .4 mile
9
Residential count within 1/2 mile
Normalized to fraction of circle full
10 Residential count within 3 miles
Normalized to fraction of circle full
11 Commercial count with 1 mile
Normalized to fraction of circle full
12 Industrial count within 2 miles
Normalized to fraction of circle full
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ELUFANT then calculated a linear combination of these factors for each small area, using a different set of pattern coefficients for each. In general, given J factors and C consumer classes, one can define
P c (x,y)
=
Z (fj(x,y)*Pj,c
(13.4)
where Pc (x,y) is the pattern match score for small area x, y to class c By definition, pj>c e [-1.0, 1.0] fj(x,y) is the score for factor j in small area x,y Pj>c is class c's coefficient for factor j and j indexes J and c indexes C. Pc (x,y) is therefore somewhere between -12.0 and +12.0
Computation of these linear combinations for all small areas, for all C classes, resulted in C pattern match score maps, one for each land-use class, which were stored in a multi-map stack for later use. Table 13.8 lists the pj c values for three land-use classes, giving an example of how the weighting for a particular factor may vary from one class to the other. Although based upon the same twelve factors, the spatial pattern maps and their evaluations developed for
Table 13.8 Pattern Match Coefficients for Three Consumer Classes Factor
1 2 3 4 5 6 1 8 9 10 11 12
Description Railroad proximity factor Near highway factor Highway proximity factor Industrial proximity factor Hi-rise proximity factor Water proximity factor Trees - local factor Major intersection proximity Residential surround within 1/2 mile Residential within 3 miles Commercial within 1 mile Industrial within 2 miles
Resid.
Retail
Hvylnd.
-1.0 -.66 1.0 -1.0 -.66 .50 .35 -1.0 1.0 -.33 -.16 -1.0
-.50 1.0 1.0 -.50 .40 0 -.16 1.0 -.2 1.0 .50 -.50
1.0 -.10 .50 1.0 -1.0 1.0 -.20 -.33 -.50 -.16 0 1.0
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Figure 13.6 Maps of preference values computed at a 160-acre resolution for two classes. Major highways (lines) are shown for reference. Shading indicates magnitude of positive values. (Negative values are not displayed.) Top diagram shows industrial preference. Path of trunk rail corridors, a major factor for preferable industrial location, is quite discernable. Bottom diagram shows preference for the retail commercial class.
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each of the classes had a far different spatial character and distribution because of the different weighting coefficients. Figure 13.6 shows pattern match maps produced by applying the retail commercial and residential patterns templates in Table 13.8. Shading indicates degree of pattern match. The reader should note that pattern evaluation is only one part of the spatial analysis of consumer growth. Its purpose is not to determine location of change, but merely to identify certain aspects of location. Pattern matches determined by linear combinations as shown in eq. 13.4 provide only a partial answer, but a critical part. When combined with other spatial analysis features in a comprehensive program, they lead to a useful, accurate forecast.
REFERENCES AND BIBLIOGRAPHY
R. J. Bennett, Spatial Time Series Analysis, London, Pion, 1979 C. L. Brooks and J. E. D. Northcote-Green, "A Stochastic-Preference Technique for Allocation of Consumer Growth Using Small Area Modeling," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabot, April 1988. M. V. Engel et al, editors, Tutorial on Distribution Planning, New York, Institute of Electrical and Electronics Engineers, 1992. J. Gregg et al, "Spatial Load Forecasting for System Planning," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. A. Lazzari, "Computer Speeds Accurate Load Forecast at APS," Electric Light and Power, Feb. 1965, pp. 31-40. I. S. Lowry, A Model of Metropolis, Santa Monica, The Rand Corp., 1964. R. W. Powell, "Advances in Distribution Planning Techniques," in Proceedings of the Congress on Electric Power Systems International, Bangkok, 1983. C. Ramasamy, "Simulation of Distribution Area Power Demand for the Large Metropolitan Area Including Bombay," in Proceedings of the African Electric Congress, Rabot, April 1988.
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Research into Load Forecasting and Distribution Planning, EL-1198, Palo Alto, Electric Power Research Institute, 1979. B. M. Sander, "Forecasting Residential Energy Demand: A Key to Distribution Planning," IEEE PES Summer Meeting, 1977, IEEE Paper A77642-2. W. G. Scott, "Computer Model Offers More Improved Load Forecasting," Energy International, Sept. 1974, p. 18. Urban Distribution Load Forecasting, final report on project 070D186, Canadian Electric Association, 1982. H. L. Willis and J. Aanstoos, "Some Unique Signal Processing Applications in Power Systems Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, Dec. 1979, p. 685. H. L. Willis and J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, p. 48, May 1979. H. L. Willis and T. W. Parks, "Fast Algorithms for Small Area Load Forecasting," IEEE Transactions on Power Apparatus and Systems, October, 1983, p. 342. H. L. Willis and T. D. Vismor, "Spatial Urban and Land-Use Analysis of the Ancient Cities of the Indus Valley", in Proceedings of the Fifteenth Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, 1984. H. L. Willis, M. V. Engel, and M. J. Buri, "Spatial Load Forecasting," IEEE Computer Applications in Power, April, 1995. H. L. Willis, J. Gregg, and Y. Chambers, "Small Area Electric Load Forecasting by Dual Spatial Frequency Modeling," in IEEE Proceedings of the Joint Automatic Control Conference, San Francisco, 1977.
14 Advanced Elements of Computerized Simulation 14.1 INTRODUCTION This chapter is the last of three to look at computerized simulation methodology. Here, the structure and flow of computation for several types of simulation is presented and the use of the various concepts and building blocks discussed in Chapter 12 and 13 is examined in detail. The detailed, overall program and numerical computation structure of a generic simulation program for spatial electric load forecasting is presented. Spatial frequency domain methods and various other advanced techniques to increase computation speed, improve accuracy, automate the forecast calibration process, or otherwise improve the program's usefulness are covered next. A discussion of these and their application concludes the chapter. 14.2 SIMULATION PROGRAM STRUCTURE AND FUNCTION Figure 14.1 shows the overview diagram of simulation program structure from Chapter 12, with the typical locations of various building blocks and elements of program operation covered in Chapters 12 and 13 shown. What might be termed the basic, and certainly the most straightforward, of widely used programming approaches for this method is shown in Figure 14.2. A majority of simulation programs uses this approach or a variation to it. It has been applied in both grid
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Year N Spatial Data
Year N Load dive Data
onsumer Classes Consumer Count Input-Output Inventory Polycentric Pole Model Pattern Recognizer
YearN+P Spatial
Preference Computation Match to Corp. totals Consumer count -> Load Year Ntp Load Map
Figure 14.1 Simulation programs generally include both spatial and temporal "sides" which work independently, their function coordinated by the use of a common set of classes and a shell program that merges their results into the final spatial forecast.
or polygon spatial basis, and with either a mono-class or multi-map framework. The program goes through one iteration of the logic shown in Figure 14.2 for each study period (year to be forecast) that iteration taking the spatial data description of the consumer amounts and locations at the beginning of the period and transforming it into a description of consumer amounts and locations at the end of the period. The new spatial consumer data is then combined with load curves computed for the end of the period, to form forecast load maps. In this way the program gradually extends the forecast into the future — 1996 to 1997, to 1998, to 2000, to 2002, and so forth. Table 14.1 summarizes typical data requirements. At the start of each iteration, a T matrix (Table 13.3 and equation 13.1) computation is used to determine the expected total change in the amount of each consumer class (alternately the amount of consumer change may simply be input by the user).
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Table 14.1 Input Required by the Basic Simulation Method Shell program • set up data defining the number and indexing range of the small areas, the units to be used • number and names of the consumer classes • future years to be forecast (study periods) Temporal • • •
model Load curves, End-use structure (if using an end-use model) K, q, and p for each class (if using approach like that in Chapter 4, section 5).
Spatial model • spatial land-use data for the base year • geographic data such as highways, railroads, canals, airports, wetlands • global land-use totals for future years, or basic industry totals and a "Lowry" T matrix • polycentric activity model data: locations of the center, height, and radii for all urban poles • definition data for the proximity and surround factor maps, which might include what factors are to be computed (but often this is hard-wired) and the profiles to be used • pattern template coefficients, for each consumer-class coefficients for each factor (similar to Table 13.8) and a coefficient for the polycentric activity center urban pole map
Using a set of urban pole locations, height and radii input by the user, the program computes an urban pole map ~ a polycentric activity center model of the large area effects in the region, similar to that shown Figure 13.3. The program next determines what small areas are available for change. At a minimum, this involves checking the current spatial land-use data to determine how much of each small area is classified as vacant unrestricted land. Additionally, some programs perform an evaluation of all currently developed land to identify where it appears likely that the existing land-use types might be razed and re-built as some other type. Regardless, this step concludes with a computed map of "available space." In a mono-class framework this is a map of small areas that are available to change to a new consumer class type. In a multimap framework this is a small area map that contains for each small area a count of the acres (or hectares, or square kilometers as the case may be) available for
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INPUT DATA
SPATIAL MODULE
Global changes or basic industry & T
Accept or compute global change totals by class
Base year customer load maps
Identify or compute available growth space on a small area basis(form map)
TEMPORAL MODULE
Available space map Compute new customer class load curves for this study period
Base year load curves
(
cente Activity center^. _ r~-^^ Form Polycentnc Activity Center "Urban Pole" influence map ocations& datay data 1-u-—-^
/'Factor definitions. l v data&profilesJ' actor & urban pole map coefficients, by class
r
~~~~~--»r 1—L
Compute factor maps
Compute preference map for each class
•oPreference maps
Allocate decline of each class by "removing" land use in small areas with lowest preferences
>=>
Allocate growth of this class to available small areas with highest preferences
Updated customer class maps Merge load curves and customer maps into load map(s) for end of period Load map(s) ;for end of study period
Figure 14.2 Overall flow of the basic simulation method's logic in computing one iteration of the forecast.
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new development and change. Regardless of pattern match or preference values, consideration for growth is applied only to small areas in this map. Next, the program computes a set of proximity and surround factor maps (usually about a dozen similar to those in Table 13.7) and forms a different linear combination of them into a pattern match map for each class (similar to Figure 13.6), to which it adds the polycentric activity center map, using a different weighting factor for each class, to form the preference map for each class. Change is then allocated based on the computed preference maps for each class. If decline (negative growth) is a concern, forecast of that is done first by removing the forecast amount of land-use (consumer count) decline from the land-use map. For each class, all small areas of that land use are analyzed. Those with the lowest preference map scores are deleted (changed to vacant available) by altering their land-use designation to vacant unrestricted. In a mono-class map framework this is done by changing the small area's class designator. In a multimap framework this is done by setting the small area's count in this particular land-use map to zero, and adding that same value to the vacant restricted map ~ e.g., "subtracting" 10 acres of residential from the residential map and adding it to the value stored for the small area in the vacant restricted map. Decline is computed first so that the "deleted areas" are available for consideration for new development of other classes. ' Finally, growth is allocated. For each land-use class in turn, the amount of global increase forecast to occur is allocated to selected vacant available small areas. Using the preference map for this particular class, the highest scoring vacant available small areas, up to the amount of growth required, are changed to the land-use class. The order of consideration of classes in this step is somewhat important. Classes are done in the order of greatest typical land value (high rise is done first, light industrial last) - land uses that can pay more for land get "first choice." In this way all of the land-use totals are allocated, and the consumer class maps have been transformed. The total amount of land use for each class now equals the amount forecast by the global model. These land-use maps are then
A few simulation programs use an interesting variation in this step. Instead of designating such land as "vacant unrestricted," they use an "abandoned" class designator, a flag set into a separate map in the map stack, which indicates small areas where buildings and houses have been abandoned but not torn down. The program is written so that it computes no load associated with such areas, but the land area is not identified as "vacant." From a purely electric load forecasting standpoint this does little to improve accuracy, at least in a simulation with this level of detail. Dealing with the flag map in this and other steps adds considerably to the program computation time.
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combined with the temporal load model's load curves to form a small area map of load. C Small area load (x,y,h) =
(Area(x,y,c)*l(c,h))
(14.1)
c=l where: Area (x,y,c) is the amount of land-use class c in small area x,y L (c,h) is the per area load for class c at hour (or time period) h x = [1,X] and x = [1, Y] index the small area in an X by Y grid or the polygon framework c = [ 1 , C] indexes the land-use class h = hour (or time period) for the load curve Often, several maps are computed, loads for different times of day (system peak, residential peak, commercial peak time) and a final map equal to the maximum of all loads on a small area basis is computed by taking the maximum of these on a small area basis, a map of non-coincident peak loads. Simulation programs taking this approach have used a variety of temporal load models — everything from a class-based model that used only a single hourly peak-day load curve for every class, to a full end-use, appliance subcategory model on a five-minute basis. Examples of programs that have used this basic approach include the CEALUS (Canadian Electrical Association Land Use Simulation) program and the SLF-1 program developed and sold by Westinghouse Advanced Systems Technology in the late 1980s and early 1990s. The chief advantage of this approach compared to other simulation methods is simplicity of programming and relatively low level of computation. Note that here, the urban pole and factor maps are combined in one linear combination to yield the preference maps. In many other simulation approaches determination of the preference maps requires considerably more computation. For this reason, this basic simulation flow shown in Figure 14.2 is the most complicated form of simulation that can be implemented using direct computation of the factor and urban pole maps, which makes it much easier to program and verify. It does not require the high-speed numerical methods to be covered in section 14.3 in order to run within practical time limits (although they certainly can be used to make it very quick). This method has two major disadvantages, which are not serious in all forecasting situations. First, it cannot assess major changes in spatial distribution of influence among the stages of growth. Second, it cannot accurately model simultaneous decline and growth of a class within the service area but in different locations. Very often, one part of a service area will be shrinking,
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another growing, due to different basic industrial influences. This approach allocates only the total change in a consumer class on a global basis. Thus, if 10,000 homes were being abandoned in one part of a state, and 10,000 built in another, this approach would determine that there was no net change and forecast no change in spatial locations. Fuzzy or Numerical Logic? The spatial preference computation and pattern recognition used for the preference engine and class-transition decision making in a simulation model are a near ideal forum for application of fuzzy logic classifiers. A number of such attempts have been quite successful. Fuzzy, or "grade" logic, has been used for the entire surround and proximity classification, determination of the preference scores, and allocation prioritization. In a fuzzy-logic preference engine, the surround and proximity factor "functions" are implemented in fuzzy rather than numerical terms. For example, the "close to railroad" factor (Figure 14.3) might be: Close to railroad factor e [very close, moderately close, moderately far, far] The preference functions then use fuzzy logic to assess the combined weight of the various factors for class by class evaluation. This fuzzy logic preference
Very Sort of Close Close
Sort of Far
.5 .75 Distance - miles
Very Far
Very Sort of Close Close
.25
Sort of Far
Very Far
.5 .75 Distance - miles
Figure 14.3 Fuzzy logic railroad-proximity function as implemented for a fuzzy logic preference engine in a 2-3-2 simulation algorithm. Left, traditional fuzzy logic linear membership functions for each grade. Right, Gaussian membership functions have certain computational advantages.
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allocation can lead to either fuzzy or non-fuzzy outputs. Preference results that are fuzzy grades are something like Residential Preference e [very likely, moderately likely, not likely, none] Their impact is then implemented through allocation of growth to all small areas for all classes in a subsequent step requiring fuzzy logic. Factors are added, subtracted, and multiplied as needed in the course of determining preference function results, using fuzzy logic rather than algebraic rules. The resulting preferences are grade-specific: high-high match to needs, high match, etc., down to no match. These classifications are then used to allocate the global totals with fuzzy allocation rules. But often the fuzzy logic preference factors lead directly to numerical results, as in this equation used in the SLF program developed by Mirando and Monteiro: //"(distance to road is Close) and (distance of urban center is Moderately Close) and terrain slope is Moderate) and domestic saturation nearby is Medium) and (14.2) industrial saturation nearby is Low) then Domestic PfD is 20 consumers per stage and Industrial PfD is 0.1 consumers per stage Here, fuzzy logic leads to numerical results. Fuzzy logic works well in highresolution simulation algorithms. In fact there is every reason to believe, based on results, that there is little difference between numerical or fuzzy logic with respect to terms of accuracy, flexibility, or other characteristics, with the possible exception of the computational speed advantages numerical methods implemented in the space domain can provide. Use of Cellular Automata A simulation method that models growth as transitions among land use and density classifications can be implemented with a cellular automata instead of the type of transition matrices and functions described early in this chapter and used ins such widely used programs as the author's LOADSITE and FORESITE programs. However, there is no difference in concept and little in implementation between the two approaches. Cellular automata are discrete dynamic systems in which each point in a rectangular spatial lattice, or cell set, can transition from one class or state to another depending on a locally applied rule, at times which are the discrete
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points in a set of transition opportunities over time. The cellular automata is basically a set of rules, applied to each cell in the lattice, that looks at local conditions (those around the cell) and determines if it will change or not depending on the status of its neighborhood and itself. The game of "Life" a popular mathematical game, is a binary cellular automata. "Binary" means each cell has only two states (filled or empty). A game's Automata involves a set of rules that determines back and forth transitions between the two states depending on the number of the cell's immediate neighbors that are filled (Gardner). Binary cellular automata are simple to implement and test, having only two states, and therefore only one decision to make with respect to transition at each iteration. There is no reason that several cannot act simultaneously on a lattice of cells. The land-use class transitions of a simulation program can be implemented using a set of binary cellular automata. The simulation rules become a set of cellular automata computing the development potential for various land use transitions (vacant to residential, vacant to commercial, low-rise to high-rise commercial, etc.) based on surrounding land-use development, present state in the cell and other conditions. Advantages of cellular automata models are that they bring a different, but formal theory to bear on the preference decision process and are simply to implement. Disadvantages are the logic and computation needed to resolve conflicts among the several binary automata functioning side by side (a vacant area can develop to any of several states, requiring a set of automata). But these advantages and disadvantages are small: in truth there is little difference and the standard simulation model is very close to being a cellular automata. Event Iterations Rather than Study Period Iterations Very often there is more than one cause of growth or major addition to the regional basic industry. For example, in Chapter 11 the growth in Springfield was due to two causes. First, there was the "normal" distributed growth of the city - a healthy local economy generates growth that appears to occur as "a little bit everywhere," generally modeled by locating an urban pole in the center of the downtown area and representing growth as "caused" by forces emanating from that location. In addition, Chapter 11 's example had a new factory that would contribute greatly to growth. This was going to be located on the outskirts of town, and it would most influence the side of the city near its location. The basic simulation model can determine the total amount of growth that takes place due to the distributed growth as well as due to the factory, by using the Lowry matrix, T. However, it will model all that growth influence as occurring from one source at one location, and allocate all growth with the same spatial basis, letting the urban pole map represent the "large area effects" as the same on all of the growth.
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The forecast of Springfield would be improved considerably if the forecast instead made two iterations for each study period: a) Apply the basic simulation (Figure 14.2) to allocate the "normal" growth expected in Springfield, what Susan allocated based on Rate and Consumer Studies Department's base forecast, using a polycentric activity center model of Springfield, and leaving out all consideration of the factory and the growth it causes. b) Perform a second iteration to model only the factory and the growth it caused. Begin by assigning the factory's land-use to small areas (typically done by "manually" editing the land-use data with the program's data editor). Using the Lowry matrix, T, compute the total growth impact (DT vector) caused by the factory, and repeat the entire simulation iteration (Figure 14.2) to spatially allocate these amounts of consumer growth, using an urban pole map with a single pole located at the new factory site and a radius of 50 minutes travel time from that site. These two iterations have to be done for each study period in which the factory is expanding. A larger city or region may have more than one large growth event such as a new factory or major employment change occurring simultaneously, in which case additional iterations, one for each of these major events, would have to be done within each study period. It is not necessary to modify the basic simulation approach in order to apply this approach of event-based forecasting. In all programs for the basic simulation approach that the author has used, the amount of growth allocated in each "study period" and the urban pole data can be changed from one "study period interaction" to another. To represent a new factory as a separate event, the user merely has to set up the data driving the basic simulation process so it is instructed to do two or more iterations per study period, calling for the following actual iterations (passes through Figure 14.2): • First forecast year distributed growth using polycentric activity centers • First forecast year's factory growth using urban pole at factory site • Second forecast year distributed growth using polycentric activity centers • Second forecast year's factory growth using urban pole at factory site • Third forecast year distributed growth using polycentric activity centers • Third forecast year's factory growth using urban pole at factory site • Fourth forecast year distributed growth using polycentric activity centers • Fourth forecast year's factory growth using urban pole at factory site
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This approach has been widely used where needed. Other than the fact that it increases run time by a factor of two or more, depending on the number of discrete iterations done for each study period, it has no disadvantages, and it improves forecast accuracy substantially. Fairly straightforward changes to the program shell and the flow of computation within the spatial module can make the multiple iterations easier on the user and the computation slightly faster. Changes to improve ease of use usually include making it possible for the user to enter all years of data on distributed growth first, then identify the factory scenario and data on all years of its trends as a separate unit, etc. In addition, features are added to allow postforecast reporting to sum results for all iterations on a study period basis. Computational changes include features that calculate the urban pole maps one time and merely swap them in and out, and re-ordering to factor maps are computed only once per study period, not once per iteration. An example of such a program was the "SLF-2" or "advanced urban" version of Westinghouse's SLF1 program, widely used from 1987 into the mid-1990s. Multiple-Pass Direct Lowry Model One of the most popular variations on the basic simulation method (Figure 14.2) is to apply a direct Lowry matrix approach in a series of "passes" rather than a total Lowry matrix approach in one pass. Programming this is not inherently difficult, except that computation time mushrooms to the extent that high speed numerical methods which are difficult to program must be applied to make the approach practical on anything more than a very small study system. The basic simulation method used the Lowry T matrix to determine the total amount of change in all land uses (L vector) and allocated that to small areas in one step. In the modified direct Lowry simulation, growth is allocated in a series of passes corresponding to the stages of the "Lowry model" discussed earlier: basic industrial growth, directly caused growth, secondary growth, tertiary growth, and so forth. This method uses the same computational steps as in the basic approach, slightly re-ordered, and applies the urban pole maps in a slightly different manner. It does the following for each study period iteration: 1. It identifies available land for growth, making a map of "growth space." It computes the factor maps as in the basic simulation. It computes the urban pole map as in basic simulation. 2. The program takes as input the basic industrial growth, for the study period. To review from earlier in this chapter, this is a vector D of land-use changes for each class. Since this is the direct Lowry model, many of these may be zero or near zero.
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3. The program computes the preference maps for all classes based on the factor maps and the urban pole map, using the input coefficients for each class. The program allocates all the direct consumer class changes (those called for in the D vector) exactly as it did in the basic simulation for all the growth (the L vector). 4. The program computes the "center of growth" of the land-use change just allocated. It computes a new urban pole map with a single urban pole at this center of growth. Radius is the average radius of poles used in the previous stage. 5. The program computes the next stage of Lowry direct growth by applying T' to the D vector determined in step 2 above. This produces a new D vector of growth for the next pass. 6. The program goes back to step 3 unless a stopping rule is satisfied. The stopping rules may be that the D vector total is below some minimum threshold, or that six passes have been completed. In some cases, it is necessary to re-compute the factor maps during one or more of these passes — ideally it should be done at the end of every pass, but the computation time is considerable and the improvement in accuracy of some passes is negligible. As a rule, if the growth allocated to any one class since the last re-calculation of factor/pattern maps exceeds 3% of a class, the maps should be re-computed. This approach can track spatial changes in the center of influence of the different stages of Lowry growth. In many cases, such as that shown in Figure 14.3, this change dramatically improves forecasting accuracy with regard to location. In many others, the improvement either is unnecessary (the centers of all stages are similar) or is not sufficient to address fully the complexity of the forecast, as will be discussed below. This approach gives improved spatial forecast ability in about twenty percent of forecast situations, where for a variety of reasons the centers of influence for residential, industrial, and commercial growth may be different. A major disadvantage is that computation time increases by an order of magnitude over that required by the basic simulation method. This becomes much more of a burden if "multiple iterations" per study period are being done to represent the different locations of factories or other growth drivers. Careful attention to program flow, looping, and a variety of "tricks" in program organization can reduce the additional margin in computation time over basic simulation to a certain degree, but without the frequency domain discussed
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in the next section, this approach is simply not practical. Examples of programs using this approach include LOADSITE, a multi-map grid-based program developed and marketed by ABB Power T&D Company Inc. from 1988 to 1994, and FORESITE, its monoclass polygon/grid successor, as well as DIFOS (Distribution Forecasting System), a program similar to LOADSITE, developed and used in northern India (see Willis et al, 1995, and Ramasamy, 1988).
Basic Simulation
Multi-Pass Simulation
Figure 14.3 Examples of how growth influences within the factory scenario are handled by the basic and multi-pass simulations. At the top, the basic model represents all stages of growth stemming from the new factory as caused by spatial influences emanating from that site (black dot). At the bottom, the multi-pass approach recognizes that the secondary growth (predominately growth of the retail and commercial consumer classes) is driven by influences emanating from the center of new residential growth (dotted ellipse), and models them with an urban pole function centered there.
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Hierarchical Allocation As mentioned earlier, an alternative approach to simulation is a hierarchical structure in which the program increases the spatial resolution of the forecast in a series of top-down stages, beginning with a forecast on a system-wide basis (no spatial resolution). The next stage allocates that growth among large regions within the service territory. In the next stage the growth assigned to each large region is allocated among large areas within it, and so forth, until the process ends by allocating the growth to the small areas. A hierarchical program may use input data identical to the basic simulation approach in Table 14.1 and appear very similar to the user. It can be applied in multi-map or monoclass frameworks, and to polygon or small area format. It works with the same preference map concept, and in many cases computes factor maps and polycenrric activity center maps nearly identical to those of the basic simulation method. For an equivalent spatial resolution and level of analytical detail, the hierarchical approach requires up to 100% more computation, depending both on how the hierarchy is defined and on how the program flow is organized. Usually, the motivation for taking this approach is to reduce computer resource requirements, particularly that for active memory, when faced with very large small area data sets. The hierarchical program can be written so that no more than one region is in memory at one time, drastically reducing necessary memory requirements at the expense of run-time. For example, a state-wide utility service area of 250 miles by 250 miles would require a grid of 1,000 by 1,000 small areas at 40-acre spatial resolution. In a multi-map framework (needed at this resolution to obtain good accuracy) this would require roughly 200 Mbytes of memory. A hierarchical structure could be defined as 400 blocks of 50 by 50 small areas each. No more than nine of these blocks (22,500 small areas or about 4 Mbytes) need be retained in memory at one time, reducing memory requirements by nearly two orders of magnitude.2 A similar savings in memory requirements can be effected when using a monoclass framework or polygon framework.
2
Memory management was much more of a concern in the 1980s and 1990s than it is today. However, memory requirement turns out to be a fairly good proxy for the overall computation burden (time, effort) required when simulation methods are implemented within modern GIS and spatial analysis systems. Organization of block size and hierarchy structure to be optimally compatible with surround factor search radii, etc., is an interesting side issue that can make a considerable difference in program speed. See Willis etal, 1977.
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In addition, a hierarchical structure is often used when the small area approach is to be combined with spatial-time series (STS) regression models or urban models developed originally for other purposes — agricultural, trade, or econometric forecasting on a regional or geographic basis (Bennett). Such models often require substantial computer resources in their own right, limiting that available for the small area pattern recognition and factor analysis. In addition, the hierarchical method's "aggregation" of statistics during its bottomup path (see Figure 14.2) has proven a useful point for "translation" from one type of small area modeling approach to another ~ for example, the data required for an STS regression can be computed from the small area, factor, and pattern recognition results and collected on a region basis at this point, to be used by an STS model operating at a regional or macro-regional level. Although called top-down, most hierarchical simulation is circular, actually consisting of a bottom-up collection of data and statistics, followed by a topdown hierarchical allocation, as shown in Figure 14.4, for a three-level (global,
GLOBAL dinuuMi^ui ciiaitye
/2.......
Assemble statistics on factors, availablility, and urban pole values in each "region"
o
o
Compute urban pole map values for all "regions" /\_
Allocate global change to "large areas" based on preferences
(Regional statistics )
'
Assemble statistics on factors and available room in each "region"
Identify available growth room
SMALL AREA
Compute factor maps for all small areas
Figure 14.4 The flow of analysis in a hierarchical simulation..
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region, small area) hierarchy. The program begins at the small area level, calculating factors and determining available growth room. It then assembles statistics on factor values and growth room on a "block" or region basis, for all regions. For the sake of clarity, define the regions as indexed by r = 1, R, and call the L vector of consumer class changes for the rth region Lr and the L vector for the service area as a whole LG. The global model performs an identical function to that in the basic simulation program. The LG vector of growth by class is allocated not directly to small areas, but to the regions. This is done by forming a preference map at the large area level (for each region a single preference value is calculated for each class) and allocating the LG class totals based on these, obtaining Lr for each region. The sum of Lr over all r is equal to LG. The program then focuses on one region (block of small areas) at a time. For each region r, it allocates the region's growth, Lr to the small areas within that block, based only on the preference map values in that block. At this point the program merges the land use in the block with the load curve data from the load module, to calculate the block's small area loads. In this manner it computes all blocks. When done, the program has allocated all the global growth, LG, to the small areas, and calculated an updated load map. Advantages stemming from a hierarchical program structure are largely those associated with reduced computer memory requirements. Its disadvantage is increased program complexity and much slower execution time, which precludes application of either the event-driven or multi-pass direct Lowry model concepts, therefore limiting accuracy compared to other simulation approaches. Examples of hierarchical programs are the ELUFANT (ELectric Utility Forecast Analysis Tool) developed at Houston Light and Power (Willis and Gregg) and PROCAL developed by Carrington et al. 14.3 FAST METHODS FOR SPATIAL SIMULATION In any of the simulation methods discussed above, quick computation of the factor maps constitutes a significant numerical challenge. As an example, consider the calculation of the "residential within three miles" factor, only one of twelve factors in Table 13.8, on an 800 by 1000 element grid of 10 acre (1/8 mile wide) small areas. Such a grid is large but not uncommon. It is required to model a region the size of Commonwealth Edison's service area in and around Chicago, but less than that required to represent greater Los Angeles or the San Francisco Bay area. Regardless, for each of 250,000 small areas, the program will need to compute the sum of consumer counts from all small areas within a 24 small-area radius, which means adding together the more than 1800 residential consumer
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counts from neighboring small areas within that radius. Each of these consumer counts may be weighted as a function of distance (as in Figure 13.5), requiring computation of Euclidean distance from the current location to the small area whose count is about to be added to the sum, table look up of a weighting value appropriate for the distance, and multiplication of that small area consumer count by that value before adding into the sum. Straightforward programming of direct computation will result in roughly four billion floating point additions and multiplications. Various programming "tricks" can reduce this by more than half, but factor computation will remain a serious run-time bottleneck. Calculation of the factor maps and urban pole applications can be accomplished in a much shorter time using methods based on digital signal processing. These approaches can be applied in either a multi-map or mono-class framework, but only in a grid format. The computation of a factor map using a circularly symmetric function like those shown earlier in Figure 13.5 is the spatial convolution of a circularly symmetric finite impulse response operator (the profile) with a real operand map (e.g., residential consumer counts). A cornerstone of applied signal processing is the realization that convolution in the time or space domain is equivalent to multiplication in the frequency domain.3 Thus, a result identical to the factor computation discussed above can be done in the spatial frequency domain as: 1. Transform the 500 by 500 element "map" of residential consumer counts into its two-dimensional spatial frequency domain spectra using a discrete fourier transform (DFT). This will result in a 500 by 500 grid, many of whose elements will be complex variables. 2. Transform the operator profile into a similar 500 by 500 spectra. 3. Multiply the two Fourier transforms point by point. 4. Transform the resulting 500 by 500 element product back to the space domain using the inverse DFT (which is essentially the DFT applied once again). The result is identical to the factor map as computed directly. If an FFT (fast fourier transform) algorithm is used to compute the DFTs, this method will 3
The reader unfamiliar with discrete signal processing may want to consult a text on the subject, specifically on application of 2-D symmetric filters. See, for example, Two Dimensional Digital Filters, by Wu-Sheng Lu and Andreas Antoniou, New York: Marcel Dekker, 1992, particularly Chapters 1 and 9.
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compute a factor map in from one half to one tenth the time taken by direct space domain computation, and with less round-off error. In addition, the following measures can be taken to further decrease computation time: A. The DFTs of the operators need only be computed once, and stored thereafter. This reduces computation time by about 15%. They are circularly symmetric so all elements in their spectra are real, which can be used in some implementations to reduce the time required for step 3 above. B. Factor profiles like those shown in Figure 13.5 and almost any applied in the course of a forecast, are low-pass spatial filters. Highfrequency components in the operand maps in interim calculations become irrelevant. Portions of the 500 by 500 2-D spectra (frequency domain "maps") corresponding to high frequencies can be ignored -the multiplication in step 3 can be applied to a portion of the points and the rest assumed to be zero, some care must be exercised in not carrying this process too far, but this reduces computation time noticeably. C. Often several factor maps are computed from the same operand map. For example in Table 13.8 there are two factor maps created by operating on residential consumer counts with different operators (numbers 9 and 10). The residential consumer map need only be transformed with the FFT once, and used to compute both. This reduces the time required to compute the two factors by 10%. D. Recall that once computed, the factor maps are added together in a weighted linear combination. The Fourier transform is a linear function. Thus, the individual factor maps need never be transformed back into the space domain. They can be added together in the frequency domain, using the same pattern template coefficients as normally applied, to obtain the spectra of the pattern match maps. Only these are transformed back into the space domain. In cases where the number of factor maps exceeds the number of classes this always reduces computation time. In cases where the number of factor maps is less than the number of classes, this still may reduce computation time if the summation and the transformations are efficiently organized.
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E. Summation of the factor map spectra as described in step D requires adding complex variables (whereas in the space domain the values of profiles and consumer counts are real) and thus should require slightly more computation time. However, most of the factor map spectra (i.e., the frequency domain maps) are low frequency and much of the grid can be ignored as described earlier, with no discernible impact on accuracy. (The author's experience is that at least 10% and often up to 70% of the points can be ignored.) In practice, FFT-based computation of factor maps using the procedures presented above reduces computation time by an order of magnitude. In the vast majority of cases, a one-dimensional FFT routine is used.4 A number of very good one-dimensional FFT programs exist for inclusion in a simulation spatial load forecast program, including that available from the IEEE and commercial mathematical analysis systems. Also, a basic radix-two FFT algorithm is quite straightforward and easy to program,5 but in all except extreme cases, onedimensional FFT's provide sufficient speed and have advantages of simplicity and flexibility. Along with several co-workers the author developed a Rivard FFT algorithm (a direct two-dimensional FFT) in the early 1980s. Its run-time advantage of about 15% (of an already reduced amount of computation time) was not enough to justify continued maintenance of the specialized program code, and its use was superceded by application of a standard one-dimensional FFT routine. (For more details on exactly how the FFT approach is implemented, along with advice on programming and FFT subroutine selection, see Willis and Parks). Distributed Urban Pole Computation Given that an FFT-based computation is available, a simulation program can take advantage of the frequency domain computations to calculate "urban poles" as spatial convolutions. This is more than a "trick" to increase computation speed. It is an improvement in the simulation model itself as well as the level of detail it can apply in its spatial analysis of land-use interactions.
4
The FFT routine is applied to every row and then every column of the grid to produce the two-dimensional transform, in a process often called "combing." The computation of the 2-D FFT on a 500 by 500 grid requires one thousand 500 point one-dimensional FFT computations. 5 However, a radix-two FFT is limited to applications on grids whose dimensions are a power of two - 64, 128, 256 points across, etc.
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Single Urban Pole
'Distributed Urban Pole"
Figure 14.5 While the multi-stage Lowry model (top) improves on the representation of the basic model's growth influences (see Figure 14.3), a distributed urban pole computation can improve its results even more. This can only be accomplished within practical run-time limits if computed in the spatial frequency domain.
As applied in a polycentric activity center model, an urban pole is a cone of radially decreasing values around a central point selected to represent the largearea influences of a downtown area, a regional employment center, or some other significant societal activity. In actuality, the employment locations of a downtown area are not concentrated at one point but distributed over a number of square miles. The urban pole might represent the influence of an area that is itself a number of miles across. Representation of the influence of such a downtown area as emanating from one location does not produce a significant amount of error. However, when a single urban pole is applied to represent the influence of a widely distributed
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subset of consumers, as it is when the direct, secondary and further passes of a multi-pass direct Lowry model are represented, a good deal of error is introduced. The top drawing in Figure 14.5 shows the distributed area of residential growth (same as in the bottom of Figure 14.3) within which the first stage of Lowry growth (directly caused) is expected to concentrate, and a single urban pole proportional to the amount of growth, located at the center of mass of that stage's growth. At the bottom is shown a "distributed urban pole": an urban pole has been located at each small area, its height proportional to the growth in the area, its radius equal to an average 50 minutes commuting distance, and all their values summed. Thus, the urban poles in the basic and multi-pass direct simulation can be replaced with "urban pole factors" ~ identical in concept to the surround factors, but perhaps applied to different land-use classes, and always with a radius ten to one hundred times greater. They can be included in the linear combination described in (E) above, producing when all urban poles have been added into the appropriate sums, the spectra of the completed preference maps. The urban pole maps represent a very low pass spatial filter, so the reduction in computation time from application of step (F) given above is very effective here. 14.4 GROWTH VIEWED AS A FREQUENCY DOMAIN PROCESS When first applied in the late 1970s and early 1980s, the Fourier-transformbased shortcuts summarized above were viewed purely as an expedient method of computing preference factor and urban pole results that required unacceptable amounts of computer time if calculated in the space domain. However, it soon became clear that these functions had a meaningful frequency domain interpretation ( see Willis, 1977; Willis and Aanstoos, 1979; Wilreker, 1981; and Willis, 1983 for a good progression of perspectives). This section presents a conceptual summary of a frequency domain perspective of land-use, consumer, and electric demand growth on a geographic basis. Given the classical economic model of demand and supply, in order for growth or change in land use to occur, there must be a simultaneous spatial match of both demand and supply. For example, if residential growth occurs in a small area, it is because there was both a demand for housing in the area and a supply of suitable housing land in that small area. A fascinating aspect of landuse modeling as applied to electric load forecasting is that if demand and supply are appropriately defined, they are respectively the low and high spatial frequency aspects of growth and change. To the author's knowledge, this concept was first explicitly used for electric load modeling in the late 1970's (see Willis, et al, 1977), but it is clearly an implicit, unrecognized element in most urban, transportation, and land-use models, whether for electric load forecasting or other applications.
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In order to fit into this perspective, demand must be viewed in terms of the geographic restrictions persons seeking expansion of a particular land-use type put on their search for sites matching their needs. Consider either the individual seeking a new home or the business owner trying to identify the best location for a new store. Both have a definite idea of what type of site they need ~ they seek good attributes in that site: a good neighborhood, close to schools, near a major intersection, not too close to competing businesses, etc. However, each restricts his or her search to a certain geographic region. Regardless of how suitable sites outside this "search area" may be, only land parcels inside this new area are considered. For example, the prospective home buyer may look for a suitable home only in the northeast quadrant of a large city, because anywhere else is simply too far away from his or her work site. The exact search area may well be fuzzily defined — "somewhere on the northeast side" — and have slightly flexible boundaries. But regardless, within this search area, this person seeks the parcel of land that best meets his or her definition of a good home site. And while this person might compromise slightly if offered "a really fantastic site" a bit out of their search area, her or she would not consider a parcel far across town even if told it is more attractive. Similarly, the business owner seeking a new retail site in the expanding periphery of this large city uses much the same thinking. The operative concept is that demand, defined as the locational restrictions on where people wish to live and work, covers a broad area within which it is indifferent to small changes in location. Both the homeowner and the business owner are indifferent to a change of a mile or two within their broad search area if it brings them a site with better attributes. So defined, a quantitative measure of "demand" must cover a broad area, and vary slowly within that as a function of location. In other words, it will be composed of low spatial frequencies. An urban pole is a good first-order representation of the homeowner's or business owner's values as applied in these search procedures. Centered at the job site, it describes a large region within which the search is conducted and indicates a preference to be nearer rather than farther away from the job site. Although mathematically the pole has definite boundaries (in the sense that it is possible to plot a circle where its values reach zero, in practice it defines very "fuzzy boundaries," with interest clearly dwindling to insignificance long before this zero-radius is reached. From a signal perspective, an urban pole is a low frequency spatial function. On the other hand, suitability of land for a particular land-use purpose is demonstrably a high frequency process. The homeowner and the business each have very specific requirements for the attributes that make a parcel of land suitable for their purpose. Such attributes as "on a major road" and "not near a railroad" go through significant change in only a quarter mile. Thus, a parcel of
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land may be ideal for a particular land-use purpose, but a parcel only 1/4 mile away may be marginal at best. If one views the set of all land parcels that are suitable for a particular land-use class as the supply of land for that purpose, then the quality of that supply has a very significant high frequency spatial component, with the suitability varying rapidly plus and minus as a function of location. These changes are modeled by the proximity and surround factors, whose values can shift from positive to negative in 1/4 mile or less. Figure 14.6 shows the spectra of both an urban pole and a factor map, highlighting their spatial frequency distributions. Application of Spatial Frequency Methods The author has found the frequency domain perspective on land-use, consumer, and electric load location and change to be a powerful tool for improving spatial forecast accuracy. The working definitions of accuracy, error measurement, and forecast requirements set forth in Chapter 8 are frequency domain related. As mentioned in item (D) earlier in this section, the factor, urban pole, and subsequent steps of preference map computation can be done entirely in the spatial frequency domain. Beyond this, analysis of frequency content of data, and of mathematical models, can be quite revealing. Referring to the maps of forecast error shown in Chapter 8, which are used to test and compare various forecast programs, the spatial frequency content of those maps can be used to identify what must be improved. If the forecast error is mostly low frequency, that is an indication that
o •o
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Figure 14.6 Spectra of an urban pole and surround factor demonstrate the significant difference in spatial frequency content. (Spectra are actually two dimensional but are symmetric about the DC axis in both directions. Values along one edge are shown here).
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the global or urban model is poorly calibrated or inappropriate. Similarly, high frequency errors indicate a poor ability to determine locational suitability (i.e., the preference maps are poorly computed) as discussed earlier in this chapter. The spatial frequency content of the electric load itself gives an indication of the degree of importance of the low-and high-frequency models of growth. If the high-frequency content of the spatial load pattern is small, the error introduced into a forecast by ignoring high frequencies may be tolerable. Alternately, it may be possible to establish that the high frequencies of interest can be tied to one particular data source, such as vacant land or to a very simplified model. Considerable attention to the high-frequency modeling is justified because cost in terms of data, computer and human resources, and complexity increases rapidly as spatial resolution is increased. 14.5 SUMMARY Simulation programs for spatial electric load forecasting share a number of common characteristics, which are discussed as to overall approach and algorithm structure in Chapters 10 and 12. Several numerical or fuzzy-logic spatial analysis methods, covered here common to every spatial simulation program. The explanation in this chapter was necessarily a compromise between the needs for concise description and for specificity and detail, and admittedly does not provide enough detail for those who wish to write the actual code for simulation programs. Basically, a simulation process performs two forecasts: a forecast of consumers and their location, and a forecast of per consumer temporal energy use by consumer class. With the second applied to the first to convert it to a spatial load distribution, the forecast of future T&D demand is produced. To do so, the spatial simulation takes the following approach: Analyze consumer growth by location on a small area basis, counting consumers or consumer density in each small area, as the foundation metric of the forecasting process. The consumer classes usually are a subset, or correspond to, land-use classes used in the spatial analysis. Track consumer class inventory overall (entire service territory, and regionally and locally). Monitor local consumer-class inventory composition (portion of one class or another) and make certain it stays within certain limits consistent with regional growth (i.e., a new factory implies so many new homes, as described in Chapters 10 and 11).
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Set up scenarios of changes in spatial growth influences based on future spatial factors such as highways, bridges, tax incentive zones. Set up scenarios of changes in growth drivers based on variations in future global or econometric factors such as new employers, closing of military bases, etc. Analyze small areas and determine suitability for growth, usually for each of the consumer (land-use) classes based on local factors. This provides the "supply" side of a demand-supply model of land-use growth. Model spatial demand for growth, by consumer class, using any of a variety of urban pole gravity models. This provides the "demand" side of a demand-supply model of land-use growth. Forecast overall totals by class or in a demographic/econometric manner (usually, copy corporate revenue forecast after suitable adjustment) Allocate the growth total(s) based on: a) meeting global, regional, and local land-use and consumer-class inventory limits and constraints, b) matching demand and supply spatially. Forecast future energy usage on a per consumer basis, by class, with some sort of end-use load curve model. Use the end-use load curves to translate consumer inventory by small area into load for each small area. Applied to good data, focused on the utility needs, and used with skill and judgment, these methods provide excellent results. Chapter 17 will discuss the practical aspects of program selection and use - how to assess the various approaches, determine which is best, and some of the issues inherent in setting up and using a simulation program as a T&D planning tool. Chapters 18-21 discuss using the programs as a planning tool — how to develop the skills and exercise the judgment needed to get good results from these programs. REFERENCES R. J. Bennett, Spatial Time Series Analysis, London, Pion, 1979 C. L. Brooks and J. E. D. Northcote-Green, "A Stochastic-Preference Technique for Allocation of Consumer Growth Using Small Area Modeling," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. Canadian Electric Association, Urban Distribution Load Forecasting, final report on project 079D186, 1982.
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J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabot, April 1988. Gardner, Martin. "The Fantastic Combinations of John Conway's New Solitaire Game 'Life.'" Scientific American, October 1970. Gardner, Martin. "The Game of Life." Amusements. W.H. Freeman 1983.
Wheels, Life
and Other
Mathematical
J. Gregg, et al, "Spatial Load Forecasting for System Planning," in Proceedings of the American Power Conference, Chicago, Univ. of Illinois, 1978. Electric Power Research Institute, Research into Load Forecasting and Distribution Planning, EL-1198, Palo Alto, Electric Power Research Institute, 1979. A.
Lazzari, "Computer Speeds Accurate Load Forecast at APS," Electric Light and Power, Feb. 1965, pp. 31-40.
Wu-Sheng Lu and Andreas Antoniou, Two Dimensional Digital Filters, by New York: Marcel Dekker, 1992, V. Miranda et al, "Fuzzy Inference and Cellular Automata in Spatial Load Forecasting," paper submitted and accepted for IEEE Transactions on Power Delivery, Institute of Electrical and Electronics Engineers, #2000TR395. B.
M. Sander, Forecasting Residential Energy Demand: A Key to Distribution Planning," IEEE PES Summer Meeting, 1977, IEEE Paper A77642-2.
W. G. Scott, "Computer Model Offers More Improved Load Forecasting," Energy International, Sept. 1974, p. 18. H. L. Willis and J. Aanstoos, "Some Unique Signal Processing Applications in Power Systems Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, Dec. 1979, p. 685. H. L. Willis and J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, p. 48, May 1979. H. L. Willis and T. W. Parks, "Fast Algorithms for Small Area Load Forecasting," IEEE Transactions on Power Apparatus and Systems, October, 1983, p. 342.
15 Hybrid Trending-Simulation Methods
15.1 INTRODUCTION An intriguing approach to spatial forecasting is a combination of trending and simulation, a hybrid algorithm. Trending has much to offer despite its generally lackluster forecast accuracy and lack of representativeness in multi-scenario studies. It uses far less data as well as more obtainable data than simulation. And it is more automatic, requiring less skill and time on the part of the user. On the other hand, the accuracy, representativeness, and intuitive appeal of simulation are part and parcel of a good planning tool. If a method could combine trending and simulation so that the resulting algorithm had all the good qualities of each and none of the bad, it would be a "perfect" forecast method — fast, easy to use, accurate, and appropriate for multi-scenario studies. This chapter discusses hybrid forecast methods. There are several ways that trending and simulation can be combined, each of which results in very different types of forecast approach. Section 15.2 begins the investigation of hybrid methods with a discussion of the philosophy behind information usage, of which there have been two very distinct channels of thinking in the past. Then, three hybrid methods, and some variations to each, are discussed in sections 15.3 15.5. Section 15.6 concludes with a summary and some general recommendations. 447
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15.2 USING INFORMATION IN A SPATIAL FORECAST Any spatial forecast method attempts to predict future electric load on a small area basis by using information gleaned from a number of sources. This information provides two sets of knowledge that are needed to produce a forecast Context: knowledge about what exists where, now Process: knowledge about the process of growth and change The first, Context, describes the starting point for the forecast. The second, Process, sets out the rules and limitations for how that starting point can and will change over time. The quality of a forecast depends on the detail and accuracy of this knowledge and the forecast method's good use of it. Successful forecast methods do a good job in both of those areas. The Role of Input Data Algorithms, no matter how smart, base their forecast on a spatial database for the study region — something that measures physical properties specific to the area being forecast. To produce a forecast of Cleveland's load twenty years in the future, the algorithm must be given data about Cleveland from which to start. The input data provides nearly all of the information about context. Sources used often include land use, transportation, demographic and other "land-use" data, measures of economic activity such as housing starts and building permit summaries, metered electric sales and demand data, similar data about other energy sources such as gas, and various other sources of data that measure something of potential use in estimating electric load. Getting information from data An important characteristic to study when comparing or designing forecasting algorithms is the amount of information they "harvest" from the data they are given. Not all algorithms get the same information from the same data. Or, put another way, not all algorithms use the information contained in the data as well. For example, trending using polynomial curve-fit via multiple linear regression uses historical peak load data on a feeder basis to determine present loading levels and their trend in each small area. LTC uses multiple regression too, and gets all of that same information out of the data. But in addition it garners estimates of load transfers between feeder areas. That information is in the data, but only one algorithm has the "smarts" to dig it out and use it. Similar examples exist among simulation methods. A 1-1-1 type simulation method uses land-use data only to compute load densities by small area. By contrast, a 4-3-3 type uses that data for that purpose (but more
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comprehensively), for a host of local-area preference computations (the "3" in the middle) and for a comprehensive analysis of urban poles and their competitive trends and interactions with the regional topology (the leading "4" in the nomenclature). The 4-3-1 obtains a good deal more information from the data and uses it. As a result, it requires much more computation time, but generally produces much better results. Algorithms vary in the amount of information they find in the data, as well as how well they use it. This is a key factor in studying forecast algorithms and designing improved versions. And there is no assurance that even the best algorithm uses all the information inherently available in its input data, a topic for further research. Algorithms Contain Information But in addition to information provided by the input data, the algorithm used to perform the forecast also provides a source of information. Trending using curve fitting basically applies algorithm-encapsulated information that says, "all growth obeys a specific equation" (e.g., a cubic logarithmic function of time, or whatever is being fitted). This is combined with information contained in the input data (e.g., differences in peak feeder loads measured on the most recent five years). Together, those two information sources contribute to the forecast trend. Simulation methods contain a wealth of encapsulated information; rules about the allowable mix of land-use categories, rules about locational preferences of certain classes with respect to transportation and topography, rules about the spatial and temporal interactions of classes and their locations, and rules about developmental trends, rules about how and why electric load is a function of class, time, and ancillary variables such as temperature. By any measure they contain and apply a good deal more information on the process of load growth than any trending method can when working only with load histories. This superior knowledge of the growth process is why they are far superior in forecasting long-range growth - they contain a better picture of what and how growth will occur. Such a wealth of information about the process of load growth, contained in the algorithm itself, means that simulation can get by while obtaining little information about the process of load growth from the input data. For that reason they can, and are usually, run with only one year of data history. That is a big advantage given the cost of developing and maintaining a land-use database and the near impossibility of maintaining error-free consistency in satellite or aerial photo interpretation for classifications among multiple years of data. But there is a downside to this feature, too. A single year of data does not provide any information on recent growth. Unlike a trending method, whose
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multiple years of load data give it a very good idea of where growth is at the moment (base year), simulation works with what is in essence a static picture of the forecast context. Thus, while simulation algorithms are very good at predicting the long-range growth of that context, they often miss clues about short-range behavior, one reason they are not as accurate as the best trending at forecasting one to two years ahead. By contrast, the best trending methods, with their multiple years of load history data, do have information available on the locations and amount of current load growth and tend to forecast short-term growth reasonably well. Table 15.1 gives a breakdown of how much of the information used by a forecast algorithm comes from each of the two sources, data and algorithm, for a number of algorithms covered in other parts of this book. Table 15.1 shows a breakdown by data source, between input data and algorithm, for a number of algorithms. It does not show how much of the available information an algorithm uses. For example, the table shows that trending using multiple-regression polynomial curve fitting gets 95% of its context information from its input data. It also shows that LTCCT gets a similar portion of its context information from its data (which is the same input data in each case). But LTCCT gets more information out of that same data: In addition to extracting the same load trend information as curve fitting does, it detects the magnitude of the load transfers among small areas and uses that to make adjustments in its forecast that improve accuracy. The amount of information actually pulled out of the data, and its use, are elements of algorithm
Table 15.1 Breakdown of Context and Process Information in a Forecast Method by Source Algorithm Type Mult. Regr. Curve Fitting Template Matching LTCCT Trending 1-1-1 Simulation 2-2-1 Simulation 3-3-3 Simulation 4-3-3 Simulation Multivariate (hybrid) Ext. Template Match (hybrid) SUSAN (hybrid)
Context Alg. Data 5 5 15 10 7 5 10 3
95 100 95 85 90 93 95 90 100 97
Process Alg. Data 25 5 20 100 65 75 80 15 10 70
75 95 80 35 25 20 85 90 30
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performance not shown in Table 15.1. That is important and relevant to this discussion, but beyond its context (who knows how much additional information can be gleaned from the data?). For the most part, however, methods that glean more information from the input data forecast more accurately, and methods that contain more information in the algorithm forecast more accurately. The Advantages of a Hybrid Model Ideally, a hybrid method would combine the long-range accuracy of simulation with the ease of use, simplicity, and short-range response-to-recent-trends of trending. The most obvious downside of a hybrid method is data needs: if it combines the data needs of both methods, it would be expensive to apply. In fact, data needs and ease of use are the two major concerns with regard to hybrid methods. While the potential for good accuracy in both the short- and long-range periods is reason enough to pursue their development, a reduction in data needs has been the primary goal of the author's work in this area during the last seven years. Simply put, a simulation program needs no input data to understand the process of growth, while trending algorithms need only inexpensive historical load data to understand the context of growth. Therefore, the ultimate hybrid method would be one that used all of a simulation method's "smarts" but would work with only the historical load data needed by trending. That ideal may be unattainable but it is certainly worth pursuing. A method with the long-range accuracy and representativeness of simulation, but the data needs and ease of use of trending would be an ideal planning tool. 15.3 LAND-USE-CLASSIFIED MULTIVARIATE TRENDING (LCMT) Perhaps the first hybrid forecast method was the "Multivariate" program developed in the late 1970s as part of EPRI Project RP-570. When developed, the program was not recognized or intended to be a hybrid method: it was developed simultaneously with the first simulation program (ELUFANT, as discussed in Chapters 10, 12, 13, 14 and 17). Terms like simulation and trending had not become widely used at that time, so no concept of "hybrid" design then existed. However, viewed from today's perspective it certainly is a cross between simulation and trending. Despite its name, "Multivariate" was more than just a multivariate trending program. It used land use to classify small areas into different groups, each of which was trended according to different sets of rules. It could therefore be termed a land-use-classified multivariate trending (LCMT) method. Multivariate's use of small area consumer data along with geographic and population counts meant that its data needs were very similar to land-use-based simulation. For that reason many planners of the period and since have assumed it was a simulation method, but in fact it was not.
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Classification by Land Use Consumer class and other "land use like" data were used to group small areas into sets called clusters. A statistical clustering algorithm assigned small areas to these clusters, or sets, in an "optimal" manner, optimizing the amount of statistical validity left for the subsequent trending step. Load histories of small areas were then trended using a different regression formula and coefficients, depending on the small area's cluster assignment. The clustering algorithm used was a very cleverly modified form of the K-means algorithm called the Long Algorithm. It used a principal components analysis to identify correlation among the variates, and then removed all such correlation. It also applied an inversion of the statistical data-space in which all the data resided, which promoted better clustering.1 Small areas assigned to one cluster (group) were not necessarily geographically close. They were instead "close" in terms of similarity in some statistical sense. The intention in the program's development was that these groups might be "all small areas that have little gas consumption and high electric winter consumption" or similar groups. In actual application, the clusters were sometimes defined by purely mathematical distinctions that made little sense and had no appeal to intuition, or real use in forecasting. But most often, the groupings of small areas fell into clusters that bore nearly a one-to-one resemblance to land-use classes or subclasses. Multivariate Analysis The Multivariate program attempted to do three things with the input data at its disposal. First, it tried to group the small areas into clusters, or sets of similar small areas, as discussed above. Second, it tried to identify relationships among the variates for all small areas within each cluster- energy and peak load are almost certainly related, hopefully gas consumption and electric consumption are too, with electric load being less in areas where gas consumption is high, etc. Other relationships may be more complicated but equally useful (load is related to the number and type of consumers) and sometimes can be established through multivariate analysis. In doing this, the program analyzed all small areas in each cluster to identify rules to be applied to the trending of each small area in that cluster. Finally, rather than trend only peak load, as normal trending does, multivariate trending identified the interrelationships among all the variates, and
This very clever clustering method was often referred to as the "Long" method, because it was developed by Dr. Wilson Long, not because it took a very long time to compute, which it did.
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then trended all simultaneously, subject to the inter-relation(s) identified within the extrapolated values. It applied true multivariate trending, in addition to its other steps. The program was essentially trending each small area's data history in a multi-dimensional space - one whose dimensions were equal to the number of independent data variates. It was developing a "trajectory" in that space (Figure 15.1) for each small area. In theory, the use of more data variates, particularly when refined by the principal components analysis, and the multi-variate trending of that data, must improve (or at least not hurt) the forecast of peak load as compared to trending done with that one variate alone. The growth of peak load, energy sales, and number of consumers is linked, and forecasting all three as one trajectory in a three-dimensional space permits the use of information contained in all three trends to be used in the forecast of each. The Multivariate program was typically run on about six small area variates, all of which were jointly trended, or trajectorized, in this linked manner.
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Figure 15.1 LCMT, as exemplified by the EPRI Multivariate program developed in the late 1970s, attempted to project the future "trajectory" of a small area through a multivariate, or multidimensional, space, one of whose dimensions was peak demand. The space typically had about six dimensions, all relevant to electric usage, not just the three shown here.
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Results and Performance When carefully adjusted and applied to a good base of between six and ten small area variates on two or more years of historical data, Multivariate could produce more accurate forecasts much further into the future than with other trending methods. Multivariate forecast with noticeably lower error levels than any type of polynomial curve fitting method. Multivariate was quite flexible in the range of additional data it could use (data beyond just historical load data). Potential variates included energy sales rather than just peak demand, the number and types of consumers in each small area (all developed from billing data), winter and summer peak loads, weekday and corresponding weekend peak loads, usage of gas and other competing energy sources on a small area basis, or even percentage of households having swimming pools in their backyard. Among its most useful features was a characteristic due to its use of principal components analysis. The program would essentially evaluate if a particular data variate would help improve the forecast of electric load, and reject it if it made no significant contribution. Further, although Multivariate required a number generally at least six — input variates in order to work, a compensating factor was that it could produce forecasts with only two years of historical data, the minimum possible for a "trending" approach. (However, the two years had to be at least five to ten years apart, and the program did work slightly better with three or four years of historical data.) The program required a good deal of finetuning and adjustment of control factors, which required a high degree of mathematical skills on the part of the user. Like other trending methods, the forecast accuracy of the Multivariate program and similar LCMT methods degrades quickly as small area size is reduced below 100 acres. (By contrast some simulation methods improve forecast accuracy as area size is reduced.) It was not a high-resolution forecasting method. Despite the great flexibility in possible data sources, EPRI's Multivariate method and several similar methods it spawned were generally applied using small area data similar to that needed by land-use simulation. Small area data normally included consumer counts by residential, commercial, industrial, and large industrial types (e.g., a type of land-use data) and other geographic data like the number and types of streets in a small area. In practice, no matter what data provided, Multivariate's results were very close to those that would have been produced by a method that simply grouped small areas into "clusters" based on their land-use class. Land use, as has been subsequently proven, is just about an ideal classification paradigm for small area forecasting. The "optimum" classification by Multivariate merely confirmed that this was the case.
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Multivariate's Legacy Despite its accuracy advantage over other trending methods of its period, Multivariate never enjoyed widespread use, for two reasons. First, while its concept was straightforward, its numerical complexity was daunting. The EPRI Multivariate program's use of principal components analysis, the Long clustering algorithm, a host of other "number-crunching" steps, and multiple multivariate trajectory fittings all in series, meant it required 128-bit computation in order to maintain satisfactory digit significance in its computations and provide acceptable round-off error (Wilreker et al., 1977). Moreover, the computer resources needed, as well as the "learning curve" involved in applying its advanced mathematics, were significant barriers to widespread usage. But more important, in terms of data needs Multivariate was less like trending and more like land-use/end-use simulation. Early land-use simulation methods, although not up to modern standards, could still outperform Multivariate in both accuracy and ease of use. As a result, Multivariate and the entire LCMT approach was eclipsed by simulation methods for practical applications. Despite these deficiencies, Multivariate is worthy of study. Its concept of classifying small areas into groups proved advantageous and will be taken up again by section 15.4's discussion of the extended template-matching method. Multivariate was developed prior to the industry's recognition that land use was nearly perfect as a basis for forecasting electric load growth, and Multivariate's near land-use-like development of clusters demonstrated that land use was the way to forecast small areas. Multivariate also predated the discovery of the spatial error concepts covered in Chapter 8. In a very real way, problems with its usage, particularly its calibration, contributed directly to the author's development of locational error and spatial frequency error concepts in 1979-1981. As a research and learning tool, Multivariate was a great success. 15.4 EXTENDED TEMPLATE MATCHING (ETM) Chapter 9 discussed the template matching (TM) method, in which pattern recognition was used to identify past trends which could be used as templates to extend present loads into the future. In that algorithm, pattern recognition is applied to historical trend shape. The algorithm makes distinctions among year to year load growth trend shapes — this small area has steady, linear growth from year to year, that one grows rapidly from nothing over a three-year period, then saturates, a third has a rapid growth ramp but takes six not three years to saturate, etc. It identifies patterns among small areas, and can compare one historical trend (pattern of year-to-year change) to another. Faced with the forecasting of N small areas, the TM method forecasts area n
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among those N with the following steps: 1) It compares the last five to seven years of area n's peak load history to six-year periods of load history for all other small areas, trying to find the best match. 2) Here, the best match it finds will be called small area m, p years ago. Among N—1 other small areas, small area m's load history from -p to -P+6 years ago matches area n's for the last five years (-5 to 0) best. 3) The forecast for small area n is simply area m's load history from -P years ago, shifted P years forward. The TM method uses area m's past load history as a projection of what area n's future load trend will be. TM then repeats the three-step procedure for all small areas, completing its forecast. As described in Chapter 9, this approach is roughly as accurate as multiple regression based curve fitting methods and has computational needs which are less than the matrix-inversion needs of multiple regression. Letting History Repeat Itself TM is a method that basically says "history repeats itself." Its concept is simple, yet intriguing. So is the capability of pattern recognition to look for patterns in data other than just load histories. The concept behind extended template matching (ETM) is simply to add other characteristics to the data set, beyond load, and to let the pattern recognition use that as well when determining what past small area situations most match those of the present. As an example to illustrate the potential advantage, suppose that TM is modified so that in addition to having data available on the last 25 years of peak load history of each small area, it also has 25 years of building permit data for each small area. This is data that gives how many permits were granted for residential, retail commercial, offices, or other building constructions for each small area in any particular year. With this additional data added, the TM pattern recognizer picks up area n and compares its recent history to the long-ago histories of other small areas, including building permit trends. Suppose that area n is mostly vacant land but that a large number of residential building permits have been granted within it during the past year. The ETM algorithm would not "know" explicitly that area n is vacant because it does not have land-use data. But the fact that the area has a low load level would imply it is mostly vacant, and the building permit data would indicate considerable growth potential, soon. That combination (pattern) low-load/high-permit level is very discernible. It is something a pattern
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recognition algorithm could search for among the histories of other small areas. The algorithm would therefore find in its data history an area m, which long ago most closely matched area n today. Perhaps 16 years ago area m had a similar recent load history (low load) and a similar recent burst of building permits issued. Then, the program would use the past 16 years of load growth history for area m as the forecast of area n's next 16 years of load growth. This concept of adding additional dimensions to the span of the pattern recognition can yield significant improvements in forecast accuracy. However, this particular example is not too feasible. It was cited here because the use of building permit data is simple to explain and its potential improvement immediately understandable. In practice, developing a 25-year database of small area building permits would be difficult and costly. Many municipal areas have GIS and facilities systems that gather data by small area and produce lists of current and recent building permits on a land-parcel basis. But none the author has seen have data archives that go back farther than about 8 years - too short for this approach to work well over the long-run. But regardless, this example illustrated the concept behind ETM: use one or more exogenous variables, hopefully a leading indicator that can help determine when the growth ramp for a small area begins, to help identify matches between now and the past. Predicting "when" an area begins an "S curve" growth ramp, either when it is vacant and first growing to suburban characteristics, or when it is redeveloping (see Chapters 18 and 19) is a most difficult but important aspect of spatial electric load forecasting. Land-Use-Based ETM In the process of producing its simulation of load growth, an X-3-X simulation computes a number of factors and preference values for any small area, which are in some sense used as "leading indicators." A simulation program that must allocate 250 acres of new housing growth to the outskirts of Raleigh in the period 2005 - 2007 searches for vacant small areas that are about to "take off up an S curve's growth ramp, using these factors as a guideline in its selection. Therefore, surround and preference factors based on land, location, or land use might be useful in an ETM method. This would make it a hybrid of a simulation method's preference engine and a TM trending method. Figure 15.2 summarizes this ETM algorithm. It is the method used to forecast the rapidly developing region, Colline Noir, used in the examples in Chapter 18. This algorithm requires small area land use for the present, or base year of the forecast (year 0). It normally works with a lengthy history of peak load data, typically 25 years (i.e., to year minus 24). It also requires land-use data (including road and transportation data) for a year about five years after the start of the load histories (year -20).
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doted Trends and Scenario data
\7 Pattern recognition driven template matching
Template History Development Surround, Proximity, and Preference Function Computation
HistoricaJ Template Database
Surround, Proximity, and Preference Function Computation
Spatial load forecast for next 15 years Figure 15.2 An extended template matching algorithm that uses land-use data massaged by a simulation program's preference engine as its leading indicator data.
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Program Flow of the Basic ETM Method Here, years are indexed with t. The base year is t = 0. There are N small areas indexed by n or m. The area (acres, km sq.) of small area n is A(n). There are L land-use classes, including vacant and vacant restricted, indexed by 1. The program's first step is to complete a "template" for each small area. This consists of three vectors:. E (n, t), a 25-value set of normalized historical load values for years t = —24 to 0 (base), where E(n,t) — weather adjusted load for small area n in year t, divided by A(n). P(n, 1, -19), an L-element vector of land-use class preferences calculated for year —19 (similar to equation 13.4, page 416). P(n, 1, 0), an L-element vector of land-use class preferences calculated for the base year (present). where P(n, 1, t) is the preference value of small area n for land-use class 1 evaluated for year t. The program's first step is computation of the P factors for all small areas for all classes, for both years —19 and 0. It then standardizes each data set, E(n,t), P(n,l,-19) and P(n,l,0) so that their mean is 1.0. These are datasets, E'(n,t), P'(n,l,-19)andP'(n,l,0. The forecast is done by template matching and extension. For each small area, n, the program examines each other small area m, computing the pattern distance between n and m, D(n,m) as D(n,m) =
L
0
(fiZ(P'(n, 1, 0)-P'(m, 1, -19))2 + (l-B)Z(E'(n,t)-E'(m,t-19))2)'/2 1=1
(15.1)
t = -5
B is a tuning factor that must be determined by experimentation. It determines the weight the program puts on land use versus historical load data as an indicator of a match. As a starting point, B = .5 generally works well. Over the set of all small areas, m = 1 to M, the template matching identifies the small area which has the highest value of D(n,m). Call this best match for small area n, small area qn. The future loads for small area n are therefore F(n,t) = E(qn,t-20)*A(qn)
(15.2)
Explained in words, the program finds the small area m, whose preference values and recent load history twenty years ago most closely match area n's preference
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values and recent load history, today. Area m's load history for the last twenty years is then used as area n's forecast for the next twenty, adjusted only for any difference in land area. This basic ETM concept works well. It can be modified or enhanced in a number of ways, a few of which are: • The land area A(n), can be used as one additional variable in equation 15.1. This makes a slight but noticeable improvement in forecasting of urban areas, particularly where redevelopment is a significant factor. • Different formulas can be used for equation 15.1. As shown, it squares the differences among the individual values and takes the square root of the total, using a Euclidean metric for its L + 6 data differences. Taking instead the sum of the absolute values works just about as well in most cases. Taking the cube root of the sum of cubed values often works particularly well when working with sparsely populated or rural areas. • Using a more "statistically valid" approach doesn't improve practical results much. Steps such as adjusting values to remove collinearity using principal components analysis seem to merely waste computer time. This is pattern recognition, not statistical analysis. • More than one year of historical year of land-use data can be entered. If land use was entered for both years -20 and -15, then the program would have twice as many matches to try, being able to compare each small area, n, or all M small areas 20 years ago, and 15 years ago. • This program can be applied with fewer years historical load data if long histories are not available. However, if applied with only 15 years of data, it can only forecast 9 years into the future, since it needs at least 6 years of load history in the matching. • Additional data can be used beyond just land use and load as illustrated here. ETM's pattern recognition can be modified so it can work with just about anything that can be measured on a small area basis. The building-permit data mentioned earlier in this section is only one example. In many planning situations there is a good deal of spatial data that is available to planners at low cost. Most of this may be of no practical use in a forecast, but a few parts of it might have use as input for the ETM program's pattern recognition. Generally, if planners look they can find data that is applicable.
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Forecast Results and Characteristics ETM methods work quite well from every standpoint except data cost. It produces forecasts over both short and long range with an accuracy rivals that of any other methods. It could be potentially the most accurate of all possible methods, if improved by the use of more detailed comparisons of land use and demographic data, and perhaps fitted with even "smarter" pattern recognizer logic. The program is also relatively fast. As described above, it must compute surround, proximity, and urban pole functions and assemble them into class-byclass preference values, only two times. This is the computation-intensive step in a simulation, but must be done five to eight times for a 20-year-ahead simulation, versus only two for ETM. In addition, there is no need to calibrate the preference function coefficients to near the degree needed for simulation. This is pattern recognition and as stated above, the rules are a bit different. The template matching (eq. 15.1), is computed but once, and is quite quick. But extended template-matching has two downsides. First, it has a very expensive appetite for input data, requiring nearly as much land-use data and detail as simulation, and three to five times as much load history as needed by trending methods. Many electric utilities do not have small area load data going back twenty years, nor do they have historical land-use data. Second, ETM is as limited in its ability to do multi-scenario studies as trending methods. But despite this, ETM is worth considering for many forecast situations. In particular it is indispensable for the type of application covered in Chapter 18, forecasting incipient load growth, where electrification brings power to consumers already in place - i.e., the load "already exists but there is no load history." ETM has proven more accurate than many methods in this situation. Like the Multivariate program (Section 15.3), one advantage of ETM is that the pattern recognition can be applied over a wide variety of already-available spatial data sets. The program was described here with respect to land use, but within reason planners could use whatever data they have available, rather than put effort into finding any particular set of required data. Flexibility and robustness are two substantial advantages over most other forecast methods. There are numerous other possible modifications to this basic approach which have not been explored. Many may make sense in particular situations. Very likely ETM will be a favored type of electric utility forecasting algorithm for development and research activity during the next few years, because of its potential to provide improved results. The author has an advanced version of ETM, incorporating several other features, that forecasts as well as any simulation in terms of accuracy and has reasonable if somewhat limited multiscenario capability.
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15.5 SUSAN - A SIMULATION-DRIVEN TRENDING METHOD This section will describe the basis for the SUSAN (Spatial Utility Simulation ANalysis), a hybrid simulation-trending load forecast program developed by the author and his colleagues in 1997. SUSAN was a success in two ways. First, it achieved its goal of equaling simulation's long-range forecast accuracy and representativeness, while using hybrid features to greatly reduce data needs and user effort. Second, it was practical and widely used. As far as the author knows the program was the most widely used formal spatial forecast method of any type used in the United States from 1997 through 2001. Third, it led, through evolution and development, to considerable further improvement.2 "Error Management" from the Frequency-Domain Standpoint SUSAN was developed using a perspective called "error management." This recognizes that error of various types and characteristics is a product of both uncertainties and unknowns in the forecast, and approximations made or accepted in the forecast process. Theoretically, forecast error can always be reduced or "shaped" in its characteristics so it has less impact, by gathering more data or applying a more comprehensive forecast algorithm. But such improvements always have a cost, be it greater computational resources, increased algorithm complexity, or most important, greater human effort for data collection and setup. Error management takes the approach of budgeting labor required against error's overall impact and designing the entire forecast process from the standpoint of maximizing results obtained for effort required. The SUSAN algorithm was designed to get the most usably-accurate forecast for the effort invested, subject to a constraint that the accuracy level had to match that of good simulation methods, and that it had to permit useful and easy-to-apply multiscenario studies. The design of SUSAN and particularly its combination of simulation and trending were guided by the spatial frequency domain performance of the two types of forecasting algorithm. In order to understand this approach, the reader needs to keep one fact foremost in mind: the resolution (small area size) of a database, and the algorithm itself, is the key to the spatial frequencies (detail in location) that an algorithm can forecast. High spatial frequencies mean small areas; an algorithm working on only large small areas can "see" only low spatial frequencies. Chapter 8 describes this in more detail. 2
The name SUSAN is an acronym created after the program was completed. It was based on Susan, the imaginary utility planner who plods through a forecast by completely manual means, as described in Chapter 11. Susan, the human, would have very much appreciated SUSAN, the program, and its goal of keeping data and labor to a minimum.
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The pattern (map) of loads for any system or study area has a 2-D spectrum, extending through low- and high-frequency components. While most forecasters do not think of it this way, a forecast algorithm is merely trying to predict how this spectrum changes over time. This viewpoint is just as valid as saying it is trying to forecast how the map of load grows and changes as a function of location, over time. A low-resolution forecast model - one run on relatively "large" small areas forfeits any high-frequency (high-resolution) detail in the forecast. In Chapter 8, Figure 8.13 illustrates this, with a diagram of the error generated by modeling loads in a city with a "large" small area size. As shown there, the low-resolution picture of load location developed with a '/i-mile size small area produces error as shown. The database cannot "see" details of load density finer than 1A mile. The resulting cross-section of error (at the bottom of Figure 8.13) "wiggles" back and forth quite rapidly with distance. It has a high spatial frequency.
1.0
8 o
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2 3 4 Spatial Frequency - cycles/mile 40 16 10 Approximate Small Area Size
Figure 15.3 Relative effort required to develop a "ready to forecast" database for both simulation and trending, as a function of spatial resolution.
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Figure 15.4 Top, spectra of error for simulation and trending forecasts evaluated on a spatial frequency domain basis, for forecasts done of major metropolitan areas three years ahead. Bottom, similar analysis of forecasts done for seven years ahead. See text for discussions of the significance of these data.
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Figure 15.3 reveals some interesting characteristics of simulation and trending methods uncovered during research by the author and Dr. Richard Brown in early 1997. The figure shows the relative labor required to develop a complete, "ready to forecast" spatial forecast database of various resolutions. Not surprisingly, it shows that the land-use base required by simulation requires much more effort than databases for trending, at anything less than exceptionally high spatial resolutions (at which point the effort in translating consumer data into load histories equals that of land use).3 Figure 15.4 compares the spatial frequency spectra of forecast error in predicting weather-adjusted peak electric loads three years ahead and seven years ahead for a 2-3-2 simulation and an LTCCT trending algorithm. These two methods are roughly comparable in overall forecast accuracy (Uf of about 3%) at two to three years ahead, with trending having a slight edge at two years, simulation a slight edge at three years. Beyond three years, simulation gains an increasing advantage in forecast accuracy, both overall and particularly with respect to Uf. But note that at three years, while overall results are comparable, simulation and trending produce considerably different spectra of error. Simulation's is mostly high frequency, trending's mostly low frequency. They produce error as a function of location with fundamentally different patterns or characteristics (see Chapter 8). Short- or long-range, simulation is most accurate in the low spatial frequencies. This means that it gets the overall patterns of load growth - where and how much load grows, more correct than trending. These lower frequencies, as was discussed in Chapter 8, are those more important to planning. This is the reason simulation is inherently more accurate as forecasts are pushed out into the future. But note that, at least in the short range, trending is more accurate in the higher spatial frequencies. From these research results, one can infer that: • Simulation's long-range accuracy advantage over trending is entirely in the low spatial frequencies. • Trending actually forecasts some components of high spatial frequency better than simulation in the short range.
Q
Figure 15.3 confirms a "commonly understood fact" not widely used by load forecasters in the power industry. A low-resolution (fuzzy detail) land-use database is much less expensive to develop than an accurate high-resolution database, but just about as useful. Work done in the 1980s demonstrated that the "fuzzy" database had roughly the planning impact of the more detailed database, even if its use generated much higher error statistics. This information along with guidelines for data collection was included in the "cookbook" database preparation guide the author prepared for EPRI RP-1979 in 1984.
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Figure 15.5 provides a final bit of information necessary to confirm the "linearity" of simulation with respect to frequency, a necessary condition for the "SUSAN" concept to work. It compares the spectra of 2-3-3 simulation forecasts done at 160 and 10 acre resolution, six years out. The two forecasts are equally accurate up to the frequency limit of the low-resolution model. It confirms that a low-resolution simulation "sees" and reproduces all the low-frequency components just about as well as a high-resolution forecast does. Running a simulation method at high spatial resolution does not improve its ability to understand and forecast "big picture" patterns and characteristics of the forecast. Seen from this light, the cost of gathering high-resolution spatial data for simulation seems very questionable. Detailed, high-resolution data produces little in the way of improved useable accuracy in a forecast, yet costs a great deal to produce and use. The cost of "ten acre" spatial data (about 4 cycles/mile) is nearly four times that of 160 acre (small areas 1/2 mile across) resolution data. Yet this contributes little to simulation's accuracy advantage over trending.
1.0
o.o
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2 3 Spatial Frequency -cycles/mile 160 40 16 Approximate Small Area Size
10
Figure 15.5 Comparison error of spectra for simulation done at 160 and 10 acre resolutions. Although the difference looks significant it is important to realize that the most important spatial frequencies for distribution planning are those below about 1.5 cycles/mile.
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Hybrid Trending-Simulation Methods Table 15.2 Major Sources of Information Used in a Simulation-Driven Trending Source Global control totals and user-supplied set-up and scenario values
Concept Permits the user to control the forecast and scenarios much as can be done with simulation methods
Use Used to assure forecast reaches correct totals and represents events and growth drivers desired to be modeled.
Rural-suburban-urban development patterns
Areas develop in only certain ways and according to certain spatial and temporal rules (the standard information used in any good simulation).
Used to control overall growth trends, applied only in the low-spatial-frequency domain and limited solely to spatial characteristics of the forecast.
"S" curve trends
Load in any small area grows as "S" trends (see Chapter 7).
Used to control overall growth trends, applied at high spatial frequency and to control the temporal nature of all small area growth.
Low-resolution land use
Land-use data on a low-spatial resolution basis, often 1/2 mile or larger area, and of only a few classes.
Used as the basis of lowfrequency patterns to control overall regional trends.
High-resolution roads and transportation and geo-restrictions data
Road, rail, and other data on a highresolution basis, from Internet sources at low cost.
Transportation and georestrictions data is a key high-resolution factor in spatial forecasting. Sources are cheap and quick, so it provides good value for the effort.
"S" curve hierarchy
S-curve growth trends in sub-areas of a larger area are "sharper" than the curve for their aggregate area.
Unites spatial and temporal growth trending.
Historical annual load peak data at highest available spatial resolution
Historical data on peak loads measured on a substation, feeder, or TLM area basis.
Historical data on loads used to calibrate "present" load map and to extrapolate "S" curve behavior.
Overall regional or corporate load growth trend
Controlling trend for the forecast, in either load or land-use class counts.
Used as the controlling overall total.
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The basis for SUSAN, then, was to use a low-cost simulation to produce the low-spatial-frequency characteristics of the forecast, and trending to fill in higher-frequency details. The reader unfamiliar with spatial frequency concepts may wish to think of this from an approximate space-domain perspective which serves well for intuitive purposes: simulation is used to produce the lowresolution "big picture" and trending to fill in the details. In fact, that is ultimately how the algorithm actually works, but its success rests on its rigorous design using the above-mentioned spatial frequency concepts and a lot of data/algorithm engineering done in that domain. Information-Based Approach SUSAN was explicitly based on the information-base philosophy discussed in section 15.2. The development goal was to maintain the advantages of the simulation method, particularly its accuracy and multi-scenario ability, while reducing its setup and data collection labor, and skill requirements, to something on the order of that required by trending. Table 15.2 lists the information, not just the data, it uses, and where it obtains this information - from data or algorithm, or both. Figure 15.6 gives an overview of the SUSAN algorithm. In order to follow the operation of this algorithm it is necessary to understand that the spatial data can (and usually is) of two different small area resolutions - different sets of small areas covering the same study area. These will be referred to here as "large" small areas (the low-resolution land-use data) and "small" small areas (the historical data and the small areas ultimately forecast). SUSAN uses a variety of input data sources, including land-use and historical load data. Land-use data is normally expensive to obtain and requires great skill to work with. However, the hybrid method requires land use of only a very lowresolution nature, both in terms of spatial resolution (large areas, resolution often 1-mile or larger area) and number of classes (only five, including vacant land). Such land use is generally available, at least for areas of the U.S., in electronic format from public domain sources over the Internet, making it quick and inexpensive to obtain. Such processes can and have been largely automated so they are fast and low-labor. The algorithm also works with historical load data, either feeder peak loads or, if possible, TLM data by collector area. This last data source is excellent where available. TLM data that can be collected by small areas provides a nearly automatic, high-resolution source of data on historical energy usage. Many utility CIS or TLM systems can provide this data on an annual, or even monthly, basis if needed. A key element of the information contained in the algorithm is its knowledge of "S" curve behavior and the hierarchical nature of "S" curve development, the
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Global trends and Scenario da Low-res land use
Simulation On "Large Area" Basis
Constraining Linkage Based on Hierarchical "S" Curve Information
/
, //-/—\-V\
Pattern recognizer
Historical Feeder or TLM data
Trending on Higher Resolution Basis High-resolution spatial load forecast
Figure 15.6 Overview of the hybrid simulation trending used in the SUSAN program.
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fact that smaller areas have sharper S-curve growth ramps (see Chapter 7). This is inherent in the algorithm, where it is combined with various pattern recognizers. They identify and calibrate the locally observed behavior of S-curve growth, and they subsequently correlate S-curve trends with overall land-use patterns. The algorithm forecasts by first using the simulation to produce a lowresolution projection of present and long-range (10 to 15 years ahead) electric load patterns, on a square-mile or even larger-area basis, using an abbreviated form of 2-3-3 simulation. The low-resolution pattern of loads for only the base year is then converted to high-resolution using the smaller small area historical data through a process called land-use/load inference. As a quick example, suppose that a "large" area has a computed load based on its land use of 2350 kVA, and that there are two of the smaller areas in this larger area, with peak loads in the most recent year of 550 and 1700 kVA respectively. The land use in the larger area is first calibrated so that it totals to 2250 kVA (the correct total for the larger area) and then allocated among these small areas so that one has 550 kVA, the other 1700 kVA. This allocation is based on application of the proximity and surround factors in company with the respective preference functions at high spatial resolution. It is constrained so that the two smaller areas end up with 550 and 1700 kVA, and with land use that most matches the patterns that would be expected on these areas based on the preference factors. It is applied not just to the same five landuse classes (as the land-use data was input) but many more (sub-classes within each input land-use class). For example, land use may have been input as "commercial" on the large area basis, but it is allocated into retail, low-rise, and mid-rise commercial. Although this was described above with division of a "large" area into two smaller areas, in application the division ratio is usually between four and sixteen. The net effect is that an allocation of land use at higher spatial resolution and in more class detail is made to the smaller areas. The program uses information about the patterns and rules of land-use location, density and electric loads by class to estimate higher-resolution land uses from low-resolution land use and high-resolution load data. This is a quite effective method. Given that the 1-mile resolution data is accurate and that recent peak load data is used, the resulting land use is nearly 90% accurate in allocating land-use classes to 18acre small areas (dividing each 160-acre area by nine). Again, as stated above, this is done only for the base year data. The smaller small areas are now trended, using a method that begins with a set of constraints illustrated in Figure 15.7. That figure shows a simple, threedimensional example of a "manifold constraint" applied in N-space, where N is the number of land-use classes. Figure 15.7 explains this based on an N of only
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Figure 15.7 A 40-acre small area must have a descriptive vector that lies somewhere on the shaded plane shown. As its land use changes over time its descriptor must likewise stay on the plane. Large dot shows a small area with 25 acres of residential, 8 acres of commercial and 7 acres of vacant land. If over time this area is predicted to grow to 40 acres of commercial development, its descriptive vector, a type of trajectory (compare to Figure 15.1), must travel along the shaded plane to the point shown with an unfilled dot.
three classes: residential, commercial industrial, and vacant. As shown in the figure, a forty-acre small area must have a land-use vector (acres of residential land, acres of commercial and industrial land, acres of vacant land) that lies somewhere on the plane shown. Furthermore, as load grows and the land use in the small area changes, every point in time must lie on this plane. Thus, a growing small area moves across this plane over time, as illustrated. In practice, N is typically between six and ten, and the "plane" is a manifold in N space, but the principle shown here is the same. The land-use vector (description of an area's breakdown by land-use class) must lie on the manifold and as the small area's land use changes it must move along that manifold. But the information available to constrain the trending is not yet exhausted. The land use in the base year defines where this small area starts on the manifold. The large-area forecast of the area containing it (remember, only the
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base year land-use data was allocated to smaller small areas) provides constraints that can be used to limit the portion of the manifold that it might move into. Perhaps in the long range all existing residential in the larger area, which this small area forms a part of, disappears - then the small area cannot end up with any residential content- this limits the region of the manifold that the trend can move across, or into, etc. Such limits are assigned to each small area. At this point in the forecast, hierarchical S-curves are fitted to each small area. In stable, already developed areas where the short-range and long-range land use indicate few expected changes, these are "flat" trends, the portion of the S-curve well past the growth ramp. But in other areas, the S curves in a group of small areas forming a larger area are fitted as a set. The program applies its rules ("its information") about the shape and slope of S curves as a function of small area size to generate these trends (the "hierarchical" part of the S curves). A larger area will have a lower slope but greater total than would any of the four or more small areas contained in it. This difference in slope means that the timing of the growth slopes in the various sub-areas within this larger area must occur at different times. They are staggered by application of their preference factors for the land uses that the large area forecast indicates will grow. For example, if a vacant large area is to grow into commercial land use, then commercial preference is used to determine which of its four or more sub-areas will make an "S" transition first. In this way, an "S" curve is fitted to each small area, with a number of properties. It matches the base year loads and the trend of the immediate past prior to that year. It grows only to and through load levels that correspond to the types of land uses on the (constrained) manifold area for the small area's landuse categorization. It has an asymptote that, in company with those of its partners in the larger area it belongs to, sums to that larger area's long-term land-use-load value. Its growth ramp is of the slope and duration that matches the characteristics of its size. And it begins and ends its growth period in an order among its peers that matches its preference for the type of land-use growth that is occurring. These trends must follow not only an S-curve pattern of some sort in each small area, but adhere as groups and super-groups to the spatial hierarchical characteristics of that behavior as well. Results and Summary of SUSAN Tests comparing accuracy and effort confirmed that the hybrid method produced accuracy equivalent to simulation methods, while having roughly one-third the total labor requirement. Figure 15.8 shows that its forecast accuracy is roughly that of simulation (it outperforms some algorithms), its total cost of application less than twice that of trending and generally about one-third of that required for simulation of similar accuracy. Chapter 17 compares forecast algorithms on the
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basis of accuracy and effort required and gives more details on accuracy over time of various methods and their performance on other bases too. As mentioned earlier, this method has been applied to a very large number of electric planning projects. These include the major metropolitan areas around and including Boston, Chicago, Dallas-Ft. Worth, Manila, the Raleigh-DurhamCary metropolitan area in North Carolina, St. Louis, and Stockholm. It has been applied to regions including the Atlantic Coast of North Carolina, northernwestern Georgia, western Kansas, areas of central England, and parts of southern Australia. Use of this algorithm over the four-year period 1997 - 2001 indicated that the pattern recognition of load densities and trends can be used to infer land-use type in many cases to a much higher degree than the land-use-load inference described above. Analysis of data and results indicates that it may be possible to do away with the need for at least some of, if not all of, the land-use data. That is the subject of current research and development building a new algorithm from the results of SUSAN, tentatively called HILDEGARD.
o
< *j o a
Multivariate
E
O)
c o
a>
SUSAN
*<sa
ETM
O) 0)
10
20
30
40
Cost of Application - ($1000) Figure 15.8 Numbers show the relative cost of application of seventeen forecast methods that will be discussed and compared in Chapter 17, plotted against their forecast accuracy (negative planning impact) for a specific utility case. Multivariate is method 8. Also shown are the accuracy and cost ranges for the other hybrid methods discussed here.
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15.6 SUMMARY AND GUIDELINES The goal of hybrid spatial forecast algorithms is to combine good features of simulation and trending while avoiding their bad qualities. A "perfect" forecast method would combine the speed, ease-of-use and minimal data needs of trending with the accuracy, multi-scenario ability, and intuitive appeal of the output displays common to simulation methods. The best hybrid algorithms to date are far from perfect, but achieve performance that is at least as good as, and often surpasses, that of the best trending or simulation methods. There are many ways that trending and simulation can be combined. This chapter looked at three specific examples. More generally, however, hybrid algorithms can be developed based on combining the desired properties of trending and simulation methods, each picked for their particular strengths and weaknesses. Design based on information context and usage has so far proven to be the most useful perspective for combining needed qualities. These concentrate on the two major areas of information needed in a forecast: • Context - information on initial conditions, trends, and limitations to growth on a small area and regional basis. • Process - information on the process of growth; how growth occurs and what governs it locally. There is a wide variation in capabilities and focus among both trending and simulation methods with respect to how they develop and handle information on both context and process. The two types of approach differ greatly in the amount and type of data they require. But within each genre, specific algorithms (e.g., LTCCT or TM trending, 2-2-3 or 4-3-2 simulation) vary greatly with respect to two basic characteristics with respect to information: • How well they develop and use information contained in their input data • How much information the algorithm itself contains. Extended template matching (ETM) is an example of a hybrid method in which the design goal in combining trending and simulation was to improve accuracy, particularly with respect to forecasting incipient load growth, a major planning issue for electrification projects in rapidly developing countries (see Chapter 18). Here, accuracy is much improved over simulation or trending (particularly for incipient load growth forecasting) but data needs are relatively extreme. By contrast, the SUSAN program aimed to combine simulation and trending with a goal of reducing data requirements of what is otherwise "simulation-level" performance. To a great extent it succeeded. Its data needs are about one-third
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those of 2-3-3 simulation programs like FORESITE (algorithm and initial version of the program also developed by the author), while accuracy and representativeness are generally similar. Both SUSAN and ETM demonstrated that hybrid combinations of selected features from simulation and trending can produce powerful forecast engines which offer advantages over the better methods of either type. Hybrid algorithms are not easy to design, for the characteristics of the two types of program have to be very carefully matched. Not all hybrid combinations of features from simulation and trending work well or even work at all. In fact the majority of attempts have not been successful. Several have been miserable failures - being difficult to use, sensitive to data errors, and far less accurate than middle-of-thepack simulation. However, the success of both SUSAN and ETM points the way to further improvements in applicability and reductions in data and user effort and skill requirements. Thus, work on hybrid methods will likely continue, further steps on the evolutionary pathway of power system planning technology. Very likely hybrid forecast methods will be an area of heavy research and development effort, and results, during the next decade.
REFERENCES R. J. Bennett, Spatial Time Series Analysis, London, Pion, 1979 M. C. DeGaulle and V. R. Potain, "Hybrid Forecast Method Helps Locate Future High Growth Areas," Proceedings of the New London Conference on T&D Technology for the 21st Century, New London, May, 1998. P. V. Lodi and R. C. Dramian, "Hybrid Forecast Algorithm Design - Some Comments Based on Experience" Paper presented at the 2nd Annual Conference on Electric Infrastructure Asset Planning, Durban, 1997. J. R. Meinke, "Sensitivity Analysis of Small Area Load Forecasting Models," in Proc. 10th Annual Pittsburgh Modeling and Simulation Conf. (Instrument Society of America, Pittsburgh, PA, Apr. 1979). Electric Power Research Institute, Research into Load Forecasting and Distribution Planning, Electric Power Research Institute, Palo Alto, CA, 1979, EPRI Rep, EL1198 V. F. Wilreker et al., "Spatially Regressive Small Area Electric Load Forecasting," in Proc. IEEE Joint Automatic Control Conference 1977 (San Francisco, CA).
16 Advanced Demand Methods: Multi-Fuel and Reliability Models 16.1 INTRODUCTION "Demand" has a number of different meanings with respect to electric power planning. In its most specific electric engineering sense, it refers to the total electrical energy usage of one or more consumers during a period of time, usually one hour. It also is often used in forecasting to refer to its more economics-oriented application ("demand and supply"). But in its most non-specific, widest interpretation, "demand" refers to everything the consumer wants or at least wants to the extent he or she is willing to pay for it. In that context and within the venue of the T&D planner, "demand" then refers to what the consumers really want with respect to energy. Most consumers are more interested in the end-use performance of lights, heating, and air conditioning, than the energy source itself. They want to obtain energy from electricity, and natural gas, fuel oil, or propane - whatever suits their needs best and at least cost. Many will also look at other sources such as solar and wind generators to provide end-uses. Ultimately, consumers also have a demand for quality. For gas and oil, this may include its lack of contaminants (sulfur, dirt), odor and noise when applied to their needs. For electricity it means consumers want continuous availability (reliable service) as well as freedom from electrical "contaminants" such as harmonics and voltage sags. This chapter looks at modifications to the simulation approach that address these needs. Only the simulation approach to spatial load forecasting is suitable for 477
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this type of study, so discussion here is limited to looking at how the basic simulation approach can be modified and applied to multi-fuel studies, and how it can be applied to study reliability. Multi-fuel studies are addressed by using a very comprehensive consumerclass based end-use model, in which demand for raw end uses (warm water, cool air, illumination) is used as the basis to determine how much energy, be it electricity or gas, a consumer might wish to buy. Section 16.2 addresses both modifications to method and application for these multi-fuel studies. "Multifuel" is the normal terminology used for these types of studies, even though they embrace consumer use of energy sources that are not quite fuels, such as solar, wind, and energy efficiency. Section 16.3 looks at modeling consumer demand in a Two-Q (Quantity and Quality) manner, a perspective that unites consumer need for power and reliability. Again, the end-use model forms the basis for the modifications needed to the simulation approach. 16.2 SIMULTANEOUS MODELING OF MULTIPLE ENERGY TYPES Many utilities own and operate both electric and gas delivery systems. Still others market conservation and energy efficiency programs to energy consumers in their service territory. "Convergence," the merger and organization of the different energy businesses into one whole, is a much anticipated and discussed trend in the utility business. A few companies have even ventured further along this road, acquiring propane, distributed generation, and/or energy service companies specializing in HVAC, weatherproofing, and factory automation services. Most consumers who have access to both gas and electric energy opt to buy some of both. Even many rural energy consumers, who are not near gas distribution, buy the next best thing - propane for heating and cooking. In addition, energy conservation, renewable energy (solar, wind) and DSM (demand side management) can be legitimately represented as a type of "energy source." Thus, some utility planners will find themselves involved with the marketing, sales, or delivery of several "energy sources." Other utility planners may view them only as competition. But for all those reasons, both sets of energy delivery planners may at different times need to model all energy types, not just electric energy, when they forecast future needs for their system. This section discusses the application of spatial forecast models to such multi-fuel applications. Overall Concept of a Multi-Fuel Spatial Model The term "fuel" as used here means a source of energy that can satisfy the consumer's need for power. The overall concept of a multi-fuel spatial model is to use a simulation approach to forecast the number and type of consumers, and then apply a multi-fuel energy model to translate that forecast into the energy
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usage in more than just the electric dimension (i.e., electric and gas, fuel oil, or solar power-suitable loads, etc.). An X-3-3 type simulation model is ideal as a starting point: The spatial consumer-class forecasting "side" of the model can be used, unmodified. Land-use or consumer-class distinctions sometimes need to be expanded, to make distinctions for gas and other energy sources, beyond just electric. The end-use model is expanded to include gas, conservation, and other energy sources as needed. The major challenges is building a good model that coordinates the interaction of the multiple energy sources well. Both sides of the simulation - spatial and temporal —need to be augmented so that they can handle the additional fuels, but otherwise, this is a very straightforward step. The basic model forecasts consumers, not just energy usage the foundation of a multi-fuel model is already in place. Figure 16.1 shows the overall concept of the multi-fuel spatial simulation program. The spatial consumer modeling is essentially unmodified. Modeling the Interaction of the Multiple Fuels The one issue that a useful model must handle well is the cross-substitution capabilities of the multiple fuels. Gas and electricity can replace one another in some applications, but not others. For example, gas and electricity are both candidates for space and water heating, while conservation and energy efficiency provide an additional, if only subsidiary, source of energy.1 But other end uses can only be satisfied by electricity. The author is aware of no manufacturer of gas-powered televisions and computers, although there are natural gas powered refrigerators and household appliances such as washers and dryers (washers and dryers that run entirely on natural gas, using it to run their motors, too). Beyond the basic issue of cross-substitution there is the issue of economics. Consumers choose gas or electricity for space heating, water heating, and cooking based on a variety of factors, chief among them cost. Conservation is favored by environmentally conscious consumers (a group much larger than just diehard conservationists, containing perhaps 20% of all consumers) but By subsidiary source, the author means that it cannot do the job alone. Conservation (within limits) and energy efficiency both improve the efficiency of a energy source in doing its job. But without the primary source of energy (gas, electric) conservation and energy efficiency can do nothing. Conservation to the point of "doing without" is outside the context of what the author will consider here.
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Figure 16.1 Overview of the multi-fuel (multiple energy product) spatial simulation approach. Compare to Figure 12.1. The load curve side of the model has expanded tremendously. Its major element is now a multi-fuel coordinator. This is basically a "smart" top level to an end-use model which handles gas, electric, conservation, etc. It recognizes that gas, electric, distributed generation, and conservation can, to some extent, substitute for one another.
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generally conservation really only "sells" when its cost breaks even within two or three years. This is the challenge that the useful multi-fuel model must meet. It must provide planners with a way to study the potential cross-substitution of energy sources, and to set up scenarios to forecast what is likely to happen under certain scenarios. Usually, these scenarios take on one of two forms: Delivery options. What happens if the utility extends gas distribution into an area now served only by gas? How much gas will be sold? Will that amount justify the cost of extending the gas system? What will happen to demand for electricity? Will that change improve (defer expenses) or hurt (reduce demand too much) economics on the T&D system? Consumer preferences and buying patterns. Given that multiple sources are available, how much of what (gas, electric, conservation) will consumers buy, where? Utilities might also want to know who will buy it, when they might shift, and why (economics or other reasons). Modified Electric End-Use Model The simplest approach to multi-fuel end-use models is to modify an existing electric "curve adder" type of end-use model so that it can track two or three types of energy sources by performing a cycle of computation for every fuel type. Each is treated independently. Fundamentally, little modification of the end-use model is needed. Like a standard end-use model (see Chapter 4, Figure 4.5) it works with consumer classes, end-use categories, and at the bottom, appliance-type curves. Modifications are few, and very simple. A "fuel type" tag must be added to the appliance level modules used to distinguish electric from gas applications, etc. The model must sum each fuel type - electric, gas, etc. - into its own individual curve at the top. It must also maintain sums by type for each consumer class and end-use category. Gas appliance "load curves" and consumer market penetration data can then be entered into the model, just as electric curves were in the standard model. Figure 16.2 (compare to Figure 4.5) shows this basic enduse "curve adder" approach as modified for gas and solar. In principle any number of additional energy sources - propane, conservation, renewable power (which could, for example, power the water well end use in residential classes directly) could be added. The model as depicted in Figure 16.2 can be used to study gas, electric usage and the impact that solar power makes on electric usage. The consumer class level curves (middle of Figure 16.2) are used to produce the electric, gas, and solar maps of demand. The electric curves are used exactly as they always were.
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Figure 16.2 This shows the major features of a standard end-use "curve adder" modified for multi-fuel purposes, set up in this case for gas, electric, and solar power studies. At the top, it accumulates totals by energy type. In the middle, for all classes, it maintains a "load curve" and associated statistics for each energy type. At the bottom, the end-use "load" curves now include gas and solar. Note that the solar model is a linked "dual fuel" curve - each requires the other and they are modeled as one entity but counted as two separate "fuels."
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The gas curves are used, in analogous fashion, to show how the electric curves are used, to produce gas demand curves, and so forth for all energy sources. Multi-fuel end use models require much more care in data preparation Shortcomings of this model include only those of the "curve adder" approach itself. However, these become much more of a burden to the planners when they are faced with multi-fuel studies than when they are doing standard electric studies. As explained in Chapter 4, a "curve adder" is not a "smart" model. It simply adds the curves together, using its market penetration, consumer class, and consumer count values and pointers. The "smarts" of an end-use curve adder have to be provided by the user, and entered as data. Thus, if a planner wants to study a certain scenario, for example a doubling in the market penetration of high efficiency heaters in the residential classes, he has to develop those numbers outside of the model and enter the load curve data, market penetration values, etc., into the model. Responsibility for consistency (the market penetrations all add up to 100% where they should, etc.) is totally the planners'. The end-use model does not check for consistency, nor could it be modified to do so in any meaningful way. In a single energy source model, (e.g., electric only), this is only a nuisance. There are seldom a lot of curves and appliance classes in any one end-use category, so keeping track of them all and assuring their consistency is not too burdensome. But this challenge becomes much more difficult to master in multi-fuel models. First, there are many more end-use appliance categories, and energy usage types, involved in the bottom level of the model. Second, the relationships are much more difficult to keep straight and consistent with the intent of the scenarios being modeled. Table 16.1, which compares electric only and a trisource model of equivalent detail, will serve to illustrate the difficulty. In the electric model, the planner has six space-heating and three waterheating load curves (in addition to the "null" option) to enter and error-check. Although care must be exercised, there is seldom a real challenge in meeting consistency and accuracy needs here. In the tri-fuel model, the user has a total of twelve space-heating options and eight water-heating options. With only a little more than twice as many (twenty versus nine) the increase in work might not seem so onerous. However, the number of items needing consistency has skyrocketed. As only one example, anyone using baseboard space heating is likely to have electric storage water heating. Therefore, in an electric model, a reasonable constraint for the user to impose on his model, part of the "consistency" referred to here, is that MP (Baseboard Space Heating) < MP (Electric-Storage Water Heating) where MP ( ) "means market penetration of
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Table 16.1 Comparison of Load Curves Involved in One Element of the Bottom Layer of an End-Use Model Standard Electric Model Class: Residential 1 End-use: Space heating Non-electric, no fan Non-electric, central fan Electric resistive Electric baseboard heat Heat pump Hi-eff. heat pump Ground water heat pump Modified Electric-Gas-Solar Model Residential 1 End-use: Space heating Non-electric, no fan Non-electric, fan Electric resistive Electric baseboard heat Heat pump Hi-eff. heat pump Gas baseboard heat Gas central heat Gas room furnace Gas high eff. Heat pump + gas assist. Electric + solar Gas + solar
End-use: Water heating Non-electric Electric storage, standard Electric storage, efficient Electric, non-storage
End-use: Water heating Non-electric Electric storage, standard Electric storage, efficient Electric, non-storage Gas standard, standard Gas storage, efficient Electric storage, solar Gas storage, solar Solar only
The only other consistency the user really has to make certain of is that in each end-use category (space heating, water heating) the various appliance types sum to 100% market penetration, no more, no less) in each year modeled. In the tri-fuel model, consistency checks such as described above are much more numerous. Electric baseboard heating and electric storage water heating still have to be consistent. So do gas baseboard heating and water heating. Further, substitution of gas for electric baseboard heating implies substitution of gas for electric water heating (and vice versa) among those two sets of consumers. That is a good deal of consistency to assure in data that is manually prepared and entered, considering that trends will mean all of these change, in a coordinated way, over time. But in addition, there are many other interactions to be modeled, too, between solar and electric and gas, among other types of
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heating and water heating. This type of model is not untenable, but it is cumbersome and difficult to use well. Any effective user of this approach will prepare the input data (curves, market penetration values, consumer classes applied to, etc., in an electronic spreadsheet or other computer model, and then transfer it in something like comma-separated format, to the spatial forecast program's end-use model input. A good spreadsheet can perform the consistency checks well and, in addition, can display factors such as various trends (Figure 16.3) that help the user visualize and represent scenarios. In fact, a well-written spreadsheet program can be an ideal "external model" of market penetration and competition studies among energy sources, used by the planners to generate the scenarios (this will be discussed later). The key is "well-written." Many planning teams treat spreadsheets with an informality that results in poor quality control, documentation, and testing. The author's experience is that most planning teams also do not put enough emphasis on setting up and following rigorous procedures and quality checks in the preparation of the actual end-use data. As a result, inconsistencies and errors, some quite large, are commonly made in multi-fuel models.
Figure 16.3 Displays from the author's spreadsheet-based end-use model. This shows the anticipated market penetration of various electric and gas heating in a small community about one hour north of the author's home in Gary, North Carolina. Electronic spreadsheets provide all the capability needed for all but the most involved multi-fuel end-use models if well-designed and developed with appropriate checks and balances to catch inconsistencies and data errors.
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In this "curve adder" approach, the responsibility for maintaining this type of consistency among so many curves is left entirely to the user. Although in principle the model is useful for mixed-energy studies the author has seen it lead to innumerable practical problems because of its requirement for intricate care in setting up data. Such models become a burden when studying three or even more energy sources or in complicated two-energy studies. Direct End-Use Model A slightly more comprehensive multi-fuel end-use model involves modeling the actual appliances. This does not require a substantial change in data structure from that shown in Figures 4.5 and 16.2. However, it requires a considerable change in the context of the end-use model itself. The basic concept of a direct end-use model is shown in Figure 16.4. Raw, undiversified end-use demand - for lighting, hot water, space heating, or whatever - is modeled on a per capita basis within each consumer class. An equipment and appliance model converts this end-use into the energy source used to satisfy the end use. Some of these "appliance conversion models" are simply multipliers (effecting a change in scale of the same curve - the electric load curve is the same shape as the demand curve). But other appliance models involve a transfer function that accounts for latency, storage and limited capabilities in an appliance. An example of the latter is an electric storage water heater, which does not necessarily switch on the instant that hot water is demanded, as a lamp will when light is demanded. A water heater may not switch on for several minutes after hot water consumption is begun, but then stays on long after a significant amount of hot water was used, until it returns the stored water to the upper limit of the storage temperature range (see Figure 3.3). Direct end-use models have two major advantages. Consistency and lack of error Accuracy is improved by a direct end-use model because its structure leaves far fewer places where mistakes and inconsistencies can be made. Market share in a direct end-use model will always add up correctly (if the program or spreadsheet is written correctly), and the load implications of these changes will also be represented correctly in every case. A simple example of the consistency issue with a "curve adder" would be a study of compact fluorescent lighting's penetration into existing incandescent markets. A curve adder would require planners to convert the curves modeling the two technologies' market penetration by the ratio of efficiencies of the devices (about 3:1). Say compact fluorescent gains 10% market share. Measured in kW, that 10% share means a loss of X in the incandescent loads, and a gain of only 1/3 X in compact fluorescent. The planners would need to adjust the curves in this way each time they made any change in the future to their modeled scenarios. Fundamentally, this presents no problem— it is a very straightforward
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process to do so. But it is a burden and a source of confusion and error when there are many curves to be revised many times in the course of a study.2 It is much easier to simply represent the lighting demand and then split the market penetration with a breakdown by that measure alone. One objection often raised by planners who don't really think the matter through is "Where will we get all the raw end-use demand curves?" The answer is from the electric data. Knowing present lighting device market penetration (e.g., in residential, perhaps 94% incandescent, 6% fluorescent) one can work 2
Imagine modeling shifts in market share among lighting technologies when there are five lighting types - incandescent, halogen, fluorescent, high performance fluorescent, and light-pipe systems. The planners now need to maintain ten conversion factors and apply them back and forth as they change scenarios and represent gradual changes from year to year.
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backwards from the present electric lighting curve to a "hourly lumens demand curve." While it may seem bizarre to use electric data to infer a demand curve that will be used in modeling future electric usage, a lot is gained. The model and future changes in it are now independent of energy values. Planning The above example brings up the other advantage of a direct end-use model. A direct end-use model is representative of the actual process of end-use energy usage. By contrast, a curve adder manipulates and models only the result. For example, lighting load is actually the result of the demand for lighting, as seen through the electrical characteristics of the appliances used to provide light. By being representative of both demand curves and appliance characteristics, the model is a better study and planning tool. The curve adder works only with the result (electric load curve). With a curve adder, if the peak value of a load curve is decreasing over time, does that mean that demand is dropping, or that energy efficiency of the devices being used is improving? The planners might know or suspect the answer, but the curve adder model does not. A direct end-use model does, and is a more useful planning tool because of the distinctions between demand and appliance capability that it makes. A good direct end-use model takes all the appliances and ratios their shares according to the penetrations they have been given. The author likes this feature. His own direct end-use energy model is a spreadsheet which can model such things as "7% of the existing heat pump market penetration converts to highefficiency heat pumps each year," and "resistive heat drops by 15% each year. Example This example involves a combination of a number of interrelated factors related to space heating and measures efficiency using seasonal energy efficiency ratio (SEER). Of course, there is the different efficiency of various technologies (heat pumps, baseboard heating, resistive heat). Beyond this, though, there is a different mix of use of these various appliance types in use in different parts of the consumer base. There are slowly changing market shares among competing technologies within these market segments. And, heating technology energy efficiency is slowly improving over time. 80% of the population consists of homes more than 40 years of age - 5% have electric resistive heat with an SEER of 6.1 - 10% have baseboard electric heat with an average SEER of 6.8 - 22% have heat pumps with an average SEER or 9.2 - 6% have high efficiency heat pumps with an average SEER or 12.4 - 33% use natural gas - 23% use fuel oil
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20% of the population are homes built in the last three years - 40% have heat pumps with an average SEER of 10. - 18% have heat pumps with an average SEER of 12.5 - 42% use natural gas Future scenario: - The only heat pumps available are high efficiency heat pumps available as replacement units. Average SEER of units available in any future year is 13.2 in year 0, increasing by .015% each year (i.e., 13.35 in year 1, 13.50 in year 2, etc.) until it reaches 15, after which it stays at that value. - 50% of electric resistive heat consumers will convert to high efficiency heat pumps when they next replace their unit, 50% will switch to gas - 30% of electric baseboard heat consumers will convert to heat pumps, 70% will convert to gas - 95% of heat pump users will replace their unit with a high efficiency heat pump, the other 5% will convert to gas - 100% of high efficiency heat pump owners will replace with new high efficiency heat pumps when their units need replacement - gas and fuel oil users will convert to high efficiency heat pumps at a rate three times the efficiency of the units (i.e., if units are 13% efficient, then 39% of gas heating consumers who replace their units will shift to heat pumps) An important fact used here is: residential heating units have an average lifetime of about 14 years, the exact nature of the distribution of replacement ages in an appliance population depending on the type of heating technology and fuel used (Figure 16.5). Therefore, in an area with relatively new housing, one cannot expect much replacement of units until the homes in the area reach about this age. Replacement is the only opportunity for increases in efficiency. By contrast, in an older area of a city, residential units will be several generations old and replacement occurs roughly on a constant basis (about 1/14 of the appliance population each year). Figure 16.6 shows the resulting market shares for this scenario over a twentyyear period. Not surprisingly, high-efficiency heat pumps are the largest gainer during the period. This model can also track average electric efficiency (market penetration -weighted SEER) of the resulting mix by year, and the other detailed aspects of usage. In combination with a standard simulation type spatial model, this market-share information can be applied spatially. Figure 16.6 shows the total residential breakdown for this scenario.
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The direct end-use model tracks the two residential subcategories in this scenario separately: old (80% of consumers) and new (20%) residential classes. If the spatial model being used also uses this distinction (and has two different types of residential), then the end-use model's distinctions on usage by those categories can be applied spatially. Differences in Program Structure and Data Flow An important point from the standpoint of program development is that the direct end-use model is not strictly hierarchical, as are the types of models represented in Figures 4.5 and 16.2. It is rather important to recognize this when developing a direct end-use model (spreadsheet or otherwise) or when modifying a curve adder type of end-use model into a direct end-use model. In particular, the different data flow and interactions need to be considered carefully when building automatic checks and balances into the program to detect errors and force consistency and accuracy. There are three points worth careful consideration. Top-down -> bottom-up data flow The market share models in Figure 16.7 are at the "bottom" of the model. Information (if not data) flows "down to them" and then after their contribution to the analysis, "flows back up" to the top. As shown, end-use information on demand first flows "down" toward the appliance models, being repeatedly divided and sub-divided into finer distinctions of class, usage, and sub-usage until it reaches the market models. After it passes through, it is then "added up" into end uses, classes, and finally aggregated up to the top (overall curve) level. This "top-down then bottom up" flow is common to nearly all end-use models, but often not recognized by developers as a required feature. Diagrams like Figures 4.5 and 16.2 look to be one-way (down) and hierarchical. They appear to be one way because their end-use load curves combine both the demand and appliance model (essentially trivial, or from a theoretical standpoint, "null" versions of each). Appliance models can be on either side of the market model Figure 16.7 shows the appliance models "above" the market models. Here, the model basically flows through the following logic, moving down the figure: 1. The structure of the model branches "down" through classes, subclasses, and end uses, to the base end-use demand curves (e.g., residential, subclass 2, ulterior lighting demand). 2. For each end-use demand curve, the appliance model computes what each possible technology (incandescent, fluorescent, etc.) would do with respect to electric, gas, and other energy source demands if each were satisfying all of that demand.
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Figure 16.7 A direct, multi-fuel end-use model works on a consumer-class basis, as shown here for just one class (only part of its model is shown). The model represents the various end uses in their natural units (i.e., lumens, BTU) of usage (top), converts those to electric, gas, and other energy demand with appliance models (middle) and then accumulates the various demand curves that result into electric, gas and other demand curves for the class. The model is a more effective planning tool than a "curve adder" model, and makes it easier to represent involved market penetration and technology change scenarios among appliances. The additional programming and set up effort required to build such a model is only justifiable if such scenarios will be routinely studied.
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3. These "all of that demand" curves are sent to the market share model where they are each weighted by their appliance types' respective market shares. 4. The resulting curves output from the market share model are added "up " within the structure of the model by end-use category, sub-class, class, and so forth, within their respective electric, gas, energy efficiency, and other venues. The flow of logic above traces the flow shown in Figure 16.7. But a direct enduse energy usage model will work just as well if written with the middle two steps reversed in order: 1. The structure of the model branches "down" through classes, subclasses, and end-uses, to the base end-use demand curves (e.g., residential, subclass 2, interior lighting demand). 2. These base end-use demand curves are sent to the market share model where they are each weighted by their appliance types' respective market shares to output appliance-type weighted demand curves. 3. For each appliance type weighted end-use demand curve, the appliance model computes what that respective technology (incandescent, fluorescent, etc.) would do with respect to electric, gas, and other energy source demands, when satisfying that demand. 4. The resulting curves output from the appliance models are added "up" within the structure of the model by end-use category, sub-class, class, and so forth, within their respective electric, gas, energy efficiency, and other venues. Different program "structure" The structure of end-use curve adders (Figure 4.5 and 16.2) is purely hierarchical — every nth-level element has only one progenitor. They are hierarchical in structure because only one energy source is involved. By contrast, multi-fuel models are not. The have dual paths on the data flow out of the appliance model. Among other points illustrated by Figure 16.7 is the "loop" structure of some parts of the end-use model for such an application. The figure shows that more than one data path flows both in and out of some elements of the model. Note in particular the gas washer-dryer appliance model. That appliance has both electric and gas components (so do gas heaters and AC units). It therefore contributes to "both" sides of this model. Such dual involvement of an appliance model is common and must be accommodated well. In fact, dual involvement is the rule if energy efficiency and conservation is one of the "energy sources" being modeled.
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16.3 SPATIAL VALUE-BASED ANALYSIS Quality of the electric power provided to the energy consumer, particularly reliability, is a major concern to electric utilities and consumers. This section will explore in more detail the concepts introduced in Chapters 2 and 4, that a spatial load forecast model can be used to forecast demand for quality value in somewhat the same manner it forecasts demand quantity of power. The section begins by looking at reliability and its market role with consumers. It then discusses the features needed for and the application of spatially differentiated reliability needs analysis and forecasting. Reliability's Growing Importance Distribution system reliability is driven by several factors including: (1) The increasing sensitivity of consumer loads to poor reliability, driven by both the increasing use of digital equipment and changing lifestyles. (2) The importance of distribution systems to consumer reliability as the final link to the consumer. They, more than anything else, shape service quality. (3) The large costs associated with distribution systems. Distribution is gradually becoming an increasing share of overall power system cost. (4) Regulatory implementation of performance-based rates, and large-consumer contracts that specify rebates for poor reliability, all give the utility a financial interest in improving service quality. Traditionally, particularly in the first few decades of the electric power industry, distribution system reliability was a by-product of standard design practices and largely reactive solutions to operational problems. Reliability was not engineered. It was achieved by standards. During the mid-twentieth century, power delivery reliability was provided by these time-tested standards and criteria - build it to these standards and service will be good enough to satisfy most consumers. However, in the first half of the 21st century, distribution system reliability has become a competitive battlefield for electric delivery utilities in several ways. First, delivery utilities do face stiff competition. Even though there may be no competing wires companies, delivery utilities face competition from alternative technologies and energy sources. Natural gas, distributed generation and energy efficiency measures are competition - if a delivery utility does a poor job, it will lose more of its market share to these competitors.
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Second, utilities also face competition through benchmarking. Regulatory commissions, consumers, and politicians all compare utilities on the basis of performance. Reliability is one of the foremost areas of comparison. And like any goal, reliability is best attained through study and planning - plan your work and work your plan. Toward that end, analysis of reliability needs and desires of the consumer base - where premium reliability may be demanded and where reliability will be needed for societal needs - is a first step. The Maximum Possible Reliability Is Seldom Optimal Planners must keep in mind that while reliability is important to all consumers, so is cost, and that only a portion of the consumer base is willing to pay a premium price for premium levels of reliability. The real challenge for a distribution utility is within tight cost constraints to: • Provide a good basic level of reliability. • Provide roughly equal levels of reliability throughout its system, with no areas falling far below the norm. • Provide the ability to implement means to improve reliability at designated localities or individual consumer sites where greater service quality is needed and justified. Reliability can be engineering into a distribution system in the same way that other performance aspects such as voltage profile, loading, and power factor are engineered. For details on methods that can be used, see Brown, 2002. Consumer Value Is the Key Quantity and quality both have value to the electric consumer. But so does cost. In fact, no factor in the decision about energy source and energy usage is more important to most consumers than cost. The three dimensions of power — quantity, quality, and cost - form a "value volume" that defines the range of the overall benefit consumers see in electric power (Figure 16.8). The author is aware that all consumers want reliability. But what they desire in terms of reliability is very close to irrelevant compared to what they will pay for reliability. The cost they will bear for the service they want measures the value they see in it. Conceptually, it is often useful to visualize where particular types of consumers are within the value volume. Some have a sufficient need for quantity and quality that they will pay a relatively high per-unit cost (integrated chip manufacturer). Others need a lot of power but have no need for reliability to the extent they will pay a lot for it (metal re-processing center). Still others need only relatively modest amounts of power, but will pay a relatively high rate to assure continuity of service (computerized data entry offices).
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c
(Q 3
o
Cost Quality Figure 16.8 Ultimately, the value electric power consumers see in their electric power supply is based on a "value volume" of three dimensions: quantity, quality, and cost.
Telecom data center
Auto wrecking yard
The author
Cost Quality Figure 16.9 Each consumer has a demand that fits somewhere in this conceptual space of quantity, quality, and willingness to pay. Every individual will have his own values, but in general groups of similar consumers will have similar interests and values they place on electric power and reliability. They form market niches. As an example, petstore owners have unique electric reliability needs (tropical fish last only a few hours without heat and air bubbling), and form one market "niche" among many.
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The Market Comb Traditionally, the price of power in the electric utility industry was based solely upon the quantity used. A consumer would pay more if he or she used more power and less if their use was less. Except in rare and specially treated cases, an electric utility would offer a "one size fits all" level of quality. Consumers got what was available, whether or not they needed and would have paid for higher quality, or whether they would have preferred a discount even if it meant somewhat lower quality. In the wake of de-regulation, many people suggested that utilities needed to provide more reliability, citing statistics that usually showed about 40% of the electric consumer market wanted and was willing to pay for more reliability. But what often went unsaid was that most surveys showed an equal amount, 40%, thought lower prices were as or more important. The remaining 20% in most surveys seemed relatively satisfied with their service/cost. The real point is that electric consumers differ widely in their need for, and their willingness to pay for, reliability of service, as shown by Figure 16.9. They probably differ as much in that regard as they do in the amount of power they want to buy. Consumers also differ in exactly what "reliability," and in a broader sense, "quality," means to them, although availability of service, quick and knowledgeable response on the part of their supplier, and power of a usable nature are always key factors in their evaluation.
Customers who put little value on reliability and are very unwilling to pay for it.
Motivated by Price
Customers reasonably satisfied by the industry's traditional reliability and price combinations.
Customers who require high reliability and are willing to pay a higher price in return.
Motivated by Service Quality
Figure 16.10 The electric marketplace can be likened to a comb: composed of many small niches, each made up of consumers who have a different need for and cost sensitivity to reliability of service. Even those who put a high value on reliability may differ greatly in how they define "good reliability," one reason why there are no broad market segments, only dozens of somewhat similar but different niches.
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As a result, the electric power demand marketplace can be likened to a comb as shown in Figure 16.10. It is a set of many small niches that vary from the few consumers who need very high levels of reliability, to those who do not need reliability, only power, and are motivated purely by lowest cost. Whether or not a utility chooses to address these needs by offering consumers choice in reliability of service, planners and management alike should realize that the market has this characteristic. "One size fits all" service leaves a lot of consumers with unfulfilled needs. Reliability Can Be a Product Traditionally, electric utilities have not offered reliability as a price-able commodity. They selected equipment, and designed and engineered their systems based on engineering standards that were aimed at maintaining high levels of power system equipment reliability. These standards and methods, and the logic behind them, were actually aimed at minimizing utility equipment outages. The prevailing dogma maintained that this led to sufficiently high levels of reliable service for all consumers and that reliable service was good. This cost of the reliability level mandated by the engineering standards was carried into the utility rate base. A utility's consumers basically had no option but to purchase this level of reliability (Figure 16.11). Only large industrial consumers, who could negotiate special arrangements, had any ability to make changes bypassing this "one-size-fits-all" approach to reliability that utilities provided. The traditional way of engineering the system and pricing power has two incompatibilities with a competitive electric power marketplace. First, its price is cost-based: a central tenet of regulated operation, but contrary to the marketdriven paradigm of deregulated competition. Traditional electric utilities don't really have a choice in this. Any "one-size-fits-all" reliability price structure will quickly evaporate in the face of competitive suppliers. Someone among the various suppliers will realize there is a profit to be made and a competitive advantage to be gained by providing high-reliability service to consumers willing to pay for it. While others will realize that there are a substantial number of consumers who will buy low reliability power, as long as it has a suitably low price. The concept that will undoubtedly emerge (in fact, is already evolving at the time this book is being written) in a de-regulated market will be a range of reliability and cost options. The electric utility market will broaden its offerings, as shown in Figure 16.12. For example, distributed generation (DG) interacts with the opportunities that the need for differentiated reliability creates in a de-regulated marketplace in two ways. First, this new marketplace will create an opportunity for DG, which can be tailored to variable reliability needs by virtue of various design tricks (such as installing more/redundant units). Secondly, DG is a "threat" that may force utilities to compete on the basis of reliability, because it offers an alternative,
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Hi
Lo
Reliability Figure 16.11 Generally, the cost of providing reliability in a power system is a nonlinear function of reliability level: providing higher levels carries a premium cost, as shown by the line above. While reliability varies as a function of location, due to inevitable differences in configuration and equipment throughout the system, the concept utilities used was to design to a single level of reliability for all their consumers.
Hi
Lo
Reliability
Lo
Hi
Reliability
Figure 16.12 A competitive market will recognize the demand for various levels of reliability and providers will have to broaden their offerings (left) until the range of options available to consumers covers the entire spectrum of capabilities, as shown at the right. Actual options offered will be even more complicated than shown here because they will vary in the type of reliability (e.g., perhaps frequency or duration is more important to a specific consumer; some may care about service 24 hours a day 365 days a year, while others want "reliability" only during normal business hours).
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which can easily be engineered (tailored), to different reliability-cost combinations. Utilities may have no choice but to compete in pricing reliability. Utilities and energy service companies have an interest in studying consumers by not only how much power they want to buy, but what quality they want to buy. Delivery utilities need to study where these needs are so they can tailor their system to those demands.
End-Use Modeling of Consumer Power Quality Needs The consumer-class, end-use basis for analysis of electric usage, discussed in Chapters 2, 4, 15, and here provides a reasonably good foundation for study of the service reliability and power quality requirements of consumers, just as it provides a firm foundation for analysis of requirements for the amount of power. Reliability and power quality requirements vary among consumers for a number of reasons, but two reasons predominate: End-usage patterns differ: the timing and dependence of consumers' need for lighting, cooling, compressor usage, hot water usage, machinery operation, etc., vary from one to another. Appliance usage differs: the appliances used to provide end uses will vary in their sensitivity to power quality. For example, many fabric and hosiery manufacturing plants have very high interruption costs purely because the machinery used (robotic looms) is quite sensitive to interruption of power. Others (with older mechanical looms) put a much lower cost on interruptions. End-use analysis can provide a very good basis for detailed study of power quality needs in power delivery planning. For example, consider two of the more ubiquitous appliances in use in most consumer classes: the electric water heater and the personal computer. They represent opposite ends of the spectrum from the standpoint of both amount of power required and cost of interruption. A typical 50-gallon storage electric water heater has a connected load of between 3,000 and 6,000 watts, a standard PC a demand of between 50 and 150
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watts. Although it is among the largest loads in most households, an electric water heater's ability to provide hot water is not impacted in the least by a oneminute interruption of power. In most cases even a one-hour interruption does not reduce its ability to satisfy the end-use demands put on it.3 On the other hand, interruption of power to a computer, for even half a second, results in serious damage to its "product." Often there is little difference between the cost of a one-minute outage and a one-hour outage. It is possible to characterize the sensitivity of end uses in various consumer classes by using this "Two-Q" end-use basis. This is in fact how detailed studies of industrial plants are done in order to establish the cost-of-interruption statistics which they use in value-based planning (VBP) of plant facilities and in negotiations with the utility to provide upgrades in reliability to the plant. Following the recommended approach, this requires distinguishing between the fixed cost (cost of momentary interruption) and variable cost (usually linearized as discussed above) on an end-use basis (see Chapter 2). An end-use load model as covered in Chapter 4 and here can be modified to provide interruption cost sensitivity analysis, which can result in "twodimensional" appliance end-use models as illustrated in Figure 16.13. Generally, this approach works best if interruption costs are assigned to appliances rather than end-use categories. In residential, commercial and industrial classes different types of appliances within one end use can have wildly varying power reliability and service needs. Thus, reliability studies are really only feasible, in good detail, with an "appliance sub-category" type of end-use model, or a direct end-use model (see Section 16.2). Modifications to an end-use simulation program to accommodate this approach are straightforward. Every appliance end-use load curve now has "two dimensions." Each summation of curves keeps two summed load curves — quantity and quality. Used with a spatial simulation approach, they produce analysis of both Qs — quantity and quality - by time and location, as shown in Figures 16.14 and 16.15. A direct appliance-level end-use model is particularly useful in this type of study because it can study the power quality needs of different appliances aimed at the same end use. For example, variable-speed chillers for commercial offices save energy, but their computer control systems are very sensitive to voltage sags and brief interruptions. By contrast, traditional chiller systems have a relatively low demand for power quality but have a slightly higher level of demand for quantity. 3
Utility load control programs offer consumers a rebate in order to allow the utility to interrupt power flow to water heaters at its discretion. This rebate is clearly an acceptable value for the interruption, as the consumers voluntarily take it in exchange for the interruptions. In this and many other cases, economic data obtained from market research for DSM programs can be used as a starting point for value analysis of consumer reliability needs on a value-based planning basis.
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Residential Bectric Water Heater
HotroftheDay
Figure 16.13 The simulation's end-use model is modified to handle "two-dimensional" appliance curves, as shown here for a residential electric water heater. The electric demand curve is the same data used in a standard end-use model of electric demand. Interruption cost varies during the day, generally low prior to and during periods of low usage and highest prior to high periods of use (a sustained outage prior to the evening peak usage period would result in an inability to satisfy end-use demand).
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Figure 16.14 Result of a power quality evaluation using an end-use model. Top: the daily load curve for single-family homes segmented into four interruption-cost categories. High-cost end uses in the home are predominantly digital appliances (alarm clocks, computers) and home entertainment and cooking. Bottom: total interruption cost by hour of the day for a one-hour outage. Compare to Figure 2.17.
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Darker shading indicates higher reliability demand
Lines indicate highways and roads
Figure 16.15 Map of average reliability needs computed on a 10-acre small area grid basis for a port city of population 130,000, using a combination of an end-use model and a spatial consumer simulation forecast method of the type discussed in Chapter 15. Shading indicates general level of reliability need (based on a willingness-to-pay model of consumer value).
16.4 CONCLUSION With few exceptions, advanced spatial forecasting applications almost exclusively use the simulation method, building upon its spatial and end-use models to apply detailed consumer and appliance-usage modeling concepts which are beyond the scope of traditional T&D planning. Simulation is a tremendously flexible approach that can accommodate a variety of different special needs. Generally, the modeling aspects of simulation are expanded in four ways: Changes in basic structure of the simulation approach, as exemplified by the shift to road-link analysis for rural forecasting (Chapter 18) or the models for redevelopment and three-dimensional growth (Chapter 19), or changes in forecast priorities for electrification (Chapter 20). End-use models are expanded, much more than just growing in the number of classes, as explained here. Generally, more classes of land-use (consumers) will be needed for any special application. Almost invariably, a "special application" is targeting
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electric or energy usage in some way. Whether spatial or otherwise, such targeting is accomplished within a simulation program through the use of more classes - more specifically, through the coordinated use of class definitions that cross over between spatial and temporal models. The multi-fuel and reliability-based planning applications covered here certainly do not exhaust the list of advanced applications for spatial electric forecasting end-use models. Others include expanding value-based planning to include power quality (voltage stability, harmonics) rather than only reliability; planning of automated meter reading (AMR) systems and automation; marketing studies in a competitive market; distributed resource planning; and power shortage (rolling blackout) planning. Regardless, spatial load forecast simulation can be applied to handle all of these and other applications, in addition to its primary role of T&D asset planning, through the use of an artfully modified and expanded end-use model.
REFERENCES J. H. Broehl, "An End-Use Approach to Demand Forecasting," IEEE Transactions on Power Apparatus and Systems, June 1981, p. 271. R. E. Brown, Electric Distribution System Reliability, Marcel Dekker, New York, 2002. G. Dalton et al, "Value Based Reliability Transmission Planning," paper presented at the 1995 IEEE Summer Power Meeting, number 95SM566. Electric Power Research Institute, DSM: Transmission and Distribution Impacts, Volumes 1 and 2, EPRI Report CU-6924, Electric Power Research Institute, Palo Alto, CA, August 1990. R. Orans et al, Targeting DSM for Transmission and Distribution Planning," IEEE Transactions on Power Systems, November 1994, p. 2001. H. L. Willis and G. B. Rackliffe, Introduction to Integrated Resource T&D Planning, ABB Power T&D Company, Raleigh, NC, 1994. H. L. Willis, L. A. Finley, and M. J. Buri, "Forecasting Electric Demand for Distribution Planning in Rural and Sparsely Populated Regions," IEEE Transactions on Power Systems, November, 1995, p. 2008. T. S. Yau et al,"Demand-Side Management Impact on the Transmission and Distribution System," IEEE Transactions on Power Systems, May 1990, p. 506.
17 Comparison and Selection of Spatial Forecast Methods 17.1 INTRODUCTION This chapter focuses on the selection of a forecasting method and its application to spatial electric load forecasting in a practical electric utility environment. The primary purpose of the forecasting discussed here is T&D planning, but targeted marketing, energy conservation and efficiency programs, and competitive planning issues are also addressed. This chapter begins with a categorization of the methods covered in previous chapters including presentation of nomenclature for identification of the key components in simulation forecast methods. A set of comparison tests of nineteen forecast programs, representative of the spectrum of available spatial load forecast methods, is reviewed. All are uniformly applied to two utility test cases - a metropolitan and a rural system. Accuracy, labor, data, computer requirements and operating characteristics, as well as special features of all nineteen methods are evaluated and contrasted. Section 10.4 covers data, data sources, and procedures for collection of the data required to support spatial load forecasting. Section 10.5 covers the selection of the most appropriate forecast method for a particular utility and application. The method presented is applied to a realistic utility problem, and its variation to fit a number of other situations is discussed. The chapter ends with guidelines for spatial forecast application.
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17.2 CLASSIFICATION OF SPATIAL FORECAST METHODS In order to compare and contrast spatial load forecast methods, it is useful to have a system to categorize them on the basis of their most important characteristics. To the author's knowledge, all spatial load forecast methods use the small area technique, in which the territory of interest to the planner is broken into a set of small areas of appropriate size and shape so that the forecasting of all individual areas will provide the required information on where load is located.1 Small areas used in the analysis of load growth can be either irregular polygons (often substation or feeder service areas) or the rectangular areas defined by a uniform grid. Regardless, what is important is spatial resolution the amount of "where" detail the forecast provides, which is related to the size of the small areas - from the standpoint of forecast detail, the smaller, the better. Categorization by Approach and Algorithm Spatial electric load forecasting methods can be grouped into three categories: non-analytic, trending, and simulation. Non-analytic methods include all forecasting techniques, computerized or not, which perform no analysis of historical or base year data during the production of their forecast. Such a forecasting method depends entirely on the judgment of the user, even if it employs a computer program to accept "input data" consisting of the user's forecast trends as well as to output maps and tables derived from that bias. As will be shown later in this chapter, despite the skill and experience of the planners who may be using them, these methods fall far short of the forecast accuracy produced by analytic methods. Trending methods, discussed in Chapter 6, forecast future load growth by extrapolating past and present trends into the future. Most utilize some form of univariate or multivariate interpolation and extrapolation, most notably multiple linear regression, but a wide variety of other methods, some non-algebraic have been applied with varying degrees of success. Trending methods are most often categorized according to the number of variates (e.g., univariate, bivariate, multivariate) and the mathematical technique used to perform the trend extrapolation
1
There are other approaches. For example, presumably one could develop a function F(x, y, t) whose value corresponded to the load at location x, y, in year t, and then through some means "grow" or extrapolate this function through time and space so that it would forecast future load when solved for input values of t greater than the present year. However, as far as the author knows, all attempts to make this approach work have met with so little success that the researchers have never even tried to publish their results.
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(e.g., linear multiple regression, vacant area inference (VAI), load-transfer coupling (LTC)). Computerization of trending methods is most often applied using standardized "horizontal application" software - programs designed for general purpose use such as electronic spreadsheets like Excel or Lotus 1-2-3, mathematical manipulation packages like MathCAD, Mathematica, and Matlab. Simulation methods analyze and attempt to replicate the process by which electric load changes in both location and time, as discussed in Chapters 7, 8, and 9. All use some form of consumer-class or land-use framework to assess location of demand, and most represent usage over time on a per-consumer basis using load curve distinctions defined on that same consumer-class basis. Most are computerized, using software developed specifically or primarily for electric power planning purposes. A number of computer programs for "land-use-based load forecasting" are non-analytic, doing nothing more than outputting (often with beautiful color maps and well-organized tables) numbers and trends input by the user. Despite the manufacturers' claims, they often do little beyond regurgitate the user's judgment-based forecast as input. However, most simulation methods apply something between a limited and a very comprehensive analysis of the local geography, locational economy, land use, population demographics, and electric load consumption. Categorization of simulation methods is difficult because of the great variety of urban models, land-use bases, pattern recognition algorithms, end-use load models which have been developed and applied, and differences in how they are put together into complete programs. However, the nomenclature listed in Table 17.1 has proven useful in distinguishing between one method and another and seems to categorize methods consistently into groups with similar performance. This terminology was first developed in the early 1980s, and a majority of significant publications on simulation spatial load forecast methods make use of it. Simulation methods are classified by a three-digit nomenclature (Table 17.1), as for example 1-2-3, with the three digits representing, respectively, the type of approach used in each of the three major portions of the spatial simulation: • The first position, X-x-x, indicates the type of global/large area model.
• The second position, x-X-x, indicates the type of spatial small area model. • The third position, x-x-X, indicates the type of temporal load model.
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Table 17.1 Categorization of Spatial Load Forecast Simulation Programs Global/large area model 0 - none 1 - input control totals, no urban pole or large area effects analysis 2 - input control totals or Lowry T matrix computation, polycentric activity center model of large-area growth influences including methods with distributed pole computation 3 - input control totals and/or multi-stage Lowry computation and polycentric activity center 4 - urban sub-areas "compression and competition" model (see Chapter 19) Small area/local attribute model 0 - none 1 - small area class changes are assigned based on preference "scores" input by the user, from judgment or a priori analysis 2 - small area class changes are assigned based on preference "scores" determined by analysis of less than six surround or proximity factors 3 - small area class changes assigned based on preference "scores" determined by analysis of more than six surround or proximity factors Temporal load model 0 - none 1 - no load curves, uses a single kW value per consumer or acre for each consumer class 2 - peak day or longer load curves per consumer or acre for each consumer class 3 - peak day or longer load curves using a consumer-class end-use model on a per consumer or acre basis 4 - spatially time-tagged consumer class areas in company with time-indexed enduse curves
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Table 17.2 Spatial Electric Load Forecast Programs Program
Year
Characteristics and Comments
1964
Spatial temporal extrapolation using a single urban pole and a monoclass land-use model to provide load densities (Lazzari, 1965). To the author's knowledge, the first computerized use of any type of "gravity model" for electric utility forecasting. Basically a 2-0-1 model.
CAREFUL
1991
A 3-3-4 monoclass land-use simulation based on Carrington's staged timetagged linear load curve model combined with a time-tag update model of energy efficiency and demographics, marketed and supported by Alerti in the early to mid 1990s (Carrington and Lodi, 1992).
CEALUS
1981
A 2-3-3 type multi-map land-use based simulation program sponsored by the Canadian Electric Association. Based heavily on ELUFANT (see below) with simplified preference function computations. The first really good implementation of the modern simulation concept (CEA, 1982).
DIFOS
1987
A 1-3-2 monoclass simulation based on a variation on the basic land-use theme (Ramasamy, 1988) coupled with a designated redevelopment area feature. It required heavy user interaction but could do quite good forecasts when set up with good inventory data. Superceded by PFUC (see below).
DLF
1980
A 2-1-1 type multi-map land-use simulation developed and marketed by Westinghouse Electric Co., 1978-1982. Widely used by utilities in the US through the late 1990s (Brooks and Northcote-Green, 1978).
ELUFANT
1977
A 2-3-2 multi-map land-use based hierarchical simulation program developed at Houston L & P, 1973-1984. The first modern simulation approach, done by a team that had the right basic idea but overcomplicated the implementation details (Willis et al., 1977).
FORECAST
1994
A 3-3-3 monoclass land-use simulation, PC-based program, developed based on many of the author's papers and marketed by MVEN Technologi from 1994 until 1998. The program ran under a PC-based GIS system called Atlas Map.
FORESITE
1992
A 3-3-3 monoclass land-use simulation, basically a simplified algorithm based on LOADSITE (see above) with improved urban renewal forecasting and a modern GUI. Currently developed and marketed by ABB Power T&D Company, Inc., and widely used by utilities worldwide (Willis et al 1995).
LTCETRA
1985
A LTC trending program developed by several utilities in South America and used from 1985 into the new century (Rodriguez).
LOADSITE
1986
A 3-3-3 capable multi-map land-use simulation that did all spatial computations in the frequency domain and included an appliance-level enduse/DSM model. Developed and marketed by ABB from 1989 through 1993. (Willis, Vogt, and Buri, 1991).
LOADSITE-2 1990
A 4-3-4 simulation multi-map land-use simulation that used urban compression, frequency domain preference functions, and a time-tagged end-use/DSM model. In the author's opinion, still the most powerful spatial forecast simulation developed to date.
MATILDA
The author's forecast and display shell procedure for working with researchlevel forecast algorithms. Used for display and interpretation of examples in various chapters in this book.
APS-1
2001
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Table 17.2 cont. Program MLF
Year 1985
Characteristics and Comments
A 1-1-1 type land-use based simulation method developed and marketed by Scott & Scott (now Stoner) in the last quarter of the 20th century. Basically a simple but useful program to assist with "manual simulation."
MULTIVARIATE 1
Developed in 1977. Historical data extrapolation with cluster analysis, landuse, multivariate regression manifold fit, and a gravity type urban model, 1977-1984. The smarter alternative to Trend developed by EPRI project RP570. (Wilreker, 1977; EPRI, 1979).
PFUC
1999
A probabilistic 2-3-1 simulation using multi-iteration Markov modeling and "majority" selection to predict land-use transitions. A year-2000 derivative improvement of DIFOS, (above) marketed in India and SE Asia by Terncala spa.
PROCFV
1985
A derivative of the method but not the program code from Multivariate, this multivariate curve fitting program used principal components analysis and multiple regression to forecast regions, groups and then individual small areas in a hierarchy of trending (Grovinski, 1986).
PROCAL
1989
A 2-2-2 type multi-map land-use based hierarchical simulation program developed in South Africa, 1987, a simple but effective program that used manual input of urban-pole like priorities and computed preference factors on a local area basis (Carrington, 1988).
SLF
1980
A 2-1-2 type monoclass land-use based simulation method developed and marketed by Westinghouse Electric Co. as a smarter version of DLF (above). Difficult to use and depended too much on the user's savvy. 19801984 (Brooks, 1979).
SLF
2000
Cellular-automata/fuzzy-logic 2-3-1 simulation program. A very slick and innovative algorithm coupled with an apparently easy to use program, developed on an Arclnfo GIS platform and programmed in Avenue (Miranda, 2001).
SLF-2
1983
A 2-3-3 multi-map land-use simulation program developed and marketed by Westinghouse Electric Co. in the late 1980s. Modified in 1984 to use frequency domain computations in its preference model (Willis, 1983 and Willis and Parks, 1983).
SUSAN
1997
A hybrid mono-map land-use simulation/trending method developed at ABB in 1997, which provided simulation-like accuracy and representativeness with 1/3 the user labor (see Chapter 16).
TEMPLATE
1986
Template matching trending developed by a south American utility and used until the late 1990s for forecasting of urban and rural loads (Willis and Northcote-Green, 1984).
TREND
1977
Feeder/substation peak history extrapolation using regression curve fit. The first result of research to take spatial forecasting beyond "dumb" regression and better than most other multiple regression approaches (Menge, 1977; EPRI, 1979).
no name
2001
A research-grade 1-3-1 land-use based simulation method. While it lacks the global model needed for a complete forecast model, it uses an innovative technique to solve for the surround and proximity factor solutions, a major breakthrough (Wan Lin Wun and Land Win Lu, 2000).
Comparison and Selection of Spatial Forecast Methods
513
This nomenclature distinguishes forecast methods by the type of modeling approach and detail used, not by the efficiency or method employed in a particular program's numerical computation and program flow. Thus, whether a computer program uses spatial frequency domain computation in its pattern recognition or not, if it analyzes more than six proximity and surround factors in the course of its preference mapping, it is a x-3-x method. Similarly, a 3-x-x method uses a multi-stage Lowry model to represent global and large-area growth influences, regardless of whether it computes them with urban poles on a distributed basis or not. Therefore, this nomenclature is reasonably good at classifying simulation methods with regard to their data needs and potential forecast accuracy, but not with regard to computer resource requirements and computer run time. Table 17.2 summarizes twenty-four computer programs which have been developed expressly for electric load forecasting, and for which publications are available covering both method and results. (References cited in table.) A majority utilize simulation for two reasons. First, most trending applications use general-purpose software to apply the trend calculations. Second, simulation has proved increasingly popular due to its higher accuracy, easier communicability, and better credibility, in spite of its generally higher resource requirements. In summary, spatial electric load forecasting methods can be grouped into three major categories based on the approach they use - non-analytic, trending, and simulation. Within the last two groups, a particular method can be further categorized by the mathematical or modeling methods employed to compute the forecast. Categorization is useful in order to compare and contrast forecast methods based on their resource needs, capabilities, and proven results. 17.3 COMPARISON TEST OF NINETEEN SPATIAL LOAD FORECAST METHODS This section presents a discussion and comparison of nineteen different spatial forecasting methods, including their application to two utility test cases. They are compared on the basis of accuracy, forecast applicability, data needs, and resource requirements. The research upon which these results is based was performed by the author while at Westinghouse Advanced Systems Technology and ABB Systems Control, from 1982 to 1995. Additional theory and evaluation concerning these comparisons is available in two technical publications (see Willis and Northcote-Green, 1984, and IEEE Tutorial on Distribution Load Forecasting, Chapter 2). However, the results and discussion given here are updated versions of those earlier works. Test Problems and Test Procedure Test case A is a metropolitan area in the southern United States, which includes a large city and the surrounding periphery, and contains both high growth and low/negative growth regions within it. Case B is a rural region in the central
514
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United States, which includes five small towns, two of which are growing at modest rates. In both tests, data from 1975 to 1981 was used to forecast 1992 loads. Table 17.3 gives more information on each of the test cases. These two cases were selected because they represent two important and different classes of problems, metropolitan areas and small towns/rural areas. The primary reason for selecting these specific cases was that the data necessary to uniformly test and evaluate all methods were available for the period 1965 through 1992. Available data were almost identical in nature and quality for both test utilities and will be discussed later. Forecasting performance was evaluated based on both error measures (AAV, Ux, as discussed in Chapter 5) and on what the author believes is the only true
Table 17.3 Forecast Comparison Test Case Utility Systems Characteristic Territory analyzed, sq. miles Number of consumers 1981 Number of consumers 1 992 1981 peak load* 1992 peak load* Residential, % peak Commercial, % peak Industrial, % peak Municipal, other % peak Agricultural, % peak 1 992 annual load factor Major transmission voltages Distribution voltages Number of distr. substations Average substation peak
Utility A 2,000 446,000 544,000 4409 5241 42 23 28 5 3 67% 345 & 138kV 12.5, 34.5 kV 118 48
* All load values are weather corrected to a standard weather year
Utility B 21,000 65,000 71,700 285 312 55 22 6 4 13 58% 69&115kV 12.5&25kV 24 15
Comparison and Selection of Spatial Forecast Methods
515
criterion - the contribution the forecast method's errors appear to make to the system planning. Figure 17.1 shows the evaluation procedure used with each forecast method. First, the forecasting method was used to project 1991 loads from 1981 and prior data. Its forecast was fed into an automatic T&D expansion planning program, which produced a minimum cost 1981-1991 T&D expansion plan to serve the forecasted loads.2 The actual 1991 loads were fed into this same planning program, producing a 1981-1991 hindsight plan (one based on a "forecast" with zero error). The expansion planning program was then asked to compare the "plan based on the forecast" with the "hindsight plan" and to "fix" any deficiencies in a minimum cost manner. If the forecast was accurate, this cost would be small. If it was poor and had misguided the original plan, it would be large. Regardless, this "fix-up cost" was added to the cost of the original plan as based on the forecast, and compared to the cost of the hindsight plan. Any margin of cost above the hindsight plan's cost was attributed to the forecast error.3 This procedure attempts to reproduce in a consistent, repeatable manner, the "real world" situation in which a forecast is used to guide expansion planning, where any forecast mistakes must be corrected after the fact with addition projects or changes to the system. The use of an automatic expansion planning program as "the planner" in this case was done both to assure bias-free evaluation of all forecasts, and because the author had nowhere near the resources to manually produce nineteen (counting the hindsight plan) expansion plans for each systems. Readers who have used automatic expansion planning programs will realize that they are far from perfect and that usually intervention and fine-tuning by the user can further refine cost. This was not done in this case - the goal here being a consistent, reasonable method of evaluation. Thus, while any of these plans could be slightly improved by further work on the part of an experienced T&D planner, all are of the same relative quality. The author believes that the numbers established by this procedure are representative of relative performance of the methods and nothing more. In terms of predicting absolute rather than just relative performance, this procedure will tend to overestimate error impact, because it does not allow for interim-period discovery and correction of forecast errors, but instead assumes that all plans are fully built through 1991 and can only be "fixed" after the 19811991 expansion has been built (and all the budget spent). In actuality it is not uncommon for errors to be discovered about halfway through a ten-year planning period, and some can be corrected.
2
Actually, a two-stage coupling of expansion planning programs called SUBSITE and FEEDERSITE. (See Willis, Engel and Buri, 1995.) 3 This difference is always positive, i.e., the "as repaired cost" will always exceed that of the hindsight plan. The hindsight plan is, within the framework of the analysis, the optimum (minimum cost) plan. Any other plan must have a higher cost.
516
Chapter 17
FORECAST METHOD
load growth earsTtoT+10
Comparison finds AAV andU
AUTOMATED
AUTOMATED
AUTOMATED
"Forecastdriven plan" forT + 10
(
load growth years T to T+10
Comparison gives cost impacts
Forecastdriven plan" forT+10
(
Forecast-\ driven plan" y \ forT + 10 /
Figure 17.1 Procedure to compare forecast methods works from a base year, T, with twenty years of load history (years T - 20 to T -1), and forecasts through year T + 10. At the top, actual (left) and forecast (right) loads were compared using load-based error evaluations. The procedure inside the dashed-line box is the actual test procedure, which produced a "hindsight plan" (left side) based on knowledge of the actual load that developed. It represents a plan done with a "perfect" forecast. This was compared to a plan produced from the forecast method being tested, which is updated "at the last minute," as a utility would when forecast errors were detected as time passed (right).
Comparison and Selection of Spatial Forecast Methods
517
However, this procedure also assumes that any desired modifications to minimize the "patch up" cost could be determined and added in time. Often it is "too late" to obtain ROW, order equipment, or install facilities that the planner would prefer to have, and less desirable (i.e., more expensive) modifications must be made because they are the only ones available at that late date. The effects of these two "real-world" inaccuracies in this test procedure somewhat cancel one another, but to what extent is not determinable. The author believes that in actual application, total impact of any method tested would probably be only about two-thirds of that indicated by the tests. Two cost impacts were analyzed for all nineteen forecast-based plans. These were capital expansion cost and losses cost. Very often, when a poor plan is "patched up" capital cost is kept as low as possible by accepting higher losses costs. Thus, the impact of poor forecasting is often to increase long-term losses costs more than capital expansion cost (although often capital cost is increased considerably, regardless). All cost impacts are reported as percentage increases above the hindsight plan's. Accuracy was also evaluated on the basis of two statistical methods, average absolute value (AAV) of the small area errors, and planning impact sensitivities, Ux error measures for the transmission, substation, and feeder levels. These are reported in terms of percentage of average small area growth. As mentioned earlier, the computer program implementation is important in the overall ease-of-use of a program. In this test, all but four methods (numbers 9, 10, 18 and 19 as listed and described later in this chapter) of the nineteen were tested within the same computer program, a research version of a commercial load forecast program called LOADSITE. The research version used could mimic, or copy, any small area forecast algorithm, through its own forecast simulation language. For the test, algorithm instruction sets representing all but methods 9, 10, 18 and 19, were each used in turn. Methods 9, 10, 18, and 19 were tested using the original programs (developed by the author), at a somewhat later date than the other methods. However, results shown in the next few pages have been adjusted to represent as well as possible the relative performance of all 19 methods. Data common to several methods were identical. For example all land-usebased forecast programs ran from the same set of land-use maps and geographic data, gathered once, verified, and used for all in order to assure that differences in the test were due to differences in forecast method, not data. The only difference was in spatial resolution - methods that used one-mile land-use grids had the land-use data accumulated to that resolution, methods that used a polygon basis had the data loaded at that resolution. Similarly, all trending methods drew from a common set of tested historical data and metered load readings.
518
Chapter 17
The Nineteen Forecast Methods Nineteen different spatial forecast methods were tested, as summarized in Table 17.4. In each case, the forecast method was applied to the data for which it was designed, in the data format (grid, polygon) and spatial resolution for which it was designed as identified in the technical references listed. Methods one through nine are trending methods. By contrast the remaining eight methods use some form of simulation to produce the forecast. The same land-use base and historical load data were used for all nineteen methods, with the format, framework, and spatial resolution varying as appropriate for each individual method. Thus, spatial resolution varied, as did whether they used polygon or grid data formats, and multi-map or monoclass frameworks - that is part of the test. The nineteen methods are: 1
Polynomial curve Jit using linear regression (Meinke, 1979; EPRI, 1979). This was applied on a feeder service area basis; the linear regression is used to fit a cubic log polynomial to the annual small area peak loads. Extrapolation was applied to the most recent seven years of historical load data and horizon values at +20 and +22 years. Data used consisted of weather-corrected historical peak loads for the past ten years for each feeder (only the most recent seven were used) and horizon year loads selected at random (see Chapter 6).
2
Ratio shares curve fit. Also referred to as disaggregation trending (Cody, 1987), this method involves regressing area loads against the system load total rather than in time. This was applied on a feeder service area basis using seven years of historical data, this having proved best among the range of 4-8 years tested for this method. Data used consisted of weather-corrected historical peak loads for each feeder and the past ten years of system peak loads (also weather corrected).
3
Cluster template matching (Willis and Parks, 1983) involves two steps. A clustering algorithm is used to group the small areas into sets. Each set consists of areas whose growth history is similar and all areas within a set are extrapolated using the set's average trend (also discussed in Chapters 9 and 16). This was applied on a feeder service area basis. Data used consisted of weather-corrected historical peak loads for each feeder for the past twenty years and horizon year loads selected at random. This method was popular throughout the 1980s and early 1990s, and is still frequently used, because it is extremely parsimonious of numerical resources. As mentioned in Chapter 6, the method's chief advantage over other methods is that it can be efficiently implemented as a computer
Comparison and Selection of Spatial Forecast Methods
519
program without decimal arithmetic, and with some slight innovation in program flow, without multiply or divide calculations as well. This advantage is of doubtful value in a world where even low-cost personal computers can perform 80-bit floating point artihmetic, but the method is included for completeness' sake. 4
Vacant area inference (VAI) curve fit (Willis and Northcote-Green, 1981) applied on a 160-acre grid basis. The individual small area load histories are trended using polynomial curve fit with linear regression, as well as the total loads for blocks (groups) of areas. Differences are "inferred" as load forecasts for "vacant" areas. Data used consisted of weather-corrected historical peak loads for the past ten years for each feeder (only the most recent seven were used) and horizon year loads selected at random (see Chapter 6).
5
Cluster template in a VAI structure following a procedure of developing templates for individual areas and for blocks of areas was applied on a grid basis. Data used consisted of weather-corrected historical peak loads for the past twenty years for each small area and horizon year loads selected at random.
6
Urban pole centroid method as first developed by Americo Lazzari (Lazzari, 1965) on a grid basis, with one pole center used in every identifiable city or town, fitted to historical loads by varying the center height, the center location, and the function shape and then extrapolated into the future, subject to the constraint that volume (total area under the functions' surface - the total load) equal the projected system total. Data used consisted of weather-corrected historical peak loads for the past ten years for each small area, land-use data for the most recent year, and horizon year loads selected at random.
7
Consumer-class ratio shares (Schauer, 1982; Cody, 1987) using a multivariate regression. This is similar to method 2, except each area is trended against the total system load in separate classes of residential and commercial. Data used consisted of weather-corrected historical peak loads for the past ten years for each feeder, and residential and commercialindustrial consumer counts.
8
Multivariate rotation-clustering extrapolation (Wilreker et al., 1977; EPRI, 1979). Basically, this procedure simultaneously extrapolates small areas based on a number of factors, rather than just load, after first normalizing and statistically adjusting their historical data to maximize significant variance of the data sets.
520
Chapter 17 Data used consisted of weather-corrected historical peak loads and energy sales for the past ten years for each small area, land-use data for the most recent year and ten years prior.
9
LTCCT curve fitting regression, the most accurate trending method the author has discovered (Willis et al, 1994) is a combination of LTC regression and geometric constrained trending (see Chapter 9). Data used consisted of weather-corrected historical peak loads for the past ten years for each feeder, and the X-Y coordinates of the "center" of each feeder (obtained by averaging the X-Y coordinates of all nodes assigned to each feeder in a distribution feeder analysis database).
10 1-0-1 non-computerized land-use based manual approach, a manual forecast dependent only on user judgment. This method was applied, with insignificant variations from the method defined in Chapter 11, by the author or those under his direct supervision, for both test cases, as the first of the cases done in each utility case (thus the judgment was not "contaminated" by knowledge of the results of the other forecasting methods). Spatial resolution was 160-acre grid for case A, and 640-acre (square miles) for case B. Data used and the method applied are given in detail in Chapter 11. 11 7-7-7 computerized method, similar to that first published by Walter Scott (Scott, 1974), operating on nine land-use classes in a multi-map format at 40-acre grid basis. Data used includes land-use distribution by class for the base year (1981), load totals by land-use class, and consumer count forecasts by class for 1975-1981 (historical) and 1982-1992 (projected in Rate and Revenue forecasts). 12 2-2-7 land-use based simulation on a 40-acre grid basis using a multi-map format and nine land-use classes (Brooks and NorthcoteGreen, 1978) and widely used by many electric utilities during the 1980s. Required data are land-use and zoning data on a small area basis, information on the locations of major roads, highways, railroad, canals, and data on "restricted use" areas such as game preserves, cemeteries, and parks. Also required are the historical and projected load by class (Rate and Revenue) and load curve data (Load Research Department). 13 2-3-2 method (Canadian Electric Association, 1982) on a 40-acre grid basis using ten land-use classes in a multi-map format. Required data are land-use and zoning data on a small area basis, information on the locations of major roads, highways, railroad,
Comparison and Selection of Spatial Forecast Methods
521
canals, and data on "restricted use" areas such as game preserves, cemeteries, and parks. Also required are the historical and projected load by class (Rate and Revenue) and load curve data (Load Research Department). 14 Combined land-use/multivariate method, an advanced form of EPRI Multivariate model (EPRI, 1979; Yau et al., 1990) operating on a 40acre grid with a multi-map format. A "Lowry" type urban model is used to provide "control" to the multivariate extrapolation procedure and an end-use model is added to anticipate changes in consumer usage patterns. This procedure is close to a 3-2-1 land-use based method of forecasting but substitutes multivariate regression in the place of pattern recognition. This program is a hybrid algorithm of an early type. Required data are land use and zoning and major roads, highways, railroad, canals, as well as data on "restricted use" areas such as game preserves, cemeteries, and parks, on a small area basis for two years, at least five years apart,. Also required are the historical and projected load by class (from Rate and Revenue Department) load curve data, market penetration, and technology trends by appliance subcategory (from Load Research Department). 15 3-3-3 method (Willis, Engel, and Buri, 1995) operating on a 40-acre grid basis using ten land-use classes in a multi-map format. Required data is land-use and zoning data on small area basis, information on the locations of major roads, highways, railroad, canals, and data on "restricted use" areas such as game preserves, cemeteries, and parks. Also required are the historical and projected load by class (from Rate and Revenue Department) load curve data, market penetration, and technology trends by appliance subcategory (from Load Research Department). 16 3-3-3 method (Willis, Engel, and Buri, 1995) operating on a 1/2 mile road-link small area basis using ten land-use classes in a multi-map format. (Also covered in Chapter 18.) Required data are base year land-use and zoning data on a small area basis, information on the locations of major roads, highways, railroad, canals, and data on "restricted use" areas such as game preserves, cemeteries, and parks. Also required are the historical and projected load by class (from Rate and Revenue Department) load curve data, market penetration, and technology trends by appliance subcategory (from Load Research Department). 17 3-3-3 method (Willis et al., 1995) operating on a 2.5-acre grid basis using twenty land-use classes in a monoclass map format.
522
Chapter 17 Required are base year land-use and zoning data on small area basis, information on the locations of major roads, highways, railroad, canals, and data on "restricted-use" areas such as game preserves, cemeteries, and parks. Also required is the historical and projected load by class (from Rate and Revenue Department) load curve data, market penetration, and technology trends by appliance sub-category (from Load Research Department).
18 Extended Template Matching as described in Chapter 15, applied on a !/2 mile basis. Test results given here reflect application to a typical urban problem area, not the developing nation area. Required are base year land-use and zoning data on small area basis, information on the locations of major roads, highways, railroad, canals, and data on "restricted-use" areas such as game preserves, cemeteries, and parks, and similar data for twenty years earlier. Also required is the historical and projected load by class (from Rate and Revenue Department) load curve data, market penetration, and historical peak feeder of TLM- area loads for the past 25 years. 19 A hybrid 3-3-1/trending program, SUSAN, described in Chapter 15. Required data are "approximate" base year land-use and information on major roads, highways, railroad, canals, as well as limits defined by "restricted use" areas. Also required is the historical load data by feeder for the past five years, and the corporate forecast. Testing of these methods was done by substituting in turn an analysis engine (set of program routines) for each of the nineteen methods into a common shell program which handled the data, controlled program flow, reported results, and computed error. All nineteen subroutine sets were professionally developed, used standardized program design criteria, and utilized the high-speed calculation methods discussed in Chapters 6 and 9, where appropriate. Comparison of Forecast Accuracy Table 17.4 gives the results and Figure 17.2 shows the ACap error costs for all nineteen as evaluated. Note that these numerical error measures bear out the behavior expected of AAV and similar error statistics as discussed in Chapter 5. AAV is not a good predictor of overall forecast value. In fact, in both cases, the worst AAV value is for method 17, which proves to have the least negative impact on planning. AAV is evaluated for any particular method at the method's small area resolution, which in method 17 is 2.5-acre grid (squares 1/16 mile across, much higher than any other method tested). The SFA-based error measures, Ux, generally bore a closer resemblance to actual impact. Despite the approximations in the test procedure discussed earlier, and the fact that only two utilities were used as test cases, the author believes these results are representative of the relative performance of the types of forecast
Comparison and Selection of Spatial Forecast Methods
523
methods tested. The following conclusions can be generalized as applicable to most situations: • Data and set-up needs vary by nearly an order of magnitude. • AAV is a very poor measure of spatial forecast accuracy, as indicated by its measure versus Ux and ACap (see Table 15.4a). Methods 1 and 2, among the worst forecasting methods tested, have roughly the same AAV measure as methods 18 and 19, which actually produce less than one-fourth as much effective T&D error or impact as methods 1 or 2. • Land-use-based simulation methods were uniformly more accurate to trending when forecasting over a ten-year period. The more comprehensive methods were generally more accurate, but more costly to operate. • Trending methods and some hybrid methods (ETM) could not perform multiple scenario studies. • Most trending methods (methods 1, 2, 3, 6, 7, and 8) could not forecast growth in small areas that had no load prior to the base year. The VAI (4) and LTCCT (9) regression could to a limited extent. Methods that could not forecast vacant area growth tended to over-estimate growth everywhere else and underestimate it in vacant areas. The LTCCT method's accuracy advantage over other trending methods is its ability to forecast vacant area growth better than the others. • Multivariate methods (methods 7, 8, 14) did no better than comparable methods using other approaches. • Land-use techniques yielded results roughly proportional to the level of detail included in the spatial analysis used to compute preference functions. The more advanced land-use methods (methods 13, 15, 16, and 17) produced errors with an apparently random spatial distribution. • Hybrid methods (8, 14, 18 and 19) differ greatly in characteristics depending on how the algorithms were designed, but potentially offer advantages in areas where they were designed to excel, at possible additional cost of loss of flexibility in other areas. • There is a slight tendency of simulation to do worse on rural area forecasting if applied at less than very high spatial resolution (more on this in Chapter 18).
Chapter 17
524
Table 17.4a Forecast Accuracy Comparison Utility Test Case A in Percent Ux Method
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Type
Curve fit Trend Ratio shares Trend Template Trend VAI Trend TempI+VAI Trend Urban centr. Trend Cust. ratios Trend Multivariate Hybrid LTCCT Trend Manual land-use Jdgmnt 1-1-1 cust. class Simul. 2-2-1 cust. class Simul. 2-3-2 cust. class Simul. Multiv. cust. clss Hyrbid 3-3-3 multi-map Simul. 3-3-3 road link Simul. 3-3-3 monoclass Simul. Extended template Hybrid SUSAN Hybrid
AAV*
ut
Us
Us
50 51 47 38 36 61 52 44 36 56 39 39 38 45 27 32 79 52 49
22 23 15 14 12 18 14 11 10 17 14 9 7 10 7 7 6 8 7
35 37 25 22 20 27 22 20 18 30 28 14 14 15 11 13 10 13 12
51 47 38 36 46 52 30 26 41 38 27 22 28 15 18 13 19 14
ACap ALosses
50 41 32 28 26 34 28 24 24 32 22 17 14 19 12 15 10 12 11
39 21 19 14 15 23 20 16 14 20 15 13 9 10 7 9 6 8 7
Table 17.4b Forecast Accuracy Comparison Utility Test Case B - % Method
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Type
Curve fit Trend Ratio Shares Trend Template Trend VAI Trend Templ+VAI Trend Urban centr. Trend Cust. ratios Trend Multivariate Trend LTCCT Trend Manual land-use Jdgmnt 1-1-1 cust. class Simul. 2-2-1 cust. class Simul. 2-3-2 cust. class Simul. Multiv. cust. clss Mixed 3-3-3 multi-map Simul. 3-3-3 road link Simul. 3-3-3 monoclass Simul. Extended template Hybrid SUSAN Hybrid
AAV*
u,
Us
us
45 47 47 34 32 62 43 36 28 40 35 31 29 39 23 30 84 52 49
20 21 20 11 11 17 16 13 12 12 14 10 7 10 9 6 6 8 7
35 37 25 24 26 39 24 27 19 18 28 21 14 15 13 10 10 13 12
50 51 47 38 36 56 43 32 30 28 40 33 27 33 22 20 20 19 14
ACap ALosses
35 38 29 26 26 50 28 34 23 19 22 18 17 22 17 12 12 12 12
23 21 20 16 15 20 22 16 16 24 17 14 9 9 8 7 8 8 7
525
Comparison and Selection of Spatial Forecast Methods
Utility Test Case A - metropolitan electric system Curve fit
< 40 a. 5
I—| Multivariate
E 0
Codified curve fit
S 30
Manual .—|
LTCCT
• —-
Simulation s imple 4— algorithm —^ complex
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— O U
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I—I I
I I—
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te.
6 7
8 9 10 11 12 FORECAST METHOD
13 14
15
16
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19
Utility Test Case B - rural electric system Curve fit § 40 5
Modified curve fi
w 0 30
flM jltivariate
| —|
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17
18
19
Figure 17.2 Planning impact as measured in the comparison tests of nineteen forecast methods for utility test cases A and B. Differences in the relative performance of the methods between the two cases (method 2 was worst in case A, method 6 in case B. method 17 was best in case A, method 16 best in case B. Manual forecasting did much better in case B than in A) are due to differences in both relative performance in urban versus rural settings, and responsiveness to growth rate.
Chapter 17
526
Table 17.5 Data Requirements for Forecast Methods Type data Feeder peaks Subst. peaks X-Yofsubst. Lo-res land-use Land-use Hi-rs land-use Land-base Cust. peak k W Load curves End-use data Corp. frcst
Prep hrs. A B 1 thru 5
Method 6 7 8 9 10 1 12 13 14 15 16 17 18 19
24 20 24 20 16 24 60 80 1 6 02 4 0 60 60 40 40 8 8 24 24 60 60 24 24
X X X X X X X
X
X
X
X
X
X X
X
X X X
X
X
X X X X X X X X X X
X
X
X X X X X X X X
X
X
X
X X X
X
X
X
X
X
X
X
X X X
X
X
X
w 600 3 O
—
I 500
g 400 uj 300
1 —1
§200 H 100 < Q
n
™_rir,runn 1
2
3 4
fin
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 FORECAST METHOD
Figure 17.3 Data collection time for the nineteen methods, for cases A (shaded blocks) and B (unshaded).
Comparison and Selection of Spatial Forecast Methods
527
• Methods which worked at a higher spatial resolution produced better forecast accuracy. This does not necessarily mean that greater resolution, per se, provides improved forecast accuracy (although occasionally that is the case with simulation). All nineteen methods were applied at the resolution for which they were designed. In general, methods designed to work at a higher spatial resolution include more comprehensive analysis of other factors besides resolution, and thus they forecast more accurately. • The techniques using clustering and pattern recognition, whether trending or simulation or hybrid, worked slightly better in the metropolitan test case than the rural case. Data and Resource Requirements Table 17.5 lists the data requirements of the various forecast methods, along with the preparation time for each source (Figure 17.3), under normal circumstances, for cases A and B. (Data sources and procedures to collect such data will be discussed in 17.4.) Data listed for the multivariate and simulation methods include the full set of data for which they were designed.4 Data required include: Historical peak load data. Methods 1, 2, 3, 4, 5, and 7, what might be termed "traditional" trending methods, require only peak load measurements on feeders for the past seven to twenty years, depending on method. Such data are certainly available at any utility that practices good record keeping, and take no real preparation time. In all cases these data are used as the basis for extrapolation of past trends as the forecast of future peak loads. In any practical situation, methods 13, 14, 15, 16, and 17 require historical peak load data on substations, used to "calibrate" the simulation base data (see Chapter 11, Step 4). Geographic location of substations. Methods 7, 9, 12, 13, 14, 15,16, and 17 require a geographic location for each substation, information used in quite different ways depending on whether the method is trending, multivariate, or simulation. Trending (7, 9) uses the locational information as the basis for comparison of trends among neighboring 4
Both multivariate and simulation methods are robust, to the point that many can produce quite reasonable results with incomplete data or with data that contains a significant amount of error. However, this test applied each method as designed for best performance, and thus lists all data required. (See Willis, Engel, and Buri, 1995).
528
Chapter 17 substations or feeders. Multivariate methods (and method 9, trending) use the data to estimate load density and attempt to use that information to improve the forecast. Simulation uses substation location to tie landuse data to historical trends for calibration purposes. Low-resolution land-use data. Methods 6, 10, and 11 work with low resolution (square mile or so) land-use data, and also require only basic land-use data at "Anderson level-1" definition.5 Land-use data. Methods 12, 13, 14, 15, and 16 use land-use data, usually on a grid basis at 40-acre resolution, and with considerably more than Anderson level 1 distinction of consumer land-use classes - nine classes is typical. This is used as the basis for the pattern recognition and the forecast itself. High resolution land-use data. Method 17 analyzes land-use data on a grid basis at 2.5-acre resolution, but as a mono-class simulation can accept land-use data on a polygon basis and convert it to grid basis without much approximation error. Like methods 12 through 16, this method uses land use as the basis for the pattern recognition and the forecast itself. Land-base data consisting of general map data, highways, railroads, and similar terrain data are required by methods 10 through 17. Peak per consumer or per acre load values, giving kW usage by future year per consumer unit of each land-use class are required by methods 10, 11, and 12. End-use load model database is required by methods 12 through 17. Methods 12 and 14 require peak and energy usage by class, methods 13, 15, 16, and 17 require load curves, hierarchical framework, and technology and market share trends by class, end use, and appliance subcategory. Consumer and energy usage trends from the corporate forecast are required by methods 10 through 17.
5
Two Anderson levels are distinguished in classification used by the United States Geologic Survey. Level 1 gives good distinction of forest cover, agriculture, etc. Anderson level 1 can be thought of as providing, at best, classification into the following categories: urban, suburban, rural occupied, agricultural, and other.
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Table 17.6 lists the labor required to set up, run the forecast method, and interpret its results; the data collection labor from Table 17.5; and the computer resources required to support each of these methods as estimated by the author, on both of the cases. Labor includes the total time required to set up, produce, and interpret the forecast results for two forecasts (the author's experience is that forecasts are repeated or scenarios studied to the extent that a single forecast is rarely done). Computer resource requirements are the required RAM when running, total disk storage, and wall-clock minutes for an efficiently written program to complete the forecast running on an Intel Pentium 1000 Mhz processor. Using values of $65 per hour for forecast labor, $50 per hour for data gathering, $50 per Mbyte for RAM, $2 per Mybte of disk space, and assuming a base computer costs $2,000, an overall application cost of use can be developed. The cost computed in this manner for each forecast method is plotted against its accuracy in Figure 17.4. The author does not represent the costs computed as accurate estimates of overall cost in an actual utility application - many other
Table 17.6 Resource Requirements for Forecast Application Utility Test Cases
Method
1, 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2, 3, 4, 5, or 7 Urban centr. Cust. ratios Multivariate LTCCT Manual land-use 1-1-1 cust. class 2-2-1 cust. class 2-3-2 cust. class Multiv. cust. clss 3-3-3 multi-map 3-3-3 road link 3-3-3 monoclass Extended template SUSAN
Type Trend Trend Trend Trend Trend Jdgmnt Simul. Simul. Simul. Mixed Simul. Simul. Simul. Hybrid Hybrid
Hours A B 60 68 72 320 144 480 240 120 200 480 240 300 280 550 71
80 160 60 320 120 240 240 200 280 240 240 240 240 470 65
Mbyte RAM Disk
Min. CPU
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15 1
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Figure 17.4 Relative cost of application of nineteen forecast methods plotted against their forecast accuracy (negative planning impact) for utility case A. Methods closest to the lower left provide the best combinations of low error and low cost. Methods nearest the upper right are both high cost and high error. Based on this comparison, the best forecasting methods appear to be 5, 9, 12, 17, and 18.
factors are involved, and some costs have been left out while others (the computer) have been overestimated. However, these costs are indicative of relative application cost. Accuracy Viewed with Respect to Time and Small Area Size The type of accuracy comparison shown in the preceding tables and figures, in which relative accuracy over a fixed time period is contrasted, is quite useful and should always be used when evaluating forecast methods. However, another way to compare accuracy is to evaluate how far ahead various forecast methods can achieve the same level of accuracy. One method may be able to forecast five
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years ahead with 10% error, while another can achieve that level nine years out, providing another five years of assessment of needs and timing, and allowing more comfortable (and hopefully more economical) planning lead. Figure 17.5 shows accuracy versus time for five of the forecast methods tested.
40
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Figure 17.5 The ACap error given by polynomial curve fit using linear regression (method 1), VAI template trending (method 5), LTCCT trending (method 9), basic simulation (method 12), high-resolution monoclass frequency domain simulation (method 17) and hybrid trending-simulation (method 19) as a function of forecast time period, from test case A. The methods achieve a 10% error level (dashed line) at four, five, seven, eight, ten and ten years ahead respectively. The additional cost and data requirements of methods five, nine, twelve and nineteen therefore provide one, three, four, and six year advantages in planning foresight over method one.
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Yet another way to compare forecast accuracy is with respect to forecast resolution. Figure 17.6 shows ten-year-ahead AAV for the same five forecast methods as plotted in Figure 17.5, evaluated on different small area sizes. Any method provides fairly good forecast accuracy at low spatial resolution, and in all cases error level exponentially rises as resolution is increased. This information can be applied either vertically or horizontally: method 17 delivers just 1/3 the error of method 5 at a 640-acre resolution (vertical comparison); or method 17 delivers a 25% error (i.e., correctly locating load to within a small area 75% of the time) at about 100-acre resolution; whereas method 5 can deliver this accuracy only to within a square mile (horizontal comparison).
1 5 9
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Figure 17.6 Ten-year-ahead forecast mismatch (ACap) for methods 1, 5, 9, 12, 17 and 19 plotted as a function of small area size. Solid lines show test results (some methods were tested to only certain resolutions), dashed lines, extrapolations to higher resolutions. Level of accuracy depends very much on spatial resolution at which accuracy is judged. Accuracy of all five methods was normalized to zero at zero resolution (system as a whole). Many methods have a slight amount of "year zero" or fitting error.
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What Is the Best Spatial Load Forecasting Method? There is no "best" spatial load forecasting algorithm, because the needs, resources, and data availabilities with which T&D planners throughout the power industry work vary from situation to situation. Forecasting, like any other activity, is often a balance between the performance needed and the budget at hand. Power delivery engineering needs and resources vary greatly from one utility to another. Planners should select the forecasting method that best matches their company's needs, resources, available data, and budget. Quite clearly, any serious effort at forecasting electric demand for T&D planning requires application of a forecast method incorporated into a computer program. Computerization gives the planner consistent application of the method, the ability to manage the tens of millions of data points when required, and very fast computation of what are often quite involved numerical algorithms. Among the computerized methods tested in this section, methods 5 (VAI trending), 9 (LTCCT trending), 12 (basic simulation), and 17 (advanced trending) offer the best performance with regard to basic, low, high, and "accuracy is foremost" forecasting budgets, respectively. The other methods are outperformed by one or more of these four as regards forecast accuracy and cost.
17.4 DATA AND DATA SOURCES No forecast method is useful unless the data it requires are available. While data requirements vary considerably, as discussed in the last section, any of the data required are available on just about any utility system, worldwide. Often, a good deal of detective work and a bit of innovation are required to obtain the data at low cost. This section will summarize and comment upon the data required for spatial forecasting methods, and where they may be obtained. Historical peak load data. All trending methods and a good deal of other approaches require, or can optionally use, peak data by feeder or substation. Seasonal or monthly peak load readings on feeders and substations are maintained by over 90% of electric utilities. Generally, weather correction of the peak load reading data is recommended, if it can be done well and quickly. However, weather correction of feeder and substation peak load data really ought to be done on a consumer-class basis (using different correction factors/formulae for residential and commercial feeders, which generally will differ from one another, and from a system average adjustment factor). This requires consumer data by class for each feeder, often not available or expensive to maintain. Weather adjustment also requires data on the time of peak for each feeder these data are available to only a minority of utilities (while peak
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Chapter 17 recordings are kept, data collection methods often do not record the time of peak). Thus, weather correction is often skipped, the hope being that weather variations from year to year will average over the historical period. This is often the case - in general, linear regression based curve fit methods tend to respond slightly better in this regard than other trending methods. Substation peak load data required for calibration of simulation methods always should be weather corrected. Calibration to nonweather corrected historical load patterns can be one of the major contributors to mid- and low-frequency spatial error components - the type of error that affects T&D planning quite negatively. Use of a simulation method implies that the consumer-class data necessary to perform weather correction on a consumer-class weighted adjustment basis are available or will be made available.
TLM (Transformer Load Management) data, or consumer usage data "dumped" by deliberate data mining methods to small areas is perhaps the most valuable format for historical electric load data. Some utilities can allocate billing record data to small areas as small as 100 meters square. Others can allocate them to circuit branch or even lateral areas. Either way, TLM data consist of estimates of annual peak demand based on consumer billing records (number, type, and kWh sales for consumers in that area). Such estimates are not perfectly accurate with respect to demand level (it is estimated from kWh sales) but are more than adequate for forecasting purposes. The key advantage of using TLM data is that they provide historical load data on a very high resolution spatial basis. Algorithms such as SUSAN and ETM can do a lot with high-resolution historical load trends. Geographic location of substations. Some trending methods and most simulation methods require geographic data on the location of substations and perhaps other facilities, with varying degrees of locational accuracy required Almost all utilities maintain maps or records that show the locations of major equipment installations to the level needed by any forecast method. From the standpoint of the forecast methods themselves, all function with any arbitrary coordinate system for locational data (i.e., the user can "make up" or use any X-Y coordinate system as long as it provides reasonably good identification of location and distance between substations). Use of a pre-existing, standard coordinate system is not necessary from the forecast method standpoint, although
Comparison and Selection of Spatial Forecast Methods it makes data collection, verification, and interpretation much easier from the user's standpoint. Land-use data. Some trending, simulation or hybrid methods require lowresolution land-use data, generally on a square mile basis, and to "Anderson level-1" classification. Simulation methods require landuse data or higher resolution and classification distinctions, generally on a grid basis at about 40 square acre grid size. High-resolution, monoclass methods (such as 17 in the previous section) may analyze land-use data at very high spatial resolutions (e.g., 2.5 acre square areas) but "read" the land-use data in polygon format. Generally, landuse data can be obtained in one of four ways: 1. Manual coding or digitizing, using paper maps or aerial photographs. Land-use maps of sufficient resolution for lowresolution Anderson-1 purposes are generally available in UGS maps and numerous other paper sources. Generally anything more than this requires aerial photos (satellite or otherwise). Manual coding is expensive, and error-prone. Two references are highly recommended, an IEEE paper on load forecasting data (Tram, 1983) and the manual or the "cookbook" land-use coding method in EPRI project 1979 and 2598 reports, (1990). As is described in those documents, manual land-use coding is quicker and more accurate when done at high spatial resolution, even if the application will eventually use the data at lower spatial resolution. 2. Heads-up digitizing from digital photos or satellite images speeds data entry but does little to improve accuracy. Skill based on experience and an aptitude for land-use interpretation on the part of the technician preparing the database are both necessary for high quality. 3. Geo-coded data aggregation of utility consumer data. It is almost always possible to aggregate consumer data, including counts of consumer by class, energy usage, etc., on a small area grid basis. Many utility consumer information systems can tie a consumer to a locator (X-Y coordinate, transformer, feeder segment) with sufficient locational precision to allow the consumer file to be related to a specific small area.
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Chapter 17 If not, consumers can be related to small areas using street address and reference to a geo-coded street file, a number of which are available from third-party data suppliers.6 This approach yields an incomplete land-use database. It provides information on where the utility's present consumers are located, but no information about those areas where no consumers are present. Data on vacant and vacant restricted areas is the most critical class distinction to a simulation method (see Tram, 1983). and is not provided in this procedure. Usually a merger of data developed in this way with Anderson-1 level land-use data will provide a sufficiently complete land-use database. 4. Transfer from other spatial databases. Often municipal, state or federal government agencies, other local utilities, or third-party commercial data suppliers will have land-use databases available in one of several standardized computer formats (e.g., Arclnfo). It is nearly always easier to translate format than to recreate the data. Planners should check carefully to determine when the data were originally created, when they were last updated, and how they were developed and from what sources. 5. Access to a public domain or commercial database of land uses by small area. There are numerous sources, some accessible directly over the internet, others available by order through mail or electronic delivery. While there are issues with quality and timeliness (often the land-use data is several years old), the author has found it unnecessary to develop land use in about half of domestic U.S. forecast situations done by his organization in the period 2000-2001.
Land-base data consisting of general map data, highways, railroads, and similar terrain data are required by almost all simulation methods. Generally, this includes some measure of relative size (number of lanes, traffic flow) of highways and roads, and perhaps similar data on railroad rights of way. This is most often digitized from maps or aerial photos/satellite images. Generally it presents little challenge or cost. Again, the internet is a powerful tool for finding this data. Commercial sources of much more information on roads and transportation that forecasters need are available on the Internet at nominal cost.
Publications such as American Demographics and CIS World have numerous advertisements from suppliers of such databases.
Comparison and Selection of Spatial Forecast Methods
Electric load data on a per consumer or per acre basis is required by some trending methods and all simulation methods. Depending on method this data requirement may be anywhere from only peak kW/consumer data to the database of a detailed consumer-class enduse appliance subcategory load mode. Load data are nearly always available from within the electric utility. Usually, some person or group within departments with names like Rate and Research, Consumer Marketing, Marketing, or Load Research will maintain usage data and forecasts by consumer rate class, perhaps broken down within rate class into subcategories based on demographics. If such departments exist (they do in 95+% of all utilities) and if such information is maintained (it is in about 80+% of all departments), such information should be used as much as possible - it is utility specific, and very likely accurate and consistent with other company forecasts. In cases where such data are not available, generally the cost of developing anything beyond peak kW/consumer class values cannot be justified for spatial forecasting alone. Representative data might be "borrowed" from neighboring utilities, but must be applied with care. Corporate forecast data in the form of projected values of system peak, annual energy sales, and number of consumers are required by a few trending, most multivariate, and nearly all simulation methods. This is always available from the corporate forecast or long-range financial plan, and should always be used. Regional population or employment forecasts data are sometimes used to drive a simulation program, rather than the corporate forecast. Such data are available from municipal, state, and federal Housing, Transportation, and Labor Departments, and from a variety of thirdparty data suppliers. Information on proposed or expected development, such as new malls, office buildings, and subdivisions, is available from newspapers, local commercial newsletters, and is often provided "free of charge" by developers. Such information is nearly always optimistic - developers never tell a utility the latest date they think they may complete their building - they tell the utility the earliest date they can, because they do not want lack of utilities to preclude development. Building permit data obtained from municipal records are somewhat more reliable, but generally give only a trend on construction already initiated, which is very short term.
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Year Figure 17.7 The number of lane-miles of new roads constructed annually from 1980 through 1995 and similar projections for 1996 through 2010, made by the Municipal Road Department of a city in the central United States. The forecast clearly assumes a higher level of funding than it has ever received in the past. A planner wishing to use this projection as unbiased data should scale back the timing to fit a more realistic budget estimate. (Dip in funding from 1984 through 1988 reflects the term of a mayor whose policy was budget reduction.)
Projections of new highway, bridge, and road construction are used in most simulation programs as a basis to predict development in the future (growth occurs only in locations that are accessible). Routes and timing of construction for new transportation facilities are generally available from municipal, county, and state highway and road department planning offices. These are reliable with regard to location and order of new construction, but not rate of construction, as illustrated in Figure 17.7. These plans exist at least in part for budget request purposes, and thus they show what the Highway Departments hope to have funded, not what realistically can be expected to be funded. Zoning data, including maps or geographic databases, describe present limits on land development. They are subject to change, and are therefore not a generally reliable indicator of what types of consumers may eventually be in an area. In general, the author's experience and analysis indicate that the zoning of any site is usually changed if there
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is a significant profit motive. There are law firms, architectural design and construction companies, and public relations firms which specialize in "busting" zoning restrictions. Where there is a profit, there is usually a way to develop the land for its highest value land use while still meeting environmental/political requirements (Garreau, 1991). Thus, for long-range forecasting (more than five years ahead) zoning is best ignored in many situations, and an assumption that land develops to its "best and highest" potential provides the most accurate simulation.7 It is also worth noting that in most places in the world, local zoning ordinances generally have less flexibility and longer staying power as one moves north from the equator. Throughout the southern United States the majority of local zoning classifications are transient and, generally where development potential is far outside the current zoned category, easily changed. The same is true throughout most of Mexico and Central and South America. However, in Canada, zoning is generally more rigid and permanent, and in the northern United States it tends to be less flexible and harder to change than in the southern United States. Land-use forecasts prepared by municipal, county, or state governments or quasi-governmental "regional planning agencies" are seldom reliable. Often municipal planning departments or regional development commissions will put much effort into the production of reports with titles such as Twenty-Year Land-Use Development Plan for the Greater Metropolitan Region. Typically, these reports provide detailed land-use expansion maps and tables showing what, when, where, how, and why the city will grow, on a detailed geographic basis, information that would tempt any forecaster to simply use these as the basis for the utility spatial load forecast. However, with very rare exceptions, these reports and their maps are political tools, not objective forecasts. This is not a cynical or harsh observation - such land-use projections serve a valuable purpose, for they permit the public, special interest groups, developers and politicians to interact in a democratic process, identifying a common vision of where the community's interests lie and what they jointly hope their region will look like in years to come.
7
Somewhat cynically, one could interpret this to mean "the best use of land is that which gives it the highest re-sale value." However, cynics should first read Edge City. Such policy makes for efficiency in the use of land, which can be regarded as minimizing cost and environmental impact to some degree.
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Chapter 17 But such plans are seldom realistic projections of growth. Too often they include visions of wide greenspaces, new schools and parks, uncrowded streets, and other premium community amenities that are always desirable, but not necessarily affordable. They show development where and how a consensus of political opinion hopes it will occur, not where and how it actually is most likely to develop. While the use of such plans as the basis for a spatial load forecast is not recommended, every forecaster should be aware of them, for they give an indication of the priorities of the local government. Wall Street financial analysts seldom believe budget projections made by Congress and the federal government, but they pay attention to them anyway, studying the policy and priorities within them.
17.5 SELECTING A FORECAST METHOD Criteria Influencing Selection Before deciding upon the type of computer program and database to be applied to a utility's distribution load forecasting needs, its planners should assess their requirements in order to assure that they select a method that matches their resources, data, and needs. Growth rates, lead times, planning difficulty, requirement for detail, externalities, budget, and other criteria vary from utility to utility. Table 17.7 shows factors which are most important in the selection process. Accuracy and applicability Clearly, accurate forecasting of future electric T&D demand is a primary consideration in the selection of a forecast method. Section 10.3 showed the wide variation in forecasting accuracy among available options, but accuracy is only one of a number of criteria (including cost) which need to be considered. The value of forecast accuracy should be assessed in terms of expected gain (in dollars) from the improved forecast. The present worth of this gain can then be matched against the expected cost of the method. (An example of this type of evaluation will be given later in this section.) Planning period If T&D planning is to be done over a ten- to twenty-year period, then both longrange and short-range accuracy are necessary, as is a multi-scenario forecast ability, because uncertainty in future conditions is the only certainty in the long term. On the other hand, if five years is the extent of planning applications, then the long-range forecast accuracy and multi-scenario forecast capability of more advanced methods are hardly worth the additional cost.
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Table 17.7 Factors Influencing Forecasting Selection
Accuracy and Applicability - forecasts that lead to the correct planning decisions are the whole purpose of forecasting. Planning Period - how far into the future can the method reliably project loads, and how far are forecasts needed? Resolution Required - what detail in location is needed to meet the "where" needs of the T&D planning process? Corporate Forecast Compatibility - consistency with the corporate forecast is essential for internal credibility. Compatibility with Other Planning - in particular marketing, integrated resource planning.
DSM, and
Changes in Factors and Scenarios - changes in the causes of growth and changes in future conditions may be uncertain Data Requirements - what data are available? What will it cost to get, to maintain, and to update more data as required? Robustness - the ability to tolerate reasonable "noise" in the input data is a practical consideration. Cost and Resources - what labor, information technology, and other resources are required? Documentability and Credibility - the method should be fully documented and have a credible track record. Communicability of Results - methods vary in how easy they are to understand and explain to those not involved.
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Spatial resolution requirements How much "where" information is required to support the T&D planning? As illustrated by Figure 17.6, achieving high spatial resolution is difficult - that means more costly. There is a reason high-resolution forecast techniques exist: their results are necessary and cost-justified in many cases. However, a planner should determine the minimum acceptable spatial resolution required to support the company's T&D planning goals, and focus on achieving good accuracy at that small area size. Forecast methods that work with a smaller size area will only be useful if the smaller area size improves accuracy versus the required resolution, or if it makes data collection, verification, or program use easier.8 Compatibility with the corporate forecast In general, a spatial forecast should base its overall, global trends on the utility's "corporate" forecast, used as a "driving input" (overall totals) for simulation or as a "total adjustment" target for trending. The reasons for this recommendation, along with several caveats and a discussion of adjustments that can legitimately be made to the corporate forecast to increase its accuracy with regard to spatial forecasting, were discussed in Chapters 1, 8, and 9. Very often, the format of a corporate forecast - what classes of consumer it identifies, how its data relate to peak demands: energy, seasonal, and temporal load variations, if, how, and how precisely it can be geo-coded and related to small areas - can have an impact in shaping the selection of a spatial forecast method. Ideally, the spatial load forecasting method should use the same classes, format, and coordinate mapping system used in the corporate forecast. Practically, some differences will no doubt exist, but they should be studied beforehand and the cost, time, and accuracy implications (if any) taken into account. Compatibility with other planning functions Increasingly, T&D planners are being asked to coordinate their planning with other activities in their company. This is particularly true if the utility practices integrated resource planning (IRP), in which T&D and demand-side management (DSM) expenses are compared and balanced for effectiveness. The load forecast serves as the common ground upon which a coordinated plan of all the resources and concerns is studied. To perform this expanded function, the T&D planning forecast must be compatible and consistent with both T&D
8
Which can be the case. Many basis simulation methods are easier to calibrate and their database is easier and quicker to obtain and verify if done at high resolution (see Tram etal., 1983).
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planning needs and those of other functions such as DSM, service quality planning, distributed generation planning, and market/opportunity planning. Usually, this means that some form of end-use load analysis is necessary, as most of the other planning mentioned in the paragraph above includes consumerclass usage based evaluation. Among other issues, this implies an expansion of the number of types of consumer classes required in the T&D forecast (see Chapter 11, Table 11.1 and associated discussion). Regardless, the best time to "build in" compatibility with other functions is before the method, classes, spatial resolution, time periods, level of detail, and other factors for the spatial load forecast have been established. Changes in growth conditions and multi-scenarios These two items are closely related, but in fact they stem from slightly different planning concerns. To begin with, it is often recognized that the future conditions shaping growth will be different than they were in the past. For example, a large military air base in the region may be scheduled to close. Even in the presence of continued growth in other segments of the regional economy, a base closing will have a negative impact in several ways, but it could have positive impacts in others, particularly if the base site is sold and made available for development. Regardless, it is clear that conditions will be different than in the past, so trending may be inappropriate, for it implies that system conditions will be similar to what they were in the past. A simulation method, at least a basic type which can react to changes in conditions such as an air base closing, would be a better choice.
Table 17.8 Factors Indicating Extrapolation May Be Unreliable Seasonal peak changing from summer to winter or vice versa. Major DSM or usage change program sponsored by utility. Addition of or change in major employer(s) in region. Addition of major new highway, bridge, or mass transit. Relocation of a port, airport, or other major infrastructure. Significant change in relative property tax rates among sub-regions. Changes in restrictions to growth (environmental, zoning). Region "uses up" available land and must change growth pattern. Municipal government declares inner-city redevelopment program.
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A somewhat different situation develops when planners are uncertain about if, whether, and how conditions may change in the future. The need to model variations in future conditions also precludes trending methods and means a simulation method should be used. However, not all simulation methods are capable of multi-scenario modeling - they vary greatly in ease of use and range of conditions they can embrace. A simulation method that can model base case conditions with the local air base deleted may not be suitable for multi-scenario analysis involving shifts in population demographics, highway construction schedules, and other changes. Table 17.8 lists the types of changes in growth factors that can invalidate the basic assumption buried inside all trending methods, that the process of growth and change observed in the historical data will remain constant in the future. Data requirements Available data and the cost of data gathering and verification are key factors in any selection process. As shown earlier in section 17.3, data collection is the major component of cost in some forecast methods. If the data required for a particular method are simply not available, then that precludes that method's use. But very rarely is data absolutely unavailable - usually almost anything needed for spatial forecasting can be gathered with sufficient effort. Therefore, the cost of various data sources must be weighed against the benefits that accrue from their enabling better forecast methods to be used. Sources, quality, and timeliness of available data vary tremendously among electric utilities. Some have timely and accurate data on consumers, land uses, end uses, appliance market shares, demographics, employment and labor, system load curves and equipment readings, and everything else required by the most advanced simulation methods, already on hand and available company-wide from a central information system. In such cases the incremental cost of preparing the spatial and temporal databases required for application may be very low. However, a few utilities are at the other end of the data spectrum, with consumer data limited only to billing data, and with little more in the way of load data than annual peak readings from "tattletale" current meters on major substations and transmission lines - readings that are often imprecise because of infrequent checking and calibration, and which never provide the time of peak, but only the amount. Here, the cost of "upgrading" to even one of the advanced forms of trending might be considerable. Therefore, the cost of data collection for spatial forecasting must be judged with regard to utility-specific availability, conditions, resources and support costs, and weighed against the need and benefits of its usage. In searching for the lowest cost data/forecast solution, planners should not forget an often attractive alternative to developing data in house - buying it from third-party suppliers. In almost all cases, the land-use, consumer, demographic, appliance, and load curve
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data necessary to support any of the simulation or multivariate methods are available for purchase from commercial suppliers. The most common error in evaluating data needs, however, is failing to look for economical sources of the data needed within the utility. T&D planners are most familiar with the historical peak feeder and substation load readings available at nearly every utility, and unfamiliar with consumer, load research, and marketing data. In many cases, the land-use, zoning, demographic, and other spatial information needed for simulation is available at low cost within the utility, or from local governments or other utilities. But there are cases where essential data may not be available, and the higher data needs for simulation always represent a higher handling and verification cost. In addition, availability of data developed for another planning purpose does not guarantee that it will completely meet T&D planning needs. Issues of timeliness (how recent is the most recent data?), periodicity (how often is the data source updated?), definitions (does "peak demand" here have the same meaning as when used in T&D planning?), and verification quality (exactly what does "verified accurate" mean to the people who gathered the data?) need to be examined, and the cost to modify or bring the data up to T&D requirements on a continuing basis determined. Robustness Robustness - insensitivity to noise in the data or the occasionally missing data point - is a desirable trait in any practical software system, for data are never perfect and occasionally far from it. Insensitivity to data error depends on both the inherent robustness of the mathematical procedures themselves (some types of calculations are more sensitive to error than others) as well as how those procedures are implemented as a computer program. Spatial load forecasting algorithms vary widely with regard to how well they can tolerate noisy data and missing data points. Among trending methods, polynomial curve fitting methods, particularly those with high order (cubic or higher) terms, tend to be relatively more sensitive to noisy data (and particularly missing data points), while the clustering and pattern recognition methods are more robust. With curve fitting methods, a useful tactic in the presence of noisy data or missing data elements is to reduce the order of the polynomial being fitted - for example, substituting a second order polynomial for the more often used cubic order function. Generally, spatial simulation methods are very robust with regard to noisy small area data, mildly incorrect geographic data of any type, and missing data points in the load curves. In this regard they are among the most data-error tolerant of planning methods available. A point generally not appreciated is that spatial frequency domain implementation of the small area preference map calculations (see Chapter 14) not only decreases computation time, but also cuts
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round-off error and sensitivity to data noise substantially (Willis and Parks, 1986). Simulation methods that use distributed urban pole computations are also much more robust than those that do not. However, the data sensitivity of the various urban models and the end-use load curve models employed in simulation methods varies widely, some urban models developed for other industries and forecasting purposes are not robust with respect to electric utility applications (Wilreker et al.,1977; Carrington, 1988). Single-stage Lowry models are generally more robust than multi-stage, but multi-stage models may still be preferable.9 Some commercial spatial load forecasting and T&D planning software systems include filtering routines, which at the option of the user can be applied during both the frequency domain computations and during temporal load curve analysis, to detect and "repair" certain types of data noise and omissions. Benchmarks indicate these work well, but their exact nature are considered proprietary by their manufacturers. To the author's knowledge no published reference on these very interesting additions to simulation exists. Cosf of application As shown earlier in this chapter, cost of application varies as much as accuracy among available spatial forecasting methods. A forecast method must fit within the budget and should be selected with an eye on overall forecasting resource limits. Absolutely nothing contributes to poor forecasting accuracy more than attempting to use a method that exceeds the available budget - the shortcuts forced on data collection, calibration and usage when insufficient time and resources are available destroy accuracy and usefulness. If the available budget does not permit quality collection and verification of the data, proper training and "learning curve" time for the staff, while still leaving sufficient resources for application and interpretation of results, then it is best to accept a less demanding method even if it is inherently less accurate or applicable.10
9
This must be kept in perspective. A robust technique shows relatively little change in computed results when the input data are contaminated with errors. Therefore, a method that produces poor results with good data, and the same poor results with error-filled data, is considered robust. The multi-stage Lowry model's results degrade more quickly than the single stage's in the presence of increasing amounts of data error, but because it started out with more accurate results, it could still be as good or better when both are using the same, error-filled data. 10 Actually, the recommended procedure is to determine what method is best overall (as will be illustrated in this section) and then convince management to devote the resources required. Often, however, budget and resources are constrained and planners must do the best they can with what is available.
Comparison and Selection of Spatial Forecast Methods
547
Documentability, credibility, and communicability Forecasts are the "initiator" of the planning process - they identify a need for future facilities and are often viewed as the "cause" of the capital expenses put into the future budget. Very deservedly, they receive a good deal of attention from upper management, who seek confidence that the needs identified in the forecasts are real and that the expenses are necessary. The resulting plans often call for rights of way and sites that will be opposed by local community groups and interveners on the basis of cost, inconvenience, and esthetics. Lastly, regulatory agencies pay close attention to both expenses and public concern, so the forecast that initiates the planning process will be examined carefully and may be questioned heavily. For these reasons, a very important aspect of forecast method selection deals with documentation, credibility, and communicability. Nothing is better with regard to these criteria than a forecast method with a long history of proven success in similar forecast situations, and with a format and output that are easy to communicate and which appeal to intuition and familiar insight. Documentability. At a minimum, every power delivery planner should make certain that all methodology is fully documented. This means having an identified methodology and procedure for its application, including 1. A spatial forecasting method using a fully disclosed procedure, hopefully one well proven and published by other parties, not just the planners' own company 2. Documented sources of data and standards for its completeness, timeliness, and verification. 3. A procedure for tracking and documenting "what we did" in the course of preparing a forecast. "Ad hoc" forecasting and seat-of-the-pants methods do not meet these requirements. Neither do non-analytic methods, computerized or not. A computer method that is well-documented in technical and scientific literature is a good start toward meeting the goals listed above, but the utility must establish procedures for items 2 and 3 and follow through. Credibility. Documentation does not make a utility immune to criticism or prevent the occasional "defeat" in the public arena. However solid documentation and record keeping of the forecast method, the procedure for its application, and the quality control that surrounds both go a long way toward bolstering credibility. Nothing contributes quite as much to the credibility of a forecast as the methodology's proven track record of success at other utilities. Publication of the method and its evaluation in major reviewed technical journals such as IEEE Transactions is also meaningful - the technical review process maintains a
548
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quality control on the legitimacy of technical claims and the validity of testing procedures used. Communicability. Usually, opposition to a utility plan will focus on the forecast, not the plan itself. Neighborhood leaders opposed to a transmission line through their backyards are more likely to argue that the forecast is wrong (i.e., the line isn't needed) than to quibble with the engineering calculations that identified the line as the best solution to the forecasted demand. In such situations, a forecast procedure that is difficult to explain, or whose mathematics are impenetrable without special study is a severe liability. Trending methods, no matter how "smart" and proven, and even if well applied and verified through rigorous mathematically correct means, remain a "black box" to non-technical people. By contrast simulation methods have a very great advantage with regard to communicability of forecast results. By putting its forecasts on a base of land usage, simulation forecast results can be explained with the aid of colored landuse maps, graphs showing population growth, and similar exhibits that have a broad appeal and are easily understood. Even the pattern recognition, urban pole, and urban models within a simulation algorithm can be summarized in a way that appeals to the experience and understanding of most people. Not only does such communicability of land-use-based methods help convince others of the validity of a forecast, it is often a great aid to the planners themselves. Nothing helps identify set-up errors, transposed data, or simple poor application faster than a strong intuitive appeal in the format of the forecasted data. A forecast that communicates well, both in complete output and in appeal to intuition and experience is valuable for this reason alone. 17.6 EXAMPLE SELECTION OF A SPATIAL FORECAST METHOD BY A UTILITY This section summarizes the evaluation and selection of the most appropriate spatial forecasting method for a particular utility planning requirement. In order to demonstrate a comprehensive analysis using "real data" for a utility forecasting situation that is thoroughly documented, this narrative will apply this method to Chapter 11 's Springfield Light and Power and Susan, its newly promoted Supervisor of T&D Planning. The method outlined here is a recommended procedure and the values used throughout are realistic. Promptly upon being put in her new position, Susan vowed to obtain a computer and software to perform all future spatial forecasting work, motivated mostly by a desire to minimize the labor required rather than to improve accuracy. (Like almost all planners, Susan was convinced that her judgmentbased manual forecast was different from all the others, and quite accurate11).
She is wrong.
Comparison and Selection of Spatial Forecast Methods
549
The question is which load forecasting method to apply. Susan and the group she supervises set out to determine what is best for SL&P and their particular planning environment and situation. Susan's method will be to evaluate the overall present worth benefit versus cost of the forecasting methods available to SL&P. She will determine an estimated future savings due to the improved planning possible with a better forecast, and weigh that against the total cost of application. Her analysis will include the nineteen methods studied earlier in this chapter and a "no forecast" option as well. Intangible Benefits Going into her evaluation, Susan is not certain she will pick the forecasting method with the highest benefit-to-cost ratio or the greatest overall savings. She recognizes that the methods she is evaluating vary greatly in how they satisfy several intangible criteria that are important to her and her company. While she can't put a dollar value on these benefits, if the additional cost of "buying" a method that satisfies these intangibles is not much more than for a basic method, she may opt to do so. The intangibles she values most are communicability and credibility. As an experienced planner, Susan has seen her share of justification battles. She appreciates the credibility that a forecasting method with a good track record and considerable published technical documentation will bring to the defense of her plans. In addition, she appreciates the potential communicability of a landuse/end-use method. The maps of land-use expansion, the tables of consumer count growth, and the graphs of changes in future electrical usage are useful exhibits whenever she is explaining, justifying, or defending her plan, whether it is before her own management, representatives of city council, local community groups, or the state regulatory agency. Nothing demonstrates more clearly the need for new T&D facilities than a map of future land-use expansion, particularly a beautiful, multi-color, high-resolution map produced by a credible computer program. This will not end criticism, she knows, but it is hard to refute if done well. Initial Screening Even though there are at least nineteen published and widely used forecasting methods available, as described earlier in this chapter and in the references, Susan narrows her evaluation to only six among them. These include manual simulation (selected because that is "the way we've done forecasting in the past") and methods 5, 9, 11, 12, and 17. (When this analysis was done in 1996, methods 18 and 19 were not yet available commercially.) She picked these five because one of this group outperforms the other twelve methods she could apply, regardless of what level of accuracy is desired, as shown in Figure 17.8.
Chapter 17
550
cL° O
2 1
"?
3
"" °
4 X
Q.
E o> c o 'c ^ c
s
x
6
10
K
x
x
8 .9 x s
11 14 12
16 13 15
E 0)
^^
"ro
O) 0)
z
-v
17 ^ x
0
10 20 30 Cost of Application - ($1000)
^
40
Figure 17.8 Data from the evaluation in section 17.3. SL&P planners pick methods 5, 9, 12, and 17 because these methods lie closest to the dashed line and thus represent the best cost-performance combinations. To this they add method 11 because they believe it may be better than rated here for their particular situation.
While Susan believes SL&P's costs and benefits will be a bit different from those represented in Figure 17.8, she doesn't believe they will differ so much that she need consider all of the others as options. Methods 5, 9, 12, and 17 were selected because they cover the field with respect to performance/cost.12 Method 11 was picked because it is a simple, inexpensive simulation method and she feels it might do a bit better at SL&P than in the tests on systems A and B. In addition, she and her colleagues will evaluate "no forecast" as an option, because they want to be able to show management what "doing nothing" would cost, so their analysis will leave no doubt that SL&P should pick something over doing nothing. However, they are puzzled over just what "no forecast" means. It could mean doing no planning at all, or using today's load levels for the future loads in what planning they do. Ultimately, they decide that "no forecasting" simply means they would straight-line historical peak load trends on a feeder basis - as one colleague of
12
The reader who examines Figure 17.8 closely will observe that method 11 did not score that well with respect to the other methods. However, Susan knows it is the simplest simulation method she could consider, a computerized form of her manual method, and has decided to examine it on that basis.
Comparison and Selection of Spatial Forecast Methods
551
Table 17.9 Forecast Methods that Passed Initial Screening Evaluation Method 1 Method 5 Method 9 Manual 10 Method 11 Method 12 Method 17
Polynomial curve fit ("no forecast") VAI-template trending LTCCT trending Manual simulation 2-2-1 simplistic simulation 2-3-2 the basic, full simulation method 3-3-3 comprehensive simulation
Susan points out, the feeder peak load readings for historical trending are readily available and cost SL&P next to nothing to prepare, and "how hard can it be to straight-line a graph of historical load?" Susan points out that in that case they might as well enter the data into a spreadsheet and do a polynomial curve fit to the data, which is essentially method 1 in Table 17.4. Thus, they decide that the accuracy and cost of method 1 will be used to represent "no forecast." They are left with the methods shown in Table 17.9 to evaluate in detail. Estimation of Cost to Apply Each Method While Susan was willing to use "generic" cost evaluations in her screening, she decides to evaluate the cost of application for the seven methods selected in the screening in detail, and specifically with data from her company. She intends to evaluate hardware, software, and purchased data costs, estimated engineering labor at $65/hour and technician labor cost at $50/hour (these are low and probably represent marginal rather than fully burdened hourly labor costs, but they are the numbers she has decided to use). The costs she evaluates are as follows.
Data Susan expects that data may be one of her largest costs in forecasting. She has her staff estimate the cost for SL&P to develop and maintain the data required for each of the items needed by any of the forecast methods. They conclude they have all the data for any trending method on hand, and only need to input it into the forecasting method and check it once entered. Land-use and geographic data for the simulation methods, however, are unavailable within the utility or from the city or other local utilities. They will have to develop those themselves. They conclude with the data collection times shown in Table 17.10, similar to Table 17.5 shown earlier, but based on SL&P's specific situation and the costs to develop data for their system in particular.
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Table 17.10 SL&P Evaluation - Data Requirements by Data Type Type Data Feeder peaks Subst. peaks X-Yofsubst. Low-res land use Land use Hi-res land use Land-base Cust. peak kW Load curves End use Corporate frcst.
Prep. Hrs. SL&P
16 8 1
1
5
X
X
Method 9 10
11
12
17
X
X
X X
80 160 200 16 16 40 50 24
X
X
X
TOTAL hours, data collection
40
40
41
X
X
X X X
X
X
X
X
X
X
X
144
160
240
298
X
X
X
X
Hardware SL&P will need a computer to run software to apply whatever method it selects. Susan understands that she probably won't use 100% of the computer's time on spatial forecasting. In fact, she is certain that she will not, but hardware cost will be a minor element in her evaluation. She sets aside $3,500/year as the cost of owning, maintaining, and replacing on a three- to four-year rolling basis a highend PC or low-end workstation and figures that is representative. Software SL&P must purchase or develop the required software for whatever option it selects. Susan assigns one of her people to look into both options for all seven methods. He reports that the trending methods are straightforward enough that any could be developed and maintained in-house using general-purpose software, but this would require effort and raise slight credibility problems regarding how exactly the SL&P method tallies with published techniques and tests. Still, in-house implementation is his recommendation for trending. He determines that the number of weeks required to write, test, and document a trending method will be two, seven, and eleven weeks, respectively, for methods 1, 5, and 9, and annual maintenance would be one week per year in each case.
Comparison and Selection of Spatial Forecast Methods
Table 17.11 Costs for Forecasting Programs Program for Method 1 Method 5 Method 9 Manual 10 Method 1 1 Method 12 Method 17
Initial Cost Annual Upkeep $5,200 $18,200 $23,400 0 $8,000 $30,000 $60,000
$2,600 $2,600 $2,600 0 $960 $3,600 $7,200
Table 17.12 Costs for Training Personnel Forecast Type Method 1 Method 5 Method 9 Manual 10 Method 1 1 Method 12 Method 17
Initial
Annual
$520 $5,200 $5,200 $10,400 $10,400 $15,600 $15,600
$260 $2,600 $2,600 $5,200 $5,200 $7,800 $7,800
Table 17.13 Cost to Perform Forecast Annually Forecast Type Method 1 Method 5 Method 9 Manual 10 Method 1 1 Method 12 Method 17
Hours Reqr'd 40 80 100 600 200 300 300
Annual Cost $2,600 $5,200 $6,500 $39,000 $13,000 $19,500 $19,500
553
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Most of this time is not that required to write the "programs," but to test, verify, and document them. Simulation programs seem to be complicated enough that they must be purchased from a commercial supplier. Commercial software is available to perform methods 11, 12, and 17 at a cost of $8,000, $30,000, and $90,000, respectively, from different vendors. Annual software maintenance charges run 12% of initial cost. Evaluating in-house development of the trending methods at $65/hour, SL&P comes up with the costs shown in Table 17.11. Training and "learning curve" time Estimated "learning time" for method 1 is one day; method 5 or 9, two weeks; and method 10, four weeks (Susan is an expert on that but will have to train someone else). Method 11 would take four weeks to learn, and methods 12 or 17 would take six weeks. Annual training costs, for renewing familiarity with the software and training new employees, are estimated at half of the initial training effort. Table 17.12 lists these training requirements, at $65/hour. Application of the forecast methods Susan believes that it will be prudent for her company to re-examine and update its spatial forecasts on an annual basis, and that she will also probably face one alternative scenario to evaluate each year. She decides to allow labor estimates for producing three full forecasts each year on the basis that in the course of doing the revision of the base forecast and a scenario, her people will probably often produce a forecast eventually deemed unrealistic, wrong, or in need of revision. Her estimates of the engineer time involved in running each of the forecast methods are shown in Table 17.13 Final cost estimates for application Table 17.14 includes initial and annual costs assembled from all categories. Shown in the rightmost column is the present worth of all the initial costs plus all annual costs over the next ten years, using an annual discount factor of 10%. These are SL&P's costs for application of each method over the next decade. Susan's choice of a ten-year period for her present worth analysis of future costs is unusual. Many utility planning evaluations use a twenty- or even thirtyyear time frame for present worth analysis. She choose the shorter period because she knows her company's management believes it is impossible to predict the long-term business environment it will face in a de-regulated utility environment. Pragmatically, she realizes she has a better chance of her recommendation being accepted if she does her benefit-cost analysis only over the next decade.
Comparison and Selection of Spatial Forecast Methods
555
Table 17.14 Cost to Apply the Forecast Methods Data
Hardw.
Present Annual Costs Softw. Trning. Applic. | Worth
520
2,000
3,500
2,600
260
18,200
5,200
2,000
3,500
2,600
2,600
5,200 | 130,900
23,400
5,200
2,000
3,500
2,600
2,600
6,500 | 144,900
10,400
7,200
-
5,200
39,000 | 357,800
Forecast Method
Softw.
1
5,200
5 9
10
Initial Cost Training
2,600
79,800
11
8,000
10,400
8,000
3,500
960
5,200
13,000 | 225,600
12
30,000
15,600
12,000
3,500
3,600
7,800
19,500 I 359,200
17
60,000
15,600
14,400
3,500
7,200
7,800
1 9,500 | 429,800
Estimated T&D savings due to improved forecasting One of the most difficult aspects of evaluating any planning methodology is estimating the savings that accrue to its application. It is difficult to judge how much one particular planning method saves over another, because it is never possible to look forward and say with certainty that specific mistakes would be made or avoided were certain planning used. Beyond this, it is often not politic to identify "mistakes" made in past plans which could be "corrected" with newer planning methods. Susan recognizes this is the case at SL&P - many of her present colleagues and several upper managers (who she must sell on her idea for computerized forecasting) are the very persons who diligently did the best they could to prepare those past plans. Pointing out their mistakes in her evaluation is hardly going to garner their favor. Susan also is not certain that a method of evaluating unproved planning by looking at "past mistakes" is a good way of estimating savings, anyway. Instead, she decides to apply the published statistics and error evaluations of the methods she is assessing to her projected T&D budget to estimate the savings due to better forecasts. From the description of the ACap error measure given in section 17.3, the discussion of error impact and the Ux error measures in Chapter 8, and technical references on forecast error and its impact on T&D planning (see Willis, 1983; Willis and Parks, 1983), she understands that either ACap or a weighted average of the Ux values is a reasonable estimate of the percent of T&D requirements that will be wrongly estimated due to a poor forecast. Thus,
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she decides to estimate the savings from use of one method over another as the difference in their ACap values times some portion of her future T&D budget. She begins by determining the correct ACap, or error impact, values for her application at SL&P. To do so, she •
Averages the ACap values from cases A and B in Table 17.4. Springfield is not a large city, as was test utility A, but it is not entirely a rural system like utility B, so she just averages the two ACap values.
•
Cuts this averaged ACap by 2/3, because (1) she believes that unlike the tests in section 17.3, she will see forecast errors in time to make some adjustments, and (2) she plans to do multiscenario planning to minimize risk in her plans.
This leaves her with the ACap values shown in Table 17.15. The final column shows the margin of improvement over "no forecast" that she can expect in her T&D planning as a result of applying one of the other forecasting methods. Next, Susan and her staff have to determine what portion of their company's expenses might be affected by the margins of improvement due to load forecasting listed in Table 17.15. One item that always gets her management's attention is SL&P's capital T&D budget. With an expected increase in system peak from 315 MW peak to about 400 MW in the next ten years (see Chapter 11), her company estimates its T&D expansion budget for the next ten years at about $22,500,000. That works out to $225/kW, a fairly lean expansion budget for a small, growing system like Springfield's.
Table 17.15 Calculation of T&D Planning Impact of the Various Forecast Methods Avg. Times 1/3 Margin Method 1
37.0 %
12.33 %
-
Method 5 Method 9 Method 10
26.0 %
8.66 %
3.66 %
23.5 %
6.83 %
4.25 %
25.5 %
8.50 %
3.83 %
Method 1 1 Method 12
22.0 %
7.33 %
5.00 %
18.0%
6.00 %
6.33 %
Method 1 7
11.0%
3.66 %
8.66 %
Comparison and Selection of Spatial Forecast Methods
557
Many of the expenses included in that $22,500,000 are unavoidable and cannot be decreased through improved planning. For example, SL&P has to run new service drops to and install a meter at every new consumer, and it has to run a primary voltage lateral along ever street or alleyway. No forecasting method can affect those costs in any meaningful way. The improved planning will influence the siting, sizing, and timing of SL&P's transmission, substation, and feeder plans, portions of the system which together constitute about 60% of the total budget. But part of SL&P's future transmission and substation expenses are already "committed" - substation sites and rights-of-way have been purchased, equipment has been ordered, and plans have been filed with various agencies who must approve them. It would not be easy or economical to change those elements of the transmission and substation plan for the next few years. Therefore, improved planning cannot affect them. Taking all of this into consideration, Susan decides that the costs that can be influenced by the spatial load forecast and its improved impact on planning include those shown in Table 17.16. Potentially, out of more than $22 million in expected budget, only $9.52 million (42%) can be reduced through improved planning methods, or roughly $952,000 per year over the next decade. At an annual discount rate of 10%, that annual level of expense for the next ten years equals a present worth of $6.4 million.
Table 17.16 Estimated T&D Budget Influenced by Forecasting, Springfield System, Next Ten Years System Level
Budget
Transmission 2,950,000 Substations 3,100,000 Primary Feeders 6,000,000 Laterals 2,475,000 Serv. Transf. 3,025,000 Service 2,925,000 Meters 2,050,000 TOTAL $22,525,000
% Affected 50% 66% 100% -
Potential $ $1,475,000 $2,046,000 $6,000,000 $9,521,000
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Susan reduces this figure by a further 17.4%, to $5.29 million. Her reduction is the equivalent of discounting the $6.4 million two years further into the future. She justifies this to her staff by pointing out that whatever new method they select today will take a year or more to work its effect into the SL&P system. Her reduction in the influenced budget moves the projected expenses influenced by her decision (and thus any savings worked into them by an improved planning method) further out in the future to allow for this factor. This last reduction is a very conservative step, added on top of other conservative measures she has taken in her analysis, but she is building a large comfort margin into her decision-making. Evaluation of Benefit/Cost for the Candidate Forecast Methods The adjusted ACap values from Table 17.15 can be applied directly to this $5.29 million to determine the impact of their respective forecasting methods. As section 17.3 explained, ACap is not a statistical error measure, but an estimate of the percent impact on budget that poor forecasting makes on a power system. The values listed in Table 17.4 are not for the SL&P system, but they are from very systematic tests on systems composed of equipment and designs not unlike SL&P's. They have been reduced in Table 17.15 to account for realities and differences between the test utilities and SL&P, until Susan and her staff believe they are realistic. Thus, the difference in budget impact between method 5 and method 1 is method 5's margin of forecast performance improvement as shown in Table 17.15, 3.66%, times the $5.29 million present worth of T&D expenses, giving $193,600 in expected T&D savings. However, the additional cost of using method 5, $51,100 (the difference between the cost of method 5 and the cost of method 1 in Table 17.14), has to be deducted, for a net savings of $142,500. Table 17. 17 shows a similar calculation of net present worth savings for the seven forecasting methods. The second column from the left gives the ACap margin of forecasting performance (from Table 17.15). The third column shows the computed T&D savings obtained by multiplying the ACap margin by $5.29 million. Column four gives the cost margin (present cost of applying the method from Table 17.14, minus that of method 1). Column five subtracts this cost from the T&D savings to produce the net savings. The final column shows the benefitcost ratio (column 5 over column 4). These are the raw evaluations that Susan's staff assembles. Method 9, LTCCT trending, is evaluated as best, saving $41,000 more than any other method. To their chagrin, method 10, the method that their new boss worked so hard to apply, and whose results were so highly regarded by upper management, appears to be costing their company $75,000 present worth. Their evaluation shows it is actually worse than doing "no forecast" - it incurs a tremendous labor cost for a very slight improvement in accuracy over that base method. Slightly embarrassed by this turn of events, they decide they have no choice but to show the results anyway.
559
Comparison and Selection of Spatial Forecast Methods
Table 17.17 Cost Versus Savings for the Forecast Methods Forecast Margin %
T&D Savings $ -
Method 1
Cost above #1 $ -
Net Savings $
BenefitCost Ratio
-
-
Method 5
3.66
193,600
51,100
142,500
3.8
Method 9
4.25
238,100
65,100
173,000
3.7
Manual 10
3.83
202,600
278,000
(75,400)
.72
Method 1 1
5.00
264,500
145,800
118,700
1.8
Method 12
6.33
334,900
279,400
55,500
1.2
Method 17
8.66
458,100
350,000
108,100
1.3
To their surprise, Susan is not the least bit dismayed. The evaluation looks good, she says, but it is a pure engineering analysis based only on forecasting accuracy. She points out that method 10 clearly had a positive value to the company, based on its use in her earlier forecast. It permitted SL&P to study the pickup truck factory scenario in a way it otherwise could not, and the detail, maps of land use and tables of consumer counts method 10 produced meshed well with the format of SL&P's corporate forecast, which helped her and other members of her company apply it well. They were also easy to understand, which went a long way toward gaining management's understanding of the forecast and its implications. In other words, its multi-scenario capability and communicability - features she and her staff had previously identified as intangibles - had sufficient value to make method 10 an asset in the company's eyes, in spite of its high labor costs and slightly below average forecast accuracy. Therefore, those intangibles must outweigh the $74,500 negative value determined for method 10. Susan and her staff decide to assign a value of $74,500 to those intangibles and see what happens in the ensuing analysis. They believe that methods 1, 5, and 9 have no ability to deliver those intangibles, while methods 12 and 17 can meet them fully. Method 11 can satisfy those needs only partially (its multiscenario capability is limited), so they give it an "intangibles credit" of one-half, or $37,700. Adding these values to the "T&D Savings" column and recomputing their results gives their final evaluated costs, shown in Table 17.18.
560
Chapter 17 Table 17.18 Adjusted Cost versus Savings from the Forecast Methods % Forecast Margin Method 1
T&D Savings -
Cost. Above #1 -
Net BenefitSavings Cost Ratio -
1.0
Method 5
3.66 %
193,600
51,100
142,500
3.8
Method 9
4.25 %
238,100
65,100
173,000
3.7
Manual 10
3.83 %
278,000
278,000
-
1.0
Method 1 1
5.00 %
302,200
145,800
156,400
2.0
Method 1 2
6.33 %
410,300
279,400
130,900
1.5
Method 17
8.66 %
535,500
350,000
183,500
1.5
Her staff shows her their attempts to put a dollar value on the intangible benefits through other means. Many of the intangibles simply cannot be assigned a value, they had decided, including the possible improvement in public relations and regulatory credibility that might accrue from a method with greater communicability and appeal to intuition. In the past, both Susan and the members of her staff have had to meet many times with developers, community leaders, or sometimes individual consumers to explain, justify, and sometimes defend the company's plans. They know that improved communications and credibility will be worth something; they just can't figure a way to put a dollar value on it. But suppose the ability to study multi-scenarios quickly so they can answer "what if questions from interveners and regulatory staff, the improved documentation and track record, and the improved credibility and understandability of a new forecast method would permit SL&P to avoid just one bad "intervener entanglement" over the next decade. The company has had several such experiences in the past decade, cases where extra time, study, and sometimes legal fees had to be devoted to justifying a new site or facility. Susan's staff took a typical case in which they had a two-year delay in getting a substation site approved, and looked at its costs. The time, travel, extra study, and legal fees billed to that project ended up costing $127,000. Further, SL&P paid an estimated $25,000 in overtime and similar expenses to complete the substation at an accelerated rate once it was finally approved. That totals to over $150,000 in additional costs, and does not include any assessment of the higher losses and equipment stress due to SL&P's having to overload other equipment
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during the two years that much needed new substation was not yet available, or the fact that they eventually had to modify their plan and spend an additional $47,000 on slightly different equipment and ROW than they had originally wanted. An improved load forecast would probably not have permitted SL&P to avoid that controversy altogether, but it would have reduced its impact. The point is, it seems clear that the $75,400 value assigned to the intangibles is reasonable, and maybe even low. Regardless, Table 17.18 shows the final evaluation figures that Susan and her staff decide to use. Method 17, the very comprehensive simulation carried out with a commercial software package, wins by a narrow margin. If the intangibles are valued more heavily (and Susan and her staff believe they probably are worth more), then its margin of victory would be greater. The entire evaluation was slightly conservative. Susan believes it is valid and feels very comfortable in making her recommendation for method 17. After weighing the options and asking numerous questions directed mainly at seeing whether method 12 (the alternative commercial software that costs only half as much) would be as useful, her management approves her recommendation. Expanded Evaluation The example above illustrated the overall recommended procedure of evaluation and comparison, the most important elements of which are • Comparison of savings and costs on an equal basis for all methods. • Use of only data and test results drawn from technical journals and similar credible and outside sources. • Present worth evaluation which does not rely too heavily on long-term benefit/cost assessment to make its case. • Evaluation of all costs involved, based on the utility's specific data, resources, computer, personnel, and forecasting needs. • Acknowledgment of the "intangible" aspects of forecasting including the need to work with other departments and communicate its results. The evaluation discussed above could have included more aspects of SL&P's potential savings and examined those it did include more thoroughly in some stages. These are discussed in the sub-sections below.
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T&D system losses and O&M costs Improved planning will reduce both T&D system losses and O&M costs by slight but noticeable amounts, yielding an additional predicted savings for improved forecast methods. Reduction in losses cost is a very well-documented aspect of planning - high losses are one sign of a system that is poorly designed or that has had to be "patched up" at the last minute. Table 17.4 included a ALosses column in the evaluation of all forecast techniques. Impact on losses is also well documented in the technical literature (see Willis and Northcote-Green, 1984). SL&P could have looked at its demand and energy cost of losses on the T&D system, in much the same manner that the discussion above examined impact on capital budget - reducing the ALosses values in the tables to reflect SL&P realities, evaluating the losses impact by level of the system,13 assessing present worth over the next decade. The present worth of "T&D losses that forecasting could improve" on the SL&P system - the equivalent of the $5.29 million figure for capital developed earlier - would be on the order of $2,000,000, and the planning impact of improved forecasting on losses costs qualitatively similar. As a result, the predicted savings from all forecasting methods would have increased by a considerable margin. However, to many utilities reductions in losses simply do not have the same priority as reductions in capital. Losses costs are an operating expense, usually passed on to the consumer, and despite what might be said publicly, management simply does not assign losses dollars the same importance as capital budget dollars. Susan and her staff would have done best to have included losses in a separate column. Their predicted savings would have been acknowledged by upper management and would have helped make the case. A somewhat more difficult case can be made of impact on O&M. Good planning reduces the amount of T&D facilities that are built, which reduces the amount that needs to be taken care of in the future. O&M cost savings on equipment not yet built are even further into the future, and are once again an operating expense. Susan and her staff probably would have done best to not include O&M cost analysis in their numbers, but to include "slight reduction in long-term O&M" in a list of additional benefits of the improved forecasting. More comprehensive evaluation of capital budget savings The evaluation of expected T&D capital budget shown in Table 17.16 is a fairly straightforward and realistic way to estimate savings. Expected savings is always the difficult point in any evaluation. As mentioned earlier, a more comprehensive evaluation would reinforce the credibility of the projected savings, even if it does not materially change their values. 13
As was the case with capital budget (Table 17.16), improved forecasting would do little to reduce losses on the service level of the system, but it would have a very great impact on feeder losses.
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The evaluation summarized in Table 17.16 could have been done separately for each level of the system (transmission, substation, feeders) and then those savings added, rather than by evaluating all T&D levels in a lumped manner. First, in evaluating impact for each of the next ten years, SL&P could have worked with its actual expected budget expense stream over the next ten years, rather than just an average of so many dollars per year. Second, the final twoyear discount factor of 17% which Susan added to account for "work already committed" (reducing the PW of influenced T&D budget from $6.4 million to $5.29 million), while valid, would have been much better if applied differently to each level - perhaps five years of discount at the transmission level and none at the feeder level, etc. Finally, with difficulty, Susan and her staff could have assessed the different impact of forecast improvement on different levels of the power system. The ACap values in Table 17.4 are impact assessed on an entire system. The Ux values shown give the estimated relative impact on transmission, substation, and distribution. For example, for method 5 in case A, the Ux values for transmission, substation, and feeder levels are 12%, 20%, and 36% respectively. Its advantages over method 1 ("no forecast") are 10%, 15%, and 14% respectively. 14 ACap and differences in ACap between methods in Table 17.4 are basically averages of these impacts by level, averages weighted by the relative budgets of the transmission, substation, and feeder levels. If the budgets for those three levels were equal, then the 3.66% "forecast improvement margin" computed in Table 17.15 for method 5 over method 1 would break out by level in rough proportion to the 10%, 15%, and 14% relative differences in Ux. This would give a predicted transmission level impact of Transmission impact % = 10%/(( 10+15 + 14)/3)
(17.1)
- 2.81 % and similarly values for substation and feeder levels would be 4.22% and 3.94%. Potentially, this type of analysis could be applied to any level of resolution required.
14
The improvement at the feeder level is less than at the substation level because this method, like most trending methods, does not have a high resolution capability in either its application (it was applied at only feeder service area resolution) or its algorithm, so it cannot "see" load growth effects at a really small area size very well. By contrast, method 17 has margins over method 1 of 16, 25, and 37%. Thus, it is about "60% smarter" than method 5 at the transmission level, but a whooping 250% better at forecasting loads with the detail needed at the feeder level.
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Actually performing this analysis would require SL&P to make some assumptions,15 and would involve more work, but it would allow the impact to be assessed at each level based on the expected improvement in planning of that level, which would provide an additional level of detail in the evaluation reports. This would change the results for SL&P only if it had very different relative budgets for the transmission, substation, and distribution levels as compared to utility cases A or B. Most likely, all this additional effort would not change the predicted T&D savings by a substantial amount, but its additional detail would convey to management a sense of greater confidence that the evaluation was thorough and valid. What If SL&P's Situation Had Been Different? While realistic, the above evaluation and selection applied specifically to one utility - a small city with a high growth rate and average data availability. This evaluation method can be applied to any utility, but it must be applied to specific data collection costs, system size, and T&D budget data for that utility. In addition, somewhat more care should be placed on estimated T&D budget savings than shown here - that care will not improve or change the resulting numbers by any significant degree, but it will provide a higher level of credibility in the predicted savings and justification, which are always the weakest point in any type of evaluation. If SL&P had been a smaller utility, costs for data preparation would have dropped slightly, but those for software, hardware, training and application would not have changed. Savings would have dropped considerably because a smaller system offers less potential for savings - a 150 MW system growing at 3% offers only half the potential savings of a 300 MW system growing at 3%. Had SL&P been half the size it was, methods 10, 12, and 17 would have netted a negative savings (cost exceeds savings). Even with the credits for intangibles, method 11 would have looked roughly breakeven, and method 9 would have been the clear winner. If SL&P had been twice as large a utility, cost of application would have been slightly higher (data costs would increase by about 25% but other costs would change little), but not twice as much. Benefits would have been roughly twice as much. As a result method 17 would have been a clear winner even without the "intangibles credit." Beyond that, on a really large system, the monoclass 3-3-3 method (17) would provide substantial additional benefit 15 In particular, Susan and her staff do not know the breakdown of expenses among levels of the T&D systems for utility test cases A and B. They really need data such as in Table 17.16, second column, to be able to make this assessment. In addition, they should realize that since the U x values are error measure computations, not actual impact evaluations like ACap, they are approximate.
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because it can model and forecast the complexity of a large metropolitan area better than the other alternatives. A city like Springfield is not nearly as complex with respect to growth influences as cities such as Kansas City, Denver, or Phoenix. In really large metropolitan areas, methods 12 and 17 would have substantial accuracy or representativeness advantages (their accuracy does not increase in such situations - that of other methods degrades), advantages which would increase the savings margin. Had the growth rate been less, the cost of application of any forecast method would have been unaffected, but the benefits would drop. A 300 MW system growing at 1.5% offers roughly 1/2 the potential for savings of a similarly sized system growing at 3%. If growth rate were half of what is was, SL&P would be able to justify only methods 9 or 11. If growth rate were twice what it was, only methods 12 and 17 would make any sense, because while all methods would show a positive savings, their savings would be substantially more. Different data availabilities at SL&P would have scrambled the ranking of the methods. SL&P had no access to pre-existing or discounted land-use and geo-base data - the costs shown earlier reflect its having to create that. Had they had access to land-use data at no cost or at a substantially lower cost, the simulation methods would have looked much better compared to trending. Roughly 30% of utilities have such land-use and geographic data available. A smaller fraction of utilities - perhaps 8% — do not have sufficient metered peak load data to fulfil the minimum needs of trending methods. Either feeder loads are not metered, or metered data are not checked and recorded periodically. Regardless, in such a case, trending will either be more expensive (the data must be obtained) or must be done on a substation rather than feeder basis, in which case spatial resolution and accuracy both fall. REFERENCES C. L. Brooks, "The Sensitivity of Small Area Load Forecasting to Consumer Class Variant Input," in Proceedings of the 10th Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, Apr. 1979. C. L. Brooks and J. E. D. Northcote-Green, "A Stochastic Preference Technique for Allocation of Consumer Growth Using Small Area Modeling," in Proceedings of the American Power Conference, Chicago, University of Illinois, 1978. Canadian Electric Association, Urban Distribution Load Forecasting, final report on project 079D186, Canadian Electric Association, 1982. J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabat, April 1988.
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J. L. Carrington and P. V. Lodi, "Time-Tagged State Transition Model for Spatial Forecasting of Metropolitan Energy Demand " in Electricity Modern, Vol 3, No. 4, Barcelona, Dec. 1994, E. P. Cody, "Load Forecasting Method Cuts Time, Cost," Electric World, p. 87, Nov. 1982. Electric Power Research Institute, Research into Load Forecasting and Distribution Planning, EL-1198, Electric Power Research Institute, Palo Alto, CA, 1979. Electric Power Research Institute, DSM: Transmission and Distribution Impacts, Volumes 1 and 2, EPRI Report CU-6924, Electric Power Research Institute, Palo Alto, CA, August 1990. M. V. Engel et al., editors, Tutorial on Distribution Planning, Institute of Electrical and Electronics Engineers, New York, 1992. J. L. Garraeau, Edge City, Doubleday, New York, 1991. J. Gregg, et al., "Spatial Load Forecasting for System Planning," in Proceedings of the American Power Conference, Chicago, University of Illinois, 1978. U. Grovenski, "Multivariate Trending of Distribution-Level Loads" in Correspondence of the All-Union Electrotechnical Institute, Vol 55, No. 3, Moscow, Dec. 1986. U. Grovenski, "Multivariate Trending of Distribution-Level Loads" in Electrik Modern, Vol 5, No. 2, Moscow, Dec. 1996. A.
Lazzari, "Computer Speeds Accurate Load Forecast at APS," Electric Light and Power, Feb. 1965, pp. 31-40.
I. S. Lowry, A Model of Metropolis, The Rand Corp., Santa Monica, CA, 1964. J. R. Meinke, "Sensitivity Analysis of Small Area Load Forecasting Models," in Proceedings of the I Oth Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, Apr. 1979. E. E. Menge et al., "Electrical Loads Can Be Forecasted for Distribution Planning," in Proceedings of the American Power Conference, Chicago, University of Illinois, 1977. V. Miranda et al, "Fuzzy Inference and Cellular Automata in Spatial Load Forecasting," paper submitted and accepted for IEEE Transactions on Power Delivery, Institute of Electrical and Electronics Engineers, #2000TR395. R. W. Powell, "Advances in Distribution Planning Techniques," in Proceedings of the Congress on Electric Power Systems International, Bangkok, 1983.
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C. Ramasamy, "Simulation of Distribution Area Power Demand for the Large Metropolitan Area Including Bombay," in Proceedings of the African Electric Congress, Rabat, April 1988. B. M. Sander, "Forecasting Residential Energy Demand: A Key to Distribution Planning," IEEE Paper A77642-2, IEEE PES Summer Meeting, 1977, Denver. A. E. Schauer et al., " A New Load Forecasting Method for Distribution Planning," in Proceedings of the 13th Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, Apr. 1982. W. G. Scott, "Computer Model Offers More Improved Load Forecasting," Energy International, Sept. 1974, p. 18. H. N. Tram et al., "Load Forecasting Data and Database Development for Distribution Planning, IEEE Transactions on Power Apparatus and Systems, November 1983, p. 3660. H. L. Willis, "Load Forecasting for Distribution Planning, Error and Impact on Design," IEEE Transactions on Power Apparatus and Systems, March 1983, p. 675. H. L. Willis and J. Aanstoos, "Some Unique Signal Processing Applications in Power Systems Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, Dec. 1979, p. 685. H. L. Willis and J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, May 1979, p. 48. H. L. Willis and J. E. D. Northcote-Green, "Comparison of Fourteen Distribution Load Forecasting Methods," IEEE Transactions on Power Apparatus and Systems, June 1984, p. 1190. H. L. Willis and T. W. Parks, "Fast Algorithms for Small Area Load Forecasting," IEEE Transactions on Power Apparatus and Systems, October 1983, p. 342. H. L. Willis and T. D. Vismor, "Spatial Urban and Land-Use Analysis of the Ancient Cities of the Indus Valley," in Proceedings of the Fifteenth Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, 1984. H. L. Willis, M. V. Engel, and M. J. Buri, "Spatial Load Forecasting," IEEE Computer Applications in Power, April 1995. H. L. Willis, J. Gregg, and Y. Chambers, "Small Area Electric Load Forecasting by Dual Spatial Frequency Modeling," in IEEE Proceedings of the Joint Automatic Control Conference, San Francisco, 1977.
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H. L. Willis, G. B. Rackliffe, and H. N. Tram, "Short Range Load Forecasting for Distribution System Planning-An Improved Method for Extrapolating Feeder Load Growth," IEEE Transactions on Power Delivery, August 1992. V. F. Wilreker et al., "Spatially Regressive Small Area Electric Load Forecasting," in Proceedings of the IEEE Joint Automatic Control Conference, San Francisco, CA, 1977. T. S. Yau, R. G. Huff, H. L. Willis, W.M. Smith, and L.J. Vogt, "Demand-Side Management Impact on the Transmission and Distribution System," IEEE Transactions on Power Systems, May 1990, p. 506.
18 Development Dimensionality: Urban, Rural and Agrarian Areas 18.1 INTRODUCTION Many regions of interest to T&D planners are heavily populated and as a result very well developed in terms of roads, infrastructure, and buildings. Others are only sparsely populated, and have far fewer roads and infrastructure, as well as development. This chapter looks at the spectrum of regional types from sparse to urban core from the standpoint of the process of growth, and how it is best modeled. What characteristics of the growth process are important to the load forecaster? Are there fundamental differences in how and why a rural area grows as opposed to an urban area? How and when does a "rural area" make the transition to "suburban" and what characteristics does that process have? In some ways, this chapter builds upon and can be viewed as an "advanced" discussion beyond Chapter 7. Here, the growth causes and "S" curve behavior discussed in Chapter 7 are viewed from the standpoint of "developmental dimensionality" - the complexity of spatial interaction that occurs among small areas within various types of regions. This chapter both discusses the concept and looks at the tools that forecasters need to apply when facing each type of region. Section 18.2 introduces the concepts of development dimensionality - the dimension of spatial interaction inherent in the region's spatial growth. Sections 18.3 and 18.4 then respectively look at rural and agrarian development from this perspective (urban development is examined in Chapter 19). Section 18.5 concludes with a summation of key points and some guidelines for planners. 569
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570 Table 18.1 Characterization of Regions by "Density of Development" Area
Elec. meters/mile
Unpopulated
Sparse
0
Characteristics/Comments
Totally unpopulated on a permanent basis. Transportation: none. Local economy: no "local economy." Examples: Most of Antarctica. Parts of Siberia and Sahara
.01 - .1
Unpopulated except for isolated outposts or villages. "Islands of load within an vast ocean of unpopulated land." Transportation: few improved roads. Local economy: natural resource extraction, fishing, scientific R&D Examples: central Australia, northern Canada.
.1-5
Land in the region is almost entirely used for agriculture. There are isolated towns and villages and even an occasional small city. Transportation: typically about one mile of improved road per mile2 Local economy: agrarian. Examples: most of western Kansas, southern Saskatchewan.
Rural
5 - 100
Land is settled for residential, commercial, and limited agriculture. Local economy: some agrarian, mostly regional metro area driven. Transportation: About three miles of paved road per square mile, perhaps twice as many improved roads per square mile Examples: rural areas of North Carolina, Virginia
Suburban
< 3000
Land is "fully developed," much of it purpose-planned in large tracts. Local economy is driven by: regional metropolitan economy Transportation system: omnipresent paved road network. Examples: Gary, NC; Katy, TX, Dalton, GA, Napierville, II.
Urban
> 3000
Dense development with a majority of multi-story structures. Local economy is driven by: regional metropolitan economy Transportation system: omnipresent road network, mass transit Examples: Inner 1/5 of radius of large metropolitan areas like Boston, Houston, Atlanta, exclusive of the downtown core.
Urban core > 10,000
Very dense high-rise development. Growth is three-dimensional. Land-use/consumer classes are mixed (residential, commercial, office in the same small areas, even when viewed at very high spatial resolution). Local economy is driven by: regional metropolitan economy Transportation system: omnipresent road network, mass transit Examples: Core of very large metropolitan areas like Boston, Houston, Atlanta, Chicago and San Francisco. Most of Manhattan.
Agrarian
Development Dimensionality: Urban, Rural and Agrarian Areas 18.2
571
REGIONAL TYPES AND DEVELOPMENT DIMENSION
Table 18.1 shows the spectrum of land-use densities and their major characteristics, from completely undeveloped to the densest urban cores. Although a major distinguishing feature among these categories is population density, there are other significant differences among them, one of those being electric load density. Most significant to the forecaster, however, growth and development act differently in each of these types of region - in the sense that in each type of region the growth and change are defined and limited by different forces and behave in different ways. An understanding of these regional development types, and "dimensionality" of development, can help planners and forecasters improve their ability to predict growth trends and anticipate how to plan for them. Proximity and Its Role One clear area of variation among the regional types shown in Table 18.1 is transportation infrastructure. Largely as a result of the population density variation, road network density also varies from less than .01 road miles per square mile in sparsely populated regions to more than 50 miles/mile2 in the heart of densely populated cities. In suburban, urban, and urban core areas, proximity to roads and to certain types of roads largely determines the value of individual land parcels and the purposes for which each is best suited. This more than any other single factor determines growth potential and the amount of electric load that will develop. The density of the road network in a region is a sort of "chicken or the egg" process: an area with high population density will have a dense road network, and vice versa. One grows as a result of the other, and the other grows as a result of the one. In fact, as most people and not just planners and forecasters understand, they grow up together, in a kind of mutually supporting relationship. Proximity - "being close to" - is important in the development of nearly all types of areas (residential, industrial, etc.) in all types of regions (rural, urban). But the "what" changes as one moves up the developmental spectrum. As one moves across the development spectrum, proximity or access to other locations becomes more and more dominant in determining growth of any one location. Each developed location in a sparsely populated region selected its specific site due to some unique quality of that site. It is the coldest place on earth, and thus a great place for scientific research. It is above a large underground reservoir of petroleum. Development in such areas is attracted to these unique characteristics of each site. They outweigh everything else with respect to the purpose of that site/facility including the isolation of the sites, the distances, and any difficulty that one may encounter in traveling to and from the site.
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Agrarian
Rural
Suburban
Urban
Core
High
High
=3 f« If
ll *o £ 0 O U (A
c o> a *:
!i
5.2 E
None
None
.01
1 10 100 1000 Population Density - persons/mile2 (log scale)
10000
Figure 18.1 The "what" in [proximity to . . . ] changes as one moves across the development spectrum. Development in sparsely populated regions is due to unique characteristics of the site(s), but that in urban areas is proximity to other development.
As one moves across the developmental spectrum from sparse to urban core, the importance of the special or unique natural features of a site as a factor in its development decrease, and the importance of proximity or access to other development increases (Figure 18.1). The "community" at Prudhoe Bay is located where it is only because it is near a petroleum deposit. By contrast, development in Manhattan is driven by, and a function of, only proximity to other human development. The vast majority of people deciding to invest in a new skyscraper or to make their home in Manhattan do so because it is near to a lot of other development and because it has access to more goods, services, and infrastructure than just about anywhere else they could choose. They probably do not consider what special features the location itself has (a great harbor, good river access to inland areas) even though those are what initially caused Manhattan to become Manhattan. Rural and Agrarian Regions: A Split Personality to "Proximity" People living and using land in both rural and agrarian areas are driven there, because of some natural quality of the land (e.g., fertility for crops). That is what motivates them and is the purpose of their being there. Roads and access to other development play a role in development and site selection within these regions, but natural qualities are the major drivers. In rural areas, this property of the site(s) is sometimes nothing more than its isolation. Second homes, hunting cabins, etc., are often located where they are because those locations are not well settled. Many people who live in rural areas
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but work in cities live where they do just because of the low development density. But usually, rural residential locations were also chosen for some other natural attribute — they are close to beautiful mountains, in a lush forest, or near a coast, or a lake, or have a particularly high wind speed, etc. In those rural areas in danger of transitioning to suburban development (i.e., those near a city), proximity to a city is a reason residents and businessmen in the area chose their location. In agrarian areas the land itself is the sought after quality. Land is this economic function's production line. Some land is much more valuable than other land ("bottom land" with rich soil generally being preferred) but mainly area - measured in square miles or square kilometers or acres - is the property being sought. Ranching can get so many head per mile, farming so many bushels per acre. But access to the regional road network, meager though it may be by comparison with urban systems is also important. Residential, commercial and industrial development within this region all want to be relatively close to this (sparse) road network because it is their primary means of transportation and access to goods and services. Commercial and industrial development will put what facilities it can relatively close to roads for a similar reason: it is efficient and lowers business cost. But relatively is an important word here: in a city, "close" might mean 150 feet. Here, it generally means within a mile. And in these areas, it is proximity to a road that is more important than distance to market and services. Traveling ten miles or thirty miles to town is quite secondary to the fact that one can go to town. To a farmer, having 1000 acres of prime land for raising grain is much more important than its proximity to shopping, services, and neighbors, or to a grain elevator for that matter. Access to a road means that they are close enough: quality of land is paramount. A good deal of the challenge in forecasting electric load growth in agrarian and rural areas revolves around modeling and balancing these two competing qualities as they affect development and electric demand. In suburban and urban areas, proximity to other development - distance to the activity centers, to local amenities - are key factors. In agrarian and rural areas, those are secondary. Access to a road is a key factor in the domain of "spatial interactions," while unique qualities of the land itself are the other key factor in determining siting for residents and businesses. Finally, rural areas near a city often create a big challenge to forecasters because they are in transition to suburban application. Overall, only a tiny fraction of all rural land falls into this category, but because of this transition, it becomes the focus of intense planning interest. It is the rural areas outside cities that make a transition to suburban development. Many of the residents in such areas work in the city or its suburbs but seek the isolation of rural areas. These particular rural areas are in transition to suburban - to a development dimension in which proximity to market, services, and employment other than in the agrarian sector is of primary importance.
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In fact, there is a progression in development from agrarian to rural to suburban that is often followed. Traditional farming or ranch land gradually is converted to higher population through spotty development of large-acre home sites and commercial development. Planned development and creation of roads then converts the area to more of a suburban context, and the area "develops." Dimensionality of Development and Growth One can view the dimensionality of spatial development and dispersion as increasing as one moves from sparse to urban core densities. This increase is important both as a concept of use to forecasters, and in choosing and setting up the right forecast tool for a region. It is summarized in Figure 18.2 Dimension refers to the context of, or the degrees of spatial freedom and interaction exhibited by, the land use and interactions in the region. In sparsely populated areas, dimensionality is very close to zero. Only a few specific, unrelated points are inhabited and used, their locations selected for scientific interest or natural resource extraction that are specific to each site, usually due to some geologic or ecological quality of the specific sites. Transportation to and from each site is done via air, sea, pipe, or if by road, over a purpose-built road run only to that site. Commerce (exchange of goods and services) is carried on with "the rest of the world" and not neighboring areas in the region. In practice, they are as far from any neighboring developments as from anywhere else. As a
Figure 18.2 Dimensionality of developmental growth roughly corresponds to the log of population density.
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consequence their dimensionality is zero: distance and proximity have no meaning. Each is as close to areas nearby as to those far away.1 Rural and Agrarian Regions: One-Dimensional Development Rural and agrarian areas represent the least populated use of land in which interaction among people, economic functions, and regional transportation plays an important role. Their analysis and planning are complicated by the fact that transportation and proximity are of only limited importance, but often take not a back seat, but one alongside of, the qualities of the land itself. Here location relative to one another does play a role in determining the patterns of development, as in suburban and denser development, but qualities of the land are often the raison d'etre. And as stated earlier, in rural and agrarian areas, the proximity-related side of development generally means "I need to be close to the road." That is enough. Later in this chapter, quantitative evidence of this concept will be presented, but what this really means is that spatial interactions of development in these areas are one-dimensional. To every person or business in these areas, "the world" outside their site consists of one long road. There is the location ("my ranch" or "my farm" or "the mine" or "my summer cottage") and there is the road, which extends in one or perhaps two directions ("left and right when I get to the road") and might as well be a straight line even if it actually twists and turns. Everything is some distance away along this road. There is no concept of being in a twodimensional landscape, in the sense of being surrounded by development and having all the points of the compass from which to choose for movement, as there is in a city. All of that would be only interesting, were it not for the fact that growth in rural areas displays a one-dimensional aspect in both its dispersion and change, and its load densities, as will be discussed in section 18.3. Agrarian area growth (section 18.4) is more complex, being dominated by two dimensions (area) with respect to value of the land, but only one with respect to locational aspects of many of the loads. This, too, will be discussed later in this chapter. Towards Three Dimensions In suburban and urban areas — in villages and towns, and over the vast majority of most major cities - spatial growth and interaction become two-dimensional. Space is the prime quality of land valued in development, space differing from area by including the concept of location relative to other locations. Thus, the term space will be used here to mean space for development - the land area is 1
Normally, to the T&D planner, these areas do not exist. Electric load at each site is related purely to that site's mission, the burdens of that mission and the volume of work to be done, and the ambient conditions at the site. Electrical facilities are planned as part of the site (by the oil company or by the scientific research division). There is no utility system in the normal sense of the word and no need for T&D system planning.
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not valued solely for its ability to produce food, but for its accessibility and proximity to other development, too. Suburban and urban development is two-dimensional. People and businesses do not live on a road, they live in a road network, an urban fabric. Beyond that, completing the dimensionality of development, at the heart of a large megalopolis, up becomes a further direction of development. Space at the core of, and in other key places, in some cities has become so valuable that it is worth creating it at great cost through building higher. When does it fill up? The reader who finds the concept of dimensionality hard to grasp might wish to consider answering the question "When is the area all used up?" with respect to each of the six types of regions in Table 18.1. Both sparse and agrarian regions are "filled up" when the attribute which makes the land valuable is completely absorbed or utilized. In mining or petroleum extraction cases it is the size of the natural resource deposit. In farming and ranching it is when the land acreage is completely used for agrarian purposes. Rural areas fill up when all the accessible parcels of land near roads are "full." They can only grow when more roads are built (section 18.3 will explore this quantitatively). Suburban, urban and urban core areas are all created from rural by building more roads so the development can be increased. They are all the same fabric, so to speak, of metropolitan development. Each is "full" when all the small areas within it are developed with roads and buildings or land use to that type's density level. Once full, growth can continue only by transition to the higher density type - suburban to urban, and urban to urban core. Core development is limited by technology and the value of construction - buildings much over 100 stories are considered impractical, due to both cost and access time to the higher floors - beyond a certain point one cannot build space that is very close to everything else in the urban core, due to "vertical travel time." Transitions and Gray Areas Finally, it is worth considering that these definitions all have gray transition zones between them. Metropolitan growth includes the process of these areas changing from one type to another, and includes two redevelopment processes: 1. "Rural/agrarian land on the periphery is made "two-dimensional" via installation of enough roads/transit that land area is converted to space ~ all of it is accessible and developed with buildings. 2. Re-development of older suburban and urban land into higher density areas is done by tearing down the old and putting up higher density buildings, invariably closer together. The distinctions in dimensionality matter to the planner because they affect the way land use and load develop, and how one area interacts with another.
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18.3 FORECASTING LOAD GROWTH IN RURAL REGIONS While the majority of land worldwide is "rural," in the sense that it is sparsely populated and not accessible through any type of dense road system, the majority of electric load is concentrated in densely populated urban and suburban regions. Therefore, quite naturally the bulk of research and development activity in spatial load forecasting has focused on predicting load growth in and around those areas, and particularly on forecasting the way in which new development springs up on the undeveloped periphery of those areas, as they expand. Rural and Agrarian Areas Rural and agrarian areas are similar in that both have relatively low population densities. However, there is a tremendous difference. In agrarian areas the land is completely (or mostly) used, but for a purpose that precludes dense human development: it is used to manufacture food. In rural areas, most of the land is not actually used and may not even exist from a practical standpoint. In the western U.S., there are vast tracts of land between the Rocky Mountains and the Sierras in which only a small portion of the land - less than 5% - is "space." In any practical sense the rest does not exist from the standpoint of the population's use of it for anything useful for anything other than isolation and view. Thus, this part of the world consists of only the land along and near roads and highways. The rest is just "there" but not relevant. Both rural and agrarian areas fit into a colloquial definition of "rural," but in this and subsequent chapters, these distinct definitions will be used for each. Forecasting Method Performance in Rural Areas Most spatial forecasting methods developed for urban and suburban load planning application do not forecast as well as when applied to rural and agrarian regions. To begin, they are far less easy-to-use and in some cases computationally burdensome - one of the few power system planning applications where computer time is still a major issue. More important, they are noticeably less accurate in these situations, as shown in Figure 18.3. This "malaise" with respect to forecasting performance does not affect just one type of forecasting approach, as shown. Both simulation and trending types show marked reduction in performance when applied to rural areas. An important clue to understanding the difference in accuracy between rural and urban applications is that the sensitivity depends on how heavily each method uses land and land use in its analysis. LTCTT trending uses land use in only the vaguest sense (it implicitly tracks area). It displays only a small performance difference between rural and suburban forecast situations. By contrast, a 3-3-3 simulation method, which uses land use extensively and in detail, shows a much larger difference. Therefore, it appears that something inherent in land use itself, or how it is modeled, is the cause of this poor performance.
Chapter 18
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Parcel Size - Acres Figure 18.4 Load versus land area for suburban (square dots), agrarian (round circles), and rural land parcels (solid round dots).
Development Dimensionality: Urban, Rural and Agrarian Areas
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Figure 18.4 shows that the relationship between load and land area is quite different in rural regions than it is in suburban and agrarian regions. The plotted data show randomly selected "residential and small commercial" land parcels from suburban, agrarian, and rural settings and provide a strong clue about the "onedimensionality" discussed in section 18.2. In urban areas (square dots), there is a nearly linear relationship between land area and load, shown by the constant load density as a function of parcel size. A parcel ten times the size is used for about ten times as much load, for every class of consumer, a parcel of 20 acres will have very close to twice the demand of a 10-acre parcel. In rural areas, neither peak nor energy correlates linearly with land area. Here, they actually demonstrate a relationship where load closely corresponds to the square root of land area. In a city or its suburbs, all potentially developable land is within % or !/2 mile of a road. Developability is omnipresent, even if development is not. But in rural areas, load growth and load growth behavior are dominated by a lack of roads only a small fraction of the land area is within !/i to !/2 mile of a road. With respect to development potential, the rest of the land "doesn't exist." Only those areas in close proximity to roads and highways will develop significant load, as illustrated by Figure 18.5. In general, the amount of a parcel that lies alongside a road on its boundary is proportional to its square root: quadruple the land area and the road frontage only doubles.
Move cursor- to OR HI t the nunDeK keu of tne required feature.
1990 Summer Peak Load 18 MW
3 miles Shading indicates load density
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Figure 18.5 Map of electric load (indicated by shading) for a region of central Texas developed from satellite imagery and consumer and substation load data. Even though roads are not shown they are easily discernible because load grows only alongside them.
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Figure 18.6 Rural parcels of land have development potential that seems to correspond more to road frontage than area. As depicted here, only a small portion of each small area is expected to develop land uses that create significant demand for power, shown shaded.
At first glance, it might appear that analytical aspects of simulation such as the "close to highway" factors described in Chapters 12-13 would account for this road-related behavior in rural load growth. In fact they do, but only to a point. A more fundamental issue is at work, as illustrated in Figure 18.6. In a rural area, only those areas near the road front seem to have development potential. By contrast, as discussed in section 18.2, in an urban area both peak load and energy are linearly related on a class-by-class basis to the area of particular land area: double the number of areas available to residential development in an area, and the residential load doubles. In a rural area this is not necessarily the case. There, load growth potential usually doubles only if the amount of road frontage doubles2 As a result, simulation methods and geometric trending methods, which compute or infer load growth potential from land area, often misidentify land parcels as "all developable" when only a small portion (that right along the highway) has any potential for load growth. This occurs even if they use "close to highway" and other transportationrelated factors in their analysis. Among simulation methods, forecast error due to this non-linearity is most pronounced in methods that employ a polygon-based small-area format. Such methods represent a single rural parcel as a large polygon, and thus do not normally distinguish details of land inside that parcel. By contrast, forecast error due to this problem can be made nearly non-existent in simulation, if the algorithm is applied with a grid-based format at very high spatial resolution. The high-resolution grid basically "breaks apart" large rural and agrarian parcels of land into very small parts and analyzes the "close to highway" potential of each. Some polygon format 2 If a parcel is made more developable by construction of roads into its "inaccessible parts," then a transition to suburban development has started.
Development Dimensionality: Urban, Rural and Agrarian Areas
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Figure 18.7 A grid-based format simulation has no problem dealing with forecasting in rural areas if a very high spatial resolution is used for the grid. Round dots above show the performance of a 3-3-3 simulation program (LOADSITE) on the area in Figure 18.3 when applied successively at 40, 10, 5, 2.5 acre resolutions. At 2.5 acres resolution it comes close to matching its urban-suburban forecasting accuracy. Square dots show the accuracy of a 33-3 polygon format program which has an automatic feature to segment polygons into small and smaller areas on demand to match any resolution requirement.
programs have a feature that permits the user to "fragment" the polygons into smaller areas, thus increasing spatial resolution of big, developing land parcels on the outskirts of cities. Repeated application of this user-controllable feature can produce very high spatial resolution. High Spatial Resolution Can Improve Rural Forecasting Thus, one way to accommodate this rural-forecasting inaccuracy with simulation is to use a high spatial resolution. When applied at a resolution better than ten acres, both formats of simulation accurately deal with the forecasting of a rural area, as shown in Figure 18.5. Either spatial format can segment land parcels into those portions along and those not along the rural roads, and deal with the forecasting of development in an appropriate manner. The problem that results for the user, as shown, is that run-time increases rapidly with spatial resolution. A grid-based program that uses frequency domain methods for its spatial surround and proximity factor computations (e.g., LOADSITE) can do much better in this regard than gridbased programs like FORESITE, which do not, or than polygon-format programs
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which cannot (e.g., SUSAN).3 As discussed in Chapters 13 and 14, frequencydomain computations mean run time increases proportionally to log N rather than N squared as the number of small areas (resolution) used to analyze a region is increased. Applications dealing with many (hundreds of thousands of) small areas run much faster. But there is a downside to high-resolution analysis of a very large rural region, even with a high-speed computer and an efficient program. It still requires a lot of computation.4 The region shown in Figure 18.5 and used in the example for Figure 18.4 is quite small (15 x 22 miles) yet still takes a considerable time with a high-speed computer. A purpose-developed spatial forecast program took over 2 hours on a 1500 Mhz machine, to produce eight forecast iterations. (It did not employ frequency domain methods.) Analysis of a large rural area with a simulation "written within" a standard GIS system would take much more time. Simple fixes improve rural forecasting Simulation methods for rural application can be implemented with a different spatial mapping context as shown in Figure 18.6. This results in accuracy similar to that achieved in urban-suburban areas, and good computational efficiency (Willis, Finley, Buri, 1995). Instead of a database structured around small areas, the simulation is applied to a data structure of small road links, as shown. Load is now associated with road frontage, not land area. These "small road links" have all the attributes associated with small areas in a simulation model - they have land-use classifications, spatial proximity factors, and a load calculated with an end-use model. They have no area - only length. Such a change from small areas to small road links is easy to implement in object-oriented database systems as well as in some types of GIS data systems. In all such systems, the user display, the context of the use of the data, remains spatial. In fact, loads are still located with x and y coordinates. Road links have x and y coordinates for both ends and are displayed and plotted as maps. Overall, the small road link concept works well. This seems to be the only change necessary so that simulation can handle these rural areas accurately and efficiently. Similarly, geometric trending methods can be modified so that they respond to the square root rather that the actual value of the computed or inferred land area (See Chapter 9, Geometric Cluster Based Curve-Fit Methods, Step 2). Both types of approach now realize their full accuracy potential without a computational overhead to do so in rural areas (Figure 18.7). 3
The author wrote, or directly supervised the development of, all three programs and believes they are equivalent in quality and potential, so this comparison is valid. Few spatial forecasting programs, particularly those embodying GIS or spatial facilities management system software, are written with computational speed as a chief priority. As a result most are rather slow, something that is not a problem in urban and suburban applications, but becomes a big headache if applied to rural areas.
Development Dimensionality: Urban, Rural and Agrarian Areas 583 One-half Mile
Figure 18.8 Simulation can be modified to work with a database of area-less "small road links" rather than small areas. This single modification in the simulation method renders it as accurate in rural forecasts as area-based algorithms are in urban situations.
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Program and Algorithm Issues Spatial road links can be either uniformly sized (all links the same length) or of variable length. Variable length links, usually limited to a maximum dimension of '/2 mile or !/2 kilometer, have been used in all programs of this type the author has seen and reviewed.5 The length limit is defined by the spatial resolution requirements of the forecast simulation algorithm. The links need to be short enough to assure reasonable accuracy in computing the proximity and surround factors. Surround and proximity factors take on a meaning in the road link context similar to the role they play in a small area based framework. However, all have somewhat greater radii of application. As a rule, proximity factors in rural areas are similar in radius to their urban counterparts only near the outskirts of cities in really developed regions (Europe, any state along the U.S. Atlantic coast). In truly rural areas, they typically have a radius of about three to five times that of similar factors in urban and suburban settings. In really sparse areas far from cities (the U.S. West) they are more than ten times their value in suburban settings. "Close to shopping" in most areas of Wyoming means less than fifteen miles from the nearest commercial development. The best computational methods for surround and proximity factors in a road-link context do not mirror the way(s) used to compute those factors in areabased simulation formats. What will be fastest depends on how the actual data is structured and how the particular GIS system being used operates. However, in general little computational speed can be gained by using signal processing tricks analogous to those that work when programs are written in basic programming code and run on an area basis (see Chapter 14). It is best to study the specifications of the specific GIS spatial data system being used to determine how its features can be best used to improve speed and accuracy of analysis. And regardless, some true spatial analysis will remain to be done in a road link analysis. The reason is that both highways and railroads must be modeled and their proximity effects taken into account. Highways are not roads. No development occurs along a restricted access highway, except at its intersections with roads. (Development alongside an interstate highway is not built along the highway. It is built alongside the highway frontage road. Thus, highways, entered exactly as in area-based programs, are kept as a separate level. Railroads are even a bit more complicated to model in a road-link structure. The reason is that heavy industrial development will sometimes accept a rural site along a railroad, even if not near an existing road. A road will be built if needed by the industry ~ a small additional expense for an otherwise good site. 5 The author has seen only three programs developed for rural applications using the concept, including his own (Willis, Finley and Buri, 1995). However, all were designed independently (even if the other two were based on the 1995 paper) and in each case the designers reached the same conclusions about which format was best.
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Highways and railroads can both be represented as separate sets (levels) of links in the simulation program, with the algorithm written to permit no load on highways, but permit heavy industrial development on railroads. It will still show a bias towards locations where railroads are close to the roads, but allow development that is not. But regardless, some amount of truly spatial analysis must be done with regard to both highways and railroads and their impact on road links and their development. A railroad will not have an impact only on road links it crosses. It will drive away residential development along nearby roads. Most GIS programs have proximity computations, which while not fast, are sufficient to compute proximity among road-like data sets. Since railroads and roads seldom change, this does not have to be computed in each iteration of the program, only for a few. Modeling Towns and Villages Few large regions are without several small cities or towns within them These can be modeled in rural study applications by using small road links to represent every major street in the town. The simulation forecast method will then forecast both rural and town load growth. In fact, the road-link method could be applied to model large suburban areas or even densely populated cities, in which case it would essentially be as accurate as an area-based format simulation. But in such situations, the number of road links required is much greater than the number of small areas required (roughly 500,000 would be required to model a city like Houston at a resolution equivalent to about 200,000 small areas). Finally, while the data requirements are not that much greater, the road-link approach cannot be applied in conjunction with various high-speed, multi-dimensional signal processing "tricks" (see Chapter 14) that accelerate computation and improve robustness. These are very useful, in fact necessary, for high-speed study of truly large metropolitan areas. The one weakness of the road-link method is that it cannot predict construction of new roads. It will not automatically add new road links into its database to model the expansion of the "local street system," as for example, the type of street expansion that occurs in major metropolitan areas when they grow along their peripheries. Area-based simulation programs do this (add streets as needed) implicitly. While they do not forecast the construction of major traffic corridors and highways, they do implicitly forecast the completion of local roads as growth occurs. The road-link method is best applied only to regions with no major cities and rather sparse population, as for example the western half of Kansas or parts of a region away from cities and towns. In general, it works well whenever the average distance between adjacent parallel roads is 1 mile or more. In such situations it gives measurably better accuracy than area-based (grid or polygon format) simulation while using far fewer computer resources than even a computationally optimal grid-based area method.
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Is Developing and Applying an Algorithm for Rural Study Worth the Effort? If a planner's need is only for an occasional study of a small- or medium-sized rural or agrarian area, then the answer to this question is definitely no. A standard simulation method, applied with a very high spatial resolution and with its surround factors set appropriately for rural/agrarian modeling, will do the job. Even though the resulting computations will require a lot of time (maybe having to run overnight on a desktop workstation), the overall procedure will be more satisfactory than maintaining a special forecasting program just for the occasional rural forecasting project. Using a special algorithm only makes sense when one of the following conditions is met: •
The service territory is all rural and agrarian. There are no cities or large towns involved.
•
The rural or agrarian area within the territory that must be studied is truly large - on the order of 30,000,000 acres or more (a region larger than 100 by 100 miles).
Even this recommendation is subject to an additional consideration. The quality and speed of the computer code can have a lot to do with the computation time needed for large problems. Planners who use programs written in high-level GIS system languages may find the area-based simulation computing time for even 10,000,000-acre rural areas to be untenable. Programs written in such highlevel languages have many advantages (including low development cost and good program stability). However, they carry with that a rather high computational "overhead" compared to programs written in more fundamental computing languages. More important, none of the high-level GIS languages the author has seen can apply the multi-dimensional signal processing "tricks" (see Chapter 14) that accelerate high-resolution spatial computations. On a large region studied at very high resolution, frequency domain techniques solve in as little as 1/10th the time of space-domain based methods. "Overhead" of some GIS languages is more than three to one, meaning that the overall ratio of GIS to a fast, purpose-written spatial load forecast program can be in the range of twenty-to-one. Thus, users will need to judge the speed of their standard software against their needs in making this determination. 18.4 FORECASTING LOAD GROWTH IN AGRARIAN REGIONS Agrarian regions are those in which the land is in full use, but population density is low, because the majority of that land is being used for agricultural purposes. This type of region does not share the parcel-level non-linearity of land area and load (or population). Here, an area ten times the size of another will have roughly ten times the electric load, other things being equal.
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Most of the electric loads will be located near roads, for a variety of reasons. Chief among these is convenience for the local inhabitants: locating their homes and work facilities near roads guarantees them easy access to their property and from it to everything else. Furthermore, regardless of where loads are actually located, the utility's obligation to provide service might be restricted to within a certain distance (500 feet, or 1/4 mile, etc.) of a road. This means that from its perspective, all loads lie along the roads anyway: Farmer Brown's house might be five miles off the road, but the last 4% miles of delivery are his responsibility. The utility has only to build one-quarter mile of line. But despite this similarity to rural areas with respect to load location relative to roads, the load growth and development behaviors in agrarian regions are different. Overall, load is roughly proportional to land area. Land area is the relevant factor in the activity that defines land use - agriculture. Twice as much land means twice as much activity means something like twice as much load. Figure 18.10 illustrates this point, showing the composite load curves for three parcels of land all devoted to dairy production. The loads are composite in the sense that two of the parcels had their load metered at several locations. Those were added together to obtain the curves shown here. Figure 18.4 also shows that agrarian loads do not follow the square root type load versus land-use relationship of rural areas although their density does drop more than suburban loads as large parcel size is reached.
Figure 18.10 Dairy farms of 160, 330, and 597 acres have daily energy uses of 356, 834, and 1575 kWh (2.25, 2.6, and 2.5 kWh/acre) respectively. Peak hourly demands are 16, 34, and 60 kW (.100, .106, and .101 kW/acre) respectively.
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Analysis and Forecasting of Agrarian Area Growth The road-link method described in section 18.3 is not a recommended approach. Instead, a standard simulation method is most applicable. If necessary in order to achieve acceptable run time, a low spatial resolution can be used. The load can be computed to a Vz mile or 1 km resolution. Even 4-mile resolution works in many cases. This brings up an important point about forecasting in rural and agrarian areas. It can be used in rural forecasts to improve accuracy, where it is a way of "tricking" a standard simulation algorithm into seeing what at lower resolution is a square-root relationship between land area and load. But such high resolution per se is not needed for planning purposes. Rural or agrarian planning needs are usually satisfied by a '/2 mile or kilometer resolution. Proper Classes and End-Use Model The simulation must distinguish the type of land use in a way suitable for agrarian applications. Dairy farms have far different needs than poultry farms, or grain cultivation, or cattle ranches. Appropriate classes need to be used and an end-use model set up to represent the various energy consumption categories in each (Table 18.2 and Figure 18.11). Publications for the American Society of Agricultural Engineers provide useful information on such loads. Seasonal Load Curves Generally, agricultural loads are very seasonal. Not all types of farms and ranches in an area will have the same peak season, as shown in Figure 18.12. Due to this diversity of seasonal peaks, it may be necessary to study load curves for several times of the year, or to use one daily load curve for each month.
Table 18.2
Loads for a 145,000 Bird Poultry Egg Production Farm
Type of Load Ventilation & Curtain Air Systems Curtain Air Handlers Hen House Lights Feed Bin and Conveyance Manure Removers and Processors Egg Collecting & Sorting Cold Storage & Fans Feed Grain Processing Grain Storage & Ventilation Misc. House Loads Road & Yard Lights Totals
Installed 40.9 0.9 9.6 35.2 18.4 12.8 4.8 11.2 4.8 4.0
Contribution to Peak
22.5 0.7 5.5 19.6 10.9 6.5 3.3 5.5 3.3 2.7
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Development Dimensionality: Urban, Rural and Agrarian Areas 589
Figure 18.11 Composite farm-wide load curve for the poultry farm from Table 18.2.
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Figure 18.12. Agricultural loads are typically very seasonal, so analysis and forecasting of an area may have to look at several months of the year.
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18.5 SUMMARY AND GUIDELINES Man's use of land covers a spectrum of developmental types from the exploitation of natural resources and special features at selected sites (sparse use) to high-rise development limited only by financial and architectural limits (urban core). Rural and agrarian uses both leave the land basically undisturbed with respect to buildings, paving, and other infrastructure that accompanies metropolitan land usage. But they both make use of the land, or at least selected portions of the land in the case of rural usage Rural and agrarian load growth behavior differs from that found in metropolitan areas. As a result, rural and agrarian load forecasting is best done with approaches slightly different than those that work well in metropolitan areas. With respect to rural areas, growth is "one-dimensional" - only a portion of the land actually exists for any practical purpose. In agrarian applications, use of the land is two-dimensional, but a lot of the considerations and use of land for non-agrarian purposes are still one-dimensional. Generally, spatial forecast methods cannot deal with these areas accurately unless they are adjusted to account for a number of factors unique to these areas. •
Spatial resolution must be high unless the forecast algorithm is modified to handle the dimensionality of the load growth behavior. If that is the case, then a relatively low spatial resolution - perhaps one mile - can be used.
•
Consumer and end-use classes need to be carefully set up to reflect agrarian and rural distinctions.
•
The influence of urban poles should be minimized. These aren't urban areas. If modeled, their radius has to be very high - "near" can mean 40 miles and "close enough" can mean 100 miles.
• Proximity factors in general have wider radii - about three times what is seen in metropolitan areas. Reference H. L. Willis, L. A. Finley, and M. J. Buri, "Forecasting Electric Demand of Distribution System Planning in Rural and Sparsely Populated Regions", IEEE Transactions on Power Systems, November 1996, p. 2008.
19 Metropolitan Growth and Urban Redevelopment 19.1 INTRODUCTION In most metropolitan areas, a portion of load growth occurs due to redevelopment old buildings are torn down and replaced by newer, taller, and denser construction, generally with a great deal more demand for electric power. Or, existing buildings might be gutted and rebuilt within their old shells, either upgraded within the same land use (older homes rebuilt as more modern homes) or perhaps changed (warehouses converted to retail on the ground level with residential lofts above). Regardless, this redevelopment causes electric load growth in areas of the system that had existing and stable load levels. Such redevelopment can catch planners by surprise. In some cases, once it has begun it is then over-forecast, resulting in expenses out of proportion to what could have been spent. Redevelopment can be difficult to forecast. It occurs in areas where there is already a power delivery system in place, meaning that the required additions are expensive and have a long lead time. These areas usually have urban congestion and a resident population that limits the utility's options and makes construction difficult and expensive. This chapter will look at the characteristics of redevelopment growth and ways to address it in spatial forecasts. Section 19.2 will look at how important redevelopment is to planners. Section 19.3 will then examine the various ways it can be accommodated, partially or fully, in spatial forecast methods, and the results these approaches give. Section 19.4 gives application advice, and section 19.5 concludes with a summary and guidelines.
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19.2 REDEVELOPMENT IS THE PROCESS OF URBAN GROWTH The process of metropolitan growth can be viewed as composed of several stages - including initially rural or agrarian, and then a transition to suburban, then to urban, and finally to urban-core development as the city continues to grow. Table 18.1 (see Chapter 18, section 2) summarized these developmental categories and their growth interaction dimensions. The series of transitions from rural to suburban to urban to urban core takes many years to complete, each generation (i.e., stable development plateau in one particular category) typically lasting on the order of forty years or more. For many parcels of land and in many areas of a city, the entire series is never completed. Urban core is not the manifest destiny of every acre of every metropolitan region. But whatever an area's eventual maximum density, it "gets there" through a process of growth that can be viewed as moving through several transitions, each of which corresponds to a "growth ramp" period in the S-curve growth behavior discussed in Chapter 7. Figure 19.1 illustrates the concept: an area of the system will undergo several transformations as it makes its way from undeveloped rural land to urban core. Electric load grows most rapidly during those multi-year periods of each transition, and grows quite slowly in between. Figure 19.2 shows the peak load history in an area that actually experienced three of these transitions in only a 60-year period.
Time
Figure 19.1 Theoretical multi-transition "S" curve (Chapter 7) of a small-area's growth history, viewed over a very long period, could contain as many as four transitions.
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Figure 19.2 Annual peak load history in a section (640 acres) NNW of the intersection of US 59 and Loop 1-610 in Houston, estimated from metered feeder loads, aerial and satellite imagery, and building counts. Trends include the effects of weather variation from year to year. The area experienced a post WWII building boom of suburban housing from 1947 through 1954 that made a twelve-fold increase in the previous largely rural load density. The area again saw rapid redevelopment into offices and mid-rise apartments in the late 1960s and early 1970s. Construction of office and condominium towers began about 24 years later. This area's history is like that of many areas in other cities (and other parts of Houston) and is rare only in the relatively short periods, about 25 years each, between growth transitions, a function of the robust Houston economy during the last half of the 20th century.
Figure 19.3 Conversion of rural/agrarian land to suburban is accomplished with the construction of roads that make all of the land accessible. Compare to Figure 19.6.
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In each of these transitions, land in a metropolitan area is "re-built" into a denser use of land, usually via construction of taller and more closely spaced buildings. This process starts with the "accessification" of rural land - the construction of roads throughout a rural parcel so that all of the land is accessible and thus available for development (Figure 19.3). This converts land to the two-dimensional context covered in Chapter 18, section 2. Planners and forecasters should understand that this series of transitions is the process of metropolitan growth, a process that means the load history of any metropolitan or urban regional core is always a "multiple bend S curve." Basically, the process is: • Metropolitan area growth begins with conversion of rural and agrarian land on the outskirts of the city into suburban development, including the extension of a road network into the area. The area becomes twodimensional, a part of a city. • Areas with the resulting suburban fabric, which will develop to urban or urban core levels, do so over time by redeveloping to that level. (Direct rural-to-urban development occurs only very rarely). • High-rise (urban core type) development usually occurs as a second stage of redevelopment from the once-redeveloped urban area. However, sometimes it can occur directly as redevelopment from suburban. This process and its transitions can be interpreted in three ways as shown in Figure 19.4. All three are valid representations which provide insight useful to planners.
Developmental •Dimensionality Perspective Land-Use Change^ Forecasting Approach
Rural
Suburban
Vacant )useable land
Residential, retail, light industry
"S" Curve Load \ Litt(e , History Behavior \ or no Perspective /load
Growth Ramp
Low growth period
Urban
Urban Core
Apartments, offices, • industry
Growth Ramp
Low growth period
High rise residential or commercial
Stable but Growth \ medium-rate Ramp / growth
Figure 19.4 Comparison of three views on land development type transitions.
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Four Types of Redevelopment One important distinction about types of redevelopment needs to be recognized early in any forecast of redevelopment or analysis of its causes and impacts. Redevelopment can be categorized into four types, which are outlined in Table 19.1. Urban core growth occurs in the downtown, usually high-rise portion of a city, as a continuous process linked to and driven by, the growth of the entire regional economy. A city the size of Chicago needs more urban core (activity center size) than a city the size of Syracuse. As a city grows, its activity centers, including but not exclusively limited to the central core, grow in company with the rest of the metropolitan fabric into which they are woven through their economic and transport interaction. Urban cores grow up as well as outward. Redevelopment through replacement of existing structures is a constant and gradual process. Over the long-term, in the center of any large metropolitan area, there is a constant process of replacement of older high-rise (perhaps 25 stories) with newer high rise (perhaps 40 or even 80 stories). In addition, the land areas covered by high-rise core development tends to gradually expand, usually not in a symmetrical pattern but in only one or two directions, occasionally jumping to other locations nearby. Strategic redevelopment areas involve the promoted (driven by government or major financier sponsorship) redevelopment of an entire part of a city or county and usually include the coordinated planning of the future layout and content of an area of from several blocks to several hundred acres. Examples from the last two decades of the 20th century include the redevelopment of the Inner Harbor area in Baltimore, the redevelopment of the area around the new baseball stadiums in both Baltimore and Denver, the Greenway Plaza/Summit area in Houston, and the Arena area on the edge of downtown Dallas. In all these cases, an external coordinating entity, either the local government, a quasigovernment coordinating committee, or a developer with deep financial and political pockets, made a master plan for the long-term redevelopment of a significant area. A common theme among all such strategic redevelopment initiatives is that the plan does not fit the existing urban pattern. The initiative is being taken in order to change that pattern. The entire character of downtown Baltimore, even to the extent of where the heart of the city "seemed to be" from the standpoint of activity and attraction, changed with the development of the Inner Harbor. Similarly, an entire side of downtown Denver changed dramatically in the years following the construction of the new stadium and the other changes made in company with it.
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596 Table 19.1 Types of Redevelopment Occurring in a Metropolitan Area Type Urban core growth
Strategic initiatives
Localized (tactical)
Nature
Predictability
Continuous growth of the downtown core and other major activity centers for the region. Growth is linked to the economy of the region Large, visionary projects whose effect, and often goal, will be to change the entire character of the urban areas around them. Almost always sponsored by or supported by local government.
Good, in principle. Involves a type of "reverse urban pole" analysis of forces driving the demand for urban activity centers. Nearly zero. These do not fit the existing pattern so they cannot be inferred from existing needs and uses. The political process that gives birth to them is unpredictable. Must be studied as scenarios. Fair. These transitions can be inferred from need or opportunistic fit by looking at the existing land use and the area around the redeveloping site(s). Good. Successful match to existing land-use class is easy to infer in simulation.
Small, isolated redevelopment projects generally done purely as business transactions. The new land use fits within the existing urban fabric. The old often did not, or was only marginal. Redevelopment Redevelopment to the same type of in kind land use as in the past. Rebuilding to increase success.
Redevelopment of this type is very likely to make major changes in land use - it is extremely unlikely that such master plans involve only upgrades or minor changes in land use. Often, the motivation behind these plans is a political desire on the part of community leaders to completely change the character of their area of the city. In fact, usually, the sponsoring agency of the redevelopment initiative wants the impact of the redevelopment project's influence on the region more than it wants the project itself. It is a strategic project, planned to shape the course of the entire metropolitan areas' future growth character. Strategic redevelopment is often impossible to forecast, because it is usually politically motivated, and if not, impossible without support of the political process. And, as mentioned above, the plan for the targeted area does not fit within the present urban fabric - such plans are nearly all visionary - based on seeing beyond what is there now to what could be. Localized redevelopment occurs on a much smaller scale. A small, singlestory strip retail center might be torn down and replaced with a two- or three-story retail/office/residential center. An old rail warehouse might be
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gutted and converted to loft condominiums with restaurants on the ground floor. Or that same warehouse might be converted to a high-tech data or telecom center. A block of row houses built in the 1930s might be replaced by a row of townhouses both taller (more stories) and with much higher load density. A good deal of this type of redevelopment is always occurring, although it is usually limited to a few areas of a city. Localized redevelopment occurs as pockets of change, individually planned and initiated, usually by small developers or the existing land owners themselves. Usually it is not part of an overall master plan. This type of redevelopment often replaces an older, worn-out subclass of a land use with a newer version of itself, or a close proxy. Major changes are rare. For every warehouse converted to loft apartments, there are four to five times as many residential upgrades. Redevelopment in kind involves rebuilding or refurbishing within the same land-use class. Older homes are torn down and new homes are constructed in their place. Old shopping is demolished to make way for new retail facilities. Often the old is not completely removed, but merely refurbished and rebuilt: the new mall is where the old was, and includes 80% of its original steel structure, but looks and feels completely new. This type of change can be viewed as a subset of localized redevelopment. But redevelopment of an area into a new version of its past land-use class requires a special focus when a land-use based simulation approach is being used for the spatial forecast. That is one reason why it is treated as a separate category. But in addition, and more important, in a very real way redevelopment in kind is different from the three types of redevelopment covered above. Its motivation and goals are different. Usually it is being done because the buildings in an area are worn out or obsolete, not because someone wants to change the area's function or purpose. In this regard it is the opposite of strategic redevelopment. The current land use is very successful and no change is desired. Only an upgrade in performance or competitiveness (in the author's view these are largely the same) of that land use is being sought. These four mechanisms for redevelopment growth occur simultaneously and interact with one another. All must be accommodated somehow in any successful forecasting process. Generally, urban core, tactical, and in-kind redevelopment can all be trended to some extent, although perhaps not with just simple extrapolation methods. Strategic redevelopment, however, requires analysis as scenarios, both due to its nature, and because of how planners most often have to treat it.
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Redevelopment: How Much and What Is It Really Like? "Redevelopment" means that some existing land use is converted into another land-use. Strictly speaking, vacant is a land-use class. On this basis, one can argue that all construction on vacant (rural, agrarian) land is "redevelopment." This is within the spirit of section 18.2's and this chapter's perspective and actually a good concept to keep in mind when designing a simulation method to handle all types of load growth. However, to many people, and certainly to most T&D and urban planners, "land use" generally means only those uses that involve the construction of permanent buildings or fashioning of the land for a specific purpose (an aircraft runway, a park, a golf course). Table 19.2 lists the ten electric consumer (land-use) classes from Chapter 11's detailed simulation example. These are the same classes as listed in Table 11.1, except that two classes of vacant have been added for completeness, and the classes have been numbered 0 - 10. In principle, all possible transitions from one class in this list to another are possible. Vacant develops to any land-use type. Old homes are demolished to make way for new homes, or apartments, or retail, or offices, or industry. Old industry is removed to make way for — anything. (Even transformation of developed land back to vacant is possible and has occurred in some communities, generally when old industrial sites are transformed back to vacant useable land prior to sale for some new purpose.)
Table 19.2 Example Land-Use or Electric-Consumer Types Number
Class
N
Vacant unuseable
0 1
Vacant useable Residential 1 Residential 2 Aprtmnts/twnh ses Retail commercial
2 3 4
Definition land not available for whatever reason land without buildings, available for building homes on large lots, farmhouses single family homes (subdivisions) apartments, duplexes, row houses stores, shopping malls professional buildings tall buildings
7
Offices High-rise Industry
8
Warehouses
small shops, fabricating plants, etc. warehouses
9
Heavy industry
primary or transmission consumers
10
Municipal/Inst.
city hall, schools, police, churches
5 6
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Table 19.3 Land-Use Change for Three Metropolitan Areas 1990 - 1998, by Class Growth of N. This Class \ 1 Residential 1 2 3 4 5 6 7 8 9 10
Residential 2 Aprt/twnh Retail comm. Offices High-rise Industry Warehouses Heavy industry Municipal/Inst.
0
1
99 93 82 71 62
2 7 8 7
75 90 89 48
Came from land that had been previously classified as . . . . 2 3 4 5 6 7 8 9 1 0 S u m
1 1 2 2 2
2 3 1 10
4 2 8 11 3
6 11 15 2
6 47
3
1
3
12
2 2 3 2 9 9 4 8 3
2 2 8 2 6 4 3 2 12
1
5 20
100 100 100 100 100 100 100 100 100 100
Table 19.3 is the first of four tables that explores the actual growth of major metropolitan areas with respect to redevelopment. These tables look at the actual land-use and load change occurring in three cities over the period 1990 - 1998. The cities were Houston, St. Louis, and Chicago. Although limited in scope, it gives some idea of how much of a limitation, if any, the classic simulation methodology's modeling of all growth as only coming in vacant areas puts on forecasting accuracy.1 Each row in Table 19.3 shows from what previous class the land for growth of a certain land-use class was obtained. The measures are area, not load density, and are given in percent of each class's total growth - each row sums to 100%. Thus, the second row shows that 93% of all new residential 2 land-use (new single-family homes on small lots) came from development of vacant land. It also shows that 1% of the land for new construction of this class came from existing homes of this class which were torn down to make way for new, and that 2% came from each of the industrial and warehouse classes. As another example, the intersection of row 6 with column 5 indicates that 47% of all land that developed into high-rise during this decade had previously been class 5 (nonhigh-rise) offices, prior to that redevelopment. This matrix says a good deal about the actual process of urban redevelopment. First, only two classes - municipal/institutional and high rise get the majority of their growth from existing development. For the rest, vacant land (class 0) is the fodder for metropolitan expansion. But in every class except residential 1 (single-family homes on very large lots) redevelopment of existing land use has a noticeable role. For apartments, offices, high rise and industry, redevelopment provides more than one-sixth of all land used for growth. 1
This data was developed from public domain satellite images, growth records, population, and load growth data by the author for randomly selected areas of all three cities.
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Table 19.4 Land-Use Change in Three Metropolitan Areas 1990 - 1998, In Total - % Growth of N. This Class . . >\ 1 2 3 4 5 6 7 8 9 10
Residential 1 Residential 2 Aprt/twnh Retail comm. Offices High-rise Industry Warehouses Heavy industry Municipal/Inst. Column totals
0 55.60 26.24 4.76 2.77 0.93 0.00 1.61 1.00 0.16 0.18 93.3
. . . came from land that had been previously classified as . . . . 1 2 3 4 5 6 7 8 9 1 0S u m 0.56 0.40 0.41 0.31 0.10
0.45 0.12 0.08 0.03
0.04 0.03 1.8
0.04 0.75
0.23 0.08 0.12
0.09 0.41
0.06
0.23 0.16 0.09 0.04
0.00 0.01 0.5
0.5
0.5
0.04
0.0
0.56 0.12 0.12 0.03 0.02 0.19 0.04 0.01 0.01 1.1
0.56 0.12 0.31 0.03 0.04 0.09 0.03 0.04 1.2
0.06
0.11
0.2
56 28 6 4 1 1 2 1 0 0.07 0 0.1 100
Table 19.5 Electric Load Changes, 1 990 - 1 998, Weighted by Peak Electric Demand Growth of N. This Class \ 1 2 3 4 5 6 7 8 9 10
Residential 1 Residential 2 Aprt/twnh Retail comm. Offices High-rise Industry Warehouses Heavy industry Municipal/Inst. Column totals
0
1
15.36 32.79 7.74 5.38 5.20 0.00 2.96 0.82 0.92 3.82 750
0.16 0.56 0.66 0.61 0.59
Came from land that had been previously classified as . . . . 2 3 4 5 6 7 8 9 1 0S u m 0.50 0.19 0.15 0.17
0.08 0.03 26
0.79 18
0.38 0.15 0.67 0.00 0.12
0.45 0.92 0.50 1.55 7.03 0.08
0.24 16
30
75
0.71 0.19 0.23 0.17 0.72 0.41 0.35 0.04 0.08 0.24 0.7 24
0.71 0.19 0.61 0.17 0.62 0.16 0.03 0.95 34
0.09
0.20
03
16 35 9 8 8 10 4 1 1 1.59 8 16 100
Table 19.6 Error in Estimating Load of New Using Old Class Data - % of All Growth Growth o f ^ v This Class \ 1 2 3 4 5 6 7 8 9 10
Residential 1 Residential 2 Aprt/twnh Retail comm. Offices High-rise Industry Warehouses Heavy industry Municipal/Inst. Column totals
0
1
00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.9 0.6 0.6 0.6 0.0 0.1 0.0 0.0 0.0 2.9
Came from land that had been previously classified as . . . . 2 3 4 5 6 7 8 9 1 0S u m 0.0 0.0 0.0 0.1 0.1 0.0 0.0 0.0 0.0 0.8 1.1
0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.3 0.8
0.0 0.0 0.0 0.0 0.7 1.6 0.0 0.0 0.0 0.0 2.2
0.0 0.0 0.0 0.0 0.0 5.4 0.0 0.0 0.0 0.0 5.4
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 -0.4 0.0 0.0 0.1 0.4 0.0 -0.1 0.1 0.2 0.4
0.0 0.3 0.1 0.4 0.2 0.7 0.1 0.0 0.0 1.0 2.7
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.8 0.7 1.1 2.3 8.0 0.2 0.0 0.1 2.4 15.6
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Table 19.4 looks at this data another way, normalizing the table so the entire table, rather than each row, sums to 100%. In Table 19.4, each row summed to 100% of the growth occurred in that row's class. But some classes grew a good deal, others by only a small amount. Table 19.4 shows the change in each class as a percent of total change in land area. The final column shows the row sum, the total change of each class as a percent of overall expansion. Thus, 56% of all land-use change was residential 1, while only 6% was high-density residential (apartments and townhouses). The column total for column 1 shows that over 93% of all land-use change occurred as transitions from vacant (rural, agrarian) land to some suburban or urban purpose. Thus, redevelopment constitutes only about 7% of land-use change. But T&D planners are more concerned with electric load, not land area or land use change per se. Table 19.5 shows this data weighted by peak electric demand level in each class. Thus, while residential 1 as a whole had 56% of all land-use change, due to its relatively low load per acre, it constitutes only 16% of all peak load growth. High-rise buildings, which constitute only 1% of land use change in total (Table 19.4) account for 10% of all load growth due to their load density. Overall, only 75% of load growth occurs in previously vacant areas. Redevelopment in some form is the mechanism of 25% of the new loads. Thus, redevelopment appears to be substantial enough that T&D planners cannot ignore it. However, the data in Tables 19.3 - 19.5 can be used to provide an even better measure of the magnitude of redevelopment's role from the standpoint of forecasting and planning T&D load. Table 19.6 shows the error that results from failing to account for all suburban and urban redevelopment. If offices at 69 kW/acre replace apartments at 18 kW/acre, then missing that redevelopment in the forecast means an error of 51 kW/acre. Table 19.6 shows these errors as a portion of all load growth. Total error due to ignoring redevelopment comes to a little less than one-sixth of all growth. How Serious Is the Potential Forecast Error? Assuming that the results developed above are general (they strike the author as reasonably representative of the average T&D forecast situation), does this mean that ignoring redevelopment leads to 16% error in a spatial forecast? No. The spatial error - what impacts T&D planning — can be anywhere between two times to only one-half of that value, depending on exactly what "ignoring redevelopment" means. This will be discussed in Section 19.3, under that heading. T&D planners need to recall that a spatial forecast has a where element not included in Tables 19.3 — 19.6's analysis, and spatial error sensitivities and interactions that need to be taken into account (see Chapter 8). However, planners should consider this: the best performance possible from simulation over a ten-year period is about Uf = 8 to 10%. Thus, ignoring redevelopment can easily double the inaccuracy in meeting requirements for a metropolitan forecast.
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What Must Be Done Well to Model Redevelopment Accurately? Before looking at redevelopment and how it is handled with various analytical approaches, it is worth considering what must be done by the forecaster who has decided to address it in some fashion. There are five issues: 1) Model the economic demand issue. Is there demand for growth here? How preferable would growth here be compared to growth in the nearest vacant areas? Generally, simulation methods have tools and processes that deal with this (global model, urban poles and activity center model), but these may need to be modified for application to redevelopment. 2) Model the supply issue. What already-developed areas are available for redevelopment? What are they suitable to become? Simulation methods use preference functions to consider these questions, and those need to be modified or extended to be able to handle redevelopment. Trending must use some sort of pattern recognition. The biggest issue: How is this already-developed land validly compared to vacant land which has no existing buildings or foundations or paving to inhibit/enable it for new construction? 3) Accounting for displaced growth. What happens to the old land use that disappeared to make way for the new? Was that land use needed overall - in other words does it move somewhere else? Or was it redundant and thus there is no need to model it being built elsewhere. This is mostly a matter of accounting for land-use change and comparing it to global totals, but it must be done. Note in Chapter 11 's example, page 359, that forecasted redevelopment growth displaces 19 acres of residential which is modeled as moving to the outskirts of the town. 4) Will redevelopment actually occur? How does one actually match demand, supply and displacement to determine which areas redevelop and which do not? Again, simulation models match demand and supply: it is constrained and controlled by their global totals. But this model must be modified to accommodate redevelopment: a metropolitan area with a 1% net growth could see 1.5% land-use change due to redevelopment and displacement. 5) Redevelopment within the same class. "Gentrification" or "yuppyfication" - whatever it is called - occurs constantly. Older homes are gutted and rebuilt, or replaced with new construction. Redevelopment in kind changes the load, but not the land-use class. Any method of addressing redevelopment has a potential need to address all five of these concerns, although some forecasting situations may not require all five to be addressed well. Regardless, the thoroughness with which a method addresses these five in a coordinated manner determines how effective and accurate it is in representing redevelopment growth of new load.
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19.3 REPRESENTING REDEVELOPMENT IN SPATIAL FORECASTS Redevelopment challenges both trending and simulation forecast algorithms, for a variety of reasons but ultimately with a different effect on the two types of method. Each of the two forecasting contexts can address in different ways and with varying levels of success, but they do so in different ways and present the forecaster with different challenges in doing so. In general, trending methods are less accurate at modeling redevelopment than simulation methods, but some simulation methods do not deal well with redevelopment either. Trending Algorithm Interactions Chapter 9 examined the reasons why load history extrapolation methods (trending) are relatively inaccurate when dealing with "S curve" load behavior. Functionally, the reason is that the growth ramp of an "S" departs from the recent historical load trend, so an extrapolation will not forecast it well. But more fundamentally, there is a basic incompatibility in the application of any trending method to areas that might redevelop. By its very nature, trending assumes that whatever process has been in control of the trend will continue. Implicit in its application is that the current growth drivers will remain relatively constant, even if the trended quantity does not. Growth transitions violate this assumption: something in the nature of what is driving change also changes, in this case the type and context of urban purpose in an area. For these reasons, curve-iit/extrapolation types of load forecasting are particularly ill-suited to situations where a planner knows or suspects there may be redevelopment. Simply put, trending is not much help here. Even quasigeometric (e.g., LTCCT and similar methods) trending approaches do not deal well with redevelopment. LTCCT is relatively successful by comparison to other trending algorithms in handling the initial "redevelopment" from rural or agrarian land to suburban load levels. But that success generally does not extend to an ability to forecast subsequent transitions to urban and urban core.
Table 19.7 Algorithm Redevelopment Performance (10 = Perfect, 0 = incapable) Forecast Type of Redevelopment Algorithm Core Strategic Tactical In Kind Basic Trending (regression) 6 0 3 8 Advanced Trending (LTCCT) 6 5 0 8 4 4 4 Basic Simulation (2-2-2) 8 Advanced Simul. (4-3-4) 8 8 8 8 8 Hybrid Methods 8 8 8
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The advanced template-matching algorithm (Chapter 15) can offer some promise of improved performance with respect to forecasting redevelopment, at least as compared to other trending methods. It employs analysis of other variables besides load as it compares a small area's recent growth history to the load history of other areas long in the past. Conceivably, if the template match were set up correctly, it might be able to identify a present suburban area that "looks" very much like an urban area that twenty years ago was suburban and beginning its transition to urban. It could then use that area's history to forecast the suburban area's future. The key to success with such a template matching would clearly be to find a statistically significant context (some variable or variables) that the algorithm could use to distinguish between suburban areas that might develop into urban and those that are likely to stay suburban. Such work has not been carried out to date. And in general, trending is not favored for redevelopment forecasting.
100
re 40
1995
2020
2025
Figure 19.5 Strategic redevelopment can be addressed to a limited extent with trending through artful use of the horizon-year loads (see Chapter 9). Here, a base (no redevelopment) extrapolation of load growth in a stable area of the system produces the dotted line trend. To this planners then add a "known" 18 MW of redevelopment additions expected in five years, and a total estimate of 42 MW "eventually" (twenty years). As recommended in Chapter 9, dual horizon-year loads are used. The resulting curve fit of a third-order equation (solid line) now anticipates redevelopment.
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Recommended steps when using trending Again, trending is not recommended. But if it must be used, then the horizon year loads are the mechanism with which to address redevelopment. External to the trending program, the forecaster should assess if redevelopment is likely and determine a horizon-year load that reflects the expected redevelopment. That can then be used in the curve fitting (see Chapter 9). In addition, if a redevelopment project is known, or suspected, a "horizon year" load somewhere in the near term can be used (Figure 19.5). Redevelopment Interactions with Simulation Within the context of the simulation algorithms covered in Chapters 10 - 14, the transitions from rural to suburban, from suburban to urban, and from urban to urban core are treated as transitions in land use or consumer class. The simulation approach's land-use change model concept matches the development type paradigm quite well. There is a one-to-one correspondence between the transitions in developmental type and changes in land use. The first transition is from vacant useable (rural or agrarian land is vacant as far as a spatial had forecast perspective is concerned) to some form of suburban land use. Subsequent transitions involve replacing that existing suburban development with denser development of residential, commercial or industrial land use. In the real world, density is increased using one or both of two methods: the new buildings are taller, and/or they are built closer together. In a simulation, the density increase must be handled by a change in land use, from a "low-density" land use to one of higher density (and higher load/acre). It is these subsequent redevelopments from suburban to higher density that challenge the accuracy and representativeness of simulation methods. One complication is the complexity of considerations inherent in determining if existing land use will redevelop. This involves something like twice as many factors as determining if vacant land will develop. The various considerations involved in answering "Could the present land use be replaced with something else?" are about as complicated as those required to determine "What is this small area ideally suited to become and how preferable is it to that purpose." Redevelopment of anything but vacant land requires answering both questions, not just the latter, so it is roughly twice as complicated. Beyond this, tracking the land-use changes as the program simulates growth is a bit more difficult. Finally, simulation programs can have some difficulty in dealing with redevelopment's relationship to urban poles. Basic simulation approach to redevelopment All spatial load forecast simulation approaches use some form of the following method to project where, when, and what growth occurs. Through some analytical means they evaluate the various small areas for how well they match the profile of the various land-use classes. Those vacant small areas that score
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well with respect to classes like residential, retail, offices, industry, etc., form part of the available inventory of growth space for each class. The simulation then designates the most highly rated of these small areas for each land-use category transition to that class, in amounts sufficient to satisfy the overall needs for service-territory-wide land-use growth (global inventory of growth). This "classic" spatial forecast simulation approach, as described in Chapters 12 - 14, routinely considers only vacant useable land for such transitions in land use. Programs such as CEALUS, DIFOS, ELUFANT, SLF-2 and FORESITE all took this approach: routine transitions in land use occurred only from vacant land. Redevelopment is/was handled within each program by the various workarounds and "manual intervention" methods to be discussed later in this section. This limitation was not serious in some of their applications for several reasons: • Most of the utilities using these were most concerned about meeting Greenfield growth on the periphery of their metropolitan areas. • Redevelopment could be handled to a limited but sufficient degree, in a manual, if messy, work-around manner. In addition, it is worth considering need in general. The simulation paradigm and the programs outlined above (or their forerunners) were developed in the mid-1970s and early 1980s, when the products of the post-war building boom (1948- 1958) were generally too new to be replaced except in very exceptional circumstances (such as Figure 19.2). Simply put, there was not nearly as much redevelopment then as there is now, twenty to twenty-five years later. 19.4
EIGHT SIMULATION APPROACHES TO REDEVELOPMENT FORECASTING
Despite the fact that a potential error of up to 15% is introduced into a spatial load forecast by ignoring redevelopment growth, there are work-arounds available for even the most classic of simulation approaches whose algorithms ignore it altogether. As a result, the actual error level in any simulation forecast due to an algorithm incapable of handling redevelopment is substantially lower than 15%. However these work-arounds will not address all of the redevelopment issues that are important to T&D planners, nor will they reduce error to the minimum possible. Table 19.8 summarizes eight methods or approaches that will be discussed in more detail below. Not all are recommended. None are complete - success requires using several in coordinated form. The order covered is basically from simplest to most complicated, of increasing the complexity a stage at a time as one moves from least- to most-comprehensive (and accurate) methodology. Method 1: Ignore Redevelopment Altogether Redevelopment has been completely ignored in many forecasts, with different results depending on circumstance. In cases where development is nearly all
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Table 19.8 Different Methods That Can Be Used to Address Redevelopment in Simulation-Based Spatial Load Forecast Programs Type Approach
Error Work Applies to Advantages
Disadvantages
1
Ignore redevelopment altogether
15% 1.00 Small towns, Simple rural areas
High level of error.
2
"Split classes" work-around
8% 1.30 Any size Allows use of metro area classic simulation or rural area program while controlling error to about one half
Effort, time and skills required for the work arounds are both high. Resulting error is usually low, but is occasionally great.
3
"Time-tagged" consumer class model
8% 1.05 Any size Requires additional Reasonable if metro area approximate model data on area ages. or rural area of the various End-use model modes of becomes much more complicated to set redevelopment. up and calibrate.
4
Manual intervention using spatial editor
10% 1.15 Any size By far the best way Labor intensive and metro area to handle strategic usually not highly or rural area growth, but accurate. inaccurate for other modes of redevelopment.
5
Preprogrammed redevelopment
10% 1.40 Any size Computerization of metro area (4) reduces error or rural area and improves documentability of the forecast
Usually inaccurate. Relies too much on user expertise, and requires skill to handle redevelopment well
6
Designated redevelopment areas
12% 1.01 Any size Simplifies modeling metro area of re-development. or rural area Very easy to set up. Requires less time, skill, and data than some other methods, Good set up of multi-scenario studies.
Not very accurate. Misses most tactical redevelopment completely and much strategic redevelopment.
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Error Work Applies to
Advantages
The single biggest 1.10 Any size metro area improvement or rural area needed to handle urban core and tactical redevelopment well.
7
Threshold factors in preference functions
8%
8
Urban pole compression model (computerized)
10% 1.20 Only very large metropolitan areas (over 1 million pop.)
More accurate than other methods at forecasting relative growth of different areas in a major city.
Disadvantages Must calibrate preference functions across-classes, which is tedious and requires great skill.
Complicated algorithm requires good expertise to set up properly.
2+7 Combine two or semi-successful 3+7 "work-around" approaches
6%
Synergy of these 1.40 Any size metro area two methods means or rural area the sum is better than the parts. Work required is not much more than that required for either.
Calibration can be difficult if this is all or mostly manual, as it is difficult to distinguish between effects of (2) and (7).
2+4 Combine all the +7 "work-arounds"
4%
1.55 Any size As good as metro area redevelopment can or rural area be handled by "work-around" methods.
Effort, time and skills required for the work-around effort are very high. Very difficult to calibrate.
4%
2.50 Any size Potentially good metro area accuracy. or rural area
Number of factors and their complexity makes for a nearly unmanageable calibration process.
or 3+4 +7 2+4 +7+ 8 or
Combine all the "work-arounds" with urban compression
3+4 +7+ 8 All of the above < 4% 1.15 Any metro All in a compatible area computerized package
As accurate as seems realistically possible.
Requires a lot of skill on the user's part. Calibration, even computerassisted, requires great skill.
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Greenfield growth, this has no consequences. Such forecasts are not uncommon. Several spatial load forecasts the author participated in for the Rio Grande Valley included no significant redevelopment because there was very little there in the beginning to redevelop. But generally, ignoring redevelopment completely is a perilous practice. Although the study of how growth occurred (Tables 19.2 - 19.4) covered earlier was limited in its scope, the conclusion that about 15 - 16% of growth occurs as redevelopment is fairly representative of most forecast situations. Planners risk roughly doubling the actual error in a forecast by ignoring redevelopment. All simulation methods evoke some process of spatial allocation. The computer program allocates among the small areas a previously performed global forecast, or it forecasts their load growth subject to a control total, which amounts to the same thing. It is worth considering the impact of ignoring redevelopment growth in this context. The spatial allocation process will allocate the global land-use change and load growth totals - in the context of spatial error discussed in Chapter 8, there will be no DC component of error. Thus, the method that cannot forecast growth as redevelopment, somewhere, will forecast that growth as vacant-area growth, somewhere else. The overall impact is easiest to picture by first considering what doesn't happen in the central, already-developed areas of the system: the load is not forecast to grow, whereas it will. Therefore, the program that cannot model redevelopment will forecast that growth to occur in outlying, vacant areas of the system. Redevelopment growth that occurs inside a city is forecast to occur on its outskirts instead. Figure 19.6 illustrates the type of forecast error that results, among the worst patterns of spatial error that can possibly occur in a T&D load forecast. While there is no DC component to the spatial error distribution, there is a great deal of low spatial frequency error. The good and bad about just ignoring redevelopment The only good aspect of this approach is that it simplifies the forecast process and reduces the effort involved. If redevelopment is not an issue, then planners have reduced their effort and made no impact on the forecast. But the "bad" usually outweighs any good. If redevelopment is an issue to any extent, the planners have introduced a significant error into their forecast by ignoring it, one which could be substantially reduced by work-arounds, even if not eliminated, regardless of how limited the programs and forecasting tools they are using might be with respect to how they model redevelopment. Method 2: Work-Around by "Splitting Classes" Normally, planners do not "totally ignore" redevelopment growth even if they are using a simulation method that models land-use change as only from vacant land. This work-around involves doubling land-use classes, creating two sets that are almost alike, but which represent land use that is redeveloping, and that
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Distance from City Core
Distance from City Core
Figure 19.6 Conceptual illustration of the impact of "ignoring redevelopment" completely with a simulation model. At the top, solid line indicates the load density of a theoretical city as one moves out from the city center, with high loads in the core and lower load density near the periphery. The dotted line indicates how the simulation, minus any consideration of redevelopment growth, will allocate load. As the forecast proceeds into the future, load densities nearest the city core will be underestimated and those nearest the periphery overestimated. Bottom, the resulting spatial error is among the lowest frequency error possible in the load forecast, and therefore has tremendous (negative) impact on T&D planning.
which is not. This doubles the number of classes that have to be used in the model. However, most simulation models were written with sufficient capacity to handle such a large number of land-use classes that it does not limit use of this approach. Land-use classes are broken into "old" and "new" sets. Both sets represent identical types of land use: residential, commercial, high rise, industrial, municipal, etc. Old land-use classes are used to represent land use throughout the system in areas that might redevelop. "New" classes are used to represent land use that has occurred so recently that redevelopment is unlikely. In general, all areas where the average age of buildings will be 30+ years by the middle of the forecast period can be classified as "old." Classes used in the end-use model have to be doubled, too. The end-use load model is used to represent differences between the load density for older as opposed to newer areas of what is
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otherwise the same class. The older areas are modeled as having a growing load on an annual basis, to account for the redevelopment that occurs in those areas. Example Table 19.9 shows an example, using as its basis the land-use classes and the class-by-class load densities from Chapter 11 's simulation example. Redevelopment in that example was not a significant issue (Springfield was basically too small a city for it to be an issue of importance) and what redevelopment there was to forecast was handled by manual intervention (see page 359). However, for the sake of this example, assume these classes, and load densities, were being used in a large metropolitan area instead of a small city like Springfield, one where redevelopment was certain to be an issue. Table 19.9, then, represents "old" and "new" class by class loads that started from the same set of class load densities (those in Table 11.8).
Table 19.9 Diversified Summer Peak Load Densities by Class (kVA/acre) for Chapter 11 's Springfield Example, Modified to Mitigate Hypothetical Redevelopment Error Consumer Class
Growth Rate
Newer areas of the system 1 Residential 1 2 Residential 2 3 Aprtmnt/Twnh. 4 Retail comm. 5 Offices 6 High-rise 7 Industry 8 Warehouses 9 Municipal 10 Heavy ind. Older Areas of the System 11 Residential 1 0.50% 12 Residential 2 0.50% 13 Aprtmnt/Twnh. 0.70% 14 Retail comm. 0.80% 15 Offices 1.10% 16 High-rise 2.10% 17 Industry -0.40% 18 Warehouses 2.20% 19 Municipal 0.50% 20 Heavy ind. 1.20%
Year Now
12
20
25*
2.97 2.87 2.73 3.09 3.03 2.80 2.75 13.98 13.75 13.52 12.99 12.50 12.02 11.80 18.18 17.83 17.59 17.40 17.25 17.10 17.00 21.69 20.51 20.00 19.86 19.75 19.65 19.55 62.69 61.40 60.50 59.50 59.00 58.80 58.65 192.00 189.90 187.20 185.00 183.00 181.20 179.80 20.58 20.00 19.50 19.00 18.75 18.69 18.66 9.21 9.22 9.24 9.32 9.20 9.28 9.30 63.04 61.80 59.35 57.50 56.73 56.73 56.73 240.64 240.64 239.00 237.00 235.00 233.00 232.00 3.04 3.09 3.09 3.06 3.03 2.99 2.97 13.98 13.89 13.79 13.52 13.27 13.28 13.37 18.18 18.08 18.09 18.40 18.76 19.66 20.24 21.69 20.84 20.65 21.17 21.73 23.04 23.86 62.69 62.76 63.21 64.94 67.28 73.18 77.10 192.00 197.96 203.43 218.46 234.83 274.58 302.30 20.58 19.84 19.19 18.40 17.87 17.25 16.88 9.20 9.62 10.06 11.00 12.05 14.37 16.06 63.04 62.42 60.55 59.84 60.23 62.68 64.26 240.64 246.45 250.68 260.73 271.17 295.78 312.61
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In this example, planners increased these old loads by the percentages shown in the second column for the "old" set. They obtained these percentage growth rates by studying load growth in older areas of the system. For example, their studies determined that over a decade, growth in the average apartment/townhouse area of the inner half of their system increased by 7.25%. This translates to .7024 percent growth, as shown for the apartments/townhouses in column 2 of the lower set of land-use classes in Table 19.9. These "redevelopment growth rates" are then applied on top of the load densities projected for normal conditions (new, or the top set, of Table 19.6). The composite growth rate is then used to adjust the base (new) land-use load densities so they grow annually, so they are "redeveloped." Note one class (industry) has a slightly decreasing "growth rate." This is rare but does happen it is being gradually abandoned/transformed to other land use types. All land use in areas of the system where the average building age is 35 to 40 years or greater is then represented with these older land-use types. The selection of this "age cutoff value" is a compromise. Thirty-five to forty years is about when redevelopment begins to occur (in most cases). However, as the forecast moves into the future, all areas of the system will age. Five years out, these "older" areas are 40 to 45 years old, ten years out they are 40 to 50 years old, and typically very ripe for some redevelopment. Thus, setting up the program in this way means that by the end of a 20-year-ahead forecast, only areas that are now 55 years of age or older will be "redeveloped." However, setting the cutoff lower (e.g., 20 years) means that early in the forecast process some areas that are "not yet ready" are represented as redeveloping. Modified method for "splitting classes" (more work) The planners could use three sets of land-use classes. They could have a new, old, and an interim soon-to-be old classification. These interim land uses would then only start growing in load in forecast year five of the forecast, thereby reducing compromise in "age cutoff date" mentioned in the paragraph above. The author is aware of one utility planning staff that used this approach. It produces a slight improvement in accuracy at a great additional cost in effort and program resources. Note that one cannot improve load forecast accuracy with this work-around by stopping the program at the end of each iteration and moving a few aging areas from new to old classifications with the program's spatial editor. (For example, areas that were only 25 years old in the base year could be moved from new to old classifications after year ten of the forecast to represent that they are now old enough to begin redevelopment). To do so would mean that the end-use model would apply ten years worth of redevelopment growth to them on the next iteration - making them "catch up" with those areas that had begun the forecast as redevelopable.
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Distance from City Core
Distance from City Core
Figure 19.7 Use of the "old and new" land-use class bifurcation reduces the amount of error and increases its spatial frequency, reducing its impact. At the top, dotted line shows the modeled spatial distribution versus actual (solid line). Bottom plot shows actual error is reduced even further - see text for details.
Impact of split classes on reducing error
Figure 19.7 shows the resulting error cross-section, corresponding to Figure 19.6's example. In examining this diagram it is important for the reader to remember that the simulation being discussed here is a spatial allocation. When using a standard simulation approach, nothing has to be done to the load densities in the outlying areas for the program to back off on over-allocating load there, if the load densities in the interior areas where redevelopment is likely have been raised. The higher "old" load density takes more of the growth and leaves less to be allocated near the periphery: over-estimation of load there is reduced.2 The resulting forecast (dotted line in the top of Figure 19.7) is closer to the actual (solid line) than was the case in Figure 19.6. Impact on T&D planning is 2
One detail not discussed in the example above. To implement this "trick" the forecaster has to first increase the load densities of the old areas of the system, as shown. He or she then must compute the increase in load that results, and manually adjust the simulation's global land-use inventory- the projection of how much land use grows overall each year, to compensate. Doing this well (to the extent possible) requires a lot of attention to detail and numerous computations. This is why Table 19.8 indicates that this approach requires up to 25% more effort. This is a tedious and labor-intensive analytical step.
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reduced even further. In the bottom of the figure, the thin dotted line shows the actual error. The heavy dotted line shows the effective error - which has been reduced even more. High-frequency components have been removed from the heavy dotted line, leaving only the "impacting" components of spatial error. This diagram is conceptual only, but the magnitude of the error diagrams here and in Figure 19.6 gives an idea of the relative level of error. This work-around cuts error due to an algorithm's inability to model redevelopment roughly in half. Advantages and disadvantages of "splitting classes" work-around This approach can be applied with nearly any land-use-based or consumer-classbased load forecast simulation. On average, it seems to roughly halve the effective error due to the program and/or users' not being able to model redevelopment. The procedure is straightforward. All analysis can readily be performed with only an electronic spreadsheet, even if it is tedious work. Against this, the "modeling" of redevelopment is really not very good, particularly with respect to spatial detail. Error is only halved. When forecasting the growth of older metropolitan areas, where there is little growth on the city's periphery, the error due to redevelopment, even if halved, would still be very significant. In addition, while the procedure to apply this is straightforward and can be done with only spreadsheets, the forecasting expertise needed to do this well is high. It requires considerable expertise to determine the rates for the older classes, to make the best compromise on setting the "cutoff age for an area, and to decide if an area is old or new or extremely high. This approach provides many opportunities for mistakes. For these reasons, it is recommended only if nothing better is available. Method 3: Work-Around Using Time-Tagged Land-Use Classes Some simulation programs not only identify the land-use class for each small area but permit the user to retain an attribute which is the "development age" of the small area - the year when the area was built out. These include particularly a version of the Westinghouse LOADSITE program (LOADSITE 2.2, August 1989) widely used in the late 1980s and early 1990s, and the CAREFUL program developed by Carrington. In these, an area of single-family homes built in 1992 would be classed as "residential 2" with an attribute of 1992. Time-tagging was originally developed to track differences in energy efficiency among older versus newer buildings. End-use models using this approach keep different load curve data for different age groups (see Chapter 4). The load curve for homes with an attribute of "1965" might reflect the lack of energy efficiency built into them, versus those with an attribute of "2002." However, time-tagging can be applied to represent redevelopment. There are no split classes. Using again Chapter 11 's set of land-use classes (Table 19.8), there would be only the original ten, not twenty. But the time-tagged end-use model would represent that after age 30, load density in residential class 2
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(residential 2) grows at .5% annually, and load density of class 6 (offices) grows at 1.1% annually. Error is reduced slightly from that of Method 2, due to better resolution of "interim age" areas which become "old enough" as the forecast moves into the future. The method is particularly effective at modeling redevelopment in the same class, which accounts for a small portion (about 2% according to Table 19.3) of redevelopment in metropolitan areas. Usually such development does change the load in such areas, something not modeled at all in most other approaches. Method 4: Manual Intervention In the Forecast Process In Chapter 11 's detailed forecast example, Susan, SL&P's forecaster, manually entered redevelopment of 19 acres near downtown into the forecast (page 359). The entire forecast process described in Chapter 11 was manual, so the handling of redevelopment there as a manual step did not seem any different than the handling of the rest of the forecast process. But any planner using a computerized simulation can apply a manual forecast of redevelopment, one done outside of the computer program and entered via the program's spatial data editor. To the author's knowledge, this can be done with every type of land-use or consumer-class-based simulation program. The process is simple to execute. The user simply determines what areas of the system will redevelop, to what land uses, in what year. He or she then uses the simulation program's data editor to change the land-use codes of the appropriate small areas at the conclusion of whatever forecast iteration is just before their date of redevelopment Figure 19.8 shows Chapter 12's diagram of the typical simulation iterative process, indicating the manual intervention. Here, the forecasters have decided to model redevelopment in year 2004. For the example here, assume they wish to model that 8 acres of municipal development, and 12 acres of high-rise commercial, would replace 11 acres of warehouses and 9 acres of light industry. As the program finishes the year-2003 forecast, they stop its operation momentarily. They manually edit: The spatial data for the areas to be redeveloped, changing the land-use codes from [warehouse] to [municipal] and [high-rise commercial] to indicate that redevelopment has occurred. The global land-use inventory, changing the counts so that on the next iteration the program will forecast 8 acres less of municipal growth and 11 acres less of high rise commercial than it otherwise would have done. If they decide that the 11 acres of warehouses and/or 9 acres of light industrial were needed in the region, and not redundant, then they add these amounts into those respective class totals for the next iteration. In this way, the growth the program does model is kept consistent with the overall global totals.
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2002 2020
2003
FORECAST A-j \ ALGORITHM
Program User
2005
2010
2007
Figure 19.8 The user can intervene in any iteration to change land use to whatever he or she believes will occur with respect to redevelopment, then let the program proceed. Here, the forecaster has intervened at the end of the forecast program's second iteration, entering data that represents redevelopment expected to occur after 2004 but before 2006.
They then re-activate the program and it completes the cycle of iterations, beginning with the iteration for the period from 2004 to 2005. The redevelopment is now included both in the totals, and in computation of the surround and proximity factors for those small areas around it. Using manual Intervention to represent strategic redevelopment In cases of known or planned strategic redevelopment, manual intervention, whether truly manual or "pre-programmed" (see method 5) is probably the best way to model the redevelopment. There are two reasons. First, even the best redevelopment algorithms cannot forecast some major redevelopment projects. Many just "do not make sense" from the standpoint of a simulation program's pattern and preference computations. The largest and most grand redevelopment projects only make sense when viewed through a "visionary lens." Often, the politicians or developers driving a major redevelopment project see how it will change the urban landscape around it. In fact, they may be driving the particular redevelopment project mostly because they want its effect on the rest of the urban area, more than they want that redevelopment itself. Baltimore's Inner Harbor redevelopment is only one example, but a great one, of a major
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initiative that changed the character of the entire region around it. Simulation programs often cannot see and therefore will likely not forecast such quantum changes in urban character. The only way to "get it right" is to manually enter it. Second, manual intervention and entry fits the needs of planners, which invariably require them to study proposed redevelopment projects as scenarios. Not all such initiatives come to fruition. Those that do have long lead times long enough for planners to consider them carefully. Often, the utility is being consulted in the matter - "If we redevelop this area what facilities will be required for electric service?" Manual entry of the redevelopment project as a scenario is the way it should be studied. Details and caveats with respect to strategic redevelopment In general, with respect to spatial data, little more is required of the planner to apply this method than the redevelopment plan's land-use being entered into the program for the areas indicated, in the year's it is planned. Considerations for the global model, however, are more involved. Planners need to determine if the particular redevelopment scenario will impact global land-use inventory changes and if so, how. Questions that need to be answered are: Will the existing land use be displaced? Should the land use be replaced by adding to the global model's land-use counts so it is "rebuilt" somewhere else in the service territory? This is the case if that land use is needed. For example, if 100 acres of homes and retail shopping are displaced as part of a redevelopment project of the city's international airport (runways lengthened, etc.) then that displaced land use needs to be "moved." This is most expeditiously and accurately done by having the program forecast it as new development in the subsequent forecast iteration. The 100 acres of land use is added to the global model's totals for growth in the next iteration. On the other hand, if the issue is 20 acres of completely abandoned and unused warehouses, then they are redundant and do not need to be modeled as displaced land use. This land use is not added into the global model. Is the redevelopment project's land use in addition to, or part of, the normal growth for the service territory? For example, a redevelopment project that includes a new convention center or stadium, along with hotels, restaurants and so forth, usually represents a net increase in the entertainment industry for a region. Therefore it is in addition to all base land-use change. An example of a net increase due to redevelopment is in downtown Denver, due to the new stadium of the professional baseball team, the Rockies. So is the redevelopment of Baltimore's inner harbor, which included a major convention center, and eventually, a new baseball stadium, etc. In such cases, the land use of the redevelopment should be added to the base-case's land-use increase amounts, as represented in the simulation's global model.
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However, a project that calls for mostly office towers and other similar employment centers represents only a planned change in where such growth might otherwise locate. Usually, this is only a change in the preferred locations of the same amount of growth that would otherwise occur. Detroit's Renaissance Center is closer to this category than it is to Denver or Baltimore's examples. It included offices and changes that were in essence competing against "edge city" development on the metropolitan periphery. In many cases, only a portion of the redevelopment is additional. Baltimore's inner harbor included shops, hotels, museums and a national aquarium, retail aimed at both tourists and local residents, and commercial space and high-rise offices. It represented a net increase in tourism, but part of it was merely relocation of commercial offices.3 Parts of that project should have been added to the global model totals (those associated with tourism) but not other parts. Using manual intervention to represent tactical redevelopment Manual intervention works well - often better than any other method - for meeting the planners' needs to study major (strategic) redevelopment initiatives. Using it to model tactical (small scale) redevelopment is much more challenging and prone to somewhat more error. However, it can be done and it has been done well at the cost of much tedious work. There are numerous approaches, all variations on the one theme to be explained here. Suppose that a detailed study of redevelopment for warehouses within the inner core (perhaps a ten mile radius) of downtown indicates that 6.5% annually are converted to retail/loft apartments. Then, planners can manually edit one out of every 16 warehouse small areas per year of forecast (in a uniform grid approach, or about 6.5% of land-use change in polygon areas). This manual intervention represents their change to retail and apartments/townhouses land use. The big issue, of course, is where the editing of small areas will be done. Planners can use their judgement, or pick those areas closest to downtown, or select random areas. All seem to produce about the same overall forecast error. A superior method, if data is available, is to identify some pattern to conversion seen in the past. There is no guarantee that past trends will continue but extrapolation of the trend is generally slightly better than random selection. This is done only in the inner areas of the system. Ultimately, with respect to tactical redevelopment, the use of manual intervention modeling is no more effective than, but just as effective as, method (2), split classes, at modeling tactical redevelopment growth.
Very few out-of-towners would have wanted to visit Baltimore's Inner Harbor as a tourist prior to its redevelopment. Now it is a popular attraction (and one of the author's favorite places for a short, fun get-away).
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Advantages and disadvantages of manual intervention The advantages of manual intervention modeling of redevelopment is that it is straightforward to apply, it works with any simulation program, and it fulfils most of the needs that planners have for modeling strategic redevelopment in multi-scenario studies. But frankly, its biggest "advantage" in the eyes of many users (and perhaps also its downfall) is that it gives planners complete control of the redevelopment modeling. They can apply their "judgement." Against these advantages, manual intervention has several disadvantages. To begin, the user's have to apply their judgement - if it is flawed, so is the forecast. And it is not good at modeling urban core, tactical, and in-kind redevelopment. Method 5: Designated Redevelopment Areas Some simulation programs permit the user to set a "redevelopment availability" flag or indicator from each small area. This was a feature in ABB's LOADSITE and in a modified form in its FORESITE programs (1992) but is now widely used, for example in Terncal's DIFOS and Carrington's CAREFUL programs. Turning this tag to "on" (setting it to 1) for a small area forces the simulation algorithm to consider that small area as vacant with respect to future development. The simulation algorithm will treat all those areas with the redevelopment flag set to "on" as if they are vacant and available for development. Generally, this approach includes land-use inventory features that count all land use that is displaced and add it into the global inventory for purposes of replacing it with "new" land-use change in vacant areas. FORESITE and DIFOS took this approach. Displaced land use is put back into the pot to be reallocated to other areas of the system. Potentially this could include other designated vacant areas, but usually it is represented as new growth in previously vacant areas of the system. The CAREFUL program uses a unique approach to this displaced land use, aimed at modeling redevelopment in a very crowded megalopolis. The algorithm forces all displaced land use to be replaced with new growth within the influence area of its nearest urban pole (actually, with an area described by 80% of the pole's radius). If no vacant land is found for this displaced growth (usually the case) the program boosts the load density of all of the land use of that type within that area by an amount calculated to match the displaced land uses' load. The approach is apparently accurate at representing a type of "continuous growth in overcrowded mixed urban conditions" which is a characteristic of cities such as Hong Kong, Shanghai, Bombay, and New Delhi (Carrington and Lodi, 1992). Modeling strategic redevelopment with the designated-area approach Use of a redevelopment flag does not do a good job of representing strategic redevelopment. It is not recommended for situations where manual intervention
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can be applied. In general, if the area proposed for a major municipally sponsored or large developer-financed project is modeled using only this approach, any simulation program will forecast it as developing into something other than what is planned for the project. The simulation will invariably pick development that fits (as much as possible) the present urban landscape around the designated area. The limitations of simulation in "seeing" the visionary overall long-term pattern of a redevelopment project, covered in Method 4 above, apply here. Since manual intervention can be used with virtually any simulation program, there are few situations where a planner should use this redevelopment-flag, designated-areas approach to model strategic redevelopment. However, if planners choose to, then the area should be zoned (if the simulation program permits this) to limit growth to only the planned redevelopment land use. Designated-area modeling and tactical redevelopment Unlike strategic redevelopment, tactical redevelopment most often does match the local urban landscape, at least in a broad sense. Thus the preference-function engine should be able to do a good job of forecasting redevelopment. However, a basic simulation program can potentially make two mistakes with respect to tactical redevelopment: it can over-forecast redevelopment, and it can get the land-use class wrong. These are potentially a problem with any forecast, but a characteristic of some designated-area models exacerbates both types of error. This has to do with how the "cost" of removing the old buildings at the site is handled by the program. Anyone wanting to build on an already-developed site has to not only buy the land, but the existing buildings as well, and then pay to demolish them. This means that an otherwise identical vacant area will always be picked over a currently-developed area for new growth. Existing development sets a threshold: land with existing use must be more suitable for its new purpose than available vacant land, in order for it to be selected for development. Simulation programs need to be able to model this cost with what are often called "redevelopment threshold" factors in order to be fairly accurate at predicting redevelopment. Thresholds: the key to success in modeling tactical redevelopment Therefore, designated-area approaches are most successful when the spatial preference factor computation applies a threshold or negative factor to the preference function calculations when the area is already developed. This threshold or negative factor represents the cost or difficulty in removing the existing land-use prior to development of the new. Looking at the preference function equation used in Chapter 13 (eq. 13.4) to compute the suitability or preference score for c class, for vacant area x,y, which was
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J PC fry) -
S(fj(x,y)*pj,c) (19-0 j=i where j indexes J (the factors) and c indexes C (the land-use classes). Pc(x,y) is the pattern match score for small area x, y to class c pj>c is class c's coefficient for factor j and by definition, pj>c e [-1.0, 1.0] fj(x,y) is the score for factor j in small area x,y Pc (x,y) is therefore somewhere between -12.0 and +12.0 for J = 12 This can be applied for a non-vacant area with the following addition of a threshold factor drawn from an N by N matrix where N is the number of nonvacant land-use classes J PC fry) = Z(fj(x,y)*pj,c-T(c,e(x,y)) (19.2) j=.l where T(c, d) is the threshold required for land use of class d to develop to class c, and e(x,y) is the existing class of area x,y In a simulation program in which preference values and all associated computations were based on absolute economic value, T would not have to be a matrix. T(c, d) would be the same for all values of d, and thus a single factor for each land-use class could represent the cost of buying and removing the old building for that class. However, most simulation programs measure preference in arbitrary units, usually normalized to a value of 1.00 = perfection within each class's context. As a result of this normalization, the same existing land use may need to have a different threshold applied for consideration of its suitability in each of the land-use classes it might potentially become. For example, suppose the cost of buying single-family old homes in an older area of the city and removing them from a site represents 10% of the total value of a new home (including lot). Then in some sense that cost represents a 10% negative factor - the site has to be very good relative to other options before someone would pay 10% more overall in order to gain a home site close to the city. Thus, an appropriate factor might be .10 for row 2, column 2, of T. But the cost of buying and removing homes represents only a tiny amount of the cost of building a high-rise building. What was a 10% factor would be far too high when judged against high-rise class preference scores. In fact, the value would be close to zero. Thus, in cases where a program uses arbitrary preference scores normalized on a class by class basis (and almost all simulation programs do), a T(c, d) matrix is required to represent redevelopment costs well. Generally, the threshold should represent the cost of removing the old land use as a portion of the all inclusive cost of the new land-use development.
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In some cases, a value should be added not subtracted: conversion of warehouses to loft apartments generally costs less than putting up an all-new apartment building. Using designated areas to model redevelopment Again, manual intervention is generally a much more satisfactory way to model strategic redevelopment than the designated area approach, and is recommended, although it does require more work and record keeping by the planners. Tactical redevelopment can be represented well if the simulation permits and the user applies well the set of threshold values in a (T(c,d)) matrix as discussed above. Some spatial load forecast simulation programs do not permit the user to apply thresholds. However, they can be set up to mimic their effect with a nearly universal work-around. Many simulation programs permit the user to enter a "development bias" factor for a small area, basically a value that will be added or subtracted to its preference scores, boosting or dropping its suitability scores in comparison to other areas and making it more or less likely to develop.4 In such a case, when the user "turns" on the redevelopment tags in a set of small areas, he or she should also enter negative factors of value for these small areas, corresponding to T(c,d). Again, this represents manual entry of the redevelopment cost of each area. And, of course, that represents the cost of clearing out the old and preparing the site for fresh development, which is a factor, T(c,d). Unfortunately, this work-around forces the planner to apply the same value for all values of d - regardless of potential land-use class the small area could become - as opposed to different values applied to each class's suitability, as was described above. Advantages and disadvantages of the designated-areas approach The advantages of designated areas are that they greatly reduce the work required of planners and forecaster using a simulation program, when modeling redevelopment. However, method cannot model strategic redevelopment well. If augmented with a matrix-based threshold value model as discussed above, it does an acceptable job of forecasting tactical redevelopment, if the threshold values are properly adjusted. There really are no disadvantages, if the approach is kept within its limitations, which means it is used only to model tactical redevelopment and all strategic redevelopment is handled by some other method (which usually means manual intervention, since programs that use the designated-area approach generally do not have any of the more advanced models discussed below).
4
Such factors are often used as a brute force way to "tune" or calibrate the dynamic characteristics of a simulation to reproduce recent growth patterns in an area. Although not frequently used, many simulation programs have features that permit this.
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Method 6: Preprogrammed Redevelopment Events Some simulation programs that use an event-driven format for their iterations have features that permit the user to enter descriptions of redevelopment events that will occur in certain areas at certain times. The user enters a series of landuse changes (from, to) for specific small areas, and a time (year). The program then applies this as a growth event. This is basically a computerized form of manual intervention (Method 4) designed to model strategic redevelopment. Everything stated above for that method applies to this. It does not work well on tactical redevelopment. Advantages of computerization over the manual (program editing) approach are that it is quicker and the user does not have to fuss with adjustments to the global model. The program handles such accounting automatically. Method 7: Generalized Tactical Redevelopment Model If a designated-area method (Method 6) is set up to work really well, with appropriately fine-tuned values of T in use, then there is little need to designate redevelopment areas within the metropolitan area - all areas, except restricted and undevelopable land, can be considered potential areas of new development. This approach can only be used when the model is very well calibrated and the T matrix is correctly calibrated. Otherwise considerable error, including obviously incorrect spatial patterns of growth, will occur. Strategic redevelopment still must be handled manually, or with Method 6. Method 8: "Compression Models" of Urban-Pole Center Growth Urban poles are used to represent the cumulative effect on regional growth of a large concentration of high-rise and urban development in an area, but what influences the growth of the urban pole's kernel - the high-rise and urban growth itself? Where in a metropolitan area does the real urban development - high-rise and dense "core" development, grow? Many planners regard the basic simulation approach as incomplete when it comes to answering this question — to modeling the locations of the causes of urban poles (industry and high-rise commercial). While the global land-use inventory model may represent that a specified amount of high-rise growth must be forecast, it does not specify where. And while preference functions (e.g., eq. 19.1 and 19.2) can compute the suitability of a location for high-rise, this is incomplete because that addresses only supply, not demand issues. What is lacking is a mechanism to represent the growth of the urban centers themselves and competition among them for high-rise growth. Does downtown continue to grow if powerful suburban centers develop? As an example, Houston, Texas, has a number of "competing" urban poles: its downtown core, Greenway Plaza a number of miles to the southwest, the Galleria/West Loop area slightly farther out to the west, a commercial office concentration at the
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intersection of I- 10 and Highway 1960 to the northwest, and many other highrise commercial centers. Just as there are different theories and examples about why cities grow, there are a large number of different methods to simulate the "competitive" growth of these types of urban poles. Among those that seem to work is the "reciprocal effect model," which will be summarized here, as representative of the general concept. Urban poles are activity centers that cannot function without an urban fabric around them, a large regional economy which can serve as the center. If the metropolitan area shrinks, so will the urban pole's basis (the high-rise and urban development), at least with regard to occupancy and economic activity). Among several different poles, their respective proximity to the rest of the urban fabric can evaluate how connected they are to the whole and thus how viable they are for future growth. Therefore, among a set of urban poles, one model of their respective development potential is to evaluate what surrounds them, not on a surround and proximity factor basis (what is nearby) but on a regional, very-low frequency spatial basis. In fact, this model usually employs the same "urban pole" functions in reverse. For each of a set of urban poles, a weighted-sum of all of the land use within that urban pole function's radii is developed, with any land use that falls in two or more urban pole radii allocated based on the respective values of each pole function. Influence for pole p at location x, y - Up(x,y) = height of pole at point x, y The economic clout of pole q, Mq, is its share of the weighted sum of land-use value within its radius, shared with other poles on an influence basis Mq = £ ^(Uq(x,y)/ZUp(x,y))x(i;A(x,y,c)*Fc) x=l
y=l
p=l
(19.4)
c=l
where A (x,y,c) = the amount of land use type c in area x,y Fc = an economic value weighting factor for land-use class c Basically, each pole gets its "share" of the land-use "value" in each small area, based on its influence over that area as compared to all other poles. The Fc weight land-use type by value - high-rise commercial land use is worth more than light industrial, etc. Usually, relative values of the Fc are based on the relative economic value of the types of land use (value in dollars to the buildings and land) are used. The actual units are unimportant since the total will be normalized to 1 .0 total for all poles below. Finally, pole q's portion of regional economic clout is computed as p)
p=»
(19.5)
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The global model's growth of urban land-use (high-rise) is then allocated to each urban pole based on its value of Cq versus the total for the region. Thus, if pole q has 22% of the economic "clout" of the region (Cq = .22) then 22% of the region's high rise will occur near its center. Even if the pole has no land use available, land is redeveloped to match this "given." The term "urban compression" comes from a perspective that the surrounding region is placing a pressure for growth on urban centers, proportional to its activity's proximity to them. Growth is driven upward if it cannot move outward. The reader unfamiliar with simulation models and growth processes might wish to consider carefully how such a model responds as the urban fabric grows. Growth of the city around a pole and the growth of the pole's basis are not necessarily reciprocal. A large pole may exert a tremendous influence over a region, yet there may be no land, or no suitable land, available for growth with its radius of influence. No land-use growth (and hence no cause-1 load growth) will occur within its influence area, despite its influence, because there is no room for expansion (or little room save for redevelopment). As a result, as modeled here, it will not grow or grow only slowly. By contrast another pole, of lesser size, may be proximate to a good deal of suitable and developable land. Land use there will develop, the land-use value within that pole's radius will grow rapidly, and its share of regional "urban clout" and hence more high rise will develop near its core. As an exercise, the reader might wish to consider what would happen with this model if a planner created an urban pole at a point where there was no highrise commercial, but assigned this new pole some influence anyway (a height and radius). High-rise commercial will begin to grow in and around the center of the pole, in the closest and most suitable local places to the pole location. If necessary, redevelopment will occur (if the simulation can handle it automatically) to force old land use out so new high rise can develop there. Thus, this model, rightly implemented, drives redevelopment. There are numerous variations on the theme of this approach, but the above equations and explanation summarize the essence of an urban-demand-driven, spatial activity center growth model. This is one way to model the demand for high-rise commercial development on a spatial basis. A standard addition to this model is that it may bifurcate urban pole influence so poles can be designated as places where only commercial or industrial, but not both, grow. Advantages and disadvantages of urban compression models When properly calibrated and set up, this model produces representative forecasts of cities like Houston, Chicago, and Los Angeles that seem to have the expected balance of growth among poles. Against this, it is quite complicated and requires a good deal of skill and often a lengthy calibration effort. If not set up correctly, a type of oscillation of growth, with growth moving from one pole to another and back again on each subsequent iteration, can occur. But the
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overriding fact is that urban activity centers do grow due to the "demand" for their influence or "services" as the core(s) of the urban areas. This model represents that, and if properly set up, can give good results. Method 8-S: Spatial Frequency Demand Urban Compression If the simulation program both implements a spatial frequency domain model and permits the user to set up "macro" commands, it is possible to implement urban compression in a frequency-domain manner which slightly improves accuracy and computation speed. The concept is the same as illustrated in Figure 14.5, with a distributed urban pole. The improvement in detail is exactly as described there, for urban pole application, and for precisely the same reasons. Some simulation programs that use spatial frequency domain computation may give the user no choice but to model urban compression with this method. 19.5
RECOMMENDATIONS FOR MODELING REDEVELOPMENT INFLUENCES
Most Important: Don't Ignore Redevelopment Above all else redevelopment should not be forgotten just because growth in new areas is easier to see, higher in growth rate, or more compatible with the type of computer program being used as a forecasting tool. Redevelopment accounts for a significant portion of electric load growth in most utility systems, and if it does not, the reasons behind that fact are worth knowing - they almost certainly influence other trends important to the planner, too. Avoid Curve-Fit Types of Trending Applied to Redevelopment Traditional curve-fit and similar trending methods simply cannot accommodate redevelopment in any meaningful manner. As discussed earlier, development of existing areas presents a classical "S curve" transition, which will create tremendous extrapolation error for any type of curve fitting. Template matching, at least the "very smart" template matching algorithms, are capable of addressing some if not all redevelopment characteristics and are much preferred among trending methods. But usually, "trending" does mean curve fitting, using polynomial functions whose coefficients are selected through multiple or stepwise regression. While not recommended, if this is the only method available then the planners have to make the best of it. In that case, horizon year loads are the mechanism with which to address redevelopment. External to the trending program the forecaster should assess if redevelopment is likely in an area and determine a horizon year load that reflects the expected completion date for the redevelopment. In addition, if a redevelopment project is known, or suspected, a "horizon year" load somewhere in the near term can be used to represent that (see Figure 19.5). A reasonable approach in some cases is to "borrow" a forecast done within this
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paradigm (e.g., a municipal population forecast) and interpret it for the horizon year loads. Regardless, this "external to the trending program" effort means the planners are in effect using simulation concepts if not algorithms. Therefore, it is recommended that they formalize their process as much as possible through development of a written procedure, along with documented notes on what and why they made adjustments and determined horizon year loads. When Using Basic Simulation, Employ All Possible Work-Arounds "Basic simulation method" as used here means algorithms and computers employing them which have no features to "grow" vacant areas or make transitions from any land-use class but vacant, that do not allow pre-programmed redevelopment, that have no time-tagging of land use, and that do not employ threshold factor (Tc) matrices. The following features are strongly recommended for any metropolitan forecast using such a basic simulation, where redevelopment might be a factor in the future growth of consumers and electric load: • Split land-use classes should be used to represent urban core, tactical, and in-kind redevelopment • Manual intervention should be used to represent strategic redevelopment projects as alternative scenarios. Planners should study the local growth rates around each of the major activity centers in the region. Based on this knowledge, program features (specifics will vary from one program to another) should be adjusted so that the growth rates of high-rise load near the center of each pole continue to grow according to recent trends. If Time-Tagging of Land-Use Is Available Time-tagging can completely model in-kind redevelopment and does an incomplete but acceptable job (i.e., better than other work-arounds) of trending urban core growth. When available, time-tagging should always be used to workaround tactical redevelopment rather than having the planner resort to the use of split land-use classes. Strategic and large-scale redevelopment should still be modeled with manual or pre-programmed intervention. If a Designated-Area Feature Is Available It should be used, but restricted to modeling tactical redevelopment. A simulation program's designated-area feature should never be used to represent strategic redevelopment projects — the simulation program is almost certain to predict the new land-use pattern incorrectly. Instead, strategic redevelopment projects should always be represented by manual intervention or as pre-
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programmed event development (essentially the same) if the program has that feature. The author has never encountered a situation that violates this rule. Generally, the designated-area feature works best when used in conjunction with redevelopment threshold factors (a T matrix) in the preference function (suitability) computations. If the program cannot apply threshold factors, the user might wish to consider the use of bias factors as an approximation (see discussion of Method 5 given earlier in this section). However, this is recommended only if the forecaster is confident that redevelopment in the designated area will lead to only one or two classes. Diversity in possible future development renders the bias approximation too error-prone (see discussion of why a T matrix is needed in Method 5, above). If threshold factors cannot be used, the user should strongly consider not using the designated-area feature and instead modeling non-strategic redevelopment with split land-use classes or time-tagging growth as recommended above. If a Threshold Factor (Tc Matrix) Is Available Some simulation programs do not have designated area features but permit the user to allow redevelopment anywhere via selection of a "redevelopment tag" or soft switch set to 1 or "Yes." In programs with this feature, the forecaster should consider using this feature to model tactical redevelopment and dispense with any need for designated areas. However, calibration of the preference functions, and of the T matrix, is now of critical importance. This applies to both the T matrix and the preference functions - they must be "dialed in" more precisely when modeling redevelopment. A simulation algorithm with this feature turned on is not nearly as robust with respect to slight set-up errors as one without this feature or with the feature turned off. When Using a Complete (Computerized) Redevelopment Simulation Forecasters using a simulation program whose algorithm utilizes time-tagging, redevelopment thresholds in preference factors, pre-programmed redevelopment events, and urban pole compression modeling have all the tools they need to represent accurate redevelopment in all its forms. These "complete redevelopment models" work with a diverse set of interrelated factors. Calibration is quite involved, and forecasters new to this level of modeling often find that keeping track of all the factors and their interactions can be very challenging. But when used correctly, the model is very representative of the entire process of metropolitan-area redevelopment growth and its competition with vacant area growth on the periphery of the region. The largest problem area in applying such a comprehensive model revolves around the interaction of urban poles and preference function/threshold values. With a number of exceptions (to be covered below), the preference function coefficients and the Tc matrix elements should be spatially invariant. In simpler
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words: the same set of function coefficients and threshold values should work just as well throughout the utility service territory being modeled, if they are set up correctly. However, if in the calibration phase it becomes clear that preference factor and threshold values are calibrated well in some parts of the service territory but not others, then one of two situations has developed: 1) The urban poles are not calibrated correctly, despite any appearance that they are. Despite all static diagnostics, the pole calibration must be revisited - it may be in error. This gets messy: preference factors need to be examined for calibration within each pole influence area. Poles where the preference factors work out well should be left alone. Those where it appears that the preference factors applied in the area show error should have their heights and radii revised. 2) The region consists of two or more very different, locationally segregated economies, so that the preference and threshold factors will not be the same. The portions of the region tied most strongly to the different urban poles are far different themselves. If differences are spotty and calibration error has any high-frequency spatial component or pattern at all, then (1) is the case. The user should apply a good deal of assessment before determining that (2) is the case, and there must be a very visible economic or demographic difference among sub-regions before this hypothesis should be acted upon. As an example of such a case, in metropolitan Houston, the east and northeast (petroleum refining, heavy industry) and west (commercial, service, high technology) sides of the city are very different "cities" that just happen to share the same urban core. Calibrate Urban Compression Last As a general rule, all dynamic features should be calibrated after all static features are calibrated. And among dynamic features, urban compression factors should be calibrated only when all other factors appear to be correctly set up. 19.6 SUMMARY Redevelopment is a constantly ongoing mechanism of electric load growth that accounts for a significant portion of the electric load growth in large metropolitan areas. It consists of four types, which occur simultaneously and intermingle their effects: 1. Urban core growth — "downtown" grows up, not just out. 2. Strategic redevelopment - large projects planned to change the entire urban fabric
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How forecasters handle redevelopment will vary depending on the situation they face, and the tools, data, and resources they have. Perhaps the most important rule is to never ignore it, and to understand what and how even if that cannot be directly modeled. REFERENCES J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabat, April 1988. J. L. Carrington and P. V. Lodi, "Time-Tagged-State Transition Model for Spatial Forecasting of Metropolitan Energy Demand " in Electricity Modern, Vol. 3, No. 4, Barcelona, Dec. 1992. C. Ramasamy, "Simulation of Distribution Area Power Demand for the Large Metropolitan Area Including Bombay," in Proceedings of the African Electric Congress, Rabot, April 1988. A.
M. Sander, Forecasting Residential Energy Demand: A Key to Distribution Planning," IEEE PES Summer Meeting, 1977, IEEE Paper A77642-2.
W. G. Scott, "Computer Model Offers More Improved Load Forecasting," Energy International, Sept. 1974, p. 18. H. L. Willis & J. Aanstoos, "Some Unique Signal Processing Applications in Power Systems Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, Dec. 1979, p. 685. H. L. Willis & J. Gregg, "Computerized Spatial Load Forecasting," Transmission and Distribution, p. 48, May 1979. H. L. Willis and T. W. Parks, "Fast Algorithms for Small Area Load Forecasting," IEEE Transactions on Power Apparatus and Systems, October, 1983, p. 342.
20 Spatial Load Forecasting in Developing Economies 20.1 INTRODUCTION While a good deal of electric load growth occurs in the United States, Europe, and other "First World" countries, the majority of T&D system expansion expected in the first third of the 21st century is in countries with rapidly developing infrastructures. In many developing nations, it is common to see electric service extended into non-electrified regions, and entire new cities built, where previously there was no development. In both cases, forecasters and planners face a forecasting situation far different from those encountered in the planning of large cities and rural regions in countries with established and stable infrastructures. Electrification Projects Electrification involves extending electric T&D facilities into a populated region previously without electric service. The locations, types, and numbers of future consumers are largely known: the present inhabitants of the region. People in the region have been without power: they have a "latent demand." Some land-use growth will occur, but it will constitute a minor part of the forecasting equation compared to the impact of the incumbent population. The major uncertainty in forecasting revolves around how much and what type of electric usage these consumers want and can afford. Added to this are two issues nearly unique to electrification projects. First, electrification of a region drives its economic growth, leading to further increases in electric demand. Second, the thriving economy attracts people from nearby non-electrified regions, who are literally attracted by the "bright lights" 631
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and employment opportunity the region now has. Population grows, and with it, electric load. And, of course, a challenge the forecasters face is that while the consumers are already inhabiting the region, and while there is no doubt they want electric power and the benefits it can bring, none of the usual data sources — load readings, utility consumer billing records, etc., exist. This problem often calls for planners to be innovative and flexible in their approach to the forecast. New Cities Similar to electrification projects, but far different in planning and forecasting challenges, is a greenfield city project, in which a national government decides to build a new city in a previously rural area. Examples of such planned cities are Brasilia (Brazil) and Abuja (Nigeria). Such city projects are not uncommon in developing nations, but are virtually unknown in Europe and the United States. Both Are a Challenge But Only One Is Unique Despite its greater challenge, new-city forecasting is actually quite like forecasting load growth in developed metropolitan areas, only with a much higher level of uncertainty in all phases of electric usage. It is difficult due to the higher uncertainty, but nothing much can be done about that except to apply the best standard simulation methods with care. By contrast, forecasting load growth in the face of an electrification project is unique. The planners face a far different type of uncertainty, and they must model different driving processes for long-term growth than from those they model in other types of forecasting. New-city and electrification projects both typically occur in developing countries. Both involve extending electric service into areas currently without substantial electric facilities. But beyond these superficial similarities, their two forecast situations are very different and they present far different challenges to the load forecaster and planner. Table 20.1 summarizes the qualitative differences in the three types of forecast situations: developed area, new city, and electrification. Table 20.2 gives the author's estimation of the relative degree of difficulty encountered in forecasting each. In the author's opinion electrification and new-city projects are respectively about 25% and 50% more difficult to forecast than normal metropolitan or rural growth. This chapter will examine both electrification and new-city forecasting, focusing on what is unique to each type of situation and how the forecaster can deal with it. Section 20.2 will look at four specific elements of electrification forecasting, and the details of how each is addressed. Section 20.3 will then review an actual electrification forecasting case, done with two different forecast approaches. Section 20.4 discusses some key points about new-city forecast projects and outlines in detail the tools and procedures to address those types of situations. A summary of key points and guidelines concludes the chapter in section 2 0.5.
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Table 20.1 Qualitative Comparison of Types of Forecast Environments Type of Aspect of the Forecast Other Forecast Land-Use Usage Issues Known, but future Biggest concern in Existing Established but slowly changing. growth uncertain. planning is that an metropolis Growth in the Future land-use existing T&D infragrowth is mostly a per capita usage structure exists and may function of a large be difficult and costly is very expensive number of factors, to handle (see ->) to enhance. Mistakes local events, and are very expensive. regional conditions Growth is dominated by land-use additions and change that involves urban interaction and is difficult to analyze and forecast Electrification Land use exists and of a region there is very little uncertainty about the what and where of usage patterns. New City Project
Land use is planned and may be well controlled, but the actual pattern that will develop is very uncertain.
No local precedent exists for usage statistics by class. Great uncertainty
Impact of electricity on the local economy In-migration due to increased attraction of the region.
Established. Planning situation is Will be similar to mostly Greenfield. class-usage patterns Forecasting worries are in other nearby cities mostly related to //"the (subject to weather). expected timing and locations of land use will develop as planned. In-migration due to increased attraction.
Table 20.2 Comparison of Uncertainty by Forecast Situation Forecast Uncertainty Faced In Type of Importance of (out of 100%) Difficulty Land Use Usage Study Area M.D. E.U. L.D. E.E. In-M 1.00 .85 .15 Established, 70% 20% 5% 5% and growing Electrification of region
1.25
.25
1.00
New city project
1.33
1.15
.35
5% 15% 30% 25% 25% 65% 20%
5%
5%
5%
M.D. = metropolitan development interactions, E.U. = end use, L.D. = latent demand and appliance acquisition, E.E. = electrification impact on economy, In-M = In-migration effects
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20.2 MODELING LOAD GROWTH DUE TO LATENT DEMAND One forecasting challenge faced by utility planners in developing nations is forecasting latent demand. A good deal of the electric load growth in such nations is due to the extension of the electric grid to rural villages and towns, communities which previously did not have electric power. As soon as (or even in anticipation of when) these areas have electric power, homeowners, businessmen, and municipal leaders obtain electrical appliances and equipment to satisfy an existing but previously unserved demand for power - a latent demand. After electrification they continue to obtain electrical appliances until they "catch up" with the demand level common for their consumer class. The process of load growth in such situations is the exact opposite of that seen in most of the circumstances covered in the previous 19 chapters, and at which normal trending and simulation methods are aimed. Developed areas. The majority of growth comes from new consumers entering the area. These are homes and businesses that were not previously in the area. They relocate or build in this area with a "stock" of electrical appliances already in hand. Developing areas. The majority of growth occurs due to homes and businesses already in the area. Over time, they acquire a stock of electrical appliances. The process of growth is different. And so are the results. Figure 20.1 shows the annual peak load level (April) for two villages, one in central Africa, one in central American, during the years after electrification. The growth trend is
•o 6
0
1
2
3
4
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8
9
Years After Electrification
1
0
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1
2
3
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5
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7
8
9
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Years After Electrification
Figure 20.1. Left, annual peak electric demand for an agrarian area (series of small villages) in central Africa, for the ten years after electrification. Right, similar data for an agrarian/fishing region in central America, for the eight years after its electrification.
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20
16 12
•o S
8
1930
31
32
33
34
35 Year
36
37
38
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401941
Figure 20.2 Current developing-area load growth does not appear to be that different in pattern from that seen during electrification of the U. S. This shows load growth in the nine years after electrification began in a rural electric system built in Kansas in 1932 up until WWII. Load growth rate during 1932 - 1936 is very high because the system is still being built and extended to new consumers.
not that different from electrification development in the U.S., and elsewhere, when electrification occurred there. Figure 20.2 shows growth of load following electrification in a rural area of the United States, displaying a broadly similar type of trend. While it is tempting to identify this behavior as part of an "S" curve (see Chapter 7) with a very long slope, it has a substantially different cause, and in detail the effect is different, as will be discussed below. General Behavior: Four Root Causes Latent demand load growth is generalized as a jump of some magnitude (immediate load) and strong but linear growth over more than a decade thereafter, as consumers and businesses gradually acquire electrical appliances and equipment. Figure 20.3 shows some of the characteristics of the behavior as they are generalized into a "developing" area load growth model. There are four phases. The immediate jump in demand when electrification is made indicates that there were electrical appliances acquired simultaneously with the extension of the electric grid into the location. Generally, municipal and community functions such as the police department and local health clinics had electric load supplied by distributed generation. Upon electrification, they switch to what in most cases is the lower cost source of power from the grid. In addition, both successful local
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industries and prosperous homeowners often had their own generation, and they too switch to the newly extended grid. Rapid growth due to acquisition of appliances and equipment by the rest of the population is the driving force behind load growth in the years following electrification. Homeowners obtain the various appliances they want to improve the quality of their life. Businesses install labor-saving equipment. Economic factors control this trend: how long will it take to acquire the appliances that homeowners and businesses want? A vigorous economy and the opportunity to work and earn money fuel rapid load growth. A recession, or widespread unemployment, slows the trend. It is not uncommon to see an initial delay in this phase of growth, due to consumer skepticism and uncertainty about the permanence of the electric supply, about how to buy and the affordability of power, and a general unfamiliarity with electrical appliances (dotted line in Figure 20.3). Economic growth spurred by electrification. Electricity does make things better. Regions with it produce more at less cost. Therefore, over time it spurs noticeable economic growth which eventually translates to higher loads. In-migration fueled by increased attractiveness of the area. In many developing countries, there is a constant "flight" from rural areas into the cities. These large and unpleasantly crowded cities are, despite all their problems, more attractive to people seeking to improve their quality of life than the rural areas they leave. One of the contributors to this attractiveness is the availability of electricity and the facilities and services it enables. Once an "electrified community" has built up a base of usage and infrastructure around electricity, if significant areas of non-electrified rural area lay beyond it, it will become a sought-after area for re-location. It will see substantial and continuing growth in population, for this reason.
1 2 3 4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 1920 Years After Electrification
Figure 20.3 The generalized load growth behavior of an area after electrification.
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637
Forecasting Latent Demand Load Growth Since the load growth process is different from that in developed areas, one would expect that the forecasting process would also have to be different. It is. Perhaps the best way to contrast the two types of forecasting is to look at the information that is known and unknown to the planner. There is a great difference in what is known: Developed area forecasting Future consumer types, locations, and counts are not precisely known. Per capita consumption and appliance preference is well understood. Undeveloped area forecasting Future consumer types, locations and counts are fairly well known. Per capita consumption and appliance preferences are not. In other words, the information base with which the forecaster can work and the target which he is trying to predict for the future are largely reversed. The consumer locations of the "new" load are known. Their usage characteristics are not. The forecast falls into four categories, three addressing each of the three phases of growth shown in Figure 20.3 and a fourth longer-term issue. After reviewing these four categories, an example forecast addressing them will be given. Forecasting considerations for cause 1 - the initial jump The jump in load upon initial electrification is best predicted with an inventory of existing and immediately expected loads. Planners can query community leaders and survey local businesses to determine existing loads and any plans for new loads to be made simultaneously with electrification. In some cases, electrification is being coordinated with the owners of local distributed generation sources, so this is quite easy to do.' The locations of these existing or immediately anticipated loads are known, so the "forecasting" of the spatial aspect of this growth can be done precisely. Often, the temporal aspect of demand can also be determined through analysis of past usage patterns. However, the author's experience is that considerable uncertainty remains, and the best forecasts of daily load curve shape are at best estimates. The reasons are that the consumers often do not really know their electrical usage patterns. In addition, usually after electrification many institutions and businesses change their usage patterns quite noticeably. Those municipal or state agencies often turn their distributed generators over to the electric utility upon electrification and work with them to integrate those facilities into the new electric system. Private owners usually keep their generators, maintaining them as backup units for use during outages.
638
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Forecasting considerations for cause 2 - acquisition Again, an inventory is a good starting point, in this case, a list of the desired appliances and equipment, by class of consumer. This provides something like a per capita horizon year load level for each class. Economic analysis of the speed with which each class can acquire these appliances then provides an estimate of the rate of load growth within each class. Consumer confusion and uncertainty Anticipating if and to what extent consumer attitude - trust, uncertainty, or confusion - will affect the acquisition of appliances and equipment is usually the most difficult part of forecasting in these situations. Situations vary widely, even within one country or region. In some communities electrification is greeted with great anticipation, and there is a rush to buy appliances as soon as or even before electricity is available. In others, there is some measure of hesitation in accepting electric power and using it. Reasons are: Distrust - installation of electric service may be viewed as intrusive. There may be cultural biases against cooperating with government and large institutions, or a feeling that electric service will put users at some obligation to the government (beyond paying their bill). Skepticism - Consumers may doubt if the electric system will work well and be safe, and if it will prove a viable business, or fail, after which power will no longer be available. Uncertainty and confusion. Consumers can have doubts about electric equipment, and concerns about if and how they can afford the power. Lack of money - it takes time to save money to buy the appliances consumers want. Many people will not start saving until they see proof that the electric system is in place and works. Predicting this aspect of latent demand growth remains something of a judgement call. However, recent experience in electrification of any nearby communities provides the best indication of what to expect. If that went well from the consumer's perspective, word-of-mouth alone will allay most of their doubts. Forecasting considerations for cause 3: electrification impact Economic development, per se, is generally included in the overall macro forecast (corporate revenue forecast) done by a utility. In a latent demand forecast, the effects of electrification are generally the second greatest cause of load growth (after acquisition). They usually "kick in" after about five to eight years of electric usage, and the local economy grows. Incomes rise, acquisitions increase, and consumption of electricity rises. Generally, this is handled by
Spatial Load Forecasting of Developing Economies
639
adjusting per capita peak load values upward repeatedly. An example will be given later in this chapter. Forecasting considerations for cause 4: in-migration growth Few other aspects of T&D planning and forecasting are as difficult as forecasting the results of economic and demographic competition among different regions and cities. Beyond all the tangible factors involved, such as economic opportunity and space for growth, etc., there is often a large measure of personal preference and cultural character to the mechanism driving growth. As a result, even the most comprehensive forecasts are often incorrect. The improved attractiveness of an area after electrification tends to attract population from surrounding areas. If the region around the recently electrified community is without electricity or infrastructure, the community will be quite appealing, and growth is inevitable. If on the other hand, the community is among the last in its region to be electrified, or if there are no nearby areas from which people can migrate, then this type of growth may be minimal. Generally, polycentric activity center models akin to the urban pole models covered in Chapters 1 0 - 1 4 will give good results if slightly modified in application. As shown in Figure 20.4, the pole models attraction is stronger nearby and weaker farther away. The two key aspects of such a model are: Population: the portion of local populations that would want to move if the distance were small Distance: the distance from the study area beyond which the attractiveness is zero.
Figure 20.4 Migration model uses a type of urban pole to represent attractiveness as a function of distance. People nearby are more likely to migrate than those far away.
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Generally, such demographic movement models represent both the portion of population that wants to move and the distance these people are willing to migrate, as functions of the economic advantage gained by those who do move. If the advantage is large enough (i.e., 10 times earnings or quality-of-life potential), very nearly all of the population would move, and all of it would be willing to move "very far away." There are historical examples of such immigration, including the migration to the United States during the 16th through 19th centuries.2 Modern examples from which to model migration models are available around the world, including the "illegal" immigration into Venezuela from Columbia and Ghana, the migration of workers to Germany from Asia and Africa, and migration, legal and illegal, into the United States, Canada, and the U.K. Migratable Population Generally, the migratable portion of a local population is considered to be that portion that is young (16 - 350), relatively healthy, and not possessed of substantial real property (dwellings, businesses, farms) in their present area(s). In a region with a very poor economy and a young average age this segment can represent a majority of the population. Migration Distance People will travel thousands of miles, and spend all that they possess, to migrate to places which have a substantially better quality of life and income potential. Figure 20.5 shows the function that the author uses to estimate "attraction radius" for models like that shown in Figure 20.4. There is no body of data or evidence to substantiate this model, but it has worked well in nearly two dozen forecasts involving in-migration, done over three decades. Model Application Migration models are generally applied as a set of urban pole attractors. Each cone-like function is centered at the population center (city, port) it represents, with its height proportional to the attractiveness of the location (Figure 20.6). Usually, attractiveness is modeled as some function of the local economy, measured in gross annual product, aggregate payroll, or average income, used as the "height." The author has had the best success using the average household income as the "height." Radius of each pole is based on its advantage over conditions in the target (migrant) population.
2
Illegal immigration to the United States from Mexico is an example, but not an easy one to use as a basis for generalization, because of the illegal nature of the migration and the impact that has.
Spatial Load Forecasting of Developing Economies
641
10
o
5
I o E o o
LU
10
100 Days Journey
1000
10000
log-log scales
Figure 20.5 The distance at least a small portion of the population would travel to gain an economic earning advantage, as a function of that advantage. Distance here is measured in travel days. Three years is about the total time that some immigrants to the U.S. spent relocating during the 19th century, when economic advantage gained was about five to one.
Figure 20.6 Application of a polycentric activity center model for allocation of migration populations. See text.
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Chapter 20
Up to this point, the application of these poles is identical to that used in standard simulation models: a polycentric activity center model in which both height and radius are functions of local conditions at the center. However, the use of these pole functions now departs from the way they were applied in the standard simulation land-use model. For migrant allocation, each of the competing areas gets a "share" of the migrant population proportional to its share of the total of all poles affecting any one area. Specifically, the influence of any one pole on a specific location, x, y is: IP (x,y) = Hp x Dp(x,y) /Rp = 0
if Dp(x,y) > Rp otherwise
(20.1)
Where p indexes the poles, p e [1 . . . P] with P the number of poles, and Ip(x,y) = influence of pole p at location x, y Dp(x,y) - V( X p- x ) 2+ ( Y p-y) 2 ) Yp = x coordinate of pole p Yp = y coordinate of pole p Hp = height of pole p Rp = radius of pole p The share of immigrants from this location, for any specific pole z, is p Share of immigrants = Iz (x,y)/(^ Ip (x,y)) P =i
(20.2)
Figure 20.6 illustrates this allocation. The dark shaded area shows that overlapped by two poles. At the small square area (shaded black) these measure respectively 38 and 92. Migrations in this location will be split 38/130 and 92/130 among these two attracting areas. The total immigrant population attracted to a specific location, z, is therefore:
X Y
Immigrant population
=
P M x
M V ( >y) ( Iz (x,y)/^j Ip (x,y))y J J p= i
(20.3)
where M(x,y) is the migratable population at location x, y The electrification forecast case to be studied in section 20.3 provides more detail in showing how this approach is applied.
Spatial Load Forecasting of Developing Economies
643
20.3 EXAMPLE LATENT DEMAND FORECAST This case is an actual forecast done in 1987 and for which more than a decadelong post-forecast history therefore exists. It was forecast using two spatial methods whose results were merged, as will be described later in this section. The spatial database was developed by ground survey (clerks walking streets and counting houses and stores) and with "aerial" photographs - literally by taking photos of the area from a small plane flying a few hundred feet overhead. Figure 20.7 is a map of the Colline Noir district (from the French for Black Hill, although the name as used locally is slightly misspelled) of towns and villages in a river valley between low mountain ranges in central Africa. The shaded area comprises roughly 400 square kilometers. Most of it was originally covered with forest, but the bottom flats along the river (including most of the shaded areas) were cleared for farming in the first half of the 20th century. The local economy is based on lumber and agee, a sisal-like vine harvested from the surrounding forest canopy and used to make rope and netting. There is also a small amount of grain drying and shipping from farms on the mountain plateaus, but this accounts for only a minute amount of the local gross annual product. The plains to the east constitute a 6400 km2 wildlife preserve (for rhinoceros), so there will never be significant growth in that direction. The figures shown in Table 20.3 were 1987 estimates (there was no national census). At that time the area had no electric system, but the Interior River Electric Authority (IREA) planned to extend electric service into the region by late 1988.
Figure 20.7 Colline Noir in 1987. Lightly shaded area is settled at low (10 persons/km2) density. Darker areas are more developed. The river is the region's predominant transportation system. Letters and arrows indicate features discussed in the text.
644
Chapter 20 Table 20.3 Colline Noir Region Factor Value Population of Colline Noir 100,000 24 Average age Population growth rate 1.7% 13,800 Dwellings 1,141 Commercial buildings 91 Industrial/shipping Schools and public buildings 62 6,800 School students Local economy based on agee, lumber, grain $13,900,000 Gross regional product (annual) Average household income (annual) $1,393 National average in nearby electrified areas $1,700
Table 20.4 Existing and Immediate Loads and Distributed Generation - kW Consumer
Location
Existing Provincial & River Police HQ Health Clinic Riverport dockyards Hotel/Waystation Radio Station Police Police Grain processing, Storage, Ship Agee Enterprises Factory Plantation Plurtan Res Plantation Welbauton Totals Existing
Installed
Peak
Gen.
A A A A A B F 30 D E C
90 50 275 1 5 10 6 10 40 120 60 687
45 50 150 1 5 10 6 10 45 70 65 395
40 35 200 1 15 3 2 diesel 45 70 75 457
G A A A A-F A-F
20 15 +25 +65 125 138 388 1075
20 15 +20 +56 125 138 191 836
379 501
Suspected & Assumed Additional
1000
250
250
TOTAL FORECAST - INITIAL
2075
1086
751
Immediate River Grain Regional Mechanical School Health Clinic Hotel/Waystation Comm.-Ind. declarations (78) Homeowner declarations (3 1 5) Total immediate Known Totals, Initial Load
Type diesel diesel diesel solar d&s solar solar diesel diesel diesel
Spatial Load Forecasting of Developing Economies
645
Estimating the Initial Load Upon Electrification Table 20.4 shows the loads in the area prior to electrification, at locations indicated by the corresponding letters shown in Figure 20.7. A total of 687 kW of electrical equipment was installed, with an estimated coincident peak demand of 395 kW. More than 500 kW of distributed generation units, mostly diesel, provide the power. An additional 125 kW of installed load was expected. Beyond this is 388 kW of "declared" load. In advance of electrification, IREA sponsored an "early sign up" program including assistance with and discounts for electrical appliances and equipment, and rate incentives, for consumers who would order utility service in advance of electrification and give proof of equipment purchase or intent to purchase. This yielded a further 407 declared consumers. The records from this program provided a body of information from which to estimate all additional load (1000 kW, 250 coincident. In total, the inventory estimated 2,175 kW of initial load, with an estimated coincident peak of 1075 kW, from a total of over 1,000 consumer sites. Five-Year Growth Projections Due to Appliance Acquisition Table 20.5 shows the eight classes used to categorize consumers and estimated counts for each. Note that households have been stratified by income, income categories being defined so that the classes have equal populations. Under income the table lists household income for residential consumers, and annual gross revenue for commercial and industrial consumers. Class total's give some indication of the importance of the class in the economy of the region and its potential for purchase of electrical appliances and electric energy.
Table 20.5 Consumer Categories in Colline Noir Class Number Income 3400 Household 1 $400 Household 2 3400 $650 Household 3 3400 $1,129 3400 Household 4 $1,750 Wealthy households 150 $20,000 Private Comm/Ind. 2800 $1,500 Commercial 210 $9,000 Industrial 53 $68,000 Large industry 6 $1,707,000 Public/Institutional 42
Class Total $1,360,000 $2,210,000 $3,838,600 $5,950,000 $3,000,000 $4,200,000 $1,890,000 $3,604,000 $10,242,000 -
646
Chapter 20 Table 20.6 Household Priorities for Acquisition of Appliances Ranking Appliance
Load - watts Coinc. Peak
Initial !S
Annual $
1
Cookplate
400
200
$22
$16
2
Television/stereo
125
90
$115
$14
3
Fan
75
70
$25
$18
4
Lights
200
15
$25
>$8
5
Refrigerator
450
120
$200
$59
6
Air conditioner(s) 1200
800
$212
<$190
Simple model of household appliance acquisition Table 20. 6 shows the priorities that households put on various appliances they can acquire, along with load and cost data for these appliances. These data are based on both the declared load consumer data and surveys of potential consumers by IREA. Coincident load estimates are very nearly pure guesswork, based on judgement, but done by applying end-use concepts and studies to the region's appliance usage, with very little real data. (Such "dead reckoning" enduse studies will be discussed later in this section.) Table 20.7 shows estimated annual discretionary income per household, by consumer class. Also shown are the number of years it will take each class to purchase these appliances, assuming: •
appliances are purchased in the order ranked in Table 20.6
•
V2 of each household's disposable income is budgeted toward its purchase of these electrical appliances
•
appliances are purchased as soon as the household has saved enough to afford them
•
payment for energy bills reduces household discretionary income on a 1:1 basis
•
households will stop spending on appliances when energy bills have reduced their discretionary household income by half
While each of these assumptions is subject to doubt, all seem somewhat reasonable and as an initial estimate, the error generated by their less than complete accuracy seems acceptable.
Spatial Load Forecasting of Developing Economies
647
Table 20.7 Predicted Household Acquisition Times - Appliances Fan Lights Refrig. Class Disc. $ Ckplt TV 2 Household 1 $45 7 -
AC -
Household 2
$90
1
3
4
-
-
-
Household 3
$200
1
2
2
3
5
-
Household 4
$350
1
1
2
2
3
5
$2000
1
1
1
1
1
1
Wealthy
Disc., discretionary; Ckplt, cookplate
Table 20.8 Contribution to Coincident Peak Loads, By Class, By Year 1 2 3 4 6 7 8 9 Class 5 .20 .20 .20 .20 .20 .29 .29 .29 .29 Household 1
10 .29
Household 2
.20
.20
.29
.36
.36
.36
.36
.36
.36
.36
Household 3
.20
.36
.38
.38
.50
.50
.50
.50
.50
.50
Household 4
.29
.38
.50
1.3
1.3
.13
1.3
1.3
1.3
1.3
Wealthy
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
Table 20.9 Weighted Peak Loads, By Household Class, By Year 1 Class 2 3 4 5 6 7 Household 1 0 680 680 680 680 986 986
8 986
9 986
Household 2
680
680
986
.1224
1224 1224 1224 1224 1224
Household 3
680
1224
1292
1292
1700 1700 1700 1700 1700
Household 4
986
1292
1700
4420
4420 4420 4420 4420 4420
Wealthy
195
195
195
195
2541
4071
4853
7811
Total
195
195
195
195
195
8219 8525 8525 8525 8525
648
Chapter 20
The model's logic and assumptions with respect to the buying patterns and electric usage in each class can be illustrated by following their application of household class 2. Each household in this class has $90 in discretionary budget annually. The model assumes that half of that, or $45, will be budgeted for purchase of electrical appliances. This means it takes each household in this class roughly 6 months to save for the cookplate ($22). Therefore, it buys the cookplate in year 1 (thus the entry in Table 20.7, column 3, for this class). Thereafter, because it is paying the energy bill on this device, this household has an annual discretionary budget of only ($90 - $16), or $74. It takes it roughly one and one-half years to save for the television set. Therefore, it is purchased in year 3. Once that is purchased, annual energy bills come to $30, reducing annual discretionary income to $60. With only half of that, or $30, to save for appliances, it takes roughly 10 months before the fan can be purchased, early in year 4. Energy bills now total $48/year. Discretionary income has been reduced to only $42, or slightly less than half of the original amount. At this point the model predicts that the household stops acquiring electrical appliances. Table 20.8 shows the coincident load per household, by year, for the first ten years after electrification, computed by using the model from Tables 20.6 and 20.7. Total peak load from the residential class is expected to reach its asymptotic value of nearly 8.5 MW within 6 years. Adding several practical but needed complications The "straightforward model" described above is too simple for application in an actual planning project, beyond its use for a quick screening study. It can be improved by altering some of the assumptions to assume some diversity of priorities among households. Not all will rate a cookplate as their top priority. In addition, some will spend more, and others less, on appliances and energy. And, of course, the commercial and industrial classes have to be dealt with in a manner similar to that shown for residential, above. The detailed examination and presentation of such a model is beyond the scope of this book, but several steps or concepts build on the model discussed above. To begin, each of the four household classes used in Tables 20.7 - 20.9 should be stratified into three or four sub-classes, based on appliance priorities and spending intentions. For example, while a cookplate is the overall top priority in class 3 households, only 55% of that class intend to buy one first 30% have their eyes on a television first, and 15% want a fan first. Classes representing these changed priorities can be set up within each class and a purchase order and peak load contribution determined for each sub-category. These different strata, weighted in proportion to the amount of the class they represent, can then be averaged to provide somewhat more accurate representation of the acquisition times and peak load contribution projections shown in Tables 20.8 and 20.9.
Spatial Load Forecasting of Developing Economies
649
Table 20.10 Forecast Peak Loads for All Classes, Both Initial Load and Growth by Year, Including the Effects of Acquisition But Not In-Migration Class
1
4
5
6
7
8
680
680
986
986
986
986
680
986
1,105
1,224
1,224
1,224
1,224
1,224
1,224
1,292
1,396
1,500
1,600
1,700
1,700
1,700
1,292
1,700
3,050
3,735
4,420
4,420
4,420
4,420
205
215
225
235
245
250
250
250
750
911
1,199
1,916
2,633
2,811
3,116
3,116
3,116
338
410
539
862
1,185
1,265
1,402
1,402
1,402
200
240
246
258
270
282
294
300
300
300
204
800
820
860
900
940
980
1,000
1,000
1,000
465
500
533
567
567
567
2
-
-
Household 2
20
680
Household 3
4
900
Household 4
140
1,000
Wealthy
175
200
Pri. Com/Ind.
225 81
Industrial Large industry
Commercial
Public/Institutional Total peak load
3 680
Initial
Household 1
680
117
300
408
1086
5,208
6,876
431
8,159
9
10,869 12,914 14,358 14,965 14,965 14,965
Figure 20.8 Forecast of annual peak load due to the consumption of power by those households and businesses who were already in the area (i.e., forecast without inmigration effects or electrification-caused economy growth).
650
Chapter 20
Commercial and industrial classes need to be stratified, too. That categorization should be based on the types of businesses (a hotel has different priorities than a laundry) rather than preferences in buying. Businesses make decisions based on financial payback more than personal preferences, in contrast to households. Thus the bandwidth of variation in priorities of similar businesses is small. The major variation is by type of business. Table 20.10 gives the resulting peak load forecast by year. Figure 20.8 shows its nine-year trend of growth. This forecast does not include the last of the three major concerns for electrification forecasting: in-migration effects. However, it shows the effects of initial load, consumer confusion (dip in growth in year 3), and that acquisition growth is pretty much over by year 7. Economic Growth Over time, electrification provides greater productivity and this results in higher income for the region and for the region's population. In this case, it was assumed that electrification-driven economic growth would "kick in" in year five and that its effects will be fully seen by year eight. The rate of economic growth was modeled as 1.25%/year, with data supplied by the national government. The revised income levels increase discretionary spending levels by more than a proportional amount. As incomes rise, people want more of the electrification that is driving their prosperity. Thus, a 10% increase in household income may mean as much as a doubling of money to be spent on electrical appliances and energy, depending on class. Such economic growth is quite easy to model with the approach outlined here. In the interests of conserving space, it will only be summarized. The effects were modeled by re-computing the appliance acquisitions and their rates as was explained earlier, and using those values to re-compute classby-class load curves. Basically, Tables 20.7 and 20.8 need to be re-computed for every three to five years, and their values interpolated for years in between. Table 20.11 gives an example of such a recomputed table, this for ten years out.
Table 20.11 Contribution to Coincident Peak Loads, by Class, by Year, after Ten Years of Economic Growth - A 13.2% Increase Class 1 2 3 4 5 6 7 8 9 "Tb~ Household 1 .20 .20 .20 .29 .29 .29 .29 .36 .36 .36 Household 2
.20
.29
.36
.36
.36
.36
.36
.36
.36
.36
Households
..29
.38
.38
.50
.50
.50
.50
.50
1.3
1.3
Household 4
.29
.50
.1.3
1.3
1.3
.13
1.3
1.3
1.3
1.3
Wealthy
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
Spatial Load Forecasting of Developing Economies
651
In-Migration Analysis A total of 25% of the population in the surrounding region(s) was considered to be "migratable" within a ten-year period. This information was estimated by the national census agency from rather limited data. Although not as solid as one would like, it was both the best data available and officially sanctioned, two overwhelming reasons to use it. Thus, 25% of the population in rural areas and non-electrified would leave and go elsewhere for an advantage great enough, depending on distance. In the eyes of these potential immigrants, Colline Noir's "electrified economy" gives it no advantage over other cities and towns that have electricity. In fact, it is not as attractive as the national capital (a metropolitan port), a much more established infrastructure, but that is about 380 miles to the south. However, compared to the surrounding rural areas, electrified interior cities like Colline Noir have an 22% advantage over non-electrified regions ($1,700 annual average household income versus $1,293 - see Table 20.3). Using the function diagrammed in Figure 20.5, the radius of attractiveness corresponding to this level of advantage is about 12 days, which for local conditions and transportation (most immigrants walk) means about 200 miles.
Colline Noir \
Figure 20.9 "Urban pole" model of the type used to compute in-migration population growth of Colline Noir. The "electrified city" is competing with three nearby metropolitan areas for in-migration. Since most of the rural population that could migrate is on the coastal plain, Colline Noir gets only a minority of the migration population.
652
Chapter 20
Figure 20.10 The urban poles viewed from above. Dark shaded areas are the electrified cities with active economies, the largest being the national capital, on the coast. Lightly shaded areas are non-electrified regions with potential immigrants. (Although this potential immigrant population is shown shaded evenly throughout, there is significant variation in both the local population density and the portion at each locale that may wish to immigrate - i.e., these features are not indicated with shading here.) Circles show the radii of attraction. Height of each pole is not indicated here.
Figures 20.9 through 20.11 illustrate the "urban-pole" analysis carried out to determine Colline Noir's share of economic migration in the region. The same radius "attractor" function was applied to each electrified city, its height proportional to the city's size, its radius based on its economic advantage over other locations. The functions are exactly as attractor functions are applied as urban poles in simulation models (Chapters 12 - 13).3 These "electrified cities" are attracting the migrant population in a type of competition, even if the migration is not completely welcomed by local and federal government officials. Colline Noir's share (Figure 20.11) is calculated to be 65,000 persons over a ten-year period. All of these migrants are assumed to relocate into the bottom household strata in Colline Noir (in household class 1). The government's demographic analysis indicates these persons will have an average 3
The map of population in electrified cities was convolved (in two dimensions) with the 200-mile radius function to provide a map of "motivation." This was multiplied times local non-electrified population at all locations to obtain an estimate of "people who will move." Colline Noir's share of this total was proportional to the ratio of its contribution to the overall convolution (its pole's share).
Spatial Load Forecasting of Developing Economies
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Figure 20.11 Colline Noir's "share" of the potential immigrant population. Its pole overlaps with those of three other cities, although the overlap to the west is null (no immigrant population in the overlap area. To its southeast, it overlaps with two other poles, sharing with both the capital (to the south) and a city to its east. To its northwest, it has no competition, being the sole attractor.
household size of 3.6 persons/household.4 This means an additional 18,055 households in household class 1, or 1,806 added per year. At mature usage rates (i.e., by the time households have had time to buy the appliances they want and can afford), each such household contributes 290 watts to regional peak demand, 1,806 contributing add an additional 523 kW of peak load each year. However, it was forecast to take time (two years) for each migrant household to become established, and only then can it began acquiring electrical appliances with the priorities and at the rates shown in Tables 20.7 and 20.8. (Such a model is easy to produce using an electronic spreadsheet.) Figure 20.12 shows the total forecast (done in 1987) for this case, including all factors discussed here, and representing the in-migration growth in this way. It also shows actual growth (dashed line) for the subsequent 13 years. Figure 20.12 indicates that growth was not as rapid as forecast. The major reason identified in a "ten-years-after" review was that the figures on household income (provided by the government) were optimistic by 32%. Acquisition of appliances took longer and never reached quite the level forecasted. 4
Table 20.3 indicates that Colline Noir has an average of 7.27 persons per household. Migrants, however, being younger and more mobile, have considerably fewer.
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Figure 20.12 Final forecast product including effects of initial load, acquisition growth, and in-migration (dots and solid line). Peak demand was expected to exceed 3 MW at one year and grow to 19 MW within 15 years after electrification. Heavy dashed line shows actual growth from 1988 through 2001.
The early trend of the actual load growth was toward an asymptotic level of just above 13 MW (as compared to 197 MW in the forecast - see Figure 20.12). This is the effect of the much lower household income (and the impacts of that on commercial loads in the areas). However, after about five years, the anticipated economic growth due to the electrification did "kick in," almost precisely as forecast. By year eight, that growth had led to noticeably elevated household income levels in the region, although by year 13 they had not yet reached the optimistic level used in the base year of the forecast. The actual rate of economic growth was very close to the rate predicted by the federal government (1.22% vs. 1.25% real income growth, year 6 to year 13). But, applied to a base that was 32% low, it meant actual load growth lagged the forecast by many years. Figure 20.13 shows the forecast re-computed with the actual household income values instead of the optimistic ones. Done in this way, the forecast is quite accurate. This demonstrates both that the simulation method is accurate if applied with good data, and that variations in household income make a big difference in overall results. However, the actual results drive home a point about any forecast, but particularly one of latent demand and developed load: a forecast is only as accurate as the data on which it is built.
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Figure 20.13 Original forecast re-run (in retrospect) with more realistic household income values (rather than the hopeful values requested by the government for political reasons), and no other changes. Dashed line is actual trend of growth.
The original forecast was a truly bad forecast. No other word describes it. The forecast for two years out (just under 7,000 kW) is a level not actually reached until year four. From a timing standpoint the early forecast is doubly optimistic about load growth rates. In later years, the forecast settles down to a nearly constant five-year lead: Forecast peak load for any year X is not actually reached until year X+5. Overall, a forecast like that shown in Figure 20.12 causes planners to build facilities between two and five years ahead of when actually needed. Spatial Allocation Up to now, this example has focused on appliance acquisition models, classbased peak load computations and the global totals for latent-demand forecasting in a region. These areas are where the major changes need to be made to the standard simulation method when it is applied to latent demand and economic development. But the goal all along has been a spatial forecast. The spatial nature of the latent-demand forecast is handled exactly as it is in any other spatial simulation
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Figure 20.14 Map showing the spatial aspect of the forecast whose overall trend is shown in Figure 20.13. This is year 3 after electrification.
forecast: the class by class peak load values are used to compute small area loads on a spatial basis. Figure 20.14 shows the spatial demand map for year 3 of the forecast done in 1988. Due to the over-aggressive growth rates forecast (Figure 20.13) the total level of load included in this (8129 kW) year 3 forecast is close to what actually occurred only in year 5 (which was 7805 kW or 4.5% lower). Total spatial difference between this 3-year ahead forecast and the actual 5-year load growth pattern is 7.4% (Uf of 7.4%). Error in forecasting where load would be was superb: roughly less than 3% (approximated as 7.4% - 4.5%). To some extent, this spatial accuracy was no surprise. As discussed in section 20.2, locational accuracy of forecasting electrification load is usually very good because the consumer locations are known. Relatively little error should be produced in forecasting where load will develop. However, as the example forecast shows (Figure 20.13) a good deal of global error can develop in these types of latent-demand forecasts, which of course affects the loads in every small area. In this case the global error (DC component of Uf) constitutes over 60% (4.5 of 7.4%) of the total error. In a spatial forecast of a metropolitan area in a developed country, one would expect global error to constitute less than 1/3 and probably less than 1/4 the total error.
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A Different Forecast of the Region Figures 20.15 and 20.16 show the results from a forecast of Colline Noir done in 1987 using an extended template matching (ETM - "smart trending") method, of the type described in Chapters 9 and 15. The forecast of peak load growth produced by this algorithm was far lower in terms of initial load and growth rates than the simulation-based forecast method's. This was largely because the trending based its forecast results on load growth histories in other electrified cities in the country, and did not respond to the overly optimistic household income data in the same way that trending did. Extended template matching forecasts small area load growth by assuming that history repeats itself. Faced with forecasting a particular small area, it searches its database of past small area load growth in other areas, for a small area that used to look like the area it is now trying to forecast. For latent-demand forecasting, "looks like" means the small area and the template have similar measures such as population, structure count, road data, etc. The algorithm then assigns the template area's load history to the small area it is forecasting, as its forecast trend. See Chapters 9 and 15 for more details. In this case, the algorithm was working from small area data gathered on a number of other cities and towns that had electrified during the previous decade. It had a maximum of 9 years of load history, with at least 5 years of load history over a sample set of 3,000 small areas (roughly 8 times the number in Colline Noir). Household income was one of the variables used in the template matching for Colline Noir. However, the national government had overestimated it in all cities and towns, so that error largely canceled out. Template matching was very "robust" with respect to error in this data, whereas the simulation was not.5 Other variables were total population, household status, total number of structures, conditions of roads (paved, graded, trail), and number of commercial establishments. This data was gathered by field survey. Year 5 was the extended trending method's best forecast year, in terms of absolute error. It forecast 8077 kW or within 3.5% of the actual total (7805 kW). Uf was 11.5% This means error in forecasting where load would be was good but not superb, since Uf > average error in the total. Still, this is outstanding for a trending method, among the best the author has seen. Figure 20.15 shows that the trending method's forecast falls short of longterm growth rates. Most of this is simply due to its lack of long-term load histories. The five to nine years of load history available are really too short to use with template matching. In this case, the algorithm simply extrapolated load growth rate and its derivative after year five or nine. 5
Generally, pattern recognition methods are robust with respect to error in most input data.
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Figure 20.15 Overall peak load for Colline Noir forecast by template match trending (solid line with squares). Dashed line shows actual load growth.
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Figure 20.16 Spatial forecast (year 5) from the extended template-matching approach at 1 km resolution.
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Postmortem on the Colline Noir Forecast The two forecasts shown in Figures 20.13 - 20.16 were produced in 1987 in anticipation of the electrification of Colline Noir in 1988. The two forecasts were averaged on a spatial (1 km) basis to provide the forecast actually used for T&D planning. The regional total peak load for this forecast and the actual load growth as it developed are as shown in Figure 20.17. A map is not shown because it looks nearly indistinguishable from Figure 20.16. Spatial error through year 12 was low - the non-DC component of Uf was only 9.5% in year ten. Generally, this forecast stayed about 1 year ahead of the actual load growth for the first decade: It tended to tell planners to spend money earlier than necessary, but much less so than the simulation forecast alone would have. Assuming carrying charges of equipment are 10%, this forecast could have cost IREA about 10% more than necessary. In fact, the forecast error worked out to be fortuitous. Delays in ordering foreign-manufactured equipment meant facilities were generally completed a year or more later than planned. In retrospect, the planning worked out very nearly optimally. However, this is definitely not how one would like to arrange to obtain good results. Using a load forecast as a "cushion" against uncertainty in supply management, right-of-way acquisition, or construction is not recommended. The overall forecast used in this project was only fair, not good.
Figure 20.17 Peak load forecast used for planning of the Colline Noir, the average ol the simulation and trending forecasts. Dashed line shows actual load growth over the subsequent 13 years.
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20.4 NEW-CITY LOAD GROWTH "New-city" projects involve a planned effort to deliberately create or "grow" a new city in a place where there was previously no city, and often not even a town, village, or any significant population. Invariably, these efforts take the backing and sponsorship of a national government, as they involve incredible commitments of funds and infrastructure, and usually involve concessions and cooperation by the government to make the project happen. The most noteworthy examples of such cities are Brasilia, Brazil, and Abuja, Nigeria. Both were created out of what was essentially jungle, as national capitals for their respective countries. New cities are usually planned as projects, not just city layouts. This means that in addition to an often detailed master plan for the city, its layout of roads and services, and arrangement of key buildings, the government has developed a schedule for the city's growth and intends to manage the city's development along the lines laid out by that schedule. Comparison to Standard Metropolitan Forecasting New-city load forecasting involves the same basic issues involved in forecasting any metropolitan area's growth. Only the ratio of new to old is different than in "normal" situations. The tremendous amount of "new" makes the uncertainty or "fuzziness" in the forecast much greater. It is very much like forecasting the very long term (30 years ahead) loads of a large metropolis. Land-use change will be significant. It will be based on today's land-use pattern but with much, much new development. Per capita usage patterns will be somewhat like today's, but probably quite different. By comparison, new-city forecasters face the following situation: Land-use change will be significant. It will be based on the master plan for the city, but perhaps not entirely following that plan. Per capita usage patterns will be somewhat like those in other nearby cities, but probably noticeably different. The complicating factors: reality versus intention Most new-city projects do not work out exactly as planned. Many of the new city plans that the author has seen turn out to be somewhat unrealistic, in that they are visions of how the government would like the city to turn out: what government hopes will develop. The government's master plan may envision a wellorganized and efficient, even elegantly laid out city, often arranged to be a national showplace. In actuality, many cities will turn out to be somewhat chaotically arranged and much grimier and less attractive than intended.
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This outcome does not necessarily reflect poorly on the government's planners or its intentions. Although it is regrettable when things don't work out as planned, one has to plan to have any real chance of getting even a part of what is desired, and often plans reflect hoped-for targets as much as realistic goals. Planners need to recognize the difference. Regardless, for a variety of reasons that will be covered later, a new city can potentially develop to a far different spatial pattern than intended by the sponsoring government. The planner's role is made easier if he or she can anticipate this and predict what will happen. What is the forecaster's goal? The first question every forecaster/planner must ask is what is the goal of his or her forecasting and planning effort for the new city? That job may be to produce a plan strictly adhering to the official plan, regardless of any likelihood that actual development might deviate from it. The government is the sponsor of the new city. Often, the electric utility serving the new city is owned and operated by the national government. The government may want an electric system designed and built to handle the new city as planned. If so, the planners and forecaster's have an easy task: take the master plan, translate it into kW by location, and plan an electric system to serve it. But often, the forecaster's and planner's goal is to design the most efficient and least costly system possible to serve the loads that will develop. Or they may need to do something essentially similar from the forecaster's point of view: to design a system that makes the best business case, paying for itself as quickly as, and with the lowest rates, possible. In these cases, the planners are trying to forecast what will happen, rather than merely add an "electric level" to the new city's master plan. They want to forecast the actual expected load growth. Forecasting Actual Growth of New City Projects Strangely, the existence of a master plan and a project schedule for a new city can greatly complicate the challenges facing the electric utility planners and forecasters. The plan may not be entirely realistic, in any of a number of ways which will be discussed below. The great challenge for the planners can be determining how much influence the government can actually exert on the city and what the actual combination of government effort and reality will produce. What is the government's goal? The forecaster's challenge is easier if he or she can identify the real purpose behind the creation of the new city and the government's goals. Historically some new cities were created as centers of government and in addition national showplaces. By contrast, other new cities were created as economic elements, with their industrial and demographic elements carefully planned. Generally, those aspects of a city that are the main goal do work out, but cities based on good economic development plans tend to succeed sooner.
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New Cities: The Urban Machine and Patterns of Growth Cities are economic machines. They grow according to rules about their content, arrangement, and the interaction of their various components. These rules are slightly elastic, but ultimately inviolate. Their basis is the overall concept about urban (and for that matter, rural) growth stated in Chapters 10 and 18. If a city is going to grow, all of its parts will grow in an interrelated, at least partially predictable manner related to the local basic industry. This applies to all cities, without any exception. Forecasters can use this concept, embodied in a quantitative analysis of its various implications, to determine clues and information from which they can base their forecast of the new city's future growth. In general, the entire Lowry model concept (see Chapter 10) applies, too. At the least, it will be applicable at a qualitative level. Section 10.3's example of a small "factory town" that grows up "out of nothing and in the middle of nowhere" illustrated the mechanics of how a new city, town, or village develops (Figure 20.18). In that example, a truck factory was being built at a location that was ideal (size and layout of the site, proximity to river, road and rail transportation) if isolated (no infrastructure anywhere nearby). This factory was the "seed" from which a small city grew. In order for the factory to "do its job" there had to be homes for its workers nearby and a full span of local market and services to support their needs. So it is in any city. Key aspects of that example that will be true for any new city project are: Driving force. Something has to power the local economy. It can be manufacturing, services, entertainment, government or some other industry. Usually, one important aspect of any new city is its role as the seat of government (e.g., Brasilia, Abuja). But regardless, the city will grow only if "powered" by some basic economic engine. It will grow to a size and content in direct proportion to this causal force. In section 10.3's example, the driving force was the truck factory employing about 4,500 workers, which created a small city of about 19,000 population. Had the factory employed 9,000 people, the city would have grown to about 38,000 population. Proportional land-use. The amounts of various land uses in the city will be locked in proportions appropriate for the functioning "urban machine" around them. No matter the size or type of city, it has to have the appropriate mixture of residential, commercial, services, and industrial parts for its "urban machinery," or some of those parts will wither, and others grow, until the proportional needs are met. Section 10.3's example had 1,270 acres of Residential 2 class and 61 acres of offices. Any development based upon a similar manufacturing economy and population demographics would have had similar proportions.
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Table 20.12 Basic Metropolitan Plan "Content" Tests 1 - Is the planned amount of basic industry sufficient to power the local economy for a city of the projected size? 2 - Are the amounts of land-use types (residential, retail, industrial, etc.) present in the correct proportions? 3 - Is the spatial distribution of land-use types appropriate for a functioning "metropolitan machine."
Appropriate spatial patterns. The various land uses will arrange themselves in appropriate spatial patterns with respect to the local topology, the road, rail and other transportation systems, and one another. Not only will the locations of each land-use class meet its own siting needs, but each class's locations will be woven into an urban fabric so they are appropriately "mixed up" with one another and yet isolated from one another in ways appropriate to their purposes. Planners should study these three aspects of the new city's development quantitatively. These, summarized in Table 20.12, are the key to understanding what and how growth will occur.
:•: Single family homes £ Multi-family homes ommercial
Figure 20.18 Example "factory town" from Chapter 10's example of growth drivers. This small town's economy is "powered" entirely by the truck factory.
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Recommended Tool for New-City Forecasting New-city projects are one situation where a really comprehensive land-use-based simulation method (e.g., a 3-3-3 type) nearly always justifies itself over the use of a merely adequate method (2-2-1). The more comprehensive spatial model will do a better job of diagnosing mismatches between plan and reality, and of determining the spatial land-use patterns and densities that result from any conflicts between intentions and reality. The more complete end-use model will permit more thorough exploration of likely peak demand levels, coincidence and load curve shapes. The land-use-based simulation/end-use load curve approach is a natural fit to the needs of purposes of new-city forecasting. It can work directly with the landuse maps and plans that often constitute the majority of detail in the city's plan. It can apply end-use analysis to predict what consumption patterns typical types of users will have in this location and climate. And, most important, it can apply the quantitative "rules" discussed above to analyze the feasibility of the city as planned, to diagnose growth trends and identify likely deviations from the plan, and to forecast the actual growth. Differences, Deviations, and Their Diagnosis The major difficulty new city projects face is one of economics. Financing the construction and "seed" infrastructure - building the roads and other infrastructure - is only part of the issue here. That infrastructure and similar work requires hundreds of millions of dollars before the new city can get off to a start. But a national government is behind the city project and can well shoulder that financial burden. But those hundreds of millions of dollars pale into comparison to the billions it takes to build the city itself. The government can build the roads. It can put up the national monuments and major government buildings. It can grant concessions to developers to finance other buildings, and offer incentives to industry to move factories and jobs to the area, but the city will grow as planned only if a functioning local economy compatible with the master plan develops along with it. The place to begin in answering the questions in Table 20.12 is to look at their feasibility over time. Not only should the eventual master plan be analyzed as a functioning urban whole, but planners should ask how the city will grow to that plan while being, at interim stages, a sufficiently robust and functioning urban machine. Does the overall plan "make sense?" The first point to investigate and assess is if the master plan for the city, as represented by its planned eventual land-use density map(s), makes sense. Does it roughly pass the three tests described in Table 20.12? Surprisingly, many new-city plans (and many long-term plans for existing cities) contain a good deal of wishful thinking, and occasionally even some pure fantasy.
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The first point to investigate in this effort is to assess the amount of basic industry (see Chapter 10) planned for the city. Will it power the city's economy as represented in its master plan? If not, is the required additional amount of basic industry likely to be attracted to the city as a result of whatever incentives the government has planned? The new city will develop only to a size compatible with its basic industry, something illustrated by the example based on Chapter 10's factory town case shown in Figure 20.19. Often, a new city is planned as a national or provincial capital. Government employment qualifies as basic industry. The city may include a national university - more basic industry. But that employment alone will generally not support a large metropolitan area (e.g., Washington DC, a large metro area, is not driven solely by government employment). Most plans for new cities plan for more than just government employment. Their success lies largely with how realistic these plans are. In many cases, the government planners will have made determined efforts to finance, persuade or cajole various industries to locate in the new city. But in a few extreme cases, the plan is woefully lacking or even completely missing this element. The city plan is only a vision. No economic plan has been considered.
Highway
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Figure 20.19 If the economic driving force is not sufficient to power the planned city, it will develop only to a size proportional to the economic force. Here, the pickup truck factory was downsized by half. Compare to Figure 20.18.
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Timing of basic industrial growth An allied point to the overall basic industry-city size equation is the matter of tuning. This has two considerations. The first is fairly obvious: If basic industry grows at a slower rate than planned, then the entire city will grow at a slower rate than projected. Perhaps the original schedule for the city envisioned it reaching 1,000,000 population, with 235,000 jobs in basic industry, within ten years. If basic employment in the region reaches only 90,000 jobs in the first ten years, the city will have a population of only around 383,000 (90/235 of 1,000,000) by that time. The second effect of timing is subtler. If the growth rate is lower, then the city may not develop to the original layout, to the same spatial pattern it would if growing quickly. Figure 20.20 illustrates this, as detailed comparison with Figures 20.18 and 20.19 will demonstrate. The factory town shown in Figure 20.20 is the same size and contains overall the same content as the original plan (Figure 20.18). However, here, the factory grew initially only to half the planned size. It first grew to that size, and more importantly, the configuration compatible with that size, shown in Figure 20.19. Then the factory was doubled in size, and it and the town around it reached the original planned size.
inimiiimmiiiimmnmimnmmmi One Mile :•:•:•: Single family homes =:ij|i: Multi-family homes Commercial ^ Other
!
Figure 20.20. The impact of slower growth. Here, the factory town grew first to the pattern shown in Figure 20.19. Then, the factory expanded ("other" land to its east - in this case light industry was razed so it could expand). The town grew to the same size as the town shown in Figure 20.20, but ultimately to a different pattern.
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But the spatial pattern is different. There are several reasons. First, powered by a smaller economy, and seeing a smaller need, the local government and developers had fewer funds and thus built fewer roads at an early stage. What growth there was went where the roads had been built. Second, land uses are different. Note in particular the commercial development north of the highway, and the commercial and other land use in the lower middle of the map. When growing to a smaller size, and with fewer roads built, some locations were found better suited to uses other than as outlined in the original plan (Figure 20.18). When the town finally does grow to the larger (Figure 20.20) size, it must build upon the configuration it reached in the interim. The result is a different pattern, not quite as simple and well-sorted out (i.e., not as "elegant"), but still a very workable pattern. A lot of this "difference as a function of growth rate" has to do with "business cases" for the investment in roads and land development. In a rapidly growing city, whoever is building the roads, be it the federal or the local government, or as is the case in the U.S. a land developer, can justify the cost of road construction based on a quick payback. The roads will "open up" new land which will develop quickly. To the land developer that means quick sales and payback on the cost of the roads. To the government that means increased tax revenues soon, and a quick payback on the roads. But when growth is slow, or done in stages spaced far apart, roads tend to lag, not lead development. The same holds true to land itself. In a rapidly growing city, a government or developer can justify holding on to a great site for a future shopping center or school, or whatever - it will soon be needed due to the rapid growth. But if growth is slower, the time until that investment comes to fruition is longer, the appeal of holding onto it for its "best and highest" use is limited, and very likely the land will be sold or applied to whatever purpose can be found for it. Recommended Overall Approach to Forecasting New Cities In general, forecasts for new cities should be modeled in stages. If using an event-driven or event-iteration simulation model (see page 429), the plans for direct government development actions — construction of roads, government buildings, national university, airport, etc., which it directly finances - should be modeled as a series of events, in the order and timing as planned. Otherwise the model should be run on a yearly iteration basis with government development actions entered on a year-by-year basis as new basic industry in each year. Land planned for their use should be restricted for any other development in previous years of the growth simulation. Either way, all follow-on development - everything not being built and financed by the government - should be filled in by the spatial simulation model, letting it determine the amounts necessary but using the master plan as the
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"zoning" for the development, setting the program to limit growth that is not in accordance with the master plan. Planners should; 1) Use a very comprehensive spatial simulation method. Having and using all the features of a "smart" algorithm is much more important in new-city forecasting than having really high spatial resolution or advanced graphics and ease-of-use. An event-driven rather than an annual iteration type of simulation model is recommended. 2) Calibrate the model properly. They should make certain it is set up, tuned, and working well. (From this point on it is assumed the program and user are both performing well.) 3) Prepare a land base of the existing development in the area. If there is any existing village, town, or roads, they may be very important to the overall development patterns. 4) Input the master plan for the future city as a zoning or "permitted development map." 5) Study the master plan with respect to the content tests listed in Table 20.12. Use the simulation model to diagnose if and how the master plan matches each of the tests, and to identify where if anywhere it falls short. If the answers to all three questions in Table 20.12 are substantially "Yes, it makes sense," then model the "zoning" as absolutely rigid and inflexible over both the short and long term. If the tests show the plan is unfeasible or weak, set up the model to gradually reduce the rigidity of the "zoning" over time, until eventually all unused land is free to be developed for any purpose that makes sense to the simulation. How does the user know if the zoning rigidity is being relaxed quickly enough? That will be addressed in step 8. 6) Set up the direct government development actions - those it will pay for and directly drive - as a series of growth events. Or if not using an event-driven simulation, represent them as annual sets of arbitrary changes to the growth. 7) Set up the database and the forecast model to permit development of vacant land that is not part of the master plan (that is, land beyond the city's planned limits, or outside designated growth areas, or where ever). This is an important diagnostic tool. If the simulation model then grows vacant areas not in the master plan, it indicates some incompatibility between land-use location needs and the master plan.
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8) Pay very careful attention to all "diagnostics." First, if any vacant land is developed (see 7 above), it indicates that either content question 2 or 3 in Table 20.12 is not satisfied. Second, the planners should look at the pattern recognition and preference diagnostics that most simulation programs provide. Most will report the threshold values for the spatial preference function pattern matches on an iteration-by-iteration basis. This is often a value such as the minimum preference score that had to be selected for growth, for each land-use class. Or it might be the percent of all available land rated positively for preference, which was developed. Either way, there is a minimal satisfactory limit reached in the selection that most programs report. The actual numerical value that is "good" depends on the specific algorithm, but the user should be familiar with what that is. In any land-use simulation, if these threshold limits drop over time, indicating that the modeled growth is having to select lesser appealing land for development over time, this means that the simulation is "running out of good land" for one or more land-use classes.6 In a new-city project, that means that content test 3, Table 20.12 is not satisfied. In most of these cases, that means the zoning rigidity is set too high and should be relaxed. 9) The simulation should proceed into the future in one of two ways: a) If the diagnostics indicate no problems, then the forecast proceeds as a series of event-driven or annual iterations that eventually fill in the entire master plan, showing what develops when, and where. b) If the diagnostics indicate there are mismatches in any of the content tests, or in any diagnostics, then: i) If the mismatches are minor, the user should "let the program tolerate them" and run the forecast with no intervention - this is what a government would do. ii) If they are major, the user should relax the zoning rigidity over time and accept development in vacant areas outside of the master plan, if the diagnostics otherwise stay high in those cases. 6
A growing metropolitan area generates new vacant land - vacant space in the language of Chapter 18). Example: as new residential areas are created, they increase the appeal of vacant areas nearby, by raising the "near residential" factor score for those areas. In a very robust, growing city the preference scores for every land-use class stay about the same from iteration to iteration, indicating a stationary process of growth. See Chapter 21 's section on the stationary process rule (page 692).
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Modeling new city development well, particularly in cases where the master plan does not satisfy all three of Table 20.12 content tests, is challenging. However, this method seems to provide a framework that works better than other approaches the author has seen. 20.4 SUMMARY AND GUIDELINES T&D planning for load growth in many developing nation's economies means dealing with newly electrified regions and new cities created by direct government action. Each of these two types of situations presents its own set of unique challenges to utility planners. Electrification projects plan to serve energy consumers where there are no facilities at present, so the system planning itself is all "greenfield." However, there is no load history, no available consumer information system database, and little directly applicable data from which to determine how much demand the new system will serve and how it will grow. Forecasters in these developing electrification areas face four issues that are not seen, at least in large measure, in fully developed economies. These are: Existing demand - there is existing electrical usage powered by private generation. Some or all of this will convert to utility service if given the opportunity. Latent demand - Acquisition of appliances by the general population will follow on the heels of electrification, its timing and growth depending mostly on how quickly local residents can afford to buy appliances. Economic growth, spurred by electrification and the benefits it brings, tends to boost a regions electrical usage. In-migration, from non-electrified areas to the newly electrified region, adds to its population. All four of these issues can be addressed in an orderly and methodical manner using either simulation or trending. Overall, forecasting of load growth in a developing, newly electrified economy is somewhat more difficult than forecasting in normal situations, if one looks at the uncertainty that the forecaster faces and the data from which he can work. The forecast case reviewed here was an example of a well-done forecast where "things did not go well" and serves as a reminder that, ultimately, forecasting is a hazardous undertaking from the standpoint of accuracy. But the factors that contributed to the rather mediocre performance of the Colline Noir forecast were not unique to or even caused by the special character of electrification types of forecast situations. Forecasting the electric load and growth of a completely new city - a Brasilia or Abuja project - is technically similar to forecasting the long-term growth of a rapidly growing metropolitan area. In addition to the obvious challenges
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forecasters face - lack of historical growth trends and consumer data - there is the very difficult issue of dealing with possible incompatibilities between the often visionary plans for the new city, and reality. Forecasting new-city growth is one situation where a very high quality simulation approach is mandatory. Comprehensive modeling of all aspects of urban growth is about all the forecaster has to go on — there is no current landuse pattern, no well-established infrastructure of roads and transit systems, no cultural preferences to areas of the city. There is nothing on the ground from which to build a picture of the future city. That exists only as a master plan and intentions of the sponsoring government. As a result, a strong forecasting model that can diagnose and help predict how the city will actually react to economic, topological and demographic forces is a necessary tool for accurate forecasting, if that adjective can even be applied to this type of situation. This chapter gave a step-by-step guideline on how to address the new-city project. However, such forecasting projects are challenging under the best of circumstances and the overall advice is for planners to develop T&D expansion plans that retain flexibility and recourse.
21 Using Spatial Forecasting Methods Well 21.1 INTRODUCTION Simulation-based and hybrid approaches to spatial electric load forecasting almost always offer the best combination of accuracy, representativeness, and useful format for studying electric load growth. Like any other tool, they work best when their functions and subtleties are well understood, and when they are applied with skill and focus. This chapter discusses some of the practical considerations in using simulation for electric utility applications. It begins with a section that reviews the most important elements behind the application of any forecast, simulation based or otherwise, in section 21.2. Despite the generality, focus of this section is predominately on concepts most useful when applying simulationbased methods, although a good deal of its recommendations are also useful when working with trending and hybrid methods. Section 21.3 discusses the set-up and calibration of simulation methods. Proper diagnosis of mismatches in and adjustments of coefficients for a simulation model's spatial allocation algorithm - calibration — are critical to accurate forecasting. Section 21.4 discusses a number of "tricks" that work around or extend some of the limitations common to the spatial engines in widely-used simulation programs, particularly many of those written in the 1990s. Partial-region forecast situations - forecast cases where the planner's study region includes only a part of a greater regional whole - are covered in section 21.5. Section 21.6 concludes by reviewing a number of forecast situations in which the simulation approach needs to be adjusted or fine-tuned with respect to some unusual characteristic of the region.
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21.2 FORECAST APPLICATION Using Forecast Methods Well A large portion of this book focused on forecasting methods and methodology, looking at specific algorithms or procedures to be used to produce a spatial forecast. The emphasis in the previous twenty chapters has been on using only rigorous and fully-documented procedures, and on avoiding the application of the planner's judgement and opinions in the forecast process. Good forecasting tools are necessary, but not sufficient. A planner's understanding, of the tools, of the forecast situations, and of the interactions between the two, is required for any success beyond "blind luck" in forecasting future load growth. Comprehensive algorithms and smart databases are no substitute for the planners' awareness of the overall driving forces behind the region's growth and insight into how they function. A knowledge of the how and why of the regional economic engine is a critical part of any forecasting effort. Step 1: Understand the "Regional Economic Engine" Every part of the world occupied by human beings has a "local economy," the mechanism from which the residents of that area provide for their subsistence and welfare - the way the region "earns its living." A few areas of the world are still so primitive that humans are basically living a hunter-gatherer existence. "Productivity" driving the local economy involves only the gathering of food from the surrounding area and the construction of a few huts for protection from rain and the definition of personal space. Anthropologists might find the "productivity" of tribal hunter-gatherers in a primitive society interesting, but utility planners are only interested in those cultures that utilize, even depend upon, electric power. The vast majority of humankind lives in such developed areas, where man has organized his efforts into activities aimed at increasing the productivity of the local geography to his betterment. Many such areas of the world have an agrarian economy, with the majority of the local residents cultivating crops and raising animals to provide food for themselves and to trade with other humans for non-food-related goods and services. Other regions earn their living from manufacturing, trade, technology, or services of one form or another. Still other regions have a diverse economy, based on a cross-section of these means. But regardless of the basis of the regional economy, in a very real sense a nation, country, region, or area cannot grow in population, wealth, or electric usage unless the productivity of that area increases. In an agrarian economy, if the residents of the area increase the productivity of the local fields, and improve the efficiency of their harvesting and processing, they produce more crops and hence have more food for themselves and to trade for other things they want. As
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a result they probably have both a greater need for electric power, and a greater ability to pay for it. Similarly, if the mills in a "factory town" are made more efficient, or people there simply work more hours, production goes up and the region increases its net productivity and income. In some sense it has more wealth. Generally in such cases, population increases and along with it, electric demand. This productivitydrives-electric-usage concept is incorporated in the Lowry model of regional spatial growth discussed earlier in this book. The Lowry model identifies the productivity base of the study region as "basic industry" - all that activity, whether industrial or otherwise, that markets or sells outside the region. Sustainable growth occurs only when this local economic engine increases its productivity or profitability. Its nature controls both the amounts and locations of all growth. That growth can occur due to luck (several years of good weather and high agricultural production), hard work (workers in the factories put in long hours), technology (factories are made more efficient) or changes in market conditions (the area produces cotton and the price of cotton rises for whatever reason). Generally, increased productivity creates opportunity which brings about increased population which drives growth. Furthermore, over the long term, the locations of growth are largely determined by these driving forces and the ways they interact with the local geography and demographics. Therefore, the first step in T&D load forecasting is identifying the basis for the local economy and understanding its function. Even if the T&D planners are basing their spatial forecast on a previously-produced global forecast (e.g., the corporate revenue forecast) they need to understand the basic driving forces behind their study region's economy. That force's content and function shape the spatial nature of electric load growth throughout the region. A "normal" forecast situation: a diverse metropolitan economy A majority of T&D planning situations involve the forecasting of load growth and planning of facilities for a large metropolitan area, or for a region that includes several large towns and/or small cities. Most such areas have a diversified economy, one not dominated by any specific industry but instead driven by a mixture of many industrial and commercial functions. Cities like Chicago, London, Houston, Buenos Aires, Toronto, Calcutta and others that have achieved large size (over 3 million metropolitan population) invariably have an economy based on a wide range of production activities. The standard concept of spatial load growth simulation, described in Chapters 10 - 14, is oriented toward forecasting load growth in such very large diverse-economy regions. Characteristics of such regions are: • A metropolitan area covers a large region, usually at least 35 miles (56 km) in diameter. • A mixture of traditional heavy, medium, and light (warehousing and
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• Multiple activity centers (urban poles). Usually, each pole is dominated by one or only a few types of industry. • At least one concentration of high-rise (over 20 stories) development, unless prohibited by law (e.g., Washington DC). • Local transportation system consisting of overlaid highways and roads, mass- and perhaps rapid-transit systems, and rail for heavy industry. This is the pattern of metropolitan development, something generally familiar to most planners for large utilities, who live in such a region and intuitively understand it, at least at a qualitative level. By contrast, economies of smaller cities are not so diverse Only a large city can be diverse in its industrial base. Many small towns are largely "one industry" towns, even if they do not match the traditional factorytown concept. For example, State College, Pennsylvania, and College Station, Texas, are both one-industry towns devoted to education (Perm State and Texas A&M, respectively). They both "earn their living" by educating students from outside their immediate region. Similarly, many small cities are based upon economies that are not highly diverse even if not built upon just one industry. Hays, Kansas (population 75,000), while having some local manufacturing and some education to diversify its economy, is largely based on being the business and services center for the surrounding 50,000 square miles of agrarian industry. Tallahassee, Florida, is largely built upon government and education. Laredo, Texas, is predominately built upon commerce, shipping and transportation between Mexico and the U.S. Forecasting Basic Industrial Growth Trends Good spatial forecasts are "driven" or guided by an overall forecast of the region's total development. That trend can be developed inside the forecast procedure by a special module that does the global forecast, or input to the spatial methodology from another source. Regardless, usually it is this global forecast that sets spatial forecasts apart from mere small area forecasts: it starts and controls the process of coordinating all the disparate small area forecasts so they are consistent with one another. This makes the forecast a spatial, rather than just small area, forecast (see Chapter 1). Usually, the recommended procedure for obtaining the driving trend for a spatial electric load forecast is to take it from the electric utility's rate and revenue forecast. As discussed in Chapters 1, 10 and 17, that forecast is invariably done with care using a comprehensive econometric forecast method or
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similar technique that is both suitable and well-thought-out in its application. Most utility revenue forecasts are done well. As completed, they are not suitable for direct application to T&D planning and engineering functions. Factors such as weather-risk adjustment, non-coincidence of load, and possibly other factors relating to the difference between financial and system planning needs must be accommodated through adjustments. But for all that, the corporate forecast should be used in all but the rarest cases. T&D planners should always endeavor to take this approach and let subsequent events prove it will not work. As discussed in Chapters 1 and 2, all forecasts being used for all planning functions within an electric utility should be consistent with one another. Reasons why a global forecast may not be available There are situations where a corporate or global forecast is not available, or should not be used. These are: The study region is relatively small and different compared to the utility service area as a whole. An example would be Branson, Missouri, a town whose economy is based almost entirely on entertainment of older Americans, and whose electric service is part of the much larger Empire District Electric system. The global forecast of the entire service area is not a reliable guide to the growth trend for an area of the system that is a small and rather unique part of its economic makeup as compared to the whole region. There is no global forecast. In a very few cases, the utility's organization and assignment of responsibilities leaves the development of all forecasts up to the division planners. While very rare, the author has seen this situation twice, in some large, state-owned utilities that operate with a rather dispersed, locally-autonomous organizational paradigm. Local planners are in charge of developing all aspects of the forecast for their region. Revenues are not projected in the normal sense because the stateowned utility sets prices as national policy, not based on projected business study. The global forecast has been challenged and a "bottom-up" forecast is desired. This might be the case when interveners, regulatory or franchise officials dispute the utility's planned additions or expenses and want to see a forecast based on spatial trends, i.e., on what is happening locally, before consenting to allow the plans to move forward. The forecast is being done by a consultant or "outsider" who has been asked for an independent assessment of total growth. Generally, any contractor or third-party hired by the utility will have access to the utility's full set of data and knowledge about its consumer base. However,
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in some cases the utility's general management may want to see a plan based on a different forecast, particularly if the outsider forecast has been challenged, as discussed directly above. The forecast is being done by a third party who has no access to the utility data. For example, a competitive electric service company who is "invading" the service territory of the traditional electric-service franchise holder for a region may wish to do a spatial forecast of the market there in order to develop their marketing strategy and plan their tactics and business case. In these cases and perhaps a few others, forecasters need to project the global growth of the region. The best way to do this is usually to forecast the driving trend - the growth of basic industry - in some meaningful way, and then use that in a forecast model driven by that trend. For example, if the regional basic industrial base activity grows by 2% a year, that can be directly input into any type of simulation forecast model, which will then produce the entire spatial forecast, including magnitudes of all other classes of load growth, from that one trend. Suitable approaches are: Third-party forecast of the region's economy or some key economic factor. Often planners can find a suitable forecast of regional employment or productivity done by the federal, state, provincial, or municipal government, or by a university or research institution. While such forecasts have to be examined with care, they are worth considering, particularly if fully documented in both data used and method applied. An example would be projections of employment on a county-by-county basis through a state, and disaggregated by industrial sector (two-digit SIC code) as produced by the Department of Labor in different states within the U.S. Straight-line trending of a key basic-industry factor. For a region that is both large and has a diverse economy, an acceptable forecasting technique for overall growth trend is to simply straight-line extrapolate the most recent (5-year) trend in overall basic industrial development. A specific quantitative factor should be trended, such as total dollar value of total regional exports, total payroll dollars, or total employment. Factors measured in actual dollar values are preferred because the use of dollars or another currency balances differences in industry - specific impact on the community that would occur with other measures. For example, employment-count trends do not weigh differences in the economic impact of jobs in different industries. Increases in furniture manufacturing employment ($9/hour average salary) do not spur regional growth as much as those in software development and marketing ($38/hour average salary).
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The trend needs to be applied in a manner that depends on the nature of its measurement. If the trend was developed in dollars, then the growth rate of this trend may just be applied to all land-use classes. For example, if regional exports are expected to rise by 1.75% per year, then all landuse classes can be given a global growth rate of 1.75%/year. Such simplistic trending is not a recommended method for small area forecasting, because small areas can change their growth trend very quickly. But large regions don't change their "growth inertia" that quickly. When dealing with a large diverse-economy metropolitan area, a straight-line trend is a useful model of overall growth. While this almost invariably produces a reasonable forecast, it seldom produces a completely accurate one; effects of recessions and economic booms are not forecasted. But those are nearly impossible to forecast by any method. Trending growth of a large, diverse economy produces a useful and representative trend to drive the forecasting of its spatial growth. Industry-specific trending. In smaller and/or non-diverse regional economies, a trend of the one or two specific, basic driving industries can be done based on specific industry study. The auto-factory employment example used in Chapter 10, section 3 is a good example. If similar projected employment figures can be obtained they can be used as the basis for such a forecast of the region. If not, then some other factor must be projected and linked to load growth. For example, in a "college town" growth might be linked to projections of future enrollment at the university (overall enrollment is a better indicator of regional growth than university employment, see section 21.6). In one case the author saw, the goal was to project the global trend for a region based on entertainment industry economy — a market segment aimed at seniors. The trend for the region was developed by first developing the growth rate of the market in general (all seniors) and then backing out market share growth for the region's competitors (a number of other areas of the country competed for the same business). Unusual Land-Use Patterns Linked to Driving Factors The land-use (consumer class) patterns in a region or city can vary from typical patterns due to unique characteristics of its driving economic base. But this is quite unusual. Land-use patterns in any diverse-economy region will be broadly similar to those in any other diverse-economy region. Such large metropolitan areas have broadly similar layouts: offices and high rise in the urban core, an industrial/shipping activity center not too far from that downtown core, a ring of "urban mixture" medium-rise around the downtown area, some of it often abandoned or of low utilization, suburban development of gradually decreasing density working out toward a feathered periphery, retail on major intersections/transportation corridors, and clusters of denser development near
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major transportation hubs (intersections and or mass-transit stops). Details within this pattern - the quantitative factors necessary to calibrate surround and proximity factors in a standard simulation model - will be somewhat specific to any particular city, but major variations occur only with respect to major cultural differences. Even then differences are small in many cases. For example, Bilbao, Spain and Philadelphia, Pennsylvania are coastal cities with similar diverse regional economies based on shipping (both are ports), and heavy industry, services, and manufacturing. They do differ in observable land-use locational preferences: Bilbao has more high-density mixed-use (retail at street level, residential lofts and apartments above) urban development than Philadelphia, a function mostly of the European preferences for style of living and transportation. But the two cities are quite alike in overall content, layout, and detailed patterns of development, in spite of this. In general, large, diverse-economy regions do not significantly display any of the specialized "industry-specific" land-use patterns unique to the special cases discussed later in this section. Of course, there are a very few exceptions to this generalization. They will be covered later in this section. But except for those, land use in a diverse-economy region is "generic," following the broad, general patterns observed in the majority of big cities, whose patterns of residential, commercial, and industrial development were discussed in Chapters 10-14. By contrast, some small towns dominated by just one industry, such as education or tourism, do have rather unique locational land-use patterns linked to that driving industry. University towns have both a different land-use content (more apartments, more "college atmosphere" restaurants) than the average city or town, arranged in different patterns (near to campus, and everywhere closer to mass transit). Similarly, as will be discussed below, tourism, retirement, and other special industries dictate special land-use patterns. However, such small towns are the exception, even among small towns. Most small cities and towns have fairly generic land-use patterns, even if based on only one industry, because most have rather prosaic industrial bases. Only a few special types of one-industry towns have unique patterns of development in which land-use locational patterns are far different from "normal" because of some special need or attribute of the local basic driving industry. 21.3 CALIBRATION OF A SPATIAL FORECAST MODEL Chapter 11 's detailed account of a fictitious manual simulation forecast described the "calibration" required to fit the simulation model to the specific region being forecast. "Calibration" of a simulation method includes fitting its database and load values so its loads fit historical load levels observed on the system, as described there (e.g., the process that includes Tables 11.14 and 11.15). However, calibration for a simulation program, as used in all real simulationbased forecasts, also involves a second step, adjusting the program's preference function coefficients and set-up data so that it matches the service territory being
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studied. As described in Chapter 13, a simulation forecast method uses a number of spatial factors (Table 13.6) which are linked to the growth, or lack of it, of the various electric consumer (land-use) classes modeled in the program. Simulation programs use numerical values to describe such things as what "close to railroad" means and just how important that factor and others are to the likelihood of industrial development in an area, and to the development of other classes. These values have to be calibrated, or fine-tuned and adjusted to fit the specific forecast situation. Most simulation-based load forecast programs developed specifically for T&D planning purposes are programmed with default values that fit mainstream forecast situations - diverse economy, metropolitan regions in the country where they were developed. Those developed in the Americas (e.g., CEALUS, FORESITE) tend to fit dispersed land use, U.S. and Canadian cities dominated by automobile transportation systems and with coordinated but not controlled land-use growth (zoning). Those developed in Europe (e.g., CAREFUL) tend to work well in cities that have older infrastructures, higher population densities, more central planning, and transportation systems that include significant mass transit. Programs developed in Asia (e.g., in Taiwan, see Wu and Lu in References) tend to fit the types of cities and regions in those areas. But there are variations in the set-up needed within the U.S., or Europe, or Asia, and there are special situations where the spatial make-up of a region requires far different set-up and calibration of some global, regional, or spatial factors used in a simulation method's model. Thus, planners always need to verify that the set-up of all factors is appropriate for their forecast situations, and make adjustments when those factors are shown to need fine-tuning. Those who purchase a forecast program from a commercial supplier can require that calibration as part of the initial deliverable items and adjustment of it as part of the continuing software maintenance service. Regardless, prudence and common sense dictate at least assessing if the program is calibrating and recording that in the forecast documentation. Calibrating in the Right Order: Top Down Calibration is easiest, requires the least trial and error, goes fastest, and is most accurate, if done in a top-down order: adjust the totals, then large-area factors, and gradually move down to high-spatial resolution items. This should be: 1. Calibrate the base-year load map so it fits recorded T&D loads. 2. Calibrate the global trend so it fits the base year. 3. Calibrate the urban poles. 4. Calibrate the surround factor values and preference coefficients. 5. Calibrate /verify the spatial dynamic factors.
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Calibration of the Load Data: Making the Load Map "Fit" The data describing base-year consumers, land-use, and temporal load curves (and end-uses, if modeled) is a simulation method's "model" of the present service territory. If this data is accurate, then the simulation program's "forecast" of loads for the base year should match metered substation loads on a service area basis, as did (after adjustment) the land-use + load data combinations in Chapter 11's example. The basic procedure to establish how accurately the database is calibrated and to identify where changes need to be made was described in Chapter 11. When using a program with a load-curve based temporal model, the computed curve shapes can be used as a calibration guide, too. A database that uses a loadcurve approach, but does not "forecast" both the amounts and the times of both daily peak and daily minimum load correctly on a total and substation-area basis, is not calibrated well. Similarly, if it does not track the general shape of substation load curves correctly over the entire twenty-four hour (or longer) period modeled, it is not calibrated correctly. The basic procedure and elements of this calibration task were summarized well in Chapter 11 's discussion of procedure. Load-map calibration depends on attention to detail and on accuracy of consumer, land-use, and load curve data. Calibrating the Global Model and Trend The overall driving trend for the forecast must be obtained, preferably from the electric utility's corporate forecast. It then needs to be adjusted to make it appropriate for spatial application. That means: Adjusting for T&D planning-based weather normalization. Chapters 5 and 6 discuss weather correction and adjustment. Typically, the corporate revenue and rate forecast for a utility is based on "average" or even "low" weather. By contrast, T&D planning needs to be based on a specific set of reasonably-extreme (rare) weather conditions. Usually, the adjustment required is only a revision of per capita demand values for each class, to take the revenue forecast's basis from the average weather conditions upon which it is based to the extreme weather used as the base for T&D planning. Weather analysis data like that in Chapter 6 can be used to make this adjustment. Coincidence of load. The corporate revenue forecast does not address the fact that local area loads, as seen in transmission, substation, and feeder loads, have their own peaks. Since all of these peaks do not occur at the same time, the sum of local peaks will exceed the actual system peak (the only peak or demand value forecast in the corporate forecast).
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When working with many simulation programs this peak-coincidence adjustment need is not an issue: the program will automatically provide it if provided with the consumer count trends and consumption data by class from the corporate forecast. Local area peaks are computed and assembled on a local area basis as needed, using load curves and local consumer concentrations. If adjustment is needed, historical data on substation peak loads and their correlation to system peak must be assembled to develop "coincidence adjustment" factors (e.g., Eastside substation was at 97% of its peak when the system peaked, therefore its actual peak is 11.91 times its share of the systems peak demand). Calibrating, or Solving for, the Urban Poles After the global trend is adjusted correctly, the urban poles are usually the next item to be adjusted. They are the "big picture" factors in the simulation program's spatial allocation algorithm. There are several methods that can be used to identify urban poles: that they exist, where they are centered, their radius, and in a few cases, their shape. In some cases and with some forecast programs, the users feel comfortable simply inputting poles that they know are reasonable. Five methods are given below. Method 1 (quickest): judgement-based/external data Taking the concept of urban poles (Chapters 12-14), in many cases a T&D planner can set up a simulation program with poles that are "close enough" simply by estimating them from information available about the region. In some cases, there are only one or two poles (downtown, the industrial area) and the determination of poles is obvious. In others, a bit of research will identify key employment areas of the city: employment statistics on total payroll or number of jobs in each pole location determine the "height" of the poles. The 45-minute rule (Chapter 13, pp. 407 - 409) provides an estimate of the diameter. Method 2 (best): spatial de-convolution This method can only be applied in simulation programs that permit the user to directly apply spatial frequency domain functions. Usually, this is permitted only in simulation programs that perform the preference function computations in the spatial frequency domain (see Chapter 14, section 3). The best implementation of this method requires two years of very consistent land-use data, a possible drawback. The steps are: 1) For a particular class (or set of classes, e.g., weighted sum of residential), form a land-use map of the difference in this class between the two periods.
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2) In a "spare map" location, create an urban pole of height 1.00 and appropriate radius. Often, this function has to be split at the corners as shown in Figure 21.1, in order to have the correct phase (shift). 3) De-convolve map (1) with (2). This is done by computing the 2-D spectrum (discrete Fourier transform) of both, then dividing the one by the other. 4) Transform the result of (3) back into the space domain (Fourier transform it again). Normalize it to the greatest value equal to 1.00. 5) The resulting map will have local maxima at points whose location represents the X-Y shift of urban pole locations from the location of the urban pole center used in (2), and whose value gives their relative importance. These are the poles influencing the land-use class used to produce the target growth map in (1). Figure 21.1 shows the results of this method as computed using MATILDA applied to the Colline Noir region from Chapter 20. As can be seen, the locations and relative strengths of the poles are discernable. In fact, the poles in Figure 20.10 were found using this method. The steps above can be done very quickly with an appropriate program and computer. Exceptions or difficulties that can be encountered with method 1 are mainly limited to situations in which pole diameter is very different among the various poles in a region. If available land in the region is very constricted, so that growth is basically "picking off marginal land because it is all that is left, this method may not work well (no method will work well). An advantage of this method over others in this sub-section is that it can better distinguish between poles that are separate but close together. Method 3 (best): Multi-year low-pass filtering The location and relative height of urban poles in a region can be estimated from land-use data using the "map mathematics" or "user intervention" feature included in most simulation-based spatial forecast programs. Like method 2, it requires two years of very consistent land-use area available, a possible drawback. With it one can solve for indications of the number, size, and diameter of all the urban poles, with the following steps. 1) For a particular class, form a land-use map of the difference in this class between the two periods. 2) Apply a very low frequency pass spatial filter to this difference map. The pass band that works well is from 0 to .02 cycles per mile.
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Figure 21.1 Map of growth for the wide region in and around Colline Noir, from Chapter 20 (see Figure 20.10). Top, weighted growth map for residential and light commercial land uses (step 1 in method 1). Middle, urban pole function, applied as a "split" pole so its center is at coordinates 0,0. Bottom, resulting de-convolution results map (step 3, method 1). Compare to Figure 20.10.
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Figure 21.2 Map of the result from Method 2 applied to the same area as in Figure 21.1.
3) Planners can examine the resulting map (Figure 21.2). Local maximum points are very likely urban poles that influence this class. 4)
Contrast enhancement of the map (see page 700 and Figure 21.10) can make identification of pole centers easier.
This method works well in about 90% of cases. Exceptions or difficulties that can be encountered are few. If available land in the region is very constricted, so that growth is basically "picking off marginal land because it is all that is left, this may not work well. The method cannot distinguish between poles that are close together - it displays ellipsoid poles and leaves the user to work out the details. Figure 21.2 shows results from this method applied to the same problem area as method 1 from Figure 21.1. Method 4 (fairly good): Single-year low-pass filtering A method that can yield nearly equivalent results in identifying poles is to perform the same set of steps as in method 3 above, but on the map of a class's land use, not on a map formed by the growth in that land-use class over the period between two years' data, as was done in methods 2 and 3. This method works rather less effectively than method 2, but still produces good results in many cases. It performs best on large cities that have had rather high growth rates in the recent decade.
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Method 5 (not too good): trial and error A rather clumsy and only partially successful method is to simply test various urban poles for their applicability. The method works best when the user has a good understanding of and intuitive insight into the urban growth process, and the particular simulation program used. The steps are: 1) For a particular class form a target map, either the land-use map of the difference in this class between the two periods, or the class itself. 2) Create an urban pole where it is suspected one is located. 3) Multiply (1) times (2) on a point by point basis. Add the result. 4) Move the pole and repeat steps 1 - 3. If the resulting value from step (3) increases, the center of the urban pole is closer to the location used in the second set of steps, if it decreased, it is closer to the first. 5) Based on the results of (4), move the pole to a new location and try again. Keep iterating until no further increase can be obtained. This method does not work well in many cases, and it is frustrating to use because often there is no discernable pattern of convergence in the location of the urban poles. This is particularly true when there are several poles involved. Advanced applications based on adjusting/solving urban poles There are a number of "tricks" one can apply based on these urban-pole solution concepts. First, the map obtained in methods 2 - 3 can be used instead of a set of urban poles. Coefficients and weighting factors associated with the simulation models "large area" effects have to be re-calibrated, but the map serves not just as a substitute, but in some ways as a superior substitute for a set of urban poles. It is, in essence, the ultimate "distributed urban pole" (see section 14.3). Second, urban poles are not completely static. They change height and in some cases their centers move, if relatively slowly. Methods 1 and 2 can be applied to different periods, if multiple years of land use are available. Changes in the relative height and location of poles can be tracked and extrapolated over time for future forecasting purposes. Third, the methods covered above tend to find the location and height of poles relatively well, but do a less satisfactory job of identifying radius and profile. Method 1 in particular is not very dependable in indicating either, one reason why experimentation with different radii was recommended. The profiles of most urban poles match the "cone" or a "gaussian" profile of constantly decreasing value as one moves away from the pole center. However, there are exceptions where a pole function's profile might be flat or even inverted. The profile can always be tested by study and experimentation. However, in this regard, method 1 is far better. Readers familiar with multi-dimensional signal processing methods and image-enhancement techniques can no doubt think of
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advanced frequency and space domain methods that could be applied to ferret out urban pole profile, but those are beyond the scope of this discussion. The next section discusses how to create poles of arbitrary profile, even if the simulation program is limited to computing only cone-shaped pole functions (most simulation programs are). Calibration of the Preference Factors What is the correct diameter and distance function for the "railroad" factor and the other surround and proximity factors of the type listed in Tables 13.6 through 13.8? What are the preference coefficients (the PJ,C coefficients in equation 13.4) for each land-use type? A computer program's manuals may provide some advice. Various technical papers reporting on values for specific cases provide a starting place for calibration (see Lowry, 1964; Tram Willis, and NormcoteGreen, 1986; Ramasamy, 1988), but accuracy in a spatial forecast is achieved only by adjusting a simulation program's factor and preference functions to reflect precisely the growth behavior as observed in the specific territory being studied. Calibration of this part of a model involves "backcasting or hindsight testing" the simulation program with its setup values against recent growth (the last two to three years) and adjustment of the factor and preference functions until the program/database combination matches actuality with its forecast. Figure 21.3 shows the density of development for a mythical metropolitan area and will serve to illustrate the clues and contrasts that can be found and used in calibration. The letters on each item below refer to the markers in Figure 21.3. A. Diameter of proximity and surround factors. The light-shaded development in Figure 21.3 indicates mostly residential development. Its locational pattern with respect to major roads and highways shows clearly that residential development locates only within about 3 miles of a major traffic corridor. Therefore, the various factors affecting residential development and highways go out to a radius of three miles. B and C. Is it a pancake or linear function of distance from highway? This mythical city shows two characteristics, B and C, which would normally not co-exist. At the north of location B is a pattern that develops from a highway-proximity factor that is a pancake function (a "close to highway" factor with a constant value of 1.0 from distance = 0.0 out to 3.0 miles). The development shown as the fragmented, or "feathered" development pattern typically seen with a pancake highway function. Planners must note that such feathering is transitory: after time the "holes" fill in with development. By contrast, the development along C's transportation artery indicates a linear, rather than pancake-function of distance, radius 3 miles. Again, normally a city would have only one type of development, B or C, in all of its parts.
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Figure 21.3 Manual, or with the right tools, computerized, study of a map of development for a city helps establish values for various simulation program factors. Letters and arrows indicate features discussed in the text.
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D and E. This "notch" alongside a set of high-utilization railroad tracks shows a pattern that can be seen in the aerial and satellite photos of many cities. There is a wealth of information here. The width of residential standoff indicates the width of the factor with regard to negative impact on residential. The distance E can be used to determine the relative weight assigned to the "don't want to be near a railroad" versus "want to be close to downtown" factors. At some point residential development will accept the negativity of a rail line for the advantage of very close proximity to downtown. This location, E, is where the two factors balance one another. F.
Similarly, at F, the development shows both how far inland the "want to be close to the water" factor runs (about 1.5 miles), and how much this factor overrides "close to highway" (this development is more than three miles from a highway).
G. The notch at the end of the development arms following each highway indicates the standoff of early residential development. This is land too close for residential and "reserved" by the system for commercial/higher density development. The radius of "too close to highway" factor can be determined from observation of these areas. H. This road, although not a highway, is clearly major enough to have the desired "highway effect" on development. As the smallest road with this impact it helps identify the lower end of the definition of "highway" for setup of the highway levels in the simulation model (what is a highway and what is just a road?). I.
Commercial attraction to intersections. The darker shading is meant to indicate commercial. Here, development patterns indicate about '/> mile wide "close enough to highway factor."
J.
Close to railroad = 1 / 3 mile. The very dark shading here along the railroad is all within 1/3 mile of the rail trunk lines. Thus the diameter of that factor with respect to positive development of industry is 1/3 mile.
Calibration requires that the planner play "data detective" with care and attention to detail. In the author's experience it is the one aspect of simulation that is best learned through hands-on experience. By identifying and studying development patterns in only one year of aerial photos, satellite images, or landuse databases, the types of clues described above can be identified and used to determine the diameters, profiles, and relative weighting of the preference factors.
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The Iso-Preference Score Rule One particular rule is quite useful in determining the relative values of the coefficients: All recent similar changes in a class should have the same preference score. One example will suffice to illustrate this concept. Figure 21.4 shows a smaller version of Figure 21.3 in which the areas of heavy residential growth in the last two years have been identified. All such areas, if being forecast for the past year, should have had a preference score that was very similar (high enough to get them selected for growth). Thus, for calibration purposes the planner can assume that the areas at A and B both have the same overall preference score. Area B, farther out but near the highway, and area A, ten miles closer in but fully three miles from the highway, are equivalent. This means that the weighted difference between being three versus one mile from a highway (close to highway proximity factor) is equal to the weighted value of being ten miles closer to downtown (central urban pole). By similar analysis of recent growth, finding and analyzing areas that grew simultaneously but had different characteristics, the relative values of factors can be identified.
Developed areas Developing areas
Figure 21.4 Illustration of the preference coefficient computation as described in the text. Recent residential growth had occurred in both areas A and B, which implied that their preference scores are similar. This fact and other similar observations about local growth were used to determine the values of the PJ C coefficients.
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identifying Missing Factors or Mismatches Figure 21.4 is based on an actual case where a factor was missing, illustrating one of the first error issues in the calibration of the original ELUFANT model at Houston Lighting and Power (1977). The program's starting calibration values forecast only residential growth in the areas marked A in Figure 21.4, when applied to back-cast growth for the prior two years. It missed entirely the roughly 25% of residential growth that occurred in the areas marked B. What it missed was obvious upon inspection. Those areas marked B were far enough north of the coast to lie in the coastal forest. Homebuyers looking north of the city could find homes on treeless lots about fifteen miles out from downtown, or forested lots at about twenty-two miles out. A portion of homebuyers were choosing each option. However the forest, and its impact on home buying, had not been represented in the database or the simulation factor setup, so the model's forecast did not reflect this. The first lesson learned by comparison of forecast to actual was that trees were important in determining residential consumer development locations. A forestation map was obtained, coded into ELUFANT's multi-map database, and used as a local factor. This was a binary map with a value of 1.0 signifying the area was forested, while 0 indicated it was not. Residential growth was occurring in both areas A and B. Therefore, both areas had the same preference scores with regard to the way the simulation modeled and applied preference scores. This meant that the advantage of "Trees = true" was equal to the difference in the weighted value of the urban poles in the areas marked A and B in Figure 21.4 (i.e., equal to the urban pole's decline over seven miles farther out from the center of the city). The residential preference factor for trees was adjusted to reflect this observation, and the program then forecast all residential growth correctly. The Stationary Process Rule As a general guideline, the process of growth of a region should be a stationary process. This means that the process doesn't change even if the city or region does. Specifically, statistics on the process of growth should remain constant over the simulated time modeled by the program. This rule can be applied to test whether the program's overall dynamics of growth are adjusted correctly. For example, in each iteration (simulation of growth over a year or more period) a simulation growth forecast program will assign growth to specific small areas based on the class-by-class preference scores. Each candidate area of growth is evaluated with respect to how well it matches the needs of each class (e.g., residential) based on its preference scores, computed on an arbitrary scale, usually in percent of "perfect" match to each class's needs. The program then
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selects the amount of small areas it needs for growth of each class (from the global model) and starts with the highest rated small areas and works down from there. Those with high scores, perhaps all small areas above 92% preference score, are assigned growth. Those below that threshold do not see any growth. The preference threshold limit - the value below which no growth is assigned should not change dramatically from one iteration of the program to the next. Suppose that a forecast is doing ten iterations, each representing one year of growth, as shown below, with the resulting iteration-by-iteration threshold values shown: Iteration: 1 2 3 4 5 6 7 8 9 1 0 Years o f Growth: 1 1 1 1 1 1 1 1 1 1 Threshold: .82 .79 .76 .74 .72 .69 .66 .64 .62 .60 Something is wrong, because the threshold values steadily decrease. Many planners make a mistake by assuming that this trend is what should happen. They reason that as the program simulates growth it will use up all the high-scoring small areas first (true) and then have to dip down into those with lower preference scores (untrue). Thus, the trend of gradually decreasing threshold values shown above is what should happen. But if the program is set up correctly, it will "restock" the supply of really high-scoring vacant land in each iteration. For example, generally the biggest factor contributing to residential preference is the "close to residential factor." During one iteration the program may use all the vacant small areas that score really high in this regard. But it is creating new residential small areas, which mean vacant areas that were previously not close to residential are now nearby new residential areas. Their "close to residential factors" have just increased. The supply of developable land that scores high increases as a result. Other concerns being equal, if the process of growth is modeled well, the supply of high-scoring vacant areas will be restocked at just about the rate that it is depleted. In every iteration the threshold value for the selection will thus remain about the same. A reasonable trend would be something like: Iteration: 1 2 3 4 5 6 7 8 9 1 0 Years o f Growth: 1 1 1 1 1 1 1 1 1 1 Threshold: .72 .71 .67 .69 .68 .68 .66 .67 .68 .68 A permitable exception is if the iterations are not each representative of the same amount of growth, as would happen with an often used method of making the latter iterations in a forecast represent longer periods. For example, suppose a program has been set up with ten iterations as shown below. Iteration: Years of Growth: Growth % Threshold:
1 2 3 4 5 6 1 1 1 1 1 2 2.1 2.1 2.0 2.0 2.0 4.1 .82 .79 .83 .83 .82 .74
7 3 6.2 .70
8 5 9.8 .68
9 10 5 5 9.4 9.3 .66 .66
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This indicates what is probably a good calibration and a stationary process. The first five years certainly indicate that, and calibration should probably be left without further adjustment (unless other diagnostics indicate a need). Very little can be inferred from the absolute values of the thresholds - a value of .92 or a value of .68 may be equally valid. These values are on an arbitrary scale and depend on the factors and coefficients and the growth rate - a forecast with a lot of growth occurring in each iteration will dip lower into each iteration's stock of available growth room. Thus, there is no set level for the threshold that is "best." Generally, however, planners should be concerned if the threshold is much above .90 or below .66. If the numbers dip below .66, the program may be modeling iterations that are too long. In the example above, the author would change the final three iterations (representing 15 years) to five iterations, each modeling only 3 years of growth. Diagnosing temporal trends in threshold values Small deviations from iteration to iteration are tolerable if the trend over several iterations is not towards an overall change. Thus, something like the following trend would be satisfactory. Iteration: 1 2 3 4 5 6 7 8 9 1 0 Years o f Growth: 1 1 1 1 1 1 1 1 1 1 Threshold: .79 .78 .74 .72 .73 .72 .74 .77 .71 .76 However, if the trend drops gradually and steadily in each iteration, something like that shown in the example below, then the factors aren't adjusted well. Iteration: 1 2 3 4 5 6 7 8 9 1 0 Years o f Growth: 1 1 1 1 1 1 1 1 1 1 Threshold: .72 .71 .67 .63 .58 .56 .52 .48 .46 .43 This very steady trend downward gives very little clue as to what is wrong, but something is not calibrated correctly. A slow consistent trend often indicates problems in surround rather than in proximity factors which need adjustment (and there are rare exceptions to that rule). Other than that there is no real clue in this. Planners should check spatial patterns of growth for additional clues. If the trend has an accelerating rate of decrease, the first suspect is any data that needs to be updated manually in each iteration. This is usually an indication that new highway data or similar manual entry changes have not been entered at an appropriate rate. Such a trend would be Iteration: Years o f Growth: Threshold:
1 2 3 4 5 6 7 8 9 1 0 1 1 1 1 1 1 1 1 1 1 .92 .90 .90 .86 .82 .77 .70 .62 .52 .45
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This indicates that, up through the third iteration, there was enough land close to highways, but that after that the better land had been used up and not enough highways were input for that year's growth. The stock of highways needs to be replenished.1 If the trend is toward increasing values, even at just a slight rate - then the opposite is true, there are too many highways or other new attributes being added in each iteration. Exceptions There are cases where the values will, and should, decrease in each iteration. The most common is when growth is being modeled in a region that is "running out of room." Marginal land must be developed when preferable land is all developed, and as a result preference threshold values should drop. One situation where this happens, but should not be allowed to occur, is in cases where the growth in a service area moves outside the utility territory. As an example, a forecast of City Electric Department's T&D loads might study only those areas inside the city limits (its service territory). Yet, as the city nears complete development, growth moves outside the city limits. If City Electric planners model only their service territory, the preference factors in that area would drop as marginal land had to be selected for growth. But that would be the wrong case. The only acceptable way to model growth in such a situation is to represent areas outside the service area, so that the competition for growth in and out of the service territory is properly modeled. Chapter 11 's example discussed this with respect to the mythical Springfield city limits and the growth of factory-caused scenarios. Section 21.6 will discuss this. If, however, there was no developable land outside those city limits (perhaps the city is on an island or otherwise landlocked by areas off-limits to growth) then one would expect that as the available, high-scoring land is absorbed by growth, land less suited to each class must be selected. Thresholds would drop. 21.4 TRICKS AND ADVICE FOR USING SIMULATION PROGRAMS WELL This section covers a number of "tricks," or ways to apply simulation-based spatial forecast programs well. These are based on using the features included in most simulation-based spatial load forecast programs. Planners using any one particular program may have to interpret the steps described here into the format of operation used in their program. However, what is covered here is appropriate for all simulation-based programs the author knows. Most simulation-based programs have a feature which permits the user to perform spatial arithmetic and apply spatial functions on a customized, step-by1
Or, perhaps there really is no more road and highway construction because of real limitations on further growth of construction. In such a case the process of growth will not be truly stationary. This does happen.
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step basis. In some programs this permits the user to interactively perform spatial analysis one function at a time. In others, the user creates small macro files which are then executed to perform a series of customized steps. Either format permits the user to add, subtract, multiply and scale various data levels, to apply various logical, comparison and extraction functions, to "filter" data maps by applying surround or proximity functions, and to perform other basic steps used in the algorithm itself. Many of the functions covered below are implementable using that method. Customizing Urban Pole and Preference Function Shapes Using Standard Linear (Cone) Functions Often, a forecast situation requires a "flat" urban pole. There is an attraction or siting requirement for proximity to a particular center or amenity, but not one with a linear attractive function of distance. Instead, it is much more digital: within a certain distance the factor is satisfied, outside that distance the factor is not satisfied. But many spatial simulation programs can only model all urban poles as "cones" with a user specifiable location, radius, and height - the value that decreases linearly with increasing distance out to the radius. A good approximation of a pancake function can be formed with two conepoles, one with a negative weighting factor, as shown in Figure 21.5. This results in a "pancake" with a height of one for a radius of nine and a "diagonal edge" out to radius ten. Figures 21.5 and 21.6 show other such "tricks." The ease with which such pole profiles can be created is one reason that most simulation programs have been written to handle many more poles and proximity factors than are usually needed, so that two, three, four or even more can be "stacked" together to shape the factor versus distance function as needed.
Distance
Figure 21.5 A "flat" urban pole can be created by using two conic urban poles. Top, cross-sections of the two poles. Bottom, 3-D view of the two, and their result.
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Figure 21.6 The pancake function is not the only customized shape that can be produced using combinations of urban poles.
Ax value
•
Figure 21.7 Top, applying a pancake function of radius 12 twice in successive steps is equivalent to applying a decreasing-value function of radius 24 one time. To perform the operation, the pancake function is applied to the base map (i.e., that upon which the factor is being applied), then the factor is applied again to the result from that first application. The result is equivalent to applying one factor with a nearly linearly decreasing cross section and a radius of 24. Bottom, a function that creates a "times two radius" pancake function can be implemented through two applications of a "shell" function, then subtraction of the values in the base map times a scalar, A, equivalent to the sum of the shell function cellular values.
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Working Around Surround and Proximity Factor Limitations Some spatial simulation programs limit proximity and surround factor functions to within rather narrow maximum radii, typically around three miles, which is more than sufficient in most cases. Others limit the profile (cross-section) to only a pancake function, and/or only a linearly decreasing weighting function of distance. Most of these limitations can be worked around using clever application of functions. Stacking (adding) factors Adding factor result maps created from the same base (i.e., with factors applied to the same map, such as railroads) can work around limitations a program may impose on the factor profile. The "tricks" shown for urban poles in Figures 21.5 and 21.6 can be applied to surround and proximity factors, to work such limitations. For example, two "close to commuter rail hub" factors can be applied for residential in a large city, one with a weighting of 1.0 and a radius of }A mile, the other with a weighting factor of —1.0 and a radius of % mile. They result in a "ring function." Such a combination models a commuter hub proximity preference that says, "I want to be close to but not immediately alongside a commuter hub" even if the program will not allow factors of such complex profile. Widening radius and shaping profiles using sequential application Users of programs that impose a limit on factor radius can generally work around this by applying factors sequentially. There are two situations in which users may need to apply factors with a wider radius than a program limit permits. 1) In special cases where a factor must extend beyond the limit permitted by the program. Such situations are rare with respect to actual proximity and surround factors. However, a user who wants to create distributed urban poles (see Chapter 14) using a program not written to provide that feature can work around that by computing them as "very wide" surround factors (radii « 15 miles). 2)
When a grid-based map format program is being applied at a high spatial resolution beyond that for which the program was designed. For example, suppose a program might have been designed around application at 40-acre resolution (grid cells V* mile to a side), and written with a limit of 12 cell widths (3 miles) in the application of all proximity and surround factors. Yet the user wishes to apply this at 1/8 mile resolution, which means 3-mile proximity factors that now require 24-cell radii.
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Applying two 12-cell radius pancake functions in succession (Figure 21.7) can produce an acceptable approximation of a 24-cell-width linear-weighted surround function. Figures 21.6 and 21.7 also give examples of other sequential operations and the results they produce. A caveat: know the basis of factor computations A few simulation-based forecast programs and some spatial data systems used to implement simulation apply search, surround, and proximity factors as square not round, functions. A surround factor computation for "all residential within 1A mile" adds up all residential in a square of X and Y dimension of 1 mile, centered on the point of analysis, instead of computing it only within the radius of 'A mile, as illustrated in Figure 21.8. Similarly, proximity factors for the nearest railroad may find a railroad at distance x=l, y=l, and return that as within one mile (actual distance 1.414 miles). This square rather than circular application is a result of shortcuts made to simplify programming and increase analytical speed. Although such approximations are becoming rarer as GIS and spatial database programs become more sophisticated, they are not uncommon. What is common is that any approximate nature of the function computations may not be documented where it is easy to find. One commercial spatial simulation load forecast program the author has seen uses square functions, but has circular functions in illustrations of its application.
Figure 21.8 Correct implementation of a surround factor in a grid (left) and an approximation used in some simulation programs (right).
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In other cases the issue is more complicated. One popular spatial database manipulation and facilities data system has two different ways or "levels" at which it can be "programmed" to perform surround, proximity and search functions. One implements square functions, the other implements circular functions. Although that distinction was documented in the user's guide, it is only explained in the details about implementation, and not obvious even to a person studying those instructions. Another issue relates to the resolution of computations on polygon programs. Some systems work with only the center of area of a polygon, computing all attributes for that location. Others analyze corner points or take other computational means to estimate area, distance relationships inside polygon areas. Figure 21.9 illustrates one such shortcut and the approximation it renders. Contrast enhancement for factor, pole, and other searches Often, planners playing "data detective" can create "custom" maps using the interactive or macro features of a program, in order to search for characteristics such as the locations of urban poles, or in order to diagnose factors and calibration. A "trick" in contrast enhancement is useful when performing studies like those described earlier where one is searching for specific small locations using a low-frequency function like an urban pole. Raising a map to a power (e.g., cubing it with the third power) can increase contrast enhancement. For example, the result maps (e.g., step 4 in method 1 for urban poles discussed earlier) can be cubed, or raised to even a higher power on a point-bypoint basis, to enhance visibility of maximum points. This technique enhances contrast and makes the highest value points stand out more visibly in displays, as shown in Figure 21.10. 21.5 PARTIAL-REGION FORECAST SITUATIONS Very often planners must deal with the forecasting and planning of cities, towns, and regions that are cut through by boundaries or barriers which are "artificial" from the standpoint of the forces and interactions controlling regional load growth, but which are very real to the planners. A classic example is a "border city" such as Laredo-Nuevo Laredo, which straddles the U.S.-Mexican border. Laredo, served by AEP West, is the U.S. side of a metropolitan area stretching across the U.S.-Mexico border. The growth of Laredo, the U.S. side, cannot be fully analyzed unless it includes some assessment of Nuevo Laredo, the Mexico side, particularly since a majority of the "metropolitan area population" resides in Mexico. Similarly, planners at CFE (the electric utility serving most of Mexico) cannot neglect Laredo, in the U.S., when forecasting Nuevo Laredo's load growth, because the U.S. portion of the metropolis contains a majority of some types of the region's commercial development.
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School |
|
One Mile Figure 21.9 A 170-acre parcel of land near the corner of Tryon Road and Piney Plains Road in Gary, NC, shown as it is modeled in a polygon format. To gain speed, factor computations in some programs would treat this polygon's attributes as all located at its center of area (marked with an X). Such an analysis would conclude that all of this land was within 1 mile of a nearby school, when in fact only about 45% of it is. The best work-around to the inaccuracies this approximation introduces when using such a program is to split the area into a number of smaller parcels.
Figure 21.10 Cubing a map on a point-by-point basis will improve contrast and make maximum points stand out. Here, the filtered result of method 2 (Figure 21.2) is cubed, greatly improving the detectability of local maxima. This is useful in pole detection as well as numerous other applications in setting up and calibrating a simulation program.
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Service and Study Boundary Situations In these situations the forecasting of load growth in a vitally important area of the utility's service territory is complicated by the following issues: •
The utility service territory does not represent the complete "whole" of the region.
• The utility service territory does not represent all of the area that is competing for growth that might occur - growth trends in this area could move somewhere else. •
Load growth in the utility area is influenced, perhaps driven by, and interacts with population, events, and development outside the utility service area.
•
Detailed system, meter, and data on these events and development is not available outside the utility territory and not available to planners.
Each of these issues will be discussed in more detail below, along with recommendations and procedures to handle then. But the overall guideline in such "boundary limitation" situations is to maintain a holistic perspective. Planners must always keep the whole region foremost in their mind, even if their job is to forecast on only a small portion that lies in their service territory. In addition to this first category of planning limitations due to political boundaries, utility planners face two other types of "boundary limitations" that are qualitatively similar. The first of these includes studies where service area boundaries, not political boundaries, limit the area the planners are forecasting. Planners at Constellation Energy cannot assess the forces shaping the growth of Baltimore's southern and western suburbs without taking into account the influence of Washington DC, outside their service area to the southwest. Similarly, the Research Triangle Park area of North Carolina (Raleigh, Cary, Durham, Chapel Hill) is served by both Carolina Power and Light and Duke
Table 21.1 Definitions for Partial-Region Study Study area
Territory that planners plan their system
need
to
forecast
to
Influencing region
The entire whole from which influences on growth in the study area emanate.
Outside area
That portion of the influencing region that is not in the study area
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Power. Planners for each utility face a challenge because they do not have the data or familiarity with the entire region. Cobb EMC, which serves the northwest corner of Atlanta, cannot assess most of the forces causing growth in their service area, if they ignore the majority of that city just because the largest part of its metropolitan area is outside their service territory. The third of the three partial-region forecasting situations includes planning situations in which the "boundary" is self-imposed. Most large electric utilities organize themselves into discrete operating divisions. Planners for the "western metropolitan" division around a metropolis may need to forecast only their division area, yet find it is part of the larger utility service area. In order to limit the effort involved they do not want to study more than "their" area, yet it is influenced by the larger service territory. Here, they can obtain data and information if they want, but they wish to limit as much as possible their study effort. Such self-imposed boundary situations should not be allowed to happen. Simply put, "district by district" forecasting of areas that are part of one influencing region is not a recommended procedure. While planners for each of the three operating districts at a utility like ComEd (Chicago) may very well plan their T&D systems in a largely self-sufficient manner, the forecast of their joint service territory should be (and is) done as one coordinated effort. Table 21.1 provides some definitions used throughout this section. As mentioned, the fundamental problem in a partial-region forecast study is that growth inside the study area is driven or influenced by factors among the outside areas, for which the planners have no or only limited data. Impacts from the "trending" perspective Within the paradigm of trending - forecasts are in some sense extrapolations of past trends - the major impact of the partial region situation is that the present trends may change due to a changing allocation of load growth among the study and outside areas. Figure 21.11 gives an example. With trending, this partial region situation manifests itself as a lack of data and lack of modeling capability for the planners. They do not have historical data for the entire region nor, usually, a tool that can use it if they did. A hierarchical regression (see Chapter 9, Figure 9.12) can often identify situations like that shown in Figure 21.11. Often, the best tool for this situation is a savvy planner who is alert for this situation and innovative in looking at it from a non-standard perspective. The goal is to reproduce something like the analytical inference that was shown in Figure 9.12, to determine when and how much growth will deviate from historical trends in already-developed areas. Utility planners should not expect too much from such a technique in a situation like this without work and some trial and error adjustment on their part. Frankly, the best solution to this situation is a group of savvy planners who are alert for this situation and innovative in looking at it from the non-standard
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GobbB/C
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Gecrcja Rower and other summing utilities
Figure 21.11 In the 1970s Cobb EMC's service territory to the northwest of Atlanta was outside the periphery of metropolitan Atlanta. As the metroplex expanded outward through the 1980s, it suddenly grew into Cobb's service territory, and growth "took off." Left, the overall trend in Atlanta as a whole did not change, but Cobb's load (right) took a radical change from historic trends. This data was estimated by the author from FERC, REA, and population data for the Atlanta metropolitan region, which is split by several electric utilities. It was adjusted to remove economic recession effects and other such influences.
perspective. Their goal should be to reproduce something like the analytical inference shown in Figure 9.12. By studying spatial trends and availability of land, they can determine when and how much growth will deviate from historical trends. The planners should expect to have to do a good deal of work in this type of situation - methodology alone will not do the work for them. Overall, this is a job for simulation, but the problem is that that they will need some inkling of the overall trends to drive that simulation. The planners must develop the overall region trend (total shown on the left side of Figure 21.11) and develop a firm basis to relate his study area to that. Generally, they will not have access to the load data on the entire region and if they do it will not necessarily be consistent or complete. Generally, good estimates must be made from other, non-load data that is available. A recommended way to develop the overall region load estimate is to use population data (census data is always available) and assumed per capita load values, adjusted for observable differences in the industrial and commercial components of the study versus outside regions. Another way is to count total squares miles of development (using satellite or aerial photos). This does not mean using a land-use approach, but merely counting the geographic development rates of the metropolitan area as a whole as it spreads out among the various utility service areas.
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Impacts from the "simulation"perspective Planners working with a simulation tool have a model that can accurately analyze the interactions of their study area with those outside it; one that can easily anticipate, quantify and time changes in historical load growth trends like that shown in Figure 21.11. The major impact of the partial-region situation is that planners do not have detailed system, meter, and consumer data on the outside areas involved. The key point here is the word "detailed." The planners cannot easily obtain detailed information on the outside areas, but they do not need detail. Simulation tools can forecast the whole region, including the study region, without having detailed information on the outside area. Thus, the planners should set up the simulation database with detail and accuracy on their study area, and with only approximate, estimated land-use data on those areas outside their service area (Figure 21.12). The resulting small area forecast of those outside areas will not be highly accurate, but that for the study area will be very nearly as accurate as if the entire database were input with a high level of detail. The reason this "trick" works is the nature of the spatial interactions that simulation mimics in its forecast. The spatial detail in a simulation's small area database is needed in order to compute the short-range factors that influence the precise locations of various land-use growths, such factors as "industrial locates within % mile of a railroad" and so forth. None of these factors have a great effective distance. Many range less than a mile and none go out beyond three miles. The long-range factors (urban pole, regional balance of land-use types) are blurred by location. Viewed from the spatial frequency domain, spatial detail is needed only to compute high-frequency components of the simulation model. Low-frequency components do not depend on the spatial detail. For example, the location and size of the next mall to develop in Laredo, Texas, is not a function of exact locations of malls and market areas in Nuevo Laredo, across the Rio Grande. Its location will be a function of short-range factors related to local roads and topology in Laredo. Its size and the timing of its development will depend on the total amount of malls, markets and retail, and population in the combined region (Laredo and Nuevo Laredo) - the longdistance impacts. The exact locations of the markets and malls in Nuevo Laredo will not affect these either. What is important is their magnitudes. Developing a "fuzzy" database like that shown in Figure 21.12 is quite easy, even if the utility does not have access to detailed demographic and system data for the outside areas. Both sides of the diagram in Figure 21.12 were developed from "public domain" data obtained at no cost over the Internet, using the sources and data, and requiring the efforts shown, in Table 21.2. The detail for Laredo, with a spatial resolution of about 1A mile, is barely sufficient to drive a 2-3-X simulation algorithm in a detailed forecast (sufficient for a study area). Total time to develop, and to calibrate the region to load data, was 4.3 hours. Total time to develop the Mexico-side data was only 36 minutes.
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706 MATILDA© Area: Border Test Database: Larsym
Title: Base Year Data Format: CMPAR
Alg: SUSI-Q Feature: Display
10:07 AM 09/14/01 LWillis ESC 3
Figure 21.12 Example developed by the author from public domain (Internet) satellite photos for both sides of the Texas-Mexico border at Laredo, Texas. This display of electric energy usage makes clear the different spatial resolution used on each side of the national border for a 2-3-X spatial simulation model forecast of the U.S. side. Nuevo Laredo is represented with very little detail, but that is sufficient for the algorithm to determine Nuevo Laredo's effects on the detailed area growth in Laredo.
Table 21.2 Sources and Development Times for Database Behind Figure 21.12 Sub-Area Laredo
Data Spatial land-use Land-base (roads, etc.) Population & Demog. System load Cust/load data Total Laredo
Nuevo Laredo
Spatial land-use Population & Demog. System data Elec load Total Nuevo Laredo
Source
Effort - hr.
TerraServer.com & similar USGS maps Municipal & state web sites FERC filings/Corp. Report Est. from experience
2.6
TerraServer.com Expedia.com Est. from experience Est. from experience
0.3 0.1 0.1 QJ. 0.6
0.2 1.0 O5 4.3
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"Competitive Land" Considerations Figure 21.13 illustrates another type of "partial area" consideration, one that affects mostly studies for municipal utilities. The significant issue here is modeling the competition among various land parcels for the growth that will occur. As a city nears complete development of the municipal service territory (i.e., the areas within the city limits) growth does not stop, it moves on beyond the city limits). Proper modeling of the region requires that the entire metropolitan region, not just the areas within the city limits (and the municipal utility's service area), be represented in the spatial model. As more and more of the highly-rated land inside the city limits is "used up," growth begins to move outside the city limits, to land ideally suited to development there. This occurs long before all the land, particularly all marginal land, inside the city limits is used. Within reason, development will move to ideal conditions farther out rather than take marginal land inside the city and spend money to make those marginal conditions closer to ideal. This is a fundamentally different issue with respect to modeling the entire region than that discussed above (Figure 21.12). Although there are similarities, the issue here is making certain that the forecast program realizes that there are other options for growth than just locations inside the city limits. The only acceptable way to model this is to represent areas outside the service area in detail, so that the natural competition for growth in and out of the service territory is properly modeled. These areas must be represented with complete detail, unlike the "fuzzy" model that can be applied to situations like that shown in Figure 21.12. Roads, undevelopable areas, and other features of the outlying land must be shown. Chapter 11 gave an example of this with respect to the mythical city Springfield, its city boundaries, and the growth the alternate scenario (truck factory) caused to occur in and out of those boundaries. What is the difference between the situations shown in Figures 21.12 and 21.13? Why can planners represent "the other part" of the region with little detail in the situation in Figure 21.12 but not in the situation depicted in Figure 21.13? In the first instance, the long-term historical trend for the planner's region includes only "their part" of the region. In the latter case, the long-term trend, and all the history the planners have to work with, includes the trend for all their region. Thus, in Figure 21.12, the planners need to only model the rest of the region to the extent needed to understand its influence on their territory. They have a "partial region" global history from which to assess and project "global" growth for their territory. But in Figure 21.13, the problem the planners have is that they do not know what part of the historical trend will move outside their city limits they need the program to tell them that. And to do that, it needs all the detail.
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Figure 21.13 Top, a growing city's peripheral development is reaching its city limits. At the lower left, if the municipal electric utility department's planners extrapolate the overall growth, but model it as occupying only areas inside their city limits, their forecast model will "fill in" marginal areas with long-term growth. As a result, they will have a distorted forecast and miss seeing the real pattern of growth, which involves a portion of the growth jumping outside the municipal city limits. A spatial model must represent the entire region over which growth could take place, in order to see the results of competition of various land parcels for the growth that will occur (lower right).
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21. 6 FORECASTS THAT REQUIRE SPECIAL METHODOLOGY Retirement and Retirement-Based Communities Some areas within the United States specialize in providing comfortable communities for older and retired persons. Sun City, Arizona, and Sarasota, Florida, are two areas that often come to mind, but there are many other areas, all essentially small cities, that are dominated by a "retirement economy." These areas are not only different from most cities in terms of demographics, but also have a different driving mechanism behind their economy. They can be modeled for spatial load forecasting using simulation methods, but planners applying those tools must modify the application through adjustment of various factors. Differences are: Residential is the basic industry. Unlike most cities and most examples in this book and those in Chapters 10 and 11, a retirement community has no basic industry of the normal sense - no factories, no corporate headquarters or R&D labs, and no industrial or commercial enterprises that "earn" money for the regional economy. The income driving the community comes from outside its region in the form of pensions and savings. Among the land-use classes, residential is the "industrial" class in the sense that it creates the region's income. Land-use mix. Obviously, the mix of land use in a retirement community will differ from that of the average city. First, there is no industry or basic commercial development. Second, there may be more, and will certainly be different, mixes of retail commercial: entertainment and recreation retail (marinas, golf courses, etc.) in addition to the more general shops, stores and retail facilities in any city. Also, the residential classes tend to be slightly more dense in development and smaller in overall size of lots. Residential siting will differ from that in cities and communities driven by basic industries. With no job site issues to constrain selection of home sites, locational options tend to cluster around amenities (golf courses, shoreline) and are close to shopping. In fact, there may be no, or few, long-range siting factors at work in the region. In the language of simulation, there are no urban poles, or at least none with wide diameters. Electric load characteristics differ. Activity patterns of retiree households are different than those of "employed" households in cities with industry and basic commerce. Daily load curves will be different. Load densities will be different. Often retail commercial load patterns are affected, too. Planned communities. Many retirement cities are well planned on a master basis, with the entire community laid out on a holistic basis. There are two reasons. First, many of these communities are planned and financed by a single developer (e.g., Sun City's Del Webb). Second, and
710
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perhaps as important, there are fewer compromises needed in the planning of the community's layout and what is zoned where. With no industry or basic commercial development to fit into the community or to accommodate, community layout can be almost entirely based on residential and esthetic needs. Master plans tend to be satisfactory to all concerned, and there are far fewer deviations over time than in other cities. Driving growth trend. With no basic industry driving the local economy, many of the recommended ways of tying the region's growth to projected employment or to government economic projections cannot be applied. As mentioned early in this book, such government projects are often done on the basis of extensive research and with involved models and are useful where there is local heavy industry and commerce. The most obvious trend to use is senior population, but available projections of this trend are often flawed, produced by someone else's trending with what turns out to be very little rigor behind its analysis. A projection of the community's income as a whole, taking into account projected population increase (due to a growing housing base) and changes in pension and investment income, is sometimes useful. Thus this is one situation where planners need to adopt one or two approaches not normally recommended: either accept the master developer's projections (with skepticism) or simply trend past population growth rates. Thus, for the forecasting of retirement communities, a standard simulation forecasting method can be used. Simulation forecasts need to be set up with different land-use inventory mixes, different global model drivers, and different preference function factors. Driving forces need to be linked to some relevant to the local economy. Finally, a set of electric load curves designed specifically for retirement areas need to be developed. When the retirement community is part of a larger region The issues raised above do not disappear if the retirement community is only a part, not the entirety of, the region being studied. The recommended way to model them in such a case is to create separate land-use classes for the retirement community. Typically it needs only distinctive classes for: Single-family homes Multi-family homes High-rise residential Retail Usually only these four classes need be made unique to cover the modeling needs for the retirement communities. The retirement community might have
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some content of other land uses (e.g., municipal, institutional), but these can be the standard land uses used everywhere else in the region. But these four classes need to be set up to model only the retirement area. They have different densities (usually higher than normal), preference functions (tied to local amenities), ties to urban poles (low), and electric characteristics than their corresponding landuse classes used in other areas. Table 21.3 gives an example, showing the typical set of land uses that might be used in a 2-3-X simulation model, with the four additional classes needed to represent the differences in the retirement community. The table shows only load density, but consumer densities, preference functions, and urban pole interactions are also different. A final complication when modeling retirement and non-retirement together is that the retirement classes must be tied to specific locations (the retirement community) and not allowed to developed in a scattered fashion around the community. The easiest way to do this in a standard model is to put aflat "urban pole" in the center of the retirement community (see Figure 21.5) with a sufficient radius to cover it. The retirement classes are then heavily linked to it, and their equivalent non-retirement classes are given a strong negative factor.
Table 21.3 Classes Used in Modeling a Retirement Community in Company with a More Normal Region Class Rural residential Single family homes Apartments/condos Retail market commercial Office/professional Institutional High-rise commercial Warehouses Light industry Heavy Industry Single family homes - ret. Apartments/condos - ret. High-rise residential - ret. Retail market commercial in retiree areas
kW/mile2 360 2200 3100 2800 3900 4400 14500 1300 3300 7800 2600 2900 5600 2500
712
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Regions with Tourist and Recreational Economies Regions that "earn their living" from tourism or recreational activities require adjustments to the model's set-up when being forecast with standard simulation. In many cities and regions, tourism and entertainment is a basic industry - one that markets its product and services to areas outside its region. However, in a few areas like Orlando, Florida, Las Vegas, Nevada, and Branson, Missouri, Myrtle Beach, South Carolina, and Dakar, Senegal, it is the major or only industry contributing to the economic viability of the region. This industry has several characteristics that planners must consider when forecasting and when using a simulation-based tool to do that: The region's basic industry has its primary elements like the theme parks, golf courses, beaches, marinas, campgrounds, parks, cruise ship terminals, and so forth, and secondary elements like hotels, motels, restaurants, and similar types of development. All are part of the local basic industry, the land-use component that fuels the region's economy. Land-use mix. The land-use mix in tourism and recreationally-driven regions differs substantially from that in a metropolitan area with a more diverse or normal economy. First, and obviously, there is no heavy industry or commercial sector in the local economy. Second, the tourism infrastructure - hotels, motels, restaurants and so forth is often quite distributed. Third, the demographics of the local workforce, and the land use required to support it, are quite different than in diverse-economy cities. The majority of jobs in these industries tend to be lower paying service jobs. Housing reflects that. Particularly if the industry is seasonal, most if not all housing will be multi-unit housing, composed mostly of smaller units. Commercial retail siting in cities with significant tourism differs noticeably from that diverse-economy and non-tourist economy cities. Tourism is one of the few basic industries that can consistently outbid commercial retail class for land. In a city like Cleveland or Atlanta, retail commercial development occupies the prime land at most major intersections and is the land-use that generally "outbids" other land uses for sites near prime high-traffic corridors. In regions with tourist-driven economies, the local basic industry usually outbids retail commercial, pushing it to sites just off the heavy traffic corridors and adjacent to, not at, major intersections. Electric load characteristics differ. The temporal load behavior of tourism economies differs from that of "normal" areas in terms of its
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daily, weekly, and seasonal variations. Most of these differences will be rather obvious to those studying the region. Daily load curves often are fairly flat, or may even peak at atypical times such as late at night - the usage pattern is linked to the temporal concentration of the tourism activities. Thus, load curves in some areas of Las Vegas are fairly flat due to the 24-hour activity at casinos and show hotels. Generally, in nearly all tourism areas, weekend loads do not fall off from weekday load levels, and in fact are often higher (due to increased weekend, short-term tourism). Finally, many tourism areas have a seasonal economy. Demand in the region varies not only among the activities directly associated with the tourism industry, but among the residential and local infrastructure development. "University" and Government Towns A number of small cities in the United States and elsewhere around the world, are "university towns" in the sense that the primary basic industry in the city is a university or institute of higher learning and research. Examples are State College, PA (Perm State University), College Station, TX (Texas A&M University) and South Bend, IN (Notre Dame). Somewhat similar are government hubs - cities which exist primarily because they are a state or regional capital, such as Tallahassee, FL (state capital of Florida and home of one of its major universities). In a community driven only by a university or similar institute, the electric demand of the entire region is most closely linked to total enrollment at the university rather than faculty count or other factors. Thus, if enrollment at Big State College increases from 10,000 to 10,500 in one year without accompanying faculty and facilities increases, there will perhaps not be an immediate 5% increase in community demand, but there will be something close to it, growing to 5% over time. Figure 21.14 is based on a small college town in the U.S., and shows full-time student enrollment and full-time equivalent faculty and staff count for the university. The diagram clearly shows that load tracks enrollment better than faculty and staff count (faculty and staff grew little during the 1990s while enrollment grew at about 2% annually, as did electric load). Regression analysis of the 1972 - 2001 data confirms that enrollment counts most; the linear two-variable equation that fits best is: Peak demand (MW) = 3.97 x Enrollment + .95 x Faculty & Staff
(21.1)
Thus, peak regional demand is most closely tied with enrollment: students count for four times as much as faculty in determining overall regional demand. Interestingly, an appliance-based input-output end-use model for year 2001 shows
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714
J
30,000
100
25,000
84
20,000
67
15,000
50
10,000
33
5,000
17
it *- 2 o0
of §E
^
T3 (0 P
LU
1
1972
1
T"
1975
1980
1985
1990
~i—i—i—i—i—i—r~ 1995 2000
Year Figure 21.14 Enrollment, faculty and staff, and peak demand for Fort Bend, a college town, from 1972 to 2001. Faculty and staff counts were kept nearly constant throughout the 1990s as enrollment increased. Electric demand grew in proportion to enrollment, not the number of faculty and staff.
the opposite. It indicates that electric load due to direct and indirect causes in the local economy is attributable to students and faculty as 2001 Peak (MW) = 2.17 x Enrollment + 5.99 x Faculty & Staff
(21.2)
Given their use of electricity at work and home, and the electric load their household's and work facilities' consumption of services and goods creates in the community, in 1986 each faculty and staff member created a demand for 5.99 kW, while students each created only a bit more than a third of that. The apparent mismatch between the explanations of regional load from equations 21.1 and 21.2 can be explained by applying the equation 21.2 to 1986, rather than 2001. For 1986, the equation works out to be 1986 Peak (MW) = 2.14 x Enrollment + 5.22 x Faculty & Staff
(21.3)
The years 1986 and 2001 are unique in the period studied because they are respectively the years with the lowest and highest ratios of students to faculty + staff. In 1986 there were 2.27 students per faculty and staff, in 2001 the ratio was 2.79. A higher student/faculty ratio increases electric usage among faculty.
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College-town land-use and spatial structure differences As mentioned in Section 21.2 university towns have somewhat different land use characteristics than "typical" small or large cities. The most important difference for the spatial forecaster is the land-use inventory, as illustrated in Table 21.4, which compares the land-use content of a "typical college town" to that of a typical small city (Springfield, from Chapter 11). The college town data is the average of three educational communities in the U.S., normalized to the same population as Springfield (here, population includes students). Land-use comparison is then in percent of the total for the typical town. The first point to note is that the university town occupies only 65% of the land of a typical city of equivalent population. The college town has less of every land use except high-density housing and institutional (the university itself) development. In some sense, the college town is concentrated more than a typical town. While it may seem as if this is due to a desire on the part of all portions of the community to be close to the university, this is not the case. The "concentration" is a result of the higher density land use. The college town trades a good deal of low-density housing space for an increase in high-density housing, and loses a good deal of low-density development such as warehouses and light industry.
Table 21.4 Comparison of Typical and College Towns of the Same Size - in percent of total land area Land-Use Class
Typical Town College Town
Residential 1
56.3%
15.2%
Residential 2
27.9%
18.7%
Apartments/twnhses
6.0%
23.9%
Retail commercial
4.0%
4.0%
Offices
1.5%
0.8%
High-rise
0.5%
0.2%
Industry
2.1%
0.4%
Warehouses
1.1%
0.3%
Municipal & Institution
0.2%
1.8%
Transmission level TOTAL
0.4%
0.0%
100%
65.3%
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Generally, there is a more uniform concentration in a university town, in the sense that the town has only one pole - it is concentrated around the university with no other major centers of focus for the community. Even a small, typical town might have two poles - one representing its industrial base and the other its "downtown" or retail and offices services center. In a university town there is usually only a short distance between the university and the downtown hub. Not so in a factory or refinery town, or in most other single-economy communities. There are few important structural differences in how the various land uses locate in a university town, as opposed to other towns and cities. The various land uses respond to proximity and surround pressures in very close to the same manner as they do in any city. Generally, mass transit is more important to local residents, and this does show in very detailed assessment of how residential land use locates. But it makes little difference because in college towns the mass transit (city and campus bus) system is much more comprehensive than in most others. As a result, the standard set-up for a simulation program's preference functions can be used.
REFERENCES Canadian Electric Association, Urban Distribution Load Forecasting, final report on CEA Project 079D186, Canadian Electric Association, 1986. J. L. Carrington, "A Tri-level Hierarchical Simulation Program for Geographic and Area Utility Forecasting," in Proceedings of the African Electric Congress, Rabat, April 1988. I. R. Lowry, A Model of Metropolis, The Rand Corporation, Santa Monica, CA, 1964. C. Ramasamy, "Simulation of Distribution Area Power Demand for the Large Metropolitan Area Including Bombay," in Proceedings of the African Electric Congress, Rabat, April 1988. H. N. Tram, H. L. Willis, and J. E. D. Northcote-Green, "Load Forecasting Data and Database Development for Distribution Planning," IEEE Transactions on Power Apparatus and Systems, November 1983, p. 3660.
Recommendations and Guidelines 22.1 INTRODUCTION This final chapter summarizes the practical aspects of spatial forecasting of electric loads for T&D planning. Section 22.2 reviews the prioritized requirements listed in Chapter 1 and indexes which chapter, recommendations and pitfalls are pertinent to each. Section 22.3 discusses ten recommended practices or policies for effective, economical electric utility spatial forecasting. Section 22.4 similarly presents some pitfalls to avoid. 22.2 SPATIAL FORECASTING PRIORITIES Table 22.1 is somewhat similar to Table 1.6 and summarizes the spatial load forecast requirements discussed in this book, assigning each a relative importance based solely on the author's subjective judgement. However, the table differs slightly in several respects from the way this information was listed in Chapter 1. First, the priorities are not listed in order of overall importance, but instead separated into two categories - (1) algorithm and procedure related and (2) applications related. The first category includes those issues that affect the selection and specification of the forecasting algorithm and the procedure the utility sets up to use that method and which a utility basically sets in stone once it has selected an algorithm and defined its procedures. The second embraces those issues of application, or how the planners choose to study, consider, and use whatever load forecast method they have. While some of these issues overlap
717
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718
into algorithm and method, these are for the most part issues which the planners can change or at least fine-tune at the time they do a particular forecast. For example, although many algorithms somewhat restrict temporal resolution that can be set up, in all cases planners can decide what future time periods they will forecast (what years, seasons, for how far into the future), even if in some cases they must innovate to work around program restrictions. Thus, temporal resolution is mostly a decision about application, and its proper application is the responsibility of the forecasters using the tool. By contrast, spatial resolution is dependent on algorithm and procedure, and usually cannot be altered once the methodology has been put in place. Thus it is the responsibility of those making the selection of algorithm and designing the utility's forecasting/planning procedures. Table 22.1 also lists for each item the relevant chapters where concepts allied to it are covered or where a planner interested in that item might seek further information and detail. It also lists the pertinent recommendations and pitfalls from sections 22.2 and 22.3 of this chapter that affect each.
Table 22.1 Priorities in Spatial Electric Load Forecasting Issues that Are Predominately Algorithm and Method Related Rank
1 2 5 9
10
Requirement
Importance Chapters
Forecast MW - how much
Recom.
Pitfalls
10 Spatial resolution - where 10 Representational accuracy - why 8
1,7,8
1,6
2
1,7,8,18,19
1,6
4
1,7,18-21
5,8
Load curve shapes Reliability value/need
4, 18,20 2,4
5 5
5 5
Issues that Are Predominately Application or User Related Rank
Requirement
Importance Chapters
3
Temporal resolution - when
10
4
Weather normalization - how
9
6 7
Consistency with corp. forecast Analysis of uncertainty - why
7
8
Consumer class forecast - who
Load curve shapes 10 Reliability value/need
9
Recom.
Pitfalls
1,6
1,2,4,7,8 5,6
3
1, 11, 13,17,21 1,7,20,21
1,4 4,5,8
6
1,8,9,18-20
1,6
5
4, 18,20
5
5
2,4
5
7
6
5
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719
Table 22.2 Required Characteristics of Spatial Load Forecasting Methods for the Electric Power Industry Characteristic
% Applications
Forecast Forecast Forecast Forecast
annual peak off-season peaks total annual energy some aspects of load curve shape (e.g., load factor, peak duration) Forecast peak day(s) hourly load curves Forecast hourly loads for more than peak days Forecast annual load duration curve Power factor (KW/KVAR) forecast Forecast reliability demand in some fashion Multiple scenario studies done in some manner
Critical?
100% 66% 85%
Yes
66% 50% 15% 10% 20% 15% 66%
Yes
Yes
Base forecasts updated - at least every five years - at least every three years - at least every year - at least twice a year
100% 66% 50% 5%
Forecast covers period - at least three years ahead - at least five years ahead - at least ten years ahead - at least twenty years ahead - beyond twenty years ahead
100% 100% 50% 20% 20%
Yes
Spatial forecast "controlled by" or adjusted so it will sum to the corporate forecast of system peak (coincidence adjustment may be made)
50%
Yes
Forecasts adjusted (normalized) to standard weather Weather adjustment done rigorously
80% 25%
Yes Yes
Consumer class loads forecast in some manner End-use usage forecast on small area basis DSM impacts forecast on a small area basis Small area price elasticity of usage forecast
35% 5% <5% <5%
Yes
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22.3 RECOMMENDATIONS FOR SUCCESSFUL FORECASTING Table 22.2 reprises the data from Chapter 1's list of industry practices (Table 1.7) to which has been added indications (a "Yes" in the rightmost column) of those characteristics that are absolutely necessary if the spatial forecast is to provide an effective planning foundation. Table 22.3 gives thirteen recommendations for effective, economical electric utility spatial load forecasting, what the author considers mandatory practices for effective forecasting. These are not listed in any order of priority: All are important, and their importance, one relative to another, will vary from one situation to another. Each of these is discussed in detail in the remainder of this section. Recommendation 1: Focus on the Plan, Not the Forecast A forecast is the first step in a process that creates and manages the T&D plan. It is not an end to itself. Every forecast should be performed while focusing on the ultimate objective: development of a sound T&D plan. The utility's documented forecast procedure (see Recommendation 1, above) should be viewed as only the first part of the planning process. All decisions about forecast method, resources, and commitments should be based on the overall T&D planning view: what do they contribute to the plan, not the forecast. In practice, this distinction is subtle but makes an important difference. Ideally, the forecast procedure is designed to be an economical but effective part of the planning process, and includes the optimum tradeoffs between resource commitments and planning results. A forecast can always be improved, by use of more data, more analysis, more time and effort. The
Table 22.3 Thirteen Recommendations for T&D Load Forecasting 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Focus on the Plan, Not the Forecast Develop and Use a Rigorous, Documented Forecast Procedure Explicitly Define All Terms and Definitions Remain Objective and Unbiased Document Every Forecast Including Data, Method and Results Weather-Normalize All Historical Load Records and Forecasts Make All Forecasts In The Company Consistent with One Another Always Use a Multi-Scenario Mindset Study Before Forecasting Keep Recent Events or Changes in Perspective Use the Forecast Unaltered Remain Skeptical of All Results Build in Continuous Improvement Use Spatial, Not Just Small Area, Methods.
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important question is whether that effort is justified based on improved planning results. A focus on the forecast itself can blur the real focus of planners and lead to improvement of the forecast that contribute nothing to improved planning. This recommendation can be misconstrued. It does not mean that the forecast is secondary as regards resources or timing. It means that while performing the forecast, planners must focus on completing it on schedule, within budget, and to the quality level needed, and keep in mind why the forecast is needed. All decisions with regard to effort and quality should be tempered with a regard for the entire plan, not a focus on the forecast as an end product. A forecast is only a first step, not an end unto itself. Recommendation 2: Develop and Use Only a Formally Documented Forecast Method Regardless of what forecasting method is used, a most important requirement for good electric load forecasting is that the utility planners have a comprehensive, fully-defined forecast procedure, and that they use only that. Whether built around a simplistic heuristic method or a comprehensive simulation, the procedure should be formally documented. When, Who, and Where. The forecast procedure document should lay out when each step of the forecast is to be performed, who is responsible for that step, and who this person will work with in performing that activity. An example would be: By Sept. 15, the Planning Division Manager will identify in his annual Feeder Loading Survey memorandum, via internal e-mail, to all Operating Division Engineering Managers, the system peak day that will be used for all load data for the previous summer. By Oct. 1, Operating Division Engineering Managers will report by e-mail memorandum and attached electronic spreadsheet the maximum one-hour load recorded on each feeder in their division on that day to the Planning Division Manager. Data: What and How and If. The procedure should identify what data is to be used, and how. Example: "Load readings by feeder will include real and reactive power, and time and day of reading. No adjustment for temperature or other unusual circumstances will be made. Unusual switching or operating configurations will be noted as such. Missing data fields will be identified as "not available" — no estimation will be made. It is important that this part of the procedure's documentation identify exactly how missing data, deviations, or inconsistencies are to be handled ("If load data for a specific feeder is not available for the requested system peak day, then the peak value recorded any time during the summer is to be used".)
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Analytical Procedure. The analytical procedure should be outlined completely, indicating the order of the steps, the exact procedure and context of each step, where and when adjustments or estimates for missing data are done, etc. Every step must be identified. Extreme specificity is needed in this step. The statement, "Feeder peak loadings will be adjusted to standard weather conditions" is far too vague. Much better would be, "Real and reactive power components of the reading for each feeder will be multiplied by the same factor, which will be determined using the Weather Adjustment table given in Appendix W of this report." Temperature used for the "actual temperature" will be the temperature recorded at the downtown weather bureau at the time of the beginning of the reading's one-hour demand period. Temperature for "adjusted to" will be for the column marked "Normal (No-Contingency) Target Levels." It is often infeasible to identify the algorithm or computer program used with complete specificity (i.e., a copy of the program code is not needed). However, full identification of the program, version, and any operating options or settings to be used needs to be made. "Forecast program used will be CAREFUL v-3.2, with the program's spatial and temporal resolution factors set to 10.0 and 1.0 respectively, and the urban pole compression feature set to "Off." Documentation. The procedure should identify what is documented, when and how. Example: "Upon completion of the weather adjustment step, a table of weather adjustment data will be printed and filed, showing real and reactive readings by feeder, along with the time, temperature, and adjusted values. An electronic copy of the spreadsheet will be retained in the planning department directory "Forecast [year]." Documentation should include all databases, both prior to and after analysis, along with copies of the set-up or overview page or display that gives the settings and operating selections for any software used. Interpretation and Adjustment. A good forecast procedure includes a explicit step in which the planner/forecasters look at the results, test to verify their validity, and explicitly decide they will use the forecast. And, given that step, the procedure to be followed in the event that step "fails" the forecast also needs to be identified. Recommendation 9, below, states that the forecast should be used unaltered, once it has been produced by a rigorous, well-documented, and well-applied forecast procedure. However, the forecast procedure must allow for a situation where the planners do not have confidence in the forecast produced by their method or algorithm. Thus, the forecast procedure should include a step in which the users check the
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forecast for overall believability and fit to their expectations, and optional steps which can be taken to adjust or correct it if it is thought to be in error. Results and Transfer and Use. Finally, the procedure should identify what results are to be conveyed to whom, and for what uses. Example "A copy of the preliminary forecast peak feeder load report for the forthcoming seven years will be sent to each Operating Division Engineering Manager for review and comment on the loads in his division territory." This procedure should exist as a document (printed and distributed) and/or electronically on the corporate network, as appropriate. It should include identification of who has authority to modify it, and how modifications or deviations from this procedure are authorized, and documented. Recommendation 3: Explicitly Define and Agree Upon All Terms and Definitions In truth, this is part and parcel of recommendation 2 above. The documented procedure should lay out unambiguously what every term and all the nomenclature means. A glossary of terms, even those often thought to be common knowledge, is recommended. Forecasting crosses boundaries of many functions within a utility and the community. The spatial forecast works with data, information, opinions, and factor projections drawn from many different disciplines - engineering, demographics, customer information, economics and finance. Each of these fields has its own terminology and nomenclature, although they often employ the same words but with different purposes. Major differences in definitions and meaning are easy to discern and cause few problems. Few people will be confused because an economist and an engineer use the word "demand" to refer to very different concepts. But subtle differences often escape notice: engineers base "demand" on measurements over demand periods of one-hour; revenue and rate departments often use quarter-hour periods. Customer service uses "customer" to mean "account" whereas operations uses the word to mean an address. This is absolutely critical, because there is no guaranteed standard terminology in use, even within the electric power industry, and certainly not any standardization that cuts across the hundreds of different industries that will seek to use distributed generation (DG) to meet their electric service needs. Terms such as "total cost," "initial cost," operating cost," "peak demand," "energy usage," "peak period," "equipment lifetime," and
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"savings" often have subtle differences from one situation to another. All should be explicitly defined in writing and agreed to up front. Anyone who cannot define these terms completely and unambiguously is not ready to begin a DG study. Beyond this, often the most fundamental definitions are not clearly articulated to the extent they need to be. A detailed and brilliantly conceived plan can be completely invalidated by the misunderstanding of a single term such as "normal operating voltage" and whether operating voltage at time of peak affected the recording load histories. Forecasters and planners should make certain that the most basic terms such as "kW," "kVA," "capacity," and particularly performance- or incremental-related terms such as "net," "normal," "emergency," "extreme" and other such adjectives are set forth explicitly, and that all parties - forecasters in all departments, planners, the electric consumer, finance, rates, and management, agree on them. Recommendation 4: Remain Objective and Unbiased Forecasters and planners need to remain objective, evaluate all options equally, and not give any undue preference in method, technique or data to a favored scenario or plan. This does not mean that they should not do "proponent studies." Often, forecasters and planners are asked to "make a case" for a particular plan, or to produce a scenario and plan that matches certain management objectives. These call for something other than "objective forecasts" and plans. Even in those situations, an objective mindset serves the forecaster best. Realistic perspective about how irregular a particular forecast or plan may be is by far the best way of assuring that it is done in a comprehensive and sound manner that meets management's requirements. Recommendation 5: Document Every Forecast Including Data, Method, and Results This is actually among the most important of the eleven recommendations, but is listed in this order because it requires a documented procedure (2, above). A utility must archive documentation that shows it followed its approved forecasting procedure for every forecast. Beyond all the sound reasons for this relating to consistency, accuracy, good recording keeping, etc., the primary reason behind this recommendation is that forecasts are often challenged, and a solid "paper trail" based upon a rigorous and approved procedure is the first defense against criticism and rejection. Each forecast should be documented by recording all aspects of following the procedure in (1) above. Step by step, documentation should be gathered and archived on data, corrections, assumptions and changes, analysis, missteps and corrections, and results and use. This should include:
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A step-by-step record of what was done, when, and the documented steps corresponding to the documented and approved procedure (Recommendation 1). This is just a written or electronic form that shows who did what, when, and where the results were placed in the forecast procedure. Archiving of all databases and interim results. Example: as the first step in a trending process, feeder peak load readings for a specific summer data are gathered. This "raw database" should be archived as part of the record. Normally, among the first steps performed is weather normalization of this data, which involves converting peaks to a normalized value under specific weather conditions. In addition to recording that this weather normalization step was done (see paragraph above) in the right order, and when and by whom, the resulting weather-normalized load data base should be archived, too. Assumptions, adjustments, and corrections should be completely documented, with the reason as well as the assumption or correction taken. For example, if the base forecast assumes a new bridge that would alter development patterns will be built (see Chapter 7, Figure 7.5) that should be listed as an assumption along with the reasons why that is assumed in the base case. Suppose that the peak load data given for a particular 12.47 kV primary feeder is 57.65 MVA, a value clearly too high to be legitimate. Planners might assume that this is simply a misplaced decimal point (actual value, 5.765 MVA). If so they should document this change. Mistakes or incorrect results and interim results that must be repeated should be archived and the entire process of creating them, finding mistakes, and correcting them documented. It is good policy to retain interim results or forecasts that are based on mistakes that are caught and corrected, showing that the correction was noted and fixed. This is far preferable to going back, after the forecast has been corrected, and altering the record so that it contains only the correct forecast. Often mistakes are made in any such "clean-up" process and the record is not complete or accurate. Final results and reports should be archived along with information on who reviewed and approved them, and to whom they were distributed. There are two tests of sufficiency that planners should apply in determining if their documentation is complete. First, could an experienced planner, but someone completely unfamiliar with this forecast, reproduce its
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results based on information contained in this archived data and record? Second, can planners defend the forecast against reasonable levels of critique and query, based on the records they have maintained? The answer to both questions should be "Yes, without doubt." Recommendation 6: Weather-Normalize Ail Historical Load Records and Forecasts All load readings and all forecasts should be adjusted to specific identified weather conditions. Normally, historical data and forecasts are normalized to standard weather conditions (adjusted to a defined set of design criteria weather conditions). However, there are cases where a forecast is needed that has been adjusted to some other set of weather conditions ("This is our forecast for next year adjusted to this summer's record levels of heat, which were above our design criteria"). Generally, weather adjustment is done to a set of design weather conditions - weather conditions that are the criteria for all planning and design (see Chapters 5 and 6) be that one-in-ten or some other period of risk occurrence. But the important point is that all load data should be indexed to account for weather, and that when used, data should be properly adjusted for differences in weather. What should be completely unacceptable to both planners and utility management is for any forecast to be produced, or any historical data used, that is not tied to specific weather conditions. Recommendation 7: Make All Forecasts in the Company Consistent with One Another All forecasts used for the utility should be consistent with one another, reflecting the same base assumptions and conditions, and driven from the same perspective. This does not mean that the spatial load forecast, to be used for T&D planning, should necessarily match the corporate forecast megawatt to megawatt. There are legitimate reasons why there should be a difference - coincidence of load and weather normalization being two adjustments which should result in differences between the totals the two forecasts represent. But beyond these explainable, deliberate, and hopefully fully documented differences, the T&D planning forecast, the corporate forecast, the marketing forecast, and any other forecast used in planning the utilities revenues, expenses or resource allocations, should all be completely consistent. There are several compelling reasons why this consistency is required. First, based on the spatial forecast and the subsequent steps in the planning process, the T&D planners will ask their executives to commit a part of projected future revenues to T&D investment. The executives, while always reluctant to spend any more than necessary, do understand that "you have to spend money to make money." But they have a right to expect that
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the forecast that is telling them they must spend money is based on the same assumptions and growth as the forecast that tells them how much money they are forecast to have in the future. The corporate forecast contains the assumptions about future economy, demographics, major political and industrial events that have been approved or at least well-studied, and not opposed, as the "corporate" vision about the general trends of the future. The T&D Departments request for investment should match the same "vision of the future" and assumptions as the forecast that the executives are using to estimate future revenues. If not, the T&D planners have failed to do their job. Beyond this, as mentioned in other parts of this book, the economists and analysts in the corporate revenue forecasting group generally know what they are doing. Their forecasts of consumer count, sales, and peak load for the system are probably as accurate (from a representational standpoint) as anything the T&D planners could ever produce. Why re-do all that work? Recommendation 8: Always Use a Multi-Scenario Mindset Even if there are no alternate scenarios that will be produced, the recommended way of thinking for all T&D forecasters is the multi-scenario framework. By its very nature, the multi-scenario approach eschews a "single future" perspective, and forces the planner to confront his forecast's sensitivity to imperfectly projected future controlling factors. It puts the uncertainties in his forecast projections front and center in his attention and prevents an undue level of confidence in them. It promotes an understanding of what is nearly certain, and what is very chancy in a forecast. Even if only a base forecast is to be produced, a realization that other events and trends might happen, an understanding of what and how this might happen, and a study of why the base scenario is the "preferred" scenario will make both the forecast and the forecaster better at their jobs. A multiscenario perspective is always a healthy attitude for a forecaster to take. Both the knowledge gained from working within this paradigm, and the skepticism and objectivity it normally produces about the accuracy of any one "forecast," will serve the utility and its planners well. Recommendation 9: Study Before Forecasting One of Dwight Eisenhower's most famous quotations is "Plans are worthless, but planning is everything." His point was that the value of a plan was in the knowledge and experience gained during the process of creating it, not in the plan itself. This is the first reason why planners need to study the situation, data, and scenarios of their forecast carefully before completing it. An important, if often implicit objective for utility planners is to retain an understanding of the future, its possibilities of growth, and what that growth might mean to their plans. This knowledge comes from study.
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But beyond that, forecasts need to be directed and managed by planners who understand the historical growth and its context, who have a feel for the process of growth and its drivers, and who understand the forecast process and its implications in detail. No forecast method, no matter how advanced, is so automatic that it can be used well by someone who does not understand the data, the forecast situation, and the context of the forecast. That understanding comes from study of the data and the forecast situation in its wider context. It does not come automatically from just "living with" the situation through long assignment to a region or planning position: some of the least knowledgeable planner/forecasters the author has met have been in their positions for years but have never taken the time to formally study, objectively evaluate, and quantitatively assess their planning situation. Many utilities, always under pressure to cut resource requirements, reduce too far the time budgeted for assessment and study in preparation for the forecast. Generally, this results in a poor forecast, both in absolute terms (accuracy, representativeness) and practical results (the forecast may not be used well). Recommendation 10: Keep Recent Events or Changes In Perspective Study and good sense help planners maintain a sense of proportion for driving events and growth influences, and particularly for how recent changes may influence the future. One of the most difficult tasks of a forecaster is to recognize change in conditions or forecast driving influences but not overreact to them. There is generally a tendency to overreact to changes or big events. For example, NAFTA (the North American Free Trade Agreement) had a major influence on the growth of communities along the U.S.-Mexico border, particularly those along major transportation routes, such as Laredo and Nuevo Laredo. However, it did not create a quantum change in contemporary trends, nor did it change the overall character of the process of growth in that region, as some people suspected it might. Laredo was growing significantly prior to NAFTA and continued to grow pretty much as one would have forecast without NAFTA. There are events which will completely change the character of a region and its future growth, but they are rare, and even they must occur in a relative vacuum of other effects and influences. The Mercedes-Benz assembly plant in the southern U.S. completely changed the growth of an entire region (the corridor between it and Birmingham, AL). However, that can only be established through study and quantitative assessment of conditions in the area. Generally, there is a tendency for forecasters to initially overestimate the impact of large, "marquee" events, like NAFTA, or the destruction of the World Trade Center in New York, on the growth of the region. Often, considerable study (see Recommendation 6) is needed to put the events in
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perspective. Thus, overall the primary recommendation is: depend on historical inertia in trends and growth character and do not overreact to any one event or change. Recommendation 11: Use the Forecast Unaltered There is no reason not to use a forecast performed using good data, a rigorously documented forecast procedure that was well founded and designed, and done by experienced planners who have studied and understand the forecast context. However, there is sometimes a tendency to adjust or "fiddle with" those elements of a forecast that seem a bit unexpected or do not exactly match expectations. This should be done rarely, if at all, and if done, only by procedure (Recommendation 1, above, included a step in the forecast process to document such exceptions and to change them). With few exceptions, if the input data is valid, the forecast method sound, and the application (use of the method and data) based on good experience and sound judgement, then the forecast should not be altered. More often than not, the forecast is correct and the user's intuitive and objections are wrong. A somewhat ignominious example will illustrate this. In late 1976 the author supervised a team of planners that used ELUFANT (see Chapters 13 and 17), one of the very first comprehensive land-use simulation-based T&D forecast programs, to perform a 71-acre (square areas 1/3 mile wide) spatial forecast of non-coincident peak demand for the entire Houston Lighting and Power service territory. This 25,000+ small area forecast was a very ambitious undertaking for the time, and used what was then an unproven new forecast method. The completed forecast was a year-by-year projection for twenty-five years ahead (through 2003). It was judged acceptable except for several small changes. Among them, the forecast showed a large concentration of high-rise commercial development around the intersection of Interstate Highway 10 and Farm-to-Market road 1960, at that time an undeveloped area in a sleepy section of the system, still quite far from the region's areas of peak suburban peripheral growth. Since the type of land use and the amount of it both seemed excessive, the author and his team "edited" the forecast to delete the commercial high-rise development and substitute low-rise development. Twenty-years later, the area had in fact actually developed to high-rise land use very much as and when forecast. Recommendation 12: Remain Slightly Skeptical of Results Mistakes, bugs, errors - whatever they are called - happen frequently and are difficult to find, as was discussed in that section. The best policy is always to look for why the answers could be in error, even if they are the result that was desired and expected.
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Recommendation 13: Build In Continuous Improvement Any process that "gets better over time" will eventually become really good if given enough time. Thus, even a forecasting procedure that is mediocre when first set up can become very good if it includes methodology to recognize areas that can be improved, determine ways to move those improvements and implement them. Thus, the final recommendation is that the utility's forecast procedure include a formal process of reviewing past forecasts, or identifying what went wrong and what went right (if it isn't broken, don't fix it) and of correcting deficiencies or areas that can be improved. Perhaps it is impossible to label this as the most important of the recommendations, but it is certainly as important as any of the others: striving for constant improvement will produce it. Recommendation 14: Use Spatial, Not Just Small Area, Methods As mentioned in Chapter 1 and elsewhere, all spatial forecast methods use the small area approach, but not all small-area forecast methods have the integrating, achieve-consistency-in-context-and-framework forecast structure of spatial methods. Spatial methods achieve better results and lead to far fewer planning mistakes. 22.4 PITFALLS TO AVOID Table 22.4 lists eight pitfalls that utility planners sometimes fall into with regard to spatial electric load forecasting. As was the case with the recommendations given in the previous section, these are not listed in any order of priority or importance. The relevance and importance will vary from one situation to another. Each of these is discussed in the remainder of the chapter.
Table 22.4 Eight T&D Load Forecasting Pitfalls 1. 2. 3. 4. 5. 6. 7. 8.
Putting Too Little Emphasis on Forecasting Applying Judgement to the Forecast Itself Letting Available Data Dictate Forecast Method Putting Too Much Emphasis on Forecast Method Blindly Importing Forecast Data from Another Utility Using Different Weather Adjustments for Normal and Emergency Planning Removing Unexplained Trends or Anomalies from the Input Data Using a Magnitudinal Rather Than a Spatial Perspective
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Pitfall 1: Putting Too Little Emphasis on Forecasting By far the biggest category of mistakes made in T&D planning revolves around some type of insufficiency in forecasting. Few utilities totally neglect this step, but many do not devote sufficient time and energy to determining just what load levels they should use as design targets for the future system. As a result, subsequent steps build on a weak foundation: plans sometimes prove ineffective and have to be revised at the last minute. Both planning resources and capital resources themselves end up being partially wasted. Although there was always an element of the electric utility industry that denigrated the forecast, in the early 1990s a growing segment of the power industry began falling into this category. Many utilities cut planning resources, and forecasting was one of the functions hardest hit. Others were led, by their desire to reduce capital spending, to various means that reduced the apparent level of load growth so that the organization did not see as much need for expansion. By the late 1990s, a number of utilities experienced serious system operating problems, including widespread outages, for which poor forecasting was identified as a key contributing factor. It is important to keep forecasting in perspective (see Recommendation 6 and Pitfall 2) but the best perspective is to devote reasonable attention and study to determining what load growth can be expected, and interpreting that into well-considered design goals for the system. "You get where you need to be by knowing where you need to go." Pitfall 2: Applying Judgement to the Forecast Itself Often, the reason a utility does not devote sufficient formal study and procedure to forecasting (Pitfall 1, above), is that its planners truly believe they "know the answer already." Keen professional judgement has an important role in T&D forecasting, but that role does not include direct application of "judgement" to spatial load forecasting. Instead, the planners' experience and judgement should be applied to decisions about what methods to use, how to use them, and the interpretation and use of forecast results. Purely judgement-based forecasts have substantial disadvantages: A judgement-based forecast is seldom accurate. Intuition and judgement tend to be qualitative at best, and are proven to be too limited. Typically, judgement-based forecasts fail in two ways. First, they fail to pick up on nascent trends due to interaction with regional and nearby growth forces: they under-forecast the first part of the typical "S" curve growth trends in an area. Second, they invariably over-emphasize and extend present trends: they fail to forecast the
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drop in growth rate from the high, mid-S-curve rates, even though this is among the most predictable aspects of spatial load growth. Judgement-only is not an acceptable practice. It is impossible to document and defend a purely judgement-based forecast method. It does not have a rigorously defined and trackable procedure. There is no way to document and verify its performance or results in any meaningful way: next year's judgement might be better or worse than this year's. This does not mean that the planners' judgement but the bottom-line on judgement-based forecasts is The use of a formal forecast procedure improves the value of the planner's judgement. A formal, documented procedure provides leverage for the expert's judgement. Many planners insist that their familiarity with their region, knowledge of local conditions and expected future events, and judgement mean they can accurately estimate future distribution-level loads without the need for formal forecast methods or further study. However, considerable evidence shows that such judgement-based forecasts are less accurate than forecasts made by formal algorithms (see Chapter 17). Judgement should be harnessed to determine what procedure is best, exactly how it should be harnessed and fine-tuned, and how the results should be interpreted and used.1 Pitfall 3: Letting Available Data Dictate Forecasting Method Many utilities allow perceived problems with data availability to restrict the options they consider for their spatial forecasting. Data limitations are perhaps the single largest area of "jumping to conclusions" in T&D planning. Often, planners at the utility are not familiar with and have not researched alternative data sources and their costs. As a result, they leap to the conclusion that only the data sources they use in other applications are available for their forecasting needs. Algorithms or procedures that require other data are rejected out of hand.
1
Examples of each of these three: "After study of resources and needs, I looked at the various considerations and picked multiple regression trending as the best compromise among results and cost for us." "After testing and analysis, we selected the cubic equation Ax3 + Bx2 + D/x + E for curve fitting." "In these areas of the system we are only going to use the short-term projections, as we don't think the long-term are accurate enough."
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With few exceptions, the data required to support any of the forecast methods covered in this book, at least to a minimal functional degree (i.e., to get it to work at its most basic level), can be obtained at any utility. Cost of data, and performance of one method against another, become an issue. That type of comparison and selection of the best was covered comprehensively in Chapter 17 (section 17.8). But many utilities never reach a comparison of a wide range of methods. They assume that only the data they are familiar with and have used in the past is available, and they restrict their consideration to the very limited range that allows. In actuality, particularly in a world of computerized databases and Internet sites, data availability is seldom an absolute barrier, and often not a cost concern, if the planners are innovative and work to get it. Generally, project teams grossly underestimate the results that can be obtained with a little effort and time. Pitfall 4: Putting Too Much Emphasis on Forecast Method (Falling in Love with the Forecast Method) The purpose of the spatial load forecasting function is to produce projections of future loads that lead the utility's planners to the correct decisions about the what, where, and when of future investment and changes required in their power delivery system. Methodology and algorithm are important. Good, accurate, and timely data is important, too. But attention to these important items can be overdone. Forecasting T&D loads is seldom if ever about creating and maintaining the most advanced forecast method and database possible. Beyond a certain level, additional spatial and temporal resolution, and even additional accuracy in prediction, are of little value to the quality of the ultimate T&D plan. A few planners simply fall in love with the technique and make refinement of algorithm and data an obsession, completely losing perspective on why the forecast is being done and the level of effort and attention it warrants. They see the forecasting tool and its database as an end unto itself, often with a never-reachable need for perfection. They devote all their resources to constant improvement, regardless of whether it yields any benefit to the planning process: computations that are linearized today should be made non-linear tomorrow; data on customers should always be broken out into more categories and sub-categories, resolution can never be high enough, etc. This usually manifests itself in the "perfect promise" syndrome: "there is no forecast available today but in a few months there will be a better one than you could ever imagine." A focus on the need for an adequate forecasting and not on the tool is the necessary perspective for the utility procedure (see Recommendation 1. The goal is to produce the best forecast to support planning, within the time and resources permitted (Recommendation 6). Management needs to make certain that this focus is established and followed.
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Pitfall 5: Blindly Importing Load Forecast Data from Another Utility Some very embarrassing forecasting mistakes have occurred because a utility imports customer, end-use, or growth behavior data from another utility without verification that it is applicable to its situation. One famous case involved a utility in New England that imported level end-use data from a number of other utilities for its appliance-level spatial load forecasting/DSM prediction program. In particular, they adopted for their use a figure of 1,100 watts peak coincident load for residential water heaters. That figure had been published in a paper by Detroit Edison a number of years earlier, and was based on a very comprehensive study of that utility's customer base, for which the 1,100 watt figure was completely valid. However, the value was completely wrong for this particular utility (their actual value was subsequently shown to be only half that). Water for residential use in their service territory came largely from deep wells and was somewhat wanner (thus requiring much less energy to bring to a heated state than cold lake water) and the average household used less hot water on a daily basis. This use of the higher figure lead to overestimation of load and potential load reductions, which lead to promises of results from DSM that could not be delivered, with dire financial and political consequences for the utility. There is nothing wrong with utility's looking at data from other systems or using it when careful consideration and study shows that it is applicable. However, the following categories of forecast-related data need to be treated carefully before translation and use: Customer preference or usage patterns — consumers in one region may have far different value systems and respond quite differently to changes in weather, economy, or electricity prices than consumers in another utility. Imported "marketing data" from another utility needs to be handled with extreme care, and attention to real cultural and demographic similarity between the two customer bases. Appliance demand and energy usage characteristics - the same appliances (water heater, air conditioner, dishwasher) can have noticeably different electrical demand characteristics in two different utility areas. The water heater load differences cited above are only one of many possible examples. This problem is not specific to just the end-use level. Even hourly load curve shapes for entire classes (e.g., residential and commercial retail) differ remarkably among utilities that might be considered part of the same region. Spatial land-use or consumer class preference patterns. Utilities that select simulation-based forecast approaches often use "standard coefficients" for the spatial factors and preference function
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calculations. While such generic values often work well enough in most applications (see Chapter 21) planners should check these values to make certain they are valid for their system. Growth behavior dynamics. Growth behavior dynamics - the significance and behavior of load growth trends - is qualitatively similar in nearly all utility systems. The general characteristics identified as "S" curve behavior (Chapter 8) are seen everywhere, but small area ramp rates, periods, and transition characteristics vary regionally (and over time). Generally, between six and seven years of historical data, and one or two horizon year estimates, works best for trending historical data. And usually, a cubic or cubic logarithmic polynomial proves the best equation to use for curve-fitting, but what works best needs to be checked by study of historical data (Chapter 9). In most cases, multiple regression rather than stepwise regression gives slightly better results. While there may be broad similarities, the specifics of each of these loadforecast related factors and other similar values used in forecasting can vary from utility to utility, and they can vary considerably among neighboring utilities, too. As often as not, these differences are due to subtle inconsistencies in definitions, data gathering, and procedures among the utilities, as much as to actual differences in load growth characteristics. But regardless of the reasons, what works best in one utility may not work nearly as well at its neighbor. Pitfall 6: Using Different Weather Adjustment Criteria for Normal and Emergency Planning A few utilities use weather adjustment targets that are different for normal and contingency planning. Planning for "normal" conditions based on extreme weather (say one-in-ten year), but analysis of N-l capability of the system and other emergency evaluations, are done using loads that have been adjusted to average weather conditions. The rationale behind this approach is that both extreme weather and contingencies are infrequent, and the simultaneous occurrence of both is extremely rare. Thus contingency planning should be aimed at average rather than peak expected loads. The first flaw in this reasoning is that the contingency planning approach is not a probabilistic method so it is not really proper to apply probabilistic reasoning to it: in any large power system there will be enough different contingencies that occur some will at or near peak conditions. Second, the difference between normal and extreme weather can be so large on some systems (15% or more) that it results in contingency planning that is meaningless - the loads used for contingency planning are not sufficient to stress the system in any meaningful way.
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Pitfall 7: Removing Unexplained Anomalies and Trends from the Input Data Trends or patterns in data are not errors just because they cannot be explained or the planners do not understand them. If the data is checked and is accurate, then it should remain unaltered, even if there is a trend or pattern which is puzzling to the planners, and which cannot be explained. For example, per capita electric usage in an area of the system might be slowly declining, despite a system-wide trend of increasing usage. The fact that the planners can find no explanation for or correlation to this trend from within the other available data they have does not mean the trend is not real and should not be used as appropriate in the forecast process. There are a number of reasons why this local trend might be occurring. While it would be best if the planners did understand its basis, the fact that they do not does not make it any less real: it should be retained in the data and used in the forecast. It does not mean that it is not legitimate. Pitfall 8: Using a Magnitudinal Rather Than a Spatial Perspective Spatial forecasting is mostly about where. This locational dimension of the forecast and its application mean that T&D forecasting is quite different from the traditional "magnitude versus time" with which engineers and economists have experience and training. Many concepts and intuitive concepts no longer apply. It can be difficult, and take time, to become comfortable with the spatial aspect of T&D planning, and forecasting. A good test is whether the planners think of error in terms of location, as much as in terms of magnitude (see Chapter 8, pages 232 to 239). Chapters 1, 7 and 8 dealt specifically with these concepts and the new techniques required to really work spatial methods well. Many mistakes in application, and many failures to see "obvious" errors or omissions in T&D forecasts, stem from the planners' unwillingness to adopt a truly spatial perspective. 22.5 HOW GOOD IS GOOD SPATIAL FORECASTING? Just barely good enough. The best spatial forecasts provide projections for future electric demands that will, when combined with good planning procedures, result in "optimal planning" in the sense that when planners look back after the fact, they will conclude that the forecast did not contribute to any inefficiencies or poor economies in their system and budgets. But a key factor is the "good planning procedure." "Good forecasting" is as much about setting up a planning procedure that does not ask too much of the forecast as it is about performing good forecasts. The planning procedure must include responsive method, provide review and recourse over time, and minimize lead times for key facility decisions (see H. L. Willis, the Power Distribution Planning Reference Book, Marcel Dekker, 1997).
Recommendations and Guidelines
737
The spatial error analysis techniques given in Chapter 8 and their application to a range of forecasting methods in Chapter 17, along with other similar studies the author has done in the past two decades, indicate that the very best ten-year-ahead spatial forecasts have something on the order of 7% spatial error impact content. This means that their error would contribute to poor T&D planning to the extent that about 7% of all investment would be wasted. The way this impact is avoided is by having a system plan that has some flexibility (never backed into a corner) and a system planning procedure that has: a) a review process so it will recognize when actual and projected trends are diverging, b) a recourse process so that plans can be changed. The single best step planners can take in this regard is to shorten planning cycles and lead times. Uncertainty grows exponentially as one has to look farther into the future: cutting one year of lead times reduces the effects of uncertainty a great deal. It is also important for planners to realize that bad spatial forecasting can be wretchedly bad - so there is real value in putting effort and attention into the first step of T&D planning. Poor technique, lack of good data, undisciplined application of judgement and undeveloped forecasting skills and sloppy execution can combine to produce projections of load that will lead to seriously-flawed T&D expansion plans. Many forecasts done by experienced planners and used by utilities have upwards of 40% spatial error impact content. Even with review and recourse, these will lead to serious amounts of investment inefficiency - often as much as 15%. But all forecasters and planners, not just those in the utility industry, should always bear in mind the fundamental rule of forecasting: All forecasts are wrong. Every planner and every forecaster should always keep in mind that every forecast contains some error, unknown as to type, location, or timing, because if the forecasters knew of any error in their forecast, they could certainly remove it. But regardless, the most important recommendations remain: 1. Use a good forecasting method well. 2. Understand the process of and drivers behind the growth 3. Use a multi-scenario approach 4. Document method and application. Good luck.
Index Abandoned land-use, 425 Abuja (capital of Nigeria), 632, 660, 662 "Accessification" of land, 594 Accuracy (of forecasts), 27, 33, 540 case study and comments on, 659 and end-use models, 486 and error, 737 and spatial resolution, 239 see also Error Activity centers, 404-406, 432-433 see also Polycentric activity center; Urban poles Aerial photographs, 335-350, 643, 674 Agrarian areas, 570-575, 577 conversion to suburban areas, 592 in developing regions (example), 643 forecasting load growth in, 586-590 Air conditioners, 78, 130-135, 150, 646 Algorithms (for forecasting), 449, 450 584, 643, 722 categorization of, 508 Anderson levels (of land-use), 528 Appliances, 38-40, 75, 493, 500, 645 acquisition of (developing areas), 636 model of load growth, 645-650 categories and subcategories, 100 data, 734 duty cycles for, 75-78 load duration curves for, 47
models of load, 491 Archiving data see Documentation Average Absolute Error (AAV), 233, 237 see also Error Blue norther (intense winter storm), 169 Border towns and cities (forecasting),700 Bottom-up program structure, 49, 677 end-use models, 95, 102-105, 123, 481, 484-487 spatial models, 312, 374, 394, 435 Boundary location errors, 352-353 Boundary problems (forecasting), 703 Brasilia (capital of Brazil), 632, 660, 662 Building and structure counts, 643 Building load simulators, 110 Building permit data, 357 Calibration of forecast models, 348, 528, 534, 544, 608, 625, 628, 680-692 contrast enhancement trick, 700 data, 682 example (map), 689 global model, 682 iso-preference rule for, 691 order of steps, 629, 681 simulation algorithms, 542, 626
739
740 for redevelopment models, 628 stationary process rule for, 692 urban compression models, 629 Causal events or relations, 148, 228, 728 Causes of load growth, 211, 304 CBEMA curves, 53 Cellular automata, 429 Centers of influence, 432 see also Activity centers and Urban poles Cities, 311, 398, 409, 592, 595, 609 basic cause of growth in, 321 large size (unique forecasting issues), 398, 409, 549, 594, 608 new or planned to be built, 632, 660 see also New cities small size (unique forecasting issues), 369, 372, 398, 570. 582, 585, 611 Climate, 131, 137. 139, 151, 202 examples (table), 137 change in over time. 144 micro-climates, 131. 151, 196. 202 map of, 138 see also Weather Cloud cover, 139 see also Weather Clustering, 452 see also Pattern recognition and Template matching Combing (Fourier transform), 439 Competitive growth (simulation of), 707 Coincidence, 73, 76, 84. 93, 350, 682 definition of, 73 example and explanation, 82-84 formula for, 82 College towns (forecasting of), 679, 713 Colline Noir (example), 643-659 Collinearity of data, 158 and inability to solve for load, 350 Comparison of forecast methods. 473-490 Compression model (urban pole), 623 Confusion (of energy consumers), 638 Conservation, 99, 327, 366, 478^81 see also Demand-side management Consistency (among forecasts), 28, 33, 347. 355, 542. 676, 704, 718. 720, 726
Index Constant current loads, 40 Constant impedance loads, 40 Constant power loads, 40 Consumer classes or types, 30,33,56,96 98, 305, 311, 330, 345, 376, 598, 645 data aggregation, 535 definitions of, 97, 376 example breakdown for a utility, 39 important qualities of and for, 98, 588 interruption costs for, 54-58 load curves for, 43, 96 projections of growth in, 320, 338, 345 sampling of, 90 tables of (examples), 330, 598, 645 uncertainty among (effects of), 638 value (of power for), 495 Context (of information), 448 Contrast enhancement of maps, 700 Convergence (of energy sources), 478 Convolution, 437, 439. 683-686 Cooling (see Air conditioners) Cooling-degree days, 135 Corporate (rate) forecast. 28, 33, 311, 347,355,367,542,676,718 data for and from, 537 see also Global model Cost and costs for forecasting algorithm use,369, 530, 541,546,551-560 of interruptions (to consumers), 54 and consumer class, 56 examples (table and plots), 55-59 preferred way of modeling, 60 prior notice (impact of), 56 and time of use, 58 in power delivery planning, 4 of poor plans and forecasts, 370, 515 delta-cap, error tables, 524, 525, 530 Coupling matrices (in trending), 288 Credibility (of a forecast), 547 see also Documentation Criteria (for system design), 131 Curve adder (end use model), 102, 488 Curve fitting (trending method). 282-295, 450,508,513.517,523,528,531 see also Trending
Index Customers (of the electric utility) see Consumer classes Data and data sources (for forecasts), 10,27,28,32,95-98, 110, 116, 325, 335-337, 423, 533, 544, 551, 732 calibration of algorithms using, 682 detective work with, 351, 690, 700 and government sources, 401 highway departments, 538 information as the product of, 448 newspaper articles, 328, 357, 360, 366, 537 typical needs for, 423 Data detective, 351, 690, 700 example of application, 688-696 De-convolution see Spatial de-convolution Demand (for power)-definition, 45 and appliances, 47, 75, 491 of consumer classes, 43, 96 duration curves, 46-47 and humidity, 150 periods, 45 for quantity and quality, 37 and temperature (models of), 153-159 and weather, 147-162 see also Electric load Demand-side management (DSM), 62, 99, 112, 114,366,478,501,542 see also Energy efficiency Demographic databases, 209 Demographic movement models, 640 De-regulation (of power industry), 6, 10 Design criteria (and weather), 198-202 Development plans (government), 539 DFT (see Fourier transforms) DG (see Distributed generation) Diagnostics (of forecast programs), 669 Differentiated reliability planning, 180 Dimensionality (of growth), 569-588 categories (table), 570 definition of, 574 Direct-cause matrix models, 401 Direct end-use model, 486-490 diagram flow chart for, 487 Direct Lowry model, 431
741 Dis-aggregation (of electric utilities), 9 Disco, 6, 7 Discrete sampling errors, 86-87 Distributed generation (DG), 498 Distributed urban poles, 687 Distribution (versus transmission), 7 Diverse metropolitan areas, 675, 679 Diversity (see Coincidence) Documentation, 721, 724, 725 DSM (see Demand side management) Duration (of power interruptions), 53, 55 Duty cycles (of appliances), 75, 78 Dynamic weather risk model, 180, 185 Education (as a local industry) see College towns EEAR (see Expected energy at risk) Eisenhower, 727 El Nino (and extreme weather), 141 Electric load, 1,38 and appliances, 39 areas with none, 206, 217, 218 coincidence of load, 75-81 consumer classes, 44 control (load control), 501 curve, 31,33, 42, 102, 112, 122,682 adder (type of end-use model), 125 end-use models, 101 forecast data calibration with, 682 sampling, 87, 91,92 proper measurement of, 85-92 telltale signs of poor sampling, 91 density, 204 duration curves, 46 - 47 growth of, causes of, 211,228, 304 characteristics of, 206 in developing countries, 634 as driver of system expansion, 205 maps of, 219, 221 at small area level, 212, 221 and spatial resolution, 219 stages of, 592 rules-of-thumb for modeling, 42 spatial distributions of, 204 example maps, 22, 48, 221, 227 types of, 40
742 chart of, 41 typical densities of (by class), 205 see also Demand Electrification (of regions), 631, 633, 638 End-use analysis, 95-120, 147, 151, 342, 343, 481, 493, 500-502, 645 End-use models, 38. 62, 64, 109-112, 305, 343, 374, 376-380, 582, 588 607,610-614,645,713 advanced versions of, 481^94 appliance models in, 38, 101, 481, 482 computerized, 121-124 diagrams of. 103, 123,482,492 error checking in, 125 example load curves for, 102 of reliability needs, 62-64, 500-502 Energy, 37, 38, 42, 45, 67, 70, 478-483 Energy efficiency, 478, 488, 493 see also Demand-side management Energy service company (ESCo), 7 Error (in forecasts and forecasting), 232 cost of. 370, 515 of forecasting methods, 624-628 locational aspects of, 237-239 mutual-substation function for, 250 spatial frequency analysis of, 245 and spatial resolution. 242, 243 spectrum of. 256 and years of data, 271 see also Accuracy Equipment-oriented small areas, 207 Error management method, 462 ESCo (Energy service company), 7 ETM (see Extended template matching) Event-driven forecast models, 429, 667 Expanded template matching, see Extended template matching Expected energy at risk (EEAR), 185 example analysis. 186-188 and peak load levels, 192 and weather risk analysis, 194 Extended template matching, 295, 299, 455,461,522,657,658 details of design, function, 456, 460 example application, 657-659 flowchart of basic concept, 458 Extrapolation (methods of forecasting)
Index see Trending Extreme weather (see Weather) Factory town (forecasts for), 318, 662 Falling in love with methodology, 733 Feeder load readings, 263, 282, 298, 339 Feeder planning impact map, 252 Frequency domain methods, 441 Forecasting methods, 507-565 advice on using well, 674-679 categorization of, 508-518 comparison of methods, 473-490 cost to apply, 551, 553 data requirements for, 423, 544 environments of (table), 633 factors for selection, 541 multi-scenario, 20-24, 227, 361, 368, 399, 433, 727 nomenclature of types, 609-610 normal situations of, 675 part of a region only, 700-705 requirements for, 25-33, 718-720 robustness of, 545 savings due to, 555-564 selection method and factors for, 540 uncertainty in (types of forecasts), 633 variations by utility type, 564 see also Algorithms Fourier transforms, 437 Fuel-type tag, 481 Fundamental rule of forecasting, 737 Fuzzy logic and data, 427, 465 Gas (see Natural gas) Geographic load forecasts, 210 Genco, 7 Gigapolis, 409 Global model. 311,435, 707 calibration of. 682 forecasts, 345, 677 see also Corporate (rate) forecast Global warming, 144 Gravity model (in simulation), 406 see also Activity centers and Urban poles Grid-based small areas, 207, 208, 307 Growth ramps. 215-222. 293, 592 diagram of. 220
743
Index see also "S" curves Harmonic power, 61 Heads-up digitizing, 535 Heat index, 134 Heat-island effect (see Metropolitan warming effect) Heat pumps, 78 see also Air conditioners Heating degree days, 136 see also Cooling degree days Hierarchical allocation, 434 Highways and roads, 307, 314, 376, 390 Highway department data, 538 Highway effect, 411, 423, 690 HILDEGARD (forecast method), 473 Hindsight plan (test method), 515 Holistic perspective (on regions), 702 Horizon year loads, 273 Houston (example of growth), 224 Humidity, 150 Hybrid forecast models, 447-475, 520 Illumination (lighting), 38, 39, 478 natural (from weather), 132, 139 see also Lighting Importing data, 734 Information, 448, 467, 470 Independent system operator (ISO), 6, 7 Input data (see Data) Input-Output models, 397, 422 Interruptions costs for consumers, 5458 Inventory of land use, 337 Insurance company (example case), 399 Iso-preference rule, 691 Iterations, 429 Jackknife function, 154 Jobs (as cause or effect of growth), 311, 312,314,317,318,321,322,661, 666 Judgement (in forecasting), 331, 508, 731 complexities that defeat it, 371 examples, 338, 358, 369 as a basis for forecast method, 508 applied to land use alone, 520
Justification (of forecasting methods), 549, 594 K-means clustering algorithm, 378 Land use, 305, 451,452, 471, classes and classification, 330 Anderson levels for, 528 coding of maps, 333- 337 in college and university towns, 715 data for, 528, 535, example tables, 330, 598, 645, 698 interpretation of (aerial photos), 336 from municipal data sources, 598 and end-use classes, 98 forecasting of, 314-320, 539 input-output models for, 397 see also Spatial load forecasting "fuzzy" data models of influence, 705 growth and change, 314 see also Electric load, growth interactions among, 321 models of spatial patterns, 324 see also Simulation multivariate analysis similarity to, 455 patterns, 312, 595 preference function models of, 391 proportionality rule in forecasting, 662 in resort areas, 712 in retirement areas, 709 Large-area models, 392, 435 Latent demand, 631 and consumer uncertainty, 636 example case study, 643-661 forecasting methods for, 637-640 root causes of, 635 Lead times (in planning), 6, 21 delaying tactics for, 24 table of for typical utility, 11 Life (cellular automata game), 429 Lighting (electric use), 38, 39, 41, 42, 60, 62, 334, 486-488, 493 Load (see Electric load) Load coincidence (see Coincidence) Load duration curves, 45-47, 181-184 and appliances, 47
Index
744 Load factor, 45 Load growth (see Electric load, growth) Load management (see Demand-side management) Load research, 338 Load-transfer forecast methods, 281, 288, 450, 520 automatic method for, 289 and regression trending methods, 284 Local factors, 412 Localized growth (redevelopment), 596 Locational error, 237-240 Long algorithm, 452 Long-range forecasting, 225 Lowry model, 311,314, 320, 322, 398, 402, 404, 431, 513, 546, 662, 675 LTC, LTCCT (see Load-transfer forecast methods) Manual counts (of consumers). 643 Market comb, 497 Metropolitan warming effect. 145 Micro-climates, 131. 139, 151, 196, 202 map of, 138 Migration of population, 636, 640, 651 Missing factor identification, 692 Mono-class simulation program, 388 Multiple regression (see Trending) Multivariate trending, 295, 450, 452 MULTIVARIATE (program). 451, 519 clustering algorithm, 452 land-use classification, 452, 455 legacy of research results. 455 trajectory model, 453 Multi-fuel models, 478-493 appliance models in, 481 diagram of, 480 program structure and flow. 493 Multi-map simulation program, 387 Multi-pass Lowry model, 431 Multi-scenario planning, 20-24, 227, 361,368,399,727 Multi-year low pass filters, 694 Mutual substation function, 249 Natural gas (energy source), 477, 482 model of with electricity, 479^90 Natural gas distribution. 117. 118, 477
Needle peaks (of electric load), 75 "Never again" design criteria, 175, 178 see also Weather, design criteria New cities (forecasting growth),632, 660 comparison to forecasting in alreadydeveloped cities, 633 content tests (table), 663 driving forces behind creation of, 662 as government goals, 661 guidelines for forecasting of, 668 recommended forecast tools, 664 Newspaper articles (as data), 328, 357, 360, 366, 537 No-load areas, 206, 217, 218 Non-analytic methods, 508-509 Nomenclature of forecast models, 609 Nyquist criteria (sampling load), 87 "Once every X years" analysis see Weather, severity diagram Operating rules (for system), 187 Pancake function, 413, 688. 696, 697 diagram of, 414 large radius (using urban poles), 696 Parking lots (as clue to land-use type in aerial photo interpretation). 336 Partial region forecasts, 700 definition of, 702 in example forecast study, 366-368 low-resolution data "trick," 705 and trending methods, 703 Pattern recognition, 293, 374, 410, 413-414,422,657 see also Template matching PBR (see Performance-based rates) Peak and peak loads, 10, 13, 17. 25, 26, 343,488,721-725.727.729 breakdown by class and use. 39 and demand periods used, 45 requirement of forecasts, 26, 719 split-peak (in demand metering), 44 summer versus winter trends, 328 and voltage sensitivity of load, 42 Per acre loads, 340 Per capita energy usage models,211,219, 219. 228, 304-308. 312. 320, 355, 376-380, 384, 645-650
Index growth of, 211 Performance-based rates (PBR), 8, 494 Personal computer (power needs), 301 Pickup truck factory (growth example), 314-321, 328, 345, 357, 662-669 advanced lessons from, 662, 665 as one of several scenarios, 330 example forecast case, 328, 357, 361 vs. insurance company example, 399 Planning, 1, 33, 225, 720 with recourse, 288 Polycentric activity center, 407, 422, 639 see also Activity centers and Urban Pole Polygon-area based forecasts, 382, 508 Polynomial curve fit, 262 Power factor, 33 Power quality, 49, 496, 503, 504 demand for, 49 and two-Q planning, 37 value of (to consumers), 49, 51 Preference models, 378, 389, 410, 696, calibration of, 688-695 missing factors in, 692 radius and radius limitations, 688, 698 stacking factors, 698 table of example factors, 411 Probability-weighted forecasts, 20 reasons to avoid, 24 diagram of, 23 see also Multi-scenario forecasting Process (information), 448-450 Products of electric usage (see End use) Proximity factors, 410, 411, 415, 572 see also Calibration Ps(d) function, see Mutual substation function "Putting out fires" type of planning, 224 Quality of power (see Power quality) Q-diagrams, 66 see also Two-Q planning Railroads (forecast factor), 306, 307, 314, 331, 358, 367, 376, 384, 390, 391,393,410,412,415 and aerial photo interpretation, 336 proximity factors for, 410, 411
745 Rate base (of a utility), 8, Rate classes, 306 Rate department (and its forecast), 29, 327,338,342,361,537,723 see also Corporate (rate) forecast and Global model Rate freezes, 9 Ratio shares forecasting method, 518 Records (see Documentation) Redevelopment (of land), 216, 222, 224, 576, 592, 629 in example forecast, 359 methods for simulation modeling, 606 table of eight methods, 607-608 portion of growth due to, 598-601 recommendations for handling, 626 redevelopment process, 594 rules for modeling well, 602 simulation algorithm set up for, 605 calibration tips for, 629 modeling and set up, 606 trending algorithm set up for, 603 types of (table and summary), 595 in kind, 596 localized, 596 strategic, 595 urban core, 595 Refrigerators, 107-108, 646, 647 Region (types of), 570-571 Regional development plans, 539 Regional economic engines and models see Lowry model Regional transmission operator, 7 Reliability, 10,65,495 broadening of offerings, 499 cost of poor reliability, 494 demand for (map), 65 differentiated, 180 market niches, 497 planning considerations for, 9, 32, 33 as a product, 498 Representativeness, 24, 27, 33, 488 Retirement areas (type of region), 709 when part of larger regions, 710 Revenue forecasts (see Rate department) Revenue requirements (of utility), 5 Rhinoceros, 144, 643 Risk-based planning (for weather), 185
746 Roads and highways, 306, 316, 331, 335 366, 367, 384, 390, 573 "accessification" caused by, 594 and aerial photo interpretation, 336 density of and area type, 571 dimensionality of, 575 frontage, 579-581 link (road-link) forecast, 521, 582 proximity to (importance), 411,414 factors for, 410, 411 see also Accessification; Highways Robustness (algorithm quality), 545 Root mean square (RMS) error, 233, 237, 269 Ruling day (weather model). 162 Rural areas, 570, 572-575, 582-586 conversion to suburban land use, 592 forecasting growth in, 577 "S" curves, 214, 273, 467, 468, 472, 592 and causes of load growth, 219 diagram of causes, 220 diagrams of, 214. 216, 592, 593 multiple growth ramp curves. 594 periods within, 215 and redevelopment. 222. 592, 602 and simulation forecast methods, 227, 309-310,605 and trending forecast methods, 271, 293, 299, 603-605 SAIDI (reliability index), 189 SAIFI (reliability index), 189 Sampling rate (of load data), 86 Sampling rate of spatial and locational data (see Spatial resolution) Sampling theorem (see Nyquist criteria) SCADA (as forecasting data source), 87 Scenarios (in forecasting), 20-23, 433 see also Multi-scenario planning Sensitivity (forecast process), 29 Sensitivity (voltage and load) see Voltage sensitivity Service territory boundary. 366,695,702 SFA (see Spatial frequency analysis) Short-range forecasting, 225 Simulation, 303, 448, 450, 479, 509 computerization of, 373 definition of. 303
Index diagnostics from and their use, 669 error spectra of, 464 event-driven models, 429 framework and structure for, 307, 311, 374, 375, 394, 421,424, 434, 435, 616 top-down, 312, 391 bottom up, 312 mono-class vs. multi-map, 386 map stacks, 384, 385 grid-based formats, 382 hierarchical allocation methods, 434 hybrid versions, 447-475, 520 iteration types, 379, 429 polygon-based forecasts, 382 preference models for, 378. 389, 410 414,415,572,669,688,696 and calibration, 688-695 missing, 692 radius and limitations, 688, 698 stacking factors, 698 table of factors, 411 "S" curve compatibility, 309, 310 scenarios for, 20-24, 361, 368, 399, 433, 727 spatial resolution of, 383 step-function simulation models, 309 Single-year low-pass filters, 685 Skepticism (of consumers). 638 Small areas and small-area forecasting, 3. 25. 207, 332, 382, 382, 392, 435, 582 definition, 210 characteristics of, 216-219 size of small areas needed, 25, 26, 33, 56, 209, 217-219, 228, 229. 239, 240, 241, 254-257, 384, 336, 388 542,570,580, 718 method for determining, 254-257 rule-of-thumb for, 254 table of general guidelines, 258 see also Spatial resolution vs. spatial forecasting, 3, 210, 730 unpredictable elements of, 220 see also "S" curves; Spatial forecasting Small cities (as opposed to large), 369, 372,398.570, 582,585,611 Solar activity cycles (and weather), 141
Index Space (for growth), 575-577 Sparsely populated areas, 570, 575 Spatial arithmetic (program feature), 695 Spatial convolution, 437 Spatial de-convolution, 683 Spatial frequency analysis (SFA), 245-248, 545 Spatial load forecasting and methods, 1 accuracy and quality in, 27, 231, 736 computer programs for (table), 511 consistency in forecasts, 28, 33, 347 355, 542, 676, 704, 718, 720, 726 consumer classes used in, 30, 122, 305 data requirements for, 448, 527 definition of, 210 documentation of, 721 factors for method selection, 541 information use in, 448 multi-scenario forecasts, 29, 30 recommendations for, 720, 731 reliability analysis (map), 503-504 representativeness of, 24, 27 requirements for, 33, 717, 718 spatial resolution of, (see Spatial resolution) savings from good spatial forecasting, 555-564 vs. small-area forecasting, 3, 210, 720 test cases and results, 514-532 temporal resolution of, see Temporal resolution uncertainty in, 20, 29, unpredictable elements of, 220 utility practices with regard to, 34 Spatial patterns, 48, 204, 667 Spatial resolution (of load analysis), 25, 26, 33, 56, 209, 217-219, 228, 229, 239-241, 384, 386,388,542,570, 580,718 and accuracy of forecast,243, 466 and behavior of load as observed, 219 and cost of data gathering, 463 method for determining, 254-257 needs in planning, 17, 25, 33 recommendations on (table), 258 required resolution, 240, 254 rule-of-thumb for, 254
747 and simulation methods, 310, 383, 384, 386-393, 428, 434, 444 table by level of system, 19 and trending methods, 217, 273, 300 Spectra of growth and errors, 443, 464 Springfield (example), 326-368 Stationary process, 669 Stationary process rule for, 692 Step functions, 310 Strategic growth (redevelopment), 595 Subsidiary source (of energy), 479 Substation planning impact map, 252 Suburban areas (type of land-use), 570 Surges (voltage), 61 Surround factors, 410, 411, 415, 578 Susan (hypothetical planner), 327-372, 462, 548-561 SUSAN (forecasting program), 450, 462, 469, 524, 529, 534 T&D planning (see Transmission and distribution planning) Tags (in forecast programs), 121, 481 Tax incentives, 329 Temperature (weather), 131-135, 147, 168-174, 196,201,202 Temperature humidity index (THI), 79, 131, 143, 158, 196 Template matching, 293, 450, 518, 519 Temporal resolution, 17, 18, 26, 33, 718 Theme parks (growth impact), 21 Threshold values, 694 THI (see Temperature humidity index) Third-party forecasts, 678 Time-tagged models, 121 TLM (see Transformer load management) Tourist-resort area forecasting, 148, 712 Training (of forecasters), 553-554 Trajectories (in forecast space), 453, 471 Transco, 6, 7 Transformer load management (TLM), 339, 468, 534 Transitions (of land use), 309, 569, 592 see also Redevelopment; "S" curves Transmission, 7 Transmission and distribution planning, definition, 4
Index
748 dividing line between transmission and distribution systems, 7, 8 forecast requirements. 13, 33, 712 justifiable expenses for, 8, 9 long-range planning for, 14-16 short-range planning for, 11-14 traditional approach to, 4 Trending (forecast method), 3, 28, 261, 273-278, 508, 673, 678, 679, 703,710, 725, 735 curve fitting methods, 282 -295, 450 choice of equation to fit, 267 improved methods of, 273 recommendations for, 270 error spectrum for, 464 example diagram, 263 factors indicating possible failure, 543 geometric methods. 295 load-transfers and coupling, 281 multivariate trending. 295 spatial resolution, 271 template matching 293, 450, 518, 519, vacant-area inference, 278 years of data required. 270 Two-Q analysis, 37. 65-68, 501 Uncertainty in forecasts (table), 633 see also Multi-scenario planning University towns see College towns Urban models, 314. 323 see also Lowry model Urban poles calibration of, 683-688 compression models. 623 trick computations with, 696—698 U x spatial error measure, 253, 254
Vacant land, 211, 217, 218, 278, 334,
598,519,669,693 Vacant area inference (trending), 278 Value-based analysis, 50, 494 example, 51 Value volume, 496 Voltage, 40 Voltage sags, 51 Voltage sensitivity (of loads), 40 Voltage surges, 61 Water heaters, 40, 47, 62, 63, 65-67, 75-78, 100, 112, 144, 115, 149, 486, 500-502 Water wells and pumps. 149 Weather, 131-146 analysis of, 131, 156-162 components of, 132-133 cycles in, 141 design criteria, 174. 200 indices measuring impact, 133-135 normalization (of load data), 27, 33. 130.147,152.165,175.718.726, 735 pattern of problems from. 197-199 predictability of. 145 relationship to load, 153, 180 risk-based planning for, 179, 194 severity diagram. 170 X-X-X nomenclature (for simulation forecast programs). 509-513 table of definitions by class. 510 examples of programs by, 511-512 Zoning and zoning data, 411, 538, 668 map and example, 335
