Power Plants and Power Systems Control 2006: A Proceedings Volume from the IFAC Symposium on Power Plants and Power Systems Control, Kananaskis, Canada, 2006 (IFAC Proceedings Volumes)

POWER PLANTS AND POWER SYSTEMS CONTROL 2006 A Proceedings Volume from the IFAC Symposium on Power Plants and Power Systems Control, Kananaskis, Canada, 2006

Edited by

Dr. DAVID WESTWICK Department of Electrical and Computer Engineering University of Calgary Calgary, T2N 1N4 Canada

Published for the

International Federation of Automatic Control By

ELSEVIER LTD

Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA First edition 2007 Copyright © 2007, IFAC. Published by Elsevier 2007. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN–13: 978-0-08-046620-0 ISBN–10: 0-08-046620-6 ISSN: 1474-6670 Printed and bound in Great Britain 07 08 09 10 11 10 9 8 7 6 5 4 3 2 1

Table of Contents A Novel Concept for Stabilization of AC/DC Network with UPFC R.K. Pandey

1

Limitation Control Procedures Required for Power Plants and Power Systems Possibility for Reducing Future Blackouts E. Welfonder and M. Kurth

7

SISO Extended Predictive Control – Formulation and Robust Analysis M. Abu-Ayyad and R. Dubay

17

Robust Decentralized H∞ Controller Design for Power Systems: A Matrix 23 Inequality Approach using Parameter Continuation Method G.K. Befekadu and I. Erlich Self-Tuning PI Controller I. Boiko

29

Development of an Extended Predictive Controller for a Speed Control System M. Abu-Ayyad and R. Dubay

35

Power System Stabilizer Design for Multimachine Power System using 41 Population-Based Incremental Learning K.A. Folly Development of Educational Web-Based Simulator for the Electricity Spot 47 Market in Korea J.W. Lee, K.M. Yang, Y.W. Jeong, J.B. Park and J.R. Shin A Cooperative Power Trading System based on Satisfaction Space Technology

53

K. Matsumoto, T. Maruo, and N. Mori Influence of Wind Energy on the Power Station Park and the Grid H. Weber, T. Hamacher, and T. Haase

59

An Approach to Optimal Dispatch of Bilateral Electricity Contracts Regarding 65 Voltage Stability B. Mozafari, A.M. Ranjbar, A. Mozafari and T. Amraee Identification of Synchronous Generators using “4SID” Identification Method 71 and Neural Networks M. Karrari, W. Rosehart, O.P. Malik and A.H. Givehchi Parameter Estimation of Power System Oscillations based on Phasor Measurements T. Hashiguchi, Y. Ota, H. Ukai, Y. Mitani, O. Saeki and M. Hojo

77

Identification of Electric Parameters of Synchronous Generator using InputOutput Data Set S.A. Saied, S.M. Bathaee, M. Karrari, W. Rosehart and O.P. Malik

83

iii

Estimation of Moisture Content in Coal in Coal Mills P.F. Odgaard and B. Mataji

89

Simplified Fuel Cell System Model Identification S. Caux, W. Hankache, D. Hissel and M. Fadel

95

An Affine Geometrical Approach to Power Systems Problems E.D. Crainic and A.I. Petroianu

101

Discrete-Time Model Reference Adaptive Regulation of Nodal Voltage Amplitude in Power Systems G. Fusco and M. Russo

107

Determination of Transmission Transfer Capability with Security and Voltage Stability D. Hur and H.J. Lee

113

Voltage Stability Assessment and Enhancement of the Thailand Power System A. Sode-Yome, N. Mithulananthan and K.W. Lee

119

Design, Implementation and Testing of an Artificial Neural Network Based 125 Admittance Relay G. Chawla, M.S. Sachdev and G. Ramakrishna A New Numerical Algorithm for Fault Location Estimation using TwoTerminal Synchronized Voltage and Current Phasors C.J. Lee, Z. Radojevic, H.H. Kim, J.B. Park and J.R. Shin Complete Fault Analysis for Long Transmission Line using Synchronized Sampling N. Zhang and M. Kezunovic

131

137

Study on the Establishment of Dynamic Performance Test Environment for 143 the Digital Protective Relay using RTDS B.T. Jang, C.Y. Choe and G. Jung Hybrid HVDC Converters and their Impact on Power System Dynamic Performance B. Qahraman, A.M. Gole and I.T. Fernando

147

Predicting Transient Instability of Power Systems based on Hybrid System 153 Reachability Analysis Y. Susuki, H. Ebina and T. Hikihara Stability Analysis of an Islanded Generator P. Lilje and A. Petroianu

159

Primary Control System and Stability Analysis of a Hydropower Plant M.R.G. Zoby and J.I. Yanagihara

165

Observer-Based Coal Mill Control using Oxygen Measurements P. Andersen, J.D. Bendtsen, T.S. Pedersen, J.H. Mortensen and R.J. Nielsen

171

iv

Fault Detection in Coal Mills used in Power Plants P.F. Odgaard and B. Mataji

177

Control Performace of Large Scale Steam Power Plants and Improvements T. Weissbach, M. Kurth, E. Welfonder, D. Haake and R. Gudat

183

Intelligent Start-Up Schedule Optimization System for a Thermal Power Plant M. Shirakawa, K. Kawai, M. Arakawa and H. Nakayama

189

A Fault Diagnosis and Operation Advising Cooperative Expert System Based 195 on Multi-Agent Technology W. Zhao, X. Bai, J. Ding, Z. Fang and Z. Li Model Based Fleet Optimisation and Master Control of a Power Production 201 System C. Joergensen, J.H. Mortensen, T. Moelbak and E.O. Nielsen Reliability Enhancement Scheme for IEC61850 based Substation Automation 207 System S.I. Lim, D.H. Park, S.J. Lee, S.S. Han and M.S. Choi Modeling Voltage Regulation in Object-Oriented Analysis of Distribution Systems Including Dispersed Generation G.M. Casolino, A. Losi and M. Russo

213

Service Restoration Considering Load Balancing in Distribution S.Y. Choi, J.S. Cha, C.D. Yoon and M.C. Shin

219

Real-Time Volt/VAR Control in a Distribution System using Multi-Stage Method J.Y. Park and J.K. Park

225

Development of the Automatic Recognition System for Distribution Facility 231 Map B.J. Yi, J.I. Song, J.H. Shin, J.I. Lee and S.K. Cho Sensor Dynamics Compensator for Temperature Measurement in Combustion 237 Chambers of Utility Boiler and Incinerators I. Boiko, and V. Mkrttchian Sub-Space Principal Component Analysis for Power Plant Monitoring L. Pan, D. Flynn and M. Cregan

243

Combustion Plant Monitoring and Control using Infrared and Video Cameras S. Zipser, A. Gommlich, J. Matthes and H.B. Keller

249

Enhancement of Electric Motor Reliability through Condition Monitoring K.E. Holbert, K. Lin and G.G. Karady

255

Performance of H∞ -PSSs as Affected by the Parameters of the Bilinear Transform K.A. Folly and K. Mocwane

261

v

Dual Input Quasi-Optimal PSS for Generating Unit with Static Excitation 267 System Z. Lubosny Experimental Studies on a Proto-Type Power System using an Adaptive PSS G. Ramakrishna and O.P. Malik

273

Extended Phase Compensation Design of Power System Stabilizer for Bisotoun 279 Power Plant G. Zafarabadi, M. Parniani, M. Rasouli and P. Ansarimehr Robust Control Design of PSS in Wide Area Power System Considering Information Reliability H. Ukai, G. Toyosaki, Y. Nakachi and S.C. Verma

285

Analytical Investigation of the Effect of Generator Modelling on Electromechanical Load Damping K. Kaberere, A. Petroianu and K. Folly

291

Comparison of Methods for Oscillation Detection – Case Study on a Coal-Fired 297 Power Plant P.F. Odgaard and K. Trangbaek Low Load Model of a Once-Through Boiler with Recirculation K. Trangbaek

303

Semigroup based Neural Network Architecture for Extrapolation of Mass Unbalance for Rotating Machines in Power Plants B.H. Kim, J.P. Velas and K.Y. Lee

309

MGP: A Tool for Wide Range Temperature Modeling A.F. Kuri-Morales and L.V. Seisdedos

315

Simulation as a Tool for Process Design and Disturbance Analysis in Industrial 321 Power Plants Y. Majanne Operator Guidance Simulator, A New Power Plant Training Tool Concept U. Tomschi, H. Jackisch and R. Newald

327

Application of Affine Transformations to Real-Time Power System EMS Functions E.D. Crainic and A.I. Petroianu

333

Autonomous Power Networks Based Power System A. Jokic and P.P.J. van den Bosch

339

Importance of the Selfregulating Effect within Power Systems M. Kurth and E. Welfonder

345

Optimal Power System Management via Mixed Integer Dynamic Programming H.G. Kwatny, E. Mensah D. Niebur and C. Teolis

353

vi

Static Characteristics Analysis of Power Systems Through a Hermitian Approach J. Zhou and Y. Ohsawa

359

Economic Dispatch Algorithm by λ-P Tables Reflecting Actual Fuel Cost 365 Curves K.I. Min, J.G. Lee, S.J. Kim, H.S. Hong and Y.H. Moon Power System Maximum Loadability with Generation Constraints C.E.M Fernandes, R.S. Salgado and L.V. Barboza

371

Optimal Allocation of Static VAR Compensators using Modal Analysis, Simulated Annealing and TABU Search S. Ebrahimi, M.M. Farsangi, H. Nezamabadi-Pour and K.Y. Lee

377

Distributed MPC Strategies for Automatic Generation Control A.N. Venkat, I.A. Hiskens, J.B. Rawlings and S.J. Wright

383

Modelling and Optimization of a Micro Combined Heat and Power Plant D. Faille, C. Mondon and L. Henckes

389

The Way of District Heating Output Control by Means of Hydrothermal Power 395 Systems - Three Modifications J. Balate, P. Jenik, B. Chramcov and P. Navratil Weighted Fouling Model for Power Plant Condenser Monitoring M. Cregan and D. Flynn

401

A Multi-Agent System-Based Reference Governor for Multiobjective Power 407 Plant Operation J.S. Heo and K.Y. Lee Adaptive Governor Control and Load Shedding Scheme for an Incinerator 413 Plant Y.D. Lee, C.S. Chen and C.T. Hsu Author Index

419

vii

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Foreword IFAC Symposium on Power Plants and Power Systems is sponsored and organized by the IFAC Technical Committee on Power Plants and Power Systems. It is held every three years and the latest Symposium in this series was held June 25-28, 2006 in Kananaskis, Alberta, Canada. Out of 110 papers submitted for presentation at the Symposium, 76 papers were accepted for presentation after independent peer review. Session Chairs were asked to evaluate the papers in their individual sessions. Based on paper quality and presentation, the Session Chairs recommended a total of 69 papers that are included in the Proceedings of the Symposium. Control plays a very important role in all aspects of power plants and power systems. The papers included in the Proceedings are by authors from a large number of countries around the world. They encompass a wide spectrum of topics in the control of practically every aspect of power plants and power systems.

ix

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Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

ELSEVIER

A Novel Concept for Stabilization of AC/DC Network with UPFC R.K. Pandey Department o j Electrical Engineering Institute of Technology Banaras IIindu University, Varanasi, INDIA

Abstract: This paper presents a novel concept for stabilization of AC/DC network with Unified Power Flow Controller (LJPFC). The system considered has the structure of two areas connected by HVDC link. 'The investigation for perturbation in ac bus voltages has been carried out and the effect on the stability deterioration has been analyzed. The new concept of control has been proposed by embedding UPFC and then generating the control decisions adequately which stabilizes the earlier one. The concept of including the Unified Power Flow Controller (UPFC) in AC/ DC network especially where a DC link is embedded to connect the two AC Systems is proposed. The proposed control design has been done utilizing a Novel Discrete -Time model of ACiDC system. The complete system stability has been studied in which the individual controller such as HVDC-SVC and HVDC-SVC-UPFC performance under varying perturbation of ac system voltage has been widely analyzed. Tht: results show that in situations the HVDC-SVC alone is unable to reject the perturbation, the UPFC along with the HVDC - SVC damps the oscillations, thus matching the real and reactive power demands adequately. This novel combination can effectively be utilized in situations when the ac system bus voltage undergoes the fluctuations due to changing P and Q requirements. Copyright 02006 IFAC Keywords: - HVDC, SVC, UPFC, Discrete-time, continuous time, multirate sampling

1. INTRODUCTION

In case of power oscillations, the converters will function by their firing angle controls. As the firing angle can vary within a certain limit as directed by the control, the Static VAR Compensator will also act accordingly. But, when the HVDC converter controls along with SVC are not sufficient enough to damp the oscillations, i.e., reactive power mismatch is not met, and then the AC system voltage will come down from normal 1 p.u. value. As this is noticed by the network. it will first land to converter control instability and associated afterwards failure and then may enter to ACI DC system interaction. Moreover, if the voltage in the AC side of the corridor becomes low, then DC link voltage, as well as the power transfer through the DC link will come down undesirably. Now, providing an UPFC block, in between the AC switchyards, parallel to the A C tie line, and the DC link. the real and reactive power both can be modulated adequately, by their multifunctional and coordinated control. The capability of UH;C has been demonstrated (Hingorani Narain G, 1999; Wang H.F.. 2000) in damping oscillations. In case, there is reactive power drop in the network, which cannot be met by SVS, etc. then, the UPFC will pump that power to the AC corridor; immediately. and thus stability of the power network can be maintained. Depending on the rating of UPFC and SVS, the real and reactive power can be modulated and the whole network can be made stable, up to a certain extent. Thus. chances of' network tripping, due to large. sudden and sustained power mismatch can be minimized a lot and stability of the AC/DC system can adcquatcly bc cnhanccd.

The HVDC transmission technology is well established nowadays. So, many schemes all over the world are running well including back-to-back, pointto-point and multi-terminal. The basic operational requirement of the HVDC schemes is adequate control action, depending upon the power ordcr for damping thc power network oscillations. Sometimes, the inadequate control action such as. absence of adequate control of Static VAR Compensator (SVC) at the converter bus. might result in unstable system behaviour. So far. no remedy has been reported in literature, where there is a variation of the AC switchyard line-to-line voltage because of external reasons; which might ultimately affect the operation of converter. A new approach has been proposed for the network in which DC link is embedded. When AC bus voltages of converter station fluctuate, the SVC may not be in a position to help to damp this and so the converter may land to control instability. This is very detrimental for the system. To alleviate this novel concept of Unified Power Flow Controller (UPFC) in between the AC switchyard has been proposed which acts as a supplementary controller for the AC network and thus regulates the system dynamics adequately in situations of perturbations in AC switchyard voltages either side, which in turn improves the overall system stability as desired. In the power system network, two regional grids can be interconnected by HVDC back-to-back. I he two converter stations are connected through the DC link and the converters have their individual controls.

1

From the results shown in this uork, it can be said that this proposed HVDC-SVC-UPFC compact system (Fig.1) is far better to design the effective control strategy for HVDC link. suited to restore stability in a wry short time, which is csscntial to ciibure bettcr stability for. a dynamically varying power network But. IJPFC also cannot sustain a ver)' large amount o f power oscillations because its DC link capacitor has a maximum limit to support the required VAR. So. this proposed model may not guaranty power network stabilization for a very high amount of perturbation. but it can definitely give a higher level of confidence to the power system researchers. In earlier research studies, no such concept has been proposed yet. so this proposed conccpt will be intercsting to powcr cnginecrs and rcscarchcrs worldwidc.

Aar(kT+T3)+ A / , [AI&(k+l)T

Inverter Side

Fig.1 HVDC-SVC-IJPFC system representation 11 DISCRETE-TIME MODEL, OF

HVDC-SVC-UPFC In standard practice stability investigations are performed using IineariLed perturbation models in which the system is linearized around a nominal operating point l o achieve [his objeclive. il is important that the behaviour of various components o f the HVDC system be appropriately represented in a linear domain

where A , to A,? and R, to R12 are linearized scalar constants. The relation ship between the DC current Id and the overlap angle IJ are derived for both the cases of rectifier and inverter (Pandey, et u1.,199O). The linearized values of the overlap angles, ;c and U, in terms of DC currents and firing angles are given as,

2.1 Discrete-time HVDC System Model

Continuous-time (Carrol and Krause. 1970) and discrete-time system representation hake been described in the literatures (Pandey, et a l , I990). Discrete-time equations for convcrtcrs in HVDC sy5tem (Pundey, et a1 , 1990) are given below Rectifier Side

(kT+Ti)]/d, Combining the transmission line and current controller model, state space expression is obtained (Since it has been assumed that. the predictive type control at inverter end, the variable Aa) has been represented in terms of the variable A/,, )

AV,,(k7;T,)

-

A-[A&(kT-Tz) + AIJ,] +A,?

2

A

=

Fig.11 Static var corripeiibator The equation for the equivalent reactance for a standard SVC circuit is given below.

This state space model represents continuous- time nature o f thc both transmission line and thc controllers. To combine the continuou+time models of the transmission line and controllen with the discrete-time model of converter, the thcory of multirate sampling has been applied (Pundey et ul

1990).

Suaceplance.

dx(kT+T/) @ T / ) d x ( k T ) + Q(1,) AC;(kT) Ax(kT T?) = q T 2 - T / )Ax (kT I T / ) I Q(T2-T,) AV, ( k 7 + f / ) h ( k T T3) = @T3-T2) AX(kT 1 T2) 1 6(T3-T2) AVd((kTt Tr ) A~x[(k+I)l= l q 1 - 7 3 ) A ~(kf l 1 3 ) + O ( 1 -13) A[/,(kTT T,) (3) where @( I @(T z- I ,), @( 1 3 - 12). @(T - I 3) are the state transition matrices evaluated at the four discrete instants. while $(TI). 8(Tz-Tl).8(T3-T2).8(T-T3) are the corresponding input matrices. Thererore. combined equation &[(k+l)T] = @(T/ ) @(T2-T/) @(T3-T2) @(T-T3) AX( k f ) + @ ( f 2 - f / ) q f 3 1 2 ) q ( T - f 3 ) B ( T / )Al’dkf) +@(Tj-TZ) (yT-T3) @T:-T/) AV,(kT+T/) +@(T-T,) H ( I 3 I,) AC’d(kT4 T z ) + B(T-7.3) AL>(/LT+T3) (4) The kector AV, in this expression can be substituted by the appropriate a\ erage expressions derived at different time instdnt5 as given in ( 1 a d 2) After simplification (4), can be converted into the lollowing homogeneous state eqn A x ( k l I ) I ’ ] = MHVDL MkO (5) This expression represents the combined DC Iinh modcl. Where MIIvDLis the closcd loop matrix o f the entire two terminal HVDC \ystem

Putting the value o f & in (8) following results

Now, linearizing (9) the perturbation equation is obtained as

(10) Therefore. the reactive power equation for Static Var Compensator, connected in the rectifier side. is AQ,,

f

= 4 ,(A%

f

1 s, +

7

W

l

I

1

(11)

Rectifier Reactive Power Equation For the rectifier. the reactive power equation is, Q, = 1.35V” I , S W Z ( ~ , ) (12) Linearizing equation (12) AG? = R,l(A%)+ R & ~ , r ) + R , , ( A V L , ) (‘3) Reactive power injectedhithdrawn in case of power imbalance in the network can be expresied as below for suitable controller design,

IIVDC-SF’C Svslem Model In the model of HVDC-SVC, thc linearized statc equations of the HVDC are taken from above. The above closed loop equation of HVDC is combined with the linearixd state equations of SVC. which are developed in the following part Calculation &Reactive Power (0)in Static VAR Comnensator

AQR,,,‘,

=A Q

AQR,,

= R, I(A% 1+ U M ‘ , ,1+ h ( A C f r )- &I

-

AQ,,,

(A%,

1

(14 At steady state, reactive power perturbation must =0 be zero, i.e. Therefore, from ( I 4)

The standard Static VAR Compensator (SVC) circuit can be represented as in figure below,

3

'This expression rcprescnts the completc HVDC-SVC model. Where, M/,vJjc.~yvc is the closed loop matrix of this system. Here also the eigen values of matrix MHvD,,.sr,c- indicate the system stability, i.e., for the stable system operation, the eigen values must lie within the unit circle.

h ( A ? ) = * ~ p l ( A ~ ,1-l <8 * ( A / d Y ) bR,,(AV,,, )

At instant KT, h , ( K 7 ) = S r ,&,(,(K7) Ei,d',,(K7) %Ab;L,(K7) and. A c ~(,K T + ) = d , Nd,( K T + ) where. S,, =l/Sr, . KP2 = l / K r .KrJ = I& Putting the kalues in (1). the equations are obtaincd as

H VDC-SVC-UPFC Comuact Model The UPFC block is connected in between two AC switchbards and the overall compact modelling is done Here, for the purpoce of cimplicity the detail modelling of AC network has not been attempted Horn ever, perturbing the AC line-to-hne voltage can accommodate the AC side variations To study the overall model, the LJPFC model is studied first 5teadj state model 01 UPFC has been given in Fig 111 The djnainic equations of the l J P K are given (Wang , (2000) as Ve=mevd J 2 ev &)

A I G ( K / v 4 ) + ( L Y & ( K / ) ~ ((K1)t ~A~

( , N wrll,)

Similarly, for other voltage expressions for discrete-time instants are obtained for rectifier and inverter both from (1) and (2) State eauations in HVDC-SVC model 1 K ACX = --

+ -Alzfi

?(

?(

~b = mh

Equations mentioned above are combined and linearized to result in

r-(k)hi#+x;4, +(-J3&%,+4JYI+x?Wi ;tX,4,

k !i &I,

c

=x," f ,

+(-A+%

v,,~2.e0

d(vdJ/dt=S nze/(4 CdJ[cos(d;I sin(s,)/ [ c f d iI d' 3 mh'(4 CJc) [cos(6b/ sln(&)] [lBd CBy]' Negledng UPFC losses, during stead) -state operation it neither absorbs nor injects real power with respect to system. It mcans, d/dt ( Vd,)=O

+(-% 3 y p ; , +(% pJ)Wl,

(15) Finally, the combined HVDC-SVC state-space model can be represented as,

-g-l/rr A-

Fig.111 UPFC in two-machine system

XI

0

-RIl.

0

0

0 0

l/('

The equations for two-machine system are obtained as (Pandey and Tuipathi, ZOOS), i/d' .DI.EI,'+D~.m,.sin(b,). vdc + Dj.(E2y'.~~~(b)-

x,

i2d.x2ddl+ mb.sin(bb). vdc 12)

X

0

1/L

O

il,

E2,!sin(O) - i2'/.X2J i2J=D4. (E2q'. cos(8)-i2J.x2d'+mb. sin(&). vd, 12)+D j

7

I'dc 1 D,E,,' Q3. nz,.co.s(6,). Vd' -.-Q,.( nzh.cos(d,,). L,,'. sin(d) f i7,,.x2,/) where,

. m,.sin(d,).

B= 0 1/L R/135L 0 0

x,=(I<;>/(.S;~T'))I ( K , I(S:,T )) +(/?i/(I 35S1,/.)) X,

= (-K,'

PI. m,.cos(&). v d c - PI.( nzb.cos(66). vd,.iZ+

~

i2
0

Vd,

12-1-

D] = Xhlr/Xdee ,D2 = - Xbd'(2.XL,,,) ,D3 = Xde/X& , DJ = xdphctec ,D j = - x,ie/!dtee,De = -xX,/!dtee,

(~
PI = X / J q v . X q e e ) ,p3 = - X q e J X p p3 = X q e W q e e ) ,

,/( S:, L ) ) - ( K /( 1.35L))

7

424 =

x, = cn;, /(s;,T,1) x,+=(& / ( S ; , L ) ) + K / ( 1 . 3 5 L ) X 5 = ( - R 2 ) / 1 . 3 5 * L + 1/ 1.35C

- xyr%/e

Those direct axis current equations and quadrature axis current cquations are lincarizcd and merged with the linearized equations of the dynamics of the two generators (Gyugyi?.et al.. 1995). For the first generator, (D,+M,.s). Act), = -AT',, = -A (irTEl,'+(xl,x16i?.ird. ilq)= - &. A Ely'- EJY'. A ily-(~lq-~Xld'). [ ify A ifd -1 ird. A iq] = - itq A El,'-[ El,'-( Xlq-xXld?. i d . A i, -I( x/*-x/J?.iql. A itd = n,,. A Ely'+nl2.A i,, +nX13. A ild s.Ab/ = ~ ~ J ~ , . A o J /

The multirate sampling theory (Pandey, et al., IYYO) is applied and the state transition matrices are evaluated at the four discrete instants, as it is done in case of llVDC model alone. Finally. the homogeneous state equation is found in the form of Ax [(k-+I)Tl = ~wfvl,c.-svc.4 k T )

4

1,ine capacitance, C=0.0405 p.u. Rectifier firing angle, aV=1 p.u. Constant extinction angle, y=l p.u The SVC block parameters are given below, Capacitance in the SVC, CC = 0.40528 p.u. Firing angle of the SVC thyristor (connected in rectifier side), aC,,v, = 130' AC L-L Voltage, VLLl= 0.74074 p.u. ,1 ransformer: ~,=0.03, xh=0.3 Transmission line: x,=O.3, xh,.=0.03 Operating condition: Vh=1 .0 p.u., 6=20.23", UPFC parameter: m,=0.5. mb=0.5, b;,=OSp.u., &=OS p.u. DC link parameter: Cdc=7pF',vdc0=l .O p.u Generator 1 : /\4l=O.O255 MJIMVA, DI=O.O sec., T ; d & ,044 sec., x l h 1 .O, xl,=O.6, x 1 ~ 0 . 0 7 6 5E1,'=1.024 , p.u. Excitation system 1: KIA=lO.O, T,,,=O.O1 secs. M2=O.O255 MJIMVA. DzzO.0 Generator 2: sec., T',l,=5.9 sec., x,1=0. 19 ,x,,=O. I63 ,x>,1=0.0765.

( l + s I.J'/O? Ah,,' = A6lf//,-(xld-xId?All
Ax = A A x + B A U Where, AX = [Ad Awl Am2 AEI,' AElll> A E2,'

AE2l-l> Av,Ic

l1

AU = [Amc Amb Ad,,]' The final state equation of UPFC connected in a two machine system can be written as,

AX = MtrpFC AX The diagram of the proposed compact model, where UPFC is combined with the HVDC-SVC system is

E7,"I.O

P.U.

Excitation system 2: K2A=20.0,T2,4=0.01secs. 111 PERFORMANCE EVALUATION The perturbation of AC line-line voltage is increased from 0.074074 p u. to 1 p.u.(i.e., approximately 25%). In this case, as the perturbation is increased considerably. the SVC will not able to sustain it and finally it will lead to 5ystem collapse (Fig. V). Some of the states have been shown below. The detailed study has been given in Table I.

4 . .

h A

A1

Fig.lV Proposed IHVDC-SVC-UPFC system

II

The state equation for the HVDC-SVC and UPFC comDact model can be written as

I

wherc, [ ~ H I . D c ~ ~ s r . c ~ - r . c= ~l

[ A c ~ s v ~ AIdF ., Aid, AVJ,L AVci A 6 AID, A w ~El,,' / ) , I > AE2q' &,ii AvdL.1 'Thus, the I-IVIIC-SVC-UPFC compact model is developed in a discrete time framework and stability study has been perlormed using this model through cigcn-valuc analysis.

a

I11 SIMUl.AT1ON OF SAMPLE SYSTEM The simulation study is carried out using MA'I1,AB software package. The parameters of the sample system are given below, No load rectifier direct voltage, F;Fo=l p.u. No load inverter direct voltage, Vd,rl=l p.u. Frequency = 50 Hz. Direct Current, 4j,.=Id,=0.25p.u. Link length=500 meter Commutating inductancc, Lc=4.99c-O4 p.u. Line inductance, L=O.0399 p.u. Line resistance, R=0.25 PSI.

I )

a

4

fj"

5

1

1

,

~

converter control. Under this siiuation. ihe concept of employing UPFC as supplementary controller for damping the oscillations has been thoroughly examined and it has been found that the induction of UPFC drastically improves the overall system stability that too in minimum time. 1he complete system model of HVDC-SVC-UPFC fi-amework has been developed in the discrete time domain and the system stability has bcen examined. wherc it has been observed that the variation of AC line-to-line bus voltage does not deteriorate the overall system stability. rhis has been reflected so because the basic feature of UPFC in the AC network is to control the power flow dynamics verj fast using VSC technology having vcry fist control of- both rcal and reactive power. UPFC has been incorporated at the back to back HVDC link to demonstrate the concept. where it has been intentionally presumed that the DC link length and the AC transmission line length (the distance between the two AC switchyards has been asumed to be 500 meters).

L

;.

8

[

113:

[:I::

I

,

:I):

CCI

"I;

13:

31::

,

CCI

]:I:

:I:#:

Tune (sec.)

(c) Fig.V Response of state variables for HVDC-SVC model by making initial perturbation of 25%; (a) AG,, , (b) A , (c) A bTable I: ComDarison between HVDC-SVC model and I-IVUC-SVC-UPFC compact model for 10% perturbation and relatively IarPe Derturbation. (25%)

perturhat'on 25%) Peak Overshoot

;:

Settling

Overshoot(p,u,)

Pandey R. K., Ghosh A and Sachchidanand (1999), Development of Novel IHVDC System Model for Control Design. Electric Machines and Power Syutem Research, 27, pp.1243-1257. Carol D.P. and Krause P.C. (1970), StabiliQ analqsis of a DC power system, PAS-89, pp. 1 I 12- I I 19. Hingorani Narain G (1999) , Gyugyi Laszlo, Ckderstanding FACTS Concepts and Technologv of Fkxible AC Transmission SyAtems. IEEE Press, New York. Wang H.F.,Swifi F.J. and Li M (1998) A un@d model for the analysis of FACTS devices in damping power systems.IEEE Trans. on Powe Delivery. No. 4. Claudio A. Canizares and Zcno T Faur (1999) Analysis of SL'C and TCSC Controllers in Lbltage Collapse, IEEE 'Irans.on Power Systems, Vo1.14. ppS8-hS. Pandey R K and Tripathi S B Mani (ZOOS), Design of Unified Power Flow Controller with State Predominant Approach, Sixth International Conjerence on Power Electronics (e Drives Systems, Kuala Lumpur, Malaysia Wang H.F. (2000). A uni$ed model for the analysis of FACTS devices in damping out system oscillations Part 111 Unij?ed Power Flow Controller. IEEE Trans. on PWRD. No. 3. Saeed Arabi, Prabhashankar Kundur and Rambabu Adapa (2000), Innovative techniques in modelling tiPFC' for power bystem analysis, IEEE Trans. on Power Systems. V01.15, pp.336-340. Wang H.F. (1999) , Selection of r o h t installing locations and feedback signals of FAC'TS -based stabilizers in multi-machine power systems, IEEE Trans. on PWRS. No. 2,. Gjugyi. L. . Schauder C.D. , Williams S.L. . Keitman '1.R. , rorgerson D.K. . Edris A. (1995) . The [JniJied Power Flow Controller il New Approach to Power Transmission Control, IEFE Trans. Power Delivery, Vol.10, pp.1085-1093.

Relaticely large

Operating Point Domain( 10% perturbation)

Control Strategies; System

REFERENCES

settling time

~

I

I

II Idi

0 489

100107 I

0 474

0 012

I

IV. CONCLUSION An investigation has been carried out of a network whcre HVDC is having back to back link and also the stability characteristics has been found deteriorating when the line-to-line voltage of the AC system is varied, because of some system disturbance. The HVDC-SVC alone could not handle the perturbation of line to line voltage change alter a certain value and this is because of the fact that SVC can not support for the external reactive power variation as this is meant to regulate the Var requirements during the

6

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

LIMITATION CONTROL PROCEDURES, REQUIRED FOR POWER PLANTS AND POWER SYSTEMS POSSlR11,I'I'Y FOR REEDLICING FUTURE RI.ACKOLITS

E. Welfonder and M. Kurth

Department for Power Generation and Automatic Control, IF'D, L'niversiv of Stuttgart Pfaffenwaldring 23, 70550 Stuttgart, Germany Tel t49 711 685-6214, Fax +49 711685-6590 welfonderQivd uni-stuttgart de

Abstract: For maintaining the reliability of interconnected power systems also in cases of extreme power transits the protective system devices should not become active when ever possible. For this reason, it is necessary to provide for limitation control procedures, and this not only on the side of power plant and system, where it has been common practice for many years to keep at least the main manipulated and controlled variables uithin their foreseen operation arcas. but also uithin the grid to contain the transmission flows of heavily overloaded system components within their maximum allowable transmission capacity. In this respect. manual short-term bottlcncck management on the system operation side turns out to be not sufficient enough, in the case of unexpected events caused by increased power transits.. Copyright 02006 IFAC' Keyuords: Power plants. poi%er systems, power transits, bottleneck management, limitatiorr control, protectiori, blackouts..

1. TNTRODUCTION

Thc original objective of interconnected power networks aimed - above all - at a joint spinning reserve power. Also with the first cross-border power transmits inside of Europe the interconnected power system was loaded only to little extent. s. in Figure 1 '.from about 1970. These power transmits were i s . caused by the purchase of seasonally lowprice naturally generated electrical power from highhead hydropower stations in the Alpine countrics and the transmission o\ er long distances to the large industrial centres such as the Ruhr area in NorthWest Germany. Since the mid 1980s. however, spccific non-seasonal power transits more often occur fiom countries with a high amount of low-price generator output into countries with a lack in inexpensive generator output. So, for example. Italy from the mid 1990s on - i s . before the liberalihon of the electrical energy market - continuouslq purchased 4 to 6 GW power from France.

Caused by these power transits speci tic high-voltage transmission lines concerned within the European pouer system have already been strongly loaded at that time, s. in I'igurc 1 "from about 1985". With the change to a liberalized energy market. the trade intensifies the use of the interconnected power sqstem as a transport network. uhere not seldom individual transmission lines are loaded to full capacity (Kaupa and Pohorny, 2004: Reyer and Weis, 2004). s. in Figure I "from about 2000". This development is verified quantitatively by the strong power ex- and import from and to Germany plotted in Figure 2 (Schnug and Fleischer. 1999; Welfonder. 2000). As the diagram shows, the power transits in 2003 already reach = 5 G W. averaged over the year.

*

Figures 3 and 4 show detail considerations for 2003, on the basi? of power ex- and import? on the third Wedncsday ofcach month (UCTE, 2005):

/

~

1970

-

I

~

2000

1985

~

t

\ 1980

1990

2000 from 1991 incl East-Germany

Fig. 1 lncreasc of maximum powcr transits within

Fig. 2 Increase of the mean power transits within Germany since the second hall' ofthe 1980s

thc European intcrconnected power system => trend behalriour

7f;"-'

a) night ( 3 : O O a.m.) 10

P [GWl 5

b) day (1 I :00 a.m.)

Export

10

P [GWI 5

0

0

-5

-5 -10

-10

1

2

3

4

5

6

7

8

1

9 101112

2

3

4

6

5

month

7

8

9 101112

8

9

month

Fig. 3 Load ex- and imports on the third Wednesda) of each month in Germany in 2003 a) night (3:OO a.m.)

1

2

3

b) day ( 1 1:00 a.m.)

4

5

6

7

8

9

101112

1

2

3

4

month

5

6

7

month

Fig. 4 Load ex- and imports on the third Wednesday of each month in Italy in 2003

8

101112

From Figure 3 can bc secn that in Germany at night (3 a.m.), power cxports of 10 GW have already been effected. and in the morning ( 1 1 a.m.), power imports of -8 GW have already been reached. Similarly Italy, as describcd in Figure 4, purchases 6 i 7 G W day and night in most of the months. Also power imports of up to 10 GW should have been occurred occasionally. In this contcxt, thc load-dcpcndinghighcr dcmand during the day is balanced out in Italy by employing pumped storage power from hydropower stations with nightly pumping capacities u p to 3 GW. Due to this ongoing development, limitation control procedures arc requircd in powcr systcms, too. Thus an installing of additional powerful transmission lines will not be realizable in foreseeable time, due to environmental and recently also economical reasons, and scheduled power transits cannot generally be reduced as for liberalized market reasons.

2. EXAMPLES FOR ALREADY IMPLEMENTED I ,IMITATION CONTROI, PROCEDURES The following examples shall illustrate the importance of already implemeiited limitation control procedures for the reliability of the electric energy supply.

2. I Power Plant Limitation Control As "the pouer plants are the actuators of the povler systcm". the individual power plant units are mostly operated during the whole day at the upper limit and. at night, often at the lower limit of their duty range. see Figure 5a. So, on the power plant side, numerous limitation control proccdurcs havc alrcady bccn implemcnted. comp. the separate I&C function "limitation control" in Figure 5b. The necessity of such limitation control measures is, among others. verified by VDIIVDE guideline no. 3500 published

in German already in 1996 and overtaken as TEC Technical Report in 2002.

2 I I Limitation Control for Steam Boilers and Turbines For economical reasons, fossil-fired and nuclear steam power plants are operated in the case of high system load at nominal power if ever possible. Thus also the live-steam is produced at as high pressure as possible. i.e. near the plant's upper limit. see Figure 5a. To prevent that, in cases of a sudden increase of the live steam pressure pD be it through increased throttling in the case of network disturbances with surplus active power or also through internal power plant malfunctions with excess heat flux overpressure protection devices do respond, modern steam pomer plant uniti are employed with overpressure limitation control, see Figure 6. centre. By means of this procedure excess steam is conducted into the condenser via the high-pressure steam b y p a s station (VDl/VDF, 1996; Welfonder, 1992: Sattinger and Welfbnder, 1993). ~

Correspondingly, at off-peak load the power outputs of fossil-fired steam power plants are often run down as far as possible. In this case. minimum load limitation control makes sure that the load does not fall below the lower limits, such 0 referring to live-steam pressure and feedwater flow (=' to ensure a still sufficient flow through the numerous heating surl'ace tube banks), and 0 referring to the fuel flou (=> to ensure a still stable combustion in the furnace), see Figure 5a "Lower Limitation Range". Uy this way. a response of the relevant protective equipment is avoided at low load operation (VDIIVDE. 1996). In addition. steam powcr plant units. to prevent excessive thermal stress in thick-walled construction components, may be started up and shut down on14 with definedload change rates. For these reasons also suitable limitation control procedures are applied, cf. "Limitation Control at StartIJpiShutdown" in Figure 5a and velocity limitation in guiding function for the reference power output" in Figure 6. top.

a) Lood dependent operotion oreos and I&C functlons of power plonts 3 wiih typical opemiion points

.Frequency voltages PrernureP

. Temperotvre~

of steam power plants

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9

b) Interaction of the different l&C functions

[7

normally 380kV down to less than 50% the high-voltage transmission (Zimmermann. 1990).

I90 k V in network

Also. the blackouts occurred in vast areas of the LJSA and Canada (14 Aug. 2003). as well as in Scandinavia (23 Sept. 2003), were caused by power line di\connections mainly due to reduced boltage at high load flow (UCTC. 2004; ETG. 2003). In this context, the inciease ofthe load flow is caused on the one hand by the fact. that after some generators had broken down, the missing acti\ e and reacti\ e power has to be provided by other, partly far distant system areas. On the other hand, with decreasing voltage on the high-voltage side. the current flows in thc high voltage transmission network increases because without appropriate countermeasures - the voltage on the low voltage side and therefore the power demand remains constant due to the re-adjustment of the tap changer transformers within the distributing nctworks. A pre-condition for the applicability of this limitation control measure on the generator side is that the machine transformers will be equipped with step changers. rhis additional actuation possibility is normally given in the case of feeding-in of large generators to the German high-voltage network. In

'G,dei "!

I

-

I Fig. 6 Overpressure limitation control in fossil-fired steam power plants =>Opening ofswitches S, and S2i f p > 1;

the other case, as soon as i, = i, is reached, a stepping up of the transformers on the distribution sidc is required which causes a decrease of the inductive power demand. Should this not be sufficient, motors have selectively to be taken out of service. i.e. a regional inductive load shedding has to be activated by means of limitation control (=> opening ofswitch S4 in Figure 7).

2 1 2 Limitation Contipol for Generators At high load generators are mostly operated mith high overexcitation due to high reactive power demand caused by motor load\ m d heavily loaded transmission lines. In order that in cases ofpoucr system incidents, such as dropout of one power plant unit. the overexciting protection depices of neighbouring power plant units do not respond additionally. the larger generators in Germany have already in the 1990s been equipped with excitation currcnt limitation control. Due to this in the case of limitation control activation the respective excitation currcnt gets adjusted to its allowable upper limit value. u hile the generator voltage and depending on that the auxiliary voltage is kept on its setpoint by appropriate atepping down of the belonging machine trarisrorrner, s. Figures 7a and b. Due to the decreasing voltage on thc uppcr side of the machine transformer5 and thus in the highvoltage network the motors in the distribution systems need less reactive power. I'or retaining this effect - as accompanying procedure - the tap changer transformers on the distribution side have to he blocked temporarily (Welfonder. 1992; Zimmermann, lYYO), s. Figure 7c. c3 This excitation current limiting procedure substantially helps to restrict the danger of possible voltage collapses. Thus such a voltage collapse occurred in 1988 in north-western France when in the Normandy. after the failure of one power plant unit. numerous adjoining units were overloaded themselves by trying to keep their voltage and were due to this shut down one after another. like a domino effect. I his resulted for several hours in a drop of the nominal voltage of

a ) Hiah voltaoe transmission svstem

A

L

380 k V I

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380 k V

c ) Load port system

Fig. 7 1 imitation procedure referring to the generator: - Change-over of controller K,, to i e limitation control - Change-over of controller Ru2 to control the generator voltage UG and - Blocking of controller Ru3

10

,

Correspondingly, for regulating the line voltage rising at low load - compensation coils are automatically switched on as soon as the respective generators reach their lower excitation level. This limitation control mcasurc has already been state of the art in system operation for many years.

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2 2 Low Frequency Limitation Control

Stme 2

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It is within the scope of the transmisvion system

operators to provide sufficient spinning resen e power in order that the drop of the \).\tern frequency remains within the allowable range of control - also in case of the maximal power outage taken into account (VDN. 2003). Should these boundarj conditions fail. be it because of insufficient reserve power, or a suddenly occurring great deficit i n active power - such as through the breakdown of entire power-generating areas within the interconnected system - or in case of high overload in a systcm area after sudden separation from the interconnected power system stagcd load shedding comcs into forcc as a limitation control measure to avoid a too great frequency drop, s. Figure 8. All partners of power \ystem\ habe already decades ago accepted this low fiequencg limiting measure as an urgent necessity to prevcnt the separation of power plants at f I 47,5 HI from the grid and due to this \ystem blackouts (VDN, 2003).

Stme 3

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Fig. 8 5-stage plan for low l‘requency dependent load shedding regulations ofVDN (2003), UCTE

Therein the protection mechanism can e.g. be activated by delayed response 01’ installed overcurrent relays or through an increased sagging of thermally overstressed high-voltage power lines, which in turn on touching tree tops for instance cause disconnections by earth fault or short-circuit. Such a direct or indirect diwmnection through an overloaded transmission line can have in consequence the overloading and disconnection of further transmission lines and hence cause the separation of s> stem areas or even the break-down of the entire power system. Thus the blackout in ltaly (28 Sept. 2003) was caused by high-level power transits (UCTE, 2004: ETG, 2003). -

3. LIMITATION PROCEDURES REQUIRED FOR SYSTEM AREAS WITH HIGH POWER TRANSITS

To

prevent the protective disconnection of overloadcd transmission lines and consequently the weakening o f the transmission s j stem limitation procedures are requires a1 least in syslem areas with a high and thus specifically directed power transit, cf. Figurc 9. n

Active power flow Reactive power flaws

141

ALine voltage angles

IAg,

Voltages and

f

Frequency

Generator powers

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Consumer loads

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Peak off load

I t Peak load

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Fig. 9 Load-dependcnt normal. borderlinc, and risk ranges of high-voltage lines and high-voltage transmission system => Minimum limitation ranges referring to voltage U and frequency fsee Fig. 5a

11

3. I 1,oadKurrying Capabiliw qf Transmission Lines

High- Voltage

The capabilitj of transmission power lines to carq load, depends on the one hand on weather effects such as outside temperature and wind speed. see Figures 10a and b. On the other hand. it is dependent on the topography "Ilere. we have lowland uith fields and meadows and. in consequence, welldefined conductoriground distances, and there are mountainous landscape with inaccessible forests and gorges and therefore highlq variable conductoriground distances.". The minimum vertical distances to treetops to be kept in the case of 380kV high-voltage power lines are according to EST1 (2003): 6.3 m for fruit-trees, and 5.3 m for othcr trccs, wherc normally nobody will climb up. According to the German standard DIN 48204 thermal limit values for the mavimum currentcarrying capacitq of typical conductors were established. in dependence of specified parameters for weather and power line conditions. see state values on grey background in Figure 10 (Hutte, 1988), as well as for compulsory conductoriground distances. These current limits are associated with corresponding thermal limit values for the various voltage levels. Ilo\+ever. as these limit values were cstablishcd fix a vcry wmmcry ambicnt tcmpcraturc of 35" C, the! may be cxcceded also stationwill, at least in winter months. cC Figure lob. The same i s true for the mid-span sag of transmission lines depending on load flow and weather conditions. Therein the sag is mainly influenced by the conductor temperature. In order that this temperature does not rise too high, the respective allowable maximum thermal load should not be exceeded if

an) possible. Thus the 380kV "San Rernardino" power line from Switzerland to Italy was "heated up" to ullne= 103" C, due to excessive north-south load flom (at Ion wind speed of vw = 0.6 mis and night air temperature of u,,, = 12" C). As a consequence. a greater mid-span sag up to Ah = 3 m ( ! ) occurred (ESTI, 2003). Independent from the general specifications, pointed out above concerning the load-carrq ing capability of high voltage transmission lines. each qyytem operator has to specify within his congestion management the maximum loads. which the individual transmission lines may bear depending on weather and landscape and based on this to which values the relevant monitoring and protection response criteria have seasonably to be set. These place- and time-variant limit \ alues should also be tahen as the bmis for parameteri~ing additional limitation control measures.

3.2 Two-Step Procedure For the activation of the respective necessarj limitation control measures, a staggered two-step procedure can be applied. This is possible because of the delayed thermal effect of power overload. In the first step, as soon as the allowable transmission load is exceeded, the fast bottleneck management gets promptly activated (Rrauner. 2004). This means that - starting out from the (n-1) calculations of reliability which have already bcen done the day before as part of the day-ahead congestion forecasting (Reyer and Weis, 2004: Zimmermann. et,al., 2001) - the transmission system operators concerned check which limitation control measures are adequate to reduce the excessive b) Decreasing outside temperature aumg

a) Increasing wind speed Vwlnd

uG

5

-

15

20

25 m/s 30

-19 0 10 20 30 35 10 'C 50 0,6 4, Fig. 10 Increase of the continuous current-carrying capacity of conductors, here: Al1St 265135 mm2 (DIN 48204) 10

Gins

-

12

Concerning the latter limitation control measure. uncritical consumers have to be shut down where possible, which means e.g. - in case of providing appropriate ripple control s> stems - temporary disconnections such as switching off washing machines and dish washers in households, reducing pumping and fan capacities in the supply engineering sector. and taking out of operation industrial plants with intermediate storage capacities, foreseen within the operation flow of production andlor manufacturing factories.

transmission load to the allowable reference power value and this as well as in a fast as well as supplyand cost-effective way. Iiowever should no countermeasures have been taken or measures taken not succeed within a specified yaiting time of e.g. Tu = 10 min, in the second step the automatic limitation control responds without any hrther delay.

3.3 Possible Limitation Control li4easures a) Load Flow Shgt In the case of highly different loaded transmission lines taking part in the transit, load flow shifting provides an effective solution and thus the possibility to reduce the exce\sive tran\mission load by means of cross regulators and corrective switching actions to increase the effective transmission impedance. As far as available also FACTS can be used for correqmnding load flow shifting rhe\e measures, already widely used within the framework of daq -ahead congestion forecasting. are especially effective when the special action is taken in a wide range and thus spreading control Lones.

The setting criteria for the required load shedding in each case have to be specilied a priori. This may simply be done in such a manner that overloaded transmission lines become sufficiently relieved by switching constant high amounts of load. However, such a simplified procedure to be always on the safe side. usually results in excessive load shedding. For this reason. it will he better to start out from calculations of load flow and (n-I) reliability carried out each time the day before as part of day-ahead congestion forecasting. Building up on this. the setting criteria for the respective necessarq load shedding can be specified online. varying in place and time e.g. by an hourly period split, depending on the predicted power transit and the respecti\ e network structure.

b) Reduction of Power Transits IT the excessive transmission load cannot be reduced sufficiently by load flow shifting, the only possibility that remains is to reduce the transit power correspondingly. Ihis should - if possible - be done on both sides. i.e. not only by the power importing netu orks, but also by the exporting networks. in the latter case through reducing the generator output concerned. The required import power can be reduced in various ways. taking as an example the power import for Italy; thus by: increasing the generation output of "highei -cost" pouer plant units which are not yet turned up to full output (if'possible). putting into operation quick-starting gas turbines (if possible). rising the power output of storage power stations in the case ofturbines operation (ifpossible). or stopping storage pumping operation (if being active) and going over to turbine operation, or last but not least by load reduction in the power importing network. All of these measures can - if applicable - be taken manually within the framework of f a t bottleneck management.

Figure 11 shows as an example the reduction of the transmission flows to Italy for the case of load reduction of 3 GW. I his value was chosen because in Italy up to 3 GMI of industrial supplies can be shed by remote control. An additional reason was that, at the Italian disturbance. in spitc of extremcly high import 3 GW power were still needed for the pumping operation during night time m ithin storage power stations. As to be seen in rigure 11 a) from data uritten in straight characters - in the case of load shedding as evenly shared as possible - the load flows on the 380kV transmission lines to France and Switzerland, decrease by AP = 400 MW each and, on the respcctive 220kV transmission lines. by AP zz 90MW each.

3.4 Automatic Limitation qf Power Transits In case the fast bottleneck management measures do not take effect at all or not in time. the only actions remaining for the automatic limitation control are the shut down of pumps operated in storage power stations - if possible - and otherwise or in addition regional load shedding, and this immediately after exceeding the foreseen waiting time of e.g. Tw = 10 min.

b) P , v p l m r i s!-eridrng in !\of+* l r d j a ) Load s h e d d i r g evenly sha-ed 1 7 Italy

Fig. 11

13

Load reduction on the transmission lines from France, Su itzerland. Austria and Slovcnia in casc of CAP\, = -3 CW load shed in Italy

O n the few - higher loaded - transmission lines to Austria and Slovenia, load tlou changes are up to 1.5 times as high. In Figure I1 b) the corresponding behaviour is shown - by the data writtcn in italics - when 3 CW of pumping capacity are switched off regionally. here in Northern Italy. As can be seen from the diagram no essential load flow change occurs. due to the specific longitudinal structure o f the Italian transmission network. As to be seen. the transmis5ion lines toward5 Frdnce are unloaded by about 10% more and in consequence the other transmission lines correspondingly less so. The calculations made are based on a detailed model ol' the European interconnected power system (Kurth and Welfonder. 2005).

4. SUMMARY 1 or economic reasons. power stations are mostly operated at the limits o f their respective normal operating range. As liberalization of the electrical energy market increases, high-voltagc transmission lines partlj are operated eien at the limit of their transmission capacity. In order that these capacities in cases of raised actual load, p o u e r plant outage or failure of transmission line -are not taken out o f service by overload protection or because of cascading fault?. it is nccessary to provide for limitation control procedures also o n the side o f the network. In the case of suddenly occurring transmission bottlenecks these procedures have the task to limit power transits superimposed to the normal interconncctcd systcm opcration to thc allowable maximum. This is done bj automatic decreasing of generator output in the exporting network section o f the intei connected powei systcm and by correspondingly increasing the generation of more expensive power units or if that is not posyible bq appropriate load shedding in the importing network section. Such mostly regional load shedding seems legitimate becauce by thih way the blackout of network sections or even the entire network system can be avoided. Then the (n-1)-reliability of normal system operation must not be impaired by superimposed high load transits. So in bottleneck situations. high load tranyits arc only possiblc to limitcd cxtcnt and thus only with reduced reliability. Due to the slow thermal effect of line overloads. the limitation control procedures - also considered absolutely necessary within the high-voltage transmission sqstem - need not respond spontaneously. but after a certain waiting timc of c.g. 1 a = 10 min. Up to this time it can be tried by means of fast bottleneck management, to activate appropriate countermeasures manually.

5. REFERENCES

,.Engpassmanagement und Intra-DayEnergiedustausch". 15.-16. Juni 2004, Miinchen. DIN 48204 ,,Leiterseile; Aluminium-Stahl-Seile" EST1 (2003). ..Berich1 des Eidgeniissischen SLarkstrominspektordtes zum Ereignis vom 28. September 2003 (Strompanne in ltalien und in schweizerischen Grenzregionen)". ETG (2002). Freileitungsnorm in neuer Gestalt EN 50341 (VDE 0210). Vortriige dcr ETG-Fachtagung vom 15. bis 16. Mai 2002 in Wiirzburg. VDE-Verlag. ETG (2003). ETG-Task-Force ,,Blackout", Nov. 2003. Iiiitte (19%). Taschenbuch dcr Technik: Elektrische Energietechnik. Band 3, Netze Springer-Verlag Berlin Heidelberg New York. Kaupa, H. und E Pokorny (2004). Nelztopologie und Abhilfe ,,Seilakt ohne Netz". Internationale Dreiliinder-Tagung D/A/CH 2004 ,,Engpassmanagement und Intra-Day-Energieaustausch. 15.16. Juni 2004, Miinchen. KieBling, F., P. Nefzger und U. Kaintzyk (2001). Freileitungen, Planung, Berechnung, Ausfihrung. Springerverlag. Kurth, M. and E. Welfonder (2005). Oscillation Behaviour of the Enlarged European Power System under Deregulated Energy Market Conditions. Control Engineering Practice, Special Section on Power plants and Power Systems Control, Volume 13, Issue 12, pp. 1455-1558;December 2005. Reyer, F. und 0. Weis (2004). Day-Ahead Congestion Forecast. Internationale Dreilander-Tagung D/A/CI I 2004 ,,Engpassmanagement und Intra-DayEnergieauslausch'. 15.-16. Juni 2004, Munchen. Sattinger. W and E. Welfonder (1993) Control Behaviour of Isolated Part Power Systems after Separation from the Interconnected Grid. 1111i PSCC. Aug 30 - Sep 4, 1993, Avignon, France. Schnug. A. and I,. Fleischer (1999). Components for Electric Europe - A chronicle of electric interDVG Deutsche connection in Germany. VerbundgesellschaAe.V., Heidelberg. UCTE (2004). Final Report of-the Investigation Committee on the 28 Septemher 2003 Blackout in Italy. U C I E (2005). http://www ucte.org/statistics/exchange/ e-default. asp VDI/VDE ( 1996). Richtlinie 3500 ,,Begrenzungsregelungen in konventionellen Damplkraftwerken-, September 1996. Transferred in IEC Tcchnical Report 62140-1 ,,Fossil-fired steam power stations - Part 1: Limiting controls", 2002. VDN (2003). Transmission Code 2003: ,,Network and System Rules of the German Trdnsnlission System Operators'.. VDN, Berlin, August 2003 Welfonder, E. (1992). Constrained Control Concepts in Power Plants and Power Systems for Avoiding Emergency Conditions. IFAC-Symposium Symposium on "Control of Power Plants and Power Systems", 9.-1 I. March, 1992, Munich, Germany. Welfonder, E. (2000) Unbundling and Safe Operation of Power Systems - Solutions for the Practice. IFAC Symposium on "Power Plants & Power Systems Control 2000", 26.-29. April 2000, Brussels. Ziniiiieimani. H (1990). Netzzus~iiiiieiibrclieaufgrund von Blindleistungs-Mangel oder -herschuss. 2. GMAETG Fachtdgung "Netzregelung", 22.-23. Mai 1990, Baden-Baden VDl Berichte 801, S 79-88. Zimmermann, D., K. lmhof and M. Emery (2001). Modular Day-Ahead Congestion Forecast as a first Step of a Congestion Management Process. 1st Balkan Power Conference, BPC 2001. Bled, SLOVENIA

Brauner, G (2004) Ursachen von Engpassen Internationale Dnelander-Tagung D/A/Cl-1 2004

14

6. ANNEX: LOAD DEPENDENT MID-SPAN SAG OF CONDUCTOR LINES In the following the correlation between loading, heat-up and sag of conductor lines are pointed out with the example of a simplified assessment. The study is done with the example of the 380-kV power linc "San-Bcrnardino", which was thc sccond to break down due to overload during the power failure in Italy. According to the Swiss fault report (ESTI, 2003) the lines concerned consists of double-bundle conductors and was loaded with I = 2703 A after the preceeding failure of the first power line called Lukmani er . Ihe necessary parameters and state variables of power linesare compiled in Tables l a and 2. The data - as far as not already published in ESTI (2003) - were put at our disposal by &!ktrzzrtutJGescllschaft I,azifenburg (Ctl). the operator of the high-voltage power line. and by the Lumpi Company (A), the high-voltage power line manufacturer. AI

Equating thc power output relations (1) and (3) and solving - taking eq. 2 into account the power line temperature results in general form to ~

1 + l 2 -R,,,

(l-pth 20°C) n (4) 1 anlrd + 1 2 - R L 2 0 Bth n and with the data according to Table l a to QLllJ,n,Stgt = 84" c. By substituting 9, in eq. 2 , the power loss per conductor and kilometre results to PLloSs= 269.5 kWikm.

annd9,

9,

=

h) Determination of the surface coefJicient The authors have determined the surface coefficient - to be given in eq. 4 - by equating eqs. 1 and 2 and wlving to

Heat-Up of Conductor(s)

a) Calculation Procedure

The power losses occurred for each double conductor line along the high-voltage power line of the length 1 are

K ' , ( 9 L ) = R ' , ( 9 L = 2 0 0 C ) ~ [ 1 + ~ t ~ ( 9 L - 2 0 0 C(2). )]

For each conductor line. this power loss has to be dissipaled 10 [he environmenl in the Corm ol' waste heat

84" C for the San Bernardino power line, cf. Table 1 .

2703 A

horizontal distance

I between towers

current resistance (at 9 I T =20"C) 0.0036 liK resistance (jth increase as a function of temperature conductor 9, Result of eq. 4 temperature ambient tempcraturc

0.0036 l/K

Table 1:

d

30.6 mm

22.4 mm

n

2

1

W

a

I

I

vertical differcnce of b tower height I conductor cross IA section modulus ol'elasticity E

1-

conductor diameter wires per cond 11 cto r wind speed surface coefficient

Based on the example case referring to the allowable maximum thermal load (Hulle. 1998) considered in Figure 10. taken as a basis in that figure, a surface coefficient of a - 19.6 W/(m2K) results. when substituting the state variables and parameters of the power line according to I able 1b. This value was taken as a basis for the above calculation of the power line temperature 9LlUn,Sts -

conductor weight per meter weightlmass conversion factor thermal conductor expansion factor conductor line tcmperature

0,6 mls I 0.6 m l s 19.6 W/(m2K) (see eq. 5)

Table 2:

Electrical and thermal conductor line parameters and state variables

15

393 m

I

100 m

I

550 mm'l 57000 N/mm2

m

1.514 kg/m

E

9.81 Nikg

cth

2.3,10-5K-'

9 L2

103OC

Mechanical conductor line parameters and state variables

c) Comparing Consideralion The h m p i Co. determined a power line temperature of 9 , "mp, = 103" C bq special calculation program

(ESTI. 2003). taking into account further influencing parameters. which do mainly actuate variables concerning heat transfer. Thus in the calculation, for the emission coefficient that depends on the extent of darkening on the wire surface, a mean value of y = 0.55 (for an oxidized conductor of average dirtiness) was assumed (for new. shiny conductor lines the value that holds is y = 0.09 and for blackened conductors exposed to weather for many qears the value is y = 0.9). By correspondingly increasing this - not quite exactly speciliable coefficient. the values determined under eqs. 5 and 4 would result as well. The reason is that the effects of the other parameters. such as wind direction and solar radiation. can be neglected in the considered case of predominantly low w ind speed (w = 0.6 mis) and at night (3 a.m.). A2

Increased Mid-Span Sag of Conduclov Lines

The following shows, again with the example of simplified mathematical relations. based on ETG (2002) and KieDling (200 I), how the higher sag of a conductor line Af, - increasing by rising conductor temperature 9, - can be estimated. This estimation i\ b a x d on the power line i conductor temperature 9, = 103" C calculated by L u m p and on the data in Table 2. Regarding the different line clearance from the ground, the conductor length y ields to

dm=

a,, = 405.1 m (6). This corresponds to a ground incline of b cp = arctg - = 15.9". a I he horizontal tensile force H2 at 9,, = 103" C can be calculated by means of the conductor state equation according to KieBling (2001). eq. 14.36. In standardired form with h, = H,/H1 this equation results to h2-1 = B/h?-(B+C) (7) a) Variant sag of a conductor line

f

=

I-(],,

IY,

W,

Therein the belonging coefficients are: E A (a . m .g) EA B= .c=--c th (9 L2 -'Ll) 24H: H1 By iterative solution of eq. 7 the tensile force H2 results for 9,, = 103" C to 1H2 = h2 HI = 0.885 . 17355 = 15363 N According to KielJling (2001), eq. 14.9. the midspan sag ofthe conductor results b)

and. for the tensile forces HI and H2, amounts to fS2 = 19.87m at 9,, = 40°C fs 1 = 17.59 m at 9, = 103" C Thus the increa5e of sag amounts to AfS2,,ISt3t = 2.28 m In comparison to this, the increased mid-span sag of the conductor line determined by EGL by means of a detailed calculation program according to ESTI (2003) amounts to: Afs2 IIEGL = 2-96 m The difference of good 20 per ccnt between the t u o calculations are mainly caused b j the simplified assumptions made by the authors: parabolic sag o f a conductor line, calculation of the conductor length as a function of the different line clearance from the ground according to simplified Pythagorean relation, regarding of only one conductor between two towers. i.e. neglecting the interferences by neighboured conductor sections, neglect of possible thermal deformations cffects.

A3

Resume

The objective of the above simplified but therefore easily understandable calculations is on the one hand to demonstrate the essential physical correlations, on the other hand, to point out the high parameter dependence of the individual results.

H, ...-

a)

..--

' ---. '

ILi Llrnit load, / -

tower " i f ? "

b) Security distance of 380-kV lines: tower

",'.

1.0 = 6,3 rn :o : ~ L I L trees = 5,3m :o other :lees

Fig. L1: Basic illustration of the sag of conductor lines

16

Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLlCATlON$ SISO EXTENDED PREDICTIVE CONTROL - FORMULATION AND ROBUST ANALYSIS Ma'moun Abu-Ayyad and Rickey Dubay Department of Mechanical Engineering The University of New Brimswick Fredericton, New Brunswick, Canada

Manioun.AhuAyyad~unb.ca,[email protected]

Abstract: A new predictive controller is developed that represents a significant change from conventional model predictive control (MPC). The method termed extended predictive control (EPC) uses one tuning parameter, the condition number (CN) of the system matrix to provide a easy-to-follow tuning procedure. The control performance of EPC is compared with the original move suppressed and recently derived shifted predictivc controllers, with improved rcsults. Copyright 02006 IFAC Keywords: Modeling, Simulation, Control Methods, and Real-Time Operation.

to industrial plants. One of the major problems of the existing MPC controllers is the limitation on the use of nu >2 which could lead to undesirable closed loop response oscillations in the plant output. In order to overcome the problem of providing fast closed loop responses, larger values of nLican be used.

1. INTRODUCTION

Several algorithms of model predictive control (MPC) havc been established as bcing important and useful methods of advanced control in industry (Cutler, 1980; Gupta, 1987; Morari, 1993). These applications of MPC in industry can be found in (Garcia, 1987; Meadows, 1997; Morari, 1993). The reason of their popularity in the industrial and academic world is that MPC offers a good relationship between simplicity and performance.

Previous investigations have attempted to improve thc closcd loop rcsponsc by focusing on lowcring thc CN of the system matrix without considering the effect of the determinant of the system matrix (Dubay, 2004; Shridhar et al., 1997). Also, lowering of the CN in these investigations did not account for the influence of the control horizon. This work focuses on developing a new control strategy that can be applied to control a wide range of processes such as servo valve control circuits requiring high-speed in power plant systems.

Tuning of constrained and unconstrained singleinput single-output (SISO) and multi-input multioutput (MIMO) MPC have been addressed by an array of researches. Cutler proposed a systematic trial-and-error move suppression tuning procedure (Cutler, 1980). Simplified Predictive Control (SPC) was proposed by (Gupta, 1987) in which the error is minimized at one point on the prediction horizon and only one control move is calculated. The drawback of SPC is that by restricting the control h01'kon to one the closed-loop response can become unstable if the number of unstable modes in the process is greater than one.

2. EXTENDED PREDICTIVE CONTROL 2.1 Initial Consideration

The general predictive control law is based on the solution of a quadratic cost function which is formulated as a least-squares problem with weighting factors on the manipulated variable moves (Dougherty, 2003)

An analytical expression for move suppression coefficient 2 was derived by Shridhar et al. (1997). The proposed method by Shridhar and Cooper still involve an iterative procedure to determine the optimal value of the CN. The most recent work on tuning MPC was done by Dubay et al. (2004). Here, the second column of the dynamic matrix A is shifted downwards by m>l, where rn is thc shifting factor, followed by the same for subsequent columns. Beside the restriction of using n , = 2, shifted DMC demands very good understanding for its application

min J = [e - AAu]' [e - AAu]+ AuTWo,(/ Au ( I ) ALI

In Ey. (I), e is the vector of tracking difference between the reference trajectory and the prediction of the process, A is the dynamic matrix, Au is the vector of manipulatcd variablc movcs, and thc paramctcr W,,," = LI, where A is move suppression coefficient. 17

The closed form solution of the unconstrained MPC law without weighting on A'A is (Marchetti, 2003)

3. ANAT,YTICAI, OVERVIEW

In this section, a mathematical formulation for the determinant and the CN for A] and A2 as a function of n,, and 1 are presented for suppressed MPC and EPC. It is assumed that the plant to be controlled is a first order plus dead time (FOPDT) model with a process gain K,,, time constant t and dead time 0, with a transfer function of the form

2.2 Extended Move Suppression

The formulation of the new control strategy begins by introducing a ncw wcighting movc supprcssion matrix W,,,, of the form

r o

-

41

-

The system matrix ArA in MPC can be approximatcd as follows (Shridhar, 1997) By introducing the error vector 2 = e - AAu in Eq. ( I ) , the general form of the cost function with W,,,,, is

A'A=K;

a,)= P - k

a,,= A , =a,, ~ =... Furthermore, it is necessary to reduce the number of move suppression coefficients in Eq. (3) that are necded to be tuned. Another stipulation is that the diagonal elements of W,,,,, should have the same increasing effect on I A'A+ W,,,,, I. At this stage, the EPC structure of the W,,,,, matrix is designed to have 3 parameters R I , R2 and d for any (nu 1 3). Thc W,,,. matrix using these parameters is now termed WkIMS where the subscript EMS is extended inove suppression. Consider a control horizon of n,,=5, the weighting matrix WE,Ms is

0

-R,A

-A

-R,A

-A

a21

a22

.

.

... .

where

The paramctcr P in Eq.(4) is thc prediction horizon. To achieve fast response with minimal oscillations, Au must be evaluated from a well conditioned systcm matrix. In order to increase M'A+W,,,J to obtain lower values of the CN, it is assumed that the even elements of the first row of W,,,,. are equal.

[

l

1

32 --+3--(z 2T

1

2

.

+ J .)

i,j= 1,2;..,n, (8)

The parameter k is the discrete dead time calculated as k=O/T+I, and T is the sampling time. Marchetti et al. (2003) showed that the AA ' matrix is singular when n,>3. Therefore, it is assumed that a5 the prediction horimn P-m, q I E q2E . .. . 3.1 Move Suppressed MPC

A general expression is needed for IA,I as a function of 1, nu and a, where a is the first element of A'A ( a = K : a , , ) . T h e A I matrixfornL,=2is

L

J

The condition number can be computed by dividing the largest singular value over the smallest singular value. 'lhen,y - g + l (where y is the CN). As 4

2-q

-

/z

yA, + 1 . This is impractical as large values

of 1 can result in very undesirable sluggish plant dynamic responses, even though

For clarity, define A, = A'A+W,,l,,, A2 = AIA+W,,,, and A3 = A'A+WbM5 which will be all used in the following section.

yA,is unity.

3.2 Neb!Move Suppressed MPC The analysis is repeated for the new extended move suppression matrix as shown in Eq. (3).

18

2a 1 . As /1 >a,yA, - 1 . This R implies that unity CN can be reached faster than the old structure. The general expressions for the determinant and CN for move suppressed MPC and EPC are given in Table 1. Similarly,

rA,

-

results shown in Fig. 2 were obtained from the dynamic matrix of a FOPDT plant with unity gain, time constant and dead time. Figure 2 shows that increasing R, while maintaining a constant value of1, a relatively lower CN and higher determinant can be achieved simultaneously. ',lo[,\!'

'

Table 1. General form of determinant and condition number equations.

'

'

'

'

'

'

'

I

h

Figure 1 shows the approximate and exact CN of A, as 1 varies from 0.1 to I . The result5 were obtained from a simulation for Process 1 (Shndhar er al. 1997)

GI ($1 =

e

-50r

(1 1)

(1 50s + 1)(25s+ 1)

Fig, 2. Importance of the weight factor Rl on the condition number and determinant of matrix A'A.

Exact Table 1

3. EPC ( 4 2 3 )

The determinant and CN of A3 will be calculated in terms of (2, R,, R2)as

01

02

03

04

05

06

07

08

09

1

Move suppression coefficient, h

yA,can be improvcd by eliminating the second

Fig. 1. The exact and approximate condition number of ArA based on Eq. (7) and General Form of Table 1 for small values of A.

element of its first row in bq. (13) by assuming RI1=a. Also, define R2 as R2=rRI,Eq. (13) becomes

The plots based on Eq. (7) deviate from the exact plots for highcr valucs of n?,. Howevcr, the plots based on the general form of the newly developed CN equations in Table I show good agreement with the exact plots. The tuning parameters P=54 and T= 16 arc used in thc simulation.

yA3is obtained by multiplying the no1111

3.3 The Structure ofEPC

norm of (A,<)-' as The analysis is expanded to the EMS structure.

Note that R2 does not exist in Eq. (12) since n,=2. The maximum value of H,ll occurs at = 5. The

4

19

1

of A by the

yA3= I[A3I[llAi' . Then, yA, is

Derive thc cxpression using A , that reprcsents yA3as a function of Y.

To eliminate the contribution of the term R,, select R,>>l. Consider RI=lO,Eq. (15)becomes

Plot yn, vs r using the derived expression and

yA4= l + . \ / r 2 -2v+1.81

(16)

Figure 3 shows the relationship between

superimpose this result with yruic,. From these plots, select the value of r that exists on the overlapped regions of the plots.

yA, and r,

uung the dynamic rnalrix of Proces5 1 and Eq. (1 6).

y[

3)

25-

T

Upto 1502 2"

2

-

t

,

5. SISO SIMULATION CONTROL

UD to

2172

A computer simulation was performed to compare

the propoyed method with the move suppressed and shifted MPC The process used tor compdrisons involved time delay and inverse response behavior (Shridhar et a1 1997)

i5-

n =3 in

G, (s) = "1

-1

"

,

?

5

4

A

7

6

I

and

4. GENERAL TUNING STRATEGY FOR SISO EPC

1

-1

Rl 1

Control Scheme

Tun. Par.

2 MPC rn MPC EPC

I =4 m=21

I

1 r = 3

IA,,,,,

I

Y?i
5.1X10' 1.35X104

76.5

4.1xld

3.2

55.1

Tablc 2. A comparison for diffcrcnt control schemes on Process 2. Figure 4 is simulation results of responses and manipulated variables for the three different control schemes for Process 2. The values of P=l15, T=24 and n,=3 were used in all simulations (Shridhar et al. 1997) for Process 2. Table 2 shows the three different tuning parameters i ,shifting factor m and r.

The main advantage of EPC is that it uses an analytical expression of y-{ A2 ] as a mechanism for tuning by reducing the number of tuning parameters to one. The tuning procedures for SISO EPC are itemized as follows Obtain open loop data from experimental analysis or from analytical models. Using this data, formulate the system matrix A'A with nu? 3. Construct the weighting matrix W,, for any 2 3 as follows values of II, -1

(15)

(100s + 1),

8

r

Fig. 3. A comparison between exact approximated condition number for Process 1.

(1 - 50s)e-'OS

1

4

0

-r

-r

0

-r

-r

0

-r

1 -_

-r

0

Fig. 4. A comparison between EPC with shifted and move suppressed MPC for Process 2

(i, i:1

Figure 5 shows the closed-loop results due to disturbances and set point changes for Process 2. The EPC controller has the ability to handle negative and positive set point changes with zero oscillations. Also, EPC controller rejects disturbances by responding quickly in order to keep good tracking of the set point.

-r

1 Rl

-r

Choose R, such that

p

0

200

400

Mi0

800

10w

1200

1400

1600

Time (sec)

0 . Obtain

the exact matrix Arroo=ATA+WI,w). Formulate the A, matrix using Eq. (14).

20

-

0

500

0


1500

2500

2000

Time

3000

3500

J

4000

(sec)

2

1

3

5

7

6

8

9

10

12

11

Gain Ratio

Fig. 5. Closed-loop simulation results due to disturbances and set point changes (Process 2).

Fig. 7. Kobustness plots lor two dilferent control horizons - Process 3 The region to the right of the lines in Fig. 6 represents the limit ol' stability Lor the predictive controllers. The effect of varying the control horizon, nu,was investigated on robust stability for Process 7. Figure 7 shows an increase of EPC robustness for increasing n , while shifted MPC does not show any significant change.

6. ROBUSTNESS ANALYSIS

Robust stability using EPC is compared with that of the move suppressed and shltcd MPC on SISO process models. The SISO plant employed to investigate robust stability were used by (Gupta, 19x7) and I $

The effect of changes in time constant on the stability limits was studied for Process 3. The simulations were carried at three different values of time constant ratio (Tr). Figure 8 shows the stability limits for the three control schemes when varying Tr. From the robustness plots, it can be concluded that the EPC is generally more robustly stable with respect to tlie parameters' variations in comparison to move suppressed and shifted MPC.

4'

e (10s + 1) "'

G, (s) =

~

The choice of the tuning parameters of the three algorithms was used based on the same value of Integral Absolute Error (IAE) of the closed-loop response for Process 3. The development of the robust plots and analysis arc described in (Gupta, 1987). The prediction horiLon P was set to 128 and the sampling interval as 0.5 to allow a finer variation in the delay ratio. The tuning parameters A=9.4, rn=96, RI=10 and r=3 are used in the simulation in order to obtain identical IAE values (25.1 1).

Shilled MPC

8

-

L A

8

4

6

8

10

12

14

11

Gain Ratio

Fig. 8. Robustness plot for different time constant ratio - Process 3. 0

I

1 2

,

3

1,

5

6

;

Gain Ratio

8

b

2-;

Fig. 6. Robustness plots for tuning parameters Process 3

7. CONCLUSIONS

A new method of predictive control termed extended

predictive control was developed. A major advantage of the extended form is that for the first time, larger

21

control horimns can be utiliLed sensibly and effectively with overall good control performance. Thc main advantage of EPC is that it uscs an exact solution to obtain the optimal range of the CN of the system matrix. Robust analysis demonstrated that EPC IS more robust in comparison of move suppressed and shiftcd MPC.

REFERENCES Cutler, C.R., and Ramaker, D.L. (1980), Dynamic Matrix Control-A Computer Control Algorithm. Proc. JACC; Sam Francisco, CA. Dougherty, D., and Coopcr, D. (2003), A practical multiple model adaptive strategy for multivariable model predictive control. Control Eng. Pructice. 11, 649. Dubay, R., Kember, G., and Pramujati, B. (2004), Well-conditioned MPC. ISA Transactions, 43, 23. Garcia, C.E., Prett, D.M., and Morari, M. (1989), Model Predictive Control: Theory and Practice - a survey Airtnmntira 25, Gupta, Y.P. (1%7), A SimplifiedModel Predictive Control Approach. Dept. Chem. Eng., TUNS: Halifax, Canada. Gupta, Y.P. (1987), Characteristics Equations and Robust Stability of a Simplified Model Predictive Control Approach. Can. J. Chem. Eng., 1993, 71, 617. Marchetti, J.L., Mellichamp, D.A, and Seborg, D.E. (1983), Predictive Control Based on Discrete Convolution Models. Ind. Eng. Chcm. Des. Dev., 22,488. Meadows, E.S., and Rawlings, J.B, (1997), Model Predictive Control. Prentice Hall. Morari, M., and Lee, J.H. (1 999), Model Predictive Control: Past, Present, and Future. Comp. Chem. Eng., 23, 667. Rawlings, J., and Muske, K. (1993), The Stability of Constrained Receding Horizon Control. IEEE Trans. Aut. Control., 38, 1512. Shridhar, R., and Cooper, D.J. (1997), A Tuning Strategy for Unconstrained SISO Model Predictive Control. Ind. Eng. Chem. Res. 36, 729.

8. ACKNOWLEDGEMENT The authors acknowledge the Natural Sciences and Engineering Research Council of Canada for the financial support of (hi\ research.

22

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

ROBUS1 DECENIRALIZEU 11, CONTROLLER DESIGN FOR POWhR SUSI'LMS: A MATRIX INEQUALITY APPROACH USIlcG PARAMETER CONTINUATION METHOD

Cctachcw K. Befckadu and 1. Erlich"

Department of Power Engineering, University of Duisburg-hen, Duisburg 47057,

Germun-y

Abstract: This paper presents a decentralized H, controller design approach for power systems. Initially a centralized H, robust controller, which guarantees the robust stability of the overall system against unstructured and norm bounded uncerlainties, is designed. The problem of designing decentralized controller is then reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized to the decentralized controller as the continuation parameter varies monotonically. Moreover, the paper proposes an algorithm to solve such problem using two-stage iterative matrix inequality optimization approach to determine the decentralized controller. The approach is flexible enough to allow designing a reduced-order controller for each subsystem with the Same robustness condition of the centralized controller. 'The approach is demonstrated by designing I'SSs for a test system. CoDJrighf02006 IFAC

Keywords: Decentralized control, interconnected systems, nonlinear systems, optimization methods and robustness.

prevent disastrous cascading. These controllers systems are usually static, in the sense that they do not adapt to changing network configurations and operating conditions. Additionally, the design and parameter settings of the control schemes do not takc into account the very system dynamic behaviours. Consequently, these and other similar developments prompted both power and control engineers to use new controller design techniques and more accurate model descriptions for the power system with the objective of providing reliable electricity services. Thus, to meet modern power systems requirements, controllers have to guarantee robustness over a wide range of system operating conditions and this further highlights the fact that robustness is one of the major issues in power system controllers design.

The deregulation of the clcctricity markets has led to increasing uncertainties concerning the power flow within the network. This is further compounded by the physical expansion of interconnected networks such as those in Europe, which makes more difficult the prediction of system responses to disturbances and severe loading conditions. Furthermore, the ever - increasing utilization of wind energy is also expected to have a significant impact on the load flows as well as the dynamic behaviour of the system. These further have created new challenges in guaranteeing end-to-end reliability of electricity service. Traditional control principles applied to local components do not take into account the continually changing of the dynamic structure of the network. Specifically, secure operations of current power systems heavily rely on the controller schemes that placed in the system to manage disturbances and/or

Recently, a number of efforts have been made to extend the application of robust control techniques to power systems, such as L, optimization (Vittal, et a / , 1995; Venkataraman, et a[., 1995), H,optiiniLation (Chen arid Malik, 1995; Klein, el ul., 1995), structured singular value (SSV or p) technique (Djukanovic, e/ al., 1998, 1999) and linear matrix inequalities (LMls) technique (Siljak, et a/.,

* Corresponding author. E-mail address: erlichauni-duisburg.de University of Duisburg-Essen, Institute of Electrical Power Engineering and Automation, 47057 Duisburg, Germany.

23

implemented in real-time configurations usually create undesirable effects such as time delays.

2002; Siljak, et al., 2004). Jnteresting robust decentralized controller schemes that are based on the concept of connectively stabilizing a large-scale nonlinear interconnected system for turbine/governor control and exciter control using the LMIs optimization (Boyd, et al., 1994) have been presented in (Siljak, et al., 2002) and (Sdjak, et al., 2004), respectively. However, the designed local state feedback controllers need the corresponding state information of the subsystems, which may be either impossible or simply impractical to obtain measurements of the full information for all individual subsystems. Spccially, thc result presented in (Djukanovic, et al., 1999) uses the sequential p synthesis technique where the design procedure is carried-out successively for each local input-output pairs in the system. Though the individual controllers arc scqucntially dcsigncd to guarantcc thc robust stability and performance of the whole system, the reliability of the decentralized controller depends on the order in which the design procedures for these individual controllers are carried-out. Moreover, a failure in the lower-loop may well affect the stabilityiperformance of the whole system. It is also clear from the nature of the problem that the order of the controller increases for each sequentially designed local controller. Another attempt is also made to apply a linear parameter varying (LPV) technique for designing decentralized power system stabilizers for large power system (Qiu, et al., 2004). The resulting controllers, however, are typically high order - at least as high as the system since the technique relies on H , - optimization; and besides the problem formulation attempts to solve an infinitedimensional LMl type optimization where the latter problem is computationally very demanding. Furthermore, the approach did not consider the entire interconnection model of the power system in the design I-ormulation.

The approach has a number of practical relevance among which the following are singled out: i) designing reduced-order decentralized controllers can be incorporated in the approach by explicitly stating the order of each controller in the specified structure and, ii) multi-objective optimization technique can easily be incorporated in the design by minimizing the H, norms of the multiple transfer functions between different input/output channels. Moreover, the paper also presents a general approach that can be used for designing a combination of any order robust PSSs for power systems. The application of this approach to a multi-machine power system allows a coordinated tuning of controllcrs that incorporatc robustncss to changcs in the operating conditions as well as model uncertainties in the system. The outline of the paper is as follows. In Section 2, the robust decentralized H , controller design problem is formulated as a matrix inequality problem using parameterized continuation method. The associated computational problem and the extension of the approach to design reduced-order decentralized controllers are also discussed in this section. The application of the approach to design robust decentralized PSSs and simulation results together with performance indices are given in Section 3. Finally, in Section 4, a brief conclusion about the paper is given. 2 . OUTLINE OF THE PROBLEM 2. I System model and problem,formulation

Consider the general structure of the ith-generator together with the PSS block in a multimachine power system shown in Fig. 1 . The input of the ithcontroller is connected to the output of the washout stagc filter, which prcvcnts the controller from acting on the system during steady state. Let the structure of this ith-washout stage be given by:

This paper focuses on the extension of matrix inequalities based H, optimization approach to problems of practical interest in power systems. The design problem considered is the natural extension of the reduced-order decentralized I f x dynamic output controller synthesis for power systems. In the design, thc deccntralizcd H, dynamic output fcedback controller problem is first reformulated as an embedded parameter continuation problem that homotopically deforms from the initially full-order designed centralized H', controller to the desired decentralized controller as the continuation parameter monotonically varies. Moreover, the paper proposes an algorithm to solve such optimization problems using two-stage iterative matrix inequality optimization method to determine the robust decentralized H , controller. The paper also addresses the possibility of extending the approach to design reduced-order decentralized controllers that have practical benefits since high-order controllers when

*Y, =

(1)

AOz

After augmenting the washout stage in the system, the ith-subsystem, within the framework of El, design, is described by the following state space equation: i , ( t ) = A , , x , ( f ) + C A , ,x , ( t ) + B , , w , ( t ) + B z , u , ( t ) ti,

(2)

z,(t)=Ci, x,(r)+ D , , , w , ( f ) + D121~ , ( r )

u , ( t ) = C , , x , ( t ) +D , , , * v , ( t )

where

x , ( ~ ) E $ { " J is

control input, z ~ ( ~ ) E ' JisI the ~~

the state variable,

y, (t)t'~iq,

u,(r)E%"'.

is the

is the measurement signal,

is exogenous signal for the ith-subsystem. Moreover,

24

regulated variables, and

W~(~)E'JT',

assume that there is no unstable fixed mode (Wang and Davidson, 1973) with respect to c, = d l d t j { C , , , c , , , ... C > , } , [A,,], \ and 1

B2 =drag{Bzl,B,2,..., B , , )

.

Consider the following decentralized output feedback controller for the system given in (2): L(t)=&,

x,,(t)+ B,, Y , W

Hence, the overall extended system can be rewritten in a compact form as follows. ;(t)=A

(3)

u,(l)=C,, x , , ( t ) + D , , Y ,U )

where x , , ( t ) t W is the state of the ith-local controller, n,, is a specified dimension, and

where

(6)

=0,

- - -

- - -

A,, = A + B , K , C , ,

B,, =B, +B,K,,D,,,

C,,=C, +D,,K,Cb,

D,,=D,, +D,,K,D>,

- . -

are constant matrices to be determined during the actual design step. In this paper, the design procedure deals with nonzero D,, , A,,, B,, , C , , , D,, , i=1,2;.., N

however, it can be set to zero, i.e., D,, ith-local is strictly proper controller.

, x(t)+B,,w(z)

~ (= tC ) ' , x ( t ) +D,,w ( t )

- - .

Considcr the following dcsign approach whcre the controller strategy in (3) internally stabilizes the closed-loop of the transfer function r,,,( 3 ) from w to z and moreover satisfies a certain prescribed disturbance attenuation level y > o , i e , IT,,, (s)Il= < y

so that the

c

In the following, the design procedure assumes that the system in (2) is stabilizable with the same prescribed disturbance attenuation level y via a centralized H , controller of dimension equal to or greater than n, := ~ ~ l inn which ~ T each controller input U, is determined by the corresponding measured outputs y , , 1 5 J 5 N . The significance of

v,,L8, PG 8

w, An n,,th-order

this assumption lies on the fact that the decentralized controllers cannot achieve better performances than that of centralized controllers. In this paper, the centralized fIz controller is used for the initial boundary value in the two-stage iterative matrix inequality optimization method.

Fig. 1. General structure of the ith-generator together with the PSS in the multimachine power system. After augmenting the decentralized controller (3) in the system, the state space equation for ith-extended subsystem will have the following form

- - -

:,(t)= (4+B,, K , C > O % ( f )

+

6, +B,, K , C , , ) w , ( t ) + Z k , x , W

2 2 Decentralized H , outputfeedback controller design using parameterized continuation method

(4)

J*f Y

x

Y

z, ( t ) = ( C , +, D I 2 K , ~

-

c ,Ox, ( t ) + ( D ,

I,

x

+ D,:, K , J),,

M ,( t ) Designing a decentralized H , output feedback controller for the system is equivalent to that of finding the matrix K,] that satisfies an H , norm bound condition on the closed-loop transfer function T,,, ( 7 ) = C , , ( ~ I - A , , ) B ,+D,, , from disturbance w to measured output z , i e IT,,^ (&)I], < y (for a given scalar constant y >O ) Moreover, the transfer functions I,,, (s) must be stable (Gahinet & Apkanan, 1994) The following proposition is instrumental in establishing the cxrstcnce o f decentralized control strategy (3) for the system (2)

where ? , ( T I = [ x i ( t ) x:, (t)f is the augmented state variable for the ith-subsystem and

Moreover, the overall extended system equation for the system can be rewritten in one state-space equation form as x(t)=

(A +B,K,

Proposition. The system (2) is stabilizable with the disturbance attenuation level y > o via a decentralized controller (3) composed of N n,, - dimensional local

c,);(t)+ (B, +B,K,,C,)w(t)

z(t)=(?, +D,,K,,?,

)x(l)+(;,,

t f i , , K , , D , ,) w ( t )

(5)

controllers if there exist a matrix K,, and a positivedefinite matrix 6 that satisfy the following matrix inequality:

where

25

( 2 ) Compute PICthat satisfies

-

@((I

2-1, ) K F + 3-kK

-

, Pi, . Ak )

0

End do

Remark 1: If the problem in Step-I of the above Algorithm fails to be feasible, then the step-length should be changed in order to compute K , , ~ that satisfies 6 ( K r j h,FA-,,A,<)
The condition stated in the above proposition seems to be the same as that of the centralized H , control case (Gahinet R: Apkarian, 1994). However, due to the specified structure on the controller (i.e., designing controllers with "block diagonal") makes the problem an N P-hard nonconvex optimization problem. To compute the optimal solution of this problem, the design problem is reformulated as an embedded parameter continuation problem that deforms from the centralized controller to the decentralized one as the design parameter varies monotonically (Richter & Decarlo, 1983). The parameterized family of the problem in (7) is given as follows: @K,, F,A):=@((l-A)Kl*+AKll,

F) -:0

(8)

2.3 Designing a reduced-order decentralized controller.

with 2, t[o, I ] such that at 2, = O (D(K,, P, 0 ) = @ ( K , , P) < 0

and at A = I

-

-

-


i 0

(9)

The algorithm proposed in the previous section can only be applied when the dimension of the decentralized H , controller is equal to the order of the plant, i e , n, = n However, it is possible to compute directly a reduced-order decentralized controller, i.e., n, < n by augmenting the matrix K, as

(10)

where

is a constant matrix of the same size as K,, and composed of the coefficient matrices A , , B , , C:, and D,; of an n, - dimensional centralized H , for the disturbance attenuation level y . Thc centralizcd can be obtained via the existing controller K, method (e.g., Gahinet & Apkarian, 1994). Thus, the term ( l - A ) K r + A K , > in (8) defines a homotopy interpolating centralized II, controller and a desired decentralized H , controller. Thus, the problem of finding a solution of (8) can be embedded in the family of problems as: &(K,,,p, A) < 0, A E [0, 11 (12) Therefore, the algorithm based on parameter continuation method for finding the robust decentralized output feedback controller has the following two-stage iterative matrix inequalities optimization. Algorithm: A Matrix Inequality Bused Parameterized Continuation Method. Initializa tion Compute the centralize d controller

where the notation * , * * are m y submatrices, and A[, i, , b,,, b,, are the reduced-order decentralized controller matrices Note that the II dimensional controller defined by K,, of (13) is equivalent to the n' - dimensional decentralized controller descnbed by state-space representation of ( A , , B, , D L , ) if the controller and observablc parts are extracted Next, define the matrix function (D(k,,, F, 2) (which is similar to (8)) as

e,,

& K l l , P , A ) = Q ( ( l - A ) K p + h K , l , P) -:O (14) Then, one can apply the algorithm proposed in the previous section with K, of n -dimensional centralized H, controller In this case, at a=o set the

matrix K,, to zero except (2,2) - block - I ,

K ,. and Po that

proceed with computing

K,>"

. !

for each

If the "

guarantees a dislurbanc e alteriualio 11 level y

and "

algorithm succeeds, then the matrices ( 4, , B, , C, ,

Set A,, = 0, k = 0 , A4 = K (Large Numbcr)

extracted from the obtained K O at h i , comprise the desired decentralized 11, controller Dn)

and K,,,, = O (ZeroMatrix)

26

Remark 2: The approach outlined in the previous section considers the problem of designing decentralized controllers for the full-order system. It is also possible first to reduce the order of the system by applying a model reduction technique, and then designing a decentralized controller for the system. 3.

SIMUIATION RESU1,TS

The robust decentralized controllers design approach presented in the previous section is now applied to a four machine test system for designing robust PSS. This system, which is shown in Fig. 2, has been specifically designed to study the fundamental behaviour of large interconnected power systems including inter-area oscillations in power systems (Klein, et a/., 1991). The system has four generators and each generator is equipped with IEEE standard exciter and governor controllers. The parameters for the standard exciter and governor controllers used in the simulation were taken from (Kundur, 1994). Moreover, the generators for these simulations are all represented by their fifth-order models with rated voltage of 15.75 kV. To demonstrate the applicability of the proposed approach second order PSSs are designed, although it is possible to extend the method to any order and/or combinations of PSS blocks in the design procedure without any difficulty. After including the washout filter in the system, the design problcm is reformulated as an embedded pararnetcr continuation problem that deforms from the designed centralized H, controller to the decentralized one as the design parameter varies to its range space. The design procedure has been carried out for the base loading condition of [PI, =I600 MW, Q l , =lSOMvar] and [P,2 =2400 MW, Q L 2=I20 Mvar]. The speed of each generator, the output of the PSS together with the terminal voltage error signal, which are the input to the regulator of the exciter, are used as regulated signals within the framework of the design. Moreover, the output of the washout block, ix., measured output signal, is used as an input signal for the PSS in the system. Area - A

PLI,QII

P I , = 1600 MW QL1=lSOMvar

behaviour after the PSS included in the system The robust decentralized PSSs designed through this ap roach arc also given in Table 1

3 8f

1 c 0 60 50

-0

3 ilc

a.30

- r # ~ t h t?SS control!ers

3.70

IifhouIL PSS controllers

i

rise is]

-9.29

Fig. 3. The transient responses of Generator G2 to a short circuit at node F. Table 1. The robust decentralized power system stabilizers for the system with M = 256 Generator G;

The Corresponding PSS .A'+ 8.2'14 5 + 20.122 ?+14.724s I 29.43 1

s2 I9.bl0 A

s'i-37.050.5

5

A

21.010

+ 22.344

~~+17.704~:22.120 .\'-b37.61 1\+17.862

.s2 I 6.21 1 , ~I 6.508 .\-

+ 1 0 . U / O S T I 1.8.12

To further assess the effectiveness of the proposed approach regarding robustness, the transient performance indices were computed for different loading conditions at node 1 [P,, , Q , , ] and node 2 [pL2,QL2] while keeping constant total load in the system. These transient performance indices, which are used to investigate the behaviour of the system during any fault and/or sudden load changes, are then normalized to the transient performance indices of the base operating condition for which the designed procedure has been carried out. Specifically, these noimalizations are computed according to the following formula: 1, =liii(.

(15)

1,3M

where I,,,. is the transient performance index for different loading condition, I,,, is the transient Performance index for base loading condition for which the design has been carried out. Moreover, the transient performance indices for generator powers (;, , generator terminal voltages v,, and excitation

Area - B

P~2.Qi2

voltages E,,,, following a short circuit of 150 ms

P, 2400 M W Q, =120M\ai 7

duration at nodc F in Area-A arc computcd using the following equations.

Fig. 2. One-line diagram of the test system.

A three-phase fault with different fault durations was applied at different fault locations and operating conditions to verify the performance of the proposed robust PSSs. For a short circuit of 150 ms duration at node F in Area-A, the transient responses of generator C2 with and without the PSS in the system are shown in Fig. 3. This generator which is the most disturbed generator in the system due to its relative nearness to the fault location shows a good damping

I' I i/i'

=c,Zr1j,;: 1 P c ; , V - SY$t = C>I, 1;p,( r ) - V,l;I df c,:,l"'IE,',, E;,( [

=

( t )-

(16a)

(1 6b) (16c)

The nomalized transient performance indices for different loading conditions are shown in Fig. 4. It can be seen from Fig 4 that the indices for I , ( E ~ <,, )

27

I , (4,) and I , (c;) are either near unity or lcss than unity for a wide operating conditions. This clearly indicates that the transient responses of the generators for different operating conditions are well damped and the system behaviour exhibits robustness for all loading conditions.

I E L : , Q L ~ ~ G . O I:.,

:b.o

37.5

59.0

~ : . b

75.0

a1.5

50.n 37.5 75.0 12.5 Load Distributions for [PLl, QLll and IPL2, QL21 in

I P T I , , > ' I I ~ G ~ . O 81.5

75.0

-7.5

Chen S. and Malik 0. P. (1995). [I, optimization based power system stabilizer design. IEE Proceedings Generation, Transmission and Distribution. 142(3), 179-184. Djukanovic, M. M . H. Khammash and V. Vittal, (1998). Application o f the structured singular value theory for robust stability and control analysis in multimachine power systems, Part-I: Framework development and Part 11: Numerical simulation and results. IEEE Transactions on PowerSystems, 13(4), 131 1-1316. Djukanovic, M. M. H. Khammash and V. Vittal, (1999). Sequential synthesis of structured singular value based decentralized controllers in power systems, IEEE Trans. Power Syst., vol. 14(2), 635-64 1. Gahinet, P. and Apkarian, P. ( I 994). A lincar matrix inequality approach to H , control. International Journal on robust and nonlinear control. 4, 42 i448. Cahinet, P. Nemiroviski, A. Laub, A. L. and Chilali, M. (1 995). L M I Control Toolbox. Cambridgc, MA: Mathworks Inc. Klein, M. Rogers, G. J. and Kundur, P. (1991). A fundamental study of inter-area oscillations in power systems. IEEE Transactions on Power Systems. 6(3j, 914-921. Klien, M. Le, X. L. Rogers, G. J. and Farrokhpay, S. (1995). FIX damping controller design in large Transactions on Power Sy.stems, 10(1), 158-166. Kundur, P. (1994). Power system stability and control. McGraw-Hill Inc. Qiu W., Vittal, V and Khammash M. H., (2004) Decentralized power system stabilizer design using lincar paramctcr varying approach, IEEE Trans. Power Syst. vol. 19(4), 1951- 1960. Richter, S. L. and Decarlo, R. A. (1983). Continuation Methods: 'l'heory and Applications. IEEE Transactions on Circuits and Systems, 30(6), 347-352. Siljak, D. D. Stipanovic, D. M. and Zecevic, A. 1. (2002). Robust decentralized turbineigovernor control using linear matrix inequalities. IEEE Transactions on Power Systems, 17(3), 7 15-722. Siljak, D.D. Zecevic, A. 1. and Neskovic, G. (2004). Robust decentralized exciter control with linear feedback. lEEE Transactions on Power Systems, 19(2j, 1096-1103. Venkataraman, S., Khammash, M. H. and Vittal, V. ( I 995). Analysis and synthesis of' HVDC controls for stability of power systems. lEEE Transactions on Power $stems, 10(4), 1933-1938. Vittal, V., Khammash, M. H. and Pawloski, C. D. (1 995). Systems and control theory jor power systems. In Chow, J. H., Kokotovic, P. V. and Thomas, R. J. editors, 64 of Mathematics and its Applications, IMA, 399-41 3. Wang, S. H. and Davidson, E. J. (1973). On stabilization of decentralized control systems, IEEE Trans. Automat. Contr.,vol. 18(5) 473-478.

130.0 0.0

[%I

Fig. 4. Plot of the normalized transient performance indices. Remark 3: The value of the normalized transient pcrformancc indcx I , (.) givcs a qualitativc mcasurc of the dynamic behaviour of the system during any fault and/or sudden load changes. A value much grcatcr than unity mcans that the systcm bchavcs poorly as compared to the base operating condition. 4. CONCr USION

A framework for robust PSS design that takes into account model uncertainties and changes in the operating conditions has been presented. The applicability of the approach has been demonstrated through dcsign examplc in a four-machine tcst system. The design problem is first reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized FI, controller to the decentralized one as the continuation parameter varies monotonically. The corresponding optimization problem is solved using two-stage matrix inequality optimization method. The possibility of extending to design a reduced-order decentralized controller has also been addressed properly. The latter which has additional practical benefits since high-order controllers when implemented in real-time configurations may create undesirable effects such as time delays. Moreover the approach is flexible enough to allow the inclusion of additional design parameters such as the order of'the controller and for each input/output channel in the system. An additional benefit of this approach is that all the controllers are linear and use minimum local feedback information.

REFERENCES Boyd, S. El Ghaoui, L. Feron, E. and Balakrishnan, V. ( 1 994). Linear matrix inequalities in systems and control theory. Volume 15 of Studies in Applied Mathematics, SIAM.

28

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ELSEVIER

~UBLICATI oNS

SELF-TUNING PI CONTROLLER lgor Boiko

1MB Controls, 740 Woodpark Blvd S W , Calgary, Alberta, 1'2 W 3R8, Canada

Abstract: A self-tuning algorithm comprising the steps of identification and tuning is proposed. The methodology of process parameters identification is based on the measurement of the locus of a perturbed relay systcm (LPRS) points from a single or multiple asymmetric relay feedback tests. An algorithm of identification of the first order plus dead time process model is developed in details. Also, a tuning algorithm using the criterion of minimal settling time subject to the overshoot constraints is developed and prcsented in the form of simple formulas for the first-ordcr plus dead time process model. Examples of simulations and application are given. Copyright 6 2006 IFAC Keywords: PJD control, identification, autotuning, relay feedback system, oscillations

informative model nf the occillation\ in a relay feedback system, which would lead to simple calculations suitable to the autotune add-on of a PID controller. The widely used model based on the describing function method (Atherton, 1975) is approximate. Although there exists method proposed by Tsypkin (1984), which offers a precise and comparatively simple model of the oscillations, the real part of the Tsypkin's locus would hardly be used f6r the purpose of identification because it represents the dcrivativc of the output that would makc the tuning algorithm sensilive to noise. There also exist Poincare mapping based models of the oscillations (Astrom, 1995) that would bc used for identification in principle but they are not simple enough for the autotune identification to be a part of the PID controller. The locus o f a perturbed relay system method (LPRS) proposed in (Roiko, 2005) offers an opportunity to itnprove the indicated accuracy problem.

1.INTROT)UCTrON PID control is the main type of control extensively uscd in various industrial applications. PID controllers are usually implemented as configurable softwarc modules within thc distributed control systems (DCS) (Astrom & Hagglund, 1984). The DCS configuration software is constantly cvolving giving to the developers many new features. One of most useful features would be the controller autotuning feature. 7his trend can be seen in the development of new releases of such popular DCS softwarc as Honeywell Experion PKSO and Emerson DeltaVO. Despite the existence of a large number of tuning algorithms, there is still a need in simple and precise loop tuning algorithms that would be imbedded as an additional autotuning add-on in the PID controllers of DCS. The requirements to the controller autotuners can be formulated as: simplicity, precision and robustness. Relay feedback test on the process is an improvement of the original closed-loop test (Liegler & Nichols, 1942). 11 has been widely used for process identification (Astrom & Magglund, 1995; Kaya & Atherton, 1999; Yu, 1998). However, the problem has not been fully solved. rhe fundamental obstacle here is the absence of a simple, precise and

2 . PRELIMINARIES AND GENERAL MET1 IODOLOGY OF IDENTIFICATION In (Boiko, 2005) the LPRS was introduced as a method of analysis and dcsign of relay feedback systems having a linear plant (Fig. I).

29

Therefore, the identification methodology can be based on the matching of the computed LPRS to the measured LPRS. Generally, the identification is proposed to be carried out as follows. An asymmetric relay feedback test is run over the process and the length of the positive control pulse f?,, the negative control pulse Q2 and the average on the period process output yo are measured (the constant inputfo, hysteresis b and the amplitude o f t h e relay c are given parameters). On the basis of the three measured values the following parameters are computed. The fi-equency of the oscillations is computed as: ~7,,~=27r40,+ 02), and the average control signal is: uo=c (61- 6 2 ) / (BI+ 6 2 ) .

Fig. 1. Relay feedback system It is defined as a complex function J(w) in the frequency domain as follows:

whcrc t-0 is thc timc of thc switch of thc relay rrom "-c" to "+c1', w is the fkequency of the self-excited oscillations varied by changing the hysteresis 2b whilc all other parameters of the system are considered constant, oo,u0 and y(t) I I=o are, therefore, functions of w. Thus, the LPRS J ( w ) is defined as a characteristic o f the response of the linear plant to its non-symmetric pulse wavcforrn input u(t) subject to j&O as the frequency co is varied. A few techniques of the LPRS computing - for different types of plant description - were proposed. If, Tor example, the plant is represented by the transfer function W(s)the LPRS is given by the following formula (Boiko, 2005): J(W) =

With those values available, the following two equations for two unknown process parameters and a formula for the process static gain KI, can be written (we assume that there is no disturbance): ReJ(Qnz)=--- 1 f o - Y o 2 uo irb lm./(Qn7) = --

4c

(7)

C kf77(-~)k+1I<eW(kw) k=l

(5)

Therefore one relay feedback test allows determination of two parameters of the proccss model, plus the process gain - via the solution of (3, (6), ( 7 ) ,with the LPRS computed as per (2) or using other techniques. In the case of more than three unknown parameters, a few relay feedback tests with different values of the hysteresis b must be carried out. Each test would provide one frequency point of' the LPRS and, therefore, each additional test would allow identification of two additional parameters. This is the general idea of the proposed identification. One particular case that involves a very common process model is considered below in details.

(2)

+ j z Im W ~ ( 2 k I)w]/(2k- 1) ~

k=l

where m=O for non-integrating plants and m-I for integrating plants. With the plant model available, the LPRS can be computed at various frequencies and the 1,PRS plot can be drawn on the complex plane (an example of the LPRS is given in Fig. 11). Once the I PRS i q computed, the frequency R o f the symmetric pcriodic solution can bc determined from the following equation: irb Im J ( Q ) = - (3) 4c

and the equivalent gain of the relay with respect to the slow component of the motion can be determined as:

2.1,PRS OF FIRST-ORDER PI,US DEAD TIME PROCESS Many industrial processes can be relatively adequately approximated by the first order plus time delay transfer function: Ke-T' W ( s )= Ts + 1 where K is the process gain, T is a time constant, T is a time delay (dead time). To apply the above idea to the process (8) we need to obtain the formula of the LPRS for transfer function (8). Consider the equation o f the periodic procew with unequally qpaced switching in the relay feedback system (Fig. I ) with the plant being the transfer function (8). At first, for an auxiliary purpose find the response of the first order plant to the steady periodic pulse control of the amplitude c, with the positive pulse length being

Both formulas: (3) and (4) directly follow from the dcfinition (1). A closcr look at thc dcfinition ( 1 ) would find that the LPRS is a characteristic that can be measured from such an experiment as the relay feedback tcst. Indeed, the real part is defined as a ratio o f two constant values (it iq defined as a limit of the ratio and the problem of accuracy of this measurement is considered below), and the imaginary part is cqual to the hysteresis value (with a coefficient). Hence, there are two factors available that are important for the solution of the identification problem. Firstly, the LPRS can be computed from the process model, and secondly, it can be measured from the relay feedback test.

30

and the negative pulse length being B2. l h e steady periodic response of such a plant can be described by the following expressions: ~ ~ * ( 8 ~ ) = y * ( O ) . e+cK(l-e-Oi -~' ) (9)

Formula (21) does not contain b o r & in the right hand side. Taking into account the relation between $1, 63 and uo we can obtain the following limit:

y"(O)-y*(O1).e-0J - c K ( 1 4 0 2 T ) (10) Formulas (9) and ( 1 0) are a return Poincare map for the feedback relay system with plant being a first order transfer function. Solution of (9) and (10) provides thc following rcsult:

Another expression for the same limit is the formula of the closed-loop system that uses the notion of the equivalent gain of the relay kil:

Equating the right-hand sides of (22) and (23) we obtain the equation for the equivalcnt gain k,. Having solved it we obtain the formula of the real part of the LPRS (taking into account the fact that the real part is the reciprocal of the equivalent gain with the coefficient -05). Finally, we put together the real and the imaginary parts and obtain the formula of the LPKS for the lirst order plus time delay transfer function as follows:

Dcnotc thc valucs of thc output at thc switching instants y,,, and y,, ( 1 1 ) and ( 1 2). With ymlr7 and ynzax available, we now can write the equations of the asymmetric periodic process in the system with the first order plus time delay plant: Y(@I) = Y m i n

y(0) = ynj,

.

e-(+r)

1

.e-('2-')

+c~(l-e-(+r)

-cK(I-e-('2-')

f o - Y ( 0 )= b

I

) (13) ) (14)

(15)

K J ( w ) = -(I

f o - Y(Q, 1 = -b

B T z where a = T = - and y=,.

r

TO

7

Now derive the formula or the real part or the LPRS. Solve equations (13)-( 16) for 0, and B2: f,+b-cK 0, = -7' In (18) f o -b +cK - 2cKey ,fo - b + cK 8, = -7 In (19) 2cKel' +,fo +b-cK Find the limiting value of the positive and negative pulse length Cor,fo+O: cti(2ey- I ) + b lim 8, = lim Q2 = 8 = T . l n (20) fo+O /"4 CK-b In formula (20), B is half of the period of the symmetric oscillations. Consequently, the ti-equency of the oscillations is: e x . /8.Now derive a formula of lirn

f h o

TC

a ) + J-K(-

2ePey

- 1) (24) 2 4 I + e-^ Let us compute the LPRS and plot it for various values of y. The plots of the LPRS for Y O (#l), y-0.2 (#2), y-0.5 (#3), y-1.0 (#4), and y-1.5 (#5) are depicted in Fig. 11. All the plots start at the point (OS,-jz/4) that correspondq to the frequency PO. Plot number 1 (that corresponds to zero time delay) comes to the origin that corresponds to infinite frequency. Other plots are defined only for the fi equencies that are less than the frequency corresponding to half of the period. Therefore, they do not come to the origin. 1 ormula (24) can be validated via computing of the LPRS for the same values of y as in Fig. II - with the use of the series expression (2). The application of formula (2) to the tramfer function (8) provide\ the \ame rewlts as formula (24). This can serve a? a proof of the correctness of formula (24). The point of the intersections of each of the LPRS and the horizontal line -1rb/4c provides the frequency of the oscillations. This corresponds to the solution of equation (3). In the case of zero hysteresis this line becomes thc real axis. The rcal part of the LPRS in that point provides the value of the equivalent gain of the relay (4). With the formula of the LPRS (24) obtained we can now consider in details the identification methodology brielly outlined above.

(16) At first derive the formula of the imaginary part of the LPRS for the given plant. According to the definition, the imaginary part of the LPRS is the value of the system output at the time of the switch from "-" to "+77. Since the input$, tends to zero, for deriving the formula of the imaginary part we can consider the symmetric oscillations. In that case y(B,)=-y(0) and the solution of equations (13)-(16) is fairly straightforward:

- ae'cosech

3. IDLN 1 I1 ICA IION ALGOKI I HM

s.

With the values: O,, 4, and yo measured from the asymmetric relay feedback test, and known constant input& rclay amplitude c and hysteresis b, we can now formulate the identification problem as the solution of the following set of equations:

It can be derived from (18) and (19)

fo

but it must be obtained the way that it should not contain b o r j i in the right-hand side. For that reason, formula (20) would be helpful for achieving this goal. After a number of transformations we can obtain:

ReJ(R,) = -(l-aeYcosech K a ) = 1 &YO 2 2 2l0

31

(25)

Table 1 'Tabulation of functionah)

-2 -1.5 -1 -0.5 0 Re J

-2.5

0.5

1

ry

0.2

0.3

0.4

0.5

0.6

a(ry)

4.965

3.197

2.232

1.594

1.126

ly

0.7

0.8

0.9

1.0

a(ry)

0.761

0.464

0.215

0

Therefore, the identification can be carried out as the following algorithm. (a) The values of 4, O,, and yo are measured from the asymmetric relay feedback test and a,,,and uo are calculated. (b) The static gain Yo K is calculated as: K = - . (c) Equation (28) is

1.5

Fig. 11. LPRS of first order plus dead time process

UO

z 2e-ae7 Irb ImJ(Q,,) = - K ( - 1) = -4 ]+en 4c

solved for a with the use of interpolation of the data of Table 1 or formula (29). (d) Once the parameter a is found, the time conslant T is calculated

(26)

. (e) And finally the dead time

T

is

@ Q ,

a=-

z

7l

1

and y = - . TL-2, T Since K can be calculated separately according to (27) we havc to solve thc set of two equations (25) and (26) with two unknown values T and z. Equations (25) and (26) can be reduced to one equation with one unknown variable a:

calculated as: 5 = 7' I n - (e" + I)] . The described 2 algorithm is very easy to program and implement as an add-on to a PID controller. In spite of its simplicity it can perform very well if the process can be described by formula (8) adequately enough. It is, therefore, very suitable for an autotune identification. 4. TUNING ALGORITHM 4 I Tuning criterion.

1

I.

I.

I.

I.

I.

I.

I.

I.

There are a number oftuning criteria that are used for selecting optimal settings of PID controllers. The most well known ones are minimum of integral absolute error (IAE), integral time absolute error (ITAE) and some others. It is worth noting that those criteria are time-domain criteria and represent some characteristics of the step response of the closed-loop system. On the other hand the most easily measurable characteristic of the step response and the most imporpant one is the value ofovershoot. In other words the referenced criteria do not account for the ovcrshoot valuc dircctly nor do thcy consider it as a constraint. In practical applications even if the tuning is optimal per a certain criterion but the overshoot exceeds a desirable value the choice would always be in favour oftuning that accounts for overshoot.

I.

0.9 ........................................................ ,< ,, ,# ,, ,# ,, ,, ,, ,< (7.8.1...:.....L ....:.....I.. ..:....i.....:....:.....I...... .... I ;, .....,..... ;, ....J,.....k, ....;........... 0 7 \! ..:...., . _ _ ,! ,. ,. ....2!......L,. _ _,............. 0.6.-.\.:., ......,. .....,. ........... I . . I -

I /

,

,

,

,

I

I

I

,

,

,

,

/

/

I

I

I

,

/

,

/

,

#

,

I

I

/

,

/

/

~

~

~

~

,

~

#

I

I

,

1

..;. ....L.. 0 I ...........I....;..---;.-.4-. : : : I 0 I

I

I

~

I

I

~

,

~

.-I-. ...I ..... 1 ~ I

,

T

-

It is proposed in this paper that a criterion that uses the overshoot as a constraint should be applied to tuning. Formulate this criterion. Consider the following problem. Assume for simplicity that the controller is only a proportional gain. 'I'he problem of tuning in this case would be the problem of finding the maximum value of the gain that satisfies the overshoot constraint. In other words, there is a tradeoff between the desired overshoot and the purpose of having the maximum value of overshoot. L,et us note that this trade-off is resolved in a very simple way in

Apparently, it would be possible to find a suitable approximation for the inverse function a=a(ly). However, the DCS software is not suitable for cyclic calculations. For that reason, we propose here to tabulate this function within the range ry40.2;1] and to use an interpolation for in-between values (Table 1). For the values ry below 0.2 the following approximate formula can be used: a c I / y.

32

Table 2. Normalized mwm-tional gain settings

this dualion: we reach the maximum of the gain subject to the constraint. Let now the controller be a PI-controller. Our objective is to increase both the proportional gain and the integral gain and to satisfy the constraint for the ovcrshoot. Howevcr, the fact that we have to manipulate two gains does not allow for a unique solution. We need to reformulate the original objective of maximal increasing the proportional gain into a different criterion, which would work for two and three gains too. This can be the criterion oj minimal settling time. Let us note that in the case of proportional gain the inaximuin value of the gain would also provide the minimum settling time. However, the former cannot be applied to the case of several parameters, while the latter can. L A us formulate the tuning criterion as minimal

settling time subject to satisbing the constraint on the overshoot value:

y,,T = 5%

y,, = 10%

y,,T = 20%

t/T=0.1

5.203

5.957

7.177

t I T = 0.2

2.624

3.058

3.702

T IT = 0.3

2.823

2.120

2.564

T I T = 0.4

I .483

1.673

2.007

tlT=0.5

1.294

1.419

1.683

tlT=0.6

1.170

1.258

1.473

t IT = 0.7

1.082

1.148

1.329

rll'=0.8

1.014

1.068

I .225

t I T = 0.9

0.964

1.008

1.146

t 1 T = 1 .0

0.924

0.963

1.086

t I T = 1 .5

0.808

0.833

0.91 5

Those settings of the PI-controller provide fastest step responsc subject to the overshoot constraints. is a settling timc, 2 8 is the step response envelope width, yo, is the overshoot value in %. In formulas (29), (30), it is assumed a unity feedback and the unity step value.

4.3 Tuning algorithm. Therefore, the complete autotuning algorithm comprises the following steps. (a) The values of 8,, 02, and yo are measured from the asymmetric relay feedback test and a, and uo are calculated. (b) The static gain K is calculated as: K = y o / u o . (c) ?'he following equation is solved for cr with the use of interpolation of the data of Table 1 or formula (29):y0/fo = ( l - e - " ) / a . (d) Once the parameter a is found, the time constant T is calculated as: = ~ / ( d 2 , , ) .(e) The dead time t is calculated as:

4. I PI-controller settings.

Solution of this optimisation problem for the Ke -?\ Ts + 1 and the PI-controller lead to the following optimal settings ofthe controller. underlying process transfer function W ( s )=

~

For overshoot 5%, 10% and 20% the integrator normalized time constant can be computed as follows (respectively):

z = T ln[0.5(ea

(0Normalised

proportional gain and integrator time constant are computcd via Table 2 and formulas (31)-(33). (g) The PI-settings of the controller are calculated as pcr (34) and (35). Ihe described algorithm is very easy to program and implement as an add-on to a PID controller. In spite of its simplicity it can perform very well if the process is described by formula (8) adequately enough. The algorithm was extensively tested in the MatlabISimulink environment.

The normalized values of the proportional gain are tabulated as follows (intcrmediate values are found via interpolation). Table 2 and formulas (31)-(33) provide values of settings that apply lo the transfer function with unity gain and time constant. For arbitrary parameter values, recalculation can be done as per the following formulas. The proportional gain is: K , = K O ,I K And the intcgrator gain is:

+ l)] .

5. SIMULATIONS AND INDlJSTRIAL APPLICATIONS Example I Let the process be described by the first order plus dead time transfer function:

(34)

iz/(s)=0.5 exp(4.5 s) I (1 .5 s + 1)

(35)

The parameters of the relay are chosen as follows: c=l, h=O. The constant input signal value is j,=0.1 .

33

involves fitting of the LPRS obtained analytically through thc underlying model of' the process to the points ofthe LPRS measured from the relay feedback test is feasible, efficient and convenient for using as an add-on to the PID controllers. Additionally, the LPRS model of first order plus time delay proccss is obtained. A new tuning criterion is proposed. The criterion is the minimum settling time at the step test subject to overshoot constraints. Simple analytical formulas are derivcd for a PI-controller. Both: the identification algorithm and the tuning algorithm are implcmcntcd in the self-tuning PI-controllcr.

The relay feedback test produce the following parametcrs of the oscillations: positive and negative pulse duration BI=l .165s, B7=0.62Ss,and the average value of the process output ~ ~ ~ 0 . 0 7 The 5 4 . process transfer function identified as per formulas (25)-(27) is: W(s)=0.4998 exp(-O.S 130 s) / (1.5059 s + 1) The highest identification error is of the dead time (2.6%). The other two errors are much smaller: 0.04% for the gain and 0.39% for the time constant. All the error values are acceptable for the autotuning purpose as the main source of error in the autotuners is the distinction between the model utilized within and the actual process dynamics. It should also be mentioned that the pulse duration in the considered relay feedback test is: 65% for the positive pulse and 35% for the negative pulse. Therefore, the asymmetry of the control is significant. That substantiates the use of the real part of the LPRS (being defined as a limit) at non-small values of the input signal. This phenomenon is considered in more details below.

REFERENCES

Astrom, K.G. and T. Hagglund (1984). Automatic tuning of simple regulators with qpecifications on phase and amplitude margins, Rutomatica, 20, p. 645-65 1. Astrom, K.G. (1995) Oscillations in systems with relay feedback, The IMA I'olumes in Mathematics and its Applications Adaptive Control, Filtering and Signal Processing, 74: 1 25. Astroin, K.G. and T. Hagglund (1995). PID Controllers Theory, Design and Tuning, second ed. Research Triangle Park, NC: Instrument Society America. Atherton, D.P. (1975). Nonlinear Control Engineering - Describing Function Anulysir and Design, Workingham, Berks, IJK: Van Nostrand Company Limited, 1975. Boiko, I. (2003). Method and apparatus for tuning a PID controller, CJS Patent Application h-o IU336369. Boiko, I. (2005). Oqcillations and tranrfer properties of relay servo systems - the locus of a perturbed relay system approach, Automatica, 41, pp. 677683. Kaya, I. and D. P. Atherton (1999). A PI-PD controller design for integrating processes, Proc I999 American Control Conference, San Diego, CA, IJSA, pp. 258-262. Luyben et al. (1987). Derivation of transfer functions for highly nonlinear distillation columns, Ind Eng Chem. Res. 26,2490-2495. Tsypkin, Ya. Z. (1984). Relay Control System, Cambridge, England Yu, C.-C. (1 998). Use of Saturation Relay Feedback in PLD Controller Tuning, L'S Patent No 5742503. Ziegler, J.C. and N.R.Nichols (1942). Optimum settings for automatic controllers, Trans Amer Soc iLlech Eng , Vol. 64, pp. 759-768.

Example 2. Let the process be described by the following transfer function, which is considered unknown to the auto-tuner:

W(s)=0.5exp(4.6 s) / (0.8 s2 + 2.4 s + I ) The parameters of the relay are chosen as follows: c=l, b=O. Thc constant input signal valuc is fo=O. I . The objective is to design a PI controller for this process with the use of the first order plus dead time transfer function as an approximation of the process dynamicr. After that the PI controller should be tuned in such a way that the system should produce the shortest possible settling time and the overshoot _(10% at the step response. The following values of the oscillatory process were measured: the lrequency of the oscillations f2,= 1.903, the average value of the process oulpul y0=0.0734, and lhe average value of the control signal uo=O. 1455. As per the described algorithm, the process parameters were identified as follows: K=0.5050, T=2.5285s, ~ 0 . 9 5 7 3 s The PI settings that were supposed to bring the required dynamics to the system are K,= I .349 and K,=3.503 The actual system step response produced 12.5% overshoot. The described autotuning algorithm was implemcntcd as an Experion PKS configuration, which was used for loop tuning of a number of industrial processes in power and petrochemical indudrieq. A n application for a 1JS Patent ha., heen tiled for the described algorithm (Boiko, 2003). 6. CONCLLJSIONS The paper proposes a self-tuning PI-controller. The algorithm uses methodology of process identification based on the asymmetric relay feedback test and the LPRS method. It i s shown that the methodology that

34

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

DEVELOPMENT OF AN EXTENDED PREDICTIVE CONTROLLER FOR A SPEED CONTROL SYSTEM Ma'moun Abu-Ayyad and Rickey Dubay Department of Mechanical Engineering The University ojNew Brunswick Fredericton, New Brunswick, Canada Mamoun.AbuAyyad~unb.ca,dubayraunb ca

Abstract: The proposed algorithm of extended predictive control (EPC) represents an exact method for removing the ill-conditioning in the system matrix by developing a unique weighting structure for any control horizon. The main feature of EPC algorithm is that it uses the condition number (CN) of the system matrix to evaluate a single tuning parameter that provides a specified closed loop response. Tuning of EPC is effective and simple since there is a direct relationship between closed loop performance and its tuning parameter. Copyright 02006 IFAC Keywords: Modeling, Simulation, Control Methods, and Real-Time Operation.

column of the dynamic matrix A is shifted downwards by m>l Tollowed by the same Tor subsequent columns. This method is restricted by using the control horizon nu =2. Extended prcdictivc control (EPC) has been recently developed an exact analytical solution for tuning SISO controllers (AbuAyyad et al. 2006). The main feature of EPC is to decrease the off-diagonal elements of ATA (AbuAyyad et al. 2006). An added feature of the proposed method is the selection of the EPC parameter from the optimal range of the CN of ATA. More importantly, this study addresses the constraint that is generally placed on the control horizon (nzl52).

1 . INTRODUCTION Model predictive control (MPC) is widely used in many industrial applications (Garcia, 1989; Rawlings, 1993; Qin, 1997). Usually, MPC controllers have been tuned through a number of parameters such as: control horizon, nu, prediction horizon, P, sampling time, T, and inputloutput weights in an objective function. The earliest tuning strategy of MPC was introduced by (Cutler, 1980). In this method, a move suppression coelficient i added to the main diagonal of the system matrix ATA to reduce ill-conditioning resulting in smaller changes in the control moves. The selection of the magnitude iwas chosen itcratively.

The tuning strategy presented here is significant because it overcomes the interrelated problem between the MPC tuning parameters. An exact method is to evaluate a single tuning paramcter based on the optimal range of the CN of ATA. The investigation compares the control performance of EPC with move suppressed MPC for speed control of DC motor.

A simplified predictive control algorithm (SPC) was proposed by (Gupta, 1987) in which the error is minimized at a point D t P on the prediction horizon and only one control move is calculated A short control honzon diminishes thc controller's ability to anticipate the effect of the future control moves Shridhar and Cooper derived an analytical expression Tor 2- and presented a new tuning strategy Tor unconstrained single-input single-output (SISO) MPC bascd on a first ordcr plus dcad timc (FOPDT) approximation, which may not work well on higher order or unstable processes The drawback ol' their work is that the CN or the system matrix A'A is dependent on the process gain Kp, the discrete dead time k, an overall time constant z, n,, and T

2. EXTENDED PREDICTIVE CONTROL The general predictive control law is based on the solution of a quadratic cost function formulated as a least-squares problem with weighting factors on the manipulated variable moves only (Dougherty, 2003)

min J = [e- AAu]' [e- AAu]+ AU 'A'Mu (1)

Recently, Dubay et al. proposed a new MPC algorithm that reduces ill-conditioning by introducing a shifting factor m, where the second

AM

In Eq. (I), e is the vectoi of tiacking difference between the reference trajectory and the prediction of 35

the process, A is the dynamic matrix, Au is the vector of manipulated variable moves, and ATA is the matrix of move suppression coefficients. The closed form solution of the unconstrained MPC law without weighting on ATA i s (Dougherty, 2003)

In Eq. (3), as the prediction horizon P+m, ATA becomes

1 1

A T A= a K j

L:

In general, by employing a first order plus dead time (FOPDT) model structure to any process, the system matrix AfA in MPC for that process can be approximated as rollows (Shridhar, 1998)

The system matrix A3 for EPC is evaluated as

A, =ATA+W,,,,

(7)

-

a--

1

2

a-1

...

a-1

a--

3 2

...

3 a-2

a-2

...

The general form of A3 for n,,> 1 is (3)

A,

-

wherc,=p-k-??+2.

=a; 1 I--

1-r

1

1-r

...

1-7

1

.'.

Rl

The EPC method uses a new

0

17.

il

I--

1 Rl

extended move suppression (EMS) weighting matrix WFVsfor any n,,>l as (Abu-Ayyad, 2006)

:

-

Equation (8) indicates that the CN of A3 is independent of the tuning variables P, T and other parametcrs z, k and Kp. Using EPC, the modified equation for the manipulated variable moves Eq. (2) becomes

Au = (A3)-'A T e where R, and R2 are the weighting factors It was shown (Abu-Ayyad, 2006) that the CN 0fA'A can be furthcr improved by eliminating thc sccond clcmcnt Thcreforc, iL of thc first row by assuming R,/Z= ~2

(9)

3. EFFECT OF R, ON EPC The condition number o r A j using n , = 3 is (AbuAyyad, 2006)

is no longer a tuning parameter Also, define the weighting factor R2 as R2=rR, Then, Eq (4) becomes

It is to be noted that the matrix A3 becomes a singular matrix for the special case of R,-m.

IA31 is calculated as follows

36

This case of R* m is to be avoided since the EPC structure is valid only for nci = 3. A simulation was performed using Process 1 (Shridhar, 1997) in order to demonstrate as an example the effect of using a relatively large value of R I which was chosen arbitrarily. Process 1 has a relatively large dead time and has a transfcr function of the form p

G, (s) =

R, = 15

s

(150s + 1)(25s+ 1)

(13) 51

I -

The results shown in Figs. 1 and 2 using Eq. (8) illustrate the contours of yAd(extracted from a 3-D plot) [or n,,= {3,4} with P = 54 and T = 16. The plot in Fig. 1 illustrates that yAs at a specific r is independent of RI for n,, = 3. In Fig. 2 the general result is that RI decreases as r increases in order to maintain the same value of YA:, . This trend is the same [or higher nuvalues. , ,y

0

1

2

3

1

1

5

6

i

R

S

r

Fig. 3. The relationship between Process 1 ( n , = 3)

yA,

and r for

Figure 3 illustrates the exact and approximate yA3for Process 1 using Eqs. 8 and 10 respectively, with the overlapping region starting at r 2.7. Figure 4 illustratcs the closcd-loop responses for RI = 15 and R I = 100 with n,, values varying from 3 to 7 using r = 3.6 from (Fig. 3) and the same P and T values The noted result i s that R I does not affect the closed-loop response for nu = 3 since the overlapping region of YA, is independent of Ri as shown in Fig. 3. However, minor differences in transient behavior occur for higher n,,values.

contour lines

, 7 8 2

14

........

12

r

Fig. 1. A contour plot of y A I for different values of R , and r on Process 1 (nL,= 3)

I

I / 0

500

,.;:

141

,,y

1000

,500

Timc (scc)

contour lines 3'

( 0 1

I

...., _--

----

._>.l._,_.:l__.-.

PO8

R, = 100

$0 6

m

mod 02 500

3000

1500

Time (sec)

Fig. 4. The effect of R, on the closed loop response for large and small values of R , for Process 1 The closed-loop response for nu = 3 illustrates zero overshoot since yAdat nu= 3 has the smallest value as compared to higher n , as shown in Table 1. The differences in y A I in Table 1 can be explained using Fig. 5 which shows that YA3 gets larger a5 RI increases at a specific r.

nzr

R,=15 R,=100

3 3.8 3.82

4 76.7 444.2

5 6 108.9 133.3 730.5 897.6

7 161.9 1092

Table 1 . CN for different n,, values - Process 1

37

4. THE EFFECR OF Y ON THE CLOSED-LOOP RESPONSE

EPC uses the stable yAJregion directly as only tuning mechanism in order to obtain a desired closed-loop response. In this section the rclation between Y and the closed-loop performance parameters such as percent overshoot ,8 and settling time Ts is presented. Using incremental values of Y starting ~ 2 . from 5 Fig. 3, which is the starting point of the overlapping region, closed-loop results for Process 1 are shown in Fig. 6 using the previous P and T values. Also, a decrease in r values causes the manipulated variables to be more aggressive with an underdamped closed-loop response. Figure 7 shows four regions for the CN and its relation to the process closed-loop performance for a higher value ofn,,= 5. The division or the yA1 into four regions is very important and useful for tuning the closed-loop response in order to achieve various control performance settings.

-4

Fig. 7 . The relationship between yA?and the closedloop performance (n,,= 5 )

A more detailed set of relations can be obtained as itemized in Table 2 for PZ, = 5 as the example. The results in Table 2 can be generated for any n , >2, showing a direct relationship between closed-loop specifications and r. The % overshoot parameter is and the settling time s'7 in sec.

; Ts

464

1189

560

624

656

Table 2. Closed-loop specifications for different values of Y - Process 1 ( M , = 5 ) Regarding the general form of the AJ matrix in Eq. (S), as the tuning parameter r approaches a,the invcrse matrix ofA3 becomes Fig. 5. The relationship between Process 1 (nu= 4)

?A3

and

I*

a

260

460

600

8bO

loo0

1MO

for

r 1

1%

Y

O ... O

1

This form of (A3)-' which is now a scalar quantity demonstrates that EPC and SPC (Guptd, 1987) algorithms become the same in terms of the number of manipulated variable being one. An important feature of this result is that EPC produces the same closed-loop response at large r values for any n , with zero overshoot and without sacrificing the rise time. This is not the case [or other MPC algorithms where increasing the tuning parameter leads to an increasingly sluggish closed-loop response.

l

Time (sec)

Fig. 6. The responses for different values of Process 1 ( n u = 5)

1

for

38

5. EPC VERSUS SPC

EPC, while the point D=3S i s chosen for SPC. The responses arc almost identical while EPC reaching the setpoint faster by 100 sec. Simulation results for Process 3 are shown in Fig. 9 where the values of P=50 and T=O.1 were used in the simulation (Kember et al. 2003). The tuning parameters ~ 2 . 4 5 , R1=10 and n,=4 are used for EPC, while the point D=6 is chosen for SPC. EPC shows a better responsc comparing with that of SPC reaching the setpoint in a shorter time.

Control simulation comparison between EPC and SPC was carried out since the latter has the best conditionality of having a CN of unity. A higherorder process with sluggish open-loop dynamics (Shridhar, 1997) and first-order process are used for comparing the closed-loop responses. The processes are

6. DC MOTOR SPEED CONTROL

A practical application of EPC was carried out on an electric DC motor coupled with a tachogenerator speed transducer. The performance of the EPC method was compared to move suppressed MPC. The closed-loop results are experimental studies on the DC motor system.

Process 3

1 G, (s)= s+l

The dynamic matrix A was obtained from an open loop test of the motor. Using RI=10 and following the EPC tuning procedure (Abu-Ayyad, 2006), closed-loop tests were conducted using 5 values of r equally spaced starting just where the overlapping region starts. Using thcsc r values, closed-loop control using EPC was conducted on the DC motor as shown in Fig. 10.

0-

I

0

1400-

100

200

400

300

5W

600

700

Time (sec)

1200.

i

\

Fig. 8. Performance comparison of EPC and SPC controller for Process 2.

1

05

2

15

25

i

0

i

2

'2 n 125

S

..<. ~

l

:

1

~

1

15

2

25

04

05

06

07

08

09

I

relation bctwecn I', p and Ts. Dcfining a closcd-loop specification of p=0.2% and Ts=0.14 sec, r was evaluated as 2.6. Figure 1 1 shows the results using EPC at the specified r and move suppressed MPC having tuning parameters of n,=2 and k=10.

505

05

03

1 Using the results in Fig. 10, Table 3 shows the

..

a -

0

02

Fig. 10. Speed control of a DC motor using different r values

2 0

0 ,

Time (sec)

Time (sec)

3

Time (sec)

Fig. 9. Performance comparison of EPC and SPC controller for Process 3. Figure 8 shows the simulation results of response and manipulated variables for EPC and SPC for Process 2. The values of P = 100 and T = 6 were used in the simulation (Shridhar, 1997). The tuning parameters ~ 4 . 5R, , = 8 and a higher valuc o f n,=4 arc used for

39

REFERENCES Abu-Ayyad, M., Dubay, R., and Kember, G.C. (2006), SISO Extended Predictive Control Formulation and the Basic Algorithm. ISA Transactions, 45, 12. Abu-Ayyad, M., Dubay, R., and Kember, G.C., (2006), SISO Extended Predictive Control Implementation and Robust Stability Analysis. ISA Transactions, Accepted for publication. Cutler, C.R., and Ramaker, D.L. (1980), Dynamic Matrix Control-A Comptitcr Control Algorithm. Proc. JACC; Sam Francisco, CA. Dougherty, D., and Cooper, D. (2003), A practical multiple model adaptive strategy for multivariable model predictive control. Control Eng. Pructice. 11, 649. Dubay, R., Kcmbcr, G., and Pramujati, B. (2004), Well-Conditioned MPC. ISA Trunsucliuns, 43, 23. Garcia, C.E., Prctt, D.M., and Morari, M. (1989), Model Predictive Control: Theory and Practice a survey. rlzttornatica. 25,335. Gupta, Y.P. (1987), A SimplifiedModcl Predictive Control Approach. Dept. Chem. Eng., TINS: Halifax, Canada. Kember, G. C., Dubay, R., Mansour, S. E., (2003) Analytical Comparison of Different Techniques Used in Model Predictive Control. ISA Transactions. Morari, M., and Lee, J.H. (1999), Model Predictive Control: Past, Present, and Future. Comp. G e m . Eng., 23,667. Rawlings, J., and Muske, K. (1993), The Stability of Constrained Receding Horizon Control. IEEE Trans. Aut. Control., 3 8, 1512. Shridhar, R., and Cooper, D.J. (1997), A Tuning Strategy for Unconstrained SISO Model Predictivc Control. Ind Eng. Chem. Res. 36, 729. Qin, S. J., and Badgwell, T. A. (1997), An overview of Industrial Model Predictive Control Technology. Proceedings of the 5th Int. Conf. on Chemical Process Control, AIChE Svmposium Series 93, Tahoe City, CA. 316, 232.

120nl

6ml 400

-

200

I-

Fig. 11. Speed control of a DC motor using EPC and movc suppressed MPC

r

P Ts

2.1 46 0.37

2.4

I 0.2

2.7 0 0.17

3 0 0.25

5 0 0.39

~

Table 3. Closed-loop specifications Tor different values or Y DC motor ~

In order to eliminate the overshoot larger values of T can be used. This property demonstrates that increasing the parameter r makes EPC tuning very simple if an overdamped and robust response is required.

7. CONCLUSIONS

A new method of predictive control termed extended predictive control was developed The main advantage of EPC is that it uses an exact solution to obtain the optimal range of the CN of the system matrix which is thcn uscd as a tuning parameter It should be noted that for any nu > 2, there 1s a single tuning parameter r for RI )) 1. In this sense, industrial use of the EPC method IS simple and applicable to any controllable process using this tuning scheme

8. ACKNOWLEDGEMENT

The authors acknowledge the Natural Sciences and Engineering Research Council of Canada for the financial support of thiq research

40

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

POWER SYSTEM STABILIZER DESIGN FOR MULTIMACHINE POWER SYSTEM USING POPIJLATION-BASED INCREMENTAL LEARNING

KA Folly University of Cape Town, Dept of Electrical Engineering, Cape TOIVFZ South Afi-ica

Abstract: This paper uses a no\el simplified version of GAS called Population-Based Incremental Learning (PBIL) to optimallq tune the parameters of the power sq stem stabilizers (PSSs) for a multi-machine system. The technique combines aspects of GAS and competitive Icarning-based artificial neural network. The issue of optimally tuning the parameters of the PSS is converted into an optimi7ation problem that is solved via the PBIL algorithm. Simulation results are presented to show the effectiveness of the proposed approach. Copyright 02006 IFAC Kcyuords: Genetic Algorithms (GAs). Population -Based Incremental Lcarning (PBIL), Power Syskm Shbil iLer (PSS), Elec~romechanicaloscil lations.

robust and powerful adapthe search mechanism. they ha\ e seheral draubacks. The performance of GAs depends on the optimal selection of its operators (e.g. population size, crosso\er and mutation rates). However, it is difficult to optimize the parameters o i GAS one at a time. These parameters t) pically interact with one another in a nonlinear manner. In particular, optimal population Gze, crossover rate, and mutation rate are likely to change over the course of a single run (Mitchell 1996). Another problem is the issue of -'genetic dril'i""which prebents GAS from maintaining diversity in the population as the search progresses. A \ a rewlt, there i \ a high probability that the population will conberge to very similar solution vectors. Once the population has con\ erged, the crossover operator becomes ineffective in exploring new portions of the function space (Baluja, 1994; Baluja and Caruana, 1995). To cope with the above limitations, man] variant forms of GAS have been suggested often tailored to specific problems (Daviq. 1996). However. it is not always easq to select the appropriate GAS l'or a particular problem because of the huge number of choices. At present. thcre is little theoretical guidance on hom to select the suitable GAS for a particular problem. Recently, some researchers hake felt the

1. INTRODUCTION

Power System Stabilizers (PSSs) are used to damp the electromechanical oscillations in interconnected powcr systems (Dcmello and Concordia, 1969; Yu. 1983). Up to nou conventional PSSs (CPSSs) are used in the industry because of their simplicit4 and their relatively good performance around the nominal operaling poinl (Rogers, 2000). However, conventional PSS based on a single operating condition cannot maintain adcquatc sy\tcm stabilio over a wide range of operating conditions. In many instances, inadequate tuning procedures of' PSS based on the sequential design have led to the destabili7ation o f the entire system (Roger.;. 2000). 1-here is a need to find a systematic tuning procedure of PSS so as to achieve optimum parameter settings over a wide range of operating conditions. Genetic algorithms havc recently found extcnsive applications in solving global optimintion problems ( D a i s 1996; Goldberg, D. E. 1989). GAS arc search algorithms that use models based on natural biological evolution (Goldberg. U. h. 1989). In the last few years, application of Genetic Algorithms (GAS) to design power system controllers has attracted considerable attention (Abdcl et a/., 1999; Sundarcswaran K, 2004). Although GAS provide

41

2. SYSTEM MODEL

need to incorporate in GAS some kind of adaptation or learning techniques (Baluja, 1994; Baluja and Caruana. 1995; Davis. 1996). Population-Based lncremental Learning (PBIL) was originall) proposed by Baluja [10]-[111. It is a technique that combines aspects of GAS with simple competitive learning. In PBIL. the crossover operator of GAS is abstracted away and the role of population is redefined. PBIL works a with probability vector. rhis probability vector controls the random bitstrings generated bq PUIL and is used to create other individuals through learning. 1,earning in PBlL consists of using the current probability distribution to create 11’ individuals. The4e individuals are e b aluated according to the objective function. The best individual is used to update the probability vector, increasing the probability of producing solutions similar to the current best individuals. As a result, PBIL is simpler. faster and more efl’ective than the standard GA (Baluja, 1994; Baluja and Caruana, 1995; Greene, 1997). In Chen and Petroianu (1998). the PSS tuning problem n a s l’ormulated in the IHw framework and PBII, was used as an optimisation tool to deal with the limitations of the Sequential Quadratic Programming (SQP) algorithm (Ahmed, Chen, and Petroianu. 1995) which is not suitable for convex systems. The objective function was the minimization of the Ilw norm of the closed-loop system. This introduccs unnecessary complications. In our previous work (Folly, 2002, 2004), PBIL was applied to tune the parameters of PSSs for a single machine-infinite bus and reported good results. In Folly (2005), the PBIL was applied to tune the parameters of PSSs in a multimachine pobker system and a comparison was made between GAS and PBIL. In all the above studies, the obiective l’unctions were formulated in terms of the maximization of thc minimum damping ratio over all the operating conditions and not related to H w norm. Also the “mutation operator” of the PBIL used in Chen and Petroianu (1998) is similar to that used in GAS a proposed by Aaluja (1994). The mutation operator used in Folly (2002, 2004, 2005) is slightly different l’rom the one in Chen and I’etroianu ( I 998) as will be explained 1ater .

The system considered in this paper is a threemachine nine-bus power system as shown in Fig. 1. The line parameters. the machines parameters and ratings can be found in Anderson and Fouad (1994). Lach machine is represented by the two-axis model (fourth order). The machines are equipped with a simplc AVR (Wu, 1983). The dynamics o f the system are described bj a set of nonlinear differential equations. I-iowever, for the purpose of controller design, these equations are linearized around the nominal operating conditions. The linearized state equations ol‘the system are given by:

i= A,x + B,u

y

(1)

+ D,u

= Cox

where the state variables are x. the system output is y and the signal u represents the control input. A,, &,, C,, D, are constant matrices of appropriate dimensions. Load C I

I

2

I 3

Fig. I Power system configuration

3. OVERVIEW OF POPULATION-BASED INCREMENI‘AL LEARNING

PBIL is an optimization algorithm closely related to Genetic Algorithin~.It is a technique that combines aspects of Genetic Algorithms and simple competitive learning. PBIL has the following features (Baluja. 1994; Baluja and Caruana. 1995; Greene, 1997): It has no crossover and fitness proportional operators. It works with a probability vector (number in range 0- 1). This probability vector controls the random bitstrings generated by PBIL and is used to create other individuals through learning. I n PBIL, theie is no need to store all solutions in the population. Onlj two solutions are stored: the current best solution and thc solution being evaluated.

In this paper, we extended the work in Folly (2002) mithout including any comparison b e h e e n GAS and PBIL (Folly,2005). Population-Based lncremental Learning (PBIL) is used to design power system stabilizers for a multimachine power system. The issue of optimally tuning the parameters ol’ the PSS is converted into an optimization problem that is solved via the PBJL algorithm. The resulting controllers ensure robust stability and good performance for both the nominal and off-nominal operating conditions. The proposed PBIL-PSSs are compared with the conventional PSSs (CPSSs). Simulation results show that the PBIL-PSSs give better perl‘ormance than the CPSSs.

The individuals are evaluated according to the objcctive function. ‘Ihc “best” individual is used to

42

update the probability vector so as to produce solutions similar to the current best individuals. As a result, PUIL is simpler. faster and more effective than the standard GA (Baluja, 1994; Baluja and Caruana, 1995). Jt has been shown in Baluja (1994) Baluja and Caruana (1 995) that PBIL outperforms standard GAS approaches on a variety of optimization problems including commonly used benchmark problems. Experience in executing CiAs and PBlL shows that the overhead for GA operations is significantly higher than for PRII, (Raluia and Caruana. 1995; Greene. 1997).

case 2 is the nominal operating condition (e.g., base case). and case 3 is referred to as the heavy load condition. P,, and Qe are the real and reactive power of the generators G I , G2 and G3. Table 2 lists the load ing conditions for the three cases considered.

A summary of the PBlL used in the paper is given below (Cireene, 1997; Follj, 2002):

where, K/) is the gain, Tl-T4 represent suitable time constants. T,, is the washout time constant needed to prevent steady -state offset of the voltage.

PRIL and GAS are applied to tune the parameters o f a fixed structure PSS o f t h e form (it.. speed input)

Step 1 . lnitialize element ol‘the probability vector (PV) to 0.5 to ensure uniformly-random bitstrings. Step2. Generate a population of uniformly-random bitstrings and comparing it element-byelement with the PV. Wherever an element of the PV is greater than the corresponding random clement, a “1’ i s generated, otherwise a ‘0’ is generated. Step 3. Interpret each bitstring as a solution to the problem and evaluate its merit in order to identify the “Best”. Step4. Adjust PV by slightly increasing PV (i) to favor the generation of bitstrings which resemble “Rest”, if Best ( i ) = 1 and decrease PV(i) if Best(i) = 0. Step 5 Apply mutation operator lo the PV. Step 6. Generate a new population reflecting the modified distribution. Stop if satisfactory solution is found. Otherwise, go to step 3.

By maximizing thc minimum damping ratio over a certain range of operating conditions we could simultaneously stabilize the family of‘ the system models and ensure that the closed-loop system is stable over a wide range of operating conditions (Folly, 2002). The following objective function is used in PBlL to achieve the above requirements:

(3) i = I , 2 . n, nndj

where

5, I

=

=

I, 2,

m

-*I>/

JF7G7

is the damping ratio

of the i-th eigenvalue in thej-th operating condition. o,/is the real part of the eigenvalue and the oil/ is the firequency. n denotes the total number eigenvalues and rn denotes the number of operating conditions. No specific constraint was put on the on the damping ratio. except the requirement that it should be maximized.

It should be mentioned that the purposc of stcp 5 is to maintain diversity in PRII,. Raluja (1994), Raluja and Caruana ( 1 995) have proposed a “mutation” operator similar to that used in the standard GAS. Greene ( 1 997) has proposed a mulalion operalor which is slightly different from the one used by Baluja (1994). That is, a forgetting factor i s used to relax the probability vector toward neutral value of 0.5. The PBIL used in this paper adopted the latter method.

Table I Possible oDeratinp. conditions Cases

1

2 3

GI

G2

G3

P,

Y‘

P,

Yb

PG

Y‘

051 072 212

-0005 032 088

110 I63 190

-024 -0001 039

03 085 124

-031 -0 12 028

All the value.; are given in per-unit

4. DESIGN OF THE PSSs

Tablc 2 Loading conditions

4. I PSS Design Rased on PRII,

Cases

The objective in this stud) is to optimize the parameter? of the PSSs wch that controllerq simultaneousl) stabilize a famil) of system models. It u a s found that a double stage lead-lag network with time constants Tl-T4and gain K;, i s sufficient to provide adequate damping to the multi-machine 54 stem shown in Fig. I . It should be mentioned that several simulations have been performed but only three are shown here as listed in Table 1. Case 1 is the light load condition.

2

A

I3

C

PL

QL

PL

PI

PI

el

07.5 I25 17.5

035 050 070

054 090

018 030 054

060 I00 180

021 035 063

162

All the value.; are given in per-unit

There arc in total 15 Pss parameters (five for each generator) that need to be optimized. It should be noted that the i x x t time COIlStallt T,, as given ill (2)

43

was not considered in the optimization process. This is because T,, is not critical. Its value was fixed to 10 sec. The optimisation was performed such that the objective function (3) is met. That is, the minimum damping ratio over all the specified operating conditions (including the three cases listed in Table 2) is maximized.

3 62 0 87 0 19 0 73 0 43

KP 7-1

T2

T? T4

The configuration of the PBIL is as follo\vs:

4 82 051

2 03 0 15

0 48 0 104 0 02

0 03 0 11 0 01

S . SIMIJLATION RESlJLTS

1,ength of chromosome: 15 bits Population: 100 Generations: 250 Learning rate (LR): 0.1 Forgetting factor: 0.005

5. I Eigenvalue Analvsis The eigenvalues of the open-loop system and the closed-loop system equipped with the CPSSq, and the PRIL-PSSs are listed in Tables 5-7, respecti\ ely. It can be seen from the open-loop eigenvalues listed in Table 5, that there are two electromechanical modes. 1-hese modes are relatively well-damped for ca5e I and become poorly damped for cases 2 and 3 (i.e., <<0.05). Tables 6-7 show the eignevalues obtained with the CPSSs, and the PBIL-PSSs. respectively. It can be seen that for all the cases. the CPSSs prmide acceptable damping ratio ranging from 0.2 (case 3) to 0.415 (case 1). The PBIL-PSSs pro\ ide "consistent" damping ratio ranging from 0.302 to 0.476 across the range of operating conditions considered.

The parameter domain for the PBI1,-PSS was set as:

0 s Kps 20 0 ITI, T 3 1 I 0.010 C: T2, T4 I0.5 4.2 Design of Conventional PSS The parameters of the conventional PSSs (CPSSs) have been well-tuned for the nominal system using a combination of trial-and error-approach and the phase compensation technique (DeMello and Concordia, 1969; Yu. 1983; Folly, 2002). In the phasc compensation tcchnique off-nominal system models cannot be included direct11 at the design stage of the controller. However, the performances under off-nominal conditions can be checked after the controller is designed. If performances under these conditions are not satisl'actory. the parameters of the controller re-tuned.

From an eigenvalue point of view, the performance of PRIL-PSSs is better than that of the CPSSs over the range of operating conditions considered. For cases 2 and 3, the damping ratio provided by the CPSS is less than 0.23. On the other, the PBlL-PSS provide damping ratio greater than 0.33 for cases 2 and 3. Table 5 Eigenvalues for the open-loop system

4.3 PSS Parameters

Cases The parameters of the CPSS, the PBIL-PSSs are listed in Tables 3-4, respectively. It can be seen that for the conventional PSS. Tl=T7 and T2 = T4. This is in accordance with the general practice. For the PBIL-PSS there are no constraints on these parameters. In Folly (2002). M C have shown that even in the case where the constraints T,=T3 and T, = T4 was imposed on the PBIL-PSS, it performs better than the CPSS for off-nominal conditions.

1

2 3

A -eigenvalues,

GI

G2

G3

K,,

2 00 0 10 0 03 0 10 0 03

5 00 0 10 0 03 0 10 0 03

1 00 0 10 0 03 0 10 0 03

T T2 T? 7-4

L

i

-1.00639.620 -1.786313 856 -0,34513'9.787 -0.440+I 3.822 -0.277+9.544

0.104 0.128 0.035 0.032 0.029

-0.053313.621

0.004

r- dainping ratio

Table 6 Eigenvalues of the system with CPSS

Table 3 Parameters of the CPSS Parameters

h

Cases 1

2

3

h -2 41448 970 -5 214+/11 421 -2 04048 935 -3 4071/15 530 -1 7 6 3 4 8 666 -3 23314.605

5 0 260 0 415 0 222 0 214 0 200 0 216

1 -eigenvaIues. <- dainping ratio Table 7 Eigenvalues of the system with PBIL-PSS

Table 4 Parameters of the PBIL-PSS Parameters

GI

G2

Cases

c3

44

h

5

-S 07849 392

1

-3 2 4 0 4 10 089 -4 73549 578 -3 578910 202 -3 29348 718 -3 92S910 618

2

3 : 1 -eigenvalues,

1

0 476 0 302 0 443 0 331 0 353 0 347

6

,

.

,

,

.

,

,

,

,

i.3

1 4 -

c- damping ratio

5.2 Time Doniain Sinzulations Non-linear time domain simulations have been performed to evaluate the perrormance of the system under [he various cases discussed previously. For all the follov ing simulations. the disturbance considered is the loss of line 7-5 without a fault. Figs. 2-3 she\\ the electrical powcr responses under light load conditions (case 1). For this case. theie is no need to use PSS since the system is relatively well-damped. (see Table 5). It can be scen that the system settled quickly after only 4 sec for both the CPSSs and PBIL-PSSs.

Fig. 3 Loss ofline 5-7 (case 1): PBILL-PSS

rigs. 4-5 show the electrical power responses of system under nominal operating conditions. Lt is clear from these Figures that the PBIL-PSSs stabilize thc system quickcr than the CPSSs. Thc oscillations lasted up to about 6.5 sec with the CPSSs. However, with the PRlL-PSSs, the oscillations settled down in about 5 sec. Also, the overshoots and undershoots of thc responses of G I and G2 are smaller with the PAIL-PSSs than with the CPSSs.

02

-.

I~

a -.

a UY-

,

/\

11

1'

,/',,

xc*_-

"

1

'

I

2

3

"

5

4

6

'

1

7

a

' 10

ci

Time ( s e c )

Fig. 4 Loss ofline 5-7 (case 2): CPSS 2

.

.

.

.

.

.

.

.

. I-GI

The responses of the system operating under heavy load conditions (case3) are shown in Figs.6-7. It can be seen that the CPSSs did not provide adequate damping as compared to the PBIL-PSSs. In particular the oscillations of G1 lasted for about 6 sec mith the CPSSs and only about 4.5 sec with the PUIL-PSSs. Also, PBIL-PSSs give smaller overshoots and undershoots than the GA-PSSs as expected from the eigenvalue analysis.

1 2 -

0

I

,,I...... lt

v

041 0

0

2

1

2

~

3

~

4

5

'

6

'

7

"

8

'

9

10

Tiine ( s e r i

-___I----

"

15-

0 6 ~

0 4 ~ . . . . . ,.

02

1' .,

,.

"

.~ .~

0

..................

~

'

I

'

"

1

1

'

2

"

3

1

4

5

"

6

7

"

8

9

I

10

Time (sec)

"

Fig. 6 Loss of line 5-7 without fault (case 3): CPSS

45

'

'

~

~

DeMello F P and Cnncordia C (1969) Concepts of synchronous machine stability as affected by excitation control. It PAS-88. pp. 3 16-329. F o l l ~K , . A (2002). Stability Enhancement of Power Sqstemq IJsing a PBIL Based Power Sqstem Stabilizer. In: 6‘” Africon Conference in Africa (AFRICOAR”02), pp 953-956. Folly. K.A. (2004). Robust controller design for ?mall-signal enhancement of power system?. ln:2004 IEEE Apicon, 7ih ilj?icon con$rence in Africa. pp.63 1-636. Folly. K.A. (2005). Multimachine power system stabilizer design Based on a simplified version of Genetic Algorithms combined with learning. In: 2005 Proc Oj ISAP’05 CA ’ I 116-I I / I 012005. Goldberg. D. E. (1989). Genetic Algorithnis in Search, Optiniization (e Machine Learning, Addison-Wesley. Greene, J. R. ( 1 997). Simulated and Adaptive Search in Engineering Deqign- Experience at the IJnikersitq of Cape Town. Invited key paper at world Conference on soft Computing (WSC3), Springer Verlag. Mitchell M. (1996), An Introduction to genetic Algorithnzs. The MIT Press. Rogers, G (2000). Power Syhlem Oscillulions, Khmer Academic Publishers. Sundarcswaran K. and Bcgum S R (2004). Gcnctic Tuning of a Powcr System Stabilizer. Euro Ii-ans Elcctr Vol. 1 4 , pp. 151-164.. Yu. Y. N ( I 983). blectric Power Systeni Dynamics. New York: academic Press

6. CONCI,I JSlONS

Po\\er system stabilizer design for multimachine power system using PBIL has been presented in this paper. I he issue of tuning the parameters of the PSSs has been converted into an optimimtion problem which is solved via PBIL. Eigenvalue analysis show that the PBIL-PSSs perl‘orm better than the CPSSs and give adequate and consistent damping for all the three-cases considered. Nonlinear simulations are presented to confirm the eigcnvalue analysis results. The main advantage of PBIL is that it is simple, easy to use and has few genetic operators. REFERENCES Abdel Y.L. Abido M. A. and a. Mantawy H (1999). Simultaneous Stabilization of Multimachine Power Systems \. ia Genetic Algorithms. IEEE Trans on Power Systems. Vol. 14, No. 4, pp. 1428-1438. Ahmed S . S., Chen I,. and Petroianu A. (1995) Robust H w Tuning of Power System Stabilizers In :I995 IEEE PoiverTech Conk p p 238-243 Anderson P.M., Fouad A.A (1994). Power System Control and Stability. IEEE Press Power System Engineering Series. Baluja S. ( 1 994) Population-Based lncremental Learning: A method for Integrating Genetic Search Based Function Optimization and Competitive Learning. In: Technical Report CMU-CS-94-163. Carnegie Mellon University. Baluja S. and Caruana R. (1995) Removing the Genetics from the Standard Genetic Algorithm. In: 7 echnical Report CM(J-CS95-141. Carnegie Mellon University. Chen L. and Petroianu A. (1998) Application of PBIL to the Optimization of PSS tuning. In :I998 IEEE Proc Of Int Conj Powercon ‘98 on Power System Technology, I’ol 2 , p p 834-838 Davis L. ( 1 996). Handbook of Genetic Algorithms. International Thomson Computer Press.

46

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS DEVELOPMENT OF EDUCATIONAL WEB-BASED SIMULATOR FOR THE ELECTRICITY SPOT MARKET IN KOREA *Joo-Won Lee "Kwang-Min Yang *Yun-Won Jeong *Jong-Bae Park *Joong-Rin Shin

* Dept. ofElectrica1 Eng., Konkuk University, Seoul, 143-701, Korea Abstract: This paper discusses the development of the educational simulator for thc electricity spot market in Korea. In the developed simulator, lecturers can set information related with market and market entities and students can bid and examine the market with lecturers. The interaction between lecturers and users can be much enhanced via the webbased programs which result in the student's learning effectiveness on an electricity spot market. Howevcr the difficulties for developing web-based application programs are that there can he the numerous unspecified users to access the application programs. To overcome the aforementioned multi-users problem, we have provided the effective system architecture, the modelling of application programs, and database efficiently and efkctively to manage the complex dala sets. The developed application program 15 composed of the physical three tiers where the middle tier is logically divided into two kinds of application programs. The divided application programs are interconnected by using the Web-service based on XML (Extended Markup Technology) and HTTP (Hyper Text Transfer Protocol) which make it possible the distributed computing technology. Copyright 02006 IFAC Keywords: Elcctricity Spot Markct, Two Way Bidding Pool (TWBP), Marginal Clearing Price (MCP), Educational Simulator, XML-based Program. (Madrigal et. al. 2004; Paravan el a1 2003, Contreras et al. 2002). Under these tendencies, wc have developed an educational market simulator based on web that can simulate the power exchange methods and market rules of thc Two Way Bidding Pool (TWBP) in Korca Thc developed simulator will provide a large merit to students and staffs who are in the field of power systems or electncity markets It will also help them to understand the operation and control mechanism of the TWBP The educational market simulator is able of the distribution process and it is designed on an objectoriented programming (OOP) so that it is convenient to add new modules Also, to let many participants bid at the same time, it is devcloped as a web-based application on a basis of TCPiIP

1. INTRODUCTION

Deregulation of the electric power industry is occurring throughout the world. Some competitive electricity markets have been established, and others are under design (Shahidehpour et. al. 2001; Stoft, 2002). Recently, because of limited experience and knowledge of the competitive electricity market, problems related to market operation can not be avoided. To resolve the market-related problems, market simulation approaches have been frequently used (Dicorato et. al. 2002; Bunn et. al. 2001; Gonzalez el. al. 1999). A well constructed market simulator may help students foresee the effect of new market structures or rules before they are actually implemented (Madrigal et. al. 2004). It may also want to use a market simulator to develop and test their bidding strategies to maximize their profit. Thus, the market simulator has become an important tool in understanding the competitive electricity energy market. In a competitive electricity market, the methodology will be the maximization of the total profit-the global social welfare-of market participants, compared with the cxisting monopoly market that pursues thc methodology minimizing the generation cost. Therefore, for a stabilized operation of the power system in a competitive market, professional employees are needed in the electricity exchange and electricity market. In the acadcmic world and relatcd organizations demand for related education and to increase efficiency of learning about the electricity market theories, several methodologies and tools are created and released

2 IMPLEMENTATION OF MARKET CLEARING MECHANISM FOR ELECTRICITY MARKET IN KOREA Currently, the Korean electricity market is operated by the CBP mechanism, which the total load is determined from the whole power system and only the generations are bid by the Gencos. But this tcrm is a temporary term before it evaluates to the TWBP market That is why, in this paper, we have implemented both methods for students to understand about the electricity market Before we look over the system architecture of the developed simulator, we need to find out what algorithm was used in this simulator. Thc simulator developed in this paper has the samc function that is formed in the MOS (Market Operating System), which i s installed in KPX (Korea Power Exchange) Actually

47

Fig 1. The MCP evaluated from the one way method

the market clearing price (MCP) will be determined by two-way bidding of Gencos and Discos without considering the transmission limit and the dispatch of generation and load will be evaluated with considering the transmission limit in TWBP. However, we have implemented the one-way and two-way bidding methods since the current MOS of Korea has applied the only one-way bidding method.

2 2 Determination MCP by Two Way Method The two way method takes offers by both of the demand and supply to determine the MCP and quantity without transmission limits. In this method, the student can be the Genco or the Retailer/Disco Fig 2 shows how to decide the MCP of the two way method The generators are stacked as the same as the one way method and the loads are stacked in d descending order. The oblect function 19 to maximize the social profit, the 5haded area Note that we can call thi5 procedure as the unconstrained dispatch since the following formulation does not consider the transmission limits.

2.1 Determination of MCP by One Way Method The one way bidding method fixes the demand and takes an offer from the supply. In this method, the students act as Geiicos and the predicted demand is fixed. As shown in Fig. 1 , the gencration blocks stack in an ascending order and the price is determined where the block is met with the demand. To determine the MCP at each hour, the developed simulator has solved the optimization problem with an object function and constraints as following equations using the commercial optimization tool CAMS. Note that we can call this procedure as the unconstrained dispatch since the following formulation does not consider the transmission limits Object Fzinction: min(c

cG4/

isL / s B

LEGj s B

Constraints:

x GQ,

itC1tB

Constraints:

where, Lei : price on j ' s block of i-th Retailer/Disco,

1Pg,i-Load = 0

LEG

PJii"i Pg,, i p;;P"

ieG

P ~=, C~u g , i jx GQu

iEG

LQLJ. quantaty onj's block of r-th Retailer/Disco,

4,,

consumption of z -th RetaileriDisco, ui,/ : state 0111's block of z-th RetaileriDisco

jeR

where, Gej : price on j ' s block of i-th generator,

( 0 5 211 I/ 5 1 ), L =total loads

GQ : quantity on j ' s block of i -th generator,

Pg, generation of I -th generator, P F y , :P'

: max/min output of z -th generator,

state on j ' s block of r-th generdtor ( 0 5 u y rl 5 1 ), G = set of generators, B = set of bidding block for a generator, Load = specified load (I e given value) u q ,/

Hcre, the optimization variable is

u g ii

, the statc of the

generator, which means the generation of its bid can be fully accepted or just a portion. Ge, and GQ,, are the price and quantity of the generator bid The fixed pardmcter is "Load " which 15 given from the power system.

Actually it is necessary to consider the transmission limit to balance between the generation and demand in real world since the power system has the network comprised with a lot of transmission line. In MOS in Korea, MCP can be evaluated from the above mechanism without considering the transmission limit but the dispatch of electricity should be required the evaluation of the Constraint-on/off dispatch according to thc binding of thc transmission limit. In this simulator, we used the DC Power Flow method to apply those transmission limits. Using the DC load

I

48

flaw method (A I Woad c.t a1 1996) and the commercial optimization tool GAMS, it is easy to determine the constraint quantity as follows Note that we can call this procedure as the constrained dispatch since the following formulation consider the transmission limits. Object function: where,

Constraints:

c c5,l pg,,-

1EG

rI~,nO,n-C . revenue obtained from the unconstrained

(343)

=0

dispatch,

1EL

n>onon-G, revenue obtained from the constrained-on

C

PInjcl =

-

jtG

C P,:

iE N

(3-4

iEN

(3-el

dispatch, n>(,,,, - G revenue obtained from the constrained-off dispatch, MCP' market clearing pncc from thc onc-way or twoway method, CONPLz . offer price on constrained-on quantity,

jtl.

N

PFlow,

Plnjc, -

=0

j=1

PFlow:yi" 5 PFlowv 5 PFlow:;"

rp ; P,.,,

rg,;Ir;y

I =

c~,.,~; xGQ,

i, j

E

(3-0

N

iEG

(3-g)

iEG

(3-h)

ie I,

(3-i)

COFFPA : offer price on constrained-off quantity

3. SYSTEM ARCHITECTURE IN DEVELOPED SIMULATOR

jeB

4.1 = C u l , i ; x'dQg

3. I System StrLictLirz

icB

where, PL,j : generation ofj-th generator at bus-i,

S",

The most simple system structure for a web-based application program is to build most of the modules in one server. With that kind of structure, the developer can have control of the program very easily and so he can save a lot of time and effort for maintenance. But a web-based application program may have unspecified users and they will access to the server requesting data dnd applications. If one server includes all modules, it will require high system specifications. To solve this inconvcnicnt problcm, wc dcvclopcd thc systcm structure as Fig 4 , the most optimum structure to relieve the computer's strew (Yang ef a1 2004)

: consumption of j-th RetaileriDisco at bus-i,

PFlow,, : the power that flows from bus-i to bus-j,

PFlow,yax,PFlow~'" : the maximin transmission limit,

PInjc; : injected power at bus-i, N : number of total buses. 2.4 Implernentution of Settlement Method

In Korea electricity market, Constraint-on/off settlement is evaluated from the difference of the MCP evaluated in the unconstrained dispatch and the offered price on generation of constrained dispatch. For time interval-t, the profit that the I -th generator earns can be derived with the difference of the revenue and cost as following equation. 7T;

=[rI',

Cllfn: T1f.l

-C,(Ph,)]

(4)

Web

Application

Server

Server

'1'd:ile Tier

mt3 Tier

Fig. 4. System architecture for developing the webbased application program

whcrc, 7 ~ ; . the profit of z-th generator in time-t,

Shown in Fig. 4. the preexisting distributed system generally has three tiers - Client Tier, Middle Tier, and the Data Tier. The Client Tier takes the input from the users and shows the output through the web browser. The Middle Tier has two functions, the Application Server that gets the input data from the Client Tier and runs the application programs, and the Web Server that shows the results in the browser. Last, the Data Tier that not only saves the requirements that was needed for the applications bus also saves all the results that the application programs accomplished.

l : , : the revenue of z-th generator in time-t, PA the required generation of z-th generator in time-t,

C,(PL ) supply coyt of 1-th generator. Here, IT;, is calculated by the sum of all revenues; Constraint onioffrcvcnuc and thc unconstraint rcvcnuc.

49

function for checking the transmission congestion. “ln/Out Module” IS for the input and output of data between the database and other modules. “MA Module’’ is where the algorithm of the market simulation is implemented. Fig. 7 shows the flow chart of the “MA Module”.

In this paper, we subdivided the Application Server into three parts like Fig 5 so that will make the system use physically separdte processors With the use of those wcb services the ones who necd more dcep study, they can add a new module with only a few line5 of coding. [Web Server] is the module for web service and when a user connects to it, the [Web Server] credtes d session to answer the user When a user requests data with the [Web Server], the response if defined in the [MI Server] [MA Server] includes the algorithm., that are used for simulating the market It i s always on stand-by until data I$ requeqted. [Market Operating Program] offers a module that is able for thc “Educator” to test the sample system and can configure the generators and loads before he creates a market We used two databases, the MI Database for the [MI Server] and the MA Database for the [MA Server].

MAServer

”,

n.n.

rmhir TIW

Dd.4

TIPI

Fig. 7. The flow chart of the MA Module 3.4 Market Operating Program

Fig. 5 Systcm architecture for developing educational electricity spot market simulator

“Market Operating Program” is divided into 4 parts of functions as shown in Fig. 8. “File” part is where you open a market or configure your market participants. In the “Edit” part you can edit the power system’s generators, loads, and transmission lines. “View” part tells you the market status and the “Add On” part has the rest functions need in the simulator.

the

3.2 M l (Market Interjace) Server Market Operating Program

The web service has a page for the student and lecturer. The module for students has some pages, such as a page to bid for his generators, a page to find out the results of his bidding, and a page that shows the properties of his generators. The module of the lecturer has the pages that controls the simulation market.

-1

3.3 MA (Market Application) Server

r i l p n t TIP^

Ihdll- T i i r

D,it,i Tier

Fig. 8. The structure of the Market Operating Program

3.5 Database

C I i c ’ l t :Icr

ci d

The database is formed with the “MI Database” and the “MA Database”. “MI Database” is the space where is saves the data of the power system data, bidding data, spot market creation data, and the market participator data. “MA Database” is the space of the temporary data that is from the simulation process, such as the flag that inform the opening of the market, the field that tells to end the simulation, and the flag that report if the simulation is still running.

. I7I c t~

Fig. 6. The structure of the MA Server The “MA Server” IS divided into three modules shown in Fig 6 First, the “Class Module” is the part that defines the data types One “Region” can have several generators and loads The Region’s name and ID, the function that calculates the difference of the generation and load in a Region is included in this module Trdnsmission lines have information of two Regions’ ID, thc maximum transmission capacity, and the

4. CASE STUDIES To verify the effectiveness of the developed web-based simulator, we configured the following sample system with 10 generators, 6 regions, and 5 Retailers/Discos and cvaluated the MCP and quantities of unconstrained

50

and constrained dispatch for 24 hours with 1 hour interval. Actually the lecturer can build as the following system through our website.

IS 1268

Gen 3

15 13077 (875) 90531

(150) 89208 (30) 1134454 (150) 1134454 (150) 3 87072

Gen 4 Gen 5

morn 1

Gen 6 Gen 7

(175)

(300) 3 87072

Gen 8 Gen 9 Cell 1c -

(300) 077112 (400) 19 152 15)

I

1134643 (625) 1134643 (62 5 ) 4 04712 (625) 4 04712 (625) 077301 (50) 19'341 (3.75)

I

15 11474 (875) 9 1854 (175) 1134812 (625) 1134832 (62 5 ) 4 22352 (625) 4 22352 (625) 07749 (50) 1953 (375)

15.13871 (87.5) 9.3 177 ( I 7.5) 11.35021 (62.5) 11.35021 (62.5) 4.39992 (62.5) 4.39992 (62.5) 0.77679 (50) 19.719 (3.75)

15.14268 (87.5) 9.45 (17.5) 1 1.3521 (62.5) 1 1.352 1 (62.5) 4.57632 (62.5) 4.57632 (62.5) 0.77868 (50) 19.908 (3.75)

*Pi : ce of i-th interval of each generator, *Qi : Quantity of i-th interval of each generator.

The bidding data of RetaileisiDiscos ale deiived fioiii a random function Each demand function of Retailers/Discos has different elasticity. The demand curve for the first hour IS shown in Fig 10 and each data are in Table 4

Fig 9. A test system To verify the result data, we organized some typical generators and assumed the generators submit their bid as their marginal cost to IS0 and each Retailers/Discos submit a linear function comprised with random variable, which can be modified randomly at each intcrvdl for 24 hours, ds their bidding data Note that the students can submit thcir bidding ddta themselves through our webiite as Genco and RetaileriDisco. The fuel cost data and the heat rate function of generators are shown in Table 1 and Table 2, respectively

Table 4. The bidding data of loads

Load 3

I oad 5

15

25 0

Region

MIN

MAX

(I,

h,

c,

Fuel ID

Gen1 Gen2 Gen3

1

150 150

200 400 500

10 10 10

2 1 3

150 150

4

300

4 5 6

300 400 5

1.1 1.5 2.0 23 1.5 1.5 1.5 1.5 2.0 3.0

0.001000 0.000001 0.000003

~ e n 4 Gen 5

100 45 65 45 40 40 215 215 17.5 2

Gen6 Gcn7 Gen8 Om9 GcnlO

Gen ID

Cenl Gen2

PI (Q1) 10.584 (150) 11.34227 (150)

ion

400 400 550 550 600 20

P2 (Q2) 10.773 (12.5) 11.34321 (62.5)

I (7;)

I

I

(7.2) (486) 9.25 (1.8)

35

25

150

(486) 15.5 l5 (1.8)

Load 6

30

1 1

(13.5) 14 (7.2)

Load 4

Price[S/Gcal] Coal Nuclear 0 3 % Diesel

Name

25

Load 2

Anthracite Coal

Cen

(01)

Load 1

Table 1. The data of fucl cost Fuel Cost ID

PI

Load ID

P3 (Q3) 10.962 (12.5) 11.34416 (62.5)

onomoo

50

0.000002 0.000002 0.000700 0.000700 0.000050 0.004000

10

P4

(Q4) 11.151 (12.5) 11.3451 (62.5)

-p a

F; -Load

1

-Load

2

Loall 3 Load 4 +Load 5

15

Load 6

10 5 0

0

10 64

64 70

200

400 600 Quanuty (MW)

800

1000

Fig. 10 The regional demand curve

81

By lining up the generator data in an ascending order of price and the load data are in a descending order, the supply and demand curve for the first hour i i plotted as in Fig. 11. The MCP is where the two curves meet and In that point the equilibrium quantity is determined. In our case the MCP i s 9 45 ($/MW) and the quantity i s 1800 (MW)

P5 (Q5) 11.34 (12.5) 11.34605 (62.5)

51

students know how the real electricity market runs and can experience the process how market participants make their revenues. ACKNOW LEGEM ENT This work was financially supported by MOClE through IERC program. REFERENCES

M. Shahidehpour, M. Alomoush, Restructured

5. CONCLUSION

This paper discusses the development of the educational simulator for the electricity spot market in Korea. In the developed simulator, lecturers can set information related with market and market entities and students can bid and examinc the market with lecturers. The interaction between lecturers and users can be much enhanced via the web-based programs which result in the student’s learning effectiveness on an electricity spot market. In this developed simulator, the system and database are developed efficiently to treat the plenty of the data and a lot unexpected users‘ access Unlike the existing educational simulators, the one we developed in this paper has a strong point by allowing the students to have an opportunity of being an owner of an electricity utility and can make some bidding strategies just like in a real market. That will make the

Electrical Power Systems, Marcel Dekker Inc., 2001. S. Stoft, Power System Economics, IEEE Press, 2002. M. Dicorato, A. Minoia, R. Sbrizzai, and M. Trovato, “A simulation tool for studying the day-ahead energy market: the case of Italy,” in Proc. Power Eng. Soc. Winter Meeting, 2002, vol. 1,2002, pp. 89-94. D. W. Bunn and F. S. Oliveira, “Agent-based simulation-an application to the new electricity trading arrangements of England and Wales,” IEEE Trans. Evol. Comput., vol. 5, pp. 493-503, Oct. 2001, J. J. Gonzhlez and P.Basagoiti, “Spanish power exchange and information system design concepts and operating experience,” in Proc. IEEE 21st Int. Conf. Power lndustry Comput. Applicat. PICA Santa Clara, CA, May 1999, pp. 245-252. M. Madrigal, M. Flores, “Integrated Software Platform to Teach Different Electricity Spot Market Atchitectures”, IEEE Trans. on Power System, Vol. 19, No. 1, pp. 88-95, Feb. 2004. D. Paravan, A. Sajn, R. Golob, ”Teaching trading electricity with the use of electricity market simulator,“ in Proc. Power Tech. Conf. 2003 IEEE Bologna, Vol. 3 ,pp. 23-26, June 2003. J. Contreras, A. J. Conejo, S. de la Torre, and M. G. Munoz, “Power engineering lab: electricity market simulator,” lEEE Trans. Power Syst., vol. 17, pp. 223-228, May 2002. A. J. Wood, B. F. Wollenberg, Power Generation, Operation, and Control, John Wiley & Sons, he., 1996 K. M. Yang, K. S. Lee, J. B. Park, and J. R. Shin, “Development of System Architecture and Method to Reprocess Data for Web Service of Educational Power Flow Program”, KlEE Journal A, vol. 6. pp. 324-333,2004.06

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS A COOPERATIVE POWER TRADING SYSTEM BASED ON SATISFACTION SPACE TECllNOLOGY

Keinosuke Matsumoto, Tomoaki Maruo, Naoki Mori Department of Computer Science and Intelligent Systems, Chduute School of Engineering, Osuku Prefecture lJniver.si@ I - I Gakuen-cho, Nakuku, Sakai, Osaka 599-853 I , Japan

Abstract: Various power trading system models have been proposed, but many of them will not aim at load reduction by making customers cooperate with power suppliers in a powcr trading market. Some researches tried to solve the problem by introducing reward in the power market. This approach was developed on an evaluation function, but it must estimate customers’ evaluation functions beforehand. Then, this paper proposes a new approach to cope with various kinds of customers by modeling a power market on a satisfaction space. In addition, we have built the proposed system as a Web application on the Internet. Copyright C 2006 IFAC Keywords: Power systems, Economics, Energy management, Intelligent systems, Modelling, Communications systems, Utility functions

1. INTRODUCTION Many power trading system models have been proposed to deregulate key elements of the electric industry worldwidc (Stoft, 2002; Dy-Liacco, 2002, Vaahedi, 2004) These systems depend on market mechanisms and they would cause a problem that electric power price fluctuates greatly with demandand-supply imbalance In order to solve this problem, a research (Matsumoto, et a l , 2001) has tried to make a cooperative power trading system that keeps a proper balance between demand and supply of electric power by making customers and suppliers have cooperdtive reldtions mutudlly Thi\ approdch has been developed on an evaluation function of satisfaction, and there I S a problem that can handle only customers that fulfill a specific condition Then, this paper describes a new cooperative power trading cystem that can deal with various kinds of customers by modeling a power market on a satisfaction space Satisfaction space technology can deal with customers without evaluation functions. In addition, this paper proposes a power reducing method using a combmatorial optimization technique. The method can be applied to a situation that the degree of customer’s satisfaction cannot be correctly estimated beforehand

flexibly correspond environment.

to

each

communication

2 . PREVlOUS COOPERATIVE POWER TRADING SYSTEM A power trading market consists of three kinds of agents supplier, customer, and auctioneer. They act independently according to the intention of themselves A supplier tries to sell electric power and make a profit to maximize the degree of satisfaction A customer is an agent aiming at purchasing electric power to raise the degree of satisfaction An auctioneer is an agent that conducts market trading impartially and controls the market stability. Configuration of the trading system model is shown in Fig. 1.

If demand exceeds supply, the auctioneer in the cooperative trading system asks customers for power reduction Reward is paid in compensation for the reduction to maintain the degree of $atisfaction of the customers. Customer

Supplier

>I

To make this business model fit for practical use, it is indispensable to develop a communication network model (Vojdani, 2003, Matsumoto, et a l , 2003) in data communication level. This paper also proposes a network model of the electric power trading systems using Web site as a platform of this network model Building a network model using Web qite enables us to create a communication network system that can

Auctioneer

K

Fig. 1 . Cooperative trading system model

53

In the cooperative trading model, supplier's evaluation function u,, is defied as a function of market price p and power supply r :

Customer's evaluation function udl is also defied as a function of market price p and power consumption f'

: u

4

=u

4(p,r)

(2)

Taking into account of reward, supplier's evaluation runctlon v,,(p,r,w) after introducing reward and customer's function v&,r,w) are shown in ( 3 ) , (4) respcctively. Wherc IV is rcward.

The left hand side of (1 I ) cxpresses the dcgrce of customer J ' S satisfaction On the other hand, right hand side of the equation shows the degree of customerj's satisfaction that an auctioneer estimates. This type of customer's g,,is a linear function, so that reward is correctly paid to the customer because both hand sides of (1 1) are equal. If another customer's ,g!> is an upward convex function, then (1 2) is satisfied:

For this typc of customers, the auctioncer estimates their satisfaction less than real values Therefore, they get rewdrd more than necessary to be paid to them If thc other customcr's g,, is a downward convex function, then ( I 3 ) IS satisfied:

If market price is p, initial power demand rd,, and reduced power demand then the reward wdl given to customer] is defined as ( 5 ) in this model

We define a degree of satisfaction of customer J as 1); (p,r,w), and also define ,q, as a satisfaction function of thc reward at a market pricc p In this case.

For this type of customers, the auctioneer estimates their satisfaction more than real values. Therefore, they will not get enough reward to maintain the degree of satisfaction. 3 . SATISFACTION SPACE We have developed a satisfaction space technology that solves the problem stated in the previous chapter.

3. I Dgfinition qf Evuluation Function Where, g,;' is an inverse function of g,,, L'd,(p,r) is a satisfaction function with regards to the power quantity r under the conditions of the market price p, which is defined as (8).

Supplier's and consumer's evaluation functions are defined as satisfaction functions like (14) and (15) respectively.

The following equation i s derived in the same way: Where, p is a market price, r i , supplier i's power supply, and w,,the amount of reward to pay. On the other hand, 7'4 is customerj's power demand, and wd, the amount of reward to be paid. Substituting (7) and (9) for (4), we get (10): Moreover, a total evaluation function of the coopcrative power trading systcm is defincd as (I 6),

Mapping ( 1 0) using g,, ( 1 I ) is derived as a constraint of this model. Where a, and bJ are weights of suppliers and coiisuincrs rcspccti vely.

54

3.2 Trading Procedure Dealings are done with the cooperative power trading system according to the following processes:

Price Decision Process 1) Suppliers and customers submit their bids for initial power trading quantities rrrlst,rdllsrand expected unit prices p.,,,p6,/respectively. 2 ) The auctioneer decides a market price p1 based on the values of the bidding. In our simulation, (1 7) is uscd to determine the pricc p , .

----____

PPP2

Power -

Id

Fig. 2. Satisfaction Space. Power ieduction is caiiied out i n the following sequences Customers present some trading points ( { ( / " d j k W d k ) I ydk< rdj2nd, "Vdrk'O, k-1, 2, 1) that they can make deals as shown in Fig 2. Using this presented information, power reduction is formulated into a combinatorial problem that determines the best power reduction plan under the condition of minimizing the total amount of rewards and maintaining thc degree of satisfaction of each customer.

Power Reduction Process 1) Getting the market price pl, suppliers and customers submit their second bids for expected ,,~ power trading quantities r,r2nd,r ~ / 2respectively 2 ) The auctioneer makes a power reduction plan to balancc thc amount of powcr supply and demand by means of evaluation functions of customers. In this process, each customer's rd and reward wd, are determined by solving the following constrained minimization problem to maintain the degree of satisfaction of every customer: Objective function:

This method can be applied to the customers whose evaluation functions can't be estimated beforehand, and it is also possible to collect the trading information of the customers necessary for estimating their evaluation functions. 4. EXPERIMENTAL RESULTS

subject to

Some simulations were carried out to examine the validity of the proposed technique. 4. I Evaluation Functions of Suppliers and Customers

Supplier's evaluation function is shown in ( 2 3 ) ,

3 ) Quantity of supplying power rsr that each supplicr actually supplies is dctermincd by (21):

Quantity of reward w,, that each supplier actually pays is dctermincd by (22):

where f is sensitivity to the power at the time when demand quantity goes over tbe optimal operating point, e, i s sensitivity to the price, and a is a satisfaction conversion factor of reward into the degree of satisfaction of the electric power.

3.3 Comhinatorial Optimization Technique for Power Reduction

As an example, the following three kinds of functions were used as the evaluation functions of customers:

You must use some information of customers to estimate the customer's evaluation functions This section dcscribcs a mcthod to make an clcctric powcr reduction plan under the conditions that sufficient infomiation can't be obtained to estimate the c ustomcrs ' cv al uat I on funct I ons

where (J&I, r ) is a satisfaction function with regards

55

to the power quantity r under the conditions of the market pricep, and it is defined as (27). U&,r)=a-bexp

(-cr)-dr-e,-

P- Pd,

On the other hand, the proposed method can make a proper power reduction plan for all customers. This means that the new method can handle properly various kinds of customers.

(27)

p4 a, b, c and d are parameters on the electric power, and e, is sensitivity to the price. Real values of the parameters a, b, c and d are estimated by means of Newton-Raphson method using initial values established in advance and the bid information of every customer.

4.2 Simulation I All customers’ evaluation functions are assumed to be known in this simulation. Comparative experiments were carried out for the previous model and the proposcd model to verify their abilities of making suitable power reduction plans. “Suitable” means that the auctioneer could reduce the power demand while inaiiitaiiiing the degree of satisfaction of customers Total power demand is reduced to the total power supply, and each customer’s demand is reduced in proportion to the amount of initial demand. Reward is determined by the calculation method of each model. Detail data arc shown in the following: Total number of customers: 90 (Linear type:30 , Logarithmic type:30 , Exponential type:30) Initial power demand: l00KW f 10% (determined by uniform random numbers) Initial parameters: a = b = 2.624, c = 0.00882, d = 0.00616 Pricing scnsitivity parameter: el =0.005 Reward sensitivity parameter: a=OS I .0 (determined by uniform random numbers) Total number of suppliers: 5 Initial power supply: IOOOKW i 10% (determined by uniform random numbers) Sensitivity parameter for excess over optimal operating point:p6 Pricing sensitivity parameter: e, =0.00 I 10) Reward sensitivity parameter: a=0.5 1.0 (determined by uniform random numbers)

-

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4.3 Simulation 2 For 100 customers and 5 suppliers, we have mdde power reduction plans using the combinatonal optimization technique and checked the efficiency of the market control and the necessary information of the customers I ) Total number of customers: 100 (Linear type 30 , Logarithmic type 60 , Exponential type 10) 2) Total number of suppliers 5 Calculating the market price and the amount of each expected power supply and demand, making power reduction plans were tried 100 times for each case, which corresponds to the number of trading points (from 1 to 4) that customers should present to the auctioneer. Every customer presented the specified number of trading points that were made at random at every time of the 100 trials The power reduction rate of this scenario is shown in Table 2 Excess amount of power supply and maximum error ratc are shown in Table 3 If the nuinbei of the trading points 15 two, five times out of 100 could not reduce power less than the total expected power supply If the number of trading points is more than three, all 100 times could reduce power less than the total expected power supply Generally, the more the number of the trading points presented hy customer? increase?, the more the burdens of the customers increase Therefore, considering the burden of the customers and stable market control, it is necessary to make power reduction plans with the necessary and sufficient amount of information The values of the total evaluation function increase with the number of trading points as shown in Table 4. This means that the power reduction plans do not always reach a perfect equilibrium point, but they are Table 2 Power reduction rate in the simulation 2

Table 1 shows the degree of satisfaction of every customer. This table shows that the previous model can deal with correctly only the type of customer IL1.

Vajl (Linear) C’d~2(Logarithmic)

VG? (Fxponential)

Before reducing

Previous method

Proposed method

0955 0 957 0 964

0955 1 194 0 887

0955 0957 0 964

Total expected power supply

Reduction ratc

9717404kW

7300941kW

24 8%

Table 3 Excess amount of suuulv and error rate

Table I Change of satisfaction of each customer Type of customers

Total expected power demand

Number of trdding points 1 2

3 4

56

Excess

amount of power supply 795 70’3 103.410 0 0

Maximum error rate 10 9 Yo 1.41 ‘% 0% 0%

Table 4 The values of the total evaluation function Number o f trading points

Before reducing

1 2 3 4

0 223 0 223 0 223 0 223

6. CONCLUSIONS

Average of

This paper proposed a cooperative power trading system that could cope with various kinds of customers by modeling them on a satisfaction space In the cooperative power trading system, it is not necessary to find the price that supply corresponds with demand of power because there is adjustment by rewards If it tries to find the price at which supply and demand correspond strictly, it will cause a price jump since price elasticity of electnc power is low.

100 trials 0 709 0 820 0 912 0 945

very close to the equihbrium point Moreover, increasing of the total evaluation function implies that the trading system can make efficient reduction plans.

This system can be applied to customers whose evaluation functions cannot be estiirrakcl beforehand. When evaluation functions of consumers can't be cstimatcd, auctioneer makcs a dcalings plan by untying a combination problem based on the information bid by consumers. The most efficient power reduction point is chosen one by one for every consumer, and this simulation is searched for a solution using the maximum steep slope method for performing electric power reduction gradually.

5. NETWORK MODEL We have developed a network model for the proposed cooperative power trading system that works on the Internet. A schematic view of the nctwork model is shown in Fig. 3. The proposed system is built on a Web server, and trading data are managed in the form of XML (extensible Markup Language) A customer inputs bid information through the Web browser The inputted information is processed on the Web server and stored in the form of XML The proposed system conducts electric power dealings based on this stored XML information

LIf-

-

view HTML/JSP

REFERENCES Dy-Liacco, T. E. (2002). Control centers are here to stay. IEEE Comput. Appl. Power, vol. 15, pp.1823. Matsumoto K., N. Mori, M. Kitayama and Y . Izui, (2001). An interactive demand side management system using utility functions. In: Proc. International Conference on Intelligent System Application to Power Systems (Isill> ZOOl), pp.197-201, Budapest, Hungary. Matsumoto K., T. Maruo, N. Mori, M. Kitayama and Y. Izui. (2003). A communication network model of electric power trading systems using Web services. In: Proc. IEEE Bologna Power Tech Conference, Paper number #49, Bologna, Italy. Stoft S. (2002). Power Syslem Economics: Designing Mai4ets for Electricity. Wiley,. New York. Vaahedi E. and M. Shahidehpour (2004). Decision support tools in restructured electricity systems: an overview. IEEE Trans. Power Systems, vol. 19, no. 4, pp. 1999-2005. Vojdani A. F. (2003). Tools for real-time business integration and collaboration. IEEE l>ans. Power Systems, vol. 18, no. 2, pp.555-562.

Power Trading System \

- Controller -

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Mobile

As a future task, we should develop an cstimating method of customers' evaluation functions on the basis of the collected customer information.

Servlet

Model XML Colltrol Real,

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H

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XSL r txtensible Style5heet L anguage rransfomdtion SMTP Simple Mail Transfer Protocol

Fig. 3. Architecture of thc network model.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

INFLUENCE OF WIND ENERGY ON THE POWER STATION PARK AND THE GRID H. Weber" T. Harnacher"" T. Haase"

"University ofRostock

""Mu~-Plunck-lr~sti~ut fur Pkusmuphysik Gurching

Abstract: The cncrgy supply in Germany was stecrcd by thc current demand of the consumers till now. It will change in an adjustment process to an energy supply led by stochastically arising energy offer by wind power stations. The development of the wind energy is pushed at suitable onshore and offshore sites. Up to the year 2030 onshore wind parks are expected with an installed power of approx. 22 GW and offshore wind parks with 26 GW installed power. The planned offshore wind parks with partly more Giga watts of power must bc connected to the existing high-voltage transmission system. Another problem is that the wind energy is mostly produced in northern Germany, but is mainly needed in the middle and Southern part of Germany such as the Rhine-Main and Ruhr district. In order to compensate for the fluctuating feeding from the wind power stations backup power plants are needed. They must be able to provide reserve power. A simplified model of the German cncrgy generation and transmission system was used for this investigation. Based on this model a conceivable scenario of the energy supply in Germany in the year 2030 will be discussed in this paper. Cop,vright 02006 IFAC Keywords: Renewable energy, bottlenecks, load management, congestion management, substitution of conventional power.

1. DEVELOPMENT OF THE OFFSHORE AND

ONSHORE WIND ENERGY UNTIL 2030 An enormous boom for the construction of onshore wind power plants was caused by an attractive remuneration of the wind energy fed into the grid as well as the obligation to accept delivery of wind energy according to the renewable energy law (Geiinan abbreviation EEG) and the rdpid technical development starting afterwards By the end of 2003 wind power stations with an output of 14 315 MW were installed in Germany By far the greatest shares hereof belonged to the energy supply companies of Vattenfall Europe ( 5 400 MW) and E ON (6 250 MW) The Geman wind energy production amounted to approx 18,6 TWh (E ON 8,5 TWh and Vattenfall Europe 6,7 TWh) in the year 2003 This devclopment will continue and the dnnual rates of increase will turn out lower due to the restricted productive onshore sites Starting from the year 20 10

saturation will occur. By then the rise of the wind energy production will be caused only by the replacement of older plants by more efficient and more productive plants. For the year 2030 an installed onshore wind power with approx. 22 GW is forecasted. The difficulty will be to maintain the extension of the wind energy use in Germany on high standard even though there will be a saturation in the onshorc arca. Thc solution will bc to gradually acquire suitable sites at sea. For these sites in the North Sea and the Baltic Sea investors have applied for 18 wind parks which partly consist of several hundred single wind power plants. At present, wind parks are planned with an installed power of 21.561 MW in the North Sea and 4.437 MW in the Baltic Sea. Also, 800 MW shall be used for the production of hydrogen directly offshore. Figure 1 gives an overview over the historic and expected development of the German onshore and offshore wind energy capacity.

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2015 -

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1990 1995 2000 2005 2010 2015 2020 2025 2030

Fig. 1 : Historic and expected development of the German onshore and offshore wind energy capacity

3 . WIND MODEL Wind power shows very special characteristics, which diffcrs considerable from conventional power plants. The following investigations are based on wind data collected on the world wind atlas (Sander + Partner GmbH, Swit7erland). The data presented on the world wind atlas has only a six hour time resolution. By special random methods also data with one hour time resolution were produced. The transformation from wind velocity to active-power output was done with data from modern existing wind turbines for onshore sites (1 MW, 1,5 MW. 2 MW) and offshore sites (2,5 MW, 3 MW).

2. SIJBJECI OF EXAMINATION

The challenge for the next years will be to develop a power station park which brings in line the different political interests and specifications. particularly the reduction of the greenhouse gases and the generation of electricity of local lignite and hard coal. With a model of the German energy generation and transmission system a scenario of the energy supply in the year 2030 w.ith an installation of 26 GW offshore and 22 GW onshore wind power is analysed. The investigation is based on the conditions that thc wind powcr plants will producc nothing but electrical power (no hydrogen) and there will be no further development of the pumpedstorage power stations. 'The power station park and the transmission system should adapt optimally to the characteristics of the wind and ensure the balance between generation and consumption. Starting from these expectations the paper will address technical and economic problems related to the integration of 48 GW wind powcr into thc German clectricity grid. Basis of the analysis are two models: engineering and an economic model. The economic model is calibrated with the help of the engineering model. The analysis will be made on two levels: 1) An economic level, which will address the possible development of the costs of wind turbines and the costs related to the installation of extra transport capacities: increased demand of control power and back-up power. The conventional part of the power system will be described in two scenarios: A business as usual scenario, with a power plant structure which is similar to the current one and a wind scenario, in which the rest of the power system is more seen as a system to balance the stochastic power supply ofthe wind plants. 2) A technical level, which will address all questions related to the bottlenecks in the transport infrastructure. 'l'here are several results of the optimization in level 1. Firstly the capacities of baseload and peak-load power plants. Secondly the optimal behaviour of the power station park related to the influence of wind power. The transport capacities between the nodes in the grid are a further outcome ol' the model. These results of optimipation are the input data for had flow calculation in level 2. The following questions shall be answered:

Are the wind power plants able to cover the base-load in the year 2030 and thereby substitute the thermal power station capacity? How much fuel can be saved by means ofthls substitution and can this lead to a considerably reduction of the C 0 2 emissions? At which sites in the transmission system can new power stations for lignite, hard coal or gas be installed cost-effectively? Where do bottlenecks arise in the high-voltage transmission system and how many transmission capacities must be built then?

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Fig. 3: Character ofan onshore site in Southern Germany Supply of power from wind turbines is stochastically in nature, the actual active-power output is more or less proportional to the third power of the actual wind velocitj. The wind velocity depends on the location and the actual meteorological situation. which itself depends strongly on the season. A

60

;

2 3

5%

Fig. 2: Character of an offshore site in the North Sea

5

6 s -

comparison between two onshore sites in the North Sea and in Southern Germany is depicted in figures 2,3. The average wind velocities and the active power related to the installed nominal power are represented for a typical year. When comparing the figures 2 and 3 it is noticeable, that the average wind velocity in the North Sea is considerably grcatcr thcn in Southcrn Gcrmany. Duc to thc characteristics of the wind power plants (P-v’) the active-power output is significantly smaller. This means, a profitable and economic wind energy production is possible only in the north part of Germany, especially offshore. On the other hand in Southern Gemany this is hardly imaginable. The German Wind Energy institute (DEWI) updates the details on the wind power installations for the single Gcrman fcderal states each month. The wind powcr plants installed in December 2003 in the German federal states were distributed among the network nodes. It was scaled to the onshore installation of 22 GW in the year 2030. Thc estimated offshore installation of 26 GW in 2030 was distributed to the network nodes in the immediate coastal area. In the year 2030 the wind current production would amount to 118,6 TWh with an offshore share of 69,2 TWh. Then the quota of wind cnergy in the total electricity generation of Germany will be up to 21 YO. 4. NETWORK MODEL The transmission systems and the power station parks of the four big German energy supply companies were united, as there are EnBW, RWE, E O N and Vattenfall Europe. In the network model the German production and consumption centrcs are represented by 30 substitute nodes. The power stations belonging to the consumption centres were summarized and subdivided according to their sources of energy or their mode of operation (lignite, hard coal, gas, pumped-storage, run-of-river). The nuclear power stations were replaced by lignite and hard coal power plants as well as natural gas fired power stations. Special attention was paid to the modelling of the pumped-storage power stations because these plants are the only ones which are presently able to store energy with a high efficiency (> 75 %). Exact data were provided by the operators of the pumpedstorage power stations in order to be able to determine the energy capability as well as the average power in the pump and turbine operating mode. The calculated total energy capability of the pumped-storage power stations in the turbine operating mode amounts to approx. 43,3 GWh and in the pump operating mode to approx. 56,7 GWh. The electrical consumer loads were taken from a UCTE data set and assigned to the respective substitute nodes. The consumer loads of every node were subdivided into 84 typical diurnal variations. These variations represent one week of each month of the year. It was calculated from Monday to Sunday because every day of the week has a specific characteristic. In order to model these characteristics the calculation was realized in a one-hour resolution. Among other things the calculation of the curves was

61

based on the load of the four German energy supply companies of the year 2003 Then they were scaled to the consumption expected for the year 2030. The transmission capacities between the substitute nodes in the 3801220-kV level wcre determined and summarized from d detailed model of the UCTE net. The surrounding UCTE net was modelled in simplificd tcrms into tcn nctwork nodcs Thc production and consumption of each UCTE member were summari7ed in one network node The transmission capacities between the European network operators were taken from the statirtical yearbook of the UCTE. Thereby a calculation of the European powcr flow IS possible in which the monthly changes are considered 1 his is particularly important since the German net is charged by power transits both to east-west duection and to north-south direction Power exports in the winter and power imports in the summer are distinctivc for Germany

5 OPTIMIZATION The optimization of the model was carried out with a linear cost optimization. The investment costs are distributed over the economic life time of the power stations with the annuity method. The optimal power stations and transmission capacities as well as the optimal schedule of the power station park result from the optimization. However, the linear optimization is not able to consider the lower efficiencies in the operating mode with partial loads of the thermal power stations. The optimization was realized with the CAMS (General Algebraic Modelling System) software package. The optimization was executed with the values of twelve randomly selected days in one year, one typical day for each month. It was calculated with a time resolution of one our. The result was projected onto the whole year with 8760 hours. This simplification was necessary because the available memory capacity of the computer was fully occupied. Additionally it was intended to reduce the computation time. In the future however these problems will be solved by way of better and faster algorithm of optimization. Besides the parameters length and efficiency of the 380-kV transmission lines the costs for investments and maintenance were also implemented in the model. Parameters like efficiency, C 0 2 emissions, fuel costs, investment costs as well as variable costs and operating costs, were assigned to the individual power station types. The calculation of the current-dependent COz emission is based on the assumption that the coal fired power stations will have an efficiency of 50 % in the year 2030. The ratio of the electricity generation between lignite and hard coal amounts 45 O/o to 55 o/. Due to this mixture the thermal emission factor results in 360 g C02/kWh. The gas fired power stations will have an efficiency of 40 % in the year 2030 and the thermal emission factor of the natural gas will amount to 200 g COz/kWh. Two scenarios were defined and examined, scenario I (without wind power installation) and scenario 11 (with a sum of 48 GW wind power installation, onshore and offshore).

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Output Data For The Optimization . . . . . . . . . . .I . . . . .......

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Fig. 4: lnput and Output data for the optimization 6. SCENARIOS

6.1 Results of the optimization with a power station park without windpower (Scenario 4 The currcnt dcmand of 571,2 TWh will be met by coal fired power stations at 84,7 %, by natural gas fired power stations at 13,l 9'0 and by hydroelectric power stations at 2,2 YO.In detail hydroelectric power stations will provide a capacity of 8.500 MW which was used as a constant value in the optimization. In addition coal fired power stations will contribute a capacity of 57.070 MW and natural gas fired power stations will have a capacity of 26.970 MW. Both capacities were determined by the optimization. The coal fired power stations shall cover the base-load whercas the gas fired power stations are designcd for the peak-load. Taking this power station mix the current-dependent C 0 2 emissions would amount to approx. 473,l million tons per annum. The then existing power supply system would be sufficient to transport the energy which will be needed. As a further result the optimization does not add any new transmission capacities. 6.2 Results of the optimization with a power station park with windpower (Scenario /()

I

A

a capacity of 45.170 MW and natural gas fired power stations will have a capacity of 36.500 MW. Both capacities were determined by the optimization. The coal fired power stations shall cover the base-load whereas the gas fired power stations are designed for the peak-load. Taking this power station mix the current-dependent COz emissions would amount to approx. 358,4 million tons per aimum. The then existing power supply system would not be sufficient to transport the energy which will be needed. In the model a 2.600 MVA transmission line between Hamburg and Rostock which will be built until the year 2030 was assumed. As a further result the optimization inserted new transmission capacities in the net model. Bottlenecks will occur at the lines which go from the coastal area of the North Sea to the south. The is caused by the fact that the electricity generation centre will be then in the north part, especially in the Hamburg area and the consumption centres will be located in the west and south part (Rhine-Main and Ruhr district). The programme inserted transmission capacities of 6.500 MVA between the nodes Bremen and Muenster as well as capacities of 5.200 MVA between Kiel and Hamburg. The total length of the new transmission capacities would amount to approx. 1.000 km based on a 380-kV Wansmission line with a 1.300 MVA transfer capability.

7 . NETWORK CALCULATION The current demand of 571,2 TWh will be met by wind power stations at 21,3 %, by coal fired power stations at 6 1,l %, by natural gas fired power stations at 15,4 % and by hydroelectric power stations at 2,2 %. In detail wind power will provide a capacity of 48 000 MW and hydroelectric power stations will plovide a capacity of 8 500 MW which both were used as constant values in the optimization In addition coal fired power stations will contribute

Various cases were investigated with the DIgSILENT software. Input quantities of the power flow calculation are the optimized power station capacities and line capacities from scenario 11. For the whole German net the optimized power station capacities are represented in figure 4 which is subdivided into seven regions. The concentration of the wind power plants in the north is clearly

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8 Fig. 5:

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Behaviour of the power station park during a week with strong wind power; grey (base load), yellow (peak-load), green (wind onshore), red (wind offshore), blue (run-of-river), purple (pumped-storage)

recognizable This means that about 80% of the German wind energy would be produced in the north It i s also outstanding, that hardly any baseload power plants but considerably more peak-load power plants would be installed in the north. Hydroelectric power stations are only available in the southern regions due to the geographical conditions. The main consumer centres are in the western and southern part where, according to the consumer behaviour, more base-load and peak-load power stations would be installed Furthermore the power stations where operated in a minimum-cost schedule. In figure 5 a strong feeding from wind energy for the German net is represented for one week from Monday till Sunday On Monday practically no wind fceding was offered Thc figure shows thc gencration schedule as known so far. The schedule i s designed for the hourly changing consumer power. The baseload power stations would cover the power up to approximately half of the expected peak-load The peak-load power stations then would follow the consumers in their diurnal variation The pumpedstorage plants regulate the need for peak-load With thc feeding of wind energy increasing on Tucsday it was noticeable that at first the power of the pumpedstorage plants and the peak-load power plants were throttled down In the night from Wednesday to Thursday the power of the base-load power stations would have to be reduced, too During the day on Friday very few peak-load power stations continue to fced cnergy into thc net The consumer dcmand then i s covered only by the base-load power stations and thc wind power stations The pumpcd-storagc plants reguldte the need for peak-load With the feeding of wind energy increasing on Tuesday it was noticeable that at first the power of the pumped-storage plants and the peak-load power plants was throttled down. In the night from Wednesday to Thursday the power

63

of the base-load power stations would have to be reduced, too. During the day on Friday very few peak-load power stations continue to feed energy into the net. The consumer demand then is covered only by the base-load power stations and the wind power stations. During the weekend the consumer demand diminishes substantially. The wind feeding, however, remains constantly high. Further base-load power stations would have to be switched off after that. The generation schedule then would be dependent almost only on the feeding of wind energy. The consumer would play a completely subordinate role in this. The load flow investigation aims at the following: - Up to which amount of wind energy feeding can the net be operated stably? - Is the transmission grid able to transport several Giga watts of wind energy through the net? These questions shall be answered by a rough estimation with the help of a simplified German network model. Figure 6 represents the active power load flow in the German as well as European net during the feeding of 25 GW wind power. A further shifting o f the load flow in north-south direction as consequence can be clearly recognized. The width of the lines corresponds to the active power flowing over the tie lines. About 113 of the consumer load is covered by wind energy at this time. The situation in the western part of the German grid system which is characterized substantially by the high feeding of wind energy from the North Sea has to be judged considerably critically. The shifting of the power flow i s carried out under the unavoidable demand on the net of the Benelux states as well as France and the Czech Republic. This here represented 25 GW case is a theoretical borderline case. At increasing feeding of wind energy in this range the transmission lines are charged extremely and the voltage cannot be kept in its operating limits any more.

-------------p n d ow F F e e d i n g X s h o r e Wind P o w e r Feeding O f f s h o r e

10.414 MW 14.988 MW

Consumption Germany

I

75.086 MW

I

Interchange Power France

* 6.011 MW

Poland

i

1.226 MW

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1.126MW

Czechia Denmark

+ 35MW

Italy

- 6 083MW

Benelux S t a t e

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28 MW

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10 012 MW

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South-West South-East

- 5 843MW - 1 4 4 7 MW - 3 313 MW - 1113 MW - 1.719 MW

Germany

This paper was based on economic power plant models which have been provided with realistic parameters. In this study the minimal costs for the investments and for the operation of the German integrated grid for the year 2030 including the wind energy have been calculated with a linear minimumcost model. Afterwards, the technical feasibility o f the optimised power station park and of the optimised German grid was investigated by means of net calculation and simulation. At first it is obvious, that the installation of 22 GW onshore and 26 GW offshore wind energy does not lead to any significant reduction of the capacities of thermal power stations. The primary benefit of this heavy wind energy installation will be to save fuel, about 8,9 million of tons per annum of hard coal and about 18,2 million of tons per annum of lignite. But the operational availability of wind power generation is poor. Secondly a considerable number of new high voltage transmission lines will have to be built to transport the wind energy from the north part to the south and west parts of Germany. The used synthetic network model is sufficiently exact for the general estimation of the network extension. In the comparison with the dena-study similar results were obtained. By comparing the scenarios I and I1 in terms of the COz emissions, then a reduction by approx. 114,7 million of tons will occur in scenario TI. This value is still much higher than in the year 2000. In neither case there would be any reduction of the greenhouse gas emissions. Regarding the installed power station capacities one has to recognize that although fewer

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8. CONCLUSIONS AND OUTLOOK

146 MW

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Fig. 6: Load Flow situation by feeding of 25 GW wind power

3 L83 MW

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base-load power stations will have to be built (20,9 YO)on the other hand more peak-load power stations will be needed (35,3 %) in scenario 11. This seems logical since the wind can cover a certain base-load for a large area. Yet the considerable fluctuation of the wind can be compensated only with the fast natural gas fired power stations which then must be available in large numbers. However, seen absolutely the potential reduction amounts to only 2,8 % of conventional power station capacity (coal and gas) if 48 GW of wind power plants were installed. In principle, one can state as follows: If in Germany 22 GW Onshore and 26 GW offshore wind power capacity were installed, the COz emissions on the side of the power stations could be kept approximately at today's level. Numerous technical and economic questions will have to be answered before there can be a considerable development of wind energy in Germany. Therefore further research and examinations are required in order to determine the necessary measures for the maintaining of today's standards as regards supply reliability. REFERENCES ETG (2005). Elelctrische Energieversorgung 2020 Perspektiven und Handlungs bedarf: dena (2005). EnergiewirtschajUiche Planung jur die Netzintegration von Windenergie in Deutschland an Land und Offshore bis Zuni Jahr 2020. Haase, T., T. Hamacher, H. Weber (2004). EinJluss der Einspeisung von Windenergie auf die Struktur des Krajherkparks und des Uhertragungsnetzes. In: ETG Konferenz 2004, Berlin Wcbcr, Il., T. Ilaasc, T. Ilamachcr (2003). Network Requirements Of Future Energy Conversion Technologies. In: IFAC Conference 2003, Seoul

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

AN APPROACH TO OPTIMAL DISPATCH OF BILATERAL ELECTRICITY CONTRACTS REGARDING VOLTAGE STABILITY B. Mozafarf, A. M. Ranjbar*, A. Mozafari'*, T. Amraee*

of Electrical* * Engineering, Sharif University of 7 echnology, Iehran, Iran k t i o n a l Petrochemical ('ornpany Emails mozafari-babakf2yahoo corn, ranjbargsharif edu, a mozafari@gmail corn

* Department

Abstract: This paper proposes a methodology for optimal dispatch of bilateral electricity contracts, which may endanger the system voltage stability in light of short-term operational planning of a deregulated power system. In this framework the value that each owner of a transaction is willing to pay will reflect how much the electricity contract is important to be implemented physically. The proposed model dispatches optimally the bilateral transactions regarding the prices offered by owners of bilateral contracts for reactive power and transmission capacity utilization in one hand and, the total operational costs of reactive power resources in the other hand. The model also includes the limits imposed by the physical constraints on the power system such as nodal power flow equations, limits on capacity of resources, voltage stability constraint and etc. The proposed framework is formulated as an AC-OPF problem and is implemented over the IEEE 14 bus test system using CONOPT solver (GAMS) to illustrate the feasibility of the approach. Copyright 02006 IFAC Keywords: Bilateral contracts, Deregulation, Reactive power, Voltage stability, OPF.

Optimal reactive power management can quite increase the available transmission capability as a consequence of the improvement of the network voltage profiles as well as reduction of active and reactive power losses. Therefore in an open electricity market, reactive power support is an ancillary service that plays a significant role in facilitating power transportation (Bhattacharya and Zhong, 2001). This ancillary service becomes very important when the loadability margin of the network diminishes due to high volume or transactions. Iri this situation I S 0 needs to follow a transparent procedure for rcadjusting rcactivc powcr rcsourccs to providc enough security level in the network. However the electrical transactions should be curtailed at least in some part, once the available reactive power resources are inadequate to achieve this goal. It is important to note that reasonably reactive power resources have different utilization prices in a deregulated power system, which may influence the ISO's selection of reactive power resources to meet

1 . INTRODUCTION Competition in purchasing and selling of a commodity so-called electricity is a new interesting paradigm in deregulated power industries which many countries around the world have found it necessary with their long run economic strategies. The prevalent market models for trading of electricity can be summarized into three groups; decentralized markets, pool or centralized markets and hybrid markets (Cafiizares, et al., 2001). The existence of an independent entity named System Operator (SO or ISO) or in some models Market Operator (MO) who should adapt market activities regarding the available transmission network capability is a common feature among the market models. In practice, the transmission capability of power systems is usually restricted by some factors such as equipment thermal limits; available active and reactive power capacities and the limits associated with the network stability problems.

65

system requirements. Up to now some standpoints toward competitive reactive power procurement have been presented in numerous research articles, which can be categorized into three groups. In the first approach, ISO, on the behalf the consumers purchase reactive energy based on the purpose of minimizing the reactive power procurement costs (Lamont and Fu, 1999; Danachi et al., 1996). In this methodology, active power transactions usually are kept constant. Recently a method that incorporates voltage stability criterion into the reactive power market formulation is presented in (Lin, 2003). In the second approach, active and reactive energy are dispatched simultaneously to meet some purposes such as minimizing active power generation costs (Baughman and Siddiqi, 1991), maximizing social welfare of active power market (Cafiizares, et al., 2001), or minimi7ing total incurred costs of active and reactive power generation (Xie, et al, 2000). This mechanism is usually proposed for hybrid or OPFbased market structure. From the point of this view, a security constraint optimal power flow is used to determine the approved transactions regarding the voltage stability criterion (Cafiizares, et al., 2001). Active and reactive marginal prices can also be determined at each location as by-product of optimal dispatch problem. In the third approach, a reactive power market is designed for a structure in which energy is totally traded through bilateral contracts (Zhong and Bhattacharya, 2003). In this structure, reactive power cost is determined independent of energy market activities with the aim of minimizing deviations from transaction requests and real power loss minimization. In this model, IS0 acts on behalf of the consumer in purchasing the reactive power. Transactions are assumed to have the same priority and hence no clear competition can be distinguished among the owners of transactions. Voltage stability problem has not yet been established in this reactive market structure. In this paper we make an attempt to develop the ideas proposed in (Lin, 2003, Zhong and Bhattacharya, 2003) and, introduce a competitive market structure for reactive power supporting in an open access electricity framework. The optimal power flow equations of the market are modified so as to include voltage stability criterion. The performance of reactive power market structure is evaluated by performing different case studies on the IEEE 14-bus test system and for each case, Locational Marginal Prices of reactive power are calculated at each node.

Synchronous generators are the main sources of active power generation in a power system, however they are also able to provide reactive power to fulfill transmission requirements. Active power generation cost of a generator is usually approximated by a second-order polynomial as a function of active power output of the generator. However it is very difficult to determine the cost of reactive power supported by a generator because no fuel is consumed for reactive power production. Reactive power cost determination for a generator is still an open issue for research, which needs further investigation, but we use here the model proposed by (Rider and Paucar, 2004) for generators’ reactive power cost calculations as following:

2. REACTIVE POWER COSTS

3. THE PROPOSED MARKET FOR REACTIVE

c:g P ( P‘9 ) = o pgz2 + b$ + c cost. Qgr :

is reactive power output of generator i.

sg1 :

is apparent power output of generator i.

K~~ :

is profit rate of active power generation, usually between 0.05-0.1

2.2

Static compensators

In general, static reactive devices are used to regulate voltage magnitudes throughout the power network. They have different characteristics in term of dynamics and speed of regulation. Switched capacitors as well as reactors have low installation and operation costs but they are slow in response to a reactive requirement. Static VAR compensators in contrast to fixed reactive devices are able to response to a reactive requirement rapidly, however their installation and operation costs are moderately high. Regardless of considering reactive power quality, in this paper static VAR compensator’s costs are modelled in term of their reactive outputs as following (Rider and Paucar, 2004): CCl(YCJ) =

ec.

Where: r . is unit cost of reactive power in $IMVAR. CJ . Q, : is amount of

supplied reactive power in MVAR.

In above equation, it is assumed that a reactive compensator is installed at bus j. POWER

Reactive power cost analysis ahs been reported in detail in (Lamont and Fu, 1999; Danachi et al., 1996). Synchronous generators and static VAR compensators are the equipment that their associated reactive power generation costs are reviewed briefly. 21

is active power production

3. I Electricity market structure

Nowadays electrical energy is provided through electricity market. Market transparency mainly depends on its clearing mechanism. In centralized electricity market, the pool would be the only place for the participants to bid for electricity and ancillary

Synchronous Generators

66

$/M W. As different transactions have different effects on the power system operation and stability problem, by this way it seems that transactions can compete with each other for using available transmission system capacity and limited reactive power resources. TFB is reported to IS0 and IS0 will not share this information with other participants. IS0 can organize TFB value into a matrix as following:

services. The IS0 clears the market taking into account the bids information and the system capacity. In this procedure, electricity and ancillary services are dispatched simultaneously. On the other hand, the bilateral market provides a good opportunity for sellers and buyers to negotiate bilateral contracts directly for the purchase and sale of electricity in a decentralized manner. To have a feasible and secure operating condition, the electricity contracts need to be adapted on the basis of the available ancillary services. Among different types of ancillary services, in this paper, we are dealing with the efficient provision of reactive power for bilatcral contracts. It is assumcd that thc 1SO has only information about amount of transactions and organize them into the Bilateral Transaction Matrix (BTM) as following: -

BTM =

w,,WI2

rm=

- 1

w, w'2 .

. .

. .

-

Y,, 'Yh,

.

-Y,wi:

(5)

.

.

fVmn -

-

TI1

TI2

.

.

TI,

72,

7i2

.

.

T2n

-T,I

3.3 Reactive power market: A competitive model

(3)

,

TN2

.

.

In general, a market operates best when there is a free and simple environment for competition. Maximizing the social welfare value in competitive electricity markets follows this purpose. For reactive power, it is nearly impossible to establish a market based on the concept of demand and supply theory because reactive power losses in transmission system are very high and the loss varies nonlinearly with the change of power system operating condition. Nevertheless, one can propose the following structure for competitive procurement of reactive power, which aims to maximize the value of the contracted transactions and simultaneously to minimize the costs of dispatching reactive power.

.,

/??In -

3.2 Transactions reqziiremenls ,for entering to competitive reactive power market

sf : r

In the absence of any constraint or congestion on the electric power system or shortcoming of reactive power resources all transactions are deemed to be accepted by the ISO. However this situation may not frequently occur in practice. To preserve voltage levels and stability margin, each transaction should be supported by efficient reactive power compensation. However, when the reactive power demand increases due to the high volume of transactions or changing power system operating conditions, there is a need to allocate reactive power resources to each bilateral transaction through a competition mechanism. In such cases, just knowing the importance of each transaction can be used by the IS0 in optimal dispatch mechanism. Prom economical points of view, it is a rational way to measure the importance of each transaction with the cost that the owners are willing to pay for approval of each MW fraction of their electricity contracts. Therefore in the proposed structure, transaction's owners are required to submit their offers to the IS0 which is called, "Transaction Firmness Bid" (TFB) in

1

Where: N is set of bus numbers; n E { N f ; {aG)c N;

67

rsm( .),g"'"( .)

represent nodal active and reactive power flow equations under stress conditions where the base load and generation have been increased by the factor ( I + C'SM); C, and @ are the vector of bus voltage magnitudes and angles; 7;, is a bilateral

Necessary condition of I .agrange equation implies that: ^.

transaction negotiated between bus i and bus j . q,'is the ij element of the transposed matrix. Qbl,Stands for reactive power generation at bus n and finally cpon indicates the load power factor angle at bus n. In this formulation, the amounts of power transactions form the control variables. Generator voltage magnitudes are assumed to be constant. In this modelling, the IS0 attempts to make an economic equilibrium between the utilization cost o f reactive power and transmission capacity in one hand and accepting bilateral contracts as closely as possible to the values obtained as results of electricity bilateral market. Lagrange theory is used for achieving equilibrium point. Equations (6) can be transformed into of following Lagrange form:

Equation (8) can be extended to:

As it is clear, offering prices, Wi, s, have a key role in

dispatch mechanism and hence competition procedure. Solving (9) gives Lagrange multipliers and slack variables. 3.4 The reactive power prices

Similar to other standard market, the price of reactive power at every bus can be determined by Lagrange multiplicr associatcd with rcactivc powcr flow equations. In this manner, marginal reactive price is dL obtained from -= 0 at generation buses. 3Q,,, 4. SIMULATION AND RESULTS

4.I The test system r

1

r

1

r

1

IEEE 14 bus standard system is used to test the proposed methodology for analyzing of the reactive power marginal price and transactions modification process. IEEE 14 bus test system has a special characteristic where generation area is rather far from the load area. This makes it suitable for voltage stability study. The one line diagram is shown in Figl. Transmission line parameters as well as generation and load consumptions are reported in (Power System Test Case Archive) in detail. However power flow solutions at normal operation are tabulated in Tables 1&2. The parameters of generation cost function are listed in Table 3. THREE

WlMIIN6

T W S F W E R EQUlV4LENT

T'

Lagrange multipliers of equality and non equality constraints. Slack variables associated with inequality constraints are:

I

lLul

-&)

<\ *IP I

J l h I E X 9i57E'

---. Bl,,

LI)X

D "*"I.,

Fig. 1. IEEE 14 Bus Test System

68

Tablel: Load flow results of IEEE 14 bus system

3 2 2 1 1 2 1 2 1 I 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 21.7 94.2 47.8 7.6 11.2 0 0 29.5 9 3.5 6.1 13.5 14.9

1 1

1

0 12.7 19 -3.9 1.6 7.5 0 0 16.6 5.8 1.8 1.6 5.8 5

0 0 0 0 0 0

0 0 19 0 0 0 0 0

1.06 1.043 1.01 1.0178 1.0198 1.07 1.0616 1.09 1.056 1.051 1.0569 1.0552 1.0504 1.0356

It is assumed that all transactions will submit the same price to the KO. For all simulations we consider that W,,s are equal to 3.6 ($/MW). To study the influence of providing a given voltage stability margin on reactive power dispatch, the VSMvalue in equations (6) is increased from 0.0 to 0.8 and following each variation the market equations are solved. The reactive power marginal price at each load bus is shown in figures 2 and 3. These values can be obtained as the by-products oC the market solutions when the locational marginal price of rcactivc powcr is dcfincd thc Lagrangian multiplicrs associated with reactive power flow equations. As seen from the figures, the reactive power price varies slightly with increasing the VSM. This observation can he explained a? following. When there is a need for increasing the security margin, the purposed market model regulates some bilateral contracts to relieve transmission capacity. The reactive outputs of the generators are shown in Figures 4 and 5 in these conditions.

0

-4 982 -12 723 -10314

-8 7769 -14 222

-13 361 -13 361

-14 94 -15098 -14 791 -15 076 -15 157

-16 034

Table2: Generation activeiReactive outputs 350 -1

PG

BUSNO

QG

VG

Qmn

Qmax

I

1

232.39

-16.671

200

-150

1.06

2

40

45.184

60

-40

1.045

3

0

23.861

40

0

1.01

6

0

12.582

24

-6

1.07

8

0

17.575

24

-6

1.09 Voltage Stability Margin

Fig. 2.Reactive Power Marginal Price @ buses 4,5,7,9

Table3: Production cost coefficients

C

b

a

0.01 0.01

10 10 20 15 45

100 100 100 100

0.02 0 02 0 03

-QLrrp@buslO

--c Q L V @ b u s l l

p

+QLmp@busl2

100

-QLmp@busl3

100

-QLmp@busl4

0

4.2 Case studies

@Q'

Gen2

Demll 3.5 0.0

Deml2 2.7 3.4

Deml3 13.5 0.0

Qb

0%

Fig. 3.Reactive Power Marginal Price @ buses 10-14 Choosing social welfare function as a main objective of reactive power procurement leads location marginal cost of reactive power to be almost constant. This can be distinguished as an advantage of competitive reactive market. According to suggested objective function, reactive power is dispatched between generators proportional to their incurred cost. This may cause reactive market power in traditional market structures. However, here in this competitive market generators are also a partaker in offering Transaction Firmness Bids to the ISO. This can effectively reduce making power market and help to increasing market transparency.

Table4: Transactions Bilateral Matrix Genl

03

Voltage Stability Margin

In all case studies Bus 1 is selected as slack bus to provide loss requirement of power system. Regulation power cost is not included in optimization model and is left for regulation market. Local loads at buses 2, 3 and 6 as well as Loads 4,5,7&9 are not entered into bilateral contracts and are fixed during the study. This system has 5 generators. Generators at bus 3, 6 and 8 operate as synchronous condensers and hence their active power outputs are equal to zero. This means that all bilateral transactions are contracted between loads and generators 1 and 2 in the form of following Bilateral Transactions Matrix (Table 4):

DemlO 9.0 0.0

0%

Deml4 0.0 14.9

69

Reactive power output of the generators is shown in Figs 4&5.

- -

05

5

04

.t x

01

c

5.CONCLUSION

I

I

I

I

01

II

I

Voltage stability margin

Fig. 4.Reactive power dispatch of generators I &2

In this paper a methodology for reactive power procurement in a competitive power market is proposed. In this market, the objective is to maximize bilateral transaction values and to minimize the utilization costs of reactive power. An OPF-based model is proposed for clearing the market. Voltage stability margin as an important index is incorporated into OPF formulation and the market equations are solved using the GAMG software which is a modelling system for mathematical programming problems. The proposed methodology is tested on IEEE 14 bus test system. Results show the efficiency of proposed structure for reactive power market design and its simulation. REFERENCES Baughman, M.L. and Siddiqi, S. N., “Real-Time Pricing of Reactive Power: Theory and Case Study Results”, IEEE Trans. On Power Systems, Vo1.6 No. 1, pp 23-29, February 1991. Bhattacharya, K. and Zhong, J., “Reactive Power as an Ancillary Service”, IEEE Trans. On Power Systems, Vo1.16 No.2, pp 294-300, May 2001. CaAizares, C. A., Chen. H. and Rosehart, W. “Pricing System Security in Electricity Markets”, Proc. Bulk Power System Dynamics and Control-V, Onomichi, Japan, pp 1-11, August 2001. Danachi, N.H., et al, “OPF for Reactive Pricing Studies on the NGC System”, IEEE Trans. On Power Systems, Vol.11 No.1, pp 226-232, February 1996. GAMS Release 2.50, “A User’s Guide”, GAMS Development Corporation, 1999 available: www.gams.com Lamont, J.W. and Fu, J., “Cost analysis of Reactive Power support”, IEEE Trans. On Power Systems, Vo1.14 No.3 pp 890-898, Auguest 1999. Lin X., David, A.K., and Yu,, C.W. “Reactive Power Optimization with Voltage Stability Consideration in Power Market Systems”, iEE Proc. Gener. Transm. Distrib., Vol, 150, No. 3, pp 305-3 10, May 2003. Power System Test Case Archive, available: www.ee.washington.edu. Rider, M. J. and Paucar, V. L., “Application of a Nonlinear Reactive Power Pricing Model for Competitive Electric Markets”, IEE proc. Gener. Transm. Distrib., Vol. 151, No. 3, pp 407-414, May 2004. Xie, K., el al, “Decomposition Model and interior Point Methods for Optimal Spot Pricing of Electricity in Deregulation Environments”, IEEE Trans. On Power Systems, Vol.15 No.], pp 3950, February 2000. Zhong J., and Bhattacharya, K., “Toward a Competitive Market for Reactive Power”, IEEE Trans. On Power Systems, Vo1.17 No.4, pp 1206-1215, November 2002.

“ 8“ x“ o“ o “; o“ $ X ~ ~ Voltage Stability Margin

Fig. 5. Reactive power dispatch of generators 3-5 The proposed method is capable of modifying the quantity of power transactions, which considers the worth of each transaction and all security constraints need to be incorporated into the dispatch process. The modification results of some transactions are shown in figures 6 and 7.

2

.o c

0 16 01 4 0 12

-Trl-ll

Q

0%

g’

0%

Voltage Stability Margin

Fig. 6.Transaction modification versus increasing VSM.

2

.P c p

2

f

0.16 0.14 0.12 0.1 0.08 0.06

I.

m~

Fig. 7.Transaction modification versus increasing VSM.

70

Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

ELSEVIER

IDENTIFICATION OF SYNCHRONOUS GENERATORS USING “4SlD” 1DENTIFlCATION METHOD AND NEURAL NETWOKS

M. Karrari”, W. Rosehart**, O.P. Malik**, A. 11. Givehchi*** *Electrical Engineering Department, Amirkabir Univeraty of Technology, Tehran, Iran

* *t.,leclrical and Computer kngineering lleparlment, University of Calgary, Calgary, Canada “““Azad University, Tehran, Iran

Abstract: Synchronous generators are multivariable systems and are well defined in a state space structure. Subspace state space (4SID) identification method is most suitable for identification of such systems. In this paper, the identification of a synchronous generator using this identification method is presented. To cover the nonlinearities, first thc overall rangc of opcration in the active (P) and reactive (Q) power plane is divided into subsections and a linear state space model is identified for the centre of each subsection. A neural network is then used to estimate the parameters for the operating conditions other than the centres of the subsections. Copyright 02006 IFAC Keywords: Synchronous machines, Parameter estimation, Identification, Dynamic modelling, Neural networks.

space model for multivariable systems using only input output data. Many papers deal with the modelling and identification of synchronous generators. In the traditional methods well specified in IEEE Standard (1 15, 1995), a known structure for the synchronous machine, using the well-established Park transformation is assumed. These approaches include tests carried out when the machine is not in service. Because of magnetic saturation in the iron parts of the rotor and stator, the parameters of a synchronous generator arc not constant and may change with the operating conditions. There are some papers dealing with this problem (El-Serafi,et al, 1993; Levi et al, 2000). To overcome the shortcomings of the traditional methods, on-line identification methods have gained attention in recent years (Shamsollahi et al, 1996; Melgoza, et al. 2001; Karrari, et al, 2004a, 2004b). The aim of this paper is to identify such a non-linear third order model for a synchronous generator using the subspace state space identification method employing easily available signals such as electrical power, terminal voltage and the field voltage. It is clear that the parameters of the state space model

1. INTRODUCTlON

Identification of dynamic systems has always been the prime concern of control engineers. Identification of linear dynamic systems has theoretically been well established and many good approaches are available (Ljung, 1999; Norton, 1986). Various approaches for thc idcntification of non-lincar systcms can bc classified into two categories. In the first category, classified as classical approaches, methods like Nonlinear Least Squares, Voltera series, Weiner series, Wavelets can be named (Billings, 1980). In the second category, classified as soft computing, approachcs like Neural networks, Fuzzy logic, Neurofuzzy networks and Genetic algorithm are listed (Brown et al, 1994). Identification of nonlinear systems i s still an active research topic. Combination of the two categories has found some attraction, like wavelct networks describcd by Liu, et ul 2000. A good recent review of the nonlincar identification approaches is presented by Nelles, 2001. Subspace state space (4SID, pronounced ‘forsid’) identification method (Viberg, 1995) has become an attractive method for identification of dynamic systems during last two dccadcs. The main advantagc of this mcthod is that it provides an accurate state

71

would depend on the operating conditions and the system parameters. To overcome this shortcoming, first the possible range of machine operation in the P-Q plane is divided into subsections. A linear state space model is identified for the centre of each subsection. Since the synchronous generator may operate in operating conditions other than the centre of the subsections, the independent parameters for actual operating conditions should be estimated using interpolation of the parameters of the neighbourhood centres. Bilinear, bicubie, spline interpolation and neural networks are among many methods that can be used for this purposc. In this paper, ncural network proved to be more accurate. The paper is organized as follows: The proposed method is outlined in Section 2. The non-linear model structure considered for the simulation and modelling of the synchronous generator is explained in Scction 3. The linearized model is also described. Application of the proposed method on the nonlinear model is illustrated in Section 4. Section 5 concludes the paper.

methods can be divided in two main approaches, realization based and direct method (Viberg, 1995). The direct method applied in this paper is reviewed here. Suppose the linear time-invariant multivariable system is described by (in discrete form): xkcl= Ax, + Bu, (1)

yk = CX, + Du,

where xk is the state vector at time k, u kis the input vector and,

y , i s the output vector. It is assumed that

X, E

R""' ,u,

E

R""' ,y k E RmX'.

The algorithm requires a window of data. If the length of the gathered data is N, one might select a sliding ' << N / 2 . window length of h The first step in the procedure is to form the following Hankel matrices:

y z

[,

Y2

'.. Y\.,Ll.i

Y ; ... y ; + 2 ] > ( l = . . . . . . . . . . . .

Y,/ Y,/4

11,

11:

...

11~~~11+1

u:

2%

...

u2.

"l,

"'

lli2

............ Z~\l+l

...

Zl,&

2. PROPOSED METHOD The proposed method is based on the fact that a welldefined linear and nonlinear structure is defined for the system. The procedure is outlined below: 1 - The whole set of possible operating conditions (PQ plane) is divided into some subsections. The number of subsections is arbitrary. 2- The synchronous generator is set to work at the ccntre of cach subscction. At cach of thcsc operating conditions the following steps are taken: 2-1 An exciting input signal is applied to the field of the synchronous generator. This input signal is added to the normal values. It should have enough frequency spectrums to cxcitc the various modes of the system and the magnitude should be small, such that it would not interfere with the normal operation of the system. A white noise with 5% of the nominal value is an appropriate input signal. Subspace idcntification mcthods would yicld bcttcr rcsults with a white noise as an input. 2.2- The applied input signal, the terminal voltage and electrical power are sampled. 2.3- A multivariable linear state space model is obtained for the system using the subspace identification method (explained in Section 4). 2.4- The identified discrete-time state space form is converted to a continuous canonical form. 2.5- A set of independent parameters is calculated from the canonical form. 3. The nonlinear structure is simulated with the estimated independent parameters. Neural network is used to estimate the parameters for the operating conditions other than the center of the subsections. The subspace identification method is explained below: The subspace identification methods have their origin in the classical state-space realization techniques. The

13 =

u

0

...

0

CB CAB

D CB

...

0 0 ...

... CA"-2R

...

. . . . . . CA'll-'R

_,_

n

c

where the nonzero singular values in determines the order of the system. When the input output data is corrupted by noise, some nonzero elements replace the zero elements. But in most cases determination of the order can easily be determined by observing the big step change of the singular values towards zero. Now suppose that the order of the system has been determined to be n and letp> be the first part of matrix

P corresponding to the first n left singular

vectors. Then it can be shown that for some similarity transformation T: (4)

72

-

4. IDENTIFICATION OF SYNCHRONOUS GENERATORS USING 4SID METHOD

N

c

So the matrix can be easily obtained fioin the fii st nz ( the number of outputs) rows of the P, It can

-

In this section, first the 4SID identification algorithm is applied to the nonlinear model at a particular operating condition. Suppose the synchronous generator is working at P = 0.8p.u.;

ako be \hewn that

P,, = A.P,,

(5)

Where.

P,, : f', with the first block ( in rows ) removed

P,2 : P,

Q = 0; vH = 1.025p.u.. The parameters of the synchronous generator were selected to be (in p.u.):

with the last block ( rn rows ) removed N

= 0.0362; x,~,,= 2.074; x,?), = 2.045;

So the matrix A can bc calculated by

D = 0.025; J

2=(P,fP,,)'eip,, (6) To dctermineD and B , suppose the matrix P is partitioned as P = [P, i Pn]then it can be proved that

xi =0.5;x, =0.2;TJcj- 8 . 0 ; ~ ' =0.4,r6=O.O;

N

PnrYU' = Pnl H

A = 0.031; B = 6.93;V,,

-

= 0.8;

Now the procedure outlined in step 2 in Section 2 is carried out First a random voltage signal is added to the field voltage and the electrical power, terminal voltage and the field voltage is sampled The sampling time was selected to be 1.5 ms. Simulation results are given in Fig 2.

(7) D and B can be calculated N

Having calculated H , using a normal least squares procedure (Viberg,

1995) 3. SYNCHRONOUS GENERATOR MODEL In this study, a third order nonlinear structure has been adopted. Compared with the seventh order nonlinear structure, it neglects the effects of damper windings and dynamics of the stator. These two cffccts can be ncglccted, especially when the very fast dynamics (sub-transients) are not of intercst. Thc effect of damper windings is approximately considered in the rotor damping factor. A synchronous machine connected to a constant voltage bus through a transmission line, Fig. 1, is considered here as the study system. HT

Q-

Fig.2: Simulation results following a random input added to the field voltage

Fig I . Structure of the study system The third order nonlinear structure derived in (Yu, et is used in this study The model is descnbed by these equations 6 = 01 1 (8) w = -(T, - T, - D 01) J 1 e, = - ( ~ , l ~ - e ~ - ( x ~ - x ~ ) . ~ ~ )

Data collected from these simulations was used for the idcntification procedure described in section 2. Thc rcsults can bc convcrtcd to thc corrcsponding continuous canonical state space form of the system wing appropriate MATLAB commands This gives

a1 , 1983, Kundur, 1994)

1

TI"

where T, = vd.id

+ v4.i, , id = .I, ~

- vy

4

.

,Iq

-

/'L

--

x,

=[

Other variables and constants are defined in (Kundur, 1994) Representation of saturation in a dynamic study accurately, is an almost impossible task Howcver with some simplifying dssumptions (Kundur, 1994), some modifications to the usual structures can be applied To be able to apply the subspace state space identification method, the linear model is required The linear model of the system is explained in the Appendix

0 0

1 0

0 1

]=I 0 0

1

0

Comparing the above estimated parameters with those

73

parameters are identified at the centre of each subsection, then there is a set of five independent parameters, described in Table 1. Note that in Table I only the parameters that depend on the operating conditions ( K l , K ; , Ki ,K:, KL ) are listed.

of lineansed model, the set o f independent parameters KI, KI ,Ki ,K; ,Ki ,D' and T,. can be estimated The estiiriated values are: D'=c"=-- 0.0972 0.1406

c,,

'

1 '- a 2 -D'

T

- 0.69

-~

1.0367-0.69 1

K ; = a , -U'.-=

T,

23.7125--

=2.89 0.69 =22.93 2.80

K ; = c l i xT, =0.1406*2.89=0.4063

Ki

= cp ,x

T,

= 0.0261 * 2.89 = 0.0754

-4. I

A comparison of the step response of the electrical power for the non-linear system with the identified linear model is shown in Fig. 3. 8)

-2

,,,

>-,

~

-

-

E

tw m n l i n w i i.?t*rr tl,C

,ior.,ir,i r c j ,

t - 1 .

Fig. 4 Step response (active output power) of the nonlinear and identified linear model at a different operating condition

I(~I'Or,

Table I : Identified linear model parameters for different operating conditions

I

Fig. 3 : Comparison of the electrical power of the nonlinear system with the identified linear model at the same operating conditions To show the strength of the algorithm, in a noisy environment, some noise was added to the outputs of the system. The results of the estimated parameters did not change much. The percentage of the paramctcr deviation was more or lcss the same as the noise to signal ratio (say YO). However, when the parameters estimated for one operating condition are used for some other operating condition, the accuracy degrades significantly. That can have easily been predicted since the system is nonlinear (especially the saturation effects). A comparison of the step response o f the nonlinear and identified linear model when the linear model is identified at some other operating condition is shown in Pig. 4. In this figure the model = 0 , but has been identified a t P = 0.8;

12

evaluated at P = 0.5; = -0.2. To solve this problem, the method outlined in section 2 has been modified. In the system under study, suppose that the range o f operation of a synchronous generator is P from 0 to 1.2p.u. and Q from -0.5 to 0.9p.u. If the dimension of each subsection is considered to be 0.2 by 0.2 pu, then there are 42 subsections. If the system

74

K:

I

K;

overcome this shortcoming, a neural network model has been developed to follow the changes in the linear system The whole range of possible operating conditions was divided into 42 subsections and a linear model was identified for the centre of each subsection The discrete-time state space model is converted to a continuous canonical state space form The derived model was used in the simulation of the system For the operating points other than the centre of the subsections, the parameter5 were estimated usmg interpolation of the neighbourhood centres Simulation results show that the proposed method can model a nonlinear 5ynchronou5 generator successfully

Each of the parameters can be plotted on the 1'-Q plane. Variation of one of the parameters ( K 2 ) on the P-Q plane is shown in Fig. 5. When using the derived model, P and Q are measured at regular intervals and the appropriate linear model parameters are selected using Table 1.

..-

EL

he mdnteurrjtem *n*lfd

n

Fig. 5 : Variation of K2 on the P-Q plane

mub*l]

Since the measured values of P and Q rarely match with the values of 42 points for which the parameters have been estimated, some form of interpolation i s necessary. Neural networks prove to be effective in such cases. Five feed forward neural networks each with 5 neurons in the hidden layer have been trained to estimate K,', i = 1,2,4,5,6. 'l'he neural nets have active and reactive powers as inputs and corresponding K,' as their outputs. The tan-sigmoid transfer function was chosen to generate the outputs in the hidden layer. The Levenberg-Marquardt learning algorithm (Hagan, et al, 1994) was used as the training algorithm for the numerical simulations. The data in Table 1 was used as the training set. The LevenbergMarquardt algorithm uses an approximation to the Hessian matrix in the following Newton-like update:

0

5

10 15 eemraipnlwr

25

30

35

4)

.16

5U

am351

Fig. 6 : Step response (active output power) of the nonlinear system and the identified model following four different step changes

APPENDIX

Wk+,= W, + ( J Z J + , d - ' . J ' e where

10

w,is a vector containing all the weights in

The linearised form of the nonlinear model, described in Section 3, is known as the HeffronPhillips model. This model can easily be obtained using eqn. (1). A 8 = Am

the neural network, e i s the error vector of the desired output and the outputs of the network , J i s the Jacobean matrix of the error vector with respect to the weights and p i s a pre-selected value between zero and one. When the scalar p i s zero, the algorithm i s simply the Newton's method, using an approximate Hessian matrix. When p is large, this becomes gradient descent with a small stcp size (Hagan, et al, 1994). To show the performance of the proposed controller different simulation results with the proposed controller are presented. Step response of the nonlinear and the derived model with the NN following four different step changes is shown in Fig. 6. It can be seen that the derived model follows the dynamics of the non-linear systems closely.

1

AW = -(AT;,, - K , A 6 - K,Ae, - 1 1 . A ~ ) .J K At. = -(AEf,] - K , A 6 - Ae,) "

@-I)

T,

whereK,, K,, K3, K, and T , are constants depending on system parameters and the operating conditions. They are given as:

5 . CONCLUSlONS In this paper, subspace state space (4sid) identification method has been used for identification of a synchronous generator The proposed algorithm proved to be a good approach for identification of synchronous generators The only problem is that the proposed method is developed for linear systems To

75

V j -(,="(-?

re.cos6,

.

V

+ x i .sin6,),fq = +.(re.sindo

= yre, z 2, =r<2 +x,.x,

XI y d =-,y,I z:

=e

x, + x, x2 = x, + Xjl

In the above equation, subscript "0' stands for the values of the Vdridbles at the operating point at which the model is hnearised Details of the denvation of these constants can be found in (Yu, et a l , 1983; Kundur, 1994) To represent the linear model, in state apace form, the states, inputs and output5 should be defined. The states and inputs are defined ds follows.

Definition of the outputs is slightly arbitrary. Considering practical aspects, in this study, we, active output power deviation per phase and Av,, terminal voltage deviation were considered as the outputs. Using these definitions the state space model of the system is: 4 = 4 g + R,'E (B-3) y=C,g where:

r

1

1

r

and K5 and K6 can be calculated by: (B-4)

This model can also be shown in a canonical form. The canonical form is:

where: A'

=I-(q-+) I

I,

I,

,)' 0 -(++K')

I,

-(/j'++)

I 1 ',J

I

and: K K 1 '- - KL K '4 --K4 K '5 --2 K '2 -- K J >

J

J

3

REFERENCES Billings. S.A. (~, 1 980). Identification of nonlinear systems-a survey. IEE Proceddings, Part D., (127), 272-285. Brown,M., Harris,C.J. (1 994). Nezirofkzzy adaptive Modleling and Control. New York, Printice Hall. El-Serafi, A.M., Wu, J. (1 993). Determination o f the paramctcrs rcprcscnting tbc cross-magnctizing effect in saturated synchronous machines. IEEE Trans. On Energey Conversion, (S), no. 3, 333340. Hagan, M. T., and M. Menhaj, (1994). Training feedforward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks. (5), no. 6, 989-993. IEEE Guide. (1995). Test Procedure for Synchronous Machines. IEEE Slcl., 11 5. Karrari M., O.P. Malik, (2004a). IdentiJication of Helffron-Phillips model parameters ,for synchronous generators using online measurements. IEE Proceedings- Generation, Transmission and Distribution, (151) ,no. 3, 3 13 - 320 Karrari M., and O.P. Malik, (2004b). Identification of Physical Parameters of a Synchronous Generator From On-line Measurement. lEEE Ttrans. on Energy Conversion, (19) , no. 2, 407415. Kundur P., (1994) Power System Stability and Control, McGraw-Hill Inc. Levi E., Viktor A. Levi (2000). Impact of Dynamic Cross Saturation on accuracy of saturated synchronous machine models. IEEE Trans. on Energy Conversion, (15), No. 2,224-230. Liu, C.P., Billings, S.A. (2000). Nonlinear system identification using wavelet networks. International Journal of System Science, (31), no. 12, 1531-1541. Ljung, L. (1 999). System Identification, theoryfor the user. Prentice Hall PTR. Melgoza J., R. Jesus, G.T. Heydt, and A. Keyhani, (200 1). An algebraic approach ,/or identiSying operating point dependent parameters of synchronous machine using orthogonal series expansions. IEEE Trans. on Energy Conversion. (1 6 ) ,no. I, 92-98. Nelles, 0. (2001). nonlinear system identification: from clussicul upprouches to neurul networks andfiizzy models. Berlin ; New York : Springer. Norton J.P. (1 986). An Introduction to Ident$cation. Academic Press. Shamsollahi P. and O.P. Malik, (1996). On-line identification of synchronous generator using neural networks. Canadian Conference on Electrical and Computer Engineering, CCECE'96, Part 2, 595-598. Viberg, M., (1 995). Subspace-based Methods for identification of linear time-invarient systems. Autornatica, (31), no.12, 1835-185. Yu, Yau-Nan, (1983). Electric Power System Dynamics Academic Press. -

'e

'<

XI =

+ x,.cos6,)

2'

K 3 , K 'b = K h ' K 3

&D J

76

,

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

PARAMETER ESTIMATION OF POWER SYSTEM OSCILLATIONS BASED ON PHASOR MEASUREMENTS Takuhei Hashiguchi' Yutaka Ota ., Hiroyuki Ukai' Yasunori Mitani * Osamu Saeki *+* Masahide Hojo ****

* Dept. of Computer Science and Eng., Graduate School of Eng., Nagoya Institute of Technology, Japan ** Dept. of Electrical, Electronic and Computer Eng., Faculty of

Eng., Kyushu Institute ojTechnology, Japan *** Dept. ofElectrica1 Eng., Graduate School of Eng., Osaka

Universit,v, Japan Dept. ofElectrica1 and Electronic Eng., Faculty ofEng., The University ojTokushima, Japan

***I

Abstract: In recent years, there has been an increasing interest in monitoring and analyzing dynamic pcrformances of power systems. such as observation of power systcm oscillations and evaluation of machine parameters. Authors have placed phasor measurement units (PMU) connected to lOOV outlets in some universities in Japan and been researching into oscillation characteristics in power systems. The purpose of this paper is to propose methods for processing actual data so as to detect power system oscillations under a steady state operating conditions. Moreover, eigenvalues of power system oscillations occurred in Japan western 60Hz system are estimated. Copyright 02006 IFAC . Keywords: Global positioning systems, Digital filters, Eigenvalues, Monitoring elements, Time synchronization

I . INTRODUCTION Electric power systems in Japan are composed of remote and distributed location of generators and loads mainly concentrated in large demand areas. In Japan westcrn 60 Hz systcm, each powcr system of six major electric power companies is connected through 500 kV transmission line over wide area. It is generally known that its longitudinal structure produces various system oscillations, such as a long term oscillation, local generator oscillations and oscillations caused by frequency control between systems. The structures having a long distance transmission tend to produce heavy power flow with increasing electric power demands. In addition, some independent power producers (IPP) and Power Producer and Suppliers (PPS) are participating in the power generation business. which

makes power system dynamics mole complex. In the circumstances. it is possible that the system causes various dynamics. So far, some dynamic characteristics have been measured in own area or in the interconncctcd tic lines. Howcvcr, thcrc was littlc obscrvation as a whole power system. In this paper a research project among some universities in Japan for developing an online global monitoring system of power system dynamics by using the synchronized phasor measurement technique is presented. Phase measurement systems by the use of GPS, which increased rapidly in the middle of 1990, were introduced into Europe and America at thc start (K. E. Martin, et. al., 1998). The use of phasor measurements for a static state estimation and various protections has been presented. Our system is char-

0 01

- - - .I-" - - - Tl~cUrn\ "I

2 -g

OOl5

mi

o1Tokuchima Hiroshima Urn\

~

002

-8

g -0025 s B

L

0 01

0 035

0 04

605

Fig. 1. Assignment of Phasor Measurement Units (PMU) in Japan western 60 Hz system

606

607

608

609 610 Elapsed nine ( s )

611

612

613

614

Fig. 2. Frequency deviation of Japan western 60Hz system less than 1 H L frorn 13:20 to 13:40 on June 27 in 2005.

acterized by the PMU installations at the domeslic lO0V outlets. Since the PMU allows for phasor measurement at the domestic outlet, the configuration of the PMU is simple and the installation is easy. Phasor measurements units have been located in some universities in Japan.

Calculating equation (2) gives phase angle referred to the GPS time. The PMU measiires the phasor results at 30 Hz sampling and records at intervals of 20 minutes all day. At the communication and functional level, TCP/IP protocols can be adopted as a flexible way of accessing and controlling thc PMUs (A. Radovanovic. 2001). Measured data are transmitted via Internet and collccted by servers in Nagoya Institute of Technology and Kyushu Institute of Technology.

The purpose of this paper is to show methods for detecting power system oscillations and extracting these required oscillations included in PMU data at a steady state. The first step is to do a power system oscillation search by FFT analysis. The second Ttcp is to resolve the resulting frequency analysis composed of plural modes into vanous single modes and examine dynamic behavior of each mode. The third step is to estimate each eigcnvalue of separated modes.

3. FREQUENCY ANALYSIS O F POWER SYSTEM OSCILLATIONS Frequency deviations less than 1 Hz from 13:20 to 13:40 on June 27 in 2005 are extracted by applying Symlet Wavclct function. The application of Wavelct transformation leads to the decompositions of a signal. The part of extracted waveforms is displayed in Fig. 2. The graph indicates that frequency deviations at each area include original modes. Fig. 3 is the iesults of using FFT analysis for frequency deviations. In this paper, frequency domain data of F I T analysis were smoothed by the approach denominated "SavitzkyColay filter" (fiftieth-Order). There are three notes in Fig 3.

2. OVERVIEWS O F PHASOR MEASUREMENT SYSTEM Fig. 1 dcpicts thc assignmcnt of PMU (Nctwork Computing Terminal Type-A of Toshiba make) (R. Tsukui, et a1.,2001) in Japan western 60 Hz system, which are located in Campuscs of Nagoya Institute of Technology, Fukui University. Osaka University, Hiroshima Univcrsity, The University of Tokushima, Kyushu Institute of Technology, Kumamoto University and Miyazaki University. Since the 60 HL system consists of six major electric power companies, at least one PMU is assigned in each company's supply area. Phasor voltage is computed using a sinusoidal voltage sampled 96 data as rollows.

( I ) Plural power system oscillations are observable a1 a frequency more than 0.2 H L . ( 2 ) An oscillation at a frequency around 0.38 H7 is a dominant mode and is observed clearly a1 the both end of Japan western 60Hz system (T. Hasbiguchi, et al. 2004). (3) An oscillation at a frequency around 0.55 Hz is quasi-dominant mode and is observed at the both ends and a center of Japan western 60Hz system.

From equation ( 1 ) it follows that

From FFT analysis shown in Fig. 7. phasor measurement at domestic outlets allows to confirm power system oscillations.

78

, , ' , ' ' mode I

5 -- - synllietic uavek~rm mode

measurement data

(1

Fig. 3. Frequency characteristics analyzed by FFT.

0.1

0.2

0.3

(1.4 0.5 0.6 Frequency (HL)

(1.7

(1.8

t1.V

Fig. 4. Curve fitting of frequency characteristics from 23:20 to 23:4Q on June 27 in 2005.

4. SEPARATION OF POWER SYSTEM OSCILLATIONS BY USING CURVE FITTING METHOD

AEsuming that a phase difference at a frequency between 0.2 and 0.7 Hz, which is extracted by Wavelet transformation, includes three modes, a synthctic wavcform is composcd of thrcc Lorcnz curves determined by the curve fitting method. Each vpectral ratio of three Lorenz curves for a synthetic waveform analyzed by FFT is calculated at intervals of frequency resolution. According to each spectral ratio, the synthetic waveform is separated into three frequency components. Inverse FFT transforms three modes of frequency domain to signals.

To further study each modc characteristic, a curve fitting method for fitting curves to data sets is done. Rcvolving frcqucncy charactcristics analyzcd by FFT into some single modes is made possible with this method. Suppose the result of FFT analysis can be represented by Loren7 curves. Let a,, h,, c, and f be height, location, width and frequency, respectively. Lorenr: curve is described in the following form.

5. INVES I~lGA'l'IUNIN A 'I'EN-MACHINE SYSTEM

Convolution in equation (3) gives

IEEJ WEST1 0-machine system (Technical Commitlee of IEEJ, 1999) in Fig. 5 consists of 10 machines and 27 nodes. Plural modes are produced by a simulation of this model. In such a longitudinally interconnected power system, the mode associating with the low-frequency oscillation between both end gencrators tends to become unstable when the interconnected line is heavily loaded. Here, the load of node 2 and the power of generator 1 arc increased by 1600 (MW) so that the line between nodes 1 and 2 is heavily loaded. This results in the de-stabilization of the quasi dominant mode (mode 2 ) in addition to the dominant mode (mode 1).

Constraints on coeflicienls lo express physical requirements are mentioned below.

This curve fitting is applied to the result of FFT analysis of a phase difference at a frequency between 0.2 and 1.2 H7 extracted by Wavelet transformation. The curve fitting, which is conducted using Gauss Newton method, divide the results of FFT analysis of a phase difference into 5 single modes. Fig. 4 is a curve fitting of frequency domain analysis for a phase dirference between Nagoya Institute of Technology and The Univ. of Tokushima from 23:20 to 23:40 on June 27 in 2005. With regard to oscillations between these areas, 3 modes are observable at a frequency between 0.2 and 0.7 Hz. Next, the algorithm for revolving into threc modcs is explained in thc following steps.

Fig. 6 shows linear participation factors corresponding to each generator rotor angle. This result shows that generators 1 and 10 participate principally in mode 1. generators 1 ,5 and 10 in mode 2, and generators 1,4, 7 and 10 in mode 3. Fig. 7 shows real parts of eigenvectors associated with each generator angle. From this result, it is obvious how three modes oscillate at each gencrator. In this paper. the linear participation factors corresponding to each generator angle are used for selecting generators participating in modes.

79

4

4

4

Fig. 5. IEEJ WEST10-machine system model. n

5

10

15 Elapsed

20

25

30

3s

40

IllllL! (S)

Fig. 8. Phase differences between generators in case of three phase ground faults occurred at three points

Fig. 6. Participation factors associated with generator angle. I 0

5

10

15

20

25

30

35

I 40

Elapsed l m e (s)

Fig. 9. Three modes between generator 1 and generator 10 in case of three phase ground faults occurred at node 1 (case I ) . modes resolved from power system oscillations in Fig. 8 are shown in Fig. 9, 10 and 12 In case 1, decomposed modes of the phase difference between generator 1 and generator 10 by the proposed method are shown in Fig. 9. Mode 1 affected principally by generator 1 and generator 10 is the dominant mode in IEEJ WEST1 0-machine system.

I 1

2

3

4

5 6 Gencratol

7

8

9

10

In case 2 , decomposed modes of the phase difference between generator 10 and generator 5 are shown in Fig. 10. Generator 1, 5 and 10 participate in mode 2 and the phase difference between generator 5 and 10 include the dominant mode and the quasi-dominant mode such as Fig. 10. No mode 3 was observed in frequency domain analysis. In this case, a comparison of two modes between generator 1 and generator 5 to between generator 10 and generator 5 is offered in Fig. 1 1 . whcre this rcsult by performing IEEJ WESTIOmachine system indicates that each phase of mode 1 at both ends of power system tends to oscillate in the opposite direction. Moreover, each phase on mode 2 tends to oscillate in the same direction. This result

Fig. 7. Real part of eigenvectors associated with generator angle. To produce plural modes, three phase ground fault is simulated at three points near generators participating in each mode. Locations of three phase ground faults are at (x) near node 1 (case I), node 1.5 (case 2) and node 17 (case 3) and each fault cleared at 0.01 s.

Phase differenccs between gcnerators participating mainly in three modes for three cases mentioned above are shown in Fig. 8. These oscillations with plural modes can be decomposed with the curve fitting method through a frequency transformation. Three

80

n 2 o

I 5

10

15 20 25 Llrpsrd iiinr (s)

30

35

40

Fig. 12. Two mode between generator 4 and generator 7 in case of three phase ground faults occurred at node 17 (case 3).

Fig. 10. Two modes between generator 5 and generator 10 in case of three phase ground faults occurred at node 15 (case 2 ) .

0.2

d

ni

BE n <

-0 I

-0.2

o

5

10

15 20 25 Elapsed time ( 5 )

30

35

mode 1 mode 2 mode 3

4n

simulation -0.04+1.71 -0.14+4.04 -0.18-tS.29

case 2 case 1 -0.05-1-1.82 -0.OS+1.68 -0.14+3.94 -0.13+3.98 -0.16-1-5.27

case 3 -0.04-1-1.69

-0.19+5.16

mode 2

6. ESTIMATION O F EIGENVALUES FOR POWER SYSTEM OSCILLATION -0 2

‘ 4 n 5 10 15 20 25 30 35 40 By the use of the proposed method,

three modes were extracted from phase differences between Nagoya Institute of Technology and The Univ. of Tokushima and between Miyazaki Univ. and The Univ. of Tokushima such as in Fig. 13. It can be seen from Fig. 13 that each waveform on mode 1 oscillates in the opposite direction and mode 2 tends to oscillate in the same direction. Therefore, it proves that dynamic behaviors measured at domestic outlets such as Fig. 13 coincide well with characteristics in Fig. 1 1 and decomposition of plural modes are attained adequately.

Elapsed lime ( 5 )

Fig. 1 1 . Mode 1 and mode 2 in IEEJ WESTIOmachine system extracted by the proposed method (case 2 ) . demonstrates that extraction of modes between generators is performed correctly because this characteristic analyied here conforms to each form of eigenvector in Fig. 7. In case 3. decomposed modes of the phase difference between generator 4 and generator 7 are shown in Fig. 12. Mode 3 is observed clearly compared to Fig. 9 and Fig. 10 because generator 4 and 7 participate in mode 3 and three phase ground faults is near node 17. There is little observation of mode 2 between these areas in the frequency domain analysis.

Next. calculations of eigenvaluef with three mode$ lead to the estimation of stability. Variations of eigenvalues on June 27 in 2005 are provided in Fig. 14 and Fig. 15. Fig. 14 and 15 illustrate the real part and the imaginary part of eigenvalues, respectively. A real part of eigenvalue can be utilired for discrimination of power syqtem qtahility. An imaginary part of eigenvalue corresponds to a natural frequency angular. From Fig. 14, the more the electric power demand increased, the lower the power system stability is. As can be seen from Fig. 15, the more the electric power demand increased, the lower the frequency of each mode is. The increase of synchronous generators, namely the increase of the equivalent inertia, leads to the lower of frequency. Briefly stated, the frequency of each mode varies with the electric power demand.

Eigenvalues of three modes in Fig. 9, 10 and 12 and eigenvalues calculated by simulation are compared in Table 1 . Assuming that three modes in these figures are separated as a single mode. eigenvalues can be obtained. From Table I , eigenvalues determined by separated modes are matched to the ones obtained from simulation and these results confirm that the proposed method provides a precise tool for the evaluation of power system stabilities.

81

-Nagoya Jnsl!hde o f Techiiology ~

-0 51

50

l h e Univ. o f Tokushima Miyataki Uiii\. -'The U o i r . ofTokushima ~

-0.08

,

I 150

100 made 2

".__

50

1

150

0.5

: 4

g

0

c

." 2

50

100 Elapsed time

Fig. 14. Real part of eigenvalues on June 27 in 2005.

150 (5)

Fig. 13. Three power system oscillations extracted from a phase difference.

I

421

For power system controls over a wide area, it is very important to monitor power system oscillations at real time and the monitoring of ill damping or frequency is made possible with continuous measurements.

7. CONCLUSION This paper presents the effectiveness of decentralized PMUs assigned in demand sides. As seen from the results of frequency domain analysis, mode 1 (long term oscillation), mode 2 and mode 3 were observed in phase difference at a frequency between 0.2 and 0.7 Hz. The result clearly shows that Savitzky-Golay filter and the curve fitting method have proven to be a useful approach for the observation of power system oscillations. Moreover, the derivation of eigenvalues on each resolved mode by the curve fitting method brings a rrioriitoririg of power syslcrri stability. Thc h c t mentioned above exhibits that power system oscillations can be detected from measurement at the domestic outlets. Therefore, it is likely that the application of acquircd data and our analysis method lead to the improvement of the wide-area power system controls. Thus, thc phasor mcasurcmcnt tcchniquc brings us feasibility in an online monitoring of power system stability.

I 0

I 5

10 15 Time (horn-)

20

25

Fig. 15. Imaginary part of eigenvalues on June 27 in 200s. units", Electrical Power and Energy Systems, V01.23, pp. 245-250. T. Hashiguchi, M. Yoshimoto, Y. Mitani, 0 . Saeki. Kiichirc) Tsuji, M. Hojo, H. Ukai, J. Toyoda and A. Matsusliita (2004). "Analysis of Oscillatiori Characteristics Followed by Power System Disturbance Based on Multiple Syncliionized Pliasoi Measur ements", Proc. of the International Conference on Electrical Enginecring (ICGG). Technical Committee of IEEJ. (1999) Japanese Powcr Systcm Models. [Online] Availablc: http://www.iee.or.jp/pes/model/english/index. html

REFERENCES K. E. Martin (Chairman), et. al. (1998). "IEEE Standard for Synchrophasors for Power Systems", IEEE Trans on Power Delivery, Vol. 13, No 1, pp 73-77. R. Tsukui, P Beaumont, T. Tanaka and K Sekiguchi (2001). "lntranet-Based Protection and Control", IEEE Computer Applications in Power, pp. 14-17. A. Radovanovic (2001). "Using the Internet in Networking of Synchronized phasor measuremcnt

82

Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLlCATlON$

IDENTFICATION OF ELECTRIC PARAMETERS OF SYNCHRONOUS GENERATOR USING INPUT-OUTPUT DATA SET

S.A. Saied* , S.M. Bathaee',

M. Karrari**, W. Rosehart*** and O.P. Malik***

'Department of Electrical Eng,Kh.N. Toosi University of Technology, Tehran, [run; Department of Electrical Eng. Amirkabir University of Technology Tehran, Iran; *** Department of Electrical and Computer Eng. University of Calgary, Calgary, Canada. * x

Abstract: A novel technique to estimate the electric parameters of a synchronous generator from on-line measurement is presented in this paper. The proposed algorithm has two steps. In the first step, replacing the damper currents by higher derivatives of field and armature d-q currents, the electric parameters of the armature are estimated. In the second step, a current estimator is designed to estimate the damper winding currents, from which the parameters of field and damper windings are estimated. Simulation results show very good estimate of the electric parameters of a seventh order synchronous generator. Copyright G 2006 IFAC Keywords:: Synchronous machines, Electrical constants, Dynamic modelling, Parameter estimation, ldentification

1.

parameters of a known structure. Usually the procedures involve difficult and time-consuming tests, such as; short-circuit, standstill frequency response (SSFR) and open circuit frequency response (OCFR) tests. These tests can mainly be carried out when the machine is not in service. The main problem with this approach, classified as white-box modelling, is that the parameters are determined individually using off-line tests. There are errors when these parameters are used collectively to simulate a synchronous generator. The errors may come from the fact that the assumed wellknown structures may not accurately model the system at all operating conditions. To overcome this source of error, different structures for synchronous machines, other than the traditional d-q axis model, have been tried (Chaii, 2001; Cui, 2004). To overcome the drawbacks of the white-box modelling, identification methods based on on-line

INTRODUCTION

Synchronous machines play a very important role in the stability of the power systems. A proper model for synchronous machines is essential for a valid analysis of stability and dynamic performance. Three quarters of a century after the first publications in this area (Kilgore, 1931; Wright, 1931), the subject is still a challenging and attractive research topic. Various studies on the ever-increasing size and complexity of power systems show the need for more accurate models of synchronous machines (IEEE Std 1 1 10,2002). The traditional methods of modelling the synchronous machines are well specified in IEEE Standard (115, 1995). These methods assume a known structure for the synchronous machine, using well-established theories like Park's transformation (Park,1933). They address the problem of finding the

83

measurements have gained attention during recent years. These methods can be divided into two categories classified as grey-box and black-box modelling in this paper. Grey-box modelling (Melgoza, et al. 2001; Karrari, et al, 2003b) assumes a known structure for the synchronous machine, as the traditional methods, and the physical parameters are estimated from on-line measurements. Although there has been some success in estimating the physical parameters from on-line measurements, a problem of wide ranges of acceptable parameters has arisen (Jingxia, et ul, 1998; Burth, et al. 1999). The main reason is that the measured on-line variables are not rich enough to adequately reflect the effect of each parameter particularly when a high order structure for the system is considered (Burth, et al. 1999). The other problem with grey-box modelling is that the physical parameters of synchronous machines change with the operating conditions (Karayaka, et a1 ,2003; Karrari, 2003c; Nelles, 2001) mainly due to saturation effects and nonlinearities. In black-box modelling (Nelles, 2001; Karrari, et ul. 2003a, 2000; Shamsollahi, et al., 1996), the structure of the model is not assumed to be known a priori. The only concern is to map the input data set to the output data set and thus the physical parameters, such as resistances and reactances are not calculated explicitly. In this paper a grey box identification method is described to estimate the electric parameters. A seventh order nonlinear model is adopted as the known structure with unknown paramters. To use least squares method (Norton, 1986) for parameter estimation, the synchronous generator structure should be converted into a particular fomat. The technique described in this paper to do this is the main contribution of the paper. Assuming that the terminal voltage (v), current (i), rotor speed (a),field current (if) are measured, there are still steps to be taken to convert the structure such that it is suitable for the least squares method. The proposed method consists of two steps. In step I , by eliminating the damper winding currents, the parameters of the armature are estimated. Then using the cstimatcd armature paramctcrs, a current-estimator is designed to estimate damper currents. The estimated damper currents are then used to estimate the field and damper parameters. Details of the identification method are described in Sections 2. The application of the proposed method on a synchronous generator and estimation results are described in Section 3. Section 4 concludes the paper.

2.

Fig 1:Synchronous generator model structure Equations obtained from Fig. 1 are: -vd=[r

[

Id

Lq 0)lq

-vq=[Ld . .

[-

o.id iq

-vf

=[ rf

Id

Lmd

Lmd [email protected]

Lrnd

. .

“llQ

-mi,

Lmd

Ld

Lrnq

If

11)*

Lq

L~tq]

.

1‘)

L ~ ~L d ~ ~ ‘D]d

O=[

‘Q

Lrnq

.Q]

[

[ ‘Q

I’

.*r .

+ . I*

‘Q

.

;i

Lf bnd] . [ if

Or[

Lrnd]

ld

iD

cl,*

’,

i,‘

‘I;]?

IQ*Y

where ( ’ ) denotes time derivative. The method proposed in this paper is based on the fact that the damper currents can neither be neglected nor can be measured. To overcome this problem, eqns. (1) and (2) are manipulated below to a form that does not contain damper currents. The new set of equations is used to estimate the stator parameters. The field and damper winding parameters are then estimated using the estimates of the armature parameters obtained before. 2. I . Stulov purumeler estinialion

The suitable form for least squares estimation (Norton, 1986) is y=B.X+e where y is the output of the system (measured variables), 8 is the unknown parameter vector and X is the known input vector of the system (Ljung, 1999). To use the least squares method and to estimate the parameters, the main problem is the presence of non-measurable damper currents. To overcome this problem, eqns. (4) and (5) are first manipulated to determine an expression for the damper currents:

PROPOSED IDENTIFICATION METHOD

The d-q axes equivalent circuits, Fig. I , of the seventh order synchronous generators are well documented in the literature (YU, et ul., 1983; Kundur, 1994).

84

.z

)

+ i,

.( r )

+ i,

.( r . ( z D

+

T

Q

)

+

L

,/

co b )

+ i,"

where p is the derivative operator. Substituting eqn (6) into ( I ) and (2) results in a set of equations without damper windings currents. Here is the detail: From (1): -Vd

=r.id +(l).Lq.iq+Od,q.iQ +lad/Wbido+Ia,d/Ob.ifo

+L,d/O)b.ino Substituting for iD' and iQ using (2)

a

.

p H

*:

p2 H

..

To overcome the problem ofthe presence of w in the equation, eqns. (7) and (8) are again manipulated to a new vector form, which is suitable for least squares identification method to estimate the parameters (Norton, 1986):

.*. p3

H

...

then: -

vd = id(r)

+ idm(r.(TD + T

. ( ~ . T ~ .+ TI ,~d

/ ~ ) b . ( ~ D+ z Q )

~

+

+) L d

/ o h )+ i d " /cub

Lmd

The parameters a and p are given in the Appendix. In the proposed algorithm, it is assumed that the terminal voltage (v), current (i), rotor speed (w), field current (if) are measured. To calculate v d ,V , ,id, i,

)+

rD

/a,

L,, i d * * * . [ L d / o ~ , , . z ~ .+~ ~

.za ) + i,

rD

and their derivatives, required in eqns. (9) and (1 0), rotor angle measurement is also required (Idzotic, 2004). In some practical plants (especially new installed plants), rotor angle measurement is available for other applications. In other cases, rotor angle can be estimated by integrating the rotor speed deviation from the "synchronized no load condition". This approach is used in this paper. If eqns. (9) and (10) are used in a least squares identification algorithm (Norton, 1986), the parameters ats and p, s are estimated. From the estimated parameters the armature parameters can be calculated by:

Substituting iD and iQ' from eqn. (6):

2.2. Field und dunzper parameters estimution In the second step for estimating the parameters of field and damper windings, it is necessary to estimate

85

iD and iQ. In order to design a current-estimator, A comparison of the actual and estimated parameters the estimated armature parameters and eqns. (1) and of the synchronous generator is given in Tables 1 and (2) can be used. It is clear that except for iD and iQ 2. To make sure that the high order derivatives in all of the currents and physical parameters in eqns. eqns. (9) and (10) do not cause serious problems in ( I ) and ( 2 ) , are known. estimating paramters, some noise was added to the Solving for iD: measurements. In these tables SNR (signal to noise ratio) is defined to be: i, =(vq-aLd.id +r.i, -(!&,,& +L, /q,.i,* +L~,,q/(~.i~)/(~~L,,,d) 20(L0g(-))

(12)

Signal

dB

Noise Solving for iQ: A comparison ofthe simulated synchronous machine i, =(vd +rid +u*L,.i, +Ld/q,.id'+Lmd/wb.if* +Ll,,d/q,.iD*) and the identified model is shown in Figs. 3, 4 and 5. The figures show that l [ ) , l Q , l d , l q , terminal voltage /(-L,,> and output power of the system with the actual (13) Having estiamted iD and iQ, ( 3 ) , (4) and ( 5 ) can be parameters and with the identified parameters are used in a least squares algorithm, to estimate the field very close. Performance of the model with the and damper parameters. estimated parameter has an acceptable performance and can be used to simulate the performance of the Using this approach, the identification method is machine. summarized below: Select a proper input signal, u, to be applied to the field voltage. The input signal should Table 1 . Armature windings parameters have a wide spectrum to cover all system Parameter Actual Estimated Estimated dynamics. It should also have a proper SNR 50:l values No noise magnitude. The magnitude should be large 0.002 0.002 0.0018 r enough to cover the non-linearities and Lq 0.474 0.474 0.472 should also be small enough so that it is safe Ld 1.304 1.304 1.3032 to perform the test. Lmd 1.19 1.190 1.189 Select a proper sampling time and final time Lmq 0.36 0.360 0.3578 (the total time for the experiment). Apply the selected input signal (item a, to Table 2. Rotor windings garameters the system and sample the input-output data Parameter Actual Estimated Estimated by a data acquisition system. Sample the values No noise SNR 50:l terminal voltage (v), current (i), rotor speed rf 5.79E-04 0.000579 0.000548 (a),field current (it). 1.303928 1.220544 LF 1.304 Estimatc rotor anglc by intcgrating rotor rD 0.0117 0.01 17 0.001 18 speed deviation from f d l speed no load LD 1.372 1.37160 1.3290 situation. rQ 0.0197 0.01970 0.01970 Calculate the variables in eqns. (9) and (1 0). LQ 0.742 0.7436 0.7438 Estimate the parameter., in (9) and (lo), using the least sqaures method. Estimate the stator parameters using (1 1 ). Estimate iD and iQ using (12) and ( 1 3). Estimate the field and damper paramters using ( 3 ) , (4) and ( 5 ) and least squares identification algorithm.

3. SIMULATION RESULTS

The proposed approach has been tested on a synchronous generator connected to a constant voltage electric network and a local load as shown in 2, using MATLAB-STMULINKFig SimPowerSystem software. In this figure, blocks A and B are the estimators of Section 2.1 and 2.2. Rotor parameters are estimated in Block B with a time delay using the armature parameters estimated in Block A. To simulate the system, the power system was first connected to the network (with some transients), and then some step inputs to the field voltage were applied. The rotor steady state speed was measured before connection to the network.

pu Fundamental

La3d

big 2. Simlulation ofthe power system

86

4. CONCLUSIONS A new method for the identification of the electrical parameters of a synchronous machine is presented in this paper. In the first step, the parameters of the stator are estimated. These parameters are then used in the second step to determine the damper currents. The performance of the currentestimator to estimate damper currents was stable and the estimated currents are reliable to be used in estimating other parameters. The simulation studies show that the machine perforinance using the obtained parameters matches fairly closely the performance of the actual machine. The next step is to apply the proposed technique on a physical machine.

-0 0868

la -0 0968 3

Irme(a)

Fig 3. Outputs of the actual system and of the -identified model (d axis currents)

I’

-31

APPENDIX

Bs

i

= L‘,

identified model (q axis currents) O’1I

’ Actual

1

I

b b

0 0999

0 099970

25

30

35

UC

I

8240,

8220h I I

Actual Estimated

’ Q

8180 8160

8140

8120 1 40

I

25

31)

35

time(s)

Fig 5. Outputs of the actual system and of the identified model (terminal voltage and p-out)

87

u 5 = ( r . ( ~+ .~r y ) + L ,

Intelligent System Applications to Power Systems, Lemnos, GREECE. 1, mq * /
88

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

ESTIMATION OF MOISTURE CONTENT IN COAL IN COAL MILLS Peter Fogh Odgaard Babak Mataji

xx

* Department of Control Engineering, Ralborg [Jniuersity, Fredrik Bajers Vej YC, DK-9220 Aalborg, Denmark, odgaardQcontro1. aau. dk ** Elsum Engineering A/S. Krufivarksvej 53: DK-7000 Fredericra, Denmark, bani,a~elsani-e~~g.coni

Abstract For coa.1-fired power plants iiiforma.tion of the moisture content in the coal is important to determine and control tlie dyriarnical behamior of the power pla.rits. I3.g. a high moisture content in the coal can result in a decreased ma.ximuin load gradient or the plant. In this paper a rnet.liod for estimat.ing the moisture content of' the coal is proposed based on a simple dyna.mic energy model of a coal mill, which pulverizes and dries the coal before it is burned in the boiler. An optimal unknown input observer is designed to estimate tlie moisture content based on an energy balance model. The designed nioist.ure estimator is verified on a couple of sets o C measurement data, from which it is concluded that the designed estimator estimates the real coal rnoist,ure content.. Copyrzght @ 2006 IFAC Keywords: Moisture estimation. Coal-fired Power Plants, Optimal Unknou~n Input Observer

1. INTROlIUCTION

plant, performance, imfortiinat,ely, the moisture content is not mea,surable.

I n order to understand this, the att.ention is addressed on the coal mill. Before the coal is burned in t.he furnace, it. is preprocessed in the coal mill. The rnain purpose of the coal mill is to dry and pulverize tlie coal. The primary air flow is used to dry arid carry the pulverized coal to the furnace. It is therefore important t,hat the primary air has suficient energy at all loads. During a load increase of the power p h t the coal flow is increased together with the primary air flow. When the moisture content of the coal is higher than assumed it would take longer time to dry the coal, resulting in cha.rigeddynamics of the coal mill, arid accumulation of coal in the coal mill. This will evidently c h i g e tlie possible performance of the power plaiit in general. 111 (Odgaard et d.2006)

During the l a k yea,rs producliorr of Danish power pla.11Ls l1as beer1 reguli-tted Illore alld more tleperldirig on the energy market, which results iri va.riatiiig load requirements. Simply due to the fact that t,he plaiit pwduct,ioii is dcperiding marc? on thc prices on the market as well as the demands for power. 'u'his aga,in results in higher focus on better dynamical pcrformaiicc of the powcr plants. In this regard it is of importance to monitor the performance, c.g. monitor thc pcrformancc in order to determine if the requested performance is achieved. One of the variables influencing the performance of a coal-fired power plant is the moisture content- of Ihc raw coal. In other words it would be useful to know the moisture content in order to make an assessment and prediction on the

89

a schcmc using Ihc estimated moisture content to limit the maximal load to an achievable one.

Pulverized coal

It is not possible to measure the coal moisture content. online for use in a real time cont.ro1 system. However, st.atic est.irna.tes of t.he coa.1 moisture content is delivered by tlie mill control system.

The focus of research in control of coal mills has not been addressed on moisture estimation. Irist.ea.d, dynamic niodeliiig a.rid tiomiria.1 c:ontrol of these coal mills have been the topic of numerous of publications. Some examples dealing with modeling of coal mills are (Itees and Fan 2003), (Zhang et ul. 2002) a.rid (Tigges et al. 1998). Coiitrollers for t,he coal mill are designed in (Hees and Fan 2003) and (Hasselbacher et al. 1992). High order dyna.mic models and observer design for coal mills are the lopics in (Fukayarna et ul. 2004). In (Rees and Fan 2003) a lion-linear dynamic energy balance model is given. In this paper the model is simplified and adapted 1-0 the specific coal mill Babcock hfPS 212, which is used in Elsam's Nnrc~jjyllandsv~rktet Unit 3. The model is suhscqucnt,ly linearized. A n optimal unknown input observer, see (Clien aiid Pattori 1999), is subsequently designed in order to est,irna.le c o d moisture content of the coal feed into the coal mill. The outline of this paper is as follows: tlie coal mill is first described and modeled: including a state representing tlie moisture coriterit. Iii the subsequerit section tlic observer is designed, it is subsequently applied t,o da.ta from a coal mill, from which it can be coiicluded that the desigiied observer estimates the coal moisture content.

\Primary

Air

/

Figure 1. An ilhistration of the principals of the coal mill. The raw coal is pulverized by tlie rollers a.nd the grinding table, the pulverized coal is subsequently dried and lifted by the primary a.ir. If tliese particles are small eriougli t.liey will be lifted tlirough and irito the power plar1t furnace.

2. 'I'HF, COAL MILL The work presented in this paper, is ba.sed 011 a. Babcock MPS 212 coal rriill used at Elsarri's Nordjyllaridsvwrktet Unit 3. However, the method proposed in tlie paper is so generic t,hat it, can be applied to other types of coal mills. The coal mill is illustmted in principles in Fig. 1. The coal is fed to the coal mill through the central inlet, pipe. The coal is pulverized on the rotating grinding table by the rollers. The pulverized coa.1 is subseqiiently blown up aiid thc moisture cont.cnt of thc coal dust is evaporated by the hot primary air. The prirnaxy air is mixed by cold out,side air and heated outside air, which is heated by hot flue gas from the furnacc. The ratio of thesc air flows arc uscd to control the temperature of the primary air flow. Coal pa.rticles which in the pulverizing have been small enough will pass through the chssifier a.nd out through the outlet pipes into the boiler. On tlie other ha.nd if the coal pasticles are not dried rnniigli t,hey ca.rinnt, be lifted niit of t,lie cnal mill

by the prima.ry air flow, since these particles are too heavy.

2.1 Control a,nd mensi~rements References to the coal flow and the primary a.ir flow arc given by the gcncral powcr plant controller, a.s well as speed for the cla.ssifier. The coal and air flow references are used as approximated values for these flows. rl"he temperature of the primary a.ir is used to control t,hc tcmperat,ure in the coal rnill at the classifier. 'I'he temperature coritroller is ofteri required to keep tempera.ture constant at 1.00"C in order to evaporate the moist,ure in the coal. A coal mill is a. ka.rsh etivirotimerit in which it is difficult to perform mea.siirement,s, this mea.iis t,ha.t, all t h e va,ria.hlrs

90

Figure 2. ,4n illustration of energy balance iri the coal mill, where Y'(t) is t,lie temperature in the mill, Qair(t) is the energy in tlie primary air flow, Pmotor(t)deiiot.es the power delivered by tlie roller rrtotors, Qcoal(t)i s the energy iit tlie coal flow, a i d QTnoisture(t) is the energy in the coal moisture. m, is the mass of the coal mill.

,

I.;

u

90

0

05

15

1 S"mp1es

are not measurable. E . g the a.ctua1 coal flow into the coal mill is only estimated. The coal flow out of the coal mill is not measurable. However, the primary a.ir flow and tempera.t,ure are. as well a8 the temperature of the coal dust at the classifier. 'The moist,ure conknt is riot online measura,ble) but measurement of off-line samples can be taken, in a.ddition a sta.tic estirna.te of the moisture is provided, t,liis c s h i a t c has bccri verified by off-

2

["I

?5

1

x 104

Figure 3 . A plot of the non-linear and linear model respoiise coiiipa.red with nieasiireiiients of a step response on the coal mill. This cotnbiried 11ea.tcoeficierit does riot deal with the fact that the specific heat of water and steam are different, however the model error due to 11ea.t of steani to a couple of degrees above 100°C: is negligiblr in t,his contcxt,.

liiie sairiples.

The dynamic nori-linear model is siibseyuently given by 3 . ENERGY BALANCE MODEL OF THE COAL hIILJ,

m,C,.il(t)

A simple energy balance model of t,he coal mill is derived based on (Rees a.nd Fa.n 2003). (Rees and Fan 2003) includes more details, but these are neglected in this work. In this model the coal mill is sccn as ortc body with t.hc mass m,,, as illlistrated in Fig. 2, in which l"(f,) is the temperature in the mill at the classifiers, Qair(i) is the energy in the primary air flow , ElluLur.(t) dcnotcs thc power delivered by the roller mot,ors, Qcoal(t)is the energy in the coal flow, and QIlloiStUTe(t)is the energy in the coal moisture. It is a.lso a.ssuined t1ia.t the input coa.1 flow is equal the oiit,piiI coal flow. Evrn Ihoiigh t,his assumption is only entirely true fo is a.ssiimed in t,liis pa.1~1' for siinpli A more detailed model which takes digerelit coal flows into account might result in more precise estimation of t.he moisture content. 'rhe eiiergy d in Fig. 2 i s given by ( I )

~

(2)

A/(

+ Pmo+or(t), where: Cm is the specific heat of the mill, T(1) is the mill temperature a.t the classifiers. rhpa(t) is the primary air mass flow in and out of the mill, Cair is the specific heat of air. T p A ( f ) is the temperature of tlie inlet primary air, & ( t ) is the coal mass How. C, is the specific heat of the coal. 7: is the outdoor tempera,ture, r ( t ) i s the ratio of moisture in the coal. C, is the specific heat of the moisture, HStpa,rarnctcr combining the la,tcnt heat of tlie st.eam arid specific lieat of the water, and P,notor(t) is the power delivered by the mill motor. All parameters in this model arc found in dat,a, books except m,, . Cn, which is identified based on nie;r.surernents of a step response on the coal mill. The model response is compared with Ineasuremerits a.s well a.s a. response of a 1iriea.rized model in Fig. 3. From this figure it. can he seen tha.t t,he responses of hot,l-i models are quit, sirni1a.r t,o the large dynaniical changes its the measiiremerits show. However, it is difficult to validate the details in the response due to the way the signals are sampled. A dead band on one per cent is a,pplied to these measiiremerits meaning that the signals shall have changes of more than one per cent from sample to saniple. 'I'he n o n - h e a r niodel (2) is subsequently linearized and transformed into

'l'he hea.ting arid evii.pora,tiori of t,lie rnoist,iire in the coal is modeled by a combined heating coefficient. 'Ylie temperature is due to the control loop is kept. at 100°C. The lat.eiit energy of t.he evaporation dominates the energy required for a few degrees heating of the moisture. The coinbined heat coefficient>I& is following defined as H5t = C& ~ S t e a , l / l O O , where Ct, is t.he specific 1iea.t of the water, and Lsteamis the latent heat.

+

'rj2pn(t)C;iir (?bA(t) - T ' ( t ) ) + @(L)Cc(7; - T ( f ) ) + y(t ) r h c ( t )c w 7k t)fnc( t )HS,7 '(t )

~

91

A. st,a.te spa,(:e representation, see (s),t,he niot,or power is also neglected from this state space model since it is much smaller than the other powers in tlie equation.

I.$1, R

A,=

where p is the pole of internal fa.& model. The model is discretizietl before any further use, 1.e. ( A q , B,, C,, E,) a,re tra.nsformed to

A. given variable z ( t )is linearized by z ( t )= x(11) - x,, x, is t,he operation point of x(l). The

where

(Ad? Bd> Cd? Ed).

operational point for t,he ~aria~bles in t,he model are fourid for a number of intervals covering the entire operational range for the c o d mill, q ( t ) is the normal distributed process disturbances; r(t) is the normal distributed measurement noises. 7kl(b) i s the measured ternpera.ture and

3.2 Opttmal unknown snpul observer The optimal unknown input observer is described in (Chen and Patton 1.999). For discrete time systems with unknowii inputs and disturbances which can be represented by

an optimal unknown input observer of the following form can be derived.

B=

+ I]

X[TL

Z[TL

+ I] + H , + L N +[ ~I].

(17)

The basic idea in this observer is to elirninate the deperidency of the unknown input from the estimation error by matrix transforms, and subsequeritly design a. Kalman est,iniator for the transin. A posit.ive side effect of this, is that the estimator gain is recomput.etl a,t ea,ch sample, meaning the model can be changed such that the point of operation can be updated. The schemes for computing the matrices in tlie optimal unknown input observer can be seen in Appendix

3.2 Model wth, moisture This lincar model is subsequently modificd for the estimation of the coal moisture content. An additional state is introduced for representing the coal moisture content. ~ [ T L ] .instead of the input 'I'his state is driven by the unknown input. deiioted m[n]. In addition the static estimate of the moistiire content ir cniisidered iis A very noisy ineasurernent, (8-13).

A. The varia,nce of the disturbance and measurement noises Q[n]arid R[n]:as well a.s the internal fault model parameter p are all found by trial arid error, ba.sed on experimenta.1 data, in the way that, tlie observer est,iinates the inoistrire conl,ent in the coal. The results can he seen in Section 4. From Fig. 4-7 in Section 4 it can be seen that the observer estimates the coal moisture content u7rl1, and it, is hereby concluded that t,he observer and niodel are well tuned.

rm[n].

(9)

4. RESULTS

where yn(t) is the generic unknown input which is low-pass filtered in order to represent tlie coal inoirtiire content. a r i d

'l'he designed moisture est,irna.tor is a.pplied t o measured da.ta from the coal mill described in Sect,ion 2. Since t,he rnoist,iire cont,rnt,is not rnea.siired

92

"I

I

II

I

0 125

1500

SO0

Sanlples I"]

lo00

1

11""

sarnpics I"]

Figure 6 . Example 3 , comparison of observer estimated, static measiired/estimated coal moisture content. 'l'he sta,tic estimate reacts on the load cha.nge at sample 1230>which the observer estimate does not.

Figure 4. Example I , comparison of' observer estimated and static measuredleslirnated coal moisture content,. Notice the static measurement is influenced by a plant load change at sample 66 and 450.

"I

' I

0105

0136-

0134 0

500

100

200

300

400

100

600

700

OW

800

, 10

1000

SnrnplPsln]

Figure 7 . Example 4,comparison of observer estimated, static niea.sured/estiinated moisture coiiterit. The third exa.mplr shown in Fig. 6 contains a load change a.pproximately at sample 1230. 'The observer estimated coal moisture content shows the increa.se in coal moist.ure cont.erit without i-ea.ctiiig011 the load change a.t sample 1230. which the static estimated moisture content: on the other hand, does.

Figure 5 . Example 2 ; comparison of observer estimated aiid static iiieasured/estirnated coal moisture content. The observer estimate does not react on the load change at sa.mple 900, which t.he sta.tic estirnat.e does. it is impossible to comparc the cslimatcd moisture content with the real rnoistuie content I-Iowevei it can be compared mitli a static estimate l'his comparison has been done for four diffeient sets of rnedsi~rernentsarid can be seen in Fig 4-7

The fiist example shown in Fig 4 contains two changes of the plant load at sainple 66 aiid 450 These load changes are influencing the static measured but not the one estiniakd by the use the proposed scheme Ex( ept from the the plant load changes both methods are following lhe increases and decreases of the moisture content

'l'he fourth example which is illustration by Fig. 7, has a, variating moisture content and plant load change approximately at sample 146. The conclusion which can be inade of this example is similar to the three others. 'l'he observer based estirna.tion gives the moisture content without reacting on tlie plant load changes, which tlie ic estimate, on the other hand, does.

The second example shown In Fig 5 contains one load change approximately at sainple 900 Again the static measuren~ent/estiniate reacts on the load changes whereas the proposed scheme does no1 Both estimates follow the iricreased moisture ( ontent well

From these four examples, illustrated by Figs. 47, it can be seen that the observer estirna.tes the moisture content of the coal well in all four ca.ses. On the other hand this estimate does not react on load changes as the static estimate does. It can hereby be concluded that the observer and model

93

Appendix A. OP‘L‘IMAL UNKNOWN INPUT

are well tuned, and the estimator can be used to estimate the moisture content dynamically.

OBSERVER A necessary arid sufficicnt condition for the existence of a solution to the given observer problem is i ~ (i C h i and Palton 1999) given as: an optimal unkiiown input observer solution exists if arid only if. rank (Cn+lEn)= rank (En).

5. CONCLTJSION ‘l’liis paper introduces a method for estimating moisture content in the coal in coal mills used in power plants. The eslimation is performed by using a simple linearized dynamic energy balance model, and an optimal unknown input observer. The designed observer is tested on four sets of cxpcrimcntal dala from a. coal mill, and it is concluded that the observer estimates the coal moist,ure content, in all these cases wit,li different moisture content.

The computation of the matrices in the observer is also givcn in (Chen and Pattoii 1999) as:

(I) Set initial values: Pg

P(O), zo CoEo (CoEo)+Yo, Ho = 0. (2) C h i p u t e H,+, = E, (C,+lE,)+. (3) Compute =

=

xg

~

+

AA+,P,C: (C,P,C: R,)-’, T and Pk+l = P,, - KA+lCILPIL (4) Cornputp TrL+l= I - Hn+lC,+I, F,+i = An - Hn+iCn+iAn - KA+lCn, K;+l = Fn+lHn, a d Kn+I = K,I,+, + K?L+l KA,,

6. ACKNOWLEDGMENT

The authors acknowledge the Danish Ministry of Science Technology and Innovation, for support to the research program CMUC (Center for Model Based Control), grant no 2002-603/400 1-93.

=

(5) Now compute

+

+

+

11 = F,+lz[n] T,+~B,u[nl Kn +1Y and x[n 11 = ~ [ n11 H,+ly[n 11. T . (6) Compute Pk+, = P,L-KA+LC,LP,L and following P , + ~= A;+, (AA+~)~+T,+~Q,,T +;+, HrL+lRn+lH:+l z[n

REFERENCES Clien, Jie and R. J. Patton (1999). Rob,ust modelbased fault diagnosis for dynamic systems. first ed.. Kliiwer academic publisliers. Fukayarria, Y., K. Hirasawa, I<. Shirriohira and H. Kanemot,o (2004). An adaptive stat,e estima.tor for pulverizer control using inornerits of particle size distrihut,ion. IEfW Ti-ansuctions on Control Syst;eni Tech,nology 12, 797-822. Hessclbac1icr7 R,., hl. Lang and C:. Laiistcrcr (1992). R.eglerentwurf fur ein kohlcninuhlenrnodell unl-er berucltsichtingurig der verfahareristecliriisclieri randbedingungen. AUt om3atisieiungst echnik 40 , 148- 157. Odgaard, P.F., J. Stoustrup and R. hfataji (2006). Preventing performance drops of coal niills due to high moisture content. Submitted for publication. Rees. N.W. a.nd F.Q. Fa.n (2003). Modelling and cont-rol of pulverised fuel coal mills. In: I’hernial power plant m n d a t z o a and con.t-r.ol (D. Flynn, Ed.). first etl. Tnst,iti.ition of Rlect r ical En ginerrs. r 1 I igges, K.D., W. Risrhoff and T. St,einha,ge (1998). ~Val2;enschusselrnuhleri als koinponerit,cn nroderner fcuerungstechnik. VGB Krafimerks‘rectinik 78, 77-88. Zhang, Y.G., Q.H. Wii> J. Wang, G. Oluwande, 1). Matts and X. X.Zhou (2002). Coal mill modeling by inacliine learning based on oiisite measurements. IEEE Tmnsactions on Energy

I.[

( 7 ) Set ri

Conversion 17, 549-555.

94

+

= ri

+ +

+ 1 arid jump t o step 2.

+

me

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ELSEVIER

PUBLICATIONS

SIMPLIFIED FUEL CELL SYSTEM MODEL IDENTIFICATION S.Caux', W. Hankache'. ', D. Hissel', M.Fadel' 'Laboratoire d'Electrotechnique et d 'Electronique Industrielle, LEEI li1\41? I N P T C N R S 2 rue Camichel31071 Toulozise cedex 7-France hankache,fadei,cazixx/cr,leeienreeihl fi. 2 Laboratoire de recherche en Electronrqzie, Electrotechnique et SystBmes, L2ES EA i'IiUlJ7BM, 13 ride zlieg 90010 Belforf I
Abstract- The use of fuel cell and supercaps as energy elements in transport application is now a reality. Having two power sources on board allows a certain energy management strategy. In order to reduce computation time consumption, a simplified physical fuel cell model is proposed. An accurate model is studied in simulation to derive a simpler model. The simplified model is used with parameters identification made on an actual fiiel cell. Results obtained on current and voltage, with an actual power demand, are sufficient to use the proposed model in iterative optimization algorithms. Copyright 02006 IFAC Keywords-Circuit

1.

Model - Identification

INTRODUCTION

Power management

-

Optimization

Numerous studies analyze the fuel cell behavior and an adequate model is requested to compute the behavior of such system (Jemei2002, Friede2002). An electro-chemical model can be built but it is heavy and computer-time consuming. A complete model must take into account fluid mechanic phenomenon linked to gas distribution in non linear pipes, electro-chemical reaction characteristics, thermal influence and so one. Based on the physics this paper proposes in the first part, a simplification approach to obtain a model of the controlled fuel cell system accurate enough to describe main phenomena for current-voltage behavior. In the second part, the simplified model parameters are identified not only on the simulator but also on an actual fuel cell. Finally, the simplified model practically tuned is fed with actual power demand and results are compared to the actual fuel cell behavior to veri@ if the simplified model behavior is quite close to reality.

Mainly due to pollution regulations, there is a growing interest in using non-conventional and environmental-friendly energy supply in transport applications. Over the last decade, among the different solutions. fuel cell systems have shown considerable promises. Using fuel cell in transport application in the heart of cities has two main interests: air pollution reduction (he1 cell only produces water, no COZ) and allows catenaries suppression (all energy sources and converters are on board). The technology chosen in this study is Proton Exchange Membrane Fuel Cell (PEMFC) working at low pressure (about 2bars or less) and mid-temperature (about 80°C). Supercaps compose the Energy Storage System, added to help the he1 cell supplying the high power demand and to absorb energy recovered from the load because the PEMFC is not reversible (Solero2001 and Corgierl997).

95

2. 2.1

FUELCELLMODEL

In the cooling water loop a pump assures a constant flow and a cooling radiator and 2 valves assure the temperature regulation with a suitable decoupling and compensating control structure. The temperature is regulated around the optimal temperature defined (8OOC). So the most difficult compartment to model is the cathode (oxygen) compartment where a compressor and a valve must provide the desired flow under the 1 Sbar absolute pressure fixed.

Based-Cell Model

Anode, cathode, membrane and electrode elements constitute the based-cell also called elementary-cell. With serial and parallel connections a more powerful fuel cell can be built to have sufficient power needed in transport application (the tramway in Lachaize,2003 uses a virtual 400kW PEMFC with 586 based-cell - actual recent tests are made on fuel cells with 3 or 20 based-cell to reach 700W). The chemical to electrical behavior starts to be well known for PEMFC and complex model can be found in. Amphlettl995 and Alstom-CEA-LEEI2002) The FC voltage Ujc, depends on the current in the fuel cell I , the partial pressures of hydrogen PH2and oxygen Por, the temperature of the cells Tsc, and the hydration of the membrane AIf2,,.

~JYC = f ( I , PO,,

PFJ,, T f i A H 2 0 )

1

McmrILwqre\or hu E l m

D 11anpop IV

uoiicr

I nd,ULr

Ollf

(1)

J

i: -

Fig 1 . Complete Fuel Cell System

Inel> +lnPH2)(3)

All controls have been studied and validated in simulation in Lachaize2004 and considered to be effective. So, a simplified model can be extracted considering the controllers acting and keeping the fuel cell in its desired settings.

The cathode activation over voltage qacris: rl,,,=P1+Pz r,+p, r,? I N 1 5 1 0 - 7 ) + P , 7,. (4) Where the concentration co2 of dissolved oxygen, can be defined by henry's law (mol/m3) according to:

23

(5)

With parameters extracted from a3= 4.3085 a,=1.229 a2= -8.5 0.9514 p2=3.12 1 0 ' ~ p3 = -1.87 1o

-~

Controlled fuel cell assumptiorzs

The main phenomena represented in the model represent the fuel cell voltage behavior taking into account the most significant dynamics in the loops. The simplified model is based on the quasi static Amphlett model used to predict the voltage response of the cell as a function of the derived current, the temperature and partial pressures of the reactive gazes. Whereas the precedent eq (2) is on an elementary cell scale, expansion to a stack of multiple cells scale is made possible by multiplying the potential of a cell by the number of cells ( NL,/!):

literature:

PI=p4= 7.4

and R,= f(Tf,, ohmic resistance (0.097mR.mZ) and for the fuel cell made with N based-cell, Rf,=R,*N*S=O.l lR, j = current density. 22

I V 111 himid

(2)

Where, the reversible voltage E,.cJ,is: E,,,=a, +a, (T,, -298 15)+a, T f i

m

hxdiopcii l',LW>,>

The output voltage expression is:

u ! = Ere, + V a t - &n

.I

Fuel Cell System

Fuel cell needs also some ancillaries to control the different gas loops and different important values as: pressure, flow and temperature. So adding compressor, pump, radiator and valves with their own control, a fuel cell system given in Fig I is obtained and modeled for simulation in Matlab/Simulink. In the hydrogen loop there is no special control because an ideal source of hydrogen is considered represented by only an infinite tank and a passive reducer to fix the 2bar absolute pressure in this compartment whatever the flow is.

To obtain this expression some assumptions are made: - For control purpose and simplified modelling, a uniform current density is considered in the stack. - A uniform temperature equal to the temperature of the outlet cooling water is considered. Moreover, with an effective control law being established, this temperature is maintained constant during the work of the fuel cell. - Non significant anodic activation voltage is assumed.

96

- The damping air-blower unit, which recuperates

feed the converter so: Ir,eL=lfc-lrux.This consumption is represented by a varying resistance R a m . Resistance of the Fuel Cell is represented by r. r, R a m and PO2 must be computed to have an accurate representation of the controlled fuel cell system behavior (figure 2). - F R ' * ( ~ e1.S) With "V586 the number of based-cell used, e=50pm width ol" the membrane, S-O,1 956m2 the equivalent surface and p depends on air humidity injected and temperature (if both are regulated p = 72.4mQ.m) - Raux=Ulcz/Pcomp. Pcomp is computed with the compressor characteristics depending on its velocity and the PO2 pressure.

water and ensures that the air has a high humidity level, has been designed and modelled ideally. So, the humidity is adequate, saturation in water vapour (thus a relative humidity of 100 %) is ensured in the cathode compartment, while the anode is supposed to be supplied with dry hydrogen. - The partial pressures of gases are considered constants inside the stack and this, by neglecting the pressure drop in the gas distribution channels due to the gas / membrane and gas I gas interactions whereas the pressures used in the Amphlett equations are on the interface electrode / gas level. - Same as temperature, the pressure at the entry of the anode and cathode compartments is supposed to be controlled and maintained constant. - The pure delays related to the progress of gases in the distribution channels are considered to be negligible compared to the system time-constants. - The inlet air flow is controlled and in particular a cathode stoichiometric ratio is maintained constant. - The tlooding phenomenon ofthe membrane due to water excess is not taken into consideration. - The migration of oxygen and nitrogen molecules from the cathode towards the anode throughout the membrane is supposed to be negligible.

r

Hc r

lelec

-

r

IdllX

Kaux Ufc

Pcoinp

0.. I

I

Fig 2. Simplified Fuel Cell Model

3I

The air pressure is fixed to 1 .Sbar so the compressor map can be read from data sheet to obtain the equivalent Pconzp to deliver the current If'. In real time U, is the previous computed voltage value. If no compressor is used Razlx disappears and C'oz law can be a little different. PO2 also varies and depends on the fuel cell behavior, so identification is first made with the complete physical fuel cell model provided by our partner (CEA).The oxygen partial pressure is computed by the number of mole presents inside the compartment, so the calculus is made in 3 steps:

Simulation based approach

To compute voltage behavior U, the current I and pressures POZ and PHZ behaviors under current solicitation must be known. 1 - If temperature Tfc and hydrogen pressure PH2are constant (inside pressure is constant because input pressure is fixed and Tfi fixes the saturated pressure in the cell), a constant source U, representing the constant voltage of the fuel cell is computed by: LJo= a ,+a, (T,-298 15)+a, 7fi +,O, +,B, q' (7) 2 - The fuel cell voltage depends on the current delivered Ir, so a varying voltage source Cr, can be detailed by writing:

* The flow in the controlled loop can be seen as a second order transfer function:

3 - The last voltage source corresponds to the voltage due to the fuel cell parameters and the oxygen pressure PO2 and the temperature of the fuel cell ipfL, so, U,i2 is written as:

with : s=Laplace operator, qhfthe flow time constant fixed in the closed loop controller (zfh70.02s), X02r,,.=21Y~the oxygen ration in ambient air at the beginning and Fret computed by faraday's law NI F = L a n d IJL is known using the power ?if

cx, and PI coefficients are the same defined above.

4F

reference: Ilc-PreJlofL A part of the current produced by the fuel cell is consumed by its ancillaries. The current needed for ancillaries (compressor, pump.. .) is consumed before providing the usable current le,i.c to its exit to

* So number of mole is known by integration: 1

nO2 (s) = -

P

97

(s)

with initial condition IC,

current profile tests of 3-cell stack are provided on Figure 4.

adjusted after a first simulation using the complete model to track the fuel cell behavior. IC depends on the fuel cell characteristics, using prefect gaz law: IC'=PcarhVcarh/R.5'). xo2,nir With: .Yo2,,,,,=8.21% oxygen ratio in the cathode; 1 lm3; R=8.1 JiKimol; Tfc=298'K PcOth=2bar;Vcati2=0.

* Inside pressure behavior can be described by transfer function ( 1 1) after parameters identification : RTj'

Po2 (s) = (no2 (s)

20L

-

(1 1)

)(Peat/?- ~ l n t L v & ) )

pcati? vcath

With K,,, a coefficient describing the fuel cell behavior which must be identified by measures made with our simulator to compute the ratio from entry and interne pressure on the compressor flow: K,,,=Ka.Fcomp+ Kb (12) And after simulation: Kb=996.2 and Ka= -0.28

Time (s)

Fig 4. Actual current demand measured and used for current demand. Due to experimental constraints adaptations, some expressions have been changed to be representative of the experimental setup and to adapt the formulation with the available sensors. The reversible voltage expression is relative to the oxydo-reduction reaction and is considered constant. The ohmic resistance and the activation over voltage are considered specific to each fuel cell and should be meawred. The relation providing qoet must be identified replacing pi by experimentally identified coefficient

This simple model is compared to the complete model which takes into account all electromechanico-chimical phenomena (fluid behavior, chemical reaction, gas propagation, direct and reverse flow see Birdl960). This simplified model generates little relative error but is 100 times faster (Lachaize2005) and details are also in section 4.

3.2

Experimental approach

Two types of tests were used, a set of static tests on a 20 cells stack with an active surface of 100cm2and a nominal power of 700W and dynamic tests on a 3 cells stack of the German manufacturer ZSW with a membrane GORE MESGA Primea Series 5.510.

No problem to compute ,Z : With the fuel cell stack feeding its own ancillaries, in particular the compressor, the current output will be the sum ,~ of the current consumed by these auxiliaries I " ~ and

Polarization curve 19

I

I

the load current (the static converter for example) I',, . The reference air flow is calculated according

I

I

to Faraday's law as a hnction of I,, and

st,, .

No problem to compute P J ~ For ~ : the anode compartment and using the simplification hypothesis stated before, p15,can be expressed as: PH2 ( t )= Punode ( t )- P H 2 0 t a l (Tf' 14 ~

0

l

p

5

l

~

! 10

p

l

p

15

l

~

20

I

25

1

(14)

30

FC current (A)

Fig 3 . Polarization curve measured on the actual 20based-cell fuel cell at Belfort.

With P~,~(,,,/( T ) ~is ~the saturation pressure of water vapour (in Pascal), pa,,,,, the pressure of the anodic

During the dynamic test, the fuel cell is subjected to a specific currenthime profile resulting from measurements of speed recovered on the course of a vehicle in urban environment and after having carried out a homothety on the power in order to make it compatible with the tested fuel cell stack. An example of the polarization curve of the 20-cells stack is given on Figure 3, in addition dynamic

compartment considered to be constant (in Pascal). As for the calculation of the inlet hydrogen flow in the compartment, F,. ( t ) , we have :

41 (4=(4,

98

(4

+(~//'),u,ui

(16)

Where ( F ~ ~is )the~ hydrogen ~ , ~ ~flow consumed by Consequently, the value of

the chemical reaction of oxydo reduction (mol/s) and (FH2)f,t,rse ( t ) the flow of the purge valve (mol/s).

Special PO2 computation: Let 4, ,~, be the oxygen

Table I : Parameters identified

reference flow, as air is a constant mixture of l?40) refei ence flow is: oxygen and nitrogen (XoZ=2

4

Fr e / =

7 he term

I

st,

(18)

x,,.4.F

ce/"i'r'

Iz',t,h

corresponds to the total number of

= Pcuih.vLarh

K.Tf(

EXPERIMENTAL VALIDATION AND COMPARISION

To test the behavior of the proposed model, actual measurements have been used to prove the accuracy of the computed behavior. The full 400kW power is used in simulation and an artificial repetition of 54s of a most varying tramway profile is used. An urban cycle is used for actual tests and simple homothetic coefficient provides reachable values.

moles in the cathodic compartment at pressureeoth, : V<,th

to be

experimentally identified. Using simple mean square algorithm fed with different actual measurements, the & coefficients are identified and given in table 1.

The valve is controlled in order to ensure on one hand the elimination of liquid water and nitrogen which can stratify the compartment, and on the other hand to verify a constant hydrogen stoichiometric ratio.

il,

K , ~ , has

and the number of O2 moles is

4. I

where 's' is the Laplace operator and 1C the initial condition in the compartment and FoZ is the air flow present in the fuel cell. With an accurate control tracking (depending on compressor dynamic if present) it is constant oxygen present in the fuel cell. On experimental device, Po? can be computed as: r,,2 = 0 )P,",,, . By taking into consideration the

Results in sinzulution

n
evolution of pressure inside the compartment, therefore of pressure drops related to diffusion between gases and to load losses inside the channels, a pressure correction is envisaged by replacing pCarh

40, = ' m , h

3501 0

. This value is then simplified by :

with term p,,,,,,

2 -

FLop,p

PIA,,.

and the outlet air flow (

150

200

250

300

350

400

Fig 5. Simplified model tuned with simulation parameters kno\+ledgecompared to complete simulated model.

) is

the atmospheric pressure thus known, the pressure is expressed inside the fuel cell system ( ~ : n l , o i i L) according to

100

Time (s)

(19)

As the test is held while the outlet pressure

I 50

The complete accurate simulator is used in parallel with the proposed three-voltage-sources model and the two voltage behaviors are given on Fig 5. With an accurate knowledge of the fuel cell parameters the main phenomena extracted and the parameters computed for the simplified model did not affect the current and voltage behavior. Non significant error is obtained and the model is about 100 times faster.

F ). The

Darcy - Weisbach equation is regarded as a good experimental formula to determine the relation between fluid pressure losses and flow inside a pipe. In this study AP = K,nt .F2 is considered, as the different coefficients in the Darcy's equation are constant values for a given system ignoring furthermore the influence of the Reynolds' number variation or other element not easy to measure. Therefore more practically:

4.2

Experimental Results

Using an actual 700W fuel cell and the simplified model parameters identified Table I, the figure 6 shows the results of the two voltage behavior. The simplified model is close to reality.

(20)

F =
In fact, there are some differences but not so important. Some amelioration in parameters

99

points outside our model range must not be considered and canceled. During biggest varying phases, simplified model dynamic is faster than the real one, a filter or the influence of double layer capacitance not considered directly in the proposed model is easily added and provide an accurate voltage behavior model.

identification can be easily made. For example the profile used has working points not taken into account in the simplified model attract parameters to different values. That concern points at very low current or when part of the actual cell is drown. A correction of + l o % on the P,,2 value computed is sufficient to correct a lake of voltage fkom the simplified model to track the actual one. To smooth the high speed voltage variation a first order filter is added to take into account some phenomenon due to double layer capacitance for example. These minor modifications provide a simplified model easy to simulate and closed to actual fuel cell voltage behavior (Fig 6) under actual current demand.

AKNOWLEDGEMENT

The complete model used in simulation is close to a real fuel cell and has been built in collaboration with CEA (partner of a precedent project named COPPACE involving Alstom-CEA-ADEME). Practical tests and actual fuel cell identification have been possible using the national fuel cell test bench available in Belfort

Actual Stack voltage behavior

32 3 28

RLrLRLNCrS

-

26

h

>

Alstom-CEA-LEEI: “Interest of using Fuel Cells in bus, tramways, shunting loco.”, FDFC 2002 October 7- 10 2002 - Forbach - France. J. C. Amphlett, R. M. Baumert and al. : “Performance Modeling of the Rallard Mark IV Solid Polymer Electrolyte Fuel Cell’: Jour. Electrochemical Society, Vol. 142, No. I, ppl-8, 1995. Bird, Stewart, Lightfoot: book, “Transport Phenomena” p48 I , Wiley international edition 1960, ISBN: 0-471-07395-4 D. Corgier: “Hydrogen air fuel cell vehicle technology FEVER demonstration project”, proceedings of EVS 14 - Orlando, Florida 1997. W. Friede, S Rael, B Davat: “PEM JzIel cell models jor supply of an electric loaaP’, proceedings of Electrimacs 2002, August 18- 19, Canada. S. Jemei’, D. Hissel and al: “Black-box modeling oJ Proton Exchange Membrane Fuel Cell Generators.“, proceedings of 2Sth Int Conf on Ind. Electronics, [ECON 2002, 10-518 SevillaSpain. J. Lachaize, M. Fadel, S. Caux and al: “Energy Management of Fuel Cell System and Supercaps Elements”, proceedings of IFAC 2005, power plant and power system, 4-8 july- Prague Tcheque Republic. J. Lachaize, S. Caux, M. Fadel, P. Shott, L. Nicod : ”Pressure, Flow and Thermal control of a Fuel Cell system f o r Electrical Rail Transport.”, proceedings of International Symposium Industrial Electronics ISIE 2004- Ajaccio France- 05-417 2004 L. Solero, A. Di Napoli, and al. : “Fuel cell FIEV’s assisted by ultracapacitor and battery storage syJtem”, FISITA-Helsinki, Finland - June 2-7 200 1.

24

U 0

5u

I00

1 150

Time (s)

Fig 6. Simplified model exit voltage tuned after parameters identification compared to actual fuel cell voltage behavior measured. 5.

CONCLUSIONS

A simplified fuel cell model is established to have an accurate voltage behavior without prohibitive simulation time. The model is based on physical main phenomena in the different controlled loops which compose the Fuel Cell System. In the three voltage sources model-circuit proposed, there are little calculus to make and few parameters to identifji. Considering effective control of &el cell’s main variables (mainly pressures, temperature) and focusing on main electro chemical phenomena, three voltages sources have been specified and linked to fuel cell parameters. Each fuel cell must be identified to obtain a n accurate set of coefficients to be used in the simplified model due to specific conception and type of fuel cell. Using actual classic static and dynamic measurements a simple least square algorithm allows to identify the six most important parameters. The simplified model obtained is under some classical assumptions, but all the actual current demand used did not always respect these assumptions. To have a better direct identification,

100

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

AN A W I N E CEOME'I'KICAL AYYKOACH '1'0YOWEK SYS'I'EMS YKOSLEMS Emmanuel D. Crainic", Alexander I. Petroianub' Logiciels de r b e a u x , lnstitut de recherche d'Hydro-QuCbec,IREQ, 1800 Blvd Lionel Boulet, Larennes, QC, Canada, J3X IS1 Department of Electrical Engineering, IJniveriity of Cape Town, iJniver5ity Private Bag, Rondebosch 7701. Republic ofSouth Afvica

Abstract: I he paper introduces modern concepts and tools from affine geometry into power system analysis. It i s shown that such an approach allows: I) a new non linear formulation of such classical problems as load flow and state estimation, ii) a more efficient way of solving such problems through non itei ative methods. The new appioach i s illustrated for a small but representative example of a load flow for a two-bus network. Copyright 02006 IbAC Keywords: affine geometry. affine transformations, linear methods, algebraic and geometric invariants, power systems load flow.

1 . AFFlNE GEOMETRY: AN INTRODUCTION

A 2-dimensional affine space E is a space of points associated to a vector space E of the same dimension, in the sense that: i) for each pair of point5 (a, b) E 15,the difference (a-b) betmeen them is a vector AH in the vector space E ,ii) For each vector in the vector space and for each point in the affine spacc E, adding the vector to this point results in an another point in the affine space E, iii) every triplet of points (a, b, c) E E satisries the relationship fa-b) + (b-c) - (a-b). Tlierehre. there is ail one-to-one mapping of the elements of the two associated spaces (BcklCmichev, 1988).

In many power system applications, some of the physical quantities involved in the formulation and the solution of the related problems are expressed either as complex numbers of a I-dimensional complex space C' or as vectors of a 2-dimensiona1 real space RZ.Both approaches have their proper merit. In the complex space C' all the four arithmetic operations among the set o r its complex numbers i.e.: addition. subtraction. multiplication and division are allowcd. The clemcnts of a rcal spacc RZ. called vectors, are regarded as entities involved in linear operations. i.e.: multiplication of a vector by a scalar and the addition of two vectors. This vector space is a linear space. Ilowever. this may constitute a limitation, since a vector space contains only vectors of the same naturc (for instancc, power, or voltagc or currcnt vcctors, ctc.. but not a combination of two or more vectors of different nature). In this paper, the authors emphasize the geometric aspects and the physical meaning of the affine space associated with the vector space usually used in the investigation of power system load flow problem (Petroianu. 1969).

An affine space E may be visualized itself as a linear space by choosing in it an arbitrary point 0, called the origin, and in the appropriate vector space E a basis (el. e2). If a is an arbitrary point in E , together with the coordinate origin 0, it defines a vector 02 E k , the radius vector of the point a, which in terms of the basis (el, e2), may be expressed as oci= xiel + x2e2. The coefficients x I , x2 are called the afline coordinates of the point a. As any space, the affine spacc is dcfincd by its gcomctry. In thc spirit of thc Erlangen Progranzm, insisting on the concept of the group rather than that of the space. Klein (1 974) saw any geometry, including the affine geometry, as the study of invariants under a group of transformations. An afine transfornzation, as linear mapping From an

* Corresponding author: Alexander I. Petroianu, E-mail address. al7etroianu/u:ebe.uct.ac.ra

101

affine space to another affine space (or to itself), is any transformation that preserves parallelism of lines and the ratio of distances between colinear points. In a 2-dimensional affine space, to map a point (x; y) to a point (x'. y') four main affine transformations. or linear combinations of them, may be used (Klein, 2004): I,

- rotation

S'mk = S m k - i0.5V2mBC"mk S'km

=

x coscp + y sincp -x sincp + y coscp

(2)

2.

A,, =V,(V*, -V*,)(gmk+ib,,,,)

(5)

where

S -km

(6)

=

= P m k +iQ,, (12) V (V" V ' )( +ibmk)= Pkm+iQkm (13) -k -k -m %k

giuk = Rini /(R2d +

bmk

(7) (8)

Pkm=-V,,,VkcOs~mkgmk-VmVkSin~mkb,,,k+v2kg~~k (1 8) Q,,= VmVksin~mkgm,-VmV,co~~,"kbm,+v2,b, ( 19) From the above expressions. the active and reactive powers in (9) and (10) are: -

Pm,

(20)

p'km = Pkm

(21)

P'mk

Q Q,,,k0.5V2mBCap",k Q km = Qk,,- 0.5V2LBc"P,k

By taking into account (14) and (1 5). the angle Ymk is defined as: tany,, = 'mk grnk (24) Pmk

Pmk =

Fig. 1. Electrical line representation:

7c

(23)

2.2 Bus voltage module

With the radius expressed as:

I

(22)

With a known voltage (module and angle) at a chosen reference bus. the system to be solved has 2(N-1) non linear equations of bus power injections, expressed as sums of ad.jacent power transit 01' type (16) to ( I Y ) , and (N-I) voltage modules and (N-1) voltage angles as variables. Its iterative solution is a well known proccdurc (for a dctailcd trcatmcnt of it, scc Dcbs (1988) or Eremia, et al, (2000)).

In power system analysis, the class of problems related to load flow (planning and operating versions) is of a mathematically non-linear type. In planning environment. the load flow problem assumes the knowledge of power in.jections and values of electrical parameters of network elements. The solution consists in finding the nodal voltages (module and angle). For a component of the network, for example a line (Figure I), the apparent power flows are expressed as follows:

wd

(14) (15)

Pmk=-V,VkcosOmkgmk+VmVksinOmkbmk+VZmgmk ( 16) Qmk = -VmVksinOmkgmk-VmVkcosOmkbmkfV2,bmk ( 1 7)

2 1 Power system loadflow formulution

k5B

x2nii)

= x m k /(R2mk+ X'mk)

In (12) and ( I 3) Pmk, Pkm are the active and Qmk, Qkm the reactive powers. They represent the real and the imaginary parts ofthe complex numbers Lkand &,:

2 AFFINE GEOMETRICAL APPROACH TO THE LOAD FLOW PROBLEM

@.5B"",

( 1 1)

(3) (4)

The affine transformations make the general affine group GA (2, R). which i s a semidirect product of the general linear group and the translations in E by vectors of . The essential difference between an affine and a vector space consists in the fact that in the affine space the operation of adding a vector to a point is allowed. The operations solely on points are also possible. but only under certain conditions: this is the subject of barycentric calculus (see MBbius (1827) or Dclodc (2000)). An affine space, not being dependent on a specitic choice of a coordinate system. is the appropriate framework in dealing with motions, trajectories, and physical or electromagnetical forces. among other things.

f

- 6k

considered to be positive (all over this paper the hypothesis is made that m is the sending and k the receiving nodes of the active power). Analytically; are as follows: the complex powers &k and

(1)

-reflection in the x axis, x' = x y' = - y 3. - scaling, x ' = Lx y'= & Y 4. - translation, x' = x + px Y5 = Y + PY

6,

Omk

the origin. =

(9) (10)

In the equations (9) and ( 1 0) the voltages are complex numbers represented by their modulcs and angles, i.e. V , , Vk respectively, 6 , , 6k with the difference:

by an angle cp counter clockwise about x' y'

- i0.5V2kBCaPmk

= &m

I t

of the circle (see Figure 2)

d

m

(25)

the foliou ing trigonometric functions may be derived for the angle 2ymk:

model

102

Fig. 2. Electrical line base angles

If the electrical state on the m-side of the line, defined by the triplet of quantities [Pmk, Qmk,and Vm], is known. the equations (30). (31) and (32) allow for the evaluation of the elecfricul state, defined by the triplet of quantities [PkmrQ k m , and Vk], on the k-side of the line.

In the arline approach to the load llou problem the notion of topological spannzng tree, that is a trec having (N-1 ) edges (lines, transformers. etc.) linking all the N nodes of the network. plays a central role. What is required to be known is one of the pairs (P& or (Pkm, Q k m ) of active and reactive power at the extremities m or k of each of (N-I) edges of the spanning tree and one voltage at the arbitrary chosen reference bus. With this information, and starting from thc reference bus, the formulae of type (32) or (37) are used to obtain thc vollage rriodule(sj at neighbouring node(s), and the formulae of type (40) or (41) to obtain its affine pair (Pkm. (Skm), respectively, (Pn+ Q m k ) Qmk)

Keciprocally. the equations ( 3 5 ) . (36) and (37) allow evaluating the electrical state [Pmk. Qmk,and V,] on the rn-side of the line when the elcctrical state [Pkm, Qkm,and Vk] on the k-side of the line is known. In other words. the systems (30), (31) and ( 3 5 ) , (36) of linear equations represent @ne transformations, each one the inverse of the other. This property is the main result put forward in this paper. For expressing the translation transformation (see (7). (8)) in a matrix form, it is necessary to use the homogeneous coordinates (which were first introduced by Mobius ( 1 827)). In these coordinates, the matrix A of the affine transformation (30). (31) is defined as:

2 3 Bus voltage angle

For any (m, k) edges belonging to the spanning tree, three basic formulae (42). (43) and (44) allow evaluating the angle difference &,,h betvceen the voltagcs at the buses m and k: taIf)rnh= ( b m h P m h - g m h Q m h ) / ( ( P ~ ~ h ~ r n ) z - ( g ~ ~ ~ h ~ ~ ~ ~ h +(42) b~~hQ~~h))

tm%h= -(bmhP~,,-g,hQ~,)/((PmhVb)2-(GmhPh,+b,,~Qh,u))

If thc values ofthe active and reactive power Pmk.Qmk and Pkl,,. Qkm are known, the following formula should be used.

This matrix A is invertible. i.e.: A A-‘ = I

(43)

(39) tmQ,, = ( P m k Q k m

Consequently, the cquations (30). (3 1 ) and, respectively. the equations (35). (36) may be written as follows:

- PkmQmk)/(PmkPkm

+ QmkQkm) (44)

Once the bus voltage have been evaluated. they are used to calculate the active and reactive transit

103

powers on the remaining (L-N+I) edges not belonging to the spanning tree of the network and. consequently. to calculate the active and reactive power injections to the N buses o f the network (Table 1).

the equations (47), (48) and (49), (50) may be expressed in homogeneous coordinates form, as follows:

Table 1 Power system load flow problem. a comoarison

Jt is to be mentioned that the matrices Bmkand are riot arfine tranaforniationa.

Line

From the equations (48) and (47) it results that (see also (24)): (54) OQmk/ ~pmk b m k / gmk tanynk

data Bus

voltage

therefore, the vector ((sP,k, OQmk)is colinear with the axis A'A (Figure 2).

md po\+ei data

Bkrn

in~ectlonsP,,, , Q,,,

transits P,,,L.Q,,,h on

(m=2,3,.. ,N)

branches forming a

2.5 Active and reactive powers between buses rn and k.

Variables

In the transient stability studies, the approximate formula for the active power between buses m and k is expressed as: (p,l,L)t r a n c m t ? t a h i l q = ((VmVk)/Xmk)sinomk (55)

Prohlein Solut~on ,

power transits

power transits on

Main

and the role of the reactive power is practically ignored. However, in the context of a competitive environment. any quantity of the reactive power, influencing network voltage Stdbility. is very important and should be accounted for.

hy-

products

2.4 Active power requirements.

losses

and

reactive

By definition, the active power between the sending and the receiving ends m and k of a line is expressed as: EPIIIh= o . j ( P m k - Pkm) (56)

power

By definition, the active power losses for the line (m, k) are: OPmh =

P m k + Pkm

and the reactive power exchanged is

(45)

EQ,,

and the reactive power requirements are

=0mmk

Qkm)

(57)

In terms of the sending end m, the equations ( 5 6 ) , (57) may be written as: &Pmk= Sln2yII&Prnk-0.5Sln2y,,,LQ,k -0.5(V2k-V2,,Jg,k (58) &Qmk=-0.5Sil12y,,hPrnk+c0S'Y,bV,k -0.5(V'k-V',)bmk (59) and in terms ofthe receiving end k as: &Pink= -sin2ymLPkln+0.5Sin2ymhQk, -0.5(V2~-v2,)g,k (60) &Q,,k= 0.5Sin2y,,kPkn, -COSZY,,,~Qkm -~.5(V2~-V',,)b,k(6 1) By introducing the matrices C,,,k and Ckj,l defined as:

104

3. AN EXAMPLE

Expressed in homogeneous coordinates the equations (58). (59) and, respectively, (60). (61) become:

In a large power utility, a transmission line 734.6 km long operates at 765 kV. The constructive parameters are as follows: 1) conductor type - Zebra, 2) number of conductors per phase - six, 3) distance between the conductors (bundle spacing) 0.4 m. ~

It is to be mentioned that the matrices Cmkand Ckl,,

In Table 2, the electrical parameters are calculated for 100 and Vhace= 765 kV. In Table 3 the results are presented that corresponds to v, = vk = 1.0 pu and to a surge impedance load of 22 15 MW.

are not affine transformations.

Pha<e =

c

Table 2 Line data

It is to be mentioned that the ratio between line rcactivc power rcquiremcnts (10.658) / (active power losses (0.485) is equal to 21.98 and the value of the line angle is equal to 27.0.55 degrees, which corresponds to the line surge impedance load in (see Tdbk 3 column 1 1 ) .

Lmc

parametel

Starting with the triplet [Pmk= 22.393. Q m k = 4.32, V, 1.01. the expression (32) gives the value Vk = 1.0; by taking into account the values of sin2ymk and Cos27,k rrom Table 2: columns 11 and 12, the expressions (30), (31) yield for Pkm and Qkm the following values: =

Table 3 Netuork element-based load flow Vi = 1 00 pu, V,,

=

1 00 pu

PI,,,= (-0.9959)(22.39)+ (0.0908)(4.32)= -21.908PU, Qim= (0.0908)(22.39) - (-0.9959)(4.32) = 6.34

PU

In Table 4, for Vk = 0.98 pu and V, = 1.02 pu and in Table 5 , for Vk = 1.02 pu and V, = 0.98 pu, similar results are presented by imposing the transit angle O m k to be the same as in the previous case, that is equal to 27.055 degrees.

Table 4 Network element-based load flo\+ VI = 0,98 pu, V,,

=

It is to be mentioned the invariant nature with the product VmVkof active power losses o P , ~= 0.488 pu (Table 4, column 5 and Table 5, column 5) and of line reactive power requirements (TQ,,~ = 10.73 pu (Table 4, column 12 and Table 5. column 12) for the two different cases of line operating conditions.

1.02 pu

4. GEOMETRIC AND ALGEBRAIC INVARIANTS OF THE ELECTRICAL LINE

Table 5 Nctwork elcment-based load flou VL 1 02 pu, V,, ~

~

7 he geometric and algebraic invariants related to afline transformations as applied to the load flow problem, are important for a better understanding of the power system and for a more efficient problem solving. Some of'them arc presented in this section.

0 98 pu

the affine transformation matrix A defined in (38), whose determinant is equal to -1, has one eigenvalue h, equal to -1, and two eigenvalues k Z 3equal to I . The two non trivial corresponding eigenvectors are orthogonal (they form a base) and are expressed as:

105

the relationship between the electrical line base angles is an invariant: 0mk = 2 x

where

(Pkm, (Pmk

- ((Pkm - (Pmk)

(75)

are used to define the power factor of

Smk and Lmr the sending, respectively, the receiving apparent powers.

-

the normal h to the axis A’A from the point m and from the point k, may be expressed either as:

All these formulae may be verified by using the information given in the Tables 2 to 5.

Fig. 3. Electrical line: some geometric and algebraic invariants 5 . CONCLUSION

or: in normalized form: U t ( h = I ) =[cos”fmk

= [siny,k

v‘(k

sinymk 01 -cosymk 01

The paper demonstrates the advantages of an affine geometrical approach for power system analysis. For a real-time and on-line operator load flow (a classical non linear problem), an appropriate affine transformation allows a linear reformulation and a faster direct solution. Other on-line applications such as parameter estimation, bad data detection and identification, and state estimation (particularly state estimation for distributed networks) are likely to benefit riom a similar ar‘finegeometrical approach.

(67) (68)

The eigenvector it is colinear to the axis A’A and the eigenvector v is colinear to the axis Y ’ \y normal to it (Figure 3). the aria.. taken counter clockwise. of (he parallelogram formed by the points Omok (Figure 3) is an invariant to any change of basis it is submitted to, i.e.: 12mk P m k Qkm - P k m Qmk (69) It is known as the standard symplectic form Q on

6. REFERENCES

RZ, and it is antisymmctric: fikm =

%k

= P k m Qmk

P m k Qkm

Beklkmichev, D.V. ( 1 988). <,’ours de giomitrie analytiyue et d’algibre linkaire. Editions Mir, Moscou. Debs. A S . (1 988). Modem Power- Systenzs Control and Operation. Kluwer Academic. Boston. Delode, C. (2000). Ghomhtrie afjne et euclidienne. Dunod, Paris. Eremia, M., .I.Trecat and A. Germond (2000). RLseuux Electriques: aspects uctuels. Editura Technique, Bucuresti. Klein, F. (1974). Le Programme d’Erlungen. Editions Jacques Gabay. Paris. Klein. F. (2004). Elementary Mathematics from an Advanced Standpoint: Geometry ”. Dover Publications, Mineola New York. Mobius, A.F. ( 1 827). Der burycentrische Calcul: ein neues Hilfsnzittel zur unalytischen Behandlung der Geometrie, Leipzig. Petroianu. P.I. (1 969). A Geometrical Approach to the Steady State Problem of Electrical Networks. Rev. Roum. Sci. Techn.-Electrotechn.Et Energ., V o l 14, No. 4, 623-630.

(70)

where Qkm is the aria of the same parallelogram, but taken clockwise. thc aria. taken countcr clockwise. of thc rcctangle formed by the points Omgk (Figure 2) is also an invariant to any change of basis it is submitted to: Anlk = pnlk b,k

- Qmk

glnk

(71)

This is also an antisynimeh-ic symplectic form: akm=

- amk =

Pkm bmk

Qmk g k m

(72)

where Akm is the aria of the same rectangle. but taken clockwise. the ratio between the above two symplectic forms is: Qlnk

/ &&= v 2 m f v2k- 2v,,vkcos0”,k

(73)

the line current may be expressed as: (74)

106

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

DISCRETE-TIME MODEL REFERENCE ADAPTIVE REGULATION OF NODAL VOLTAGE AMPLITUDE IN POWER SYSTEMS Giuseppe Fusco Mario Russo * A

universal& degk Studi di Cmsino via G. Di Biasio 43, 03043 Cassin,o (FR), I t a l y 'c

{ f u s c o , russo)@unicas. it

Abstract: This paper deals with the problem to regulate the nodal voltage amplitude in electrical power systems. A discrete-time linear model that embeds an unknown bias representing the no-load voltage is adopted to describe the power system dyna,rriics. Due to thc unprcdictablc and unknown variations of thc power system normal operating points the model pamtneters are unknown and t.imevarying. 'l'o ensure that the controller exhibits the required performance even in presence of a mch variations, the controller pa.rameters are varied according to adapt,ive laws. 'l'hese laws are developed on the basis of a gradient approach to miriiniize the squared augmented error. l'he properties of the designed adaptive laws are studied employing Lyapunov analysis. 'lhe results of i~uniericalsirnulation a.1.e reported t.o valida.te tlie proposed desigii. C o p y r i g h t @ 8006 IFA C Keywords. Power system voltages, Discrete-time systems, Model-reference adaptive control. Gradient method.

1 . INTRODUCTION

A power system is rriairily composed of transformers, traiisniissioii lines, syriclirorious generators, static and dynamic loads a,nd electronic eyuipments. It represents a complex nonlinear system which continuously undergoes unpredictable wriations of its normal operatirig points due to setpoint changes, load increasing and/or decreasing, lines opening. Such vasiations are classified as small disturbances. Conversely, raridom large disturbances, such as faults, represent abnormal variat,ions t,hat comproniise the stability of the power system (Kundm, 1994; Sa.uer and hi,1998). The voltage regulat,iori in power systems has the objective to keep a n almost constant. voltage magnitude at, all t,hc notlrs of Ihr nctwork in any operating point, to guarantee an acceptable lcvel of supply quality (Cigre, 1992; S a i d . 2001). Improving t,he performance of the system voltage control in terms of noda.1 voltage amplitudt. yields a.n iiicrease of the service quality, an enliaiicemerit of tlie security of the system operation. a reduction of transmission losses and an increase of the power system t.ra.risfer capability (Berizzi e t al., 2004; Corsi et al., 2004). To attain power system voltage regulation, the volta.ge amplitude at all the nodes

could be controlled, but such coritrol would he bot,li inipracticable and nneconornical. Act,ually, some actuators, such as syiichronoiis generators, Under-Load Tap Clianger (IJL'I'C) tra.nsformers, and electronic compeiisatms, mainly Static VAR Systems (SVS) and STA'~COhIs,are connected to some key nodes and locally control the nodal voltage by varying the reactive power injection (Choi and Kim, 2001; Rao et al., 2000; Fusco el al.; 2001). l h e local controller must ensure the regulation to a variable set-point, satisfying assigned transient specifica.tions. The set-point is iisiially determined by another system apparatus, which handles the rea.ctive power injections in one or rriultiple iiodes (Cigre, 1992) or clamps the oscillations of generating units (O'Brien and Ledwich, 1987). Since t hr powrr system opcra.t,ing points unexpectedly vary. it is necessary to adopt ada.ptive techniques in t,he controller design to ensuring the satisfaction of the regnlation task and the fulfilment of the assigned specifications (Fusco et al., 2001: Fiisco arid Russo, 2005; Socis and 0.P; 2001). According to this considerations: this paper illustrates the dcsign of a voltage corit,rollcr based on discrete-time model reference adaptive control theory (Astrorn and Wittenniark, 1989;

107

'l'ao, 2003). Starting from a discrete-time linear model describing the power system dynamics from the rcgulat,ioii node, a coiit,rollcr based on the solut.ioii of tlie riiodel-followirig probleili eiisures that the regulated nodal voltage amplitude tracks t,he oiitpiit, of A. refeiwice inodel. Tn pi'esence of unknown and unexpected operating points variat,ions, the controller pamrneters are modified according to adaptive laws designed on the basis of a gradient approach to minimize the syua.red a.ugmcnted crror. 'l'hc propcrties of the designed adaptive laws are analyzed using Lyapunov analysis. Numerical-time siniulation ha.s been rim t o evaluate the controller performance.

Fig. 1. Block scheme corresponding to model (4). siich that

u(tc,k)

tracks a given reference output

so that the error

v,(t,,k)

e ( t c , k ) = '!(tC,k)

-

(5)

~urn(t,,k)

is small. The reference signal v m ( t c , k )is generated from a. reference model system l'he power system dynamics are described by means of the followiiig discrete-time linear niodel A(.-1)

(il(t, k )

-

u o ( t c , k ) ) = 2-d B ( z - 1 ) u ( t , k ) ( 1)

in which

A ( z - ' ) = 1 +a1 z-'

I?(,?-')

= bo

where A,@') arid R,(z-l) are stable polynomials with brno # 0, arid r ( k ) is the command signal. 'l'he controller law assumes the form

+ . .... .+ann zPn4

+ b, z-1 +

,

.., ..

+ b,,,

z-,IJ

are algebraic polynomials iri the delay operator zP1 with bo f 0, where t , , k = k?,, being the sampling period. In model (1) u ( t , , k ) is the regulated nodal voltage amplitude at the fimdamcntal freqiieiiry, ~ t ( f k, ) is tlic inpiit, d positive integer representing a known delay. and v o ( I c , k ) the no-load voltage representing the nodal voltage when u ( i , k ) = 0 (Kundur, 1994). In tlie re ni aindeI' 1t will be assumed that poly norn ial R ( z - l ) ]ins oriI.y stnble IOOLS arid it L N ~ be I writLen as

where F * ( z - ' ) , G * ( z - ' ) and N * ( z - ' ) are ;tIgebraic polynomials. Sirice u o ( t c , h ) is inodeled as ( 3 ) , according to the in,te.mul model praacaple, the controller will contain an integrator, that is

F * ( z - ' ) = F*(z-') B+(z-')

Ad(2-l) =

F&:(z-')Ad(.-')

(8)

where the degree of F"(z-'.) is n l'he polynoniials

-

p = n ,,-+ n ~

-

+ Ez-1 + . .. . . . + j;-z-"F G"(2-l) =go* + 9;z-l + . . . . . . + g;1, z h'"(z-1)= 1

+ 1.

7

wherc the sign of bo is assumed to be known. Model (1) describes in an approximate way the rclationsliip brtwccn u(I, k ) and v ( t , , k ) at the rcgulation node The no-load voltage vo(l, k ) can be thought as generaled from the dynarnical system

Ad("-')vo(tc k )

=

(1 - 2 - l ) vo(t, k

) =

~

a.rc t,hc solut,inns of t,hc LXophent,inc cqimtion

A(2-l)

Ad(2-l) F " ( 2 - l )

+z

- bo ~ G"(z-l) = (n)

A o ( z - ' ) A,(z-')

D 6 ( t ck ) ( 3 )

where DS(t,,k) i s a pulse. It can be easily recognized L1ia.t: u o ( t c , k ) is a step function. At this point, embedding model ( 3 ) in model (1) one has

-

being A0 ( z - ' ) an assigned observer polynomial. Eqn. (9) has an unique solution if A@') arid H ( 2 - l ) a,re coprime arid the following compatibility conditions are satisfied ( h t r o i n arid Wittenmark, 1989) n..4,,

2 ~ T ? , A+ /LA,,

-

ng+ - n..4,,, -

1=

2.n~ ng+ - nA,,

+

nc: < nA n ~ =, ' n A n F 2 d - 1.

see Figure 1.

3 . MODEL REFERENCE DESIGN

+1

(10)

Finally F * ( z - ' ) is obtained via (8) while H " ( z - ' ) is given by H * ( z - 1 ) = 1L;

The model-reference design has the objective t o firid an output feedback control signal u(t,,k) for the model (4),with n A , n R . a, and h, known.

Ao(.-1)

= Ao(z-')

108

B,(z-l)

Bm(~-l)/bo.

~

~

4. ADAPTIVE DESIGN In presence of operating points diRererent from the one corresponding to model reference design, the parameters a,: bJ and D are unknown. Thus the lollowilig at lap^ ive versioii ol law (7)

where, according to ( 8 ) , F k ( 2 - l ) is expressed as

Moreover: let us define the following vector

0=

(JV.1

. . . fv,n,--l

go . . g,,,, I

h0jT € lRn'r

with n~ = n,p + n G + 1. The symbols 2-l will be temporarily omitted. 'Yo design an adaptive law to update vector 0 an expression for the error ( 5 ) will be derived. 'lo this aim niultiplying both sides of (9) by 71(t,,k) arid adding and subtracting the c p n t ity AAd (Pi;?k - d / B + ) v ( t , . k ) one has

A,, A,,

V(tc.k =)

A A ~ ~ F = ~+( b,,~ ~, . *~ )~

( t ~ , ~ - ~ ~ )

+AAf1(Kj;k-d/B+)V ( t , , k )

A A d ( F d B + ) v ( t c , k ) . (13) At this point niultiplying (4) by f ; ; , , k - d / B + , using (12), and (1 1) cvaluatcd at thc k-d step yields AAd(Fv.k-d/.B+)V(tc.k) -(:k-d

rl(tc.k-d))

=

bo ( H I M

r(tc.k-d)

+ A(Fu,k-d/B+)D6(tc.k)

which subst.ituted into (15) gives

-

+

A o A , , , V ( t , , k ) = A A d F X ~ ( t c , k )b O G * V ( t c , k - d )

-A& +bo

(F u . k - d / B + ) V ( r c , k )

(Hk-d T(k,k-d) - Ck-d V

+A (Fu .k -d / B

+

)D6 (t

b

)

)

lirn

c ,k )

kioo

that can be rewritten as

A,, A,,, c(t,,k)= AA,@*

+ (1Tk-d 60

represents the contribution due t o the no-load voltage. It coincides with the iinpulse response of filter AF*/(AoA,). Since Ao(z-l)A,(z-l) are stable polynomials the signal d(&) E L2 and d ( t , , k ) = 0.

Defining the augmented error as -

r(fL,k-d)

( ~ ~ , ~ - ( ~ / ~ + ) ) c ( t , , ~4 t)C . k )

+ AGk-d u ( t c . k - d

1 A(Fv,k-d/A+) D J ( t C , k )

)>

where

+P(k.k) <(k.k)

(19)

is the estimate of bo and T

%,k)

(14)

being A(2k-d = C:*-C:k-d. Now multiplyiiig b d h sides of (4) by (f*- F v . k - d / B f ) and using (8) and ( la ) yields

p(tc,k)

=4tC.k)

= (Q(t,.k&d)

-

Q(tc.k))

Pf(tc,k-d)

it is finally possible to rewrite (19) a.s 4tC.k)

=d

( t C h )

+butl(f,~k).~pf(tc,k-d)

+F(tc,k)E(tc,k)

109

(20)

which. based on (21)),can hr rewrittell

beirig

AS

Q ( f & k ) = Q* - Q ( f & , k ) T ( t C . k ) - P ( t C . k ) - bo. By changing the paramrt,ers in the direction of the negative gradient of the normalized quadratic cost function given by

one obtains

Looking a t ( 2 3 ) it is easy to recognize that. the term in bracket parenthesis is positive by choosing the adaplive gains as follows 2 O<7<2 O < max{yi) < -

where

m2(tc.k)= kl

+

+ ’Ff(tc,k-d)T’pf(tc,k-d)

bil

where hif

(23)

E2(fC.k)

2 Ihol. Accordingly, one h a s

with kl > 0. In adaptive laws (21)-(22) r = d i a g { y i } of wlsdinierisiori , with 7 and yi positive gains. To study the properties or t,he adaptive laws let us consider the following positive definite function (‘l’ao,2003) v ( G ( t e , k ) ,P(tC.k)) =

bo +?-I

Expressing eq. (24) a l yields

r

H j t c d

for some

(24)

0,> 0. Now, since 2

pJL(fc.k).

($4tC,k)

and using (21)-(22)

-

d(L.1)

the following inequality holds 191 2

2C ( t C , k )

4tC.k)

5 2 ~

f

(tC.k)

20

+ P,2 d 2 ( t C , k ) -

which substituted in (26) gives

The time increment of function (24) along the trajectories (21)-(22)is then given by

c 11

Choosing r‘ = rT.the first two terms at the riglit hand side of (25) are equal: their sum added to the last term gives

Lo

c=o

110

1

Q(tc,k+u+l)

- Q ( k k+B)

112

I i l l Ln

Fig. 6. Controller and saturation. F,;'

(2-1)

Fig. 2. Considered power system.

Fig. 7. Cont>rollerscheme avoiding wind-up.

Fig. 3. SVS configuration.

Fig. 4. Block scheme of the open-loop system

I

8

O

r

resistors and inductances. The model of the 10 MVAR SVS includes active losses and detailed modeling of t,he thyristors. The t,inie delay introduced by the SVS is approxirriat,ely equal to T d = 3.4 ms (IEEE Working Group, 1994). Since it has been set T, = 0.001 s it, results d = 4. The considered system has been simulated in Matlab/Simulink environment also resorting to Power Syst,em Blockset,. Concerning volt,ages, reference is made in the following to the phase voltage expressed in per unit of the system base. As usually in power system control. a third-order model is assumed to represents the system dynamics (Soos and O.P, 2001)

A(.-')

=1

+ alzpl + a2 z-' + a3 z P 3 + b1z-l.

B(z-1) = bo I 0.5

1

'I'he polynomials appearing in (6) have been chosen equal to

U

Am(.-')

Fig. 5. Plot of a: = f - ' ( u )

The power system represented in Figure 2 has been considered as test system. The actuator device is a Static-Var System compensator represented by a Fixed Capacitor-Thyristor Controlled Reactor (FC-TCR), see Figure 3, connected to the node 4 t,o regulat,e the voltage amplitude u q ( t , , k ) . Figure 4 shows the open-loop scheme in which tlie nonlinear function f ( a ) is given by (IEEE Working Group, 1994)

f ( a )= - 7l

+ 0.8648 zp2

B,(zpl) = 0.0048.

5. CASESTUDY

20

= 1 - 1.86 zpl

sin(2a) ~

7l

-1

with 7r/2 5 a 5 T. Consequently, 0 5 f ( a ) 5 1 and the input u(t,.k) is sat,urat,edbetween 0 and 1. In practice, for a given value of the regulator output u* in the considered interval, the corresponding value of the firing angle a* is determined by numerically solving the implicit equation

f(a*) = ?L*. or by resorting to a look-up table whose points lie on the diagram reported in Figure 5. The three-phase 132 kV - 50 Hz power system is assurned to be balanced in all it,s components. The transmission lilies are represented through the series of elementary cells, each one representing the equivalent circuit for a length of a 10 km. In particular each cell is constituted by a series resistance, series inductance and shunt capacitance. Loads are represented by means of shunt

(28)

so that the step response of the reference model presents a rising time about, equal to 50 ms (t,hat is, 2.5 times the fundamental cycling time and a settling time at =t2% equal to about 80 ms that is, 4 times the fundamental cycling time) According to n A = 3 , 'ng = 1, n&, = 2, d = 4 and looking at, ] 5 . no = 3 constraints (10) it, has been set T L A ~= and r r = ~ 3. The observer polynomial

2

Ao(zp')

= 1- 2

+

. 5 9 ~ ~ '2 . 5 6 7 ~ ~ -'1 . 1 8 7 9 ~ ~ ~

+ 0.243 zp4

-

0.01474 F5

has been designed by imposing that its dynamics are faster than the desired closed-loop response determined by A m ( z- ' ) . Since the output of the controller u ( t c . k ) must be bounded between 0 and 1 a saturation function is added in the controller structure. see Figure 6. In particular. the polynomial F ( z p l ) has been substituted by tlie cascade of the polynomials F,(z-') and A d ( z - ' ) . However, since the saturation may cause the wind-up of the integrator. the scheme shown in Figure 7 is employed to avoid the wind-up. As concern the positive gains appearing in the adaptive laws (21)(22) the diagonal matrix r is composed by the following sub-matrices

where bt' = 0.001. In addition it has been set k l = 1 arid y = 1.5.

111

operating point variations the controller parameters adapting laws have been developed on the basis of the gradient approach and their properties malyzed Simulation results have validdted the performance of the designed controller in tracking the output of a rcfcrcricc niodcl in prcwncc of unpredicted power system operating points

Fig. 8. ‘l’iine evolution of ,v

(dash-dot) and

ELE1JE.ELEKCE.S Berizzi: A,, P. Maraiinirio, AI. AIerlo, AI. Pozzi and F. Za.riellini (2004). Stea.dy-state and tlyna.rnic

u4

approaches for the evaluation of loadability rrmgins in the presence of secondary voltage regulation. I E E E Tranwaclions on, Povw Systerris 19, 1048-1057. Choi: J.-H and J. C. Kim (2001.). The online voltage control of ultc transformer for distribution voltage regulation. Electrical Power and E,rrergy Syslerrrs 23, 91-98, Cigre, Tf (1992). Voltage and reactive power control. Pa,ris, France. Corsi, S., M. Pozzi, C . Sabelli and A. Serrarii (2004). The coordinated automatic voltage control of’the italian transmission grid part i: Rcasoris of thc choicc arid ovcrvicw of the consolidated hierarchical system. IEEE Yin.nsaction,s on Pouier Systems 19, 17231732. Fusco, C., A. Losi arid M. Kmso (2001). Ac1a.ptive voltage regulator design for static var systems. Control Engineering Practice 9. 759 767. Fiisco, G . and M. Riisso (2005). Nodal volta~ge regulatioii employing an indirect self-t uning approach. IEEE Proc. Conference on Control ~ 7 1 , Applicdions d IJP.797-802. IEEE Working Group, Special Stability Controls (1994). Static var compensator models for power flow and dyna,rnic per formance simulation. IEEE Il’ra,n,sa,ctions on, Power Systems 9>229-240. Kiindur, P. (1994). Power system slability and con.lrol. McGraw-Hill,Inc. New York, IJSA. O’Krien, 11. and G. Ledwich (1987). Static reactive-power compensator controls for imtern stability. LLE Proceedings t‘t. C 134,38-42. Rae: P., M. L. Crow and Z. Yang (2000). St.ntcorri cont,rol for power system volt,age control applications. IEEE Transactions on Power D el i f i ~ r 15, y 1311-1317. ,\striim; K.J. and K. Wittenmark (1989). Adaptive control. Addison-Wesley Publishing Cornpany. New York, USA. Saied. hf. hf. (2001). The global voltage regulat.ioii: a, suggested measure for the supply yuality in distribution network. Eleclrical Power and Energy Systems 23, 427-434. Saucr, P. arid M. Pai (1998). Po,wer systeni dynamics and stability. Englcwood Cliffs, Ncw York: Prriitice Hall, [JSA. Sobs, A. arid O.P. Malik O.P (2001). An 1i2 optimal adaptive power system stabilizer. I E E E Transactions on Enwgy Conversion, pp. 143149. Tao,G. (2003). Adaptive control design and a n d ysis. John Wiley & Sons, New York, USA.

(solid).

-20

0

05

I

-

The time series of the regulated nodal voltage u d ( t c , k ) arid of the oiitpirt, reference model ~ , ( t , , k ) are reported in Figure 8. At time instant C = 0.8 s a 20% step increase of load L4 is demanded. It must be not.iced that such vasiation concerns the loa,d connected at the same node or the SVS. Furthermore the ainplitude of the assigned load variation has been imposed cornparable to the rated power of the considered SVS. To better point, out, the tracking capa,bility of t,lie controller, Figure 9 shows tlie obtained time evolution of the error. Finally, Figure 10 reports the time evolution of t,he SVS firing angle a ; it is apparent that Q exhibits quite smooth variations after the first time instants corresponding t,o the st,art-up of the sirnulation.

The paper lids presented tlie development of discrete-time model-reference adaptive laws to regulate the nodal voltage amplitude in electrical power systems A discrctc-time linear modcl representing the power system voltage dynamics has becrr proposed such model IS used to solve the model-referreiiw prublein by determining I lie controlleI parameters as the solutions of a Diophantiiie equation. In presence of power system

112

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS DETERMINATION OF TRANSMISSION TRANSFER CAPABILITY WITH SECURITY AND VOLATAGE STABILITY Don Hur and Heung-Jae Lee Kwangwoon Universib,Department of Electrical Engineering, 447-1 Wolgye-dong, Nowon-gu, Seoul, 139-701 Republic of Korea

Abstract: There has been an increased interest in quantifying the transmission transfer capability of power systems. Transfer capability indicates how much a particular bulk power transfer can be changed without compromising system security under a specific set of operating constraints and voltage stability capturing various contingencies. Hence this paper will touch on the security-constrained optimal power flow and P-V methodology for providing insight into the secure limit of interface flow between areas and steady-state voltage stability. An attempt to cover as much of the field as possible has bccn madc by quoting tests on 2003 Korcan electric power system. Copyright 0 2006 WAC Keywords: Continuation power flow, Optimal power flow, P-V analysis, Security, Steady-state voltage stability, Transmission transfer capability

1. INTRODUCTION

and survive any of the contingencies specified in the criteria.

An operationally secure power system is one with low probability o f blackout or equipment damage. The power system control processes needed to maintain a designated security level at minimum operating cost are extremely complicated. The task becomes much more problematic in liberalized electric industries, where competitive market pressure makes the operator reluctant to take expensive preventive actions in order to guarantee stability, unless the system is in imminent danger of instability (Ruiz-Vega and Pavella, 2003). They gradually depend upon securityconstrained optimal power flow that expends the optimal power flow problem-solving capacity to include the effect of contingencies, while meeting steadystate stability constraints. Since optimality and security are normally conflicting requirements of power system control, they are slowly becoming coalesced into a unified hierarchical mathematical problem formulation instead of treating them separately.

A salient feature of this paper is the development of a possible framework aimed at determining the TTC for a particular transaction area pair at a single instance of time and under specific system conditions. TTC calculation is mainly composed of two distinct stages; security-constrained optimal power flow and steadystate voltage stability analysis based on a powerversus-voltage (P-V) profile. Each approach is designed to be suitable for computer simulations to find a reliability-based TTC for the identified paths within the interconnections.

I . I Securify-conslrained optimal powerjlow Typical on-line optimal power flow applications at the present time prottuce statically secure and optimal solutions with respect to the base-case security and operating constraints. However, serious erosion o f the power system’s steady-state security in case of a contingency is possible. The inclusion o f contingency constraints is the foremost challenge but it is expected that eventually security-constrained optimal power flow will become a standard tool in the industry. The need for modelling contingency constraints in optimal power flow formulations for practical applications is relatively well understood. As utilities move toward a more open and competitive environment, more and more third party generation, such as qualifying facilities and cogeneration, will seek access to their markets. Evaluation of requests for transmission access in the context of system security will put a high premium on utilities to respond rapidly to a huge number

In fact, one of the most important services performed for any interconnected power system is the dctermination of transmission transfer capabilities, or transfcr limits. The underlying concept is that the overall system should be able to survive the sudden occurrence of any reasonable contingency without ensuing overloads, low voltages, or loss o f customer load. Transmission transfer capabilities may be expressed in many ways, but thc most common in usc today is thc total transfer capability (NERC, 1996), or commonly abbreviated to TTC, over a specified group of transmission lines. This is the maximum megawatt power flow a given group of transmission lines can carry

1 I3

of energy players that undoubtedly will stress the power system networks even further. The increasing number of transactions that need to be evaluated calls for the development of new tools among which the security-constrained optimal power flow will play a central role.

where, I = 0 is the base-case, and 1 > 0 represents the ith post-contingency configuration. N is the number of contingencies considered U,~91,,,is the vector of control variables for configuration I &EX,, is the vector of state variables for configuration 1 Z,~91,+,,= [U,4 'is the decision vector for the ith configuration. /' 91,,,+, -+ %, is the base-case objective function rcprcscnting operating costs C,. X,,, -+ 9?a is the vector function representing the load-flow constraints for the zth configuration H, ill,,,-,,+ 9?b IS the vector function representing operating constraints for the zth configuration

1.2 Steady-state voltage stability analysis by P-V methodology

As transmission systems become available for open access, they may be utilized in ways that were not envisioned in their original designs. When power systcms are often exposed to highly strcsscd conditions, the P-V inethodology is useful for cvaluating the steady-state voltage stability limit of tie-lines under both pre- and post-contingency operating conditions. In this paper, the P-V plots measuring the power transfer across the specific interfaces and the voltage at a monitored bus are strongly developed by suggesting a generation shift parameter that is readily inserted into the power flow equations.

This formulation (2.1)-(2.3) is very conservative in that it allows no room tor post-contingency corrective actions. It places much more emphasis on maximizing security than on minnnimg operating ~ o s t s In preventive mode security-constrained optimal power flow, the system operating constraints under various configurations are added to the normal optimal power flow problem to impose additional limits on line flows and bus voltages for the postdisturbance configurations resulting from a given set of contingencies. That is for each contingency considered, the post-contingency variables, power flow, and operating constraints are appended to the basic pre-contingency optimal power flow formulation to represent the contingency condition. This greatly increases the size and computational complexity of the problem formulation. In general, the appended constraints depend on both the pre- and post-contingency variables; however, an approach based on linearization of a pre-contingency base-case can simplify the representation of the constraints.

In section 2, we present a well-reasoned description on the inclusion of contingency constraints into the convcntiondl optimal powcr flow schcmc ln scction 3, wc develop a locally parameterized continuation technique used in conducting the P-V analysis, thereby determining the steady-state voltage stability limit of interface flow on a set of tie-lines between one area and others In section 4, two case studies are pcrformed to demonstrate the viability of the proposed schemes and orderly procedures expounded in sections 2 and 3. The major numerical results for the whole of 2003 KEPCO peak and off-peak systems are presented first, followed by a discussion on the TTC of the interfaces between the metropolitan region and the rest of the system in every aspect such as thermal and steady-state voltage stability limits In section 5 a concluding remark on the proposed method and a future research direction pertinent to the presented work arc stated briefly

To incorporate Contingency constraints, we will use an LP approach that iterates between solution of a base-case and calculation of post-contingency states (Stott, et al., 1987). In each iteration, a precontingency hase-case optimal power flow i s first solved. For each contingency, the post-contingency state is determined based on the solution to base-case. The post-contingency constraints are then linearized in terms of the solution to the base-case. The linearized contingency constraints are appended to the base-case optimal power flow. Jn each subsequent iteration, tlic base-case optiinal power flow incorporates the linearized contingency constraints from the previous iteration.

2. SECURITY-CONSTRAINED OPTIMAL POWER FLOW 2.1 Formulation

Thc traditional notion of sccurity has relicd almost exclusively on preventive control. That is, the requirement has been that the current operating point be feasible in the event of the occurrence of a given subset of the set of all possible contingencies. In other words, the base-case control variables are adjusted to satisfy post-contingency constmints A preventive control formulation has the form (Hur, et ul., 2003): Min ,f (Zo) (2.1) I!"

2.2 Implementation In this subsection, we propose to solve a securityconstrained optimal power flow problem in a sequential manner as follows. The secure operation of tielines is of prime importance in a large interconnected system. OLU approach concentrates on the tie-line security.

x,

s.t. G , ( U o , X , ) = O , i = 0 , 1 , 2,...,N

(2.2)

Wi(Uo,Xi)< 0, i = 0, I, 2,..., N

(2.3)

1 I4

that an adequate amount of interface flow would be available in terms of voltage stability.

To begin, we solve a power flow on the model, which has been implemented by solutions to the base-case optimal power flow problem, with N-I contingency outages under consideration to run a network scnsitivity calculation When all contingency power flows are complete, all the contingency constraints are added to the pre-contingency optimal power flow model and it is solved. In this case, line outage distribution factors (Wood and Wollenberg, 1996) calculated from the contingency power flow analysis are used to formulate the appended constraints By definition, the line outage distribution factor has the following meaning.

The continuation power flow (Ajjarapu and Christy, 1992) has been used in trying to overcome the numerical instability by slightly reformulating the power flow equations and applying a locally parameterized continuation technique. From its conception, the purpose of this continuation power flow was to find a set of soliltions from a base-case up to the critical point for a given import increase scenario. Since then, certain intermediate results of the continuation process have been recognized to provide valuable insight into the voltage stability of the system and the areas prone to voltage collapse.

wherc, dik denotes line outage distribution factor when monitoring line 1 after an outage on line k /If; is the changes i n flow on line 1 5' is thc original flow on line k bcfore it was out of service.

P-V analysis is a steady-state tool that develops a curve, which relates voltage at a bus (or buses) to flow across an interface. Bus voltages are monitored throughout a range of increased real power flows into a region. The benefit of this methodology is that it provides an indication of proximity to voltage collapse throughout a range of interface path flows for the simulated system topology. A full P-V curve can be replicated by increasing flows across an interface (i.e., shifting generation from the receiving region to the external regions). The methodology which should be followed for development of a full P-V cuiw for studies involving interfaces is described in Fig. 2 (also see Fig. 3):

The post-contingency tie-line flow on line 1 with line k out can be determined using (2 4)

f,' =

r; + d ,

i

f:

(2 5 )

Finally, we solve the post-contingency optimal power flow problem by making the added tie-line flows less than the thermal limits of thc corresponding branches to dctermine the secure simultaneous transfcr capability of each tie-line between adjacent regions

Step 1 Choose a receiving region a5 the study drea wherein generation will be incrementally reduced Step 2 Identify severe contingencies to be applied using the

Once the secure transfer capability of each tie-hne is determined, the steady-state voltage stability analyciy is done wing a locally parameterized continuation technique described in section 3 Fig 1 naturally summarizes the procedure for implementing securityconstrained optimal power flow

contingency screening Step 3 Choose the bus (or buses) In the study area at which the voltages will be monitored as the power trdnsfers into the study area are increased The monitored voltages are the Y-axir data of a P-V curve The X-axis data will be interface flows, measured in either MW or MVA

Step 4 Shift generation from the study area to the external drea lhe generation shifts can bc larger at lower path flows than at higher path flows, which are near the pointof-collapse Initially, a generation shilt 01 0 1% of the study region generation should be eftective If the power tlow case fails to converge to a solution after a generation shift, return to the last solved case, and reduce the shift by one-half or one-fourth of the previous attempt

Solve the iioii-contingencyconstrained optimal power flow; kl-1. Determine the secure interface flow limit on all the tie-lines in preventive mode; Repeat { Increment k; Run a power flow on the model with all the N-l contingency cases; Calculate the network sensitivity factor, line out-

Step 5 Iktcrmiiie the worst coiitiiigciicy with tlic ledst interface flow margin and find the quantity of generation shift at the maximum point p , Step 6 Find the intertace flow level (pz) in the P-V curve of the prc-contingency case At this level, the quantity of generation shift is the same as the one obtained in Step 5

age distribution factor; Solve the full optimal power flow with the revised set of tie-flow constraints; ) Until the solutions converge to within tolerance; Perform steady-state voltage stability analysis.

Fig. 2 . Procedure of P-V curve test

Fig. 1. Implementation of security-constrained optimal power flow

As shown in Fig. 3, the interface flow margin measures the distance from interface flow limit by security-constrained optimal power flow to Pz.

3. STEADY-STATE VOLTAGE STABILITY ANALYSIS The main purpose of this section is to address stability criteria and the associated methodology to ensure

115

Table 1 Critical interface lines in KEPCO system. Route

Frombus

Tobus

41

Slnjecheon

Dongqeoul

112

Cheongwon

Sinyongin

#3

Sinseosan

Sinansung

4. CASE STUDY The objectives of case studies are, first, to discover the viability of the proposed method in real implementation and, second, to determine the secure limit of the real power flow on a sct of specified tic-lines considering severe contingencies with a concept of total transfer capability, which is limited by the physical and electrical characteristics of the system like thermal, voltage, and stability limits.

#4

Asan

Hwaseong

K6

U1.jin NIP

Ui.jeongbu

Voltage level [kV]

Thermal rating [MVAl

I 2

345 34s 345 345

2192.0 2192.0 1096.0 1096.0

76s

72~n.u

765 345 345

7290.11 2191.1 2191.1

345 345

2191.1 2191 I

1

2 I

Pilnterface F l o ~ i

Fig. 3. Concept of interface flow margin

CKT ID

2 1

2

1 ~~~

2

with the 48035 MW load demand and that with the 43012 MW load demand correspond to 2003 summer peak and off-peak states of the system, respectively. Total real power generation capacity in the system was 51222 MW in 2003. The results of cases as to two load levels are described in the following subsection.

4. I Test system descriplion Fig. 4 is a schematic showing locations of major generation and transmission facilities reproduced by permission of the Korea Electric Power Corporation; 950 buses, 1900 lines, 408 transformers and 233 generators characterize this network.

4.2 Test results Selected case study results are offered in this subsecLion. The securily-conslrain~doptimal power flow method is used to evaluate the simultaneous transfer capability of the interconnections. Under any probable contingency and in the normal system condition, there should be no violation in the load constraints and the operating constraints. With P-V analysis, the limit of the real power flow on the interface lines related to the worst contingency is determined in terms of the steady-state voltage stability. Peak load demand: First, we perform the power flow analysis for the entire interconnected system to calculate the linear sensitivity factors of all interface lines as defined in (2.4). Then we determine the secure transfer capability of tie-lines by solving the securityconstrained optimal power flow with a revised set of tie-flow constraints. Table 2 shows the real power flows through the tie-lines in case of optimal power flow and security-constrained optimal power flow, respectively. Table 2 Secure transfer cai>abilityat aeak load Route #I

#2 *3

As can be seen in Fig. 4, there are six major interconnections, consisting of 765 kV and 345 kV lines which connect the metropolitan region and the neighboring regions. 'I'he lines belonging to the critical interface are summarized in Table 1. In all simulations, the configuration of KEPC0'03 system is used where two load levels, 48035 MW and 43012 MW, are adopted. Suffice it to say that the system condition

N4

#S #6 Subtotal 154kV Totdl

116

OPF [MW]

Circuit # I

Circuit #2

774.3 400. I 1262.4 1389.9 790.6 729.4 11036.7 312.1 11348.8

775.8 400. I 1262.4 1464.7 1057.6 729.4

SCOPF [MW] Circuit #I Circuit #2 766.7 384.5 1262.4 1369.9 748.8 723.8 10882.2 310.3 I1 1923

768.2

384.5 1262.4 1451.9 1035.3 723.8

As mentioned in section 3 , we can easily determine the interface flow margin at the peak load demand after selecting the worst contingency case In Fig 5, the point p 2 has the same generation shift as the maximum point p , of the P-V curve applying the outage of route 5 Consequently, the maximum voltage stability limit of real power flow on all tie-hnes i b approximately 11443 31 MW as shown in Fig 5 It should be pointed out that the voltage limit of real power flow through the interfaces at the peak load demand is more than the secure limit obtained from security-constrained optimal power flow by 250 81 MW

Table 4 Comparison of fuel costs at each load level Load 1 ,.,,,=I

Peak

orfnea k

ED [ KR won]

OPF [KR won I

SCOPF [ KR won]

1,167,578.900

1,274,815,600

1,279.880,000

939,954,800

1,089,838.800

1,124,636,200

101 1 00

C $9 1c

a'

ICIBC

i c m

iiic

n..m

1ic.x

1 1 7 ~

'i'w

121x

lnteN3ce F l m I1Al.l

C 9,

Fig. 6. P-V curves in base-case and six contingencies at off-peak load demand

c rs c 95 C*

lC5

I

Intemcr Fog. I W A

Fig. 5. Determination of interfacc flow margin at peak load demand OfJlpeak loud demand; ln a similar fashion, we can compute the secure tie-line flows joining the regions at the off-peak load demand after the contingency on a specific transmission line has occurred. The numerical results are presented in Table 3. One can see that the sccurity-constrained optimal power flow yields smaller tic-line flows in overall than does the ordinary optimal power flow. This is mainly due to the post-contingency system security constraints imposed on the security-constrained optimal power flow problem. Table 4 shows the fuel costs at each load level for economic dispatch, optimal power flow, and security-constrained optimal power flow, respectively. An optimal power flow is distinguished from an economic dispatch by the fact that it constantly updates a power flow of the transmission system as it progresses toward the minimum of the objective function.

,jl?;%M;.

0 46

jmc

#I #2

#3 ii4

#5

#6

Subtotal 154kV 'Total

SCOPF [MW] Circuit #I Circuit ii2

929.7 512.0 1057.1 1138.0 688.9 792.4 10576.2 277.4 10853.6

939.8 544.6 996.4 1055.4 659.6 796.7 10507.7 277.2 10784.9

931.1 512.0 1057.1 1148.9 1014.8 792.4

IOBE,)

I'?X

1138~

iim

~ v i c

I:<~C

12183

lncelfjce FIOI [lr161

Fig. 7. Determination of interface flow margin at offpeak load demand peak load demand, as can be confirmed in Fig. 6. In Fig. 7, thc proccdurc for dctcrmining thc stablc limit of interface flow against voltage collapse at the offpeak load demand is vividly revealed. As far as the voltage stability limit of tie-line flows is concerned, the point p 2 has some 350 MW interface flow margin as compared with the solution of security-constrained optimal power flow. 5. CONCLUSION

This paper has concerned itself with a systematic procedure to calculate total transfer capability for the interconnected transmission network. Both individual mechanisms, namely security-constrained optimal power flow and P-V technique for the evaluahon of the steady-state voltage stability limit, were introduced to fairly determine the transfer capability in MW across the fixed Interfaces.

Table 3 Secure transfer cauability at off-peak load OPF [MW] Circuit # I Circuit #2

.AV'

bs

This scenario is somewhat differcnt froin the pcak load demand case; the outage of route I with a margin of 362.71 MW is the worst contingency at the off-

Koute

.% ..

-

D';?

941.2 544.6 996.4 1140.6 1095.7 796.7

In a nutshell, the full-fledged algonthms are hailed as

a viable alternative to a reliability-based total transfer capability calculation for a pair of areas, allowing for economic^ and stability requirements These combined algonthms have been applied to determine the

117

maximum interface flow limit at both peak and offpeak loads of 2003 Korean electric power system.

REFERENCES Ruiz-Vega, D. and M. Pavella (2003). A comprehensive approach to transient stability control: Part 11- Open loop emergency control. IEEE Trans. Power Syi/., 18, 1454-1460. NERC report (1996). Available transfer capability definitions and determination. Novth American Electric Reliuhility Council, [Online] Available: http://www.ncrc.com/publications/rcfcrcncc. html Hur, D., J.K. Park and B.H. Kim (2003). Application of distributed optimal power flow to power system security assessment. Electr. Power Cornponents Syst., 31, 71-80, Stott, B., 0. Alsac and A.J. Monticelli (1987). Securiy analysis and optimization. f’roc. IEEE, 75, 1623- 1644. Wood, A.J. and B.F. Wollenberg (1996). Power generation, opercition, and control, chapter 1 1. John Wiley & Sons, New York. Ajjarapu, V. and C. Christy (1 992). The continuation power flow: A tool for steady state voltage stability analysis. IEEE Trans. Power Syst., 7, 41 6-423.

Based on the evaluation of total transfer capability as outlined in this paper, it is necessary to provide an initial framework on available transfer capability that will likely be expanded and modified as experience is gained in its use and as more is learned about how the competitive electric power market will function. It stands to reason that the determination of available transfer capability must accommodate reasonable uncertainties in system conditions and provide opcrating flexibility to ensure the secure operation of the interconnected transmission networks for a commercially viable wholesale electricity market.

118

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

VOLTAGE STABILITY ASSESSMENT AND ENHANCEMENT OF THE THAILAND POWER SYSTEM Arthit Sode-Yome*, Nadarajah Mithulananthan*”and Kwang Y. Lee*”* *Department of Electrical Engineering, Siam llniversity, Bangkok I01 60, Thailand Energy Field of Study, Asian Institute of Technology, Pathumthani 12120, Thailand *** Department of’Electrica1Engineering The Pennsylvania State IJniversily, PA 168O2, IJSA **

Abstract: This paper presents voltage stability study of the Thailand power system by considering the existing Static Var Compensators, generation and load directions. An approach to determine appropriate voltage settings of existing Static Var Compensators is proposed in order to maximize static voltage stability margin of the system. Two most recent methods, namely Maximum Loading Margin and realistic load direction methods, are applied to the Thailand power system in order enhance loading margin of the system in a practical way. With the applications of the proposed and existing techniques, the highest and practical voltage stability margin of Thailand power system is obtained. This provides a guide for electric power utilities to enhance voltage stability margin of power systems in a practical way. Copyright C 2006 /FAC Keywords: Thailand power system, Maximum Loading Margin method, realistic load direction, Static Var Compensator, voltage setting

1 . INTRODUCTION

Voltage instability is one of the instability problems threatening the present electric power systems, as it can be observed from many incidents such as the worst and most recent power interruption in North America in August 2003 (Kundur, 1994), (PSERC, 2005). Hence, electric utilities around the globe have devoted a great deal of erforts in the static voltage stability study to avoid voltage collapse by incrcasing voltagc stability margin or loading margin (LM) of the system. Major contributory factors to voltage instability are power system network, generation and load patterns. Power system network can be modified to enhance voltage stability margin with the help of Flexible AC Transmission System (FACTS) controllers such as Static Var Compensator (SVC). Generation pattern or “generation direction” (GD) can be specified in such a way that generation from appropriate locations are dispatched to provide low reactive power losses, thus high LM. The load pattern or “load direction”, which is defined as the rate in which various loads increase from the base load, also have a significant impact on static voltage stability margin. In typical voltage stability studies, the loads at each load bus are raised at the same rate. In a practical power system, however, the load at each bus may not increase in the same direction andlor at the same percentage. Thus, representing load

direction based on the actual load variation is important and necessary in static voltage stability study of practical power systems. By considering these three factors at the same time, the highest and practical voltage stability margin may be obtained. In (Sode-Yome et al , 2004a), voltage stability study with various shunt compensation devices including shunt capacitors and shunt FACTS controllers, i.e., Static Var Compensator (SVC), Static Synchronous Compensator (STATCOM), are studied and compared. In this study, voltage settings of SVC and STATCOM are fixed at 1.0 p.u. At the fixed voltage setting, the system may not have the highest voltage In (Sode-Yome et al., stability margin or LM. 2005a), a new generation direction approach, namely Maximum Loading Margin (MLM) approach, is proposed to find the generation direction that provides the maximum LM. With the MLM method, the global solution can be guaranteed. In addition, It is easy for utilities to use commercial software for the study. Realistic load direction is proposed in (Sode-Yome et al., 2005b) based on daily load curves of a practical power system, namely Thailand power system. With the methodology, realistic and practical LM can be obtained. Based on the above observation, attention is drawn in this paper to propose voltage stability study of a practical power system. the Thailand power system, by considering SVC, generation and load directions 119

The total losses of the system are 5.2 % including those occurred in power stations and transmission lines (Sode-Yome et a/., 2004b). The transmission system of Thailand is a fully connected system having the highest voltage level of 500 kV. These 500 kV transmission lines are designed to carry bulks of power from generation sources located in the North, East and West to the major load centers located in the capital city and central area. The 230 kV lines are distributed throughout the country.

simultaneously. A methodology is proposed to find voltage control settings of SVC that maximize voltage stability margin of the system. With the help of the proposed methodologies, the practical and maximum LM of the Thailand power system can be obtained. This provides a guide for electric power utilities as well as Jndependent System Operator to obtain the maximum voltage stability margin of power systems in a practical way. This paper is structured as follows: Section 2 describes the Thailand power system in general including generation, transmission systems and load demand of the country. Section 3 summarizes the MLM and realistic load direction approaches. In Section 4, a complete voltage stability study of the Thailand power system with an existing and the proposed approaches is presented. Finally, in Section 5, a summary of the main conclusion is given.

A

2. THAILAND POWER SYSTEM

svcz

2 I Overview Electric Supply Industry in Thailand consists of three utilities, namely the Electricity Generating Authority of Thailand (EGAT), Metropolitan Electricity Authority (MEA) and Provincial Electricity Authority (PEA). EGAT is responsible for generation and transmission grids of high voltage levels, while MEA and PEA are responsible for distribution levels.

Metropolitan

SouthBangkok ~

AwIgChok

*

0

I

I

Rajjapr blia

Khanom

\-”‘“”

*

2 3 0 IkV Line

Krabi

Fig. 1. Power stations, 2301500 kV transmission lines and SVCs of the Thailand power system.

SVC is only one type of FACTS controllers installed in the Thailand power system. There are two SVC controllers, one located at the Thatako (TTK) substation between northern and central regions (SVCI), and the other one located at the Bangsapan (BSP) substation between southern and central regions of the country (SVC2). The capacity of SVCl is +150 MVar whereas the SVC2 capacity is +300 and -50 MVar. SVCl is installed to improve angle stability while SVC2 is installed to increase both angle and voltage stabilities. Fig. 1 shows major power stations, 230/500 kV transmission lines and SVCs of the Thailand power system.

lntermnnection

2 2 Generation and Transmission Systems Fig. 2. Contributions of energy of various producers to Thailand power system.

Electrical power system of Thailand is a medium size power system, compared to those in US, China, or Japan. As of March 2004, EGAT consists of 196 substatioris arid 28,330.8 circuit-kilometer transmission system. The total installed capacity of the systcm is 25,324.92 MW including gencration from EGAT power plants, Independent Power Producers (IPPs), Small Power Producers (SPPs) and power from neighbouring countries, i.e., Lao and Malaysia. Fig. 2 shows contributions of energy of various players to Thailand power system (SodeYome et a / , 2004b). From Fig. 2, EGAT and lPPs are major contributors of generation in Thailand.

2.3 Load Demands

The highest load demand of the Year 2004 occurred on March 30th 2004 during the summer season. Hence, the day is named as “peak day”. The maximum demand was 19,325.8 MW, occurred at 14.30 hrs with the temperature of 35.7’C at EGAT headquarter office (in the vicinity of Bangkok). Load demands are distributed among regions of the country including metropolitan (Bangkok and vicinity), central, north-eastern, southern and 120

northern areas, which can be viewed in Fig. 3. From Fig. 3, the load demand is concentrated in the central part of the country, where the capital city, Bangkok, and most of industrial estates are located.

3. MLM GENERATION DIRECTION AND REALISTIC LOAD DIRECTION 3. I MLM Generation Direction

Fig. 4 shows daily load curves of the system, and metropolitan, central, northeastern, southern and northern regions on the peak day. From Fig. 4, it is obvious that there are three peak times in Thailand: at 1 1 .OO, 14.00 and 20.00 hrs. Metropolitan and central regions are industrial regions having the same load characteristics. The rest of the regions are rural regions, having similar daily load curves. The load factor of the system on the peak day was 0.86. In 2003 and 2004, there are more than 1000 MW increase in load demand with 6.65 and 8.63 percent increases, respectively. The maximum daily energy consumed for Thailand was 383.8 GWh occurred on March 25,2004, five days before the peak day.

Generation pattern or “direction” is defined as the rate of changes of generation to serve the desired load increase and losses of the system. Let Kc;?be the factor for active power increase at generator i and Pbe the generation at the base case, then, the generation PG? at a higher loading point can be written as

where i = 1,2, ...n, for all participating generators. The MLM method identifies a vector of the GDs of generators that gives maximum LM by approximating the surface of the LM as a function of the generation directions (Sode-Yome et a1 , 2005a). If one can approximate the LM surface as a function of all generation direction variables (Kc;,), optimization technique can be used to provide the highest LM point. Mathematically, the method can be formulated as follows (Sode-Yome et a1 ,20054:

Northern

Maximize

subject to Fig. 3. Load demand in each region of Thailand.

0 80001 ,

5

10

15

20

I

I

I

I

c ’ KG, =

(3)

O
(4)

where KG, is generation direction of generator connected at bus j , B,,[,are the coefficients terms, B,] is a constant term, p is the power term and n is the number of terms of the polynomial approximation. If generation is increased according to this direction, the system will have the maximum LM (Sode-Yome et al., 2005a). I

3.2 Realistic Load Direction

5

0 -1mn I

10

15

,

20 ‘

I

Load pattern or “direction” is defined as the portions of load increase a1 each bus in the systein. Let &,, be the direction scalar of real and reactive load increase at bus i and f l l , o , Qul0 be the active and reactive load, respectively, at the base case, therefore, Pill and (2ik at a higher loading point can be written by ( 5 ) ,

. ..

,. ,

.._~.-._.__,_. ,--.. ____._...( 1000

0

5

10

15

In

Time [hrsl

Fig. 4 Load curves of the system and all regions.

Where h is the loading factor (L.F.) and i = 1, 2, ..., n for number of load buses. Equation (5) represents the same rate of increase in real and reactive power load. This means that the load is increased at the same power factor. 121

In conventional voltage stability studies, the loads at each load bus are raised at the same rate or same percentage. This, however, may not be practical in a real power system environment. In a practical power system, loads at each bus may increase at different rates. Thus, actual daily load curves of a practical power system are used to capture realistic load increases in each region (Sode-Yome et a1 , 2005b). The load directions in each bus in the particular region can be identified from daily load curves by

Where AF, is an Area Factor of the area J , KIl,(l is a conventional load direction. Area Factor for the area I is defined by

Voltage Control Settings of SVCs [ p u ]

Fig. 5 Effect of voltage settings of SVCs on system loading margin. 4.2 Weakest Buses

Where

AP’,, is

The weakest bus of the system is defined as the one that is nearest to experiencing voltage collapse. It can be identified using tangent vector, which is a byproduct of continuation power flow process. Table 1 shows the first three weakest buses (substations) in the Thailand power system, based on tangent vectors. From Table 1 , all of the weak buses are located in the If a voltage collapse is north of the country. occurred, it is initiated at these buses and spread throughout the region unless protections are properly operating.

percent load increase in the area j

obtained from the lowest to the maximum demand in the afternoon or evening in the daily load curves, A
Table 1 Weakest buses of Thailand power system

1 Weakest Bus N o

4. SIMULATION RESULT

0.1064 0.0638 0.0637

4.3 MLM Generation Dii*ection

In the beginning, an approach is proposed to determine voltage settings of SVCs. Then, voltage stability assessment of the Thailand power system is investigated. After that, the MLM generation and realistic load directions are applied. Simulation and discussion are presented in the following subsections.

I’hailand power system is composed of 20 power stations including EGAT power stations and TPPs. In the actual case at the peak load, spinning reserve is distributed among five power stations; each of them has more than 1000 MW capacity. Table 2 shows these five power stations with their capacities. Thus, only 5 power stations shown in Table 2 are considered as participating generators.

4 I Voltage Control Setting of SVCs

An important parameter of SVC to improve voltage stability is voltage setting. An approach to find an appropriate voltage setting of SVC is proposed by looking at the relationship between LM and voltage setting. Fig. 5 shows the plot between the LMs and voltage settings of SVCs of Thailand power system. From Fig. 5 , it is obvious that setting the voltages of SVCl at 1.02 p.u. and SVC2 at 1.06 p.u. provides the highest voltage stability margin. If voltages of SVCs are controlled at these values, the maximum LM can be oblained. These voltage setlings are, therefore, used for the rest of the study. However, the present voltagc stctting of thcsc two SVCs arc at 1 .00 p.u.

I

1 ITaneent Vector1

CM2-5 CTG-2 CTG-I

Table 2 Power stations with more than I000 M W caoacitv

I Name I RB I MM I BPK I SB I W N I

I

Cap. (MW)

I

2600

I

2238

I

2060

I

1740

I

1400

PV curves of base case and MLM method are shown in Fig. 6. The business as usual case for EGAT system is the case where MM power station is the only one to serve the load increase. MLM method dispatches generation at MM and BPK with the 0.3

122

and 0.7 C m s , respectively. Obviously, MI,M method gives almost 15 percent higher LM than the conventional method. This improvement is about 300 MW, which is equivalent to the capacity of a medium size thermal power station.

i -

...............

_--

2?nIo[ 0n 64

\

........... -,..-.

, i '

.

---

/-

/-

rn

..........

x

...............

........ ...................

...,....

.,.~..

n2

1 .... Basecase

Fig. 7 PV curves with conventional and practical LDs at the afternoon and evening peaks.

- MLM tvlethod for Thailaild Power S:stem Case 0

no2

0

006

no4

one

01

012

LF IPUl

Fig. 6 PV Curves at the weakest bus. 4.4 Realistic Load Direction

The peak demand in urban area is at 14.00 hrs while the peak load in rural area is at 20.00 hrs, as seen from Fig. 4. Thus, only two peak demands are considered in this study. Table 3 shows the percent load increase and realistic load directions for the afternoon (at 14.00 hrs) and evening peaks (at 20.00 hrs) of Thailand power system for all regions. It can be noticed that maximum LD is 1.00 and it is occurred at the area where the demand is highest. LDs of other areas are in proportion to the highest LD.

4.5 MLAd Generation and Realistic Load Direction

PV curves of the system with MLM method and the conventional and realistic LDs at the afternoon and evening peaks are shown in Fig. 8. In this case, LM can be extended up to 0.16983 p.u. at the peak load. In another word, about 1400 MW o f load can be increased further if the MLM generation and the realistic load directions are used. It is noticed that, with the MLM and the realistic LD, LM of the system can be increased without requiring any new power system facility.

Table 3 Realistic LD in Each Regions

I

Afternoon

Region

I Metro

A

I

I Evening

16 I A 52.32 I 1.000 I 26.67

IS

I 0.405 I

Central o

A: Percent Load lncrcasc B: Realistic Load Direction

PV curves of Thailand power system with conventional and realistic (practical) LDs in the afternoon and evening are shown in Fig. 7. From Fig. 7, it is obvious that LM of the system is lowest for the case of conventional LD. LM in the afternoon is lower than that in the evening because the load demand in the afternoon is higher. If the realistic LD is applied, LM is increased from 0.0992 p.u. to 0.12016 p.u. at the peak load. This means that about 400 MW of load can be increased further if the realistic LD is used.

o112

0C14

1306

CIOS

'

F

01

u12

1114

c116

1 0

IS

IP"1

Fig. 8 PV curves with MLM and LDs at the afternoon and evening peaks. 4.6 C'ontingencyRanking

Contingency ranking is one of important issues in voltage stability assessment. Practically, the worst N-1 contingency of any power system facility is required to be managed at all times by electric utilities. PV curves of three worst N-l contingencies in the Thailand power system are plotted in Fig. 9, based on the operating condition at the peak load in conventional case. It is obvious that N-l of SVC2 at BSP is the worst contingency since it reduces LM of the system the most, or resulted in the lowest LM. Thus, special maintenance should be performed to increase reliability o f this equipment.

123

system. The weakest buses of the system are identified by using tangent vector analysis and they are located in the north. Generation directions based on the MLM approach along with the realistic load directions are applied to the Thailand power system to maximize the LM in a practical way. The study also shows the worst N-1 contingencies in terms of voltage stability as well as the next appropriate location of a new FACTS device. This provides a guide for utilities to enhance voltage stability margin in a realistic way.

- Basecase vilh SVC represenlatian N-1 SVC at l l K N-l 500 k‘/Trl<-MM3 Line N-1 SVC at BSP

02

o

nni

002

on3

004

005

noc

007

nnu

009

REFERENCES

nt

CaAizares, C. A. , et. al (2004). UWPFLOW C’ontinuation and Direct Methods to Locate Fold Bifilrcations in ACIDC FACTS Power Systems, University of Waterloo, available at http:llwww.power.uwaterloo.ca. Green, S. , I. Dobson and r. L. Alvarado (1997). “Sensitivity of Loading Margin to Voltage Collapse with respect to Arbitrary Parameters,” IEEE Trans Power Syst, Vol. 12, No. 1, pp. 262-272. IEEE/PES Power System Stability Subcommittee (2003). Voltage Stability Assessment Concepts, Practices and Tools, special publication, final draft. Kundur, P. (1994). Power System Stability and Control, McGrawHil, New York. Lee, B. H. and K. Y. Lee (1993). “Dynamic and Static Voltage Stability Enhancement of Power Systems,” 1EEE I iansactions on Power Systems, Vol. 8, NO. 1, pp. 231-238. PSERC (2005). Blackout of 2003: Description and Responses,Available: http:/iwww.pserc.wisc.edul. Sode-Yome, A. and N. Mithulananthan (2004a). “Comparison of shunt capacitor, SVC and STATCOM in static voltage stability margin enhancement,” International Journal of Elecfricul Engineering Education, UMIST, Vol. 41, No. 3 . Sode-Yome, A. and N. Mithulananthan (2004b). “Role of Small Power Producers as Part of Peak Serving Scheme,” invited paper in Power Gen Asia Conference, Bangkok. Sode-Yome, A., N. Mithulananthan and K. Y. Lee (2005a). “A Maximum Loading Margin Method for Static Voltage Stability in Power Systems”, IEEE Transaction on Power Systems, in press. Sode-Yome, A. and N. Mithulananthan (200Sb). “Effect of Load Direction in Static Voltage SLdbilily Study,” IEEEiPES Trdnsmision and Distribution 2005 Asia Pacific Conference, Dalian, China. Sode-Yome, A. and N. Mithulananthan (2005~). “Generation Direction Based on Optimization Technique for Power System Static Voltage Stability,” Australasian LJniversities Power Engineering Conference, Tasmania, Australia.

Fig. 9 PV curves of the system with base case and three worst contingencies. 4 7 Voltage Stability Margin Enhancement

The weakest bus of the system is at CM2-5 for the business as usual case. When the MLM approach is used, the weakest bus of the system is changed to BSP. Both weakest buses are located in distribution level, thus introducing shunt FACTS devices at the weakest bus is the most effective way to increase LM (Sode-Yome et al., 2004a). Fig. 10 shows PV curves for base case and the case having SVC installed at BSP substation. From Fig. 10, in the case of MLM and double capacity of SVC2, LM of the system can be increased to 0.14 p.u. ‘I

I

Fig. 10 PV curves of base case and system with double capacity of SVC at RSP substation. From the results, it can be concluded that LM of a practical power system can be enhanced to the highest value with appropriate voltage settings of existing SVCs, the MLM generation and the realistic load direction approaches. This would guide utilities to use existing power system facilities in an effective way.

5. CONCLUSION This paper presents voltage stability assessment of Thailand power system based on peak demand of the Year 2004. A methodology to find voltage settings of existing SVCs is proposed to rnaxirnize LM of the

124

Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLICATIONS

DESIGN, IMPLEMENTATION AND TESTING OF AN ARTIFICIAL NEURAL NETWORK BASED ADMITTANCE RELAY Caganpreet Chawla, Mohinder S. Sachdev, C. Ramakrishna Power Systems Research Group, University of Sushtchewan, Suskutoon, Canada

Abstract: Artificial neural network based technology, which is inspired by biological neural networks, has developed rapidly in the previous decade and has been applied in power system protection applications. Protection o f transmission and sub transmission lines is most frequently done using distance relays. This paper discusses the design, implementation and testing of an artificial neural network (ANN) based distance relay that implements characteristics of a mho (admittance) relay. The Artificial Neural Network based designs of distance relays proposed so far work well for faults well within the boundary characteristics of a relay, but are not able to maintain the integrity of the boundaries of the relay characteristics of generic designs. Copyright 82006 IFAC Keywords: Neural networks, power systems, fault detection, protective relaying and admittance relay

1 . INTRODUCTION

Ovcr thc past dccadc, various dcsigns bascd on ncural network technology have been proposed. Specific applications include direction discrimination for protecting transmission lines (Sachdev, Singh and Sidhu 1995; Fernandez and Ghonaim 2002); fault classification for faults on double circuit lines (Balamurugan and Venkatesan 2002) and ANN based distance relays (Agganval, Dunn, Bennett, Johns and Xuann 1999). The proposed designs of distance relays proposed so far work well for faults well within the boundary characteristics of a relay, but are not able to maintain the integrity of the boundaries of the relay characteristics (Fernando 1997). This paper presents a design that fully exploits the potential of ANNs in designing a generic admittance relay that will relain the inlegrily or the boundaries or its characteristics. A methodology for developing the ANNs by analyzing and utilizing the rclationships between the input data and the outputs expected from the ANN is then presented. The proposed methodology helps in fully utilizing the potential of ANNs in implementing generic distance relay characteristics in such a manner that the integrity of the boundaries of the relay characteristics is maintained.

a line. Zone 1 protection is the procedure of setting a distance relay to trip instantaneously for faults which occur in the first 80-85% of the transmission line length. Also, the Zone 1 protection scheme is inherently directional in nature, which implies that the relay does not operate for all fault locations which are behind the relay location which is shown by point A in the characteristics. The admittance relay should operate for all the faults that lie within its reach, i.e. within the circular boundaries of the relay characteristics (shown in white) and should not send a trip signal for any fault outside these boundaries (shown in gray). These generic characteristics of a Mho (or Admittance) Relay were used to train an ANN which can be implemented as an admittance relay which will work well near the boundaries of the relay characteristics.

jx

1.I Pvotection of a Trunsmission line using an admittance relay

Figure 1 shows the characteristics of an admittance relay where Zrl is the impedance reach for which the relay is set. Usually, the value of Z,, for Zone 1 protection is 80-85 percent of the total impedance of

A

i Relay LOC

ion

Figure 1 : Characteristics of an admittance relay

125

of pre-processed samples (13 samples each) of current and voltage patterns, making each data window of a size of 26 samples The training was done in such a manner that the ANN gave a +I output for all the patterns belonging to points within the circle and -1 for all the patterns belonging to points outside the circle.

The ability of neural networks to model non-linear functions and to recognize complex relationships between voltage and current signals corresponding to different phases, kinds of faults and changing system conditions make them highly suitable for their implementation as transmission line protective relays. Neural Networks, once trained possess the capability to generalize and adapt to certain system conditions like source impedance that they might not have encountered before (Sachdev, Singh and Sidhu 1995). This enables them to recognize the signals thcy havc sccn ncvcr bcforc, thus making thcm superior to conventional relays.

The training method used was a combination of batch and incremental training. All the samples of the current and voltage data were presented to the ANN in a batch modc whcrcas wcights of thc ANN wcrc updated after each such pattern was presented following thc principle of incremcntal training. Figure 2 shows an example of the input data pattern. The input data is given in form of ccqucntial data windows as shown in the figure.

2. PROPOSED DESlGN The proposed design inculcates the implementation of an ANN based relay for a single phase only. Similar rclays can thcn be used in parallcl for different phases as well as different types of faults. The design of the ANN based relay comprises of two phases: a. Training Phase b Testing Phase

2. I Truining qf the ANN As mentioned before, the training of the ANN was done using the generic characteristics of an admittance relay. The training patterns used as the training data for the ANN were the computer generated current and voltage samples obtained using these characteristics. Using typical values of Z,l from a power system, the values of current and voltage values were obtained for various different points on the characteristics. Input data sets for training (in form of current and voltage samples) were produced at a sampling frequency of 1.44 KHz. These samples in the form of data windows comprised of various points within and outside the reach of the relay.

I

s

I

I.

v', .ump,,.

1

c

t,

YYrnhl.,

Figure 2: Sample Data windows for Current and Voltages signals Another two important steps in training phase were the selection of the configuration and training algonthm of the ANN The choice for different configurations of the ANNs was based on certain criteria For an optimal design the number of hidden layer neurons was always chosen as 2j +1 where J is the number of input layer neurons Since only one output was needed from the relay, the number of output laycr ncuron was always kcpt cqual to onc The only variable was the number of input neurons, which was changed and the other parameters were calculated accordingly Multi-layer feed-forward networks with configuration4 10-21 -1, 12-25-1 and 15-3 1- 1 were taken into consideration

The input patterns had to be pre-processed and scaled down so that they could be used for training the ANN The pre-processing and scaling of these computer-generated signal\ was done by converting the values of all these data samples in terms of perunit, hence restraining these values to he only between -1 and +1

After intensive training of these different configurations of ANNs, the network with a configuration of 12-25-1 was chosen for this application. The ANN uses back-propagation algorithm and sigmoid neurons in all the three layers Figure 3 depicts the structure of the ANN used and

Once the pre-processing of the input voltage and current patterns was completed, these patterns were fed into the ANN in the form of sample-data windows. Each data window had about half a cycle

126

patterns used for the training. The input data windows were fed into the first layer of the neural network. These data values were multiplied with appropriate weights which result in outputs from the first layer. These outputs become inputs for the hidden layer and this process was continued till an output was obtained from the output neuron. The output was then compared with the desired output and the error between these two values was back propagated to update the weights. The weights were updated through the iterative procedure till the error stoppcd rcducing and thc gradicnt bctwccn cpochs was lesser than It was then concluded that the desired set of input layer, input-hidden layer and hidden-output layer weights had been obtained. The wcight matriccs of the sizes 26x12, 12x25 and 25x1 respectively were thus obtained which was in accordance with the described training method.

11 I2 13

... ...

I

I13

abovementioned criteria. The ANN was then tested to analyze the accuracy of the results obtained. In case the ANN did not perform well during testing, it was trained again after changing various parameters. This iterative procedure was continued till a desired degree of accuracy is achieved in the results. The details of the results have been presented in the subsequent sections.

2.2 Testing and Implementution

Jt is very essential to test the trained ANN The testing was done using the data patterns for which the ANN was not trained In other words, the ANN had ncvcr seen thc data patterns uwd for testing and wcrc different than what were used to train the ANN The ANN was tested for only the values that were not used in training This was done in order to determine if thc traincd ANN was capable of maintaining the integrity of the boundary conditions of the generic relay charactcristics. The test pattcrns wcre produced by using increments of 5% of the length of the line For the values wcll within the boundaries, the test patterns were generated for 59'0, 15% etc till 75% After this value of 75%, the test patterns wcre geiieiated with iiicieiiients of 1YOof tlie length of tlie line This was done in order to obtain the closest possible estimate of the point where the ANN gave accurate results

Vl

1 output neuron

v2

v 3

... ... V13 v

25 hidden neurons

Figure 3: Description for the training of the ANN To ensure as well as test the generalizing capability of a neural network, it is very important to use different data sets for training and testing. In this case, the voltage and current patterns used to train the ANN were chosen at intervals of 10 percent of the line (10 YO,20 %, 30 % and so on). The training was done in such a way that the output obtained from the ANN for fault pattcrns within 80%0 of thc linc was equal to +1 and for fault patterns outside these boundaries, the ANN was trained to give an output of -1. The training was stopped as per the

I X Figure 4: Data used for testing of the ANN The ANN was tested for various values and the results obtained from the tests have been discussed in the next section The transfer function used for the neurons in all the layers of the network was sigmoid function Thus, the values of outputs obtained were between -1 and +1 However, these values were rounded off in order to obtain the nearest integer

127

values of either -1 or + l . In some cases, it was difficult to round off these values because of the fact that the output values kept fluctuating between -1 and + I as data patterns were given in a sequence, indicating that the ANN was not able to detect the fault condition correctly in that case. Figure 4 shows a few points (not to exact scale) foiwhich the trained ANN was tested by using the current and voltages input patterns. Points indicating a cross “x” sign are four points within the reach of the relay, whereas the points with a plus ‘+’ sign are outside the reach of the relay characteristics respectively. For a correctly trained ANN, the outputs for the points that lie within and outside the impedance reach of the relay should be +I and -1 respectively. For points on the boundary of the relay characteristics, it is acceptable to a certain extent if the output value for this particular value is not determined correctly. However, the acceptability depends on the margin or the band for which the ANN does not perform correctly near the boundary conditions. A satisfactory margin near the relay boundary is essential to ensure that the proposed modcl of thc ANN bascd rclay is ablc to maintain thc integrity of the boundaries of the generic relay characteristics.

rounded (towards minus infinity) as -1 .O. For voltage and current fault patterns belonging to distances between 79% and 81% of the line, the outputs fluctuate between -1.0 and 1.0 as data windows progress in a sequence, thus giving an incorrect output. However, it should be noticed that this leads to an error of only k 2.0% which is significantly lower than any of the models proposed so far. Therefore, these results confirm that the adopted methodology of the ANN maintains the integrity of the boundaries of the generic relay characteristics. Table 1 Comparison of desired results and results obtained by testing of the ANN

% Of the line

Desired Output

Output of the ANN (rounded)

15%

+I

+1.0 (FAULT)

45%

+l

+1 .O (FAULT)

78%

+I

+1 .O (FAULT)

79%

+I

+1.0 (FAULT)

80%

+1

+1/-1 (Incorrect)

81%

-1

-1 .O(non-fault)

3. RESULTS

82%

-1

-1 .O (non-fault)

Table 1 shows the comparison of the desired results and thc rcsults obtained by testing the proposed ANN model, The first column of the table refers to the different distances (in terms of percentage) for which the ANN based relay was tested. As discussed in Scction 2.1, thc input data sets used for training and testing are required to be different to test the generalization capability of an ANN. As mentioned before, the ANN was trained for values with increments of 10 YO.As can be seen, the testing data results shown in Table 1 have been calculated for different values than those used to train the ANN.

105%

-1

-1.O (non-fault)

Column 2 of the table shows the output that should be given by an accurately operating distance relay and column 3 shows the rounded off results when different fault patterns are fed into the ANN In the first four cases when the voltage and current data windows for 15%, 45%, 78% and 79% of the line are fed into the ANN, the ANN gives an output of more than 0 9 value which has been rounded (towards infinity) to + I 0 For the sixth and seventh and eighth case, when the fault patterns at 79% and 81% of the line respectively are fcd into the ANN, the output obtained 15 lesser than -0 9 which has been

Since the trained ANN implements the generic characteristics of an admittance relay, it can be tested for ground faults for any phase of a transmission line. The training of the proposed ANN dcsign was done using purely sinusoidal waveforms’ magnitudes. Thus, before its implementation in a real power system, it is essential to remove the D.C. component, if any and othcr frcquency harmonics that exist in a power system to obtain voltage and current magnitudes as close as possible to the fundamental frequency. This can bc achieved by using antialiasing (low-pass) filters to remove high frequency components before sampling and a FIR filter to remove any D.C. component. These signals should then be scaled appropriately so that they can be inputted to the ANN to achieve desired results. To further test the feasibility of the proposed model

of the reldy in a real system, three other components were added to these computer generated current and voltage signals to make these signals “noisy”. These components comprised of a white Gaussian noise with a signal-to-noise ratio of 20 dB, 113 ratio of third

128

and 1/5 ratio of fifth harmonic components A third order butter-worth filtcr with a band pass of 50 and 70 Hz was then designed to filter out the fundamental frequency component These noisy signal? were then passed through the filter before being tested with the proposed ANN Figure 5 show? one of the original (in red), the noisy (in green) and the filtered (in blue) current signal waveforms The ANN was able to successfully produce the same results as described in Table 1 This procedure further proved that with the use of appropriate filters, the proposed ANN can be succcssfully implcmcntcd in a rcal powcr systcm

Figure 5: Noisy and Filtered signals

4.CONCLUSION A new design that fully exploits the potential of an artificial neural network for its application to protect transmission lines has been presented. The generic characteristics of an admittance relay were used to train an ANN so that the integrity of the generic relay characteristics is maintained. The trained ANN gave

good results for faults inside and outside the relay boundaries. Furthermore, the feasibility of the proposed ANN in a real power system was also tested by the use of noisy signals and it can be concluded that the results obtained were very encouraging. KEFEKENCES

Aggarwal R.K., Bennett A, Dunn R. W., Johns A. T. and Xuanii Q. Y. (1999), A Novel Classification Tcchniquc for Doublc-circuit lincs Bascd on Combined Unsupervised/Supervised Neural Network. IEEE Transactions on Power Delivei-y, Vol. 14, NO.4, pp 1250-1255. Balamumgan B and Vcnkatesan R (2001), A RcalTime Hardware Fault Detector Using an Artificial Neural Network for Distance Protection," IEEE Transactions on Power Delivery, Vol.16, No. 1, pp 75-82. Fernando, Ioni T. (1997), Protection of transmission lines sharing the same right-of-way, Ph.D. dissertation, University of Manitoba, Canada. Fcrnandez A.L.0 and Chonaim N.K.I. (2002), A Novel Approach using a FIKANN for Fault Detection and Direction Estimation for High Voltage Traiismission Lines, IEEE Transactions on Power Delivery, Vol. 17, No. 4,pp 894-900. Sachdev M.S., Sidhu T.S. and Singh. H. (1995), Design, Implementation and Testing of an Artificial Neural Network Based Fault Direction Discriminator for protecting Transmission Lines," IEEE Transactions on Power Delivery. Vol. 10, NO. 2, pp 697-706.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

A NEW NUMERICAL ALGORITHM FOR FAULT LOCATION ESTIMATION [JSING TWOTERMINAL SYNCHRONIZED VOLTAGE AND CURRENT PHASORS Chan-Joo Lee, Zoran Radojevie, Hyun-Hong Kim, Jong-Bae Park and Joong-Rin Shin Department for Electrical Engineering, Konkuk University, Seoul, Korea

Abstract: This paper presents a new numerical algorithm for fault location estimation which uses data from both end of the transmission line. The proposed algorithm is based on the synchronized phasors measured from the PMUs (Phasor Measurement Units) installed at both terminals of the transmission lines. Rased on the length of the transmission line, the proposed algorithms are divided into the short line (without shunt capacitance) and long line algorithm (with shunt capacitance). For the purpose of the unknown fault distance the phasor calculation method is used. The proposed algorithm is tested through computer simulations to show its effectiveness. Copyright 02006 ZFAC Keywords: Fault location, Arc resistance, Protection, Transmission lines, Spectral analysis, Two-terminal.

1 . INTRODUCTION

In the competitive electricity market, a rapid fault restoration on transmission line is faced with the quality of utility's power service. The occurrence of fault on transmission line provokes some economical losses and social problems. Moreover, the fault occurring on healthy transmission lines becomes a problem for the entire power system. From views of economics and quality of power systems, the importance of the accurate fault location estimation on transmission lines is increasingly. Distance relays respond to the impedance between the relay location and the fault location. These distance relays are mainly utilized for the transmission line protection system, sampling and analyzing voltage and current signals from the line terminals. It makes the decisions to trip the breaker when a fault occurs. With the modern distance relays and circuit breakers, the process of fault detection and tripping can occur as quickly as within 1.5 to 2 cycles (33.33 ins) from the time of occurrence of the fault. Distance relays calculate the fault distance in real-time, while the fault location programs are executed after the fault using stored fault data. However, the rapid progress in microprocessor technology give us a hope that some numerical algorithms devoted to fault location will be used as algorithms for distance protection (M. Sachdev, 1997). Therefore, in order to provide the service continuity to the customers and minimize the damage to the system and equipments when occurring the

fault on transmission lines, development of an accurate and efficient numerical algorithm is needed. To aid the rapid and efficient service restoration, many fault location algorithms have been proposed in the past (T. Takagi, et al., 1982, I. Zamora, et al., 1996, RadojeviC, Z., et al., 2002, Chi-Shan Yu, et al., 2002, J.A. Jiang, et al., 2000). Most fault location algorithms was to consider the use of data from one end of transmission lines, and several two-terminal fault location techniques have been proposed.

In this paper, a new numerical algorithm for fault location estimation, derived in spectral domain, is presented. The proposed algorithms are based on the synchronized phasors obtained by assumed PMUs installed at both terminals of transmission lines. Based on the length of the transmission line, the proposed algorithms are divided into the short line (without shunt capacitance) and long line algorithm (with shunt capacitance). To verify the validity of the proposed algorithm for the fault location estimation, the algorithm testing is provided through the computer simulations. Also, the results of algorithm testing through computer simulation are given. 2. SHORT LINE APPLICATION To derive the short line algorithm, it assumes that aphase arcing ground fault occurs on the transmission lines at .c! away from the sending end as shown in Figure I. Shunt capacitance will be neglected for the

131

initial discussion. In Figure 1 all variables have radian frequency h o and all line parameters are calculated in term of h(o. The fault point is denoted by F a t a distance 4 from the sending end (9.Here, index h denotes the order of harmonic, D is line length, subscript S and R corresponding to the sending- and receiving end of the line, respectively. Bus S

Transmission Lines

Bus R

where,

v;;),,?;;!,

l~

: the positive-, negative-, and zero

sequence phase voltage of the h-th harmonic at both ends of the lines, i (sph )' Rl>.U : the positive-, negative-, and zero sequence phase current of the h-th harmonic at both ends of the lines, 't;, ,, n : the positive-, negative-, and zero sequence faulted phase voltage of the h-th harmonic at the fault point, i('*): the positive- or negative sequence line impedance for the h-th harmonic, zOi'') : the zero sequence line impedance for the h-th harmonic. no

Fig. 1. Single-phase to ground fault on transmission line.

By adding the above equations and using the basic symmetrical component equations, the phase voltage and current of the h-th harmonic can be obtained:

The three-phase circuit from Figure 1 can be presented by the three qingle-phase equivalent sequence circuits of the faulted lines as shown in Figure 2. The three single-phase equivalent circuits are a positive (p), negative (n), and zero (0) sequence circuits, respectively.

and

The phase voltage of the h-th harmonic of sendingand receiving end is given by:

Fig. 2. Equivalent sequence network connection of the faulted line. For the equivalent sequence network depicted in Fig. 2, the following equations can be obtained:

and

where, i;") = (if)- i("))/ i(")is the zero sequence compensation factor, which can be calculated in advance. In this paper only fundamental harmonic fault model will be used for algorithm development because minimal number of harmonics needed for algorithm development is the first harmonic. Subtracting cquation (13) from (12), thc cquation for fundamental harmonic can be obtained:

The fault location t calculated as follows:

132

from equation (8) can be

Subtracting equation (18) from ( 1 9), one equation for fundamental harmonic can be obtained:

Equation ( 1 5 ) is the explicit fault location expression for the a-phase to ground fault on transmission line.

The known parameter (" from equations (16), (17), and (20) can be calculated as follows:

3. LONG LINE APPLICATION

If the fault location algorithm does not compensate for shunt capacitance in long line model, error of the fault location estimation may be increased. To estimate the more accurate fault location on transmission lines, the n line model is adopted to the long line application. The n line model is shown in Figure 3.

Equation (21) is the explicit fault location expression in long line model for the a-phase arcing ground fault on transmission lines.

Bus R

BUSS Transmission Lines

4. COMPUTER SIMULATED TESTS

}/

To test the validity of the proposed algorithm for the fault location estimation, the test was performed using the Electromagnetic Transient Program (EMTP). The schematic diagram of the power system on which the tests are based is shown in Fig. 4. Here v(t) and i(t) are digitized voltages and currents, and D is the line length.

Network .A

.1

D

I.

Network B

Fig. 3. Schematic diagram of the faulted system with shunt capacitance. In Figure 3 the unknown parameter !* is the fault distance away from sending end considering the shunt capacitance and is shunt admittance. Here the fault location t is calculated using the approximated formula (15).

From Figure 3 the positive sequence phase current of the h-th harmonic at both terminals of the lines can be obtained as follows:

where, i('*)"and i:: 5,

are the positive sequence

phase current of the h-th harmonic in the series impedance at the sending- and receiving ends, respectively. The positive sequence phase voltage of the h-th harmonic at sending- and receiving end is given by:

Fig. 4. Test power system. In this computer simulation, a synchronization error of 0 degrees is added to the test input data and the pre-fault load is present on the line. Single-phase to ground faults are simulated at different points on the transmission line. The left line terminal voltages and currents are sampled with the sampling frequency .h = 3840 Hz. 4.1 Cuse 1: short line model (without shunt)

In case of the short line model, the line parameters I' =0.0325 R k m , x =0.36 Rikm, are D = 100 h, ro = 0.0975 !2 /km and xo = 1.08 !2 /km. Data for network A are: R A = 1 C2, LA =0.064 H, R A O = 2C2 and LAO = 0.128 H. Data for network B are: RH = 0.5 R,LR = 0.032 H, RRO=1Rand LBO=0.064 H. The equivalent electromotive forces of networks A and B are E4 = 400 kV and EB = 395 kV, respectively. The fault resistance is Rr= 2 R and the fault inception is 33ms. 133

Results obtained by processing an example of short circuit with different fault point = 10, 20, 50, 80, 90 km) will be demonstrated. In Figs. 5 and 6 the faulted a-phase voltages and currents obtained by changing the fault location are presented, respectively.

(e

By processing input data, the calculated fault locations according to the variation of fault point are plotted in Fig.7.

- Sending End

zaB-;

i= 20km

0 16

36

57

77

97

117

137

157

I77

197

tlrre[ns]

Fig. 7. Calculated fault distances (exact values used by EMTP are 10,20,50,80,90km) Fig. 7 demonstrates clearly that the proposed algorithm i s not affected by different fault locations. Also, the calculated fault distances converge fast to the correct value after fault inception. For the purpose of fine analysis of the error and speed of convergence, Fig. 8 presents the relative errors for the cases depicted in Fig. 7.

J

time [rns 1

Fig. 5. Input faulted a-phase voltages and currents generated by EMTP at the sending end (! = 10, 20, 50, 80,90 km).

I

- Keceviiig Fnd

tirdmsl Fig. 8. Rclativc crrors in calculating fault location. As shown in Fig. 8, the relative errors obtained by changing the fault location are less than 0.01%. The reliable information of the fault dktance can be obtained in 20 ms after the fault inception.

I

I

‘I I

15 time Ims I

Fig. 6. Input faulted a-phase voltages and currents generated by EMTP at the receiving end (0 = 10, 20, 50, 80, 90 km).

To investigate the impact of different synchronization errors on the estimation of the fault distance, six synchronization errors are tested. The synchronization errors of 0, 0.125, 0.25, 0.5, 0.75, and 1 ms are added to the test input data. Fig. 9 shows the estimated the fault location with various synchronized errors. Here, the exact value of fault location used by EMTP is set as 10 km away from BUS S.

134

Table 1 Calculated fault distance for the different

002 Om OM

Om

00'

OCB OM 011 012 013 015 Olh 017 319 02C Ir l E I I B C 1

Fig. 9. Estimated fault location with various synchronized errors. As shown in Fig. 9, in spite of the synchronization error with 0.25rns, the fault distance is calculated almost correctly. Since a GPS receiver provides time synchronization to f Ip accuracy, the proposed algorithm for the fault location estimation is suitable for practical applications. From the algorithm speed and accuracy point of view, the results obtained confirm that the algorithm is useful for the application to real overhead line protection.

I I

1 1

250 280

2578580 2875740

I I

26193 25247

I I

2489560 2788860

I I

03480 03713

In Table 1 the maximum and minimum error calculated by considering the shunt capacitance are approximately 0.3 and 0.003%, respectively. Thc crrors of cstimatcd fault location with long linc are shown in Fig. 10. 3c3

,

4.2 Case 2: long line model (with shunt) In case of the long line model, the line parameters are D = 3 0 0 km, r = 0.1 Rikm, x = 0.36 Rikm, ro= 0.25 Rikm, ?co = 0.6 Rikm, c = 3.0 ,uF , and co = 2 . 0 , ~ f. Sequence impedance of network A are: ZAP - 5+j13 R , Z,, - 4+j10 R, and ZA0 3+j6 R . Sequence impedance of network B are: Z= , 5+j18 R, Z,, = 4+j 14 R,and Z,, = 3+j 19 R.The equivalent electromotive forces of networks A and B are E4= 133 kV and En = 100 kV, respectively. Here, network A and B are equivalent power system connected to sending- and receiving end of transmission line.

10

20

50

100

150

200

233

280

line leng:h[tml

Fig. 10. Errors of estimated fault location (D=300km).

~

For the long line (D=300km), the simulation results for the different fault points on transmission lines are shown in Table 1. Here, the first column of the table specifies the exact values used by EMTP. The second column is the calculated fault distance obtained by using a simple lumped impedance model and the last column is the calculated fault distance obtained by using a n line model. The fault location error to evaluate the algorithm accuracy, in percentage terms, is calculated using the following equation:

were, t , and C, represent the actual fault location and the calculated fault location, and D denotes the whole line length.

Since the shunt capacitances parallel to the fault resistance affect the accuracy of the fault location estimation, accurate compensation for long lines should be considered to develop the fault location estimation algorithm. From the test results, the proposed algorithm for the fault location estimation can be applied to the long line model. 6. CONCLUSION

This paper presents the two-terminal numerical algorithm for fault location estimation based on the synchronized phasors measured from the PMUs which are installed at both sides of the transmission lines. The proposed algorithm is based on the spectral analysis of the input phase voltages and line currents signals measured by numerical relay. Only findamental harmonic phasors calculated by Discrete Fourier Technique are needed for algorithm development. In case of the short line model, the proposed algorithm is extremely robust and fast. From the algorithm speed and accuracy point of view, the proposed algorithm is useful for the application to real transmission line protection. In case of the long line model, the shunt capacitance in order to obtain the more accurate result is considered. The proposed algorithm for long line model is relatively simple and easy to be implemented in the on-line application.

135

I I

ACKNOWLEDGEMENT This work is supported by the Korea Ministry of Commerce, lndustry and Energy (MOCIE) and Korea Electric Power Research Instituted (KEPRIj through IERC program. REFERENCES M.Sachdev (19971, Advancements in Microprocessor Based Protection and Communication, lEEE Tutorial Course Text, Publication No. 97 TP120-0. T. Takagi, et al (1 982), Development of a New Fault Locator Using the One-Terminal Voltage and Current Data, IEEE Transaction on PAS, 101, pp. 2892-2898. I. Zamora, J.F. Minambres, A.J Mazon, R. Alvarezlsasi, and J. Lazaro (1996), Fault location on two-terminal transmission lines based on voltages, IEE Proc. Gen., Trans., und Dist., 143, pp. 1-6.

RadojeviC, Z., Lj. Popovic, (2002j, Digital Algorithm for Distance Relay Including Grounding Impedance at Fault Place, European Transactions on Electrical Power(ETEP), 12, pp. 269-274. Chi-Shan Yu, Chih-Wen Liu, Sun-Li Yu, and JoeAir Jiang (2002), A New PMU-Based Fault Location Algorithm for Series Compensated Lines, IEEE Trans. on Power Delivevy, 17, pp. 33-46. J.A. Jiang, J.Z. Yang, Y.11. Lin, C.W. Liu, and J.C. Ma, (2000), An adaptive PMU based fault detectionAocation technique for transmission lines part I: Theory and algorithms, IEEE Tvuns. on Power Delivery, 15, pp. 486-493.

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Copyright 8Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlON$

COMPLETE FAULT ANALYSIS FOR LONG TRANSMISSION LINE USING SYNCHRONIZED SAMPLING Nail Zhang * Mladen Kezuiiovic * * Texas A&M UrLiverszt:y, Department o,f Electrical and Computer Engineering, College Sla,tion, 1;. 77843-3128,

U.S.A.

Abstract A complete fault analysis scheme for long transniission line represented with distributed parameters is proposed in this paper. The syiichronized samples from both ends of the transmission line are thc data sources for this scheme. The paper derives a speci c feature which equals to zero for normal situation and external faults, and is close to fault current diiriiig the internal faults. 1his feature is uscd for fault dctcction and classi cation Fault location is then implcnicntcd by selecting di ereiit methods according to the classi ed fault type. The results from a comprehensive evaluation study demonstrate an excellent performance of entire fault analysis. Copyrzght @2006 IFAC Keywords: fanlt analysis, fault detection. fault classi cation. fault location, synchronized sampling.

1. INTRODITC'I'ION

Aiitoniated fault analysis tool for transmission lines is vcry useful for on-line con rniatiori and o -line lrouble-slioot,ing. When it is used on-line, the system operator can obtain the detailed information about t he disturbances before he issues corrective coritrols. It ca,ri help correct the relay rnisoperalions a.s soon as possible to prevent tlie occurrence of a large-scale blackout. When used o -line, tlie disturbmces can be fully analyzed and the relay syst ern operat ions can be assessed in a very detailed way Wit,h the lasl development of signa.1 processing, computer and communication technologies, new approaches have been deployed in the fault analysis providing better solutions in faull delection, classi cation arid location. An expert system b a e d a,pproach is described in (Girgis a,nd .Johns, 1996) a.nd a phasor measnremeiit unit (P1cITJ) based a.pproach is described in (Jia,ng el

id., 2003). 'l'hose approaches depend 011 the phasor calculation. A neural network based fault a.nalysis tool is developed in (Oleskovicz et al., 200l), but it is hard to prcciscly obtain a, fault location since neural network is not good at precisely c l a sifying the continuous va,ria,bles. NIethods based on traveling waves and recently based on faultgenerated high-frequency transients have been used extensively in protection schemes (Chamia and Liberman. 1978; Ro et al.! 2000). Most of those techniques require very high-speed sampling rate which is still not widely used in existing devices. A time-domain fault lomtion techniqi.ie wa.s tleveloped at Texas A & N IJniversity (Keziniovic et al., 1.994). The digital fault recorder with Global Positioning Systerri (GPS) satellite receiver is the source of the data for this approach. Data from both ends of transmission line a.re used to achieve high accuracy of the fault location. This method will be more attractive when the concept of Wide

137

Area Measurcnicnl Syst,em (WAMS) and Phasor Measurement Unit (PAIU) are further developed. Previous e orts were aimed at implenient ing accurate fault location algorithms for short line represent.ed with lumped parameters aiid long liiie represented with distributed parameters (Kezuiiovic el d.,1994; Gopalakrishiian aiid Kezunovic: 2000). A conrplete fault analysis tool was proposed for sliort line (I<exunovic and Perunicic, 1996). Due to the e ect of shunt capacitances in long line, t,he wave propagation and t,he fa,ult, analysis principle is quite di erent from those in the short, line a.lgoritlnn. 'lhe developrnerit of fault a.nalysis schcrne can not shift to thc long line model directly. In this paper, a complete fault analysis scheme including fault detection, classi cat,ion and location is developed specially for long tra.nsmission line iriodel. 'lhe paper rst derives the tlieoret,ical basis in detail, and then designs the complete fa.ult a.nalysis scheme according to the derivat,ion in the 1-heoretical basis. At the end: a. comprehensive evaluation study is implemented to evaluate the statisticad performance of the proposed approach.

Fig. 1. A homogeneous transmission line

Fig. 2 . A faulted trmsmission line transmission line with the distance of Ax, as shown in Fig. 1. Corribiriirig (2) a.nd ( 3 ) to e1irninat.e ~ ~ - ~1)(and k i j P l ( k 1) we get

+

+

(4)

When there is no internal fault 011 the line, which means the line pa.rameters are lionlogeneous; equation (4) can be expressed as t h e relation hctwccn t,hc scriding end a.nd receiving crid samples. Sihstitutc j - I with S and j witahR and not,e t,hr tiirect,iori of 1, . Eqiia.t,ion (4) is clianged t.0

2. TIIEOKETIC'AL BASIS

where d i s the length of tlie trarismission line, P is tlie sample di ererice if the wave travels from tlie sending end to the receiving end with the time of PA2 I>e ne

For long transmission line represented by distributed parameters, the voltage a.nd current along the line a.re functions of tlie dista.nce li' and the time t ,

Similarly, we can get another form of equation (5)

mliere R,L , C are per-unit-length resistance, inductance and capacit,ance respectively. A discrete form of the solution of (1) is derived as follows (Gopalakrishnan and Kezunovic, 2000):

as

I

l',(k)

And de nc

= -[v7-l(k-I)+?,7-l(k+1)] 2

27,. +[Z,-l(k 2

- I) - i,-l(k

+ l)]

*

KAx [z,-l(~--I)+~,-I(k+1)]--

(2)

-Ki )A( xk ) 2

iL [G)-l(k 22

!,(k)=

1 +5[7,-,(k-

+

- 1) - G , - l ( k

I)+l,-l(k+l)]

R A5 ~

4 2

+ I)]

[Z,-l(k

When there is no internal fa.ult on the line, obviously & ( k ) and & ( k ) should equal to zero.

(3)

Now consider tihe situation of an internal fault. As shown in Fig. 2, at a certain time, the fault current and voltage at the fault point can be expressed a,s the signals from sending end and receiving end:

+ 1) - L1-1(k - I)]

where An: = A t / m i s the distance that tlie wave travels with a sampling time step At; .Zc =

+

z r . ( k ) = z,..s(k) Zi..]l(k) v p ( k ) = u , . , y ( k ) = ?,.),(A")

IS the surge inipcdancc. Subscript J is the position of the discretized point of the line and k is the sample point.

(9)

Note t h t , for long t,ra.nsmission line; i s ( k ) f i ~ ~ ( kand . ) i ~ ( k )# i ~ ~ ( due k . )to the traveling wavc issue. According to cquat,ion ( 5 ) , if we note

'lhe two equations de ne the relation of voltage and current samples between two poinls on the

138

the current direction for each current signal shown in Fig. 2, we have

wheie F‘s arid F‘R are the sample di eiences i f the wavr t iavels from the fault point to tlie sending end with the time of PsAt and to the receiving end with t h r tiinc of PRAf respectivrly d~ and CjR are the dirtiincr\ froin the fault point to the sending end and to the recriving end respectively

Substitute k with k - PR in equation ( l o ) , and rniriiis equation (11) to elirnindte ~ > F ( ~ - I ’ Note R) that P = P5 PR and d = d5 + d ~ then . the lefth m d side i s changed to

+

1s(k-P)

[

z.1

1 - - +z,q(k)

[If- 3+ ?: ~

P)>Rd 2 2,

First of all, use transformation rna,trix 7’ to transfer the line parameters and the measured phase values into tlie modal donmin,

It is noted that the translhrnmation matrix T and its inverse matrix have the unsymmetrical form. From equation (19); we can get the modal components with respect to the reference phase “a”. Siinilarly, we call get the rriodal conipoiients with respect t,o tlie pliases “b” and “c” bjr rothtiou. Note that the O-inode has the same form irrespective wlmt the reference phase is. We can get seven sets of modal components: [Zi(k).z ( k ) ] , ,[;u ( k ) .i ( k ) ] , , - , , 2 : [v(k).i ( k ) ] b L l 2 : [u(k).Z(II:)]‘--1,2 (20)

And the right-hand side is changed t o

For realistic transmission line, 2 RdIi 2,. << 1, then i < f l ( k )N ir.,(k - PI,)

2 <<

I and

‘I’hose components will he selected for the uses in fault detection, classi cation and location. From the seyirence network analysis, we can rid the a~a~ilability of each niodal component to detect the di erent fault type, as shown in ‘Table 1. It is noted that there is 110 unique modal component that can be used to detect all the fault types. ‘l’hat should be noted when designing the fault amlysis algorithms.

(14)

3. FAIJL’I’ AKALYSIS SCIIEhIE

Similarly, if we start from equation ( 7 ) ,we can get s,rz(k)

=2r(k

~

Ps)

(15)

With the help of synchronized sampling, the current and voltage samples used for calculating 7 d l ( k ) or 7ca(k)are available from tlie both ends of transniission line In our fault analysis scheme. z d l ( k ) is used as the main feature for long line modcl in faiilt tlrtcrtion and clessi cation Thc equations (2) and (3) are the recursive equations iised for farili local ion.

3.1 Fuull Delectaon

De ne

c,I? (.?I?!? 11

=

j=k-iL+l

N

k-N+2

,k (21)

Table 1. Availability of di eient modal components to correctly detect the different fault type

2.2 ‘I’hme-phase Calculation

0 -

~

For a three-phase system, all the line pa.ra.irieters and the measured voltage and current, signals sliould be traiisforined irit,o modal dorna.in 1 s t to get the tlecoiipletl systems and the derivation in previous section is still fill lled for each iiiodal component.

~

139

~

-

~

a1 ~

a2 ~

bl -

-

~

b2

Cl -

~

~

c2 ~

AG

J

J

X

J

J

J

J

BG CG

J J

J

J

x

AB Rr

X

X

X

x

CA AB‘G BCG CAC, A BC

X

J

J J J J

J J

J

J J

J J

J J J

J J X

J J J J

J J

X

J J J J J J 4 J J 4 J J J J J J J J X -J J J J J J J

J J

where r n is the related modal component. M is the iiurnber of samples iii one cycle. ‘The criterion for detecting an internal fault is given as m a s [ I , i l - , , - ~ ~ , I ~ - ! ~ - ~ , I , J I -1 , -TI ]I

( 22)

In equation (22): a threshold is set t,o tolerate the model aiid nieasurenient imperfection. ‘l’he average value of id1 ( k ) iii one cycle is conipased to that threshold. The calculation is carried out usiiig %l”, %-l”arid %l” modal components.

AEG

cy

ABC BCG

3.2 Fault ClasslYficatton

1Y

CAG

‘l’hrough sequence network analysis with di erent boundary condit,ions,we can nd the features for classifying the fault types using di erent modal components ( G e , 1993): as shown in Table 2. T h e entries in the table are the modal fault current components at the fault point. As derived in equation (14): i d 1 ( k ) i s directly rclatcd t,othe fault current with several samples delay. ‘l’herefore, we can use i d l ( k ) to design the fault classi cation scheme according to the Table 2.

Fig. 3 . Flowchart of fault classi cation Discretizethe line into equal segments with length of

An: build voltage profiles for each point using equation (2) and (3); do the calculation from sending end and

receiving end respectively

I Locate the approximate fault point by finding the point that has minimum voltage difference calculated from the two ends

1

The owchart of fault classi cation is shown in Fig. 3, where ‘ i d l - n has ideutical de nitiori as equal-ion (21). The thresliolds 75 and ?; are set to tolerate the nrodel and measurement inrperfection, as well as t-lie algorithm approximation.

Build a short line model surrounding the approximate fault point, and refine the location using the algorithm based on lumped line parameters

Fig. 4. Procedure of fault. location

3.3 Fuult Location 0

The fault location calcula.tion follows the rnctliods shown iri Fig 4. According to the fault type, the calculation will based on the selection of the prominent- modal components to achieve an aclcura.te result. ‘rhe select.ion scheme i s as follows: 0

0

0

For ground fault (A(:, RG, C G , ARG: BC,!G, CAG) the calculation is inipleinented using “mode 0” components. ‘I’he obtained fault location is thc na,l one. For AB fault: tlie calculation is implernented using (‘a-1” and “b-1” modal components,

0

‘I’he nal fault location is the average of t,he two results. For RC fault; the calculation is implemented using “b-1” and ‘(c-1” modal components. The rial fault location is the average of tlie two results. For CA fault, the calcihtion is irnpleinerittrd using “ ~ - 1 ”arid “a-1” rriodal components. The rial laull 1oc:atiori is llie average ol [lie two results. For t,liree-pliase fault, the calcula,tioii is implemented using %-I”, “b-1“ and “c- 1“ modal components. The iial fault location is the average of the three results.

Table 2. Features for classi cation of di erent fault type

-?.d Implementation

of

Entire Fuult Anulysts Scheme

Fault Type

4G BG

CG AB HC cA ABC BCC CAG RHC

The entire fa.ult analysis including fault detection, claqsi cafiou and location can be irnplenierited in tlie same software package. The owchart is shown in Fig. 5. The data window used for calculation is one cycle, arid the da.ta window is moving forwa.rd with selected time step At. The fault is detected if the equation (22) is ful lled for a. successive cycle. T h e n t h e post-fa,i.ilt values are used for f;tult classi cation and fault location, using the methods demonstrated in the previous sections.

140

Table 3. Test sets for performance study

Initialization, 1=0. count=O

.t

Obtain synchronized data from both ends

Cuscs

&

I=

Normal Condition

500

Mode Transformation

Calculate

I,, Extcrnvl Faults

500

Feiull ollault o e l e i i ~ o r

P

A

count=count+@t

A

=

Set 5

=

count 2 one cycle?

scheme shown in Fia. 3 OI

Fault location using selected

4

Generate Fault Analysis Report

I

Fig. 5 . Flowchart of fault diagnosis scheme rising syri cb 1'01 iized satnpl ing

Fig. 7. Result of fault detection scenarios each, as shown in 'lable 3. For each test set, the fault para.rneters are randomly selected from uniform dist.ribution of: all fault types, fa,ult distances (0 - 100%): fault resistances (0 - 50R), and fault inception angles (0 - 180").

4.3 Ilkst Results and Discussions

Fig. 6. Cent-erPoint Energy STP-SKY model

1. hlODEL IMPLEMEN'l'A'lION AND PE;KP'OKMANCE E VAL IJ A 1'1ON 4.1 Power System Models 'l'he proposed fault analysis scheme is evaluated using Alternat.ive 'l'ransient Program (A'L'P) (Alternntizie lkansients Program (AYP) - Rule Rook, 1992). Ari actual 345kV power system sect ion lrorn Cent erPoint Energy (Ristanovic el al., 2001) is used for various fault event sirnulat.ions. The STP-SKY line is the liiie ol interest. in this study, which is shown in Fig. 6.

4.,2 Generution

of

7kst Sceraurzos

The performance evaluation is based on randomly generated fa.ult scenarios, which ca.n dernorist.rate the statistical performance and robustness of the proposed scheme in all kinds of situations. There a.re ve test set.s generated in our study with 500

The test result shown in this section is based on the sampling rate of 2 0 K H z . 'l'lie sa,tnplirig rate does not a. ect the perforrnance of fault detection and fault classi cation. bul it will a ect the accuracy of fa.ult location. From Fig. 4)we know that if the sampling rate is higher, we tizc t,hc liric into more scgrnents. When building [lie sliorl liiie niodel, llie suspect area is narrowed to a small section of the transmission line. The error of fault location is not expected to bc largc then. The correctness rate of fa.ult detection arid classi cation are 100% for all given test sets. 'I'he result of fault. detection is shown in Fig. 7. The horizontal axis is the scenarios in the ve test sets, and the vertical axis is de ned as: Y = I ~ { V L O Z [ L ~ ~1. 1, 111 (23) IL

It is seen that the values of Y for the internal faults scenarios (Setl-Set4) are well di erentiable from the values for the external faults cases (Set5). Hence the threshold 2; in equation (22) is very easy to set. Similarly, the thresholds TJ and T, in fault classi cahon are also easy to select. An example of fault classi cation is shown in r / lable 4. 'l'he entries a.re ca.lcula.trd I d l - m with tli erent modal components in ten fault. types. We can cornpare with Fig. 3 to see the e ciency of the proposed approach.

141

Table 4. An example of fault classi cation result 0

a1

bl

C I

4.50Ef03 S.SIE-I 03

D.O6E+03

453E+03

5 . ~ 2n:3~ 5.15EfO3 2.56E+04

8 l5Ef03

2 56E+04

4 53F-03 6 81E 03 103E-04 7 02

~

AG

BC CG A5 BC

5.043+03

CA

1.16E-03

4RG

3.m~+113

3C'G C'AG

3.06Ei-I13 4.03EfO3 3.2lE-04

4BC

1.04E-03 i.n6~-03

1.163 104

+

a2

b2

ca

3.93

153E-03

4 53E+03

6.813 ! 03 5.18Ei03 8.54E+03

5 163-03 8 54F>-O3

1 71 E+O4

3.95

6.81E I 0 3 3 81

6.66

2.74E I 0 4

2 74E

1.32E I 0 4

9.13E 03

0.13E I 0 3

2.lOEf04 2.54E+04

6.66 a.GnEtn4

2 IOE-04

7.01Ei03

I40E-04

347~113

3.118Ef03

2.81)Ei-04

L hYE-04

Y . I I ~ E + O ~8.4317-113 1.X3E + 0 4 8.72E-03

7 02E+03 I .7113+04 9.XlE -t 0 3

2.OGEt0.1

3.Y8E+0:3

2 1FE-04

7.73E+03

l.40E-04

6.81E+O3

2.63E-tO4

3.3134-04

2 753. 04

1.833+04

1.40E---04

1.71E -104

JRctual Location - Computed Location1 Line Length

04

Ge, Y. (1993). New Types of Proteclive Relaying and Fault Locution, Theory and Techniques. Xi'an Jiaotong University Press. Xi'an, China. Girgis, A. A. and M. B. Johns (1996). A hybrid expert system for faulted section ident,i cation, fault type classi cation a.nd selection of fault location algorithms. MhY Del.ivery 4(2), 978-985. Gopalakrishnan. A . and M. Kezunovic (2000). Fault location using distribut transmission line model. IEEE Delivery 15(4);1169-1 174. .Jiang, J.! C. Clieii and C. Liu (2003). A new protection scheme for fa.ult detection, directiondiscrirriinatiori, classi cation, arid location iii tra.rmmission lines. IEEE Trans. POUJW Deli,~e'ry18(l ) ,04-42. Kezunovic, M. and B. Perrinicic (1996). Autoiriat.ed transiriission line fault. analysis using synchronized sampling a.t two ends. IEEE 7'ran.s. Power Systems l l ( 1 ) ;441-447. Kezunovic, M., B. Perunicic and .J. hlrkic (1994). An accurate fault locat>ion algorit,lim rising syrichronized sampling. Electric Power Systcnrs Rcscarch Jou,rnal 20(3), 161-169. Oleskovicz, M., D. V. Coury and R. K. Aggarwal (2001). A coniplet,e scheme for fault, detectiori, classi cation arid location in transmission lincs using mural networks. In: Proc. IEE Seventh Irit. Corif. o n Developments in Power System Probeclion,. pp. 335-338. Ristanovic, D., S . Vasilic and M. Kezunovic (2001). Design and implenientation of scenarios for rva1ua.ting a.nd testringdist,a.nce relays. Tn: Proc. Non'h. Arn,ericnn Power Symp.. College Station, TX. pp. 185-192.

For almost 90% of the scenarios, the fault location error is under 2%. 'The error of fault location for a single fault scenario is de ned as: error(%) =

I

(24)

1 h e average error Tor internal fault cases SetlSet4 are 0 547%. 0 576'%, 0 528% and 0 539% iespectively corresponding to about 0 8 rnile with respect to the h i e length of 167 44 miles The performance of fault location is less a ected by di ererit fault parameters, system operating conditions The results sliow tlie consistency of the cllgULItlII~1iUL edLll k b l 5t!l 'Illdl I S OUL' 01 Llle advantages using t wo-end synchronized data

5. CONCLUSION This paper proposes a complete fault analysis tool for long transmission line with distributed parameters. The calculation is carried out, in the tinre domain, t,herefore the calculation of a phasor is riot an issue in the proposed approach. With the a,vaila.bility of the synchronized data from two ends, the fault analysis can he very accurate. The proposed scheme can be iniplemented in an integrated soft.ware package as an add-on function for digital fa.ult recorder. The comprehensive study in this paper proves the excellent performance of t>lie proposed fault analysis tool.

R.EFER.ENCES

Allernative Transienls Program (ATP) - Rude Book (1992). CanArri EMTP User Group, Portland, OR. Ro, Z.Q.. F. Jiaiig, Z. Chen, X. Dong, G . Weller and M. A. Redfern (2000). Transicnt- ba.scd protection for power transmission systems. In: Proc. IEEE PES Winter Meeting. Vol. 3. Singapore. pp. 1832-1837. Chamia, h l . and S. Liherrriari (1978). Ultra high speed relay for EHV/IJHV t,ransrnission lines - development, design and application. IEEE Y h n s . Poirier Apparatus and S?/stems 97, 2104 2112.

142

Copyright 0Power Plants and Power Systems Control, Kdnanaskis, Canada 2006

PUBLlCATlONS

Study on the establishment of dynamic performance test environment for the digital protective relay using RTDS ByungTae Jang, ChangYoul Choe, GilJo Jung

Abstract: A performance test of'digital protective relay is divided into three parts ; a static test, a dynamic test, a EMC test. Among these, a dynamic test is increasingly important, but it is not easy to diffuse a technique for dynamic test because of the intricate approach to real time digital simulator. In order to solve these problems, KEPRI(Korea Electric Power Research Institute) has established en\ ironments for performance test, which consist of a system model and a performance test procedure for the dynamic test. Copyright 02006 IFAC Keywords: Dynamic test. K1 DS(Keal Time Digital Simulator), performance test procedures.

1. Introduction

In Korea. most ofpower system protective relays are introduced and operated in KCPCO(Korea Electric Power Corporation). The transmission line protective relays were digitahed Grrt, so that currentl) most of the transmission line protective relaj s use digital protective function. 1he digital protective relays for bus protection and transformer protection were recently introduced and they were started being applied in the field system. Also trip signal or alarm signal is generated through the sequence logic in order to be used the rewlt of multiple protection relay element under various conditions. When considering these characteristics. the necessity of verification for comprehensive operational characteristic on various fault conditions comes to be more emphasized than general static test. Conscqucntly, both thc standardizcd systcm modcl and performance test procedure are necessary Tor amicablq performing dqnamic test of digital protcctivc relays. Thiq paper describes a process o f estahlishment of an environment for d j namic performance test and its results through the protection forms used in KCPCO. 2. Subject

2 I KEPRIS dynnmic test equipmenis. KEPRI has 26 RTDS racks. 12 current and voltage amplifier panels and 4 optical isolation cubicles for dqnamic test. Components of each equipment are as follows.

- RTDS rack -

-

: 3PC card X 12, lRC(lnter-Rack Communication) card X 2. WIF(Workstation Interface) card X 1 Amplifier pancl : 8 channels of amplifier(current channels of A, R. C, N and voltage channels of A, B, C, N ) - lEC3620 model produced bj Techron Optical isolation cubicle : IMC(1nterface MUX Card). llC(lso1ation Jnterface Card)

Fig. I . RTDS Lab in KEPRI 2 2 Suggested perjorm~ancetest procedures.

In Korea, 765kV, 345kV and 154kV class substations are being operated. This paper describes an establishment of performance test procedures for protective relay excluding 765kV. - 154kV transmission protective relay using DCU(directiona1 comparison blocking) scheme - 154kV transmission protecthe relay using PCM current differential scheme - 345kV transmission protecth e relay using DCB(directiona1 comparison blocking) scheme - 345kV transmission protcctivc relay using PCM current differential scheme - 154kV bus protective relay using current differential schcmc - 345kV bus protective relay using voltage differential scheme

143

-

154kV transformer protective relay using current differcntial scheme - 345kV transformer protective relay using current differential scheme

In addition to performance test procedures referred preLiouslq, u e made out a PSCAD and a RTDS application procedure in order lor users who are poor to use PSCAD/RTDS to easily use. - PSCAD application proccdurc - RTDS application procedure

2.3 R TDS procedure

Cl;

PSCA D procedure.

Differing Crom the general test equipment, RTDS has a strong point to examine real time close-loop test. However. since users should articulately use both software (PSCAD) and hardware (RTDS). it is difficult for thc users to access a dynamic performance test. In order to solvc thew problems, we produced PSCAD and RTDS performance procedures to test protective relay. PSCAD procedure includes using methods for DRAFT Module, RunTimc Module and T-Line Module, and each component and composition method of enbironments for system simulation on DRAFT and sequence. Also, it includes connection methods with cxtcrnal devices, composition procedures of DRAFT and disposal methods in case of error generation. liegarding the R I D S procedure, we described in detail the cornposition o f hardware, and tuning methods of analog output signal. Also in order for users to easily use the hllowing contents, we described principals of operation, using methods, examples ofreal connection and so on. - Using method for analog output of K I D S - IJsing method for TripiClow input of protcctivc relay - Providing method for contacts signal of circuit breaker to protective relay - Input method for TripiClose contacts using optical isolation cubicle 2 4 Process of performance test.

In order to carry out respective protective relay performance test referred previously. ~e have to accomplish test following figure 2 .

I

~ @

Q

1 2

Fig. 2. Process of performance test 2 4 I System modeling

System modeling means that we construct sy stem environments which are same as real power system. and inputhutput logic of analogidigital signal for communication between RTDS and protective relay

in PSCAD module. In this paper, in order to construct most general test enkironments, we accomplished system modeling to be equal uith general substation environments in Korea. This paper proposed basic models to test 1541345kV transmission protcctive relay, 154/345kV bus protective relay and 1541345kV transformer protective relay. Also several kinds ot models are added to procedures according to test elements. For example, in case of performance test model for 345kV transmission line protectike relay, it is separately composed of system models foi testing SOTF. heavy load flow. STUB and current reversal, in addition to the basic model. Also regarding performance test model fix 345kV transformer protective relay, performance tests of distance scheme used in secondary protection have to be considered and, therefore, qystem models are subdivided into primary side fault model, secondary side fault model. and so on. In addition, test model such as inrush current tert model and overexcited model should be separatelq considered. Figure 3 shoms a part of basic test model for 154kV transmission protecth e relay.

1;

”:

”’

T I II

~

P

”I

~

Fig. 3. A part of test model for 154kV transmission protective relay

2 4 2 Parameter setiing We have performed system modeling by using equivalent impedance data of transmission line, equivalent impedance data of bus and no load loss data of transformer. And these data ale reflected a field system as much as possible. Each test procedure contains a method to transform a field system data into a parameter required for PSCAD. And according to the test type. parameters required for setting are arranged and contained.

~

Q

2 4 3 Hardware setting

Hardwarc sctting mcans analysis on 3PC card. IRC card, WIF card, HVIF panel. ODAC16 card, CBUS controller, amp for amplification of current and voltage and Optical lsolation Cubicle. And it also means connecting activities betmeen RTDS and protecthe relay. The establishment of testing environment is dependent on the case whether it

144

~

applies to the protective relay, the protective relay panel or what t)pe ofrela) used. Figure 4 shoms a test environment for 345kV transmission line protective relay using PCM scheme.

#1 Bus Bus PT phase B

Bus CT phase A 0.C

Section 4 - Iest for current differential scheme external fault Section 5 - Test for Multi-fault Section 6 - Test for Evolving fault Section 7 - Test for Breaker failure function Section 8 - Test for 27D function Section 9 - Test for detection of CT saturation Section 10 - Test for detection oI'PT failure Section 11 - Test for detection of DS failure Section 12 - Test for detection of CT open Section 13 - Test for Bus Tie Blind function Section 14 - Test for Bus Section Tie Blind function l'here are explanations on prepared system model, data transformation on each constructed item, input cxamples and fhult simulation method in thc section I.

I

1110

Contact x 6

Close Contact x 6

I

Fig. 4. Hardware setting - Test for 345kV TlL protective relay using PCM scheme Especiallj, in case of the dynamic test for transmission line protective relay such as ligure 5 , in order to kerify the reclosing performance. the trip and close signal of protective relay should be provided to the KTDS and state information (52a or 52b) of circuit breaker in PSCAD needs to be provided to the protective relay. Figure 5 shows a connection to transmit a signal of contacts. The left side of ligure 5 shows a connection to transmit a state information of circuit breaker to protective relay. The right side of figure 5 shows that 3 phase trip and close signal are connected to the optical isolation cubicle in order to test a 1+3 high speed one shot reclosing performance of TlL protective relay.

There are explanations and examples needed for testing of protective relay in the section 2 . In other sections. there are meaning of relevant test, location and certain terms of fault and detailed test procedures and test report. 2.4.5 7est

In order to verify the suggested system model and secure the reliability of test procedure. we performed a dynamic performance test using following protective relay. - Protective relay for I54kV TIL + MDT-F(Mitsubishi. Japan) + 3 11L-7( SEL, America) - Protective relay for 345kV 1 /L + 3 I 1 L-7(SEId. America) - Protective relay for 154kV bus + MBP-IIl(TMT&D, Japan) - Protective relay for 345kV transformer + GRT 1OO(TMT&D. Japan) + GRZlOO(TMT&D, Japan)

I- ig. 5. 1eCt)connection fur CB conkacts to relay right)connection for triplclose signal to R TDS

2.4.4 Test item In every performance test procedure, test items based on the protective relay type are constructed as a reference of purchasing specifications of KEPCO. And each performance test procedure could be applicable independently. Contents of a performance test procedure for 154kV bus protective relay are as follows. Section 1 - Construction or an environment for PSCAD Section 2 - Construction of an environment for RIDS Section 3 - 'lest for current differential scheme internal fault

Fig. 6. Digital protective relay used for performance test Among the above protective relays. SEL-3llL-7 model is used for testing of transmission line protcctivc relay. And TMUX2000 models, produced bq IiFL corporation. are used for communication devices.

145

1w'o communication devices are mutually connected through 2 kilometers optical cable. Figure 7 shous a runtime module of PSCAD for 154kV transmission line protective relay using DCB scheme. And figure 8 shows a part of multi-fault test which generates simultaneously an internal ( 1 00ms) /external (2.000ms) fault.

a@*

8-

0-

Q

Fig. 7. I'SCAD Runtime module l'or 154kV T/L protective relay

3. Result We elicited test items, conditions and methods for each protective relay through the analysis of dynamic test procedures performed at home and abroad. And we hake performed an analysis regarding the manual of RTDS(3PC). the manual of PSCAD(Version 2.2), doinestic and abi oad technical data and thesis. Based on this analysis, 17 sqstem models and 10 pcrformancc tcst proccdurcs havc bccn madc out. Prepared system model and performance test procedure enable for users to convenientlj and easily test a protective relay with attached standardked yystem model and procedure When carrying out performance test of the digital protective relay by using RTDS in domestic and overyeas organizationq, engineers can utilize this procedure for examining reliability and propriety in terms of the result of performance verification test. In addition, in the case of the development and performance test of IED wihich would be a core component of substation automation syqtem, these procedures ma) be applied as a basis of verification for protective algorithm built in the IED

Trial Normal mnditior (Runtime Menu)

REFERENCES

Verification Target of relay

Verification TripiClose timr

4

I

Makeoutarepon

I

Fig. 8. Process of multi-fault test Each number of figure 8 are referred to each section of identical number of runtime module in figure 7. Area 8 and area I I of thc figurc 7 show a state of circuit breaker. and current, voltage. etc., respectively.

[ I ] MOCIE, "System modeling and establishment of procedure for performance test of digital protective relay", 2005.4 12 [ KEPCO, "Correction guide of digital protective relay", 1999.1 131 KEPRI, "RTDS hardware - Development and installation for analysis ofpower system", 2001 .I0 141 KPX, "A draming of electric supply system". 2002 151 Youho Electric Corporation, "A Drawing for 1 S4kV Bus Protection Panel (lOF/D, DUAL)" [6] Seondo Electric Corporation, "A drawing for 345/154123kV transformer protection panel" 171 SEL. SEL-3 11L-7 Relay Instruction Manual [8] M. Kezunovic, Y. Q. Xia. Y. Guo. C. W. Fromen. D. R. Sevcik. "Distance Relay Application Testing using a Digital Simulator", IEEE Transactions on Power D e h e r y , vol. 12, no. 1, pp. 72-82, Jan. 1997.

2 4 6 Test report

Each procedure contains a test report in order to record results and particulars and to test various essential items. Figure 9 shous a test report which records a result of short term fault test of 34SkV transmission line protective relay using LICB scheme.

Fig. 9. A part oftest report

146

Copyright

0Power Plants and Power Systems Control, Kananaskis, Canada 2006

HYBRID HVDC CONVERTERS AND THEIR IMPACT ON POWER SYSTEM DYNAMIC PERFORMANCE B. Qahraman”, A. M. Cole*, 1.T.Fernando’ “Dept. ojElectricul and Computer Engineering, University qf Manifobu, ’Sysievri Plunning Depi., Munilobu Ilydvo

Abstract: Hybrid converter HVDC transmission is a new hybrid transmission system for connecting two AC systems. Because it uses different converters, this new configuration offers several advantages over conventional HVDC systems. This paper demonstrates the superior performance of hybrid converter based HVDC transmission systems with respect to increased stability and terminal ac voltage control. A control system is developed for the hybrid system and its dynamic performance is investigated. The hybrid system performance with emphasis on commutation failure during severe disturbances and its results is also compared with a conventional HVDC scheme. Copyright 0 2006 IFAC Keywords: HVDC converters, hybrid converters, Voltage Sourced Converters, simulation, coordinated control

1. NTRODUCTION The conventional HVDC transmission systems that utilize Line Commutated Convcrters (LCC) have advantages over HVAC systems such as their ability to connect ac networks non-synchronously and their ability to carry power economically over large distances. Unfortunately, these schemes do have certain disadvantages such as a need for reactive power, commutation failures, higher over-voltages and poorer recovery especially when they are connected into weak terminating AC networks. Unlike the LCC which relies on the ac voltage for successful valve commutation, the Voltagc Sourced Converter (VSC) uses special devices that can be turned off with appropriate control signals. While maintaining most of the advantages, VSC based HVDC schemes also overcome a number of disadvantages inherent to conventional systems. Rather than consume reactive power, their ability to generate lagging or leading reactive power permits them to operate and provide voltage support to very weak ac networks. Thus they are an ideal option for providing reliable power to remote locations such as offshore plants. Their disadvantages include higher costs, sensitivity to DC side faults, higher power losses due to the high frequency of switching, and smaller ratings in comparison to conventional LCCs. Appropriately sized VSC and LCC converters can be incorporated into a single composite “hybrid’ converter which combines the lower costs and robustness o f the conventional LCC converter, at the same time introducing the additional benefits of the VSC converter. Several dirferent topologies suitable

to such combination have been proposed in literature (Andersen, et uL, 2004). This paper introduces a hybrid topology which includes a series dc-side connection of an LCC and VSC as shown in Fig. 1. The paper studies dynamic control performance, fault recovery transient performance and commutation failure susceptibility of the proposed scheme and shows it to be superior to a purely conventional LCC based scheme.

2. PROPOSED HYBRID CONVERTER The hybrid topology may employ the LCC and VSC converters connected either in parallel or series on the dc side More complex schemes may not be justified easily due to control complexities, expcnscs, nced for larger space, etc In a parallel hybrid configuration the converter voltage rating is limited to the highest voltage level permissible for the VSC converter, which is much 1OWt.I thdll that Or d COUlpdIdble LCC drld consequently limits the power rating of the topology The proposed hybrid converter is labeled a “Series Hybrid Converter” (SHC), as it includes one LCC dud one VSC in senes In contrast to some earlier approaches in which the VSC is only used for reactive support (Andcrscn, et al , 2004) or for active filtering (Jiang, et a / , 1998) the proposed topology uses both converters for real power transfer

147

3.BAISCS OF THE PROPOSED SHC SYSTEM

4. CONTROL OF THE SHC SYSTEM

MODEL The schematic for the proposed SHC has been depicted in Fig. 1. The sending end (rectifier side) has been assumed to be a LCC converter station and the receiving end (inverter side) is a LCC - VSC series connection; along with its harmonic filters. The 1000 MW "Firsf CIGRE HVDC Benc,htriark Syslern" (Smhtiiian, el u/., 1991) has been used as the test bed for evaluating performance. The Rectifier's LCC is structurally identical to that of the CICRE benchmark. At the inverter side, the VSC used is a modified version of another paper (Qahraman, ef ul., 2004). Considering the VSC's rating, the LCC has been re-sized so as to keep the overall ratings identical to that of the CICRE benchmark systems.

The system dcsign philosophy has been based on two control objectives: 1) Terminal voltage of the hybrid converter must be maintained at 1 P.U. 2) Power delivered to terminal during normal working conditions must be I P.U. The SHC control block diagram has been shown in Fig. 2. In this figure the upper and middle parts depict the rectifier and inverter angle controls, respectively. The bottom part illustrates the VSC controls

The hybrid converters' voltage / power ratings were derived based on an optimization conccpt. The pertinent data are given in Appendix. The major part of the inverter's real power demand (P,flv)is delivered by LCC and the unsupplied part will be generated by VSC (Pvsr). + phase

Fig. 2 SHC's control block box

1

lrnoedance

1

The basis for SHC controllers 1s a coordinated version of LCC-HVDC (Siechtman, et ul , 199 I ) and VSC-NVDC system (Andersen, 2003) controls

converter

Fig. 1 Scries hybrid inverter schematics

In the SHC presented here, the rectifier's LCC works in current control mode while the inverter's LCC works in extinction angle (y) control mode, using the current control as its backup (Gole, et u l , 1995) The current order signal that would end up to LCC's inverter angle order (a,,,%) is outputted from terminal power error signal

The LCC generates voltage harmonics but as the VSC switches at rather high frequencies (around 15 KHz) it will only add high frequency harmonies to the system. To canccl out thc dctrimcntal effects of these harmonics and help to meet the system's harmonic requirements filters have to be installed. These filters will provide voltage-dependent Q supply to the inverter side. The major filters installed in the hybrid are 1It", 13"'and 23'd for LCC and 2Yth harmonics of the fundamental frequency (60 Hz) for VSC. The 25'" is in common use for both. The total filter reactive power is around 80 MVAR.

The VSC inverter control system shown in Fig 3 hai two degreei of freedom The firit is uied by the VSC's DC voltage capacitor controller which signal The generates the reference real current (ItliLi) second is used to control the terminal voltage via the reference reactn e current (Iqre,) signal

During the steady state conditions the VSC has to provide the un-supplied reactive power needed Tor the LCC converter. It has also to supply the extra reactive power during the transient conditions to provide voltage support at inverter terminal. The ability of VSC to supply voltage support depends on its electrical rating and the coordination between LCC and VSC controls. The dynamic response is also a function ol'the DC capacitor(s) size. A suitable dc capacitor size has been selected to give an acceptable dynamic response; however, in this paper, no attempt has been made to optimize this perfectly.

A phase locked loop (PLL) is used to synchronize with the ac network voltage and generates the synchronizing dngle signdl (0) which i s used to generate the Iiring pulses for the IGBT devices of the VSC

The d and q current errors are used to generate the and 7,) through a corresponding voltage orders (7, dccoupled controller block These are converted into a modulation index magnitude (m) and phase (4) signal

This paper describes the principles o f the proposed SHC system along with its main control strategies including the terminal voltage control, real power control at the iccervrng end and invcrtei DC capacitor voltage control I

I

Filters will reduce the harmonic content o f voltage to meet the standards for harmonic le\els

Fig. 3 VSC control in SHC

148

I

5.OPERATlON ISSUES IN HVDC SYSTEMS

parameters for the controllers were selected for overall performance and were not optimized for any particular disturbance event.

5. I Commutation Failure Phenomena

5 3 SyAtem step response

Commutation failure (CF) i s one of the most onerous transient events experienced by HVDC systems. Its causes include sudden transient reductions andor phase shifts in the ac voltage and sudden transient reductions in the direct current. The sensitivity of a HVDC inverter to CF depends on the main circuit design and its control system. In conventional converters, commutation failure likelihood is significant when there is a 10% or larger voltage reduction caused by an AC system disturbance 0.

To investigate both systems’ responses to set point changes. the conventional (CIGKk benchmark) Lonverter option was subjected to a IOYO changc in power order Also as the hybrid system operates directly in power control, its controller was subjected to a 10% change in power order The results are shown in Fig 4 In the system with the conventional converter only, the steady state terminal voltage settles to a different magnitude after the change is applied, due to the resulting mismatch in reactive power. As the VSC in the hybrid control option is capable of reactive power generation and is tasked with maintaining the ac voltage at rated magnitude, the ac voltage eventually returns to its post-fault magnitude.

The main reason for CF is that the excessive reduction in the extinction angle during its initiating system disturbance. This decrease could be caused by an increase in the converter’s overlap angle due to ac voltage reduction or due to a change in the commutation margin resulting rrom a sudden change in the ac voltage phase. Having larger commutation margin in normal operation improves the system’s CF susceptibility, but this also results in a poorer powcr factor and potential over-voltage problems on load rejection.

As can be seen from Fig. 4 both options show a quick and well damped response to the set-point changes. However, the VSC option shows a smaller settling time with a slightly oscillatory response.

In a conventional HVDC converter, the fault induced CF leads to power disruptions. In some cases there are repeated CF occurrences from which rccovcry i s not possible without a full restart. Additionally, CF also causes over-current in the valves. The VSC in the hybrid HVDC conkerter cannot CF T ~ I U S HVDC trdrlbrrllbblOll systerris W I ~ hybrid converters are less susceptible to CF related power disruptions Aluo, the same fault which would have resulted in serious system failure in the conventiondl converter hds a much Tmdller impact on the hybnd converter burrel

The disruption of the normal switching sequence following a CF will lead to considerable wavelbrm distortion of the commutating voltage waveform making the problcm unsuitable for analytical formulation. Thcrefore numcrical simulation on an electromagnetic transients solver is required to assess the behavior of the system. Here the PSCADiEMTDC software has been selected for simulating the system and studying its behavior.

Steu Resuonse O P t (CIGRE)

2

10PtiHYbridl

~ I

OEt(CIGRE)

-

a 3

F

P

O . 7

0.80 T k )

0.h ’

0.h

’ 0.b ’ 0.60 ’

0.b

1.h

Fig. 4 Small dynamic disturbance responses 5 2 Dynamic Response and Faull Performance A well dcsibmcd HVDC system should show reaLt rapidly to set-point changes and also show rapid recovery from system faults In order to assess these issues, the dynamiL behavior of CIGRE benchmark and the proposed scncs hybrid convcrter HVDC systems will be compared The hybnd’s robustness Urlder srUd11 drld large dyIldrrilL dlbtUrbdrlLeb W i l l be demonstrated Next, the two HVDC systems will be compared by simulating their performance rollowing singlc and 3-phase to ground faults of carying %verity

6 CASE STUDIES

The following section contains simuldted results for the dynamic and fault perlormance of the conventional and hybrid HVDC alternatives The

5.4 System fcarlt response

To investigate both systems’ responses to large dynamic disturbances a symmetrical three phase short circuit to ground at the inverter terminal was applicd for 0.1 second (6 cyclcs) to cach systems’ terminals. Various fault impedances were used, but the case reported below only shows the response to the most severe fault which is a solid short circuit that reduces the terminal voltage to essentially zero. One difference between the two systems is that in the hybrid case the arrester connected across VSC’s DC capacitor limits the over voltages of DC capacitor to 25%. Fig 5 shows the pre and post fault terminal voltage and power curves obtained based on applying such a fault In comparison to the conventional option, the hybrid option shows significantly faster

149

power recovery with 90% power restored wiihin 200 ms after fault clearance The corresponding conventional option requires approximately 400 ms

Fault Response 0

1.20,O Pt( H v b r i d '

1.20,

2

-0.20

T(SeC)

0 Et( Hvbr i d )

Pt ( C I G R E )

oEt(CIGRE)

J

0.60

'

oh

'

0.b '

0.60

' 0.b ' 1.h

Fig. 5 Large dynamic disturbance responses However, the conventional option shows a more gradual voliage recovery without any over voltage strcss on thc cquipmcnt Thc hybnd option, on account of its voltage control function, causes the voltage to be rapidly regulated, and in doing so experiences a modest 10% over voltage dunng recovery.

5.5 Commutution Failure perjorruunce Several other tests were conducted with vanous different fault impedance values (inductive) to investigate the impaci of fault severity on the pei formance The VSC showed geiieially supeiior fdult recovery times in all cases Also for certain less wvcre (high impedance) faults, the Lonventional converter bayed system expenenced total power loss whereas the hybnd system managed to continue operation during the faulted period Fig 6 show., the lowest ac voltage and power magnitude? reached dunng the fault for varying fault induciance values Both three phase-to-ground as well as single phase-to-ground faults were applied As can be seen the hybnd converter was able to maintain Lurrcnt and powcr to abovc 90% cvcn with fault impedances of 1 H or higher for both types of fault, whereas the conventional converter starts experiencing similar reduction? at a much less severe fault inductance of 2 5 H Fig. 7 shows the extinction angle (y) and power variations for the two options subjected to three phase and single phase faults of varying inductance. Again, for the conventional case a fault with 1 H inductances causes cornmutation failure (three phase fault) whereas the hybrid converter only experiences commutation failure (of its conventional converter) for three phase faults severer than 0.5 H. The ranges for single phase faults show similar trends with fault and converter types, but the fault severity required to cause failure is marginally smaller for each case

Single and three 3.phase fasult responses

+Hybnd, 3phase +CIGRE, 3Phase ..Om1 H$rid,lPhase ~~+~lCIGRE,IPhase

Fig. 6 LPV curves

150

-0.2

Fig. 7 LPG curves The above tests were conducted with the short circuit ratio of the ac system set to 2 5 , which conyidered fairly low and hence expected to cause challenges for the transmission options IHowever, because o f the VSC’s fdst dyrrdrrri~ iesp~nst:to reactive power demands the proposed hybrid converter also bas the unique capability of working under even lower short circuit ratios (SCR) where the conventional convcrtcr would not be able to operate at all

u

Gole, A.M., R. Verdolin and E. Kuffel (1995). Firing angle modulation for eliminating transformer DC ctrrrents in coupled AC-DC systems. IEEE transactions on Power Delivery, Volume 10, pp.

2040-2047.

Jiang, M. and A. Ekstrom (1998). Harmonic cancellation of a hybrid converter, IEEE transaction on Power Delivery, Volume 13, pp. 1291-1296. Qahraman, B., E. Rahimi and A. M. Gole (2004). An electromagnetic transient simulation model for voltagc sourced converter based HVDC transmission, Canadian Conference on Electrical and Computer Engineering(CCECEU4), Volume 2, pp.:1063 1066. Thio, C.V., J.B. Davis and K.L. Kent (1996). Commutation failures in HVDC transmission systems, IEEE Transaction on Power Delivery, Volume 2, pp. 946-957. Szechtman, M., T. Wess and C.V. Thio (1991). First benchmark model for HVDC control studies, CIGRE, WG 14.02, Electra, No. 135, pp. 54-73. ~

7. CONCLUSIONS

Using a coordinated controller for a SHC (Series Hybrid Converter) HVDC transmission system results in superior inverter terminal performance in response to small and large dynamic changes in comparison to a conventional converter case (CIGRE benchmark). As such, the proposed configuration may be counted as a promising configuration for delivering real power to systems that feed more sensitive loads. Using digital time domain simulation with PSCAD / EMTDC program and cmploying convcntional closed-loop structures it has been shown that stable operation of the proposed configuration can be insured in a broad range of operating conditions without resorting to complicated control strategies with thc addcd benefit or superior system performance (less power / voltage drop, less chance of commutation failure and shorter recovery time using equal fault inductances).

REFERENCES Andersen, R R (2003) Voltage Sourced Converters, CIGRE report, B4-37, pp 35-37 Andersen, B R and L Xu (2004) Hybrid HVDC system lor power transmission to island networks, IEEE Transaction on Power Delivery,” Volume: 1 9 , pp 1884- 1890

APPENDIX : MODEL DATA HVDC system rating: 1000 MW; 500KV DC Line parameters: As per CIGRE benchmark model. Rectifier electrical specifications: As per CIGRE benchmark model. See: (Szechtman, el a1.,1991). Inverter electrical specifications: SCR: 2.5; LCC converter: 390 KV; VSC dc voltage: 1 10 KV.

PI controller parameters: Rectifier: K=0.8, T= 0.08 / LCC Inverter: K=0.6, T=0.08 / VSC voltage controller: K=l.l, T=0.4 Terminal voltage controller: K-0.1, T=0.4 Decoupled controller parameters: K(Id)=0.6, T(Id)=0.3 ; K(Iq)-0.45, T(Iq)=0.38 Terminal power controller parameters: K=0.55, T=0.06

151

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

PREDICTING TRANSIENT INSTABILITY O F POWER SYSTEMS BASED ON HYBRID SYSTEM REACHABILITY ANALYSIS Yoshihiko Susuki * Hiroaki Ebina * Takashi Hikihara *

* Department of Electricnl Engineering, Kyoto Universitv, Katsura,, Nishikyo, Kyoto, 615-8510, J a p n

h b s h c t , : This paper s11ovr;sa novel met,hod for predicting t,ra.nsiemt,instability ol' power syst,erris based on reacha.bilit,yanalysis of hybrid syst,eins. The analysis is performed by computing reac:hable sets of uiisafc sets in iioiilinear hybrid ;i.ut,oinata. that, represent, bot,h cont,inuous e1ect)rc-mechanical dynamics of generat,ors and discrete operations by relay devices. The unsafe sets hcre arc subsets of syskm states in which pom7er syst,enis show unaccepta.ble operations such a,s stepping-out, of generators. Then t,he t,ransient>instabilit,y of power syst.ems ca.n be est,iInat,ed by investigating whether a systmi st.atc exists in t,lie rea,c.liablesets or not. The est,iinat,ion is possible at. any oiiset of accident.al f;Lult,s such as line and plant. t,rips. This paper demonstxates the proposed method through an analysis of singlemachine infinite bus system. Keywords: power systems; models: transient stability analysis; hybrid modes: reachability

1. INTRODUCTION

Tlicrc is grcwiiig rccognit,ioii t,l-la.t, blic dynamics of electric power systems become cornplicat,ed as tlic current cliangc of tcdinological bascs and ocoriorriic crivironmciit, (Fairlcy 2004, Gcllings anti Yeager 2004). As a technological aspect, various including HVDC systenis and FACTS arc applied to convcntional ac traiisnrission systems. As an economic change, regulatory reforms of electricity markets require a subst,antial niodificat,ion of convent~ionalsyst.em operation. Tlicxc t3cclinical and non-t>echnical trends poshibly cause h e dyna,rnics ol power s y d enis t o he complicat,ed. It is by now widely recognized that we caniiot fully ai~alyzcand cont,rol such complex dynamics using conventional framework This research is partially supported by the hliiiistry of Education, Culturc, Sports, Sciences aiid Tecliiiology in Japan, The 21st Century COE Program (Grand

of power cnginccring. A coniprchcnsivc approach to the analysis and control has been therefore st,ronglg required (Talukdar et nZ. 2003, Dobson et nl. 2004). Hybrid dynamical tern and cont.ro1 are a.ctive research subject,s in comput,er scieiice and cont rol erigirieeririg (Dorrieiiica et al. 2001, A ~ L arid U Pappas 2004). A hybrid automat,on (Hcnzingcr 1996) is a well-known mathematical formdation of hybrid systems. Tlie formulation is applicable to motlcling and a,iialysis of complex cnginccrcd systems that involve both continuous and discrete d yn mn i cs. Reach a,biI i ty analysis of h ytri d automata is here of paramount. iniport>aricefor safety specifications of engineered systems: for examples; steam boiler and flight) management syst,ems (Lygeros et al. 1999, Toinlin et aZ. 2003). The analysis is usually perforined by comput,iiig reacliabie sets of the hybrid antoma>taand therefore urges iis to develop several riiimerical schemes

No. 14213201).

153

siich as level set rnet,horls (Mit,chell and Toailin

0

2000, Tomlin et al. 2003). This paper proposes a novel rnct.liod for prcdicting transient) iiistability of power systems based on reachabilily analysis. The slabilit y of power systcrns is a. ~rcll-cst,a.hlishcdsubject, with a long hist,ory of research (Kiinbark 1947). Several researchers hiivc recxntly worked on the intersect~ion t,em st,a,bilit,ya i d hybrid and Pai 2000, Deililarcm et al. 2003, Fonrlas et al. 2004, Kwatiiy et al. 2005). The a.ut>hors(Hikihara. 2005, Siisnki et crl. 2005) also propose a general framework for niorleling and st~abilityanalysis of power syst,ems based on nonlinear liybrid automata. This paper focuses on transient stability problems antl proposes a novel inet~hod for tlie predict>ioiiof t>rsnsieiit st>abilityof power systems based on reachability analysis. A key itlea in the proposed method is to co~nput~e backward reacliablc given power system models. This paper demonstrates t>heproposed metliod through an andysis of single machine-infinite bus (ShIIB) system. For a prelirniiiary tiiscussion of the work reported here, see (Ebina. ct al. 2005).

0

0

0 0

-

2.2 IYrst of all convenl-ional problem setting lor transient. st abi1it)y analysis is revicwed. The readers can refer t'o (Chiang et al. 1987, Chiang et al. 1995). For the t,rarisient stability analysis, the following system described by a set) of three differential equations is examined:

{

5 = fpre(z) for t < t f , ri. = fon(rr.) for tf 5 t < tc5 5 = ,fpost ( x ) for t, 5 t ,

(2)

where T staiids for the s t a k vector that includes rot,or angles, rotor speed devia.tioii. a.nd so on. The differential equations f,,,, foil. and fi,ost reprero-rriechanical dynaniics of genera1,ors. At some time tf a power syst,eni undergoes a large fault, that is, t,here is a t,opological change of the const,itute transmission network. This is represeiited by the change of Lhe rliffereiitial eyuatioris from f,,, to f u n . Before the fault, i t i s assiimetl t1ia.t we have t,he pre-faiilt. differential equation fpre. The topological cha.iigei s caused by controllcd and imcontrollcd linc swit,ching: rchy opera.tioiis antl accident.al faults such a.s line brip a.nd plant outage. At t = tc(> tf) the fault, is cleared. Tlic dynamics are tlicn govcrncd by t,lie post-fault differeiitial equation fpost. In addition, by re-closiiig operation, at t = t,(> t c ) tlie network t,opology rct,iirns to t,lic prc-fault one. The differential equat,ion is t.2ien fixed at. j,,, .

2. PREDICTING TRANSIENT INSTABILITY: A NOVEL METHOD This section proposes a iiiethotl for predictring traiisierit iiist,a.bilitybased on reachability analysis of nonlinear hybrid automat>a.Note that, the authors (IIikihara. 2005, Susuki et al. 2005) show a geiieral framework for power system stability analysis based on 1iyk)rid systcin thcory.

2.1 Nonlinear hybrid autommtori H

A nonlinear hybrid automatoii H (Tomlin 1998) is clefiiirtl to be the collrction

The nonlinear hybrid automatori can combine the transient, tiyiiamics cvitli line switching operations. In H the vect,or field f is descrihed by the diffcrential equations Jpre. Jon, and fposl: in (2). On the ot.her hand5discrete variables { q?} are assigned t,o the above system st,at>es: pre-fault,, fault-on. and post.-fault oi~cs.Tlic discrctc transition E ca,ntlieii describe the t,opological change of tlie const
Q x X is t,he stmatespace, wit,li Q {yl, y1,. . . ,q m} a finite set of tliscretc states aiid X a n-dimerisional manifold. A st~at,eof the system is a, pair ( q i , x ) E Q x X ; U x D c RUx Bd is t,he product of t,he set of continuous c:ont,rol inputs arid the set, of conThe s p ~ of e acceptrbance trajectories are dcnot>edby { u ( . ) E PCO I E VT E R} andD A { d ( . ) E PCo I d ( ~ E) DVT E X } . PC" denotes t,he space of piecewise contiiiuous fiiiictions over R; Z,u x E d i s tlie product of the finit,e set of ete control act,ions antl t,he finit,e set, of d iscret.e d ist.11rlmnce a.c1 ions:

u

f : 0 x X x U x D + Y'X is the vect,or field which associat.es a nonlinear control system f ( q ,x,'IL, d ) with each discrete statr: q E &: E : Q x X x Zu x Z d 2QXx is the discrete t,raiisit,ion fimct,iori; Inzl C Q x X i s t~heinva.riant associatcd with each disc;ret,e state, meaning t,liat the system evolves according t,o k = f(y, x . u,d ) only if ( q , x ) E Jnv; I & Q x X is the set of initial states; E is tkic t,rajoctory ac:ccpt~ancocondition .

u

bd = Obt.' for b' CJ x X . 0 denotes a map, called property, from the set of all executions of II t o {True,False} (1,ygeros ~t n i . 1990).

154

power systems siich a s d c links by ? I ( . ) E T i arid unrcgulatcd powcxr flow duc to clcctricity trading as d(.) E D . Hence {he nonlinear hybrid auloinaton H is applicable to modeling of the transient dynamics with taking thc relay opcrwtioiis into account.

EeJo

EeJs

generator

transmission line

infinite

bus Fig. 2. Single machine-infinite bus (ShlIB) system

EeJs Pm

The present subscction int,roduccsa novel nictliod

for predictsingtlic transicnt, instability. Now tlcfinc an unsafe set G c Q x X for t,he hybrid automaton €3. The unsafe set is interpreted as a subset, of the systein states in which a power system shou~s iinaccept a.hleopera.t,ions:for esu.mples, occiirrence of large rotor speed deviation and stepping- out^ of generators. A reachable set &(G) for the time t ( < 0) in the hybrid autornalon H is then defined by a subset of Q x X in wliicli aiiy systein state readies the bountlary UG of G in It1 time despite of any control ( , u ( . ) , g u [ . ] ) Fig. . 1 shows t,he concept of reachable set,s in contiiiuous st ate space. The concept of reachable set,s is much important for estiniat,ing tlie transient instability of power syst,em. If a. system st,a.t,eexists in X t ( G ) , then we call evaluate tliat the power xysterri will reach unacceptable operation in It1 t,irnc.Thc esiirnation is possible at any onset, of discret,e transit,ions such as acciclerit,alfaults, clea.ring and re-closing operations. Namely7 by evaluating the roachable set>s, we caii tliscuss at, t,he onset of accidental faults whet,l-ier t h e power system goes t,o iinucceptable opcrat,ions or not. Thc reac:liabilitjyanalysis t,liiis makes it possible to predict the transient, instabil-

(a) fault-on

4 3 (b) one line operation

( c ) two lines operation

Fig. 3. Fault condition following control sequence of relay devices

3.1 Fault condition The subsection gives us a fa,ult condition for t~he analysis of ShlIB system and model it via. the hybrid automaton H . Fig. 3 shcxvs t~hefmlt cnndition following control sequence of relay devices. The thrcc modes in t,hc figure arc represented :is follows:

Fig. 1. Conccpt of rcachable set for continuous state space. G is an unsafc set in which a power systcni slio~.vsunacceptable operations.

3. APPLICATION T O SINGLE hf ACHINE-INFINITE BUS SYSTEhI

This section applies the proposed iiiet,liod to an a.nalysis of siiigle iriachirie-irifiiiite bus (SMIB) systeni in Fig. '2. Tlie SMIB syst,em consists of it syixlironous mactiine, an iiifiiiit,e bus, and two parallel transmission lines. An infinite bus is a. source of voltage constant in phase, magnit,ude, and frequency, and is not, affect,ed by t,lie amount, of current, wilhdrawn from ii (Kimba.rk 1947).

0

0

fault-on (a) is the state during a sustained fault, on one line. Tlicn tlic generator cannot supply it,s electric power output to the ac transmission; one line operation (b) is th ing the falilt, line by protective relay operation; and two lines operation (c) is tlic statc: after reclosing the faull; line.

The fault-clearing time t, and the reclosing time as cmnf.rol pat-a,meters in i,he following The onsetr of acciclent,al faultr is fixed at, zero in t.his paper.

3.2 Descr'pt'on osf '-I Tlie fault condition and a,ssociated transient dynamics are now modeled via the following iionlinea,r hybrid aiiiomai.on H :

155

Go - {qi.qz,q3} x { ( S . U , Z ) dG I

G

= ( q i . q 2 , ~ 3 }x ( ( ~ , w , zE ) = (41) x

X ; X;

> wC}.

~ w I =wC},

((6.w, z ) E x;121 < w,, z

= 0>,

(4)

wlicre w, = 2.0. h y st&c in G physically iniplies unaccept>al)leopera,tions of the SMIB syst,em tjecarLse I , L ~occurrelice r o ~ o rspred dcvia.tion and stepping-out of gcncmtor. dt

Note that the tiefinit,ioii of unsafe sets is crucial for t,he proposed metfhod i n this paper. The estimation of instability strongly depends on how TVC fix iinacccpt,ablc st,atcs of powor syst,cins. In the present automat.on H , continuous dynamics are described by tlie swing equation system. The system represent.s the stepping-out state of generat>oras a stable limit cycle of the second kind (hlinorskg 1947). The location of limit cycle is w M plr,/k (Hasegawa and Ueda 1999). Therefore. to avoid t Iic largc rot.or spccd deviation and stepping-out,:in t,liispaper, w, is &xed a.t,the above value which does no{, exc

cv = 0.5 if q = 4 2 .

q q 1 , (4d.tJT. a l ) = ( q 2 , (6, JJ. t J T ) . q q z , ( b J . t r ) T , a 2 ) = (qd. ( b J , t r ) T ) . 3

Inv \

=

U(n&.x), $=I

The above descriplion is based on (Tomlin 1998). Table 1 shows t lie phvsical rricming of variables and parameters in N. The variables and paramctcrs are in per unit system. In H the discrete variablc ql is assigncd to tlic fault-on stat<>,q2 to the one line operation, and q3 to the two lines operation. Tlic clraring a i d redosing operations are also regarded
3.3 Hvbrid reaciinblr set and predicting trnnsien,t

instability The present, section gives 11s a nurnerical result of hybrid reac.ha,blc set,. Fig. 5 shows the rexlia.ble set, of t>liehybrid aiit,ornat80nH under tc = (0.1 s ) / t b and t, = (0.6 s ) / t h . The numerical int,cgration is pcrfornicd in sufficicnt,ly lasgc time at t.he discrete st.ate q3. This figure shows t,he set I of initial conditions. The reachable set is now clccoiiiposotl iiit,o tlic t~hrccsubscts R1 , Ra, and R3. R1 is the subset of 1 from which any trajectory rcaclies aG before tlie discrete t>ransitionfrom q1 to QJ. Rz is the sitbset of I which goes t,o (3G betm~?eiit.he discrete t,ransitions from q1 to ~2 arid from q 2 to qJ. R3 is also t,he subset of I after the discrete t>ransitioiifrom QJ t>o43. The whitre region in Fig. 5 therefore corresponds to transient. stlability region (Chiang et 01. 1987) wit,h taking the discret,e t,ransitioiis into account. Fig. 6 shows

depends on every discrete variable. The discrete transitions E are driven by the control action5 a1 and a2.Fig. 4 tlescribcs tlic hybrid mtoniaton H iiicluding the two control actions.

2 lines operation

Fig. 4. Hybrid aut,oma.t,onH . H includes tlic two discrete control actions which represent, t>he clearing and re-closing operations. Tlie unsafe set G and thc set I of initial conditions are defined for the present analysis bj-

2.5 2 1.5

Table 1. Phybical mcaning of variables and parameters in N rotor position with respect to synchronous rcfcvncc axis rotor speed deviation relative t o system arigiilar frequency clamping cocdlicicn( mwlianical input power critical power of two lines operation onsct timc of fault oniet time of clearing operation onset time of re-closine orleration on (Tomlin 1998). quantity of Lime rricming of variables

6

Pm

0.05 0.2

b

0.7

ff

(0S ) / h

sc

* / A ,

3

d

k

L

I

-1 -1.5 -O.: -2 L

-2.5 -7T

Go 0

1 7T

6

t,

Fig. 5. Hybrid reachal-)leset under t, = (0.1 s ) / t b and t, = (0.6 s ) / f b . The rPa(+iatAP set i s dccomposecl into three subscts XI.Rz, and R? based on transient behavior.

t, tb

156

1

3

3

0

0.5 0

/

-1

t

-2

i

L

-4. -3

0

1

0.5

(a) 5

1.5 2 TIME Is

(o), IR

1

2.5

i

3

(0)

4

3 2 1

3

0

I / ( i 3

: -3 -4

1 ' 05 0 -0 5 -1

0

(b) z2

I

i

-2

0.5 (o), z 4

1

1.5 2 2.5 TIME Is (filled 0 with black)

3

Fig. 6 . Tkansient behavior with four initial points in Fig. 5 the tra.nsient behavior with four initial points in Fig. 5. Fig. 6 implim t1ia.t the solution from the initial point. :I'Z in R3 actailally r the re-closing time t, = (0.6: s ) / t b . and t,hc2t8the sol~rt~ion from the white region rema.ins in tjlie supplenient of G for any time. The prcdict,ion of t,ransient inst,ability is hence possible at the onset of the accidental f a d t ba.scti on t,he hybrid reachable set,.

3.4 Clarifying the effect of relay con,trol to t r m -sient stu,biliza,tio.n The rcachabilit,y analysis can also clarify thc efect. of clea.ring operat,ion to tra.nsient>st,a.bilization of power systems. Fig. 7 describes the rcachablc sets ;tllti projcctccl trajectories ont,o t,he set) I of initial conditions under (tc.t r ) = ((0.05 5 ) / t b , (0.55 s ) / t b ) and ( l C ,tr) = ((0.15 S)/L,,, (0.65 s ) / t b ) . Thc figiirc shows how- tlir: control action o1 affect,st.he reachable set).The t>rajectory in Fig. 7(b) st&s from h e same inilial c:ondition as the oiie in Fig. 7(a). The trajectory in Fig. 7(a.) reaches aft,er t,he discret,e transition from (12 to q 3 . On the other limd, t,he t,rn.jec:toryin Fig. 7(b) converges t,o a stable equilibrium of the vector field on the invariant, {q3} x X . This implies that the power syst,em can survive froin t.lie fmlt. by t,he slow clearing not, tlie fast one. Such effects of t>ransicnt st,abilizatiori are not, lully clarified using conveiit ional inet,hods of transie a.nalysis. The rea.chabi1it.y malysis t,hus makes it possible to confirm the effect of rclay control to transient stabi1izat)ion.

ac

4. SUhIhlARY AND FUTURE DIRECTIONS

This paper showed a. metjhotl for predict>ingt,ransicnt instability of power syst,ems based on hybrid system reacliabilit,y analysis. The nonlinear hybrid automata, can represent both transient, dyiiariiics arid discrek traiisitioris caused by transmission line swit,ching. The hybrid model also makes it. possible to analyze continuous and discrck controlled sy ins by dc links and transmission switching. can therefore contribute to the synthesis of stabilizing cont,rollers for power syst,erns. O n t h e of i.he hybrid motiel, 1,his paper proposed a 1 method for t,he predict,ion of transient instability at the onset of accidental faults based on reachablc sets of hybrid automata. Of course, the proposed method is valid at the onset, of relay operations or control. This paper shows its effect,ivcness for not, only predicting the transient instability but also clarifying the effect of rclay control to transient stabilizatioii of power systems. Future directions are in (i) reachability analysis using level set, methods (hlitchell arid Tornliri 2000, Toinlin et nl. 2003); (ii) appliciltioll of tlie proposed method to practical syst,em a.nalysis (Sakiyarna el al. 2006); (iii) volt8agcstability aiialysis ltasctl on hybrid sy m reachability aiialp i s (Susuki and Hikihara 2006); and (iv) hybrid controller synt,liesisvia power apparat,uscs siicli as IIVDC: syst>emsa.nd FACTS.

157

1€LYl4 Symposium on Logic in Cornp,uter Science. pp. 278-292. Hikihara, T. (2005). Applicat,ion of hybrid syst,em theory t ~ opower system analysis (I). In: Annual hfectin,g Record I.E.E. Japan. Vol. 6.

The authors are grateful t o Nr. Takiiji Uemura, Mr. Takavlii Ochi, antl hlr. Taknya Sakiyamti in Kansai Electric Power Company Ltd. for valiiable discussions.

p. 187. (in Japanese). Hiskcns, I. A. aiid M. A. Pai (2000). Hybrid syst.erns view of power syst.em modeling. In: Proceedings of the 2000 Iriternatioriul Symposium REFERENCES on Circuits and Systems. Vol. 11. Gcmcva. Alur, R.. anti Palopas, G. J . , Eds. (2004). H ~ j b ~ i d Switzerland. pp. 228-231. Systrrn,s: Com,p7rtation and Con,i'rol. T,ec-t,iirs Kimbark, E. W.(1947). Power- ${plerrz SLubilily/. Notes in Computer Science 2093. SpringerVol. I. John Wiley k Sons. New York. V(:rlag. Kw-a.tny,TI. G., E. klensah, D. Yiehur and C. 'l'eoChiang, H. -D., C. -C. Chi1 arid G. Cauley (1995). lis (2005). Opt,inial shipboard power sysDirect stablily analysis of electric power system management, via niixed integer dynamic t,cms using energy functions: Theory, appliprogramming. In: Proceedings of the 2005 cations. and perspect,iw. Proceedings of the IEEE Electric S11ip Techrroloyies Sgmpo IEEE 83(11), 1497-1529. Philadelphia, USA. Chia,ng, H. -I)., F. F. Wu arid P. P. Vara.iya and S. Sastry (1999). (1987). Foiintlat,ion of direct, methods for ability specifica,tions for power syst,c>nit,ransicnt, st abilit,y malysis. nmtica 3 5 ( 3 ) , 349-370. csuctions o n Ci7%'2L%t.s urcd Systems Minorsky, M. (1947). Inlroductiorc to Non-L%rzear CAS-34(2), 160-173. M e c h m i c s . Edwards Brothers. Arin Arbor, Dehlarco, C. L. (2001). A plia.se t,ransit,ionmodel USA. for ca.scading network failure. IEBE Control Mitchell, I. and C. Tomlin (2000). Lcvcl set mcthSgstems Magazine 21(6), 40-51. ods for comput,at,ion in hybrid systems. In: Dobson, I., B. A. Carreras, V. E. Lynch and Hybrid Systems: Cornputation und Conikol n. E. Nemiman (2004). Complex syst,emsanal(B. Krogli iiiicl N. Lyiicli, Ecls.). Lecture N o h ysis of scrics of blackoi&: Casca,tling failin Comput,cr Scierice 1790. Springer-Verlag. ure, crit,icalit,y,and self-orgmization. 111: Propp. 310 323. ceedings of the Bulk Power System Dynamics Sakiyama, T., T. Uerriiira,: T. Ochi, T. Hikiand CovitroZ-VI. Cortiria. tl'hmpezzo? Italy. liara. Y. Susuki arid €I. Ebiria (2006). Appp. 438-451. plic.at,ion of hybrid system theory t c Domenica., NI., Beiiedett,o, D. and Sangiovannisyst,eim analysis (TV). In: An,nmal Vincentelli, A., Eds. (2001). Hybrid Systems: Record I.E.E.Japan. Vol. 6. pp. 269Computation und Control. Lecture Notes in Japaiiosc). Comput>erScience 2034. Springer-Verlag. Susuki, Y . a.nd T. Hikihara (2006). Application Ebina,, €I., Y. Susuki and T. Hikiliara (2005). of hybrid system theory to power system Aii aiialysis of transient. dynamics of voltage stabilit,y malysis. In: 9th Intern.atina2 tric power systmri based on reachable Workshop on Hybrid Systems: Computation Technical Report NLP2005-31. IEICE. (in a71.d Control. Santa Ba.rabala., USA. (post,er Japaiiesc). present a,t.ion). Fairlcy, P. (2001). The unruly power grid. IEEE Susuki, Y., H. Ebiiia arid T. Hikihara (2005). ApSpectrum 41(8), 22-27. Aicat,ion of hybrid system theory to power Vorir1;ts~ G. K.: K. J . Kyriakopoulos antl C. D. tern stability aiialysis. In: Proceedings o f Vouriias (2004). Hybrid systems inocleliiig for the 2005 International Symposium on Nonlinpower systems. IEEE Circuits and Systems ea,r Th,eory and its Application,s. Bruge, BelMugazine 4(3). 16-23. gium. pp. 202-205. Gellings, C. W. and K. E, Yeager (2004). TransTalukdar: S. N., J. Apt, M. Ilk, L. 13. Lave and forming the electric infrastructure. Physics M. G. Morgan (2003). Cascarliilg failures: Toda?/ 57(12)!45-51. Survival wrsiis prevent ion. Thr N e c k i c i l y Geyer. T., &I. Larsson arid M. Morari (2003). Journ,cd 16(9), 25-31. Hybrid emcrgency voltage control in power Tomlin, C. J. (1998). Hybrid control of air t.raffic systems. In: Pro(;ecddinp o f the Europeun management systems. PhD disserhtion. UniContial Confereme 2003. Cambridge, UK. vr:rsit,y of California. at, Bcrkclcy. Hasegawa; Y. and Y. U(-:da (1999). Global basin 'Lbmlin, C. J., I. Mit,chell. A. L.1. Bayen and st,ruct>ureof att,raction of two degrees of freeId. Oishi (2003). Cornputjational techniques dom swing equation system. Intemakional for the verificat,ion of hybrid J o ~ ofd Bifurcnr'ion and CI~ao.9 9(8), 1549ceedings of the IEEE 91(7), 986-1001. 1569. Henzinger, T. A. (1996). The t,heory of hybrid autoinat,a.. In: Prnccetlings of the 11th Rn,n,ual

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

STABILITY ANALYSIS OF AN ISLANDED GENERATOR P. Lilje', A. Petroianu2 'PhD Candidale; 'Univevsily ($Cape Town Abstract: The authors investigate the stability of an islanded generator. They examine the effect of a predominantly resistive load on small-signal (frcqucncy) stability of' an islanded gcncrator. Thc authors derive a new linear generator modcl for the islanded power station, and pcrform small-sibma1 arialyscs usiiig tliis rnodel. The analyses arc also pcrkmcd using Lwo industrial -grade soflwarz packages, and thc results arc compared. The authors show that prcdominantly rcsistivc loads lead to poor damping of the spccd rcsponse, and that an increase in the L/R ratio further dccrcascs the damping. The use of a power system stabilizer is proposed to increase the damping of the speed response by varying the generator terminal voltage in response to speed changes. In this sense the PSS is also contributing to frequency control. Finally, the authors study the effect of the turbine and its control system on stability. Copyright 02006 WAC Keywords: Generator modeling, small-signal analysis, islanded power station

1

lNTRODUCTION

Major power system disturbances can result in the formation of islands in which one or more generators supply local load. A conventional power system has a self-regulating characteristic, i.e. the load dccrcascs Qncrcascs) if thc frcquency decreases (increases). This is not the case in a power system with a resistive load- in such a power system the load power is independent o f frequency, If the load voltage is constant the generator electrical power is also constant, but the electrical torque decreases (increases) with an increase (decrease) in speed (Lilje et a/., 2004). Resistive loads can &crease damping, and are therefore of particular interest. One example of a resistive load is a smelter Another conceivable example is that of a high-energy resistor used to dissipate some of the excess energy produced by a power plant when it is disconncctcd from thc power system (Lil~cet a1 ,2004) Such a resistor can be used to mitigate problems occurring in a power plant (e g blades overheating) following the disconnection The long-term operation of an islanded power station with a predotnnantly resistive load needs to be investigated from the small-signal stability viewpoint

generator does not represent a typical power system for which generator models are developed (IEEE Std 11 101991). The linear generator models found in the literature (Kundur, 1993, de Mello et n l 1969, de Mello et 01, 1975) do not include the effects o f speed variation on generator voltage. To include the relationship between electrical torque and frequency a? described above it is necessary to include thc effects of speed variation on voltage for the power system studied in this paper The linear model is used in small-signal stability studies. In these studies thc effect on damping of various combinations of resistance and inductance is determined. A power system stabilizer is proposed to increase the damping by varying excitation in response to speed changes. The PSS is similar to a conventional power system stabilizer, but in this case it is specifically used to aid in frequency control. Lastly the effect on stability of the turbine and its control system is investigated.

2

DERIVATION OF A LINEAR MODEL

This section presents a summary o f the derivation of a linear model of an islanded generator supplying a resistive load. The structure of the model is shown in Fig. I.

In this paper the authors study the dynamics, and specifically the frequency control, of a single generator supplying a resistive load The calculation o f damping is conservative as it ignore5 the damping that would be iiitroduced by inductioii motor loads. A new linear model of an islanded generator supplying a resistive load was developed. This was done to aid in the understanding of the dynamics, and since a small-signal analysis using two commercially available software packages yielded slightly different results. The islanded

. Fig. 1 : Structure of linear modcl

159

2 1 Linear model ofgenerator, excitation and load The model includes: Shaft dynamics Core saturation; The dynamics of the field circuit; and The dynamics of the excitation system.

ed = idRE- X E i q e, = i, RE + XEid

The model is based on the following assumptions The fast statoi tiansieiits iepreseiited by the pll/ tcrmv in the stator voltage equations may be neglected, The effects of the damper windings may be neglected, and The external impedance R, + j x b is con-

A linear form of (6) was obtained by differentiating with respect to W and The partial derivatives (at !he

v,d.

initial operating point) of

and i, were

derivatives (at the initial operating point) of the stator currents, the paramctcrs u,b,c and d were introduced

The proccss followed in deriving a linear modcl is similar to that used in deriving a linear single-machine i n h i t e bus model (Kundur 1993; de Mello et a/., 1969; de Mello et a/., 1975). The critical difference is that the effects of speed variation on terminal voltage are consdered.

in thc derivation:

Aid = d UK ld. vfd Aiq = cAo+ d A V ,

The shaft dynamics are described by the following firstorder differential equation:

K,

V u d V,,, , id

calculated using equations (3), (4) and (7). The partial derivatives were then expressed in terms of the perturbed variables A@ and A v f d .In !he case of the partial

stant

In (I),

(7)

Finally, the perturbed electrical torque was expressed as a function of Am and A V , d ,

accounts for mechanical damping, i.e. bearing

where the parameters

K2 and K7 depend 011 the initial

operating point.

friction and windage. It is noted that the term K,p.I approximates the true mechanical characteristics, since although bearing friction is a function of 0 , windage is a

It was assumed that the same saturation characteristic applies to both the d-axis and the q-axis, i.e. = Krq,

Yd

function of 0 2The . linearized form of (1) is:

The perturbed field flux was expressed as a function of the perturbed field voltage and perturbed shaft speed:

AT,, -ATF = 2 H d A w + ~ , ~ w(2) dt The model is based on the synchronous machine equations (3)-(6), and the circuit constraints (7).

ed =-my, - R,id e, = +myd - Ruiq

AE, (3)

is obtained from the excitation system transfer

function, GL,(s) and the perturbed terminal voltage,

Ae, which I S approximatcd as follows.

The resulting linear model is shown in Fig. 4, where the parameters are defincd in cquations (16)-(38).

160

2.2 Linear model of turbine and its control system Typical models of turbines and turbine control systems are presented in (Kundur, 1993; IEEE, 1991). The model used apply to a 3000 rprn, single-reheat, tandem corn pound steam turbine with an clectrornechanical control system- see the block diagrams in Fig. 2 and Fig. 3. Linear models were derived by reducing these block diagrams. Note that the output of the turbine model was modeled as mechanical torque, not power. This is a conservative choice as it will lead to a lower calculated damping than if the output were modeled as mechanical power. Throlle

3

presI"re

STABILITY ANALYSlS

In this section the eigenvalues of the islanded generator supplying a resistive load are calculated.

3.1 Anulysis neglecting turbine control system The transfer function A 0 was obtained from the

CVP

/AT

model of Fig. 4 The transfer function

Fig. 2 : Turbine model

AOIATnl was

then derived using equation (2), and the roots were calculatcd from its dcnominator (in this scction thc turbinc output is assumed to remain constant, hence hcrc ATn

is represents a disturbance torque). Table 1 shows the results. Also shown are the eigenvalues as obtained from two analysis software programs. The results are almost identical in the three cases.

Fig. 3 :Turbine control systcm modcl

Equation (12) shows the linear model of the turbine control system. Similarly, (13) shows the linear model of the turbine. Multiplying (12) and (13) yields the transfer function ATm/ A m .

The system is unstable, because although the turbine torque is constant, the electrical torque decreases (increases) with an increase (decrease) in speed.

Fig 4 Linear model of single generator supplying a resistivc load

161

pole of the transfer function

Table I heenvalues for a load o f 0.826 + 10D U (turbine controls excluded) MATLAB

DIgSLENT

0 -24.496 +2 1.2991 0.198

0 -25.190 k17.3991 0.202

Linear model

3.2 Analysis including turbine control system

-25.38 izj25.10 0.199

The effect of the turbine and turbine control system were investigated using the linear models presented in section 2 and MATLAB’s ‘sisotool’ function. The load power was set to 0.826i~j0.3pu, and the PSS gain was 2. Fig. 6 shows the root locus and bode diagram of the system with an increasing turbine control system gain, K G .The system is stable even if K , = 0 due to the

PSS. Increasing this gain iinpmves the system danipiiig, although thc systcm bccomcs unstablc again at vcry large gains.

Table 2 Unstable ciescnvaluc from linear model for loads of different LE l R , ratios

LE i R,

0.826+J0

0.826+J0.3 0.826+j0.6

into the

stable region (from 10.25 ris to -0.58 r/s).

The introduction of a series load inductancc further decreases the damping, as shown in Table 2 At higher (lower) frequencies the higher (lower) reactance reduces the voltage applied to the resiqtor, thereby reducing (increasing) the electrical torque in the generator

Load power (PU)

AwiAT,,, well

The squares in Fig. 6 show the closed loop pole positions for a gain K , = 25. The system has a significant

Unstable eirrenvalue 0 0.205 0.363 0.247 0.726 0.339

phase inargiii and gain margin, as indicated in the bode diagrams. Root Locus Editor (Cl

O P ~ ~ C OBode O P Editor (Cl

5

A PSS adds damping to the system, and stabilizes the inner loop (i,e, the electrical loop in Fig. 1). The authors proposc a PSS shown in Fig. 5. In the invcstigations of this paper no phase lead was included in the PSS, i.e.

. . . ...*.. . . . ..

4 3

2

Ti =Z, = 0 , because:

1

a) at frequencies of up to about loris the clectrical loop

0

and mechanical loop act in unison. h) at higher frequencies the gain of the electrical loop is about 50dB more than that of the mechanical loop.

1

Fieq 4 01 radisec

-150

Sllbb im(?

1

0

2

10

-90

3 -180

4

Points a) and b) above can be verified by comparing the bode plots of the following two transfer functions:

5

3

1

-2 Real Axis

-270 0 0.0001

1 10

ImW

Frequency(radlsw;)

€ig.6 :Root locus and bode diagrams for system including turbine controls

4

Fig 5 Power system stabilizer The gain

CONCLUSION

The authors studied the stability of an islanded generator that supplies a resistive load A linear model has been developed It wa5 used to calculate the system’s eigenvalues The model differs from other linear models found in the literature- i t includes the effect of speed variations on the terminal voltages. The dominant pole was found to be unstable, and the damping decreases with an increase in the LIR ratio. The PSS can provide suffj~ientdamping to StdbiliZe the islanded generator supplying a resistive load In this case the PSS is used specifically to improve frequency control. This differs from the Conventional use of a PSS

K, determines the additional damping

introduced by the controller. In the case of a load of K, = 2 moves the unstable

0 826+jO 3 pu, a gain of

162

to increase the damping of oscillations in multi-machine power systems.

E,ci field voltage in pu

K , mechanical damping constant in pu a,b, C , d variables used in the calculation of the constants K2,K, ,K, ,K,,K,

The authors further studied the effect of the turbine and its control system on the damping The turbine control systcm provides additional damping to the specd R sponse As the gain of the turbine control system is increased the system becomes oscillatory. If the gain is increased too much the system becomes unstable

Ro,R , armature resistance, field resijtance all in pu R,, RE series equivalent resistance and external resstancc of high-cncrgy rcsistor, all in pu

x,, xTqtotal d - and q-axis reactances L,, x, external inductance and reactance, pu

SYMBOLS constants used in describing the generator

A, B

CVP i, j

L, ,L,,

saturation characteristic control valve position complex operaton

tance

,Layssaturated values o f d - and q-axis mutual

vd,vCl d- and q-axis stator flux linkages in pu y ',

inductances

Ladzrunsaturated value of d-axis mutual indutance Ge.y(s) linear transfer function of excitation system K, ,s,,, ,s,, stabilizing controller gain and limts

field flux linkage in pu

id,i, d- and q-axis stator currents in pu

. .

zdc1, lye, initial d- and q-axis armaturc currents in pu

i,

initial armature current in pu,

zd, + zqO .J?L

APPENDIX A: EQUATIONS D E F M G THE PARAMETERS OF THE LINEAR MODEL

ed,eq per unit d- and q-axis stator voltages

edO,e4, initial d- and q-axis armature voltages

e terminal voltage in pu,

The parameters for the model of Fig. 4are calculated using the following equations:

,/=

e, initial terminal voltage in pu,

Jm

@(, initial powcr factor angk

6,, initial internal machine angle, in radians 6 rotor angle relative to infinite bus, in radians

n

p operator dt

c,,mechanical power in pu A refers to a perturbation in a variable

h ' shaft inertia constant in seconds K , excitation system gain K , ,KAqsaturation constants

KVn,incremental

slope of the non-linear valve charac-

teristic Z, field circuit time constant in seconds

s Laplace operator (complex frequency) electrical torque in pu

T,n mechanical

torque in pu

u) rotational speed in pu W , ratcd rotational speed in pu, W ,

leakage inductance and field circuit induc-

=1

W , rated rotational speed in rs.'

163

APPENDIX B GENERATOR PARAMETERS The parameters o r the generator used in the paper are given below. Unless otherwise indicated, all values are in per unit.

S=211.7MVA

U , =13.2kV

Ld =2.01

L:, =0.24 L, =1.96 L, =0.14

Ra = 0.001 K,=0.01 K , = 200

z,' = 11 o,,~ = 1 0 0 ~ H = 2.0 A=0.03 B z 6 . 9 ~,~=0.8 Z, = 0.02

REFERENCES de Mello F. P., C. Concordia (April 1969). Concepts o f Synchronous Machine Stability as Affected by Excit ation Control, IEEE Trans. PAS, Vol. 88, No. 4, pp. 316329 deMello F. P., T. F. Laskowski (May/ June 1975). Concepts of power system dynamic stability, IEEE Trans., Vol. PAS-94, No. 3 IEEE Std. I 1 10-1991, Power Engineering Society, IEEE Guide for Synchronous Generalor Modeling Praclices in Stability Analyses

K , = L [ - b R u +d(Luyr+ I,

,,)I+ (35)

IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, (May 1991). Dynamic Models for Fossil Fuelled Steam Units in Power System Studies, IEEE Trans. Power Systems, Vol. 6, No. 2 Kundur P. (1993). Power System Stability and Control, Electric Power Research Institute, MGraw-Hill Inc., ISBN 0-07-035958-X Lilje P., A. Petroianu (2004),Power plant islanding with the aid o f a controlled resistor, IEEE Afiicon Conference, Vol. 2, pp. 775-781

164

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

PRIMARY CONTROL SYSTEM AND STABILITY ANALYSIS OF A HYDROPOWER PLANT Maria Regina Gomes Zoby, Jurandir Itizo Yanagihara Department ojMechanica1 Engineering - Polytechnic School of the University ofS60 Paulo

Abstract: The objective of this work is to study the primary control system of a hydropower plant operating isolated. The plant is modeled by differential equations and the results are compared with Geld data from an actual hydropowcr plant, with dcviations lowcr than 1 .O%. The study of thc primary control systcm is conducted in order to define optimal parameters for the controllers. Four controllers are studied: traditional, PI, PID and PIPD. The controllers’ performances are evaluated by stability criteria and a performance index. For the hydropower plant studied, the PI controller has the best performance. Copyright 02006 IFAC Key words: modcling, hydroelcctric systems, primary regulation, optimal control, stability

1.

INTRODUCTION

This work deals with the operation and control of hydropower plants and its basic equipments and presents an analysis of the dynamic behavior of an actual hydropower plant. The main objectives are to model an actual plant using a nonlinear model based on differential equations with parameters that can be easily estimated or obtained from field tests and to study the primary control system for the plant in isolatcd operation in order to define the optimal parameters for the chosen controllers. The power plants have particular control systems to ensure stable operation. The satisfactory operation of a power system rcquires a frequcncy control that keeps it to acceptable liinits when the system is submitted to significant load variation. As the frequency is common to all the system, a change on the active power at one point will be reflected on the net as a frequency variation (KUNDUR, 1994).

1.1. Primary Control System The primary control system is composed of the speed sensor, the controller, the actuator and the hydraulic supply system. Its main functions are to maintain the

angular speed constant and equal to its nominal value and to change the distributor position when the load varies or the operation conditions (as head) changes. Each operation condition has its requirements so the controller parameters that are adequate to one condition may not be adequate to another one. The use of adaptive control is an option to satisfy different operating conditions. Otherwise, the usual procedure to define the controller parameters is to considcr thc isolated condition that imposcs thc most severe operation requirements and guarantees that the stability will be sustained in this case (SILVA, 2000). This procedure is adopted in the stability study of this work.

2.

MODEL EQUATIONS

2. I . Hydraulic Circuit The model is based on the assumption that water is as an incompressible fluid and that the penstocks are rigid. Two kinds of plants are presented: single penstock and multiple penstocks with a common conduit.

165

For the individual penstock,

Single Penstock. A single pcnstock plant has onc conduit wpplying each turbine. From the laws of momentum, the rate of change of flow in the penstock is (IEEE, 1992):

(h, - h , - h )-=gA dq I dt

’

(1)

h, =jq2

(2)

In this equation h,, is the static pressure of the water column at the turbine’s admission [m], h,, is the pressure at the turbine’s admission [m],h,, is the friction loss on the individual conduit [in] and T,,,, is the time constant of each individual penstock [s].

In these equations ho is the static pressure of the water column [m], hL is the pressure at the turbine admission [m], h, is the friction pressure loss [m], g is the gravitational force [ m / s 2 ] , A is the conduit’s transversal section [m’], 1 is the conduit’s length [m], q is the flow rate [m’/s] and f is the loss coeficient of the conduit. In per unit it becomes,

The equation can then be written as,

2.2. Equipmcnts

The basic equipments on a stability study of a hydropower plant are the turbine and the generator. The following models represent their operation and the distributor action.

The water starting time is defined as: (4)

Distributor. The equation 12 represents the relation between the gate position (Y) and the prime control system signal, K Y= (12)

If the penstock presents different sections then,

(T,s+ l)(T,s + 1)

Multiple Pemtocks with a Common Conduit. A plant with multiple penstocks with a common conduit is rcpresented on the fol 1owing fi gurc .

where T, and T2 are the actuator’s time consCants.

Turbine. The turbine can be modeled by its valve characteristic,

T

Common Conduit

/

u

, # , /

r

cr=G&

b

G(s) =

G is defined as,

(13)

Go

(14)

~

1+T,s

G , ( y )= d o + d , y + d , y 2 Fig. 1 . Multiple Penslocks supplied rrom a Common Conduit

(15)

where y, is the gate position ( y = 1 for nominal position and J = 0 for closed position) and T2, is the gate time constant. The gate time constant in this work is considered 1.0 second.

From the equations presented, the rate of flow change in the penstocks is (IEEE, 1992),

The mechanical power can be writen as (IEEE, 1992),

P,

= pgh,q

-

K

0’

(16)

where P,, i s the mechanical power [W], p the water density [kg/m3] and wthe angular speed [Hz]. The turbine’s loss coefficient (Kl) is defined a5 a sccond order equation,

K , = a l q 2 + b, q+ c +

where h,, is the static pressure of the water column at the bifurcation [m], k , is the pressurc at the bifurcation [m], hfcis the friction loss on the common conduit [m], T,, i s the water starting time constant of thc common conduit [s] according to equation 4, q( is the flow rate in the common conduit [m’/\l and qLis the flow rate i n the individual penstock [irr’/s].

(17)

Generator. The difference between the values of the mechanical power (P,n) and electrical power ( P p ) causes a variation on the axis torque which genearates the angular speed variation. If we define the constant H a s , 166

1

5

2

Jwo H = kinetic.energy.at.nan.speed-nominal.aparent. power

S,

(18)

whcrc J is the generator inertia [kg.m2], q,is the nominal speed [Hz] and S, is the nominal apparent power [V.A], then we can write,

or, in per unit,

Proportional Integral and Proportional Derivative. This controller is the combination of a proportional integral controllcr and a proportional derivative controllcr and is shown in the following figurc.

Fig. 3. Controllcr - PI-PD - Proportional Integral and Proportional Derivative

We can also define,

Proportional Integral and Derivative. This controller has the following transfer function,

G, (s) = K , 1+

The electrical powcr can be writtcn a5 function of the load power (PG)as (Kundur , 1994),

hp, = AFG+ FGD,,floo.AiB

(22)

As result, we obtain,

-AFti = ~H.S.AW+?~,;,,,~CO~.AW (23)

@?,

3.

+ T,s

~

K

s

1

FIELD TESTS RESULTS OF ACTUALHYDROPOWER STATION

(27)

AN

Field tests results of an actual hydropower station with three Francis turbines built in Brazil are used to evaluate the model and to calculate its parameters. Fig. 4 shows the plant circuit and Tab. 1 presents its main geometric characteristics.

2.3. Controllers The four controllers studied in this work are represented i n Fig. 2. Fig. 4. Hydropower plant hydraulic circuit

Fig. 2. Schematic View of the Control System Traditional Controller. The traditional controller has the following transfer function (CEPEL, 1999),

The head water level (hM)is 479.2 metera and the tail water level (h,) varies from 303.7 to 3 1 1.8 meters. So the net head varies approximately from 165.4 to 173.5 meters. The inertia of the generator is 600 ton.m2. The optimal operation conditions are, speed: 450 rpm; power: 32.37 MW; flow rate: 2 1.O mz/s; net head: 168 m. Tablc I . Hvdraulic Circuit

where r is the transient droop and T, is the controller zcro parameter.

Circuit

Proportional IuLtegrutive. The transfer function of this controller is,

whcrc T, is thc intcgral constant.

167

L [m] d [ml A [m2] T, I turbine 0.74 29.84

Conduit 1

1728.0 6.16

Conduit2

355.0

4.00

12.57

0.36

Individual 1.2.3 Spiral Case 1.2.3 Draft tube 1.2.3

40.0 16.6 10.9

2.20 1 .Ill 2.36

3.80 2.57 4.37

0.13

Total

1.34

0.08 0.03

[F]

The net head is calculated by,

h, = h,w - h,

- 0.000964

Cq 2

(28)

Table 2. Operation points - 167m net head

Y [pul 0.5 0.6 0.7 0.8 0.9 1.0

Table 5. Base Values used to Calculate the Paramctcrs in Der unit [mi/sl Flow rate at the optimal point 21.0

qbase

Q [m3/sl q [“h] P [MWI 15.2 18.0 20.9 23.3 25.3 27.4

91.5 93.5 94.4 94.0 93.5 92.7

22.6 27.4 32.0 35.6 38.5 41.4

hba\e [m] Gross head at the nominal point 168.4

[Hz]

[kWl Nominal Apparent Power

Nominal Sped

35966.7

7.5

Pbare

Table 6. Model Parameters in per unit Tw [s] f‘ d, + d , y + d , y ’

1.34

0.002524 -0.570+ 2 . 0 2 3 ~ -0.142~~

Table 3. Operation points - I68m net head Y [pul 0.5 0.6 0.7 0.8 0.9

Q lm3/sl 15.3 18.0 21.0 23.4 25.4 27.5

1.0

q [“/.I 91.5 93.6 94.4 94.1 93.5 92.8

Table 4. Operation points

Y [pul 0.5 0.6 0.7 0.8 0.9

Q lm3/sl 15.3 18.2 21.0 23.4 25.6 27.7

1 .o

-

P [MWI 23.0 28.0 32.4 36.0 39.0 42.0

0.469

7.407

6.95 1

0.197G2- 3490+ 0.204

The gate time con5tarit 1 5 estimated a5 1 .Os. For the actuator it is considered that T2 is zero and Tl represents the time necessary to open the gate from y=0 to y=0.632, which is 5.94s. This yields the following first order equation,

169m net head

Y=

q [“h] P [MWl 91.5 23.0 93.6 28.0 94.4 32.6 94.0 36.3 93.5 39.3 92.8 42.2

1

(5.94s

(28)

+ 1)

4.2. Model Results The model results for different gate positions with the condition of one turbine operating are compared to the field results. The deviations were very low, varying from -0.54% to 0.7607, as shown in Tab. 7. These results were considered satisfactory to validate the model of this hydropower plant.

The stability study is conducted based on the range of operation close to thc optimal conditions. This range comprises net head varying from 167 to 169 meters (operating conditions shown in Tabs. 2, 3 and 4). Thc loss coefficient Ks is determined by the results on the graphic shown in Fig. 5. The gate opening time is 9.4 seconds.

Table 7. Model Deviations compared to Real Results

ym1 q m 1 hL[%O] Pm[%I PG [%’.I Awlpul 0.7 0.8 0.9 1.0

K ~ Qx 7 6Ei03

0.60% 0.38% -0.54% 0.04%

-0.01% -0.03% 0.01% 0.06%

0.76% 0.29% -0.15% 0.49%

0.76% 0.29% -0.15% 0.49%

0.0006 0.0004 0.0010 0.0045

F 65E+03

2 p

55E+03

5 . PRIME CONTROL SYSTEM ANALYSIS

45E+03

3 5E+03 150

175

zoo

225

2511

275

The controllers studied are the traditional, PI, PID and PI-PD. To compare their performances and to determine the optimal parameters, a performance index is introduced to evaluate the speed deviation when the system is submitted to a load variation represented by a ramp from 0.779 to 1.009pu in 10 seconds. It is also required that when the system is submitted to load variation, the third peak of the speed variation is not higher than 5.0% of the ramp or 25% of the value of the first peak. The permanent droop is considered constant and equal to 5%. The performance index is defined as,

300

P [m31sl

Fig. 5. Turbine loss coeficient as a function of the flow rate for different net head conditions

4.

MODEL SIMULATION

4. I . Parameters Calculation The base values used to calculate the model parameters are presented in Tab. 5. Thc parameters of the model are listed in Tab. 6. 168

5. I . Traditional Controller

5.3. Proportional Controller

The range of values studied is T, varying from 0.5 lo 2.5, and r varying from 1.0 to 20. The performance index calculated in this range shows that the lower both parameters are, highcr is the index. The lower value of the performance index is 1,=0.664, for T I = 0.5 and r = I .0 m (Fig. 6). TRADITIONAL CONTROLLER

Integral

Derivative

(PID)

T o the PID controller the range is also the recommcndcd by Hovey (1988). The proportional gain (P=K,) varies from de 0 to 20, the integral ( I = K f l l ) from 0 to 40 and the derivative (D=K,.T,J from 0 to 20. The best performance index is 1,,=0.457, obtained Tor P= 2.0, I = 40 e D = I .0 (Fig. 8). PID CONTRQLLER 0 85, /

0 80

0.75 0 70 0.65: 0 60,

25

05

Fig. 6. performance Index as function of TI and r ’I raditional Controller Fig. 8. Performance Index as function of D and I PID Controller - P=4.0

5.2. Proportionul Integrul ( P I ) Controller The proportional (P=K,) and intcgral (I=K,/T,) gains are evaluated for P varying from 0 to 20, and I varying from 0 to 40, which is the range os values proposed by Hovey (1988).

S.4. Proportional Integral (PI-PD) Controller

-

Proportional Derivative

In this work PI is considered 1.0. The adjustable parameters are P2, I e D , and Pz varies from 0 to 20, I , from 0 to 40 and D, from 0 to 15. The results in Fig. 9 show that for higher values of D, the system has a lower performance index. For valuer over D= 15 the response bccames too oscillatory and stability is not achieved. The minimum value of the index is 1,=0.657, for P,=l.0, D=15, P2=5.0 and

PI CONTROLLER 1.0

0.91

1=40. 0.5

PI-PD CONTROLLER

20

I

Fig. 7. Performance Index as function of P and I PI Controller The lower value of the performance index for the PI controller is 1,,=0.456, for P= 4.0 and I = 40.0. In Fig. 7 , the surface shows that for higher values for the integral parameter there is a significant reduction of the index when these values vary from 0 to 25. However for values higher than 25 the reduction is not significant and we verify that for values higher than 40, the system performance is no more influenced by this parameter. Besides, for low values of the integral parameter, higher values of the proportional parameter reduce the performance index. On the other hand, for high values of the integral parameter, the proportional gain does not influence significantly the system’s performancc.

Fig. 9. Perrormance Index as runction of P2 e I - PIPD Controller - PI=1.0 e D=9.45

5.5. Controllers Cornparison

After analysing each controller submitted to different values of its adjustable parameters, the optimal system’s performance is presented on Tab. 8. The lower performance index is for the PI controller and the higher is for the Traditional Controller.

169

Table 8. Ootimal Values of the Performance Index Traditional 0.664

PI 0.456

PID 0.457

Figure 12 presents the speed variation when the system is submitted to the demand curve. The speed is kept to stability limits and the system has a good dynamic behavior with the PI optimal controller.

PI-PD 0.658

Controllers Performance

--2 8

6. CONCLUSIONS

0 02

This work combines the nonlinear model analysis with a primary control optimization. The main objectives, the model’s validation and the definition of the vptiinal parameters, ale achieved.

0

002 004

D a6 0 08 200

210

220

230

240

2511

2611

270

The model’s results with its parameters calculated based on an actual hydropower plant operating with one turbine are satisfactory and present flow, power and speed deviations lower than 1.0%. These deviations are due to approximations on thc model parameters.

Time Is1

Fig. 10. Comparison of the controller5 when the system is submittcd to a ramp AP(, = + 0.23 pzi Figure 10 shows that for all controllers the system becomes stable in about 50 seconds. The traditional controller’s response is the most oscillatory and presents the higher initial peak of -0.07 pu. The responses of the PI and PID controllers are very close to cach other. They present an initial peak of -0.68 p u and are damped and not oscillatory. The PIPD controller has also a not very oscillatory response but the system stabilizes slowly and has an initial peak of 0.60 pii.

The analysis shows that the PI controller presents the best performance index (Zd,,,,,,,=0.456) and the traditional controller has the worst performance (1,,,,,,,,=0.664). The model response with thc optimal PI controller for a real demand curve presents a behavior within the stability criteria for this kind of power plants and the mechanical power follows the demand power.

5.6. Optimal Controller Behavior ,for a Demand

REFERENCES

Curve

Centro de Pesquisa de Energia ElBtrica - CEPEL (1999). Electroinechanic Transients Analysis ANATEM - Handbook. Research Center of Electrical Energy (in Portuguese). Dorf, R. C. and R. H. Bishop. (2000) Modern Control Systems. Prentice Hall, New Jersey. Hovey, L. M. et a1 (1988). IEEE Recommended Practice for Preparation of Equipment Spcifcationsfor Speed-Governing of Hj~druulic Turbines Intended to Drive Electric Generators. The Institute of Electrical and Electronics Engineers. IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies (1992). Hydraulic Turbine and Turbine Control Models for System Dynamic Studies. IEEE Transactions on Power Systcms, Vol. 7, No 1 . Kundur, P. (1994). Power System Stability and Control. Mc Graw-Hill Inc., Ncw York. Ohishi, T., Soares, S., Cicogna, M., Laudanna, P., Lopes, J. (2002). Optimization of the Dispatch of Paranapanema’s River Machines. University of Campinas. (in Portuguese). Silva, A. S., Costa, A. J. S. (2000). Control and Stability on Electrical Power Systems. Federal University of Santa Catarina. Available in: (in Portuguese).

To verify the dynamic behavior of the PI controller with best performance (optimal controller) the demand curvc presented in Fig. 11 for one day is chosen. The curve’s critical stability regions are those with higher demand vaiiation. Demand Curve 12

-2

1 08

g 08

Y

g

04

02

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hours

1 0Demand 1

Fig. 1 I . Demand curve (Ohishi et al., 1999) for one day Response to the Demand Curve

1 2 3 4 I 6 7 8 9 10111L1314151617181Y2021222324

Hours

Fig. 12. Speed variation when the system is submitted to a power demand curve

170

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

OBSERVER-BASED COAL MILL CONTROL USING OXYGEN MEASUREMENTS Palle Andersen, Jan Dimon Bendtsen and Tom Sandergaard Pedersen * Jan Henrik Mortensen and Rene Just Nielsen **

* Aalhorg Universio, Department of Control Engineering, Fredrik Bajers Vej 7, DK-9220 Aalborg 0, Dentnark c-inail: {pa,dimon,tom}@contrt,l.aau.dk ** Elsanz Engineering Krafivct.rk5ve.j 70, DK-7000 Skarbct.k, Denmark e-mail: {jhm,rejnl @els~am-mg.com

Abstract: This paper proposes a novel approach to coal flow estimation i n pulverized coal mills, which utilizes ineasurenients of oxygen content in the flue gas. Pulverized coal mills are typically not equipped with sensors that detect the amount of coal injected into the fui-nace.This makes control of the coal flow difficult, causing stability problems and limits the plant’s load following capabilities. To alleviate this problem without having to rely on expensive flow measurement equipment, a novel observer-based approach is investigated. A Kalman filter based on measurements of combustion air flow led into the furnace and oxygen concentration in the flue gas is designed to estimate the actual coal flow injected into the furnace. With this estimate, it becomes possible to close an inner loop around the coal mill itself, thus giving a better disturbance rejection capability. The approach is validated against a fairly detailed, nonlinear differential equation model of the furnace and the steam circuit using data measured at a Danish power plant. Keywords: Coal mills, Kalman filters, flue gas measurements, observer design

1. INTRODUCTION

In the power generation industry, the current trend toward market deregulation, coupled with increasing demands for maximization of natural resources and minimization of environmental impact, places greater and greater locus on elfective plant-wide operation and conirol systems. I m z f Jdlowing, i.e., ihe ability of the power plant to meet the power production demands at all times is becoming a major concern due to the growing competition between power companies and other market forces (Garduno-Ramirez and Lee, 2001).

’ The work presented in ths paper w;t) sponiored by Vwrneforsk

Scrvice AB, 101 53 Stockholm, Sweden.

However, when modern coal fired power plants are forced to operate under many different operating conditions, effects of variations in behavior of the coal mills supplying fuel to the plants tend to cause disturbances in both the furnace and steam systems, forcing thc power plant control to be inore cautious than what could be hoped for during load changes in order to avoid undesired transients, oscillations etc. If, on the other hand, the coal mills can be controlled precisely, it is possible to input exactly the required amount of coal into the furnace at the required time, thus improving the transient behavior dunng load changes and enabling the power plant to “ramp up” (or down) to a new operating point in a rapid manner.

Tn principle, tight control of the coal mills would bc possiblc by closing a local loop around thc coal

171

Live steam pressure

Fig. 1. Overview of Benson Boiler including control system. Only parts of the steam circuit are shown. mills; under normal circumstances, however, there is no sen,sor equipment available to measure the coal flow leaving the mill and hence no local feedback can be made. Specific coal flow measurement equipment is available on the market, but is highly expensive and not straightforward to employ in practice. Methods to detect thc coal flow using the available sensors are thus desirable, which motivates the work presented in this paper.

and finally, Section 6 sums up the main points of the work and discusses possibilities for future work.

2. CONVENTIONAL COAL MILL CONTROL Figure 1 shows a sketch of the combustion control scheme cmployed at CHP plant Nordjyllandsvmket, unit 3 (NJV3). The figure uses a mix of simplified control notation and simplified process drawing symbols in order to explain only the most essential components. The combustion control scheme consists of two control loops, a live steam pressure (LSP) loop and an oxygen concentration (CO,)control loop. The LSP loop functions as an outer loop while the Co, loop produces a correction to the excess air ratio to the LSP loop.

The main contribution of this work is the design of a state estimator for the actual coal flow that utilizes the total air flow and oxygen sensor measurement as inputs to a Kalman filter, which estimates the amount of coal combusted in the furnace. Based on this estimated coal flow, it is possible to close an inner loop around the coal mill to reject disturbances. In (Flynn, 2003) a siinilar method to estimate the pulverised coal flow using a Kalman filter approach is presented. In (Flynn, 2003), however, the coal flow estimate mainly relies on measurements from the steam path of the boiler whereas the work in the present article uses measurements "closer" to the coal mills, seen from a process technicaudynamical point of vicw.

When a deviation between the LSP and LSP reference (P5s,,-q-) occurs, the PID controller changes the reference uiit/.,,,,j to the coal inills in combination with the boiler load signal. Furthermore, this signal is fed into the air controller where the total amount of combusand the excess air tion air is calculated from rizg,,f ratio.

The outline of the rest of this paper is as follows. First, in Section 2 we review the conventional approach to Benson boiler operation and coal mill control, focusing on available measurements etc. Then, in Section 3 we present a Kalman filter-based estimator design that utilizes measurements of oxygen content in flue gas, which enables a much faster feedback, and hence more efficient control, than conventional approaches. In Section 4, the concept is validated using actual measurement data from a Danish power plant together with a fairly dctailcd simulation model. Next, Scction 5 discusses a potential observer based control scheme, which utilizcs thc novcl obscrvcr in a cascadc sctup,

Of the total combustion air approximately one fourth

(called primary air) is used to convey the pulverised coal from the coal mills to the burner nozzles. The reinaining air is injected through three inlets positioned around each of the 16 burners (burner air) and above Lhe Pour highest positioned burners (over$re air). With the introduction of overfire air and quadruple burner air inlets, including the primary air, it is possible to reduce the generation of NO,, by staging the combustion. The purpose of the Co9control is to maintain a slightly lean combustion in the furnace to ensure that all carbon oxides are spent. The concentration of oxygen in

172

explained in the previous section. The oxygen concentration in the flue gas duct at the furnace outlet, Co,, is influenced in the positive direction by contributions from the inflow of primary air and in the negative direction by the (stoichiomctric) combustion and the outflow of flue gas to the smoke stack. Next we will present the equations necessary to observe coal flow using measurements of oxygen and the total air flow. Fig. 2. Setup for fuel observer design. the flue gas i s measured at the boiler outlet immediatcly after the top pass and is compared to thc refcrence value Co2r e f , which is a l-unction of the current boiler load and the number of coal mills in operation. From thc Co? dcviation a PI controllcr produce\ a correction sigiial to be multiplied with the flow reference signals to the burner and overfire air.

2.1 Coal nzrll control In the vertical roller mills used at NJV3, the raw coal from the coal bunkers is dropped through a chute onto a rotating grinding table. The centrifugal action forces the coal outwards under three static rollers where it is pulverised, and hot primary air passing the rim of thc grinding tablc from bclow drags thc pulvcriscd coal upwards. Immediately the heavy grains drop back on the grinding table while the light particles are dried and swept on to the rotating classifier vanes. Here a further filtration process occurs where only the finest particles will be conveyed to the burners via the primary air, and the remaining coal particles return to the grinding table for re-grinding. In order to control the mass flow of coal leaving the mill, three control signals are used, the primary air p o w , the raw coal ,flow and the classij?er rotational speed.The three inputs affect the net coal flow in different ways: obviously the flow of raw coal affects the amount of pulverised coal inside the mill. However, if the primmy air pow is not supplied accordingly over time, the mill will either choke or exhaust, and thus the air flow call be used for teiniporarily release or retaining coal from the mill. Likewise, the classifier rotational speed can be used for increase or decrease of the net coal flow. Because no measurement of the flow of pulverized coal is available these three inputs are controlled in a feedforward manner in dependency of *.fu,re,f with the aim to give correct steady state behaviour with dynamic compensation in order to give proper transient responses. In this paper this adjustmciit will not be considered, but we will use estimations of the coal flow in order to manipulate the coal flow reference.

3. KALMAN FILTER-BASED ESTIMATION OF COAL FLOW Figure 2 shows a block diagram of the combustion system with eiiiphasis on the oxygen control loop, as

The oxygen mass balance of the furnace can be written on state space form as

- f uCU:.fu )

co, = xo2

(1)

(2)

where V is the volume and pjs is the density of the flue gas. Co2 and Colair are the concentrations of oxygen in the flue gas duct and atmospheric air, respectively, while CO?,J,is the amount of oxygen consumed by stoichiometric combustion of 1 kg coal.2 We note that although (1) is a nonlinear model that lumps the contributions from several subsystems together, it can be considered a "well-behaved" system, i.e., the parameters do not ch<mgesignificantly over time and the nonlinearities are smooth. The coal flow r i ? ~ is , ~ described ~ using a simple linear second-order model:

(4) =Xff,]

(5)

where ao,al,ho and hl are scalar parameters. This model reflects the coal mill dynamics as well as the overall behavior of the existing control system. Using such a simple model is obviously a gross oversimplification, but since the focus in this work is on estimating the fuel flow for control purposes and not on estimating internal states in the coal mill itself, this is deemed acceptable within the scope of this work. The performance of the entire concept can likely be improved by replacing (3)-(4) with a more detailed model. inair denotes the

total air flow governed by the following first-order air fan model:

&,, = xnzo

(7)

This simplified model reprcsents the behavior of the regulated air supply system. It is noted that the model will yicld biascd cstimatcs of thc air flow in thc prcsences of disturbances such as leakages. In this plant

' In this paper, we use SI units for all physical quantities.

173

it is supposed lhat leakage flows are of minor importance since the furnace pressure is regulated to only slightly below ambient pressure, such that the the small differential pressure yields negligible leakage flow through unintcndcd openings etc. The 0 2 control block is composed of a fuel reference feedforward given by

aid a PI controller providing an aidfuel ratio correction signal, which is multiplied by the fuel reference feedforward signal and used as a reference to the air fans. The integral state of the 0 2 controller is given by

where Kl,,O, IS the conlrol gain and 7;,02is the inlegration time of the PI-controller. This implies that the air fan reference signal is XPIX f ~ L J

%.teJ

(10)

Equalions (I), ( 3 ) , (4), (6), (8) and (9) represent the model of the oxygen control loop used here. The equations can be combined into a single state space model of the form dx/dt = f ( x ,u ) , y = Cx, where

are the skate, input and output vectors of the system, respectivcly.

approximation. The model matrices ( A , B ,C) thus depend on the operating point, and it can be expected that if the load changes significantly, new model matrices may be required. In this case, linearizations in a fcw more load conditions can be evaluated, and the model matrices for a given load can be approximated by interpolation. F and G are constructed according to observations of the noise levels obtained from measurement data. In the general Kalman filter theory, F and G represent thc intcractions bctwccn thc Gaussian noisc and cach individual state or output. In our approach, we chose F and G to be diagonal, with each entry on the main diagonal representing the standard deviation of a corresponding noise channel: F = diag(1, 1,

lop3}

G = diag(3.2, lop3} Finally, K was found by solving a steady-state Riccati equation.

4. VERIFICATION OF CONCEPT In order to evaluate the potential ability of the Kalinan filter to improve control of pressure in the LSP loop of the power plant, the estimated coal flow is used as an input to a fairly detailed nonlinear simulation model. This nonlinear model was derived from energy and mass balance equations and has been validated against actual power plant measurements (Andersen et al., 2004).

To estimate the states in the above state space equations, we employ a Kalman filter. The general form of a Kalirian filler for a liiiear sy\lein

dx

- =Ax+Bu+Fv

dt y=Cx+Gw

where F and G are weighting matrices and v and w are white, zero-mean Gaussian noise sequences with standard deviations of I , is

dP =Ax^ Bu + K ( y - C.?) dt

-

9 = c.t

+

(13)

(14)

Here, K is the so-called Kalman gain, which essentially acts as a measurement feedback control driving the prediction el-rory - C.f to zero. The theory is well established, and will thus not be discussed any further here; refer to e.g., (Grewal and Andrews, 2001) for further treatment of the subject. The model equations are linearized around an appropriate operating point (&G); using a standard Taylor

Fig. 3. Nonlinear model structure. Figure 3 shows the structure of the nonlinear model. Note that the figure does not \how all states and ineasureinent points in the model, only the mosl important ones. The primary inputs to the model are the fuel reference infu,refto the coal mill and the feedwater flow &,,. The primary outputs are the pressure Pye and the enthalpy h,, = h(Pse.Ge)of the steam leaving the evaporator. All signals indicated by arrows going into the block diagram, e.g. the feedwater temperature c,,and the recirculation air flow &ca,f, are external inputs that must be supplied through measurements.

174

Figure 4 shows a simulation performed using this model along with actual power plant data acquired during the spring of 2004 from the Danish power plant I/S Nordjyllandsvaxket Unit 3 (Nordjyllandsvzrket, 1998). For most of thc scqucncc, thc plant opcratcs at a load of around 85%,but around the middle of the sequence it changes operation to almost full load, then back to 85%.

3 32-

0

1

2

3

4

5

6

7

8

"0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

I

I

$2 0

- - Measured

6)

The second and third plots in the figure show that the estimated oxygen concentralion and air flow correspond well to the measured values, which is quite natural, since they are outputs fi-om the Kalinan filter.

From this figure, it is obvious that the estimated coal flow varies rapidly during the one-hour sequence, although the reference is entirely conslant. Furthermore. it is noticed from the lower two plots that the plant dynainics observed in the ineasuremeiit data are captured better by using the estimated coal flow than by using the coal flow reference. In parlicular, the variations in the estimated fuel flow from around 1.2 to 1.6 hours are clearly reflected in both the estimated furnace temperature and live steam pressure, while the simulation using simply the coal flow rcfercncc docs not reflect these details. The peak seen in the simulated furnace temperature at 1 .I5 hours is obviously caused by the corresponding peak in the recirculation air flow. Since the peak does not occur in the measured furnace temperature, this is in fact likely to be a single outlier in the recirculation air flow measurement data. Furthermore, it is noted that the slow variation in the recirculation air flow, which appears to be reflected in the measured furnace temperature, is apparently not reflected fully in the model.

.

F

In figure 4 the results of a Kalman observer estimation of the coal flow are shown in the top plot along with the reference coal flow to the mill. It may be noticed that the observer estimates a flow that matches the fuel reference around the low operating point, but is slightly lower at full load. More importantly, the variations reflecting the state in the furnace can be seen. Note that the variations are more interesting than the steady state behavior, because they can be used in an inner cascade control loop controlling the coal mill. The steady state behavior is of less interest because the LSP loop will invariably contain integral action and hence remove any steady state errors.

The last two plots in the figure each show one measured and two simulated data sets. The first simulation was performed using the coal flow reference as input to the simulation model explained above, whereas the second simulation was performed using the coal flow estimated by the Kalman filter. Figure 5 shows a zoomed view of Figure 4 during a part of the sequence during which the coal flow reference was kept constant. Note that in Figure 5 , the plot of the oxygen percentage is replaced by the recirculation air flow in order to explain some of the variations observed in the data.

Estimatedtl

-.-. ~ i r n u l a t e d tfuel ~ , ref.

I

4

8

I

2 3501 - -Measure

id"

0

1

2

3

5

6

7

Time (hours) Fig. 4. Simulated and actual measurements. 5. OBSERVER-BASED CONTROL SCHEME

The estimated value of the coal flow may be used in the existing control scheme as illustrated in figure 6, where the estimated value is used in an inner loop feedback (cascade) in the LSP loop. This inner loop is able to reject variations caused by e.g. variations in the humidity, fuel grain size and calorific value or the coal. Furthermore it has a stabiliLing effect on the outer pressure control loop when the coal mill dynamics vary. It should be noticed that a prefilter is added in the controller in order to compensate for the new dynamic response of the controlled coal mill, so that the dynamics of the prefilter in series with the controlled coal mill has a response similar to the coal mill operated in open loop. Using this prefiller, the LSP loop will not have to be re-luned. The design of the cascade controller should reject fuel disturbances in a frequency area where the disturbances propagate to the watedsteam circuit. Observations from figures 4 and 5 indicate that the observer estimate variations in the frequency range froin 0.01 to 0.1 rad/sec, which may also be seen in the measurements of Tip2.Only the lower fi-equencerange propa-

175

26.5

8 5 9

26

LL

25.5'

501

' 0.8

1

1

1.2

I .4

1.6

I

I

1 1.2

1

i.4

1.6

Fig. 7. Coal flow disturbance rejection, assuming sinusoidal disturbances. 6. CONCLUSION AND FUTURE WORK I""

0.8

1

264 262

1.2

\

1

1.6

I .4

1.6

-r 3 -

0.8

I .4

i

1.2

Time (hours)

Fig. 5. Zoomed view of Figure 4.

i

In this paper, a novel fuel flow observer for pulverized coal mills, which utilizes mcasuremcnts of oxygen content in the flue gas, was suggested. A Kalman filter based on measurements of combustion air flow led into the furnace and oxygen concentration in the flue gas was designed to estimate the actual coal flow injected into the furnace. The Kalman filter was derived from a simple model oP the coal mill and the combustion in the power plant furnace. The approach was validated against a fairly detailed, nonlinear differential equation model of the furnace and the steam circuit using data measured at a Danish power plant. Furthermore. a cascade control scheme was proposed, which utilizes the estimated coal flow. Closing the loop around the coal mill in this way exhibits potential for better disturbance rejection and load following capabilities of the plant.

O1 Control

I N

' I

I I

Fig. 6. Cascade control scheme based on fuel flow observer. gate to Pse and h,s, due to the dynamics of the cvaporator. This indicates that a bandwidth of 0.1 radtsec would be more than sufficient. In figure 7 a bode plot of the disturbance rejection ratio of a controller with a bandwidth of 0.07 rad/sec is shown. Another way of using the idea of a Kalman filter is to regard the system from the air Bow and coal flow inputs to the oxygen content and steam pressure outputs as a 2 x 2 system and design a multivariable state space controller for this system. In this set-up an observer for the system will include an estimation o f the coal flow. The advantage of a multivariable controller compared to the two SISO controllers where the airflow controls the oxygen content and the coal flow conlrols the stream pressure is lhat both inputs are active in controlling each output, making a more optimal control possible.

From here, the plan is to test the concept on an actual power plant. In this contcxt, it will be an interesting problem to devise a performance measure that can indicate the relative improvement of introducing the concept outlined in this paper. This is far from trivial, since the operating conditions of an actual power plant are difficult to reproduce.

REFERENCES Andersen, l?, J. D. Bendtsen, J. H. Mortensen, K. J. Niclsen and T. S. Pcderrcn (2004). Obscrverbased fuel control using oxygen measurement. Technical report. Vrirmeforsk Service AB. Flynn, D., Ed. (2003). Therrnul Power Plant Simulution and Control. LEE. Carduno-Rainirez, R. and K.Y. Lee (2001). Overall control of fossil-fuel power plants. In: Proc. cf the 2001 Wititer Meeting of [he IEEE Power Engineering Society. Grewal, M. and A. Andrews (2001). Kultnun Filtering. 2 ed.. John Wiley & Sons. Nordjyllandsvaxkct, IS (1998). Nordjyllandsvmkct unit 3 - advanced technology and high efficiency.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

FAULT DETECTION IN COAL MILLS USED IN POWER PLANTS Peter Fogh Odgaard Babak Mataji s s

* Department of Control En,g%n,ecring,Aalborg Universitg,

Aalboy, Denmark, od,[email protected] ** Elsam Engineermg A / S , Kraftverksvej 53, DK-7000 Fredericia, Denmark, [email protected]

Abst rac t In order t,o achieve high performance and efficiency of coal-fired power plant.s, it. is highly important to control the coal flow into the furna.ce in the power plant. This means suppression of disturbances and force the coal mill to deliver the required coal flow, as well as monitor tlie coal mill in order to detect faults in the coal mill when they emerge. This paper deals with the second objective. Based on a sirnple dynamic rriodel of the energy balance a residual is formed for the coal mill. An opt.irria.1unknown input observer is designed to estirrmte this residual. The estimated residual is following tested on nieasrired data. of a fault in a coal mill, it can hereby be concluded tliat this residual is verj' useful for detect,ing faults ill the coal mill. Copyright @ 2006 IFAC. Keywords: Fault Detection, Coa.l-fired Power Plants, Optimal Unknown Input Observer

1. IN'I'RODUC'L'TON Thc performance of a. coal-lircd powcr plant is highly dependent on the supplied coal flow into tlie furnace. In order to achieve good performance or the power plant, this coal flow should be known and controllable. In other words the performance requirements of the power plant can be trarisfered to the coal mill wliicli delivers the pulverized coal to the burners inside tlie power plant furnace. One thing is to guarantee the required coal flow, in terms of suppressing pla.nt disturbaiices. It isl however, another thing to monitor tlie coal mill for detecting faults. In order to avoid additional failures and decreased performance in the power plant unit,, it is important to dctcct any fault as soon as possible, and hopefully as the fault emerges. In most coal mills it is not possible to measure the pulverized coal flow out of the mill. 'lhe coal flow into the mill is only indirectly mea-

sura.ble. Implying that the ea.rly fault detection based on detection of drops in the coal flow of the coal mill, is iiot so sirriple as it. seeins. A critical example on a f h l t in the coal mill is caused by a blocking in the raw coal inlet pipe, a coal mill is illustrated in Fig. 1. This blocking of tlie raw coal inlet, pipe will with t,ime result in a. stopped coal flow from the coal mill to the furnace, and since the actual coal flow into tlie furnace cannot be measured, the fault in the coal mill cannot he directly detected. Dynamic: rnodeliiig and nominal control of these coal mills have been tlie topic of ninneroiis of publicatioiis. Soinr examples dealing with modeling of coal rriills are (Rees arid Flzri 2003), (Zharig et u6. 2002) a ~ i d(Tigges e l d.1998). Coriirollers fur the coal mill are designed in (Kees and Fan 2003) and (Hassclbaclicr et ul. 1992). High order clyIianiic models a.nd observer design for coal mills

177

are the topics in ( h k a y a m a et al. 2004). However, the interest has not, previously been addressed on the monitoring of the coal mills wit,h the purpose of detecting any emerging faults. ‘lhe temperature of coal dust, flow after the classificr is a good indicat,or OF the “health” of t,he coal mill, since a non-intendanl change in tlie in and out flows of the coal mill will result in a va.ria.tion i n the temperature. However, the measured ternpcralure caririol be uscld to detect faulls directly: sirice a coritrol loop is foriried to keep (,lie irieasured temperature at lOO”C! in order t o evaporate the nioist,ure in the coal. Meaning that, the fault can be seen by combining the temperature and the energy in tlie primary air. 1.e. it might be iisefiil to moriit,or an energy balance state space model of the coal mill, which lias the cricrgy flows in and out of the coal mill as inputs, a.nd the tcmpcraturc as out.put. A fault in the coal mill is in this setting an extra energy input to t,liis model. If this extra energy input could he estimated, it would be a useful residual for monitoring the coal mill, wit-11 the intension of detecting cvcntual faults in the coal mill. This residual can be estimated by inlroducing a. slate representing t,lie fault in the energy model. This state is driven by a.n unknown input which is filtered through the fa.ult model. This described estimation problem cim he solved by t,he use of a.11 opt,iinal imknown inpiit observer, see (Chen and Patton 1999). Such an optimal unknown input observer is as a consequence designed for estimating the residuallfault signal arid the temperature. A threshold method is subsequently applied to the residual with the purpose of detect.irig the fault in coal mill. It is A.S well int.eresting t.o invest.igate t.he sign of this energy balance, sirice it can be used to separate the possible faults into two cla.sses which help in the fault isolation. The fault detection method is subsequently applied to data sampled during a fault in a coal mill. This experinlent shows the potential of the proposed residual estimated based on the energy balance niodel of the coal mill.

2. THE COAL MILL

The work presented in this paper, is based 011 a Babcock MPS 212 coal mill used at Elsam’s Nordjyllandsv~rkt.et TJnit 3 . However, the method proposcd in thc papcr is so gcncric that it ca.n be a.pplied to other types of coal mills. The coal mill is illustra,ted in principles in Fig. 1. ‘The coal is fed to the coal mill through the central inlet pipe. The coal is pulverized on the rotating grinding table by tlic rollers. The pulverized coal is then blown up and the moisture content, is evaporakd by the hot primary air. The primary air is mixed by cold outside air and heated outside air, which is heated

Pulverized coal A

Grinding table

\Primary

Air

/

Figure 1. An illustration of the coal mill. by the furnace. The ratio of these air flows are used to control t,lie t,emperatiire of the primary air flow. Coal particles which in the pulverizing have becri sma.11 cnough will pass through the classificr a n d out through t.he out,let pipes int,o the fiirnace.

2.1 Conlrol arid measurements References to coal flow a,nd priina,ry air flow are given by the general power plant controller, as well a.s rotational speed of the classifier. The temperature of tlie primary air is used to control the t,emperatiire in t,he coal mill at t,he classifier. . L ’ k temperature controller is often required t o kccp tcmpcraturc constant at 100°C in order to evaporate the moisture content in the coal. A coal mill is a harsh environment in which it is difficult to perform measurements, this niearis t1ia.t all the variables are not measurable. l3.g. the actual coal flows in and out of the coal mill are not measurable. However, the primary air flow and temperature are, as well as the temperature at the classifier.

178

102

Figure 2 . An illustration of energy balance in the coal inill, where Y ' ( t ) is the temperature in the mill, Qair(t) is the energy in the primary air flow, Prnotor ( t ) denotes the power delivered by the roller motors, Qcoal(t)is the energy in the coal flow, and QInoisture(t) is tlie energy in the coal rrioistuie. ~tn,,deriot,es the inass of the mill.

0

05

1

2

15

25

Salnplas I"]

2.2Faults A number of different hults can occur in t,he coal mill, aiid if the fault leads to a decrease in the o u l p u l coal [low Liorri Llie coal mill, Lliis ca,ri lead to drop out of t h e entire power p h n t unit. Some examples on critical fa.ults are: choking of tlie raw coa,l irilct, faults iri primary a i r supply both the fan a.nd the t,emperat,iire contmller, arid finally all the sensors, etc. All these ase fa.ults which it are urgent: t:o detect.

x to(

Figure 3. A plot of the non-linear and linear inodel response compared wit,li measiireineiit,s of a p response on the coal mill. are different, however the model error due to heat of steam to a conple of degrees above 100°C is neglectable in this context.

The t3yn a.inic rion-1 inra.r model i s siibseqiientl y given by 7rLII1Crn?(t) =7fLpa(t)Cair( T P A ( t )

-

T(t))

+ h C ( t ) C C(& q q ) + 7(t)7iz,(t)Cnr. Y; '

3. ENERGY BALANCE MODEL OF THE COAL MILL

-

(2)

~ ( t ) f n , ( t ) I & tT ( t ) + Prnotor ( t ) -

'

i

A simple energy balance model of the coal mill is derived based on (Rers and Fan 2003) In this rnodcl the LO^ inill is seen
712,

ern

( t )= Qair(t)

-

Qcoal(t)

- Qrrioisture(t)

+ Prnotor(f)

(1

1

l'he heating and evapordtiorr of the moisture iii the coal is inodeled by a combined heating coefficient l'hr temperatiire ir diie to the coritiol loop is kept a t 100°C The latent energy of the evaporation dominates the energy required for a few degrees heating of the moisture The combined heat coeficient, Hqt,is following defined as f15t = C, L,team/lOO, where C& is the specihc heat of the water, and Litelm is the latent heat 'I'his cornbiiied lieat ( oeffic ient does iiot dedl with the fact that thc spccific heat of water and stearn

+

where: Cm is the specific heat of the mill, T ( t ) is the mill temperature at the classifier, rkpa(t) is the prirnasy air mass flow in and out of' the mill. Cair is the specific heat of a,ir: 'r;n(t) is the terriperature of the irtlet y i r r i a r y a,ir)' r i h C ( L ) is [lie coal mass flow, C, is the specific heat of the coal, Y; is the surrounding teniperature, y(t) is tlie mtio of moisture in the coal, Curis the specific heat of the moisture, H,, parameter cornbiriing the latent heat of the steam and specific lieat of the wa.ter, is the power delivered by the mill and Prnotor(t) motor.

All parameters in this model are found in data books except m,, .Cmwhich is ident,ifietl based on nwmirements of a step response on the coal mill. The model response is compared wit'li mcasurements as well as the response of a linearized model in Fig. 3. From this figure it can be seen t1ia.t tlie responses of' both models ade quit similar to the large dyrianiical changes as tlie measiirements show.However, it is dificult to validate the details in the response due to the way the signals a.re sanipled. A dead band on one per cent is applied to these measurements meaning that the signals shall have changes of a given size before this change is sampled. The non-lirwir model ( 2 ) is subsequently linearized and transformed into a state space representation, see ( 3 ) , the motor power is also neglected from this s h t e space model since it is

179

inncli smiillei~than the other poweis iii the e q i i a -

where p is t,he pnle of internal residiial model,

tion.

Q ( t ) is the estimated residual/fa,ult signal ( corresponding to tlie needed energy flow to balance the model), Qn( t ) is the generic unknown input which is low-pass filtered in order to represent tlie residual, and A,=

where a given variable .z' is linearized by r: = IC - 2 , : IC, is the operation point of 2 . these operationa.1 points are fourid for interva.ls of the

1'1, 0 -P

operat.iona1 range of the plant, q(1) is the norinel distributed process disturbances, r(t) is the normal distributed measurement noises, ?;,( t ) is the measured ternperat lire arid

E, =

I:[

where Blx(l...3) denotes the three first elements of B. 'lhe model represented by (8-13) is discritizied before an observer is designed to estirna.te the s h k s i n the rrivdel. arid hereby llie residual) see (14-1s).

(15)

c = I. 4. RESIDTJAL GENERATION

'lhe energy balance given by ( 2 ) and iii a linear statc spacc vcrsion in (3-7) would in caw of a fault deviate from the coal mill which indica.tes an unba.la.nce in the model. The unbalance in the model can be represented by an additional fault input. In addition a static est,iinate of the coal moist,iire content is provided which is not valid during dynamic behavior of the coal mill. By combining tliese two model inputs to one unknown input, which represents both the fault energy and coal moisture, an estimate of this unknown signal can be used as a residual for detection faults it1 the coal mill. It can be assumed that the moisture content is changing much slower than a. fault can occur or ernerge. Jlowever, in order to estimate the need cnergy/fa,iilt, signal it is more convenient, t,o represent it, by a.11 internal st,a.t,ein the model. The simplest represent,atiori is a first, order lowpass filter which is included in the model. 'l'his results in the linear model given by (8-13))

where Ad, B d , cci,E d are the discritixied representations of A,, B,, C , , E,. 'l'his model is a system with an unknown input, tlistiirba.nces aiid measurement noises, i.e. an optimal u~ikuown input observer would be an obvious observer to i ~ s efor estimating tlie residual.

4. I

Optzniul unknowri 'input observer

.L'he optimal unknown input observer is described in (Chcn and Patton 1999). For discrctc timc systenis with unknown inputs and disturbances which ca.n be represented by x[n + 11 = A,x[n] + B,u[n] + E,,d[n]+ q[n.l,

y[n] = C,x[n]

+ r[n],

(16)

(17)

a11 optimal

unknown input observer of the following form can be derived z[n

+ 11 = Fn+lz[n]+ T,+,B,,u[.n] 1 Kn+lY[nI.

+

+ +

+

(18)

X [ T L I] Z [ T L I] H , + ~ y [ n I]. (19) 'l%e basic idea in this observer is to eliminate the dependency of the unknown input from the estimation error by matrix transforms, and subsequently design a Kalman estimator for the transformed system. A positive side effect of this! is that the estirrmtor ga.iii is recoinpiitetl at ea.ch sample tneariing that the rnodel can be changed such t1ia.t the point of operations can be upda.ted. Tlie schemes for computing the matrices in the

180

l"MO

,5000

I

I -05

,100

llbO

,200

,210 la0 Srmplas ["I

1381

lUW

3450

Figurc 4 Conipariion of the estimated energy due to the coal nioisture and the static calculated of this energy.

Figinre 5 . A plot of the signal nsed in fault detection method 1.

optirrinl unknon n input obsei ver can be seen in

possible, with the const,raint t.ha,t false detect.ion of faults are woided.

Appendix A The variance of thc disturbance and measuremcnt noises Q [ n ]and R[v].as well as the internal fault model parameter p are all found by trial and error, bdsed on expeiirrieiitdl data, in the wdy that the observer mtiinate? the energy 5ignaI in the falilt free situation well see Fig 4 From this figure 11 can be seen that the observer estimates the fault signal due to thc coal moisture contcnt well, and it is heieby concluded tlidt the observer arid niodel is well tuned

.I.[&

4.3 Fault isolation Ea.rlier in this paper it was mentioned that the sign of the energy balance can be used to separate the possible faults in two groups. A stopped coal flow will result in a positive energy halance. This means that the sign of the energy unbalance can he uscd for fault isolation if it is combined with additional itiformation in a logical decision scheme.

4.2 Detection rules In this scction two methods for detecting thc, faults bawd on Ihc rcsidual arc described. Thc first method is to use a simple threshold p, and coinpare the absolute value of with a tl.ire5.hold /3 as in (20). This means that a fault is detected based on tliis rnlr if 1lCj[n111 is larger tliari the threshold 0. In the following f,i[n]denotes a signal which is equal 1 in case of a fault and 0 elsewhere.

Another method pa.rtly removes the coal moisture by dividing it with the energy influence from flow contribution from the coal, before the threshold is applied: see (21).

4[n]

(0

else were. (21 1

The differences betwcen these two methods are tiiat the fiist method reacts faster on vaiatioii in Q[n],and a detection based on method 2 IS more certain to actually be a detection of a fault and riot due to a vdriation in the coal flow or in the moisture content in the ~ o d lFor both methods the threshold ?!! is found, such that it gi\es a dctection of the beginning of the fault as early as

5. EXPERILIEN'TS 'l'lir irttrucluced fault dekctiori rrirtltods based UIJ the estimated residual can detect a number of

In p r x t i c e only data. of one given fault t,ype is ava.ilable. It is a fault where the coal inlet pipe has been stopped by the raw coal. The sample t i m e iri this experiment is 60s. By visual inspection of the data from the coal mill the beginning of this fault can be detected a t sample 1115. 'lhe estimated residual &[n], can for this given fault be seen in Fig. 5. 'rhe other suggested method normalizes the residual by the energy in the coal flow! m,,nl Q n This normalization has the effect that variations due to process va.ria.tions is out compensated, and it is hereby much more certa,in that a given detection is due to a fault, in t,he coal mill and not a disturbance e.g. in terms of variations in the coal flow. The detect.ion signals of both detection methods are illustrated in Fig. 7 , from where it can be seen that method 1 detects the fault earlier than the visual illspection did: at sample 1110, and tha.t nietliod 2 did detect the fanlt 1 sa,mple later than the visual inspection, i.e. 1116. different, fault,s in thc coal mill.

c;c.\23-T,,,,).

6. CONCLUSION

A simple energy balance model is formed of a coal inill with the purpose of monitoring the coal

181

REFERENCES Cheri, ,Tie arid R. J . Pattori (1999). Robu,st rriwdelba,sed fault diagnosis for dynamic syslcms. first ed.. Kluwer academic publishers. Fukayama, Y., K. Hirasawa, K. Shirnohira and H. Kanenioto (2004). An ada.ptive state estimator for piilverizer control wing moments of particle size distributiori. IEEE '1kansuctions on Control System Technology 12: 797-811. Hasselbacher? It., 16. Lang and G. Lausterer (1992). Reglerentwurf fur eiri kohlenmuhlenniodell unter berucksiclitinguiig der verfa1ia.rensteclinischcn ra.ndbedingungen. n u tomat isierun,gstechnik 40,148- 157. Rees, N.W. and F.Q. Fan (2003). Modelling arid control of pulverised fuel coal mills. In: 'I'hermul po~uerp l a n t siniulntion, and con,trol (D. Flynn) Ed.). first ed. Irist,it~ut.ionof Electrical Li ng'irieer's. Tigges, K.D., W. Bischoff and T. Steinhatge ( 1998). Wir1xensc.hussel n I uhle ri als kor nponenten moderner feuerungs Kraftwerksll'echnik 78, 77-88. Zliang, Y.G., Q.H. Wu, J . Wa.rig, G. Oluwande, 11. Matts and X. X. Zhou (2002). Coal mill modeling by machine learning based on onsite measnrements. IEEE Transactions on Energg Coriversion 17,549-555.

Figurc 6. A plot of the signal in h l t detection Qn method wi [ n ] C \?!-T[n]) '

I

I

Mathad I M*hM

-0)

IIW

1106

ill0

111s sampios I")

1120

1121

Appendix A. OI'TIhIAL IJNKNOWN INPUT OBSERVER

2 ,130

Pigi.ire 7. A plot of the fault detection based o n the two proposed methods.

A necessary and sufficieiit coiidition for the existence of a solution to the given observer problem is in (('hen and Pattori 1999) given as: a n optimal unknowii input observer soliitiori exists if arid only i f rank(Cn+lEn)= rank (En).

mill, for detecting faults in the mill. A state is introduced representing the fault. The monitoring problem can be viewed as a system with an unknown input and dist,urbairccs arid inea,surcment, noises. An opt irnitl urilinown input, observer is subsequently designed. Thresholds are chosen sucli tha.t they do not result in false detections and at the same time detect. the fault as early as possible. The method is followiiig a.pplied to a fault example where the coal inlet pipe is stopped by the coal. Using the estimated residual results in a detection of fault 5 samples (5 minutes) earlier than a delect,ion based on visrial inspection. In addition a normalized residual is used for the detectioir a.s well. l ' h i s method, however, results in ,ion of the beginning of the fault 1 samples (1 minute) later than the visual inspection did. 'lhe proposed observer based method ha.s showed to be a promising method for detect.ing fau1t.s in coal mills.

The computation of the matrices in the observer is also given in (Chen arid Pattoii 19%) as.

7. ACKNOWLEDGMENT The authors acknowledge the Danish hhtristry of Science lcchnology and Innovation. for suppoi t to the research program CMRC (Center for Model Based Control), grant no 2002-603/4001-93.

182

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS CONTROL PERFORMANCE OF LARGE SCALE STEAM POWER PLANTS AND IMPROVEMENTS T. Weissbach*, M. Kurth* and E. Welfonder* D. Haake*' and R. Cudat** * Department of Power Generation and Automatic Control, W D , University of Stuttgart

Pfajfiwwaldring 23, 70569 Stuttgart, Germany 49 71I 685 66209, F a : 49 71I 685 66590 tobias.iseissbach@ivd uni-stuttgart.de

Tel.: XI

~

~

Vattenfall Europe Generation AG & Co KG

Abstract: Current energy market developments stimulate a dual electric power supply, which correspondingly increases the demands concerning flexibility and manoeuvrability of large-scale steam power plants. For these purposes, a joint research project between the University of Stuttgart and Vattenfall Europe Generation' has been initiated with the objective of creating an improved unit control concept, using advanced control techniques like nonlinear model-based and flatness-based feed-forward control. In a first step, however, the dynamic behaviour of existing large-scale generating units had to be analysed, which not only included an isolated analysis of each considered unit, but also the novel approach of a comparing analysis. Discrepancies in the control behaviour even between structurally identical units were detected. Considering the mentioned background, the overall results show that the currently dominating linear unit control concepts have several dynamic and static restrictions, especially when a unit is participating in the network frequency control. Copyright 02006 IFAC Keywords: steam power plants, power plant control, control performance, model-based control, flatness-based control, network frequency control, feed-forward control. 1. INTRODUCTION The increasing amount of electricity generation based on a mix of renewable energy sources, mainly wind power and heat-load-dependant combined cycle units result in a dual electric power supply (Welfonder, et al., 2004). If it comes to the worst case, especially during off peak times with simultaneously high wind intensities, not only the large scale lignite-fired 900-MW-units in the eastern German part of the Vattenfall Europe Generation' power system have to be operated at their minimum load level, but also their older 500-MW units. Since the latter are designed as duo-plants - two steam

generators feed one turbine, see Fig. 1 b this can lead to an unsmooth transition between duo- and mono operation with a power output of not more than P*c;,,,= 35% of the nominal power, see Fig. la, during extreme constellations. An alternative unit scheduling, including the temporary shut-down of some of the already in off-peak mode operated power plants, is often not possible, since the large scale lignite-fired units need several hours for the shutdown and start-up processes. Additionally, the system load increases significantly after 6 a.m., especially on working days. The units have then to be able to react correspondingly to the rising power demand immediately. ~

I

' Vattenfall Europe i s the 5th largest energj company in Europe 183

Most promising, however, appears a combination of the two approaches where possible.

Another aspect is a possible drop of the feed-in by wind power units caused by a sudden decrease of the wind intensities, or by a sudden shut-down of entire wind parks in case of too high wind speeds exceeding 25 mis to 30 mis. In case of such feed-in drops the conventional generating units have to increase their generator output instantaneously.

Apart from ensuring a secure steady operation, the main task of the unit control is the handling of the set point setting for the generator output, provided by the dispatcher and, in case the unit participates in the network control, by the network primary and secondary controller. In any case, the compliance with the unit design parameters has to be ensured.

Due to the above mentioned reasons, large scale steam power plants must be able to be operated flexibly in all load conditions to compensate the feed-in fluctuations, a challenge which has led to the initiation of a joint research project between the University of Stuttgart and Vattenfall Europe Generation. However, before developing a unit control concept, the current control performances of the considered large scale steam power plants had to be analysed first. For this purpose, a methodology was designed following a novel approach, which is not only based on an isolated analysis of one single unit, but on a direct comparison between different units in different operation modes. The advantages of this approach and some of the results, which partially can also be used for other related questions, are also shown in this paper.

The difference between a “classic” process control concept, which can be found in most units today, and a model-based process control concept is shown in Fig. 2. In the classic process control concept, see Fig. 2a, the feed-back controller has the function of both controlling the process according to the set point inputs and compensating disturbances on the process. A partial decoupling between these two functions can be achieved by an additional feed-forward controller which takes over the process open-loop control to some extend. The model-based control concept, see Fig. 2b, contains a superimposed process model, which computes a reference process output yret.If the process model is accurate enough, then the reference process output yrefcomplies with the real process output y if no disturbances occur (z=O), and the error variable Ay becomes very small. In that case, the process openloop control and closed-loop control for compensating disturbances can be designed separately.

2. NONLINEAR MODEL-BASED UNIT CONTROL CONCEPT

For thc dcvelopmcnt of a control conccpt, which not only enables the large scale steam power plants currently in the planning phase to meet the above listed requirements, but also the already existing older units, the project aims at a dual approach. The new control concept is designed in such a way, that the already existing and optimised unit control structures largely can be kept. The advantage of this approach is not only an uncomplicated integration into the unit control and communication system in the end, but also the possibility of continuous testing during the development phase without major disturbance of the scheduled unit operation. The chosen dual approach consists on the one hand of a nonlinear, model-based feed-back control (Pitscheider, et al., 2000), and on the other hand of a flatness-based feed-forward control (Rothfuss, et al., 1997), whereas the more suitable method has to be determined for each special case.

The process model used in the desired unit control concept, which also is the basis for the flatnessbased feed-forward control, originates from nonlinear modelling of the entire power plant process. The University of Stuttgart has already developed and published the models and a nonlinear model-based unit control concept, which thanks to its white-box-design has also been included into the new guideline VDIiVDE 3508 “Unit control of thermal power stations” (VDI, 2004). However, to adapt the theoretical model to the control of the considered large-scale lignitefired steam generating units, the dynamical behaviour of these units has to be analysed first, which was done in the first part of the research project.

a) ,,classic” process control concept with feed-forward control

.................

i.

...j feed-fommd U.t......................................................... I control ~

,,

.................

I

disturbance z

~

I

feed-back

W:

b) model-based process control with feed-foward control

w

feed-foward control

4.f-

disturbance z

1

Fig. 2: “classic” and model-based process control 184

3. CONTROL PERFORMANCE

3.I . Steadv operation Fig. 3a shows plots of the generator output of the three units A, B and C during steady operation in comparison to each other. For a consistent and clear representation in one single diagram, a time period of 3.5 h has been chosen. Since all of the units are participating in the network primary control during the considered time period, a relevant part of the observed oscillations in the generator output can be assumed to be caused by the network frequency noise. From the corresponding measured frequency plot, see Fig. 3b, a frequency bandwidth of approximatcly ‘I30 mHz was dcrivcd in all thrcc cases. With the frequency bandwidth known, the influence of the network frequency noise on the generator output was estimated using the proportionality 6 of the primary controller, which in this case is 6= 13 for all three units:

The VDliVDE-guideline 3.508 deliberately states only imprecise general information on the topic of control performance of thermal power stations. The reason for that is the dependency of the control performance on a variety of influence factors, which not only include the type, design, operation mode and control concept of the generating unit, but also the size and resulting system frequency noise of the interconnected or part power system the plant feeds in. This led to the fact, that momentarily the control performance of a power generating unit is not a precise defined parameter, but rather fuzzy and based very much on experience and personal assessment. However, a more precise determination of the control performance is possible if well defined operation states are considered, including process and test conditions. The composition of the Vattenfall Europe power plant fleet offered the opportunity not only to determine the control pcrformancc of single units, but also to compare the control performance of several structurally identical units, since the during the 90s built 900-MW lignite-fired generating units are almost of the same type and control structure. Together with Vattenfall Europe Generation, initially three 900-M W-units have been selected, which are denoted with the letters A, B and C in the following.

The above calculation results in an estimated generator output noise with a bandwidth of 5 0.5% of the respective nominal generator output, which originates from the participation of the unit in the network primary control. This generator output bandwidth is also shown in Fig. 3a. The comparison of the generator outputs of the units A, B and C (see Fig. 3a) points out, that the units show a highly varying control performance. Unit C shows the most balanced generator output, which practically ncvcr lcavcs thc gcncrator output bandwidth of k 0.5%. The generator output of unit A is more disquiet; however, violations of the generator output bandwidth only occur at few specific moments and are related to outside influences. Therefore, its overall control performance can still be rated as acceptable.

Since the nominal power outputs of the selected units are not identical, all analyses issue variables in the ‘3ev-unit-systeng”, which are denoted with a 11*m (i.e. x*(t) = x ( t ) i x ~ ~ , , , , ~That ~ , ) .way, variables can be compared more easily, even if they originate from different units. The following details focus as does the guideline 3.508 - on the variable “generator output”, since it is the most important control variable for power generating units.

’1

I -t ...

1%

095-

0

5002 5000

49.96

2

1

3

time [h]

0 12%

~

L , 0

1

2

3

time [h]

Fig. 3: System frequency and generator output of the units A, B and C during steady operation

185

The most disturbed progression of the generator output shows unit B. Here, particularly a superposed periodic oscillation stands out, which can be observed during the entire considered time period. The periodic oscillation can not be traced back to any outside influence and can also be detected in variables of the subordinate unit control circuits. This outcome indicates a considerable optimisation potential for unit B and has prompted further-going investigations, including the use of more sophisticated tools for signal processing and analysis like for instance spectral analysis.

like output change, with the same oscillation characteristics than in the case of steady operation. Also noticeable is the generator output of unit C, which reacts much slower to the ramp-like set point value trajectory than the other units, although the overall ramp gradient of 1.2 %/min is less high compared to the ramp gradients of the units A and B which is 2 %/min. 3.3 Step-like output changes Fig. 5 shows the generator output of the units A, B and C after a step-like change of the corresponding set point value. The data results from the corresponding pre-qualification procedure for the participation in network primary control (VDN Transmissioncode, 2003), namely for the operating mode “modified floating-pressure operation” with a turbine valve throttling rate of 3% and activated condensate retention control near the inaxiniuin load. The step-like change of the set point value for thc gcncrator output is gcncratcd by a virtual stcplike change of the system frequency set point by AAct = 200 mHz, which corresponds to a step-like change in the generator output set point by AP*G,set = 3%. The most important indicators for the step response of the generator output of the units A, R and C, the overqhoot y , and the response time T,, are illustrated comprehensively by using bar charts in Fig. 6. These indicators are also included in Fig. 5.

3.2. Ramp-like output changes P‘G [PUI

- actual value

--- desired value

\_______--.-.

-

0 71

1.1;

0.7 1 lun,tL..

-+

....A~

0 71

30

0

The comparison of the step responses of the three selected units in all load situations enables an overall evaluation of the corresponding control performance for the given conditions. Unit C shows the lowest value for 1; in each evaluated load situation; hence it is the fastest reacting unit. However, unit C is also the unit with the biggest overshoot. Unit A is well balanced compared to unit C; its response time is slightly higher but the overshoot much lower. The evaluation for unit B again points out a considerable potential for optimisation, especially because of the too long response time 7>, during minimum load.

t [min] 50

Fig. 4: Generator output of the units A, B and C during ramp-like output changes Fig. 4 shows the control performance of the units A, B and C during negative ramp-like output changes of -21% and -24% respectively. Because o f the partly stepped progression of the set point value trajectories, which normally is different for each unit, the conclusions derivable by a direct comparison of the generator outputs are rather limited. However, one point to emphasize is the occurrence of periodic oscillations in the generator output of unit B after the completion of the ramp1

0.95

- actual value - - - desired value

Fig 5:

0 5 f[min] 10 Generator output of the units A, B and C during step-like output changes

186

4. SIMULATIONS

a) overshoot y,

,.

12 I

Based on the results from the evaluation of the dynamic behaviour of the considered units, a nonlinear model was parameterised, which is intended to be used in a model-based controller. Before implementing and testing a model respectively modelbased control concept under real conditions, the behaviour of the model has to be investigated in numerous simulations. 4.1. Simulation of step response

peak load

medium load off-peak load

The first simulations focus on the control performance during network primary and secondary control. Therefore, the simulation model also includes a simple model of the European power system and its interaction with the power generating unit under consideration. Basic condition for the simulation is an off-peak system load situation already addressed in the introduction.

b) resl mse time TA 60

TA 50

B

I

40

30

The activation of the network primary and secondary control is evoked by a sudden drop in the system power feed-in by 2% of the system off-peak load of 150 G W (VDN TransmissionCode, 2003), which in reality might be caused by an emergency shut-down of a large power plant, and which causes a respective drop in the network frequency. Hence, the basic condition for the simulation is, apart from the size of the disturbance and the take-over by the network secondary control, similar to the conditions during the certification procedure mentioned in section 3.3. The result of the simulation is the step response of the modelled unit under realistic conditions.

20

10 0 peak load

medium load off-peak load

of

Fig. 6: Overshoot and response time generator outputs of units A, B and C

Beside the process variable “generator output” as the most important variable for power generating units, other process and control variables have been analysed similarly with a special focus on their interaction, like thermal power, live steam pressure, or live steam flow. These analyses revealed needs for optimisations also in the area of the subordinated control structures.

Fig. 7 shows the control behaviour of the simulated generating unit model with activated condensate retention control and turbine valve throttling of initially D* = 1% to minimize throttling losses.

a) system frequency (100s- 300s)

d) fuel mass flow (0s- 2000s) 1.04r

&

b) ti

:

0 96l

08,

t [S] 300

100

0

t [s] 2000

________________________________________.-, f) level feed-water tank (0s- 2000s) c) turbine valve position (0s- 2000s)

r d : $ v ~

o 48

fO% 096, 0

Fig. 7:

0 46, 0

,

t [s]2000

t [s] 2000

Simulated control behaviour of the nonlinear model of a large-scale generating unit after a feed-in drop by 2% of the off-peak load of the European power system ( 1 50 CW)

187

A throttling of I % proves to be necessary, but also enough, to compensate the chaotic grid frequency oscillations. The condensate retention is only activated after frequency drops of IAA > 30mHz. As can be seen in Fig. 7d and e, the activation of the immediate-reserve capacity is evoked both by the very fast opening of the 1%-throttled turbine valve and by the reduction of the condensate flow. The latter causes an emptying of the feed water tank by approximately 2%, while the replenishing of the tank already starts after about 250s and is finished after 800s, compare Fig. 7f. The almost step-like increase of the generator output during the first seconds, see Fig. 7c, can be traced back to the release of rotational energy after the frequency drop, compare picture 7b. After 30s, the entire immediate-reserve power is activated, as is demanded by the TransmissionCode, see Fig 7c. After the complete take-over by the network secondary control, all process variables return to their initial values as they were before the load disturbance. The characteristic of each simulated process or control variable is as expected, and the model performance shows a good agreement with the real unit performance.

based unit control concept, including a nonlinear process model and a model-based feed-forward controller. Before designing the control concept, the control performance and dynamic behaviour of the considered large-scale generating units had to be determined. Therefore, a comparing and comprehensive analysis including three existing similar generating units has been carried out. The results show considerable discrepancies in the control behaviour, even though type and control concepts of the considered units are structurally identical. The outcome also highlights optimisation potentials and needs for action, especially for the operation near the minimum load level, which is particularly important to prepare the units for the rising requirements following the increasing dual electric power supply. This fact can be seen especially from the high response time of unit B during off-peak load operation. Beside dynamic issues, problems were also identified during steady operation of the plants. Each considered unit shows an oscillating behaviour of its generator output and also subordinate process variables, which cannot be traced back to oscillations in the system frequency. Therefore, their cause can be found in control- or plant-related issues.

4 2 Plannedjirture proceeding

The present simulations show the behaviour of the nonlinear unit model and its interaction with the power system. However, the set point values resulting from the model have to be assessed carefully with regard to their compliance with the unit design parameters; so that it is ensured that no technological system boundaries are violated. Additionally, the flatness-based feed-forward control has to be parameterised and tested.

As for the controller design, first simulations have been carried out to test the dynamic behaviour of the considered nonlinear process model after a step-like input function. The model performance shows a good agreement with the real unit performance. 6. BIBLIOGRAPHY Pitscheider, K. and Welfonder, E. (1996). Modelbused Online 12ilininzizalion of NOxemission in Power Plants with pulverized coal Combustion. 13th IFAC World Congress, San Francisco, USA. Pitscheider, K., Meerbeck, B. and Welfonder, E. (2000). Robust model-bused unit control concept with regulated deactivation of preheaters and heat condensers. IFAC Symposium on Power Plants & Power Systems Control 2000, Brussels Rothfuss, R., Rudolph, J. and Zeitz, M. (1997). Flatness 4 neiv approach to control of nonlinear systems, at-Automatisierungstechnik 45, R. Oldenburg Verlag, p. 517-525 VDIIVDE: Guideline 3508 (2003). Unit control of thermal poiver stations, VDI, Beuth Verlag, Berlin VDN: Transmission Code (2003). Nehvork and System Rules of the German Transmission Systeni Operators, Verband der Netzbetreiber e.V. beim VDEW Welfonder, E., Kurth, M., Tillmann, H.-B., Hodurek, C. Radtke, H. and Nielsen J. (2004). Dzrnl Electric power szrpply with increasing wind power generation, requirement for an advanced secondary control concept, CIGRE 2004 Session, Paris

Therefore, a detailed dynamic model library for power generating systems developed by the University of Stuttgart can be used to represent the real plant, including the aidfuel-side of the process on the one hand and the waterlsteam side on the other hand. To simulate the control performance comprehensively, the control concept is applied on the detailed dynamic model of the considered unit. Starting from the network primary control, the control concept will be tested for every operation mode. The planned time horizon for the design of the entire unit control concept in the joint research project is 2 years (2006-2007). 5. CONCLUSION Due to the rising demands concerning manoeuvrability and efficiency of large-scale power generating units, improved control concepts are required, which allow the units to be flexibly operated in a wide range of load conditions. For this purpose, the range between the process-related boundaries has to bc utiliscd cntircly and expanded, if applicable, especially with regard to a lowering of the minimum possible load. For this purpose, a “classical” linear control concept, which can be found in most units today, proves to he not sufficient. The aim is the design of a comprehensive nonlinear model188

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

INTELLIGENT START-UP SCHEDULE OPTIMIZATION SYSTEM FOR A THERMAL POWER PLANT Masakazu SHIRAKAWA", Kensuke KAWAI", Masao ARAKAWA** and Hirotaka NAKAYAMA***

* Toshiha Cor*poration,2-4 Suehiro-cho, Tsurumi-ku, Yukoharna-shi,Kanagawa 230-0045, Japan (masakazul shirakcnua@loshiha co j p ) **Kaguwa University, 221 7-20 Flayashi-chu, Takanzatsu-shi, Kagawa 761-0396, Japan ***Konan llniversity, 8-9-1 Oknmoto, Higashinada-ku, Kobe-shi, Hjiogo 658-851, .Japan

Abstract: I his paper proposcs an intelligent start-up schedule optimization system for a thermal power plant. This system consists of a dynamic simulation, a neural network, and an interactive multi-objective programming technique. The features of this system are as follows. (1) The start-up schedule can be optimized based on multi-objective evaluation and ( 2 ) thc optimal start-up schedule can be determined with a reasonable computing tiinc and calculation accuracy through interaction between human beings and computers. Copyright 02006 [FAC Keywords: Power generation, steam turbines, optimintion, multiobjective optimisations, neural networks, genetic algorithms, simulation, dynamic models.

1 . INTRODUCTION

7 ypically, the start-up scheduling problem of a thermal power plant has sevcral conflicting objective functions, such as those for start-up time, fuel consumption rate, lifetime consumption rate of machines, and pollutant emissions rate. rhese parameters are affected by the varying market price of electricity as well as fuel, maintenance, and environmental costs. Therefore, it is important to achieve a flexible start-up schedule based on multicriteria decision making in the overall plant management strategy.

The start-up characteristics are evaluated by using a dynamic Firnulation; however, determining the optimal start-up schedule is complicated because it is necessary to iterate the dynamic simulation on the basis of trial and error wing the engineer's intuition and experience. Several methods for optimizing the start-up schedule have been proposed. For instance, a f u z q expert system (Matsumoto, et a1 , 1996), a genetic algorithm with enforcement operation (Kamiya, et a1 , 1999), and a nonlinear programming technique (Shirakawa, et a l , 2005). However, all these authors aimed to optimiLe a single-objective function (e.g., only the start-up time is minimized under the operational constraints). In cases with multi-objective functions, it is very difficult to adjust the weights of each objective function. Moreover, the computing time increases drastically, making applications to practical problems impossible.

This paper proposes an intelligent start-up schedule optimization system for a thermal power plant. I'his system consists of a dynamic simulation, a neural network, and an interactive multi-objective programming technique. This system can determine the optimal start-up schedule among multi-objectives with a reasonable computing time and calculation accuracy through interaction between human beings and computers. 2. COMBINED CYCLE POWER PLANT

2 I Plant configuration

'l'his study considers a multi-shaft type combined cycle power plant, as shown in Fig. I . It consists of three gas turbine units, three heat recovery steam generator (HRSG) units, and one steam turbine unit. I h e gas turbines and the steam turbine drive the generators. Also, the HRSGs generate steam for the steam turbine using waste heat from the gas turbines. This plant generates a total output of 670 MW.

2.2 Start-up scheduling problem The start-up schedule of this plant is shown in Pig. 2. In this study, the following schedule variables, objective functions, and operational constraints are considered to optimize the start-up schedule.

189

To Condenser r::itturbinespeed SecondlThird gas turbine speed

801

8

‘(3

J

.’;

40tp7v, 60

+ / -I 1 dno~

gas Firstturbine , load

6 20

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1

1

*

1

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j

12.5% ,

I

SecondlThird

HRSG

First unit Gas turbine

D J

F

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n

s

e

60 40

r

Time Fuel I

,i

SecondlThird unit Gas turbine

f Stack

To

f Synchronize Start-uD time

@

I

I

Fig. 2. Plant start-up schedule.

‘y E~

emission ratc from thc plant. The thermal stress of the steam turbine rotors in the above-mentioned objective functions has an upper limit to prevent mctal crccp and Fatiguc. Thc NOx cmission ratc from the plant increases significantly with the rapid startup; however, it has an upper limit in accordance with the environmental regulations.

Fig. 1 . Plant configuration

Schedule variables The steam turbine start-up schedule has a significant effect on the start-up characteristics of the entire plant. This is due to the thermal stress that develops in the steam turbine rotors, which is a factor that is particularly decisive for reducing the start-up time and fuel consumption rate. Therefore, four schedule variables are selected, i.e., the steam turbine acceleration rate xI , lowspeed heat soak time x2,high-speed heat soak time x3,and initial-load heat soak time x4 ; these are shown in Fig. 2. These schedule variables restrain the developed thermal stress by gently warming the steam turbine rotors.

3. CONCEPT OF THE SYSTEM A high accuracy plant simulator has been developed by one of the authors (Shirakawa, et al , 2005). The dynamic models are derived from first principles (thermo-hydraulic conservation equations), and they are implemented in the software packagc MATLAB T”/SimulinkTM.When the values of the whedule variables are provided, the values of the evaluation functions (the evaluation functions represent both the objcctivc functions and operational constraints) can be obtained by using the dynamic simulation. However, the high accuracy plant simulator is extremely time-consuming because detailed, largescale, and nonlinear model are used. Moreover, there are many optimal solut ns that are referred to as “Pareto solutions” in the multi-objective optimization; hence, a considerable amount of labor is requited to find the final solution. Therefole, it is well known that the multi-objective optimiration methods using the dynamic simulation require an unrealistic amount of time to obtain the optimal startup schedule because they require a large number of dynamic simulation calls. In order to obtain quick solutions, the dynamic simulation, a neural network, and an interactive multi-ob.iective programming technique are integrated by a cooperative humanmachine system. Figure 3 shows the functional structure of an intelligent start-up schedule optimization system proposed in this paper. The major part ofthis system consists ot‘a plant simulator, a human interface, and an optimization calculation.

Objectivefunctions. The ob-jective functions are to minimize the start-up time, fuel consumption rate, and thermal stress of the steam turbine rotors. A smaller thermal stress has the effect ot‘ t‘urther extending the service lifetime of the steam turbine. However, these objective functions have a trade-off depending on the above-mentioned schedule variables x/ to xi . As the acceleration rate xI increases and the heat soak times x2,x3,x~ decrease, both the start-up time and fuel consumption rate decrease; however, the thermal stress of the steam turbine rotors increases. This trend of the fuel consumption rate becomes more significant as the initial-load heat soak time x4 is varied because the gas turbine load is higher with xi than with the other schedule variables XI,xz,x3 . Il)p~mtionalconstrnints rhere exist many operational constraints in this plant. However, most of these operational constraints are safely controlled within the limits at any time (e.g., the drum water level and the steam temperature). As a result, the operational constraints consider only the thermal stress of the steam turbine rotors and the NOx

3. I Plant simulator part

190

The dynamic simulation of a variety of start-up schedules is executed beforehand. Further, the simulation results are saved as training data Tor the neural network.

Start-up schedule optimization system

3 2 Human interjace part

The user (i.e., the plant operator, manager, or engineer) needs a final solution among the Pareto solutions taking into account thc trade-off relationship between the objective [unctions. The proposcd system can easily dctcrmine the final solution through interaction between human beings and computers. The user performs only two functions in the human interface section. The first is to set the desircd value of the objective functions, which is called the “aspiration level,” and it is sent to the optimization calculation part. I hen, the start-up schedule (one of the Pareto solutions) that is closest to the aspiration level is obtained from the optimization calculation part. The second is to judge whcthcr or not the obtained start-up schedule is satisfactory. If the user is not satisfied, the user modifies the aspiration level, and it is sent to the optimization calculation part again. If the user is satisfied, the optimal start-up schedule is set in the plant control system. The plant control system subsequently operates the power plant according to the optimal start-up schedule.

Additional training?

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Fig. 3. Start-up schedule optimization system. aspiration level (Nakayama, 1995). This method can determine a solution of Eq. ( 1 ) through interaction between human beings and computers while eliciting information on the basis of the user’s judgment. The is modified aspiration level at the k-th iteration as follows:

ik

3 3 Optimization calculation part

An intelligent optimiLation method is developed using the neural network and a genetic algorithm to a satisficing trade-off method that is one of interactive multi-ob-jective programming. This is explained in detail in chapter 4. Since the dynamic simulation is computationally expensive, approximate functions using the neural network are introduced to create inexpensive surrogate models. Further, the start-up schedule closest to the aspiration level is searched with the approximate functions by using the genetic algorithm. The judgment whether additional training for the neural network is required is used to improve calculation accuracy.

Here, the operator P selects the Pareto solution that is nearest, in a certain sense, to the given aspiration The operator T is the trade-off operator level that changes the k-th aspiration level f k if the user does not agree with the shown solution P ( T k ) . Indeed, since P ( f k ) is a Pareto solution, there exists no feasible solution with all criteria that is better than the criteria with P ( T k ) ; thus, the user will have to trade off among the criteria if some of the criteria have to be improved. On the basis of this trade-off, a new aspiration level is decided as T P ( T k ). The process is similarly continued until the user obtains an agreeable solution.

4. INTELLIGENT OPTIMIZATION METHOD

On operation P. The operation that gives a Pareto solution P ( f k ) nearest to is performed by the following auxiliary scalar optimization of Eq. (4) using the Tchebyshev scalarization function F of Eq. (3). Here, the operational constraints can be included in Eq. (4) as the penalty function.

4 I SatisJicing trade-oflmethod

Multi-objective programming problems are typically written as follows:

7“

0

Tk

minimiLe f(x) = [ f , (x),f 2 (x),. . .,f , (x)] subject to g,(x)lO. j=I,Z:..,m

(1) 117

rninirnirie ~ ( x ) C +p j ~ , g , ( x )

where x = [x, ,x2,.. .,x n ]‘ represents the vector of the schedule variables; f , the objective functions; and g , t h e operational constraints, in this study. The satisficing trade-off method is an interactive multi-objective programming technique based on the

I

K, K,

(4)

1-1

0, if g , (x)< 0, j otherwise

=

/ . 2 , . . . ,m

= 1,

where a is usually given as a sufficiently small

191

positive number, such as lo-‘, and pi is given as a sufficiently large positive number. The weight w/i is given as follows:

where J;* is an ideal point that is usually given such that $* <minf,f,(x)lX E Xf , X is the set of all feasible solutions.

Hence, the training of RBFN can be solved directly by thc lincar simultancous cquation of Eq. (10). As a result, the training speed improves significantly and the local minimum problem is avoided.

On operation T. In cases where the user is not satisfied with the solution for P ( T k ) ,the user is requested to provide a new aspiration level T ” ” , and classify the objective functions into the following three groups: 1 . the class of criteria that are to be improved further, 2. the class of criteria that can be relaxed, 3. the class of criteria that are acceptable as they are.

4.3 Genetic range genetic algorithm

The minimization of Eq. (4) is solved by using the genetic algorithm. The genetic range genetic algorithm (GRGA) is applied in this study. Since it automatically adopts a searching range according to the situation of the generation, GRGA converges rapidly. See (Arakawa, et al., 2002) for more details.

4 2 Radial basis fiinction network

The radial basis function network (RBFN) is a type of neural network that consists of a number of radial basis functions. RBFN consists of three layers, i.e., the input layer, hidden layer, and output layer. The input values are each assigned to a neuron in the input layer and passed directly to the hidden layer without weights. The Gaussian function is used as an activation function for the hidden neurons. Then, linear output weights are connected between the hidden and output layers. The overall input-output mapping equation of RBFN is as follows:

4.4 Numerical algorithm The numerical algorithm has the following steps: The training data for RBFN are prepared by dynamic simulation. These training data contain datasets of the schedule variables and evaluation functions. Sfep2. The user sets the aspiration level of the objective functions. Step3. In order to create the approximate functions, RBFN is trained using the values of schedule variables as input values and the values of evaluation functions in terms of schedule variables as teacher’s values. The approximate function of the Tchebyshev scalarization function F of Eq. (3) to the aspiration level is created by either of the following methods: 1. The method that directly acquires the form of I; by similarly using RBFN 2. The method that calculates using created approximatc cvaluation functions Step4. The start-up schedule closest to the aspiration level is searched to minimize the auxiliary scalar optimization of Eq. (4) on approximate functions by using GRGA; it is obtained as an approximate optimal solution. Steps. In order to evaluate the approximation errors, the dynamic simulation is executed according to the obtained start-up schedule. If the approximation errors are large, some additional training points for RBFN are provided to the neighborhood of the obtained start-up schedule. Further, Steps I to 5 are repeated until the approximation errors become small. If the approximation errors are small, the obtained start-up schedule is displayed to the user. Step 6. The user judges whether or not the obtained start-up schedule is satisfactory. If the user is not satisfied, the user modifies the aspiration level. Further, Steps 2 to 6 are repeated until the user obtains an agreeable start-up schedule. If the user is Step 1 .

where x = [xI.x2,...,xn]”represents the vector of the input values; 0 , the output values; h, , the Gaussian function; w i , the weights; q , the number of hidden neurons; c, , the center of the hidden , the neurons; r, , the radial parameter; and Euclidean norm.

11. 1 1

The training equation of RBFN is defined as follows:

where w = [ w /,~ ‘ 2 . .. ..w‘/] ‘ represents tile weights vector; y , , the teacher’s values; p , the number of teacher’s values; and A, is introduced for the purpose of regularization. Equation (8) is reduced to the normal equation as follows: H ’ y = H70+ilIw= HrHw+AIw

(9)

H=

192

satisfied, the optimal start-up schedule is determined. 5. APPLICATION RESULTS 5. I Formulution

Simulation studies have been executed for a warm start-up condition, i.e., the initial temperature of the steam turbine rotors is 180OC. The steam turbine acceleration rate x, , low-speed heat soak time x2 , high-speed heat soak time x 3 , and initial-load heat soak time x J , are treated as schedule variables (See Fig. 2). Here, x, is a discrete variable with three values, and x2.x3,xi are continuous variables with upper and lower limits. The start-up time .fi is from the start of the first gas turbine to the plant base load operation. The fuel consumption rate f 2 is the gross weight during start-up. The thermal stress of the steam turbine rotors, f 3 (= g,,), is the maximum value during start-up. The NOx emission rate from the plant g,, is the maximum value of moving average per hour during start-up. Further, g,, and g,, have upper limits g l , and g12, respectively. The problem is to find the vector of the schedule variables x = [x,. x 2 . x: .x, ] , in which the objective functions fi, f 2 , f 3 are minimized under the operational constraints g,, I gi, and g,, I g12 . This problem can be summarized as follows:

140 180 220 260

(a)

60 70 80 90 actualf, [ton]

(b)

actualf, [min] 4 x

2

Q

9 (c)

60 80 100 120 actualf, [%I

-0.5

(d)

1.o actual F

Fig. 4. Results of the RBFN models. error defined by the relative error are summarized in Table I . The approximate functions created from RBFN agree well with the actual dynamic simulation results.

‘

{ 120 rpm/min. 180 rpm/min, 360 rpm/min) 5 min S x2,xs, xJ S 60min xI

E

5.2 Training oj’RBFN The dynamic simulation executes 250 start-up schedules randomly in order to prepare datasets of schedule variables and evaluation functions. The datasets have been divided into two parts. The first (SOYOof thc datascts) is uscd as training data for RBFN, and the second (20% of the datasets) is used as a validation data. RBFN is trained for all evaluation functions f,. f 2 . f 3 , g c i . g L 2on the training data. The results obtained for the validation data are plotted in Fig. 4. Figures (a), (b), and (c) show the values of f,, f 2 , and j 3 , respectively, made dimensionless by the upper limit. Figure (d) shows the values of the Tchebyshev scalarization function _ _ _I; of Eq. (3) to the aspiration level ( f , , f 2 , f 3 ) = (200 min, 74.4 ton, 94.9%). The average and maximum values of the approximation Table 1. Approximation error of the RBFN models Error

fi

f 2

f3.S‘I

g‘2

Average

0.13%

0.49%

0.58%

0.21%

Maximum

1.43%

2.14%

1.92%

0.58%

5 3 Multi-objective optimization

As a typical example, the results of the following interactive multi-objective optimization are explained. The initial start-up schedule (xi.x2. x3. xd ) = ( I 80 rpdmin, 40.0 min, 40.0 min, 30.0 min) is shown in Fig. 5 as the result of the actual dynamic simulation corresponding to the first aspiration level. This startup schedule was determined only by the trial and error of a heuristic approach; hence, it was inadequate. Let the first aspiration level be --I --I -/ ( f , f 2 f ; ) = (200 min, 74.4 ton, 94.9%). Then, the first solution is ( f ~ ’f,r ’ , f3’)=(175 min, 71.6 ton, 88.5%) and (XI.XZ.X;.X~)=(360 rpm/min, 5.0 min, 41.9 min, 48.3 min). Now, suppose that the user wants to further decrease the value of f i significantly and that of f 2 slightly. Since the present solution is already one of the Pareto solutions, it is imposible to improve all the criteria. T h e r e h e , suppose that the user agrees to relax 3 and let the -2 second aspiration level be ( f , . f 2 , f, ) = (I60 min, 70.0 ton, 92.8%). Then, the second solution is (f,’. f 2 * , f j 2 ) (162 min, 70.3 ton, 93.6%) and (xI,x2,x3,x4) = (360 rpmimin, 5.0 min, 22.4 min, 53.6 min). Although thc obtained solution docs not completely attain the aspiration level of J, and f , , it should be noted that the solution is improved than the previous one. The improvement of f, and f 2 does not agree with the wish of the user because the amount of relaxation of J 3 is not sufficiently large to compensate for the improvement of f , and f 2 . The optimal start-up schedule of the second solution is demonstrated in Fig. 6 as the result of the actual dynamic simulation. In Fig. 5 and Fig. 6, GT denotes the gas turbines; ST, the steam turbine; Stress, the normalized thermal stress of the steam turbine rotors:

-L

193

aspiration level and satisfy the operational constraints.

x

Y

0

-I

73-

a a,

I 100 I 50

0

Q

cn

IL

GTsDeed GT load

rn I

ST w e e d ST load

0

60

120 180 Time [min]

I-

IOOX

-50

- 0 240

5

p

6

The computing time depends on the size of the training data. In this case, it takes approximately 90 s (details, training of RBFN is approximately 30 s and searching by using GRGA is approximately 60 s) to obtain an optimal start-up schedule per aspiration level using a personal computer (IntelTMPentiumTM M processor 2.13 GHz). This is sufficiently quick for practical use. Table 2. Results of the objective functions

g 100 1 Limitation 2

G

f l

50

o

0

60

120 180 Time [min]

100

g

50

x

0 240

4

f 2

f 3

Aspiration level # I

200 min

74.4 ton

94.9%

Solution (RBFN) # I Solution (Actual) # I

175 min 175 min

71.6 ton 71.9 ton

88.5% 87.7%

Aspiration level # 2

160 min

70.0 ton

92.8%

Solution (RBFN) #2 Solution (Actual) #2

162 min I61 min

70.3 ton 69.8 ton

93.6% 92.3%

6. CONCLUSIONS Fig. 5. Initial start-up schedule corresponding to the first aspiration level.

:100 0

A

50

a a,

0

d

A cooperative human-machine system is proposed to optimize from among multi-objectives for the startup schedule in a thermal power plant. The application results show that the optimal start-up schcdulc can bc obtaincd with a rcasonablc computing time and calculation accuracy.

Q

cn

REFERENCES

0

120 180 Time [min]

240

Limitation

I

g o I Limitation

I

g 100

I

60

&

$ 50

ij

50 0

0

60

120 180 Time [min]

x

0 2

240

Fig. 6. Optimal start-up schedule obtained for the second aspiration level. and NOx, the normalized NOx emission rate from the plant. The results are summarized in Table 2, where Solution (KBFN) represents the results of the RBFN models, and Solution (Actual) represents the results of the actual dynamic simulation. Both the first solution and second solution are the Pareto solutions that are start-up schedules closest to each

Matsumoto, H., Y. Ohsawa, S. Takahashi, T. Akiyama and 0. lshiguro (1996). An Expert System for Startup Optimization of Combined Cycle Power Plants under NOx Emission Regulation and Machine Life Management. IEEE Transactions on Energy Conversion, Vol. 11, NO. 2, pp. 414-422. Kamiya, A., K. Kawai, 1. Ono and S. Kobayashi (1999). Adaptive-Edge Search for Power Plant Start-up Scheduling. IEEE T?unsactions on Systems, Man and Cybernetics, Part C, Vol. 29, NO. 4, pp. 518-530. Shirakawa, M., M. Nakamoto and S. Hosaka (2005). Dynamic Simulation and Optimization of Startup Processes in Combined Cycle Power Plants. JSME International Journal, Series B, Vol. 48, NO. 1, pp. 122-128. Nakayama, H. (1995). Aspiration Level Approach to Interactive Multi-Objective Programming and Its Applications. In: Advances in Multicriteria Analysis (P.M. Pardalos, et al., Eds.). pp. 147174. Kluwer Academic Publishers, Netherlands. Arakawa, M. and H. Ishikawa (2002). Development of Adaptive Range Genetic Algorithms Considering Inheritance of Searching Range. Proceedings of 2002 ki'ibfE Design Engineering Technical Conferences, DETC2002iDAC-34081 in CD-ROM. Montreal, Canada.

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Copyright 0Power Plants and Power Systems Control, Kdnanaskis, Canada 2006

ELSEVIER

A FAULT DlAGNOSIS AND OPERATlON ADVISING COOPERATIVE EXPERT SYSTEM BASED ON MULTI-AGENT TECHNOLOGY Wei Zhao, Xiaomin Bai, Jian Ding, Zhu Fang, Zaihua Li

China Electric Power Research Institute

Abstract In this paper, d new fault diagnosis and operational processing approach based on cooperative expert systetn combining with multi-agent architecture is proposed. For solving the complex and correlative faults, the cooperative expert system can overcome the deficient of single expert system It can be used not only for diagnosing complex fault in real time but ako giving operation advice timely It introduce\ the agent technology, designation of the cooperative expert system combining with multi-agent architecture, the realization of the system and application case. Copyright B 2006 IFAC Keywords Expert systems, fault diagnosis, power systems, agents

1. INTRODUCTION With the development of power system which is becoming more and more complex, more and more amount of real-time alarm messages from the SCADNEMS and WAMS about switchgear and protection, etc. will be sometimes about hundreds or even thousands per-second following system faults to the control center, which is far beyond the capacity of digesting the information for operator. So the research and development of fault diagnosis system will bring out the necessary condition for timely identification of fault or malfunctioning devices and for realizing the automatization functions of dynamic supervisory control system. The prevailing fault diagnosis approaches in power systcm are: expert system (Fukui, and Kawakami, 1986; Young, el al., 1997), artificial neural network (He, et al., 1999; Bi, et ul., 2002b), the fault diagnosis based on optimal theory (Wen, and Han, 1994). The fault diagnosis approaches based on fuzzy set theory (Lee, et ul., 2000), information theory (Tang, et al., 2003) and rough sct theory (Shu, et ul., 2001) aim at settling the incomplete and uncertain information problem. The paper (Bi, et al., 2000a) has comment on some diagnosis approaches mentioned above about the merit and defect. Jn these approaches, the approach of expert system based on rulcs is favored for its characters such as: clear in concept, the knowledge is easy to study and accumulate, quickly in calculating online etc. The fuzzy expert system of fault diagnosis (Young, el al., 1997) is discussed in order to solve the problem which the expert system based on the logic reasoning is poor in dealing with the uncertain reasoning process. It uses the voltage and current value for h z y reasoning arid advancing lhe Paul1 diagriosib by combining with the information of protection and breakers (Lee, et a/., 2000). This work was supported in part by the National Basic Research Program of China2004C'B2 17904.

Although the combination of two technologies of the fault diagnosis approaches above is partially implemented, it shows us that it is still a single expert system. The fault diagnosis approach bascd on cooperative expert system can carry out logic inference of complex fault, and the judge of uncertain information in complex fault alarm mcssages so as to getting thc diagnosis rcsult at the same time. After the diagnosis, it can also give the operation advice to operators in time. When the cross district fault happened, the approach can carry out cooperative diagnosis through communicating the diagnosis information and collaborated in function. For the question mentioned above, the fault diagnosis and operation advising cooperative expert system (it can also be called group expert system) of power grid is presented which is based on Multi-agent technology. In the system the alarm information from the SCADAEMS and protection devices is used to identify and forecast the fault devices and in the same time offer the on-line operation advice. The system is the development of the single fault diagnosis expert system and the effectiveness are highly improved by introducing the Multi-agent technology. Compared with the previous single expert system, the cooperative fault diagnosis among the sub-systems can increase the veracity and speed of diagnosis and are more capable in dealing with the fault diagnosis when the trips of protection relays and breakers are improper, or multi-fault occurs, at the same time offer the operation advice and decisionmaking according to the fault diagnosis results correspondingly. 2. MODEL OF IMPROVED AGENT UNIT AND SUB-EXPERT SYSTEM UNIT

There are several architectures of multi-agent system, for cxamplc, thc IRMA architccturc which is bascd on the BDI (Belief-Desire-Intention) model, the collahorated agent architecture, ARCHON The architecture of unit, whtch IS the methodology for 195

constructing agent or expert system which is the unit of the system, dcfines the modulcs of the unit and the interaction (data & control stream) between them, translates the information input (data from the sensor & message received) and defines the process of decision making according to the status of the units. The IRMA architecture presented first by Bratman is a typical agent architecture based on BDI (BeliefDesire-Intention) model. The belief of BDI model is the understanding of the circumstance and the agent itself. It is different from knowledge which is the true belief in common. Both the desire and the intention are the state of the event agents hoped, the main differences between them are: Intention controls the agents' future activity and plays a crucial role in inferring process; however desire is a goal agents aimed to but may achieve or not. Once an intention is created by an agent, it will propel the agent continuously to achieve the intention until it is finished. That is to say intentions control the coming agent actions and lead the current actions to choose agents. ARCHON is a collaborated agent architecture developed by London University, UK. It shows the basic means to solve cooperative problem and tasks as a general purpose frame for designing collaborated agents. The ARCHON architecture is divided into two layers: collaboration and control layer and domain-specific layer. Domain-specific layer is existed in advance or designed especially for certain tasks of domain (e.g.: some existent function in SCADA/EMS). Collaboration and control layer is the meta controller working on the domain-specific layer so that it makes sure that the activity of an agent on local doinain-specific layer i s consistent with others'. By integrating the two architectures as well as the fault diagnosis expert system we had accomplished, the architecture or the unit [or cooperative expert system is presented. The cooperative agent, based on the BDI model and the understanding of the sort and the function, integrates the IRMA architecture and the ARCHON architecture, as shown in Fig. 1. Structure of cooperative agent Fig. I

r

In the structure of the cooperative expert system, "'the communication manager is in charge of the information collection from external systems such as SCADAIEMS, WAMS and etc, the broadcast of diagnostic results and operation advices, the communication and consultation with other subexpert systems and agents. The alarm information and data from external systems and the internal collaborating information form the cooperative belief set. "*The cooperative belief manager manages and assigns the cooperative belief set and forms new belief set. "The cooperative inference engine forms the cooperative intention with the help of rulesifacts in the '?'common knowledge base, in order to do inference about the external environment. '5'the Means-Ends analyzer decides which plan will achieve the intention of a unit and which task will be assigned for the sub-expert system. "the cooperative opportunity analyzcr collects the results from the sub-expert systems for the cooperative inference engine, monitors the circumstance for decisionmaking opportunity and broadcasts the operation advices. The cooperative intention is executed by the cooperative executer using rules/ facts in common knowledge base, and stored in the knowledge base in the form of rule. The cooperative intention which is not achieved returns to intention forming process in the inference unit op the Means-Ends analyzer. Structure of sub-expert system Fig.2 I-

--

The sub-expert system, which based on the ARCHON architecture which has 2 layers, can be divided into 3 layers: domain-specific layer, control layer, collaboration layer (shown in Fig.2). Domainspecific layer is composed of SCADAIEMS, fault information system and WAMS. They are not only the data resource of every sub-expert system, but also executer of operating advice. All kinds of special tasks executed by domain-specific layer must be dispatched by skill of agent. However, these tasks (operation scheme) need to be confirmed before they arc executed at prcsent. AS for the control layer, its function5 include to decide which task should be executed by itself, to decide when and how to cooperate with other agents, to receive cooperate request from other agents Firytly the circumytance analyzer module analyzes thc task Sccondly, if thc fault diagnosis sub-expert

196

system can’t execute valid fault diagnosis, i.e. the Certainty Factor of diagnosis result can’t reach the threshold, the cooperate module will call self module and acquaintance module for reasoning, then send message to cooperative agent, to request a diagnosis result. At last, if the diagnosis result is available, the cooperative module will call acquaintance model module for reasoning, and then send message to cooperative agent, to request the next cooperative work. Circumstance analyzer and cooperate module are also forward chaining systems, they have their own infer engine and working memory. Experts’ knowledge and experience of operators can be written down as text according to some certain rule and format first, then he compiled as code by compiler and be saved into knowledge base, to be used by infer engine. Infer engine gets alarm messages from SCADAIEMS, WAMS and etc, calls APL of expert system and save these messages, and gets parameters of equipment from database, then calls knowledge base and executes fault diagnosis. Using event API, diagnosis analysis unit receives diagnosis result from other layers, and executes module diagnosis through information engine. After getting diagnosis result, infer engine sends them to MMI through integrate API, so as to be consulted by operators; and it sends them to other layers through diagnosis analysis module, so as to he consulted by other sub-expert system. As an interface to domainspecific layer, control module takes charge of managing all interactions with domain-specific layer. 3. OVERALL STRUCTURE OF THE SYSTEM The coopeiative expert system 111 which each unit can work indcpcndcntly is fit bettcr for using in the modern operation system of power grid than thc aingle expert system and multi-agent system for its flexible characteristicc; H i 4 unit which can handle the multidimensional and interactional information in real time is an intelligent and autonomous software entity which can transfer belief, desires and intention etc effectively It is fit for the needs of software in practical application which handle several tasks in real time. The unit model has been prehented at previous part Overall structure of the system Fig 3

197

Each unit cooperates with other units by fully using of the distributed intelligence, information and technology, which can enhance the adaptability of diagnosis system to dynamic environment and capability of handling the uncertain information so as to realize the distributed calculating and the settlement of questions through LAN. The structure of this system will be: (1) communications rnanager and Inanner Communications manager is a tool which can send or accept request information with environment. It is appointed which are the sender and the priority of the information from the sender so that start the rules to accept and handlc the valid information. Then it will send its information with some priority and transmission velocity. The information exchanged within each unit takes the client/scver communications manner in KQML language. So each unit must choose some type of information to send to a certain unit for some purpose. The types of the information include: asking fur data, asking for executing skill, aiisweririg the request, reporting current state, etc. each type of information include format of content and the expectation transmission data quantity. (2) perception and learning intelligence agent unit The cooperative unit handled the communication information with a series process and give synthesis agent unit for getting the result that will be learned by itself again. So it forms a circled self-leaming process. The perception and learning unit make the whole system adopting the change of environment and adding the knowledge to base by themselves. So it is a very important part of the whole system. (3) fault diagnosis expert system The unit uses the alann messages and data of SCADAiEMS and WAMS systcms for common fault diagnosis by logic inference with knowledge base and cascade fault diagnosis by calculating by means of improved OPA arithmetic. (4) operation advising expert system The unit will infer according to the diagnosis result and match the operation advice rules so that to give one or several rational operation advices in real time. ( 5 ) decision-making expert system The unit will evaluate the risk of the advices submitted by operation advising expert system by logic inference and analysis with the correlative data. It will give queue of the operation advices according one criterion. At the end it will give the best operation advice to operator. The unit is in process of devclopmcnt. (6) cooperative agent unit The unit is the centre of the whole systems. The messages communicated within the unit will be through the unit which dispatches all the other units and support the negotiation and coordination of each unit. (7) uncertain reasoning and fault diagnosis system Bascd on the belief network, the unit takes the SCADAIEMS alarm messages, protection messages and WAMS messages as the basic data for cascade

fault diagnosis by means of MCMC arithmetic. The results referred by other units are posterior probability of happened faults or the coming faults and uncertain messages about protections or breakers. (8) synthesis agent unit The unit synthesizes the results of fault diagnosis to be somc rules which will be addcd into the knowledge base. At that time, the synthesis results will be sent back to the cooperative agent unit and units which submit thc qucstions. To enhance the system responding performance in real timc, each process must has a time consume limit if which be cxceeded the process execute on the unit will be accelerated to shorten the executing time for responding in real time. The cooperative expert system is constituted by several distributed structures. So it improves the efficiency and reliability of question solution, and makes the system to be an opened system and more fit for using in the power system. The cooperative agent unit is h e centre or the system which disassembles the tasks, cooperates and dispatches the other units. It is shown on Fig. 3. Each unit communicated and cooperated through LAN with messages. The cooperative agent unit dispatches the tasks to each unit, directs them to synthesize the diagnosis results and broadcasts the diagnosis results and operation advice which come from fault diagnosis expert system and operation advising expert system. The agent unit and expert unit in the cooperative expert system have the structure shown on the Fig.2 and Fig.3. The expert system unit can distribute on the LAN and become a distributed structure for fault diagnosis. Firstly, thc cxpcrt systcm unit intercommunicates the information among the modules itself. Secondly, it solves the questions base on the messages of communicated within the units of the system. At last, it will judge the state of itself and give the self decision-making results to relative units of the system or directly to operator of power grid. The units take the message as the information communication format. The cooperative agent is servcr and the other units are client. The cooperative agent accepts and sends the mesaages to other units and achieves the whole aims of the cooperative expcrt system.

4 COOPERATIVE PROCEDURE OF THE SYSTEM The main function of this system is: to finish handling a great deal of data, which means to get useful alarm messages and data, to sift, classify and synthesize them, then to table a fault diagnosis outcome and operation advice, to give a real-time evaluation and fault diagnosis result sequence of uncertain information in allusion to faults about relay and breaker no action.

Firstly, the system transacts accepted alarm events, sifts them then sorts them according to their importance, the more important, and the more priority to arrange. The system divides alarm information into 3 grades: gl, g2, 83, every grade is related to a kind of operating statc when thc fault occurred in the power grid. Secondly, the systcm uscs the cxpcriencc of cxpcrts and operating experience, through infer engine and fault diagnosis expert system, diagnosis some certain fault symptoms which is token of some kinds of alarm data, and makes conclusions. Because some kinds of premonitions may have several different kinds of corresponding fault, the fault diagnosis expert system should make the most of the external information resource, catch useful information of dynamic circumstance, and make an integrative judgment about the operating state of the power grid. However, there is still some uncertainty in the diagnosis conclusion. It can bc cvaluatcd and arranged by uricertairi reasoriirig arid rault diagnosis system. The subsystem uses the original evidence come from the handled alarm messages, updates the belief network, makes an uncertain inferring with Markov chain Monte Carlo method(MCMC), attains the posterior probability of fault-inferring, then gets the diagnosis conclusion. The first data of the belief network were set by developer, expert and engineer, according to their experience and the summarization of former faults of the power system. After the subexpert system is running, the parameter of the belief network can be regulated in detail, though self-study. There are 3 kinds of strategies as below to respond the cooperate-request in this cooperative expert systcm: When a sub-expert system can’t finish a task, as a client, it will send a cooperate-request to the cooperative agent; when the cooperative agent received it, the cooperative agent will judge and answer it. If the cooperative agent admitted then it’ll analyze which kinds the task belongs to and send cooperate-request to corresponding subexpert system. The sub-expert system checks its job and current state, then decides to accept the task or not. Various sub-expert systems communicate with each other by infomation and send cooperaterequest of either sides oi- more directly. It’s necessary that all sub-expert systems know about cach other well. The cooperative agent set up an evaluating system of task decomposing and execntion. First, it decomposes the whole task, and assigns to every sub-expert system, then evaluates the task execution, so as to distribute tasks effectively. When the cooperative agent received a request that a sub-expert system can’t finish in time or a rcfusal rcsponse, it will reassign thc wholc task, assign the whole task or part of it to another sub-expert system.

198

Owing to the structurc of the cooperative expert system based on multi-agent, not only distributing diagnosis, information communication and resource sharing is likely to become possible, but also has better open ability. When facing to resolve and diagnosis complex problem, a sub-expert system only need to use appropriate cooperate and assignment strategies, distribute the diagnosis procedurc cffcctively, then all of the sub-expert systems can coordinate and cooperate with each other, finish the whole diagnosis task. In the fault diagnosis cooperative expert system , various sub-expert systems communicate with each other through the actions such as negotiation, promise, cooperate, but not strictly predefined interface, so the system can response dynamic information in time, and has robust adaptability.

protection of Zero 1 (zero sequence I), high frequency and distance takes action to trip the BI. At the S1 side the protection had not opened, which cause the protection Zero IV tripped breaker B7. On 220kV line S+;, protection of Zero IV causes the relay tripping the B3, B4 breaker. It is ensured as false trip confirmed after the fault analysis. The protection linking with the Sl and Pi doesn't cause the relay tripping the Blo and Bll, and the low voltage protection of 1,2,3,4 transformers doesn't cause the relay tripping the breakers so that the 01-04 breakers of transformer tripped at the 220kV side. On 220kV line S1S9, protection doesn't causes the relay tripped so that the BI7, BI8 and BZ4 breakcr trippcd. On 220kV line SIIS7, protection of high frequency relay tripped at Si side.

5 DIAGNOSIS CASE

Thcrc is a case of a ccrtain powcr grid, shown in Fig.4, it's used to explain how the fault diagnosis cooperative expert system realize cooperative fault diagnosis and give real time operating advice, and how to help operators to diagnosis and adopt measures to hold fault back from enlarging. . A portion of some local power grid Fig. 4

There is an example considering the portion of some local power grid shown in Fig.4. Suppose that a fault occurs on line SISs followed by a series of breaker and relay trip which cause 6 lines outage, a power station shedding from the power system. The fault is over after 2 I minutes in which there are 12 breakcr tripped. In the course of the fault, expert system received 14 piece of alarm messages (in which two messages are false) about breaker trip, 48 alarm messages about protection relay trip, and 436 the other messages. After the faults, the investigation group gives their analysis, the results of analysis about fault were' u. There happened a permanent fault on 220kV line SIS5, the phase A, C short circuit and grounding. At the breaker Bi sidc, the

199

In ordcr to test the coopcrativc function, the powcr grid i s divided into 2 parts. D1 and D2 The system composed of 10 units, both DI and D2 have separate fault diagnosis sub-expert system, uncei tam reasoning and fault diagnosis system and operation advising sub-expert system, other parta is in common.

When the fault occurred in Linc SIS5,according to the relay and breaker information, i.e. the Zero Sequence 1, High Frequency, Distance Relay of S5 side and breaker BI information, the fault diagnosis expert system of Part D1 tabled diagnosis result R1 as follows, because of the lack of breaker B2 information, the Certainty Factor (CF) of rules is 0.8; for the lack of information, the fault diagnosis subexpert systcm will send coopcrativc diagnosis rcquest to cooperative agent. The cooperative ageril triggers a unit selected according to content of the request, while the triggering unit is uncertain reasoning and fault diagnosis system, it will ask the cooperative agent for the information processed by fault diagnosis expert system as proof, so as to update the brief network. The posterior probability of event which breaker B2 didn't trip, reasoned from MCMC, is 0.9799, the posterior probability of fault occurred on Line SlS5 is 0.9682. When a cascade fault occurs, such as the fault of part D1 extends to part D2, i.e. when there's a crossdistrict fault, the fault diagnosis expert system and the uncertain rcasoning and fault diagnosis system and dispatch expert system of part DI, will send prealarm information to the cooperative agent, according to the diagnosis result, and request the diagnosis unit of part Dz to diagnosis, then the cooperative agent will trigger the related units. In the case, diagnosis result R4 is resulted from both the diagnosis unit of part D, and the diagnosis unit of part Dz, during the diagnosis, the 2 parts send requests to the cooperative agent, so as to get related information as diagnosis foundation.

The operation advising expert system searches suited operating advice according to the real time didgnosi$ result, and then the cooperative agent puts out the diagnosis result and operating advice through a communication manager to operators The diagnosis results and operating advice given by this system are: 1 . 220kV linc SISc grounding, pcrmancnt fault, Zero I, high frequency, distance protection trip the relay, CF:0.8; The posterior probability of Breaker B2 which not tripping is 0.9799, the posterior probability of fault occurred in Line SISs is 0.9682: Advise: the outage may occur on the adjacent line, if the breaker reject to trip, switch it off; patrol the line and remove the fault. Rule number: BNFl loo5 2. An outage occurred in an adjacent line: 220kV Line SIS8, to separate a permanent fault in 220kV Line S1S5,the Zero Sequence IV tripped the beaker, CF: 0.95; the posterior probability of h u l t occurred in Line SlS8 i b 0.9548; Advice: to patrol along the line to remove the fault; Rule serial number: BNFIIOIL. 3. 220kV line SiS* load shedding, B3, B4 false trip, Zero IV protection cause relay tripping the breaker of line SIS8, CF: 0.90; the posterior probability of fault occurred in Line SISs is 0.3268; Advice: switch on the breaker manually. Rule number: BNF13002 4. 220kV line S1S5grounding, permanent fault, B2 not trip. # I and #2 lines on line SIPi have not relay or breaker trip messages, CF: 0.85; Advice: switch off the linked correlation breakers manually. Rule number: BNF12004 5. # I low voltage protection causes relay tripping thc 01 brcakcr, CF: 1.00; Advice: Bio, B12 not opened, switch off them manually. Rule number: BNF1200F 6. #2 low voltage protection causes relay tripping the 01 breaker, CF: 1.00; Advice: Blo, B12not opened, switch off them manually. Rule number: BNFl2005 7. #3 low voltage protection causes relay tripping the 01 breaker, CF: 1.00; Advice: Bio, Bll not opened, switch off them manually. Rule number: BNFlzoos 8. #4 low voltage protection causes relay tripping the 01 breaker, CF: 1.00; Advice: Blo.B12 not opened, switch off them manually. Rule numbcr: BNF12005 9. 220kV linc SoSl load shedding, permanent fault, relay at S9 side reject trip, BI7,BI8,BZ4trip, CF: 1 .OO; Advice: finding the reason, and restoring the power supply. Rule number: BNF13003 According the above diagnosis result, operators can easily get the diagnosis results. The results of 1, 2 from the system equal to the above-mentioned analysis u and h, 3 equals to the analysis c, 4, 5 , 6 , 7, X equal to d, 9 equal to e.

After a fault occurred in a power grid, according to the diagnosis result and operating advice given by this system, operators have no need to analyze original information, according to the diagnosis result, carry out the prepared emergency scheme, switch off related lines, then the extends of fault can be hold, thus a more serious cconomy loss can be avoided. 6. CONCLUSION The presented system in the paper is a fault diagnosis and operation advising cooperative expert system based on Multi-agent technology, which is the combination of the agent technology and cooperative expert system. It overcomes the deficiencies of the single expert system, and it is capable of offering both the diagnosis rcsult and operating advice simultaneously, therefore a better aid for operator is achieved. In order to put the system into practice, BNF compiler is employed as a tool to obtain the expert knowledge and some practical fault scenarios are tested in the system which the satisfied results are obtained. The system has been used in a district power grid of Shangdong province for a year, and has got a satisfied response from the user REFERENCE Fukui C., Kawakami J. (19x6). An expert system for fault section estimation using information from protectivc rclays and circuit breakers. IEEE Trans. On Power Delivey,Vol.l, No.4,83-91 Young M. P., Gwang-Won Kim,Jin-Man Sohn(l997). A logic based expert system(LBES) for fault diagnosis of power system. IEEE Trans. On Power Systenzs, 12(1), 363-369 Bi T S, Ni Y X, Yang Q X(2000). An evaluation of artificial intelligent technologies for fault diagnosis in power network. Automation of Electric Power Systems, Vo1.24, No.2, 1 1 - 16 He Y H, Han S M, Cheng S M(1999). Development of fault diagnosis based on multi-neural network Proceeding of’ the joined inference. CSEE ,19(12), 57-60,65 Bi T S, Ni T X, Wu F L et al. (2002). A novel neural network approach for fault section estimation. Proceeding ofthe CSEE ,22(2), 73-78 Wen F S, Han Z X (1994). Fault section estimation in power system using genetic algorithm and simulated annealing. f’roceeding of the (SEE ,14(3), 29-25 Lee H J,Park D Y,Ahn B S et al. (2000). A fuzzy expert system for the integrated fault diagnosis. IEEE Trans, Power Delivery ,15(2), 833-838 Tang L, Sun H B, Zhang B M et aL(2003). Online fault diagnosis for power system based on information theory. Proceeding of the CSEE ,23(7), 5- 1 1 Shu H C, Sun X F, Si D J et a1.(2001). A study of fault diagnosis in distribution line based on rough set theory. Proceeding of the CSEE ,21(10), 5-1 1

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PUBLlCATlONS

MODELBASED FLEET OPTIMISATION AND MASTER CONTROL OF A POWER PRODUCTION SYSTEM

Claw Joergensen", Jan H. Mortensen", Tommy Moelbak"", Erik 0. Nielsen"

*Elsum Kruz A& Overgude 45, Skaerbaek, 7000 Fredericiu, Denmark Enzarl {clj, jhm, eon)@elsarn corn * *Elsum Engineering A/$ K r u f i m r h v e j 53, Skaerbaek, 7000 Fredericia, Denmark Ernail tmc@elsarn-eng corn

Abstract: Being the largest power producer in Denmark, Elsam faces a complex operational optimisation problem at portfolio level as well as at the individual power plant level. The utilisation of advanced modelling and control systems at all levels of the power production system and the integration between these levels play an essential role in optimising performance on a commercialised market. The applied optimisation concept is introduced as a distributed multi-level control problem, and the primary fhctionalities at top levels are presented, including short-term load planning, balancing power control, frequency control, marginal costs calculator and multi-variable master control. Practical examples illustrate the interaction between the functionalities and emphasise the importance of using advanced modelbased control methods. Copyright 02006 LFAC. Keywords: Load dispatching, power plant control, optimisation, modelling, multi-level control

. 1.

INTRODUCTION

The Danish power production system is a very complex system - in both a technical and a business sense. Therefore, it is most beneficial to utilise advanced modelling and control in relation to this system. The business objective is to make the best possible use of a distributed power production system in a deregulated, but still constrained market. Elsam, the largest energy producer in Denmark, is used as a case study on this topic.

A set of dynamic constraints. This depends on the production system, the authorities, etc. In Elsam's case, it consists of eg environmental regulations, grid capability, fuel contracts, district heating contracts, etc.

From a business point of view, it is essential to be able to optimise plant operation within this framework, and optimised modelbased control forms a very important part of system optimisation. Considered from the aspect of control, the power production system is a multi-level distributed system, see Figure 1.

In brief, the system optimisation problem is composed of three elements: A distributed power production system. This can be very different from one producer to another. In Elsam's case, it consists of fossil fuel-fired thermal plants, biomass-fired thermal plants, waste incineration plants, on- and offshore wind power and district heating storage.

.

BOILER

8

A deregulated market. On the power exchange, power and regulation power are traded on an hourly basis. Trading of district heating resources is performed through bilateral contracts.

SUPER

TURBINE

Figure 1 Multi-level power production system.

201

Performance optimisation of the system in Figure I implies that all levels are optimised to some extent, and that the integration is optimised between the levels. This means eg that optimisation at a low level (servo level) is a precondition for optimised control at other levels.

Primary control reserve. On frequency deviations a load reserve can be activated within 30 seconds. Pricing will be fixed according to the reserved power (fMW) in a monthly-based price. Secondary control reserve. On market balance deviations a load reserve can be activated with a predefined load gradient. Pricing will be fixed according to the power reserve (kM W).

In recent years, advanced control has played an important role in the performance optimisation of power plants, and considerable efforts have been dedicated to control optimisation of each level of the hierarchy shown in Figure 1. Examples at system level can be found in (Welfonder, 1997), in which the dynamic performance of power plants in power systems are examined and in (Honig et al, 2000), in which short-term load scheduling is discussed. At plant level, (Lausterer, 1998) discusses master control of power plants. These are only a few important examples of previous works.

Regulation power (Energy) to cover differences in production or consumptions. Prices on activated regulation power will also be determined every 24 hours. Automatic regulation power (Energy). In real time, the power balance in the Danish grid is controlled by a TSO operated controller, which is directly connected to the power producers. Pricing is linked to prices on the spot market.

This paper focuses on two top levels: The system level and the plant level. It is a realistic case study on the utilisation of advanced modelbased optimisation and control, including a number of practical examples.

2.

Finally, these market conditions express the substantial demands in the Danish power system. Figure 3 shows an example of a 24-hours actual operation illustrating the conditions and demands. Due to increased power consumption and reduced wind power production around noon, it was necessary to increase the central unit production considerably (approximately 50% during two hours).

MARKET REQUIREMENTS

The power market includes - from a producer’s point of view - two costumers: The power exchange(s) and the Danish TSO (transmission system operator). The power exchange is typically owncd by a numbcr of TSOs in this case the Nordic power exchange Nordpool is owned by the Nordic TSOs. The commodities traded in the power market appear from Figure 2

4000,O 3500,O 3000,O

~

y d

j

2500.0

g 2000,o 1500,O 1000,o 500,O 0,o

COMMODITIES

1. ENERGY

/

-Central

units

E x p r l (net)

-Small CHP units -Mnd -Consumption

ttrbines

Figure 3 24-hours production sequence from Western Denmark.

3. OPTIMISATION CONCEPT It proved necessary to develop a system control level due to the fact that the power production company had to comply with the requirements on the power market mentioned in section 2. The entire data communication is performed automatically without any human interaction required in the loops. However, operators are required to supervise the system and make different strategic decisions for the operation of the system.

l _ _ _ _ _ _ _ _ _ _ _ _ _ l

Figure 2 Power market commodities The different products differ in time scale and settlement and may briefly be explained as: 8

Energy. The power exchange will every 24 hours set an hourly-based price based on all the players’ offers and all the buyers’ assumed demand.

202

POWER I POWER

OPTlMILATION

EXCHANQE I PRODUCER

GOALS

II

Figure 4 System control concept (simplified) A diagram of the system appears from Figure 4. Notice that the diagram is simplified. Far from all actual signals are present, only the primary signals are mentioned in order to explain the principle functionality. The basic system components are: 1 1

1

1

1

4.

Short-term load scheduler (STLS) 2-24 hours. Power controller (PC) 5 minutes. Frequency control scheduler (FCS) < 30 seconds. Marginal cost calculator (MCC). Master control (MC)

IMPLEMENTATION OF FUNCTIONALITY

In a control system context, the STLS may be regarded as a very complex feedforward controller with the load plans representing the feedforward control signals. The short-term load scheduler consists of a set of models and an optimisation algorithm (control algorithm). Compared with models at lower levels, these models are simple. They are steady-state models focusing on the economic features of the plants. The optimisation problem is composed of a unit commitment problem and a load-schedule problem, which often lead to an optimisation problem with several thousands of unidentified variables. Assuming that power prices have been set, and that district heating demands are known, the objective function will minimise the following costs:

In the following, each of the above-mentioned components is described in detail.

1 1 1

4 I Short-term load scheduling 1

The objective of the short-term load scheduler (STLS) is to perform the calculation of the economically optimal load schedules for each controllable production unit, taking into account a number of constraints, different scenarios, contracts and the actual power sales. A further input to the STLS is the estimate of the actual marginal cost for each unit. The output of the STLS is a 5-minute based, 24 hours ahead, electrical and district heating load schedule for each controllable production unit. These are in real time automatically communicated to each unit and ahead of the process delay time in order to supply power to the grid in time. Recalculation of the load schedules for the remaining part of the day is perliormed when required - ie when required by the operator.

Fuel costs Fuel related costs - eg transport and deposition Load related costs - eg maintenance and load ramping. Other costs - eg taxes and district heating

Furthermore, the requirements for calculation time are very strict. These are the reasons for using Quadratic Programming and Mixed Integer Programming as basic optimisation algorithms. 4.2 Power balance control The objective of the power controller (PC) is to minimise the deviation between the total electrical power production reference value and the actual power production in a feedback manner (since the production deviation is economically penalised on a grand total basis and not for each unit). In this way, the PC attenuates the unavoidable discrepancies of the STLS feedforward actions, such as non-exact wind power prognoses, production disturbances on thermal power plants, ie trips or power reductions. A

203

implementation by use of Real Time Workshop generated code.

further functionality is to support the TSO in balancing the power production with the demand in its geographical area. The functional purpose of the PC in a control system context is both to perform disturbance rejection and reference following. The PC outputs are corrective signals to the load schedules and other fast responding control actions: Corrective signals to the electrical load schedules, one for each production unit. The response to these power demands is relatively slow as most plants are operated in natural sliding-pressure mode. Corrective signals to the district heating load schedules, one for each production unit. The responses to these demands are faster than the above-mentioned response, though they are limited to the speed at which the large district heating flow rates can be acceleratedldecelerated. Each unit has a district heating storage tank to ensure just-in-time delivery and district heating.

Frequency control

4.3

The objective of the Frequency Control Scheduler (FCS) is to fulfil the TSO requirement for frequency control in the required proportion and in the economically most efficient way.

In relation to power, the primary control can be produced as a grand total allowing performance of the primary control in the production units and at the lowest possible cost for this functionality. For each unit a set of values defines the primary control device. Figure 5 shows these six variables, a deadband, a control band and the maximum power for both over and under frequency. P [MWI . . . ~ . ...........~ ...........................

Corrective signals to the condensate systems of the power plants, which increaseidecrease the condensate flow resulting in a decreaselincrease steam flow through the low-pressure turbines leading to decreaseiincrease in the electrical production. The response to this demand is fast, but this can only be maintained temporarily as long as the maximum and minimum limits of the condensate level in the feedwater tank are within their limits. Therefore, the steady-state gain of this response is 0, and supplied energy must be resupplied to the system in order to normalise condensate levels. Corrective signals to steam turbines with control stage (multi-nozzle). The steam reservoir capability of the boiler is utilised. This response is also only temporarily until the limits on the steam pressure are exceeded. The steady-state gain of this response is also 0, and the supplied energy must be resupplied to the system to normalise the steam pressure.

v

POWER MM

nr

Figure 5 Primary control function. Based on this, the FCS calculates the individual P = f(AQ so that the sum equals the required total. An algorithm is developed, which matches the total primary control function from the individual ones in the most cost-effective way. An example of a calculated total primary control function appears from Figure 6.

Corrective signals to wind farms. The electrical production from the wind turbines can be increasedldecreased very fast, ie from minimum to full load in seconds. Normally, wind turbines are operated at their rnaximuni relatively to the actual wind speed; hence production can only be reduced. However, the operators can choose to reduce the production to maximum production resulting in the capability of increasing the production as well. Though, being an obviously uneconomic solution, this is only rarely carried into practice.

'igure 6 Total primary control function. The blue colour shows the required function, the grey shows one of the individual functions, and the white colour shows the total fitted function.

In order to develop a control system using these corrective signals all with different dynamic performances, a modelbased approach was required. MatlabiSimulink was applied to the development and

44

Marginal cost calculation

For each production unit, the marginal cost calculator (MCC) calculates the marginal cost for the next electrical and thermal MW. This information is 204

transmitted to the short-term load scheduler in order to minimise the overall fbel consumption.

1

The master controller is often based on traditional linear SlSO principles even though the process is highly non-linear and multi-variable. Therefore, further optimisation of the dynamic performance during load changes is often necessary. For this purpose, a complementary non-linear MIMO concept based on LQC control was used successfully. Further details can be found in (Mortensen et al, 1998).

The MCC system is able to map the fuel consumption and the Cv-value within the entire load area of the power plant unit during varying heating and power situations. As an example, Figure 7 shows a PQ diagram for one of the units (unit 3 at the CHP plant Skrerbrekvzrket). The diagram is based on 144 model calculations. I- or each calculation point in the PQ diagram a Cv-value and a gross boiler input are attached so as to render possible a quick estimate of fuel consumption. The PQ diagram provides the plant operators with a precise overview of the actual mobility of the plant operation. .,

Tumbr PO DiagnrntONLINE,

Time

Feedback correction of the primary output variables (pressure and enthalpy).

4.6

Infrastructure

The realisation of this system level required the development of an appropriate inkastructure. This applied both to the information technology platform for the central calculations and to the communication with the geographically different locations. The one first mentioned has been implemented in various systems all using a Wonderware Application Server solution (www.wonderware.com); the latter via an Internet MPLS network solution (Hvelplund, 2005).

12 01 2005 08 i0 01

5. PRACTICAL EXPERIENCES 1

To illustrate the functionality of the part of the system, which works in closed loop, the primary signals related to the Power Controller (PC) have been chosen for the illustration in Figure 8.

Figure 7 PQ diagram for unit 3 at the CHP plant Skzrbzkvzrket. The PQ diagram calculation is based on a steadystate modelling of the plant and onlinc measurements. In principle, it is a dynamic diagram, ie the diagram changes when the plant changes, or if the operational boundary conditions change. In future updating of marginal costs, data will automatically incorporate this. However, at present updating is initiated manually. Further details on the marginal cost calculator can be found in (Johansen, 2004). 4.5

Figure 8 shows that the load changes in the morning after nighttime, ie at 5.00 a.m. the load was approximately 1200 MW, and at 7.00 a.m. the load changed to approximately 2700 MW. It is apparent that the TSO Balance Controller must make some corrections in order to maintain the area balance.

12//aster control

I

The existing master control (MC) systems at each power plant are utilised as interface from the system level. Modifications of the master control were performed in order to provide the control actions with the required properties. At some plants, it was also necessary to alter the plant in order to obtain satisfactory process and control characteristics. The master controller includes: a

1 1

1

1

1

- -

-

I

A set-point calculation part. Calculation Of the primary set points for the plant, such as pressure set point and enthalpy set point. A decoupling network. The multi-variable nature of the plant is taken into consideration by using MTMO dynamic models of the plant. A feedforward network. Calculation of set points of the primary control variables (feedwater and fuel). A feedback control part.

. -1

Figure 8 Power demand and actual power production. Signals refer to Figure 4 In Figure 9 the eight individual control signals from the Power Controller (PC) acting as a correcting signal to the Electrical Power Schedule for the eight involved power plant units are shown for the same period. Hence the sum of these eight signals equals the signal “Sum Power Controller” in Figure 8.

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(2005) Short and Long Term with Online IT Communication to I&C Systems (in German). VDE “IT-Solutions in der Energieerzeugurig ”, hfarzrzheiin 26-27 April 2005, ISBN 3-8007-2894-X

Hvelplund, R., Optimisation Power Plant Cocference

Johansen, A..O. (2003) Simulation and optimisation of thermal power stations by use of Turabs. Proceedings of ECOS 2004, Mexico, 2004, 1267-1277. Lausterer, G.K. (1 998) Improved manoeuvrability of power plants for better grid stability and economic dispatch. Conlrol Engineering Practice 6, 1549-1557.

Figure 9 Power Controller output #2 (Correcting control signal to Electrical Power Schedule).

Mortensen, J.H., Moelbak, ‘I ., Andersen, P., Pedersen, T.S. ( 1 998). Optimization of boiler control to improve the load-following capability of power-plant units. Control Engineering Practice 6 (1998) 1531-1539.

It appears from Figure 9 that the load changes for all units constantly. One of the consequences of introducing this system is that plants hardly ever operates at steady state. Another consequence is that a particular load disturbance is transferred to the other active units. Thus if a plant has an oscillatory performance, this oscillation will be spread to all units. In case of that, the source of oscillation must be located at first. The oscillation may either derive from the TSO control loop, or from the Power Producer’s own Power Controller loop. In case of the latter, it is essential to make an extra effort to locate the oscillation producing plant and then locate the source of oscillation at the plant in question.

Welfonder, E. ( 1 997) Least-cost dynamic interaction of power plants and power systems. Control Engineering Practice 5, 1203.

6. CONCLUSIONS This paper focuses on the importance of utilisation of modelling and advanced control for optimisation of a distributed multi-level power production system. Based on the general discussions and the application examples, the following can be concluded: 1

.

Optimisation of each control level is important. The top business level performance depends on the low-level performance - even on the lowlevel servo control. I’his means that optimisation at all levels, eg using advanced modelling and control methods, is essential. Integration and coordiriation between the levels are important in order to obtain a high-quality performance. Dcsign at one level depends on thc underlying levels, and normally this is handled by a bottom-up approach starting at the lowest level. In general, optimisation should be performed at the lowest posqible level.

REFERENCES Honig, P., Welfonder, E (2000) Optimization of short-term scheduling of power plant units in large-scale cogeneration systems. Proceedings of IIsAC Synaposium on Power Plants and power systems control 2000, 377-385

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

RELIABILJTY ENHANCEMENT SCHEME FOR lEC61850 BASED SUBSTATION AUTOMATION SYSTEM Seong-Il Lim, Dong-Ho Park, Seung-Jae Lee, Seung-Soo Han, Myeon-Song Choi

Next-Generation Power Technology Center, Myongji University, Korea

Abstract: Reliability of lEDs in a substation is a critical issue in power system operation and in practice, use of different IEDs from different manufacturers has been causing many difficulties in maintaining reliability. In this paper, a new reliability enhancement scheme for a IEC61850-based substation automation system is proposed. It utilizes a redundant backup IED and software-moving on communication network. A Fault detection technique based on pattern checking is also proposed. Reliability analysis of the proposed scheme is given as well. Copyright 02006 IFAC Keywords: Substation Automation, IEC6 1850, Fault Tolerant System, Intelligent Electronic Device.

1 . INTRODUCTION

In order to resolve difficulty in information exchange among IEDs in a substation due to a use of diffcrcnt IEDs from different manufacturers, standardization has started in the beginning of 1990s and as a result, IEC61850 has been generated as a global standard [I 1. Recently construction of IEC61850-based substation automation system has been reported around the world. Dcvclopmcnts in IEC61850-bascd substation have introduced many advantages in maintenance and operation. However, reliability issue has not been paid much attention. Note that a conventional redundant scheme is weak from the security point of view while it enhances dependability. Upon introducing IEC6 1850, taking advantage of networking-based information exchange, reliability issue can be dealt with in a very different way. A fault tolerant technique, another direction to improve reliability of TED has been developed during last two decades. The main idea is to use various types of redundancy to tolerate a possiblc error. One most popular technique is NVP (N - Version Programming) [2]. NVP uses n versions of algorithms to solve a problem and then obtain an optimal result from n results. This idea was further developed by others [3-41. NMR (N-modular Redundant) is another widely used method in which

m or more of which must be functioning for the system to be operational assunling that the system is composed of n identical and independent components. The idea of redundancy is used in almost every aspect of power system. J.Nahman suggests a method to optimize a number of spare items of substation components, which have to be stored at the beginning of each year throughout a planning period [ 5 ] .The fault-tolerant software implementing a stable memory to substitute a stable storage device is reported [6]. In this paper, a new method to improve reliability of a substation is proposed. This method, which we call SRET (System Reliability Enhancement Technology), is based on the latest substation automation system standard-lEC61850. SRET scheme is a fault tolerant technique at system level and utilizes backup IEDs and software moving capability over the communication network.

2. IEC618.50 BASED SAS The scheme presented in this paper used many features of IEC61850 to improve reliability of a substation automation system (SAS). The main features of IEC61850, which make our scheme possible, are network based data transfer, standard interface, and SCL (Substation Configuration Language) based engineering.

207

CID file is downloaded to its appropriate IED through communication network. Note that reconfiguration of the data path can be easily done through such SCL based engineering. ~

fl .ICD

I II~CilS~OBn\cd\z\

(b) 1EC61850 based

SSD : Systein Specificatioii Description ICD ’ IFD Capability Desrriptioii SCD . System Coiifiguratioii Desci-iption CID : Configured IED Description

SAS

Fig. 1. Migration of structure of substation protection and control system

Fig. 2. SCL based engineering

2. I Digital dutu trunsjer

2.3 Standard Interface

In a existing substation protection and control system, analog data such as voltage and current are fed into protection relays from CT and PT which are installed on the primary protection equipments such as transformers and circuit - breakers through hardwires (Fig. 1 - a). When using mechanical protection relay, those analog voltage and current data are used directly. In case of digital protection relay, those analog data are converted into digital data by AID converter inside the relay. In the 1EC61850 - based substation automation system, analog signal will be converted into digital data by the process IED installed on the primary protection equipment and be sent to the bay IED through the process bus (Fig.1 - b). The largest difference between the two schemes above is whether the data transfer path can be changed during operation. In the existing system, analog data are transferred through hardwiring, so data transfcr path cannot bc changcd unless the physical connection is changed. In the communication network, data are transferred over the network, so the data transfer path is determined by changing the destination o f data packet.

In IEC61850, all the information about the substation is modeled into the standard interface called LN (Logical Node). Data exchange between these IEDs is possible as long as all these lEDs follow the standard LN interface regardless of IED hardware structure or algorithm. For example, suppose there are two distance relays made by different manufacturers, whosc signal filtering, calculation of RMS, error detection algorithm, and hardware are different. Note that as long as two relays have the same services and the same LN interface, one can replace another as illustrated in Fig.3.

I

I

I

Fig. 3 . Concept of logical node interface

2.2 SCL based engineering 3. SYSTEM RELIABILITY ENHANCEMENT TECHNOLOGY

For integration of various IEDs, IECGI 850 suggests a standard engineering technique. The key is in the software called System Configurator and IED Configurator. Figure 2 shows the course of IEC61850 engineering. First, System Configurator gathers all the information about the substation from the SSD (System Specification Description) file that contains system related information and the ICD (IED Capability Description) file that contains IED related infoimation, and then it creates the SCD (Substation Configuration Description) file that configures the function and data flow for each TED. All the files mentioned above are made by XML - based SCL (Substation Configuration Language). The TED Configurator receives the SCD file and creates CID (Configured IED Description) file that contains the format suitable for IED. Finally

3. I System Structure System Reliability Enhancement Technology System Structure The structure of SRET-based substation automation system is shown in Fig. 4. Note that station unit, bay IED, process IED, and engineering unit (EU) coiistitute a subslalion auloiriatiori system, which follows IEC61850 standard. A Backup IED (b TED) and trouble manager (TM) are added to the system for implementing SRET. The trouble managcr is in chargc of dctccting thc IED crror and the backup IED is a redundant IED that is to replace the faulted IED.

208

IED Trouble Test

Fig. 4. Structure of SAS reliability improving SRET system

I

Fig. 5. 1,N based standard interface

3.3 1ED error detection 3.2 Procedure of error detection Trouble manager penodically checks functioning of each bay IED to determine whether the IED is faulted. The fault detection procedure of trouble manager is as follows: 0)TM requires information of the UUT (Unit Under Test) bay [ED dnd b [ED from engineering unit and asks the engineering unit to reconfigure the system for tcsting. EU informs the function of UUT IED to b - IED and prepares the functional software that makes b - IED operate same as UUT IED. @ EU crcatcs the SCD configuration filc that sets up the data transfer path between b - IED and other IEDs sdme as the previous data exchdnge between UUT IED and other IEDs. @ EU uses the IED configurdtor provided by its manufacturer to create the CID file using the SCD file and sends them to IEDs. With this step, the reconfiguration is finished, which let the backup IED replace the UUT IED. 6 1EU modifies the CID file of UUT IED, in order to make UUT IED get the data from TM and also send output to TM. TM sends the previously prepared test pattern to UUT IED over the process bus. UUT E D performs its function using the data provided by TM dnd sends output to TM over the station bus. I M determines whether there is an error on U U I IED by comparing the output of UUT IED with correct result data in TM. [f no error is detected on UUT IED, TM requires EU to reconfigure the system to return to the original operation of UUT IED and then continue to check the next IED. If error IS detected, the system will inform the operator. b-IED will rcpldcc thc failcd UUT 1ED until it is rcpaircd.

a

If an output of the IED to a certain input is different from the expected, it could be a sign of IED error. So by checking outputs for all possiblc inputs, IED error can be detected. A test input is provided to IED from TM on the station bus and its output is sent back to TM through the process bus (See Fig. 6). By comparing the results with pre - calculated results, TM will determine the status of the IED Many test patterns have been generdted by EMTDC and the set of test patterns arc prepared for all differcnt types of IEDs that are to be tcstcd.

I 01 100011 I*** I

Result Pattern

I

Station Bus

Trouble Manager Process Bus

I

01 10001 1 I*** Test Pattern

I

Fig. 6. Error detecting method 4. RELIABILITY ANALYSIS

Fig. 7. Structurc of IED system Reliability of the proposed SRET-based SAS is studied using the system in Fig.7. Note that only bay IEDs, backup JED (b-IED), trouble manager (TM), and engiiieering unit (EU) are considered and others such as station unit and process IED are not included

209

where F(t) is the general lifetime distribution of IED device, nz is number of devices (in the dual structure, m is 2), and

for reliability analysis since they do not affect the reliability of the SRET-based system. In the structure above, engineering unit and trouble manager play a role of a switching system, which switches bay IED by backup IED during testing. Let o(t)be a lifetime distribution function of trouble manager and engineering unit. A reliability model of the switching system composed by trouble manager and engineering unit is a serial model, whose reliability can be represented as

R,,(t)

= [l - D(t)12

F ( t ) = 1 - R(t)

(6) Here R(t) is the reliability distribution as mentioned above. Note that this OR operation could cause incorrect result in case any IED misoperates, thus deteriorating the security. This makes a dual structure different from a parallel system. Probability of this 211 -A);&...,

where” is the failure rate of an case is IED device, including both no - operation and

(1)

Note that when the switching system works correctly, SRET system can perform correctly. This means that if a failure of a bay IED is detected, then Failed bay IED is replaced by backup IED. In this case, those normally operating bay IEDs and backup IEDs can be regarded as a subsystem, whosc rcliability model is a traditional NMR model (N-modular redundant) shown below.

mis - operation, and ”.’.’ is the failure rate of mis - operation on an IED device. Now the reliability model of dual structure can be represented as R , , , [1-2(1-K)K7,] and the model of existing IED systcm that Is composed by many dual - structure units as

c(:t

: R, ( t )=

i =”rn

.

(t)‘(1- R(t))”-‘

Here, nz is a number of bay IED, n is a sum of number of bay IED and backup IED, and R(t) is a rcliability distribution o f a n IED devicc. But in case that the switching system fails, this SKEI’ scheme can’t perform correctly. Failure of any bay IED can’t be detected and the backup TED become useless. In this case, there are only bay IEDs in our system, the reliability model of these bay IEDs is also a serial model that has

Before calculating the reliability distribution of SRET system and existing system, the following assumptions are made. - lifetime distribution F(t) of an IED device is an exponential distribution; - lifetime distribution D(t) of trouble manager and cngincering unit is same as F(t); - the switch between bay IED and backup IED is instantaneous.

W“

4,( t )= (3) R(t) is the reliability distribution of IED device mentioned above. So, the reliability model of the SRET system can be expressed as:

The CDF and reliability of exponential distribution are given as F ( t ) = 1- e-i’t and R(t)= e-”t (8)

In the current IED system, dual structure is widely used. From the reliability point of view, the structure can be simplified as one in Fig. 8.

u

-

Here 2 is the failure rate. Now let’s calculate the F(a> . IS a numbcr vcry close to 1, and failure rate. If all failures are assumed to happen uniformly, for every time interval , there will be one failure. And,

CX=TIN,

Bay

where T is overall time, and failures in time T. Therefore,

OR

A T

(9)

Bay

where I

I -

a=

Fig. 8. Dual structure of existing IED system

(0= 1- W)’”

is the number of -

=1-e - E (10) is a number very close to 1. So

-N f

ln(1T

E)

(1 1)

From [7], it can be seen that for every million hours, there will be 48.65 no - operation failures and 37.28 mis-operation failures. Iin ‘ , M (4s .ds + 31 .2s 1, so and set & = 0.939 , then we have the failure rate of IED device is x = 5 .mx x 10 -.I . And for the failure rate

Same data are sent to two IEDs with same function, and then two results will be operated by an OR operation. This structure is very similar to the structure whose reliability model is a parallel model, but there is an obvious difference - OR operation. In the parallel model, the system will get correct result as long as at least one unit gets correct result. So its model is Rparalkl

’

-TAIN,

~ ( a= 1) - e-*’-

A+.

MI

-

-

hr _., = 37.23 operation, , othcrs are samc. A,.,, = 2.5752 x10” so we have

of mis

(5)

210

-

With those numbers, the reliability of both systems can be calculated by reliability models.

5. CONCLUSIONS

SRET, new reliability enhancement technique that can be applied to the IEC61850-based substation automation system is proposed in this paper. The proposed SRET-based system detects failure of IED automatically and replaccs thc failcd IED by backup IED, securing availability of [ED all the time. Reliability analysis performed in this study has shown the effectiveness of the proposed scheme. Application of SRET is not limited to electric power substation, but can be extended to other automation systems adopting communication network-based operation. REFERENCES

0;

2000

4000

6000

8000

10000

Time

[ 11 IEC61850 International Standard

Fig. 9. Lifetime distribution of an IED device

Time (hours)

Fig. 10. Reliability comparison with 100 IED Figure 9 shows a lifetime distribution F(t) for an IED device and Figure 10 represents comparison of reliability when there are 100 bay IEDs in the IED system. Further another case with 100 lEDs without use of dual structure, represented by ‘old no bk’ is shown in the figure. The model of this system is a

[2]

Elmendorf, W. R., “Fault-Tolerant Programming,” Proceedings of FTCS-2, Newton, MA, 1972, pp. 79-83 Avizienis, A., “The N-Version Approach to Fault-Tolerant Software,” IEEE transactions on Sojhare Engineering, Vol. SE-I 1, No. 12, 1985, pp.1491-150 I Chen, L., and A. Avizienis, “N-Version Programming: A Fault - Tolerance Approach to Reliability of Software Operation,” Proceedings OfFTCS - 8, Toulouse, France, 1978, pp. 3-9 [ 5 ] Nahman, J.M. and Tubic, D., “Optimal sparing strategy for substation components”, IEEE Trunsuclions on Power Delivery, Volume 6 , Issue 2, April 1991, pp. 633-639 [6] Deconinck, G., Bott, O., Cassinari, F., Dc Florio, V., Lauwereins, R., “Stable Memory in Substation Automation: a Case Study,” 1998 Digest of Papers. Twenty-Eighth Annual Intel-national Synzposiunz on Fault-Tolerant Conzputing, 23-25 June 1998, pp. 452-457 [7] Ding Maosheng, Wang Gang, Li Xiaohua, “Reliability analysis of digital relay,” 2004 Eighth IEE International Conference on Developments in Power System Protection, Volumc 1 , 5-8 April

R,.:,;: ,,.+(, = Wf.1

”

, where m=100 is serial model, so the number of bay IED. In Fig. 10, the curve ‘old bk’ represents the reliability of the existing TED system that uses dual structure for 100 bay IEDs case. The other four curves are the reliability of new SRET system with 100 bay IEDs with 5, 10, 15, and 20 backup lEDs from left to right. Figure I 1 is the reliability comparison in the case of 200 bay IEDs. The other four curves marked ‘lo’, ‘20’, ‘30’, ‘40’ represent the reliability of SRET system with 200 bay IEDs with 10, 20, 30, 40 backup IEDs respectively.

21 1

This Page Intentionally Left Blank

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

MODELING VOLTAGE REGULATION IN OBJECT-ORIENTED ANALYSIS OF DISTRIBUTION SYSTEMS INCLUDING DISPERSED GENERATION

G.M. Casolino * A. Losi * M. Russo * * CTniversitiLdegli Studi di Cassino v i a G. Di Biasso 43, 03043 Ca,ssin,o (FIZ), Italy { c a s o l i n o ,l o s i ,r u s s o } @ u n i c a s . it

Abst,ract,: Dispersed Gerierat ion (DG) afTects the operation of distribution systems; the rrla.t,ed modeling and analyzing techniques are affected too. A novel approach to the distribution load flow problem has been recently proposed: based on the Object Oriented (00)paradigm and including DG. In t.liis paper! the 00 rnodeling and algorithm a.re extended to account for the inclusion of Tiul'c transformer's vollage regulation. 'lb validale the proposed stea,dy-slate model and to verify its assumption of stability, a detailed dynamic model is developed in Matlab/Siinulink eiiviroriiiierit fnr a simple case study. The numerical results give evidence of the efkctiveness of the proposed steady-state model which accounts for the interaction between DG and UUI'C voltage regulation. Copyright@ 2006 IFAG

Keywords: Voltage regula>Lion,Distribution system analysis, Object,-oricnted nicthods, Dispersed generation.

1. INTRODUC'I'ION

In distribution systems Dispersed Generation (DG) is coririected close to the loads. It caii illcrease the power quality and reliability from the ciIst,oiners' perspective md help the ntilities t,o face the load growth by delaying the upgrade of distribut,ion lilies. Moreover, DG using renewable energies is often encouraged and financially supported thanks to its low environmental inipa~ct. The connection or small generating units strongly affects the operation of distribution systems. (Dugan and McDermol-1, 2002; Zhu and 'l'omsovic, 2002; Caire et al., 2002: CIGRE Working Croup 37-23, 1999) which are usually designed for uriidirect.iona1 power flows: the presence of DG introduces a.dditional supplying nodes and may change power flows. Then, it is required to revise the classical distribution load flow models and solving 1-echniques (Cheng and Shirmohammadi, 1995: Srinivas, 2000). In (Losi a.rtd Russo, 2003) a novel Object Oriented ( 0 0 ) approach has been proposed for load Row analysis of bala,nced distribution systems with radial or weakly-meshed topologies. The 00 al-

gorithm is based on an approxima.ted NewtonRaphsoii (NR) technique and its convergence characteristics have been studied in details. . L ' k 00 approa.ch assures great advantages especially in terms of expansibility, flexibility and easiness of niaint'cnance of the softwarc (Ncyer et al., 1'3'30). Moreover, it can be easily impleniented in parallel/distributed coaiputa,tional architectures, thus fully exploiting tlie features of modern corriputirig systems (Dy-Liacco, 1994). In (Losi arid Russo, 2005) detailed DG component rnodels have been introduced into the 00 distribution load flow; they account, with the required acmiracy, for the various electric devices interfacing to tlie network, such as synchronous generators, iiiductJiou machines: power elsctroiiics converters.

111this paper, the 00 distribution load flow modcling is cxtcndcd to include also thc voltagc rcgulatiorr in hilV distribution system. In particular; t,he modeling of HV/MV transformers equipped with Under Load Tap Changer (IJLTC) control is studied and the related equa,tions a,re introduced into the 00 load flow. 'l'he resulting tool allows to analyze in details the interartion be-

213

t,weeri the dist,rihiit ioii syst,eni vol t,age reg111 a,tiori aiid DG. To validate the proposed steady-state

eqiiipped wit,l-ivolt,age control syst,erns. '1'l-ieri. t,he

stability of tlie dynamic interaction between the two control systems niiist be verified too, because it is an implicit assuniption of steady-state loadflow analysis; usually it is vcrificd bccausc thc UUrC control action is slower than the DG voltage control action. due to the current cornniuta.tions between transfornier windings. However, to validate both the results of the steady-state modeling arid the hypothesis of stability in which they a.re evaluated, also the dynamic modeling of IJUI'C regulation and of DG are examined.

model a,nd to verify its assumption of sta.bility, a deta.iled dyna.mic model is developed for a simple caw study in RIatlab/Sirnulirik cnviroiirriciit, using Power System Blockset library. The numerical results give evidence of the effectiveness of tlie proposed steady-state niodel mliich accounts for the effects on the distribution system voltage profile of various types of dispersed generating devices (such as controlled and uncontrolled synchronous generators, asynchronous generators) and of various options of thr vollage regulation (such as with or without Line Drop Compensation).

2.1 Steady-stale m m d e h g 2. VOLTAGE REGULATION MODELING

'l'he steady-state inodeling of the distribution system for 00 load-flow modeling (Losi arid Russo, 2003; Losi and Russo, 2005) is based on the class Iiiera.rc:liy sliowii iri Fig. 1. ?'lie basic abstracl class is named connection and is defined by tneans of ports, port variables anti computational methods. A connection port is said incoming or outgoing based on the conventional direction of power at the port; it is char rized by four variables, which represent the ve ( P ) and reactive (Q) powers and tlie real ( and imaginary (V,) cornponent,s of the voltage at the port. From abstract conneclion, concrete classes are derived. In particular tlie class branch is iised to represent physical lines or tmrisforrriers, including sliurit corripoiients at thc rccciving busba.r, such as loads arid conipcnsating devices.

Iniproving nodal voltage profile in a LlV distribution syst.ern is usually at.tairied by changing t,he HV/hlV substation transformer ra.tio rising the U U K and by connecting/disconnecting the capacit,ors in the substation and along the feeders of tlie distribution system. The volt,age regulation problem in M V distribution system is h d i t i o n ally split into two hierarchical levels: the off-line opt.imal set.ting problem arid the on-line control problem (Hu el al., 2003). The off-line problem determines, t,ypically on a da.ily schedule, the optimal settings for the on-line voltage control reference signals and the optimal sequences of connection/discounectioii of the capacitors. The problem is usually tackled adopting dynamic programming (Liang and Cheng, 200l), genetic (HI* et al., 2003) or simulated aniiealing (Liang and Waiig, 2003) algorithms.

'Lo iriclude DG rriodelirig IltaL accouribs lor. Ihe type of electrical machine, the interfa.ce t o the distribution system and the control actions that are perfomied: a set of concrete classes, derived from bran& has been adopted:

The on-line problem aims at ULTC control by closed loop regulation so as to keep tlie voltage aniplit,ude close to the reference value. The controlled voltage is either the measured transformer secorida.ry voltage or a. calcula.ted voltrage a.cc:ording t.o the Line Drop Compensation (LDC) principle. In the latter case, from the rneasuremerits of the transformer secondary volhge and current, a. volta,ge along tlie feeder is estimated; in this way tlie voltage drop along the feeder is partially compensated. ' l h e on-line closed loop voltage regulation varies tlie transformer tap ratio and consequently its steady-state response must be accounlctl for in distribulion load flow sludics (Royt.elnian and Ganesan, 2000).

0

0

0

0

AsyncBranch, that models branches with asynchronous generators. Inve~-tHranch,that models branches with line cornmiit a.ted inverters. SyncBramch, tha.t models branches with synchronous generators with constant excitation (uncontrollcti). PQBranch, that models bra.nches with generators (synchronous generators, switching inverkrs) equipped wiLli active and reactive power control as well as bmnclies without DG devices.

In addition a class named PVbusbar, directly derived froin abstract class connection, is used to model DG devices which are capable of regulating busbar voltage (synchronous generators and fourquadrant swit,chirig inverters with active power a.nd vo1ta)geamplitude controls).

1he perforniance of' the on-line voltage regulation ongly affected by DG connected to the distribut.ion system (Choi arid Kim, 2001; Ronhornme et al., 2001 ; Kim a.nd Kirn, 2002; Kojovic, 2002). In some cases, the presence of DG may cause overvoltages along the feeders; in other cases, when LDC is adopted, DG rnay came undervoltages because its presence reduces the current supplied by 1-he 1-ransformer and, comequently, the ULTC compensation. The interaction between t.he distribution system voltage regulat,ion and the DG varies significant,ly according to the type of electrical interfaces connecting each DG device to t,he distribution system. All such feature must be included into the load-flow analysis. Sorne DG devices, such as synchronous generators or switching power electronic converters, rnay be r >

In this paper, the class root, which is a coanection with only a.n outgoing port representing the supplying system, is extended to include tlie voltage regulation modcling. The stcadynodeling refers to the equivalent elect,rical shown in Fig. 2 ) where complex pha.sor represent,at.ion is adopt~ed;in t,he following, roma,n lettering is used for assigned para.nieters arid for quantities detiermined by tlie off-line voltage programming, whcrcas italic lettering is a,doptcd for variables. In Fig. 2, VHVis the voltage phasor a.t the IIV busba.r, I/J,~,. i s the voltage pha.sor a.t the ~

214

~

:

Evaluation of P,dnd Q,

Fig. I . Distribution system hierarchy of classes \'oltage

Regulator ULTC Trandormer

Fig. 2. 'lhnsfornier equivalent electrical circuit. lclV busbar, RTI +jXT1 is the transformer primary series impedance and R.l.2 jX.l.2 the transformer secondary series impedance, a, is the transformer ratio and Po +jQa is the apparent power supplied by the transformer to the distribution systeni.

Fig. 3. UL'I'C control scheme.

Thc complex equalion describing thc circuit shown in Fig. 2 is givcn by:

2.2 Dynamtc modelsng

+

.....................................

'10 validate the results of the proposed steadystate UIXC aiodel arid to verify tlie stability assiirnptiori, a riyna.rnic modeling of t,he on-line loop control of Fig. 3 has been built, using the Matlab/Power System Blockset environment. The modeling of LL'I'C transformer has been obtained by rncaiis of a sclcctor of ixultiplc parallel ccpivalent generat.ors: the voltage amplitude and internal impedance values of the equivalent generators are chosen according to the transformer ratio associated with each t a p position. 'llie choice of the t a p position and, coiiseyueiitly, of the equivalent d is decided by the voltage generator to be sel regulator. l'lie aiiii of the regulat.ioii is to guararit.ee tliat the error between the controlled voltage level a.nd t,he volhge reference is kept to zero within an accepted t.olerance, despite dist.urbances. For t.his purpose) the regulator, by acting upon the actuator, can discretely modify the t a p position. 'l'he rcgulator output command is deterrniricd by an integrator arid influenced by the dead band, which is used to reduce the phenomena of transient volt,age variations and the presence of unnecessary tap changing operations. Referring t o Fig. 3 . the general case of LDC tias been considered (whereas the r e g i h i o n of the transformer secondary voltage can be trivially obtained by assuming a zero LDC) and thc following notation has bcen adopted: where Vrrf is the ULTC control voltage reference set point,, which is pre-determined by the solution of the off-line optimal setting problem, arid R., 1 jX, is thc impcdancc assumcd for Ihc LDC (trivially equal to zero if no LDC is considered).

E ~ ( 2 ) ,~( 3 ) a,rld ~ (6) ~ rorrrl . t,ile set tilree eyuations in the five variables Vfi.,t, v 9Vl.n,lv a , PO a.nd & a , rieeded to describe the steady-state behavior of 21. U U l C transformer. l'he solving procedure reported in the Appendix can be implerrierited according t.o the 00 modeling a.pproac:h of (Losi and R.usso, 2003) and used to extend the definition of the class root. ~

&:. e, c,

n,

is the 1,DC signal; is the volt,age cont,rol error: is t.he actuator conmmnd; indicates the tap position of the C L ' K

From the scheme it, is a.pparent that the voltage arid current at the secondary of the transformer are used both to evaluate the control error e and the values of Po and Qo rieeded for LDC according to (6). Finally, t o model the presence of DG, vasious configurations can be considered exploiting the Power System Blockset built-in library which includes machines and power electronic converters.

215

T h e simple distribution system in Fig. 4 has been considered t,o t,est, the st,eady-state model a,nd to va.lida.teits results. The DG device is assumed to be a controlled synchronous machine (PV bus) which can be connected to any load busbar. In the steady-state modeling, the implementation of PV bus ha.s beeii obtained by inea.ns of the homonymous class defined in (Losi aiid RUSSO, 2005), whereas in the dynamic modeling, it has been attained using a. synchronous generator of tlie Matlab/Power System Blockset enviroiiment equipped with the control scheme sketched iri Fig 5 . 'lhe system data are reported in 'lable I in which t.he p . ~ (pintities . are referred to the rated powers of each device and to the system base voltage (20ltV).

Fig. 4. I'est distribution system Prime

Gencrdtnr

a

3.1 Stead!/ state analysts

To evaliiate t.he DG's influelice on the system s beeii considered by operat,ion, different, c a ~ e have varying the position of P V bus along the feeder. The values o l the voltages along the leeder obtained respectively by the steady-state results of the dynamic siniulation and by the 00 load flow are reported in Table I1 for each position of the DG device. T h e results have been obtained assuming a LDC at, bus 3 and considering a voltage reference for the UL'I'C transformer equal t,o 95%. The reference voltage for the PV internal control ha.s been set to 104%> wherea,s the niechanical power is equal to 0.66 p.u. referred to the machine rated power. From 'lable I1 it. is apparent that, in all the cases, the proposed stea,dy-sta.t,emodel assures high accuracy of the results. So, when the transient phenomena ca.n be neglected, t,he interaction between the U U l C control and the DG can be accurat'ely niodeled by the 00 load flow, which is extremely flexible and requires very low computational burden even in the case of large distribution systems.

S.2 Validation of the stability assumption

To validat,e the st,a,bility assurript~ion,the case of LDC ad bus 3 and of DG conneckd to bus 1 has been considered. Various other ca,ses have been analyzed but this ca.se is reported because it dctcrinincs the major coupling bctwwn the DG and the UUrC vokage regulations and then may cause stability problems. The voltage reference for t,he DG is equal t,o 105% and for t,he U L T C to 95%. The time evolutions of the DG excita.tion voltage Vj and speed deviation A w . of the voltages at bus 1 a.nd 4, a.nd of the ta,p r h o a a.iid the TJLL'C command are reported in Fig. 6. Let's analyze Fig. 6. The first voltage transient. is induced by the TJTXC control action; which varies a t o achieve llie sleady slale value (I'rorii 0.845 lo 0.83). 'l'lie secoiicl tra.nsient is due to a, step increase of VHV equal to 2% at time iristarit equal to 20s: the T X K control changes its command of a , but the variation is not large enough to determine a. new change of tlie tap position and t.he error on the controlled voltage remains within the dead band of t,he TJUI'C' regulator. It is interesting to

Filter

Regulatni aiitl ~

Fig. 5. Voltage control scheme for the DG device. notice that the dispersed generator increases its exciting voltage to achieve the required volta,gc at its terminal. As a coi~sequeiice,the voltage a,t tlie ending bus 4 is quite higher due to the overcompensation of the LLDC action. Finally it is apparent that tlie response of the DG voltage control arid of' the UL'I'C voltage regulation are quite decoupled.

l'he paper has tackled the issue of' accurate rriodeling of vo1ta.ge regulation in distribution systems including DG. The frame of a previously-proposed. 00 distribution load flow modeling has been extended to include the hlV distributioii system voltage regulation. In particular, tlie modeling of HV/MV transformers equipped with UL'I'C control has been studied arid the related equations have been introduced into the 00 load flow. To validate the steady-state model and its stability assurnpLion, a dynamic rriodel has bccn dcvclopcd in I\iliitln.b/Powcr System Blocksct crivironmcrit. The riiinierical resiilt,s obta.ined from both the steady-state arid the dynamic rnodels for a. test system have been compared proving the accuracy of the proposed model. The resulting 00 tool allows to easily analyze tlie interact ion between DG aiid Ii1,l"C regulat.ion aiid the effect of DG on system volta~geprofile also for very lasge distribution networks. 5. APPENDIX The modeling of IJLTC transformer implements the solution of (2),(3) arid (6). that describe

216

Table 1. Test system data

0 8675

1,OAC)S

LINES

LI

DI

Type of

v1

P, [MVA]

;2i";i/,

winding

YgY L1 rp.u.1 0.0398

2.6

[Vrms] 380

R2

L2

b U . 1

bU.1

0.00398

0.0398

,

Ri

V2 [Vrrns] 20000

[p.ii.] 0.00398

s

Lm

Rm bU.1 500

1

I

bl

t

26 4375

26 25 25 1875 26125 26 0625 26

5

10

15

20

5

10

15

20

25

30

35

40

25

30

35

40

25

30

35

40

25

30

35

40

25

30

35

40

bU.1

500

DISPERSEDGENERATOR Rotor type Sa ient

I

dde X
,

[P.U.]

3.28

r:,

P,, [MVAI

x:, [p.u.] 0.322 T:;

I

v,,

I

I

f,,

R..

1

Time

[vrms]

[Hi]

[p.;.]

constants

380

50

0.003

t;;;;

x:;

x,,

[P.U.] 0.161

[P.U.]

r::

H

F

1.88

x:: [pu.] 0.181

xi

1

"I" 3

[P.U.] 0.04

[el

P

[sl

[SI

is1

Is1

[P.=l

1.1

0.35

0.0036

0.0036

2

0.01

2

10

15

20

10

15

20

~~

; 10625 2

105 >-I 0375 1 025 10125

5

Table 11. Stea,dy sta.t,evolt,ages \\'ITHoUT

f IS1

1 o 9875 0 975 0 9625

DG

[P.u.1 1.074 70 1.00012 0.96587 0.95136

[P.U.]

1.07472 1 .ooo13 0.96587 0.95137

~

~

0 925 00125~

0 05

10

15

20 1 Is1

Pig. 6. Tiine evolutions of a , the UUI'C" corninand. the DG excitation voltage V f and specd deviation A w , voltages a t buses 1 and 4

0.98773

0.98776

0.95389 0.93956

0.95393 0.93959

0.95613

DG 0.98577 0.96303 0.95619

0.95Ci21 AT BUS

4 0.98588 0.96316 0.95633

the circuit shown in Fig. 2 , into the iterative procediire of (Losi and Rimso, 2003).

Substitutirig (10) into (8) arid (9), and then 71 and 7 2 into (7). the value of' a is obtained Then tlie discrcte value of the transformer ratio 6 can be chosen according t o the rule. if a 5 anlLn

By (2) and (3). tlie value of a is expressed in the form:

amor

217

if a

2 amnr

where amzn and anzar:are the minimum and n ~ x imum value of transformer ratio respectively, fi i s dn integer, which valuc reprcscnts thc chosen sclection of the tap changer, valued as

and d, is defined as follows:

in which nposis the number of available selectiorw of the tap changer Updating the values of a,,p, in (4) and (5) and of -,I a n d yz in (8) and (9) by rncanb of ii. the following relations can bc derived:

Cheng, C. S. and D. Shirniohammadi (1995). A three-phase power flow method for rea.l-t,ime clistribution system analysis. IEEE T'rans. on Power Systems 10(2), 671-679. C h i , J.-11. arid ,J.-C. Kim (2001). Advaiic agc rcgulation nicthod of powcr dist syst,ems interconnected with dispersed storage and generation systems (revised). IEEE Transactions on Power Delivery 16(2); 329335. CIGRE Working Group 37-23 (1999). Impart. of increasing coritribution of dispersed generation on the power system. CIGRB Find Re-

port. Dugan, R. C. a.nd '1. E. McDerinott (2002). Distributed geiieratioii. IEEE 1rdmtr.y Applications Magazine 8(2), 19-25. Dy-Liacco, T. E. (1994). Modern control centers and computer networking. IEEE Computer Application,s in, Power 7(.1); 17-22. 1311, Z., X. Warig: H. Chen and G . A. 'Paylor

where:

that represent the new possible wliies of V ~ , h l v and V ~ , n l vin , which:

Tlien, to ensure that the tllo5ell value of Ci gives thc best values of V ~ I Vaccording to the control law (6), the solving procedure is repeated for the alternative value &,lt given by

The final value is chosen between Ci a.nd Cialt according to which one determines the whie of V b j v closer to the control law (6). The new values of VRJIV and V I , ~ , , are subsequently used in t,he ii,erai,ive NR. procediire descrihed in (Losi a n d Rwso] 2003) to obtain the updated values of Po and Qo.

CWP'J.;CWN C:ES Bonhomme, A,: D. Cortinas, F. Boulangcr arid J.-L. Fraisse (2001). A new voltage control system to t'acilitate the connection of dispersed gerietaliori to clist,ribuliori syslerris. h: Proc. CIRED2001, I E E Conference Publzcution,. Vol. '182. Caire, R., N. R,etiere, S. Martino, C. Andrieu and N. IIadjsaid (2002). Impact assessment of LV distributed generation on MV distribution network. In: Proc. IEEE PES S i m m e r Meetin,g. Vol. 3 . pp. 1423-1428.

218

(2003). Volt/ws control in distribution systems using a time-interval based approach. IEE Proceedings - Gener. Tromsm. Distrih. 150(5), 548-554. Kim, T.-E. and J.-E. Kim (2002). Considerations for t~hefea>sibleopera,ting range of dist,ributecl generat.ion interconnected t.o power distribution system. In: Proc. IEEE PES Germral Meetin,g. pp. 42-48, Kojovic, L. (2002). Inipa.ct of dg on voltage regulation. In: Proc. IEEE PES General Meeting. pp. 97-102. Liang, It.-H. and C.-K. Clieng (2001). Dispatch of main transformer ultc -arid capacitors in a distribution system. IEEE 'lkunsuctio,ns on Power Delivery 16(4), 625-630. Liang, R.-€1. and Y.-S. Wa.ng (2003). Fuzzy-ba.sed reactive power and volta.ge control in a tlistribuLiori S J S L ~ I I J . IEEE !Ikurisaclkms o,r~Po,wer. Delzuery 18(2), 610-618. Losi, A. aiid iLI. Russo (2003). Object oriented load flow for radial arid weakly meshed distribution systerns. IEEE IIbms. on Power Systesrns 18(4), 1265-1274. Losi, A. and M. Russo (2005). Dispersed generation modeling for object oriented distribiition load flow. IEEE Trans. on Power Delivery 20(2). 1532-1510. Neyer, A . F., k'. P'. Wu and K. lnihof (1990). Object-oriented programming for flexible software: example of a load flow. IEEE '1kun.s. o n Pofwer Systems 5(3): 689-696. Roytelman, I. and V. Ganesan (2000). Modeling of local controllers in distribution network applica.tions. IEEE T'ransactions on Power D ~ Z ~ U 15(4), ~ U J 1232-1237. Srinivas, 1I.S. (2000). Distribution load flows: a brief review. In: Proc. IEEE PES Winter Meeting. Vol. 2 . pp. 942-945. Zhu, Y. and K. Tomsovic (2002). Ada.ptive power flow inetliod for distribution systems with dispersed generation. IEEE Trans. on Power Delivery 17(3),822-827.

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

SERVICE RESTORATION CONSIDERING LOAD BALANCING IN DISTRIBUTION

Sang-Yule Choil), Jae-Sang Cha”, Chang-Dea Yoon’) ,Myong-Chul Shin@) Ii

Dept.of Electronic Engineenng , lnduk Institute of Technology, San 76 Wolgye-dong, Nowon-gu, Seoul,Korea

*’ Dept. of Media 1 echnology Seoul National Univ of 1 echnology 172, gongreung 2-dong, Nowon-gu ,Seoul, Korea ’) (”

School of Electrical and Computer Engineenng, Sungkyunkwan University, Suwon 440-746, Korea School of Electrical and Coinputei Engineering, Suiigkyunkwan University, Suwon 440-746, Koiea mcshin@ yurim skku ac kr

Abstract : Service restoration is an cmergency control in distribution control centers to restore out-of-service area as soon as possible when a fault occurs in distribution networks. therefore, it requires fast computation time and high quality solutions for load balancing. In this paper. a load balance index and heuristic guided best-first search are proposed for these problem. The proposed algorithm consists of two parts. One is to set up a decision tree to represent the various switching operations available. Another is to identify the most effective the set of switches using proposed search technique and a feeder load balance index. Test results on the KEPCO’s 108 bus distribution system show that the performance is efficient and robust. Copyright 6 2006 IFAC

Key words : Scrvice Restoration, Load Balancmg, A Load Balance lndex, Heuristic Guided Search

1.

INTRODUCTION

Electric distribution networks maintain radial structure with normally closed sectionalizing switches along a feeder and normally open interfeeder tie switches for proper protection coordination. For every tie switch closed, another sectionalizing switch is opened. Under feeder faulted conditions, switches are used for fault isolation and service restoration. The resulting feeders must remain radial, without any violations of branches loading and voltage limits. Because of these requirements, the problem of service restoration is a very complicated mixed-integer, non-linear optimization problem. Since there are a numbers of switches in a practical distribution networks, the problem appears to be best solved by heuristic search methods. Heuristic approaches do not guarantee optimal solutions, but they lead to sub-optimal solutions that are technically acceptable. Many heuristic algorithms dealing with feeder restoration have been presented. Taylor et a1 1990, proposed a switch exchange type heuristic method to determine the network configuration for overloads, voltage problem, and for load balancing simultaneously. Its solution scheme sets up a decision tree which represents the various switching operations available, and a best-first search and heuristic rules are used to find feasible switching

operations. Wu et al. 1991, extended the method proposed by Taylor et al by developing explicit exhaustive method that solves the problem of overloads, phase current unbalance, servicerestoration, and maintenance. This method is to set up a feasible switching options tree which represents possible switching options under constraint of radial structure. Evaluation functions and heuristic rules are used to find feasible switching operations. In this paper, the authors present a heuristic service restoration algorithm considering load balancing based on an effective exhaustive search method. Its main steps have been implemented in two stages. First stage is to set up a sub-tree that was presented by Wu et al. 1991. Second stage is to identify the most effective the set of switches using proposed search technique called “cyclic best-first search” and a feeder load balance index. This procedure favors solutions with feeder load balancing when feeder faults are restored Numerical calculations are carried out to show the effectiveness of the proposed algorithm.

2. DESCRIPTION OF DEVELOPED FEEDER LOAD BALANCE INDEX When feeder faults are detected, the loads in the isolated feeder section are energized by transferring these load to adjacent feeders. If adjacent feeders are

219

already overloaded, the load must be transferred to another adjacent feeders. Therefore, when loads are transferred, it must be distributed to adjacent feeders whose actual load are less than their projected loads. In this paper, to distribute loads in proportion to feeder nominal capacities, the authors presents feeder load balance index. This indcx extents heuristic index proposed by Taylor et al. 1990 by considering feeder load balance during service restoration. The

4

@

T

...T..._.

4

FL, = FNC x tCK CTAC

Sl2

@

ttu

whole process is as follows FLi ' Projected load of feeder I (MVA) LI,,,, Fcedcr load balance index SLi : Actual load in feeder i (MVA) TACi Nominal capacities in transformer i (MVA) FNCi ' Nominal capacities in feeder i (MVA) U Set of transformer K Set of feeder

Fig 1 Three-feeder example system If feeder section S1 experiencing an fault, then the amount of load on isolated feedei section must be transferred to feeder 1 and/or 3 without creating an overload on either of these feeders To transfer load at node 1 1 from feeder 2 to feeder I , the notation (TI, S4) is used to denote the operation of closing switch TI and opening switch S4, henceforth. Feasible (close, open) switching options can be found by searching sectionalizing switches When each tie switch of the isolated feeder section IS closed, d complementdry sectionahzing switch to be opened is found by searching from the tie switch, and moving upstream along the faulted feeder to its source, the circuit breaker of the isolated feeder section Fig. 2 shows a searching path for finding feasible switching options when feeder 2 is overloaded

During service restoration, the object in distributing feeder loadings with respect to their nominal capacities in the proportional manner is to minimize feeder load balance index. In this paper, the service restoration considering load balance is to find feasible switch pairs for minimizing feeder load balance index with cyclic best first search.

3. SOLUTlON ALGORlTHM The proposed search scheme starts by constructing sub-tree that wa5 sugge5ted iri Wu et a1 1991, in ordcr to decrease scarching spacc, and finding feasible switching operation with a cyclic best-first search and feeder load balance index

T2 -

1-

3 1 Constructing the sub-tree Under the constraint of the radial structure in the load transfer process, closing a normally open tie switch should follow the opening of a complementary normally closed sectionalizing switch Thcrcfore, if n tic switchcs are closcd, then n sectionalizing switches has to bc opened. Fig 1 . shows a sample distribution networks proposed by M F, Baran 19x9, consisting of three feeders with three normally opened tie switches and thirteen normally closed sectionalizing switches.

3

9

A

A

CB

1

-

Fig 2 Main search paths for examplc system If the amount of load on isolated feeder section ic transferred to only feeder 1, then TI and either S4. S1 or Sl constitute a switching pair. So feasible switching options are expressed as {(TI,&), (TI, S3), (TI, S,)], and one of switching options would be a solution for transferring the isolated feeder section. Similarly, the amount of load on isolated feeder section may be transferred to feeder 1 and 3 simultaneously by choosing one of following feasible switching options {(TI, S,), (T2, SZ)l>{(TI, S4)> (T2, S J I , {(TI, Si), (T2, %)I> {(TI, Si), (T*, S J t , {(TI, S3), (TI, S,)) But when TI and Tz are used simultaneously, the switching option {(TI, S1), (Tz, S,)} is not a feasible one due to radial structure constraint.

220

If the results of these feasible options are examined, thcn the corresponding sub-tree of figure.3 IS obtained. In figure.3, both TI and T2 are tie switches of isolated feeder section and dotted line represents switching options.

Level 1 w

4

Fig 4. The first Step of best-first search In the end, nodes {6~,@,6),,@,@} are found by best-first search. By always expanding the most likely node, it is possible to get to a goal node or a solution quickly. But tbis procedure achieves the trade-off between optimality and computational speed. It is possible that unexplored path would have yielded a solution. Therefore, optimality is sacrificed for the sake of increased speed in best-first search. But, in cyclic best-first search, with circulatory reevaluating the unexplored nodes and path, more effective solution for feeder load balance could be found. Although the search space of cyclic best-first search is slightly larger than that of best-first search, the computation difference is negligible due to using heuristic based sub-tree. The cyclic best-first search process is as follows:

Level 2

Fig 3. Sub tree with two backup feeders 3.2 Cyclic best-first search An exhaustive search evaluates all feasible switching options o j the above sub-tree and it guarantees optimal solution. But this is probab[y not realizable jor large sub-tree because of heavy computation. On the other hand, by using heuristic search, time and effbrt can be saved by finding reasonable solution promptly. There ure usually three heuristic search way,s to find optimal(or nearoptinzal) switching pairs on the above sub-tree : depth-first, breadth-first, best-first. The advantage of the best-fivst search usually, but not alway.s, yields solution faster than any other heuristic search. Rut the problem is thut it does not always give the optinzal solution: unexplored path would have given an optimal solution. To overconie this defect, the new methodology (so called cyclic bestTfirst search) is presented in this paper. This methodology is based on best-first search. But, by using cyclic methodology, it can usually find more effective solution than best-first search. As an e-rample for a best-Jirst search, consider is the start node and node @ figure 4, where node is a goal node. Node 0i.s e.rpnnded into it.7 rhildwn node @ @ @ 0. Since the losses of node @ is 1e.w than other nodes, node @ is chosen jbr expansion. This is continued until a goal node has been found.

First step: nodes are selected by using best-first search.

Second step: Constructing the reversed sub-tree and a search is proceed by using best-first search. Reversed sub-tree is constructed by reversing levels of sub-tree that was previously constructed. As an example, consider figure 5 , the level-4 of the subtree in first step becomes the level-0 of the reversed sub-tree in second step, and the level-3 in first step becomes the level-1 in second step. After reversed sub tree is constructed, a best-first search is used to select near-optimal nodes in a reversed sub-tree

/

r''o

Y

6

((f

.O

0

0.0

Fig 5 . The second step of best-first search

22 1

Level 4

In the second step of best-first search. nodes in each level are evaluated on condition that nodes in the lower levels are already chosen by the first step of best-first search. As an example, node @ is are already selected on condition that nodes 8,0,0 detcrmined from first step. Similarly, node (8 in levcl-2 is selected on condition that nodcs arc already determined from first step. : In the first step of best-first search, the nodes in level-2 are evaluated on condition that node 8 in level-3 and node 63 in level-4 are not selected by expansion. On the contrary, in second step, nodes @ @ was already selected before evaluating nodes in level-2, and nodes was also determined from first step. Due to using near-optimal solution from first step, more effective solution can be found in second step. After the second step of best first search, are selected. a new nodes {

Q,a

@,a)

( FAULT ON FEEDER SECTION 80)

When feeder fault is detected on section 80, The first step of best-first search for initial sub-tree is shown in figure 7. Initial sub-tree level is defined by T114, T111, T117, T118, T119, T124, T123, T122, T115, T116, T118 sequentially due to the different voltagc across

Level 0

T114

Level 1

TI11

Level 2

TI17

Level 3

TI 18

Level 4

TI19

Level 5

T124

Level 6

T I 23

Level 7

Ti 22

Level 8

TI15

Level 9

T t 16

Level t o

Tt13

Level 11

@,@,@,a,a] 4. TEST RESULT

The distribution network for KEPCO 108 bus system is used to demonstrate the validity and effectiveness of the proposed algorithm. The network consisting of two feeders with 108 busbars and 14 tie switches as shown in figure.6. The total load are 72.27[MW], 32,78[MVAR] . Table 1 shows initial feeder loadings

Fig.7. First step of best-first search for restoration on fault line section 80

L

Fig. 6. Initial configuration of 108 bus system Table 1. Feeder loading5 for 108 bu5 system

Feeder

Feeder

14.47

5.17

Feeder 13.04

Feeder

Feeder

Feeder

Feeder

8.38

14.34

9.88

13.80

In figure 7, the selected (close, open) switching pair for level 1 is (TI 14, 19) and feeder balance index is 2.579 foi the switching operation. In the process of checking nodes of each level, if checked nodes would increases index then the rest of unchecked nodes are ignored and searching proceeds to next level By pruning of the most unlikely nodes, this procedure makes it possible to get a solution much faster even if it deep down in the tree After the fir\t step of be\t-first search, selected (close, open) switching pairs are {(Tl14,19), (TI 11,26), (TI 17,44), (T118,73), (T119,77), (T115,50), (T116,42), (T113,36)) This solution seems feasible but it is only locally optimal, because the first step of best-first search dose not examines all the possible nodes. Therefore, it is possible that unexplored path

222

would have presented more feasible solution Thus, to find more feasible solution, reversed sub-tree IS constructed by reversing the level of sub-tree that was constructed in first step The second step of bestfirst search is executed in figure 8

Level 1

T116

Leva 2

T115

LeYel 3

TI22

Level 4

LeYel

T123 !

!

2

5

1 1 188

T124

Level 6

7119

LeYel 7

-a

T118

5 CONCLUSION In this paper, a new heuristic algorithm and feeder load balance index was presented for service restoration considering feeder load balance in distribution networks. The proposed search algorithm adopts the concept of sub-tree proposed by reference J. S. Wu Et.al 1991, and utilizes cyclic best-first search and feeder load balance index developed by the authors. Cyclic best-first search is using best-first search that gets a solution much faster even if it lies deep down in the tree. And, by using revered sub tree, it compensates best-first search for not obtaining the best solution eveiy time. Feeder load balance index is presented in order to distributing feeder loadings with respect to their nominal capacities in the proportional manner. Test results on the KEPCO‘s 108 bus distribution system show that the performance is efficient and robust.

Level 0

r i i 3

nominal capacities.

ACKNOWLEDGEMENTS This work was financially supported by MOCTE through ElRC program.

Level 8

1149

T117

Level 9

7111

Lrval 10

T114

Level 11

REFERENCES

Fig 8. The second step of cyclic best-first search After the second step of best first search, switching pairs((TI14,19), (TI 11,26), (TI 17,44), (TI 18,72), (T 1 19,77), (TI 15,50), (TI 16,42), (TI 13,36)) arc sclected to minimize feeder balance index. Comparing feeder loadings before service restoration with those of after service restoration is presented as below table 2 and 3. Table 2 Feeder loadings before service rewxation when T 120 i\

closcd to cncrgizc ibolated section Feeder loading [MVA] Feeder1 Fecded Feedcd Feeder( Fcedei Feeded 1 5 I 6 1 1 2 1 9 1 4 14.47 5.17 13.04 8.38 26.06 0

1

I

1

1

I

I 1

Feede 7

13.80

rable 1 Feeder loadings after service restoration when T 120 I$ clo\ed to energize i\olated section Feeder loading [MVA] Feeder1 Fecded Feedcd Feeder( Fcedei Feeded Feede 1 5 I 6 1 1 2 1 9 1 4 13.171 11.291 13.04 11.701 17.911 0

1

I 1

7

13.80

The above comparison indicates that loadings on feeder 5 IS decreased after service restoration, therefore loadings on isolated feeder section after fault are distributed in proposition to adjacent feeder

223

T. Taylor, D. Lubkeman, “Implementation of heuristic search strategies for distribution feeder reconfiguration”, lEEE Trans. on Power Delivery, Vol. 5 , No. 1, pp. 239 - 246. January 1990. J. S. Wu. K. L. Tomsovic, C. S. Chen, “A heuristic search approach to feeder switching operations for overload, fault, unbalanced flow and maintenance”, IEEE Trans. on Power Delivery, Vol. 6, No. 4, pp.1579 - 1585, October 1991. M. E, Baran, F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing”, TEEE Trans. on Power Delivery, Vol. PWRD-4, 1989, pp. 1401-1 407, April 1989. D. Shirmohammandi, H.W. Hong, “Reconfiguration of electrical distribution networks for resistive line losses reduction”, IEEE Trans. On Power Delivery, 1989, Vol. 4, N0.2, April, 1989. W-M.Lin, et al“ Distribution feeder reconfiguration with refined genetic Algorithm” IEE ProcGener. Trdnsm.Distrib,Vol. 147, Noh, November.2000

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

REAL-TIME VOLTNAR CONTROL IN A DISTRIBUTION SYSTEM USING MULTI-STAGE METHOD

Jong-young Park, Jong-keun Park School of Electrical Engineering, Seoul National University, Korea

Abstract: This paper proposes a method for real-time control of both capacitors and ULTC in a distribution system to reduce the total power loss and to improve the voltage profile over a day. Multi-stage consists of the off-line stage to determine dispatch schedule based on a load forecast and the on-line stage to generate the time and control sequences at each sampling time. It is then determined whether one of the control actions in the control sequence is performed at the present sampling time. The proposed method is presented for a typical radial distribution system with a single ULTC and capacitors. Copyright 02006 IFAC Keywords: VolWAr control, Distribution system, Real-time control, Under-load tap changer (ULTC), Capacitor

I . INTRODUCTION

VoltiVAr control is important to the daily operation of distribution systems, because the proper dispatch of voltNAr devices not only reduces the total power loss, but also improves the voltage profile for distribution feeders. With the development of communication and power electronic technologies, integrated control of all the available Volt/VAr devices, including the under-load tap changer (ULTC) and capacitor banks installed at substations or distribution feeders, becomes available for distribution systems. Over the last two decades, several techniques have been proposed to deal with the voltNAr control problems in distribution systems. Most of the previous techniques have been accomplished in the off-line environment by finding dispatch schedules for capacitors and ULTCs based on the load forecast for the day ahead. Some papers have proposed a dynamic programming approach for voltiVAr control problems [ 1-31, Some researchers used neural-netbased methods to control the voltiVAr devices [4-61. In [7], a time-interval base volt/VAr control method used a genetic algorithm to divide the daily load into several load levels and to find the optimal tap positions for each load level and the dispatch schedule of capacitors. Since the loads in real distribution systems are subject to non-simultaneous variation, the control of

volt/VAr devices should follow the often changing load conditions to reduce total power loss and to improve the voltage profile. For this purpose, this paper proposes a real-time voltiVAr control method based on the difference between the measured and forecasted loads. In the off-line stage, a dispatch schedule is determined using the hourly load profile available from load forecasting and then the load profile at each sampling time is calculated by applying a cubic spline interpolation to the hourly data. In the on-line stage, the time and control sequences at each sampling time are generated based on the off-line dispatch schedule. To reflect the power system conditions at each sampling time, the generated time sequence is adjusted based on the difference between the measured and forecasted loads. It is then determined whether one of the control actions in the control sequence should be moved up to the present sampling time. The proposed algorithm is demonstrated in a typical radial distribution system and compared with the off-line control method. 2 . PROBLEM FORMULATION

The distribution system under study is shown in Fig. 1. The main transformer is installed with a ULTC to keep its secondary bus voltage close to the preset value under changing load conditions. Since the primary bus voltage changes slightly over a day

225

(1). For this minimization, this paper uses the timeinterval base voltiVAr control algorithm presented in [7]. During the minimization, the voltage profile at hour h, Vh, is obtained by solving the following equation: 18

-

9

15

28

2i

29 30

-e

IG 17

where P,l,/,, QjTi1 are forecasted active and reactive loads of node n at hour h and,L7is load flow equation of node n including the consideration of the operation of voltIVAr devices.

Fig. 1. Distribution system under study compared to the secondary bus and feeder voltages, the primary bus voltage is assumed to be a constant. Two shunt capacitors are installed at the secondary bus to compensate the reactive power flow through the main transformer. In addition, some capacitors are installed at feeder buses to maintain the voltage profile within the acceptable limits and to minimize the power loss. In this paper, it is assumed that the proposed algorithm will be applied to this central unit.

3.2 Interpolation of the forecasted load data

Although the proposed algorithm requires load data at each sampling time, ollly hourly data are available from the load forecast, In order to determine the load data at each sampling time, a cubic spline interpolation is applied to the hourly data and then the interpolated load data are discretized with the sampling interval At,:

To minimize the total power loss in a distribution

system and bus voltage deviation from the desired value, the dispatch problem can be formulated as follows:

where iv,, iv2 are weighting factors for the power loss and voltage profile, IV is total number of nodes in the distribution system, L h is total percent loss in the distribution system at hour h, and &/, is voltage deviation of node n from 1 .O pu at hour h. The objective function of (1) is subject to the following inequality constraints:

where P,(t) and Qj,(t) are interpolated active and reactive load of node n at time t. Then, the forecasted voltage profile without any voltage control during a day, vll], is obtained by solving the following equation:

where f,: is load flow equation of node n without considering the operation of voltiVAr devices.

4. ON-LINE STAGE

(3) h=2

At sampling time io, the future dispatch schedule can be divided into time sequence T o [ i o ] and control sequence C, [io] , as shown in the equation

where V,, is voltage of node n at hour h, V,,,, Vmm are nodal voltage limits, 7Af'h is tap position at hour h, MK, is maximum operating number of the ULTC, C, h is status of capacitor m (on or off) at hour h, and MKC, is maximum operating numbers ol"capacitor m. 3. OFF-LINE STAGE

where jk is k-th scheduled time, ck is k-th scheduled control action, and K is total operating number of all volt/VAr devices after io. In this step, it is important to reduce computational burdens to perform the proposed method in real-time. For this purpose, the following assumption is made:

3. I Ofi-line dispatch schedule

With the day-ahead load profile available from a load forecast, the off-line dispatch schedule of the voltiVAr devices is determined from minimizing J in

Lon4 ass~mmption:The future difference between the measured and interpolated loads is the same as the present difference.

226

This assumption originates from the fact that when the measured load exceeds the forecasted one, the load in the future is more likely to also be larger than the forecasted load. In addition to the time sequence in (10), the control sequence is also adjusted for on-line control. Considering the computational burden, the following constraint is used in this step: Control constraint: only one element of the control sequence can be moved up to the present sarnpling time and the order of the others should be preserved without any change. When the p-th control action, c/,, is moved up to iO, the schedule of (10) is changed to

J3

- 'G

11

I,

According to the schedule of ( I l ) , the voltage profile at the sampling time j k ,qrf,],which corresponds to the voltage profile just after ck is performed at is obtained by solving the following equation: V[y,] such that

flllli

Fig. 2. Example of re-forecasted voltage

.J. <',

.

j,,

Fig. 3. Calculating the objective function .Ip(io)forp = 0 , ..., K The objective function J , (io) of (1 4) represents the

where Pn[ j k l and Q , [ j k1 are forecasted active and reactive loads of node n at j k , P,[i,] and &[ioI are measured active and reactive load at node n where device dk is installed. With the obtained V [ j k ] and the load assumption, the voltage of node n can be re-forecasted as

total power loss and voltage deviation when c, is performed at io. As shown in Fig. 3, repeating the procedure from ( 1 1) to (14) yields J,(in) for pzO,.. .,K. Note that J o ( i o ) corresponds to the objective function when no control action is performed at io, and Jp(io)corresponds to when p-th is performed at io. control action of pJ,[lo~

If J J j ( j o ) has a minimum value at k

=

p , the p-th

control action, c,, is performed at io and the future dispatch schedule at the next sampling time becomes

where V, [m]is interpolated voltage at node n at the sampling time m > io given by (9). Fig. 2 shows an example of the re-forecasted voltage. Using the reforecasted voltage ?,Jtn] of (13), the value of the following objective function J p ( i o )is calculated:

where A4 is total sampling number in a day, i [ n z ] is total percent loss at the sampling time m, and D,[m] is voltage deviation of node n from 1.0 pu at the sampling time m.

If J k ( i o )has a minimum value at k = 0, no control action is performed at io and the future dispatch schedule at the next sampling time becomes the same as ( 1 0). To iinpletnent this system, each control unit of capacitor or ULTC should have the information of the off-line dispatch schedule of voltiVAr devices in a distribution system. This information is generated in a central unit day by day, so the communication system which transmits it once in a day is required. Control systems for on-line calculation are also necessary for each control unit. 227

Table 1 Capacitor data for test distribution system

5. SlMULATlON RESULS The distribution system shown in Fig. 1 is used to evaluate the performance of the proposed algorithm. Two capacitors (C1 and C2) are installed at node I and the ULTC is placed between nodes 0 and 1 . The ULTC can change the voltage from -5% to +5% with 17 tap positions ([-8, -7, ..., 0, 1, ..., 7, 81). Table 1 describes the detailed data for the capacitors. The impedance of the substation transformer is (0.0178+j0.3471) pu and the maximum operating number of the ULTC, M K 7 , is set to 30. Assuming that the voltage at the primary bus is 1.O pu, and the voltage at each bus is limited to between 0.95 and 1.05 pu.

Capacitor number

Location

SiLe

Maximuin

(bus no )

LkVAr]

operating number

CI

I 1 13

C, C,

15

900 600 600 600 300 900

6

C2 C!

19 23 25

Ci

c-

In the simulations, the load at each bus consists of 50% constant-power and 50% constant-impedance. It is assumed that the load at each bus changes during the day according to the daily load curve shown in Fig. 4, but that it varies randomly by 15% around the nominal level, in both real and reactive parts. In this way, loads for all 24 hours are obtained.

6

2 2 2 2 2

900

01

3

a

$ 008 ~

0 06 0 04

-9

0 02 0 " " " " " " " " " " " ' "

With the coefficients w I and 1v2 of ( I ) set to 0.5 and 0.5, rcspectivcly, thc dispatch schedule is obtaincd from the time-interval base voltiVAr control algorithm in [7]. Following the procedure described in section 3.1, we generated the off-line dispatch schedule given in Table 2. IJsing this off-line dispatch schedule, the distribution system is simulated with the sampling interval set to 30 sec. Table 3 shows the operation records of voltlVAr devices and Fig5 shows the voltage profile of bus 14 of which the voltage is the lowest in test system.

0

4

8

I?

16

24

20

time, h

Fig. 4. Forecasted daily load curves for each device was performed within the maximum operating number in the off-line diqpatch schedule, because the proposed method only adjusts the scheduled times and changes the order of control actions using the difference between the measured and forecasted loads. Table 4 summarizes the simulation results for the proposed method. As expected, the proposed method performs better than the off-line control without increasing the operating

In the proposed method, the real-time control action

Table 2 Off-line dispatch schedule generated at the off-line stage device

time

move

device

time

move

device

time

move

C6 TAP TAP TAP I AP TAP

5 00 00

I +2 +3 +4 +5 +6

c2 c2 c2 C1 TAP 'TAP CI TAP TAP TAP

9 00 00 I I 0000 I3 00 00 I4 00 00 15 1830 I 5 46 30 16 00 00 16 I4 30 I6 42 30 17 10 30

1

C1

0 1

c2 c5 c5 C6

I9 00 00 20 00 00 23 00 00 24 00 00 24 00 00 24 00 00 24 00 00 24 00 00

0 0

6 23 00

c2 'I AP

6 44 00 7 05 00 7 27 00 7 52 00 8 00 00 8 00 00 8 1700

c1

9 00 00

c1

0 0

+7 1

0 +6 +5 1 +4 +3 i2

c1 c2 TAP

0 1

0 1 I +I

Table 3 Operation record of voltiVAr devices in real-time control device

time

move

TAP CI c2

4 29 30 4 30 30 431 30 5 30 00

+2

TAP TAP C6 C2 TAP c2 TAP

6 06 00 6 2 1 00

6 27 30 7 06 37 6 58 30 7 08 00

0 0

+3 +4 1 1 +5

0 +6

I I

device

time

move

TAP

7 39 00 7 40 00 741 00 8 1800 10 51 30 I I 2230 1 1 53 30 I4 40 30 15 11 30 I 5 42 30

+7 I I 0 0 I 0 +6 +S +4

C1

c2 C2 C1 C1

CI TAP TAP TAP

228

I I

Device

time

move

c5 I AP TAP C5

15 54 30 16 13 30 I6 44 30

+3 +2

C1 TAP

c2

16 45 30 20 01 00 22 I6 00 22 73 00

0

I I +l I

104

I

102 1

o 98 0 96 3

a094 1

I

>

0 92

,

I

/ _ _ I

proposed method ~

~

0 86

off-line setting control without control

sequences at each sampling time are generated based on the off-line dispatch schedule. Using the control sequence and the interpolated load profile, it is determined whether one of the control actions in the control sequence is performed at the present sampling time. The performance of the proposed method was evaluated for a typical radial distribution system with a single ULTC and capacitors. Simulation results showed that the proposed method performs better than the off-line control method with the same operating numbers of volt/VAr controI devices.

0 84

0

a

4

12

16

20

24

time h

REFERENCES

Fig. 5. Voltage change of bus 14 over a day Table 4 Simulation results Off-line dispatch schedule

Proposed method

1 otal Loss [kWh]

2134 57

1881 45

Average voltage deviation [pu]

0 01392

001321

numbers of volt/VAr devices. In addition, simulations indicated that the proposed method will be more useful when the actual load differs from the forecasted load considerably.

6. CONCLUSIONS This paper proposes a real-time voltiVAr control method based on the difference between the measured and forecasted loads to reduce total power loss and to improve the voltage profile over a day. To reduce computational time, the proposed method is divided into two stages. In the off-line stage, the dispatch schedule is determined using the hourly load profile available from a load forecast and then the load profile at each sampling time is calculated by applying an interpolation technique to the hourly data. In the on-line stage, the time and control

[ I ] F. Lu and Y. Hsu (1 995), Reactive powerivoltage control in a distributions substation using dynamic programming, IEE Proc Gener Trunsm Dihtrib , 142, (6), 636-645. 121 R. Liang and C. Cheng (2001), Dispatch of main transformer ULTC and capacitors in a distribution system, IEEE Trans Power Deliv., 16, (4), 626-630. [3] Y. Liu and X. Qui (2000), Optimal reactive power and voltage control for radial distribution system, Proc IEEE PCS Summer Meeting, 1, 85-90. [4] N . I. Santoso and 0. T. Tan (1990), Neural-net based real-time control of capacitors installed on distribution systems, IEEE Trans Power Deliv., 5, (I), 266-272. [5] Y. Y. Hsu and C. C. Yang (1994), A hybrid artificial neural network-dynamic programming approach for feeder capacitor scheduling, IEEE Trans Power Syst., 9, ( 2 ) , 1069-1075. [6] A. Saric, M. Calovic, and M. Djucanovic ( I 997), Neural-net based coordinated control of capacitors and ULTC transformer in daily operation of radial distribution systems, Elect Power Syst Res., 43, 169-1 77. [7] Z. Hu, X. Wang, H. Chen and G. Taylor (2003), VoltiVAr control in distribution systems using a time-interval based approach, IEE Proc Genet" Transm, Dirtrib., 150, (3,548-554.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

DEVELOPMENT OF THE AUTOMATIC RECOGNITION SYSTEM

FOR DISTRIBUTION FAClLlTY MAP

Bong-Jae Yi', Jae-Ju Song, Jin-Ho Shin, Jung-I1 Lee, Seon-Ku Cho

Korea Electric Power Research Institute, Republic of Korea

Abstract: In this paper, we propose a recognition technique of electric poles and wires which are drawn on a power distribution facility map. The map represents power supply facilities. Proposed technique is based on circularity and connectivity, and consists of four phases. At first, we extract a power distribution facility area fiom input image using threshold value. Secondly, we apply a thinning. At the third step, we extract candidate poles based on circularity. Finally, aftcr clcctric wircs bctwccn two branch points is rccognizcd bascd on connectivity, candidate poles with at least a wire are confirmed to electric poles.. Copyright 02006 IFAC Keywords: GIS (Geographic Information System), distribution facility map, automatic recognition, thinning process, histogram analysis, binarization

I. INTRODUCTION Recently GIS has increasingly become a focus for its ability of efficient management of enormous geographical data and a lot of useful information which is provided with. To develop GIS system we need to construct database with spatial information of target areas and base maps, but it is expensive and labor-intensive work to construct database. At the first stage, we can acquire data for GIS system through either photogrammetry or existing paper maps, compared to photogrammetry or surveying, existing paper maps are a rather low-cost sowce of input data [I]. There are two kinds of methods to acquire relevant digital geographic information for CIS from paper maps: Manual digitization using overlay of scanned map in an interactive editor; Automatic conversion methods based on scanned maps. The latter is considered more efficient with regard to cost effectiveness and economy of time [2]. In this paper, we propose a recognition technique of pole and wire symbols which are main facilities of power distribution map. Studies on automatic recognition of electric circuit drawings [3], mechanical drawings [4], logic drawings [5] and maps [6] have been performed since 1970's and several methods are already in practical use [7]. But it was not long before studies on recognition of national utility map have

got focused. The techniques for national utility maps are proposed in [2] and [S], but they are inapplicable to our case due to different map features and description format. To recogniLe drawing, at first, we thinned image on the assumption that input can be considered as a binary image. Then symbols can be recognized hom the thinned images. There are several existing methods based on different symbol recognition technique like closed curve method [3], graph-based method [6], knowledge-based method [6] and probabilistic relaxation method [ S ] . Basically they recognize symbols on the assumption that they are connected with solid lines. In this paper, we propose method that extracts candidate poles and wires based on circularity and connectivity and conforms them by selecting real poles fi-om candidate poles. 2. SYSTEM OVERVIEW Distribution facility map contains drawings representing cadastral information, drawings showing distribution facility information and coordinate lines for section information. In the drawings, white represents background area, black stands for distribution facility area and gray indicates cadastral area and section indication area. Target symbols or the proposed system are shown in Table 1. 23 1

Table 1. Recognition target symbols Pole

Wire

Symbol

Name

cl

Single Pole

0

Transformer Pole

Symbol

Name

---ili

lii

High voltage Circuit Low Voltage Circuit Subsistence 1 ine

Recognition technique proposed consists of four steps. At first step, preprocess the file using binarization to eliminate cadastral areas and extract only facility areas. Binarization process is based on the threshold value which is obtained by histogram analysis. We call the preprocessed image as “Distribution Facility Image”. A5 the next step, image is transformed by thinning for easier selection of poles and wires. At the third step, after a branch pixel of the thinned image is extracted, candidates of poles are selected based on circularity which can be measured around that branch pixel. Finally based on connectivity between the branch points of candidate poles, we can recognize the wires. ARei iecognitiori of wires is finished, pole recognition would be performed by extracting candidates which are connected with wires. Figure 1 shows the system architecture of proposed system.

performed, so that only the distribution area can be extracted. Binarization uses threshold value Thl obtained by hidogram analysis [9]. To calculate threshold value, histogram which represents brightness distribution of input image should be obtained by (l), i.e.

Histo(l(x,y))+ +, For all pixels on input image (1)

I(x,y) is brightness value of input image at the point or row x and column y . Most of histograms obtained by (1) are shown as Figure 3. Local minima shown in Figure 2 become main obstacles for finding target threshold value. To avoid local minima, we used histogram smoothing expressed in (2). In expression (2) brightness value i is from 0 to 255 and integral number, because it was defined as a byte (=8bits). So, I could be represented from 0 to 255. We should apply (2) for several times to get accurate histogram, but it is difficult to find out proper number of repetition times. While it is easy to Call into local minima in case of too small number of times, it is hard to obtain threshold value we want in the opposite case because it lowers the valleys of the histogram. Since the number of times for smoothing process varies with features of input image, it can be decided empirically. We use 10 which is obtained value by examining 30 sample distribution maps. Figure 3 shows smoothed histogram with 10 times iteration of (2).

7. Extraction of Branch Points

0 Binarization

Distribution

P n&ti

-\

/--

Thinning,

kw

t

I

Thinned Image

T

I

: Iniage

w : Process

Fig. 1. Overview oS Distribution Facility Map Recognition System 3. EXTRACTION OF DISTRIBUTION FACILITY AREA To recognize symbols of poles and wires in the distribution map, at first, binarization should be

,Pn&tnec:

Fig. 2. Fig. 3. Fig. 2 and 3. An example of histogram and smoothed histogram As the distribution facility areas are almost blackcolored, threshold value matches to the value of the first valley of histogram. The position of this valley is the first point at which the value fiom ( 3 ) turns €?om (-)to (+). oiff[i] = s ~ i ~ t o[s i ]~ i . m + [ i11, O
232

4. EXTRACTION OF CANDIDATE POLES BASED ON CIRCULARITY To recognize main components of facility map, firstly candidate poles have to be extracted. Single pole is described as single circle and transformer pole as doubled circle. Since transformer poles are just poles with transformer, there is no need to distinguish each other. There is at least one branch point around pole of the thinned image. The following process shows proposed method selecting candidate poles based on these branch points. First, it finds out the position of branch point pixel based on the thinned image, and then finds the maxiinum formation of circle in the search area around branch point. If the value of the maximum formation of circle becomes larger then specific value (about 0.85), then it can be confirmed as a candidate pole.

(TransitNutn(x,y) 2 3 ) ) return TRUE; else return FALSE;

1

TransitNum in Algorithm 1 represents the number of transition times and can be calculated by (4). That is, the number of times the transition occurs from 1 to 0 after 8 pixels around the T(x, y) pixel is arranged as shown in Figure 5 . Figure 6 shows an example of a branch point. As the first value of TransitNum is 3 and the second is 4, center point T(x, y) can be treated as a branch point. 7 -

TrunsitNum(x,y) =

Anl

(4)

i=o

Where, An, = 1 0

$(N

== 1aizdN(,+,),,,d8 =O),

otherwise

I

I

Fig. 5. Order o f surrounding pixels

I”F1 F;FI

Fig. 4. Search method for extracting candidate poles Figurc 4 shows scarch arca Tor cxtracting candidate poles. Thick solid line represents input drawing, “x” mark means branch. Thin dottcd line corresponds to pixels used for extracting circularity and thin solid line stands for central pixel of pixels used for extracting circularity. In this paper, the former represents “search area” and the latter represents “central area”. Central area consists of circles with radius [?om rl to r2.rl and r2 represents the minimum and the maximum radius of pole in drawings and are given as a prior knowledge before the recognition process. The search area consists o f pixels of circles Eormed by radiuses whose center point matches to each point in central area. Circularity can be calculated by averaging brightness values of these pixels. As multiple circularity values are derived from one branch point, we should choose the maximum as confirmed circularity value of given branch point. If the circularity value is larger then predefined value, it is confirmed to a candidate pole. As shown in Algorithm I branch point can be found by examining that the pixel value OC thinned image T(x,y) is l(i.e. matched to object), and the number of transition times is larger than 3 . ExtracteBranchPoint(x,y){ If ((T(.x,y) == 1) AND

0 Fig. 6. An example of branch pixel

Circularity is obtained using (5). Brightness value of same position in search area of input image is compared to threshold value Thl which is derived from binarization. When it is larger then Thl, then 1.O is accumulated, otherwise converted value of difference between brightness and threshold into ratio is accumulated. After processing all the pixels of search area, circularity can be calculated by dividing accumulated value with the number of pixels. We accumulate converted ratio which represents the distance from threshold, even when brightness value is larger than threshold. Therefore, the pole which was disconnected due to noise can be a candidate and then be considered as pole in next step.

1

C

G(x,y ) n (x,j)cMunheAi-m

Circularity = -

(5)

ij”(I(x,y ) > Th,) [ 2 - Th, otherwise I1 .o As shown in Figure 4, there are several branch points on one pole. This it should be examined whether branch points share one pole or not. In case of shred pole, it should be added to branch point lists of candidate poles. Where, G(x,y)=

233

lows the process for extracting candidate poles. ExtractePoleCandidates () { For (all branch points (bx, by) of thinncd image ) { For (i=minimum pole size; i<=maximum pole size; i++)

Calculate pole radius r(ii2); For Q=-r;j<=r; r++) { Calculate the boundary coordinate (cx, cy) formed by radius j Calculate the circulai-ity whose center point is (cx, cy) and which has radius j, save the center point, radius, and circularity value when maximum circularity.}

to recognize them is to distinguish the solid line from dotted line. Solid line represents highvoltage circuit or subsistence line while dotted line means low-voltage circuit or noise. There are cases that the solid line i q broken into fcw dottcd lines due to noise, we use the ratio of black pixels extracted from defined search are to recognize this dotted line as a solid line.

, The Maximum length of wire ,

I

If (maximum circularity > LOWERBOUND) {

Search nearest center point in the candidate pole list; If(YES) { Change parameter value of candidate pole in candidale pole 1151 and add the branch poinl lo thc branch point list; } Else { polecandidate = new PoleCandidate; Set the parameter to poleCandidatc and add to pole candidate list;

I

) )

5. RECOGNITION OF ELECTRIC WIRES BASED ON CONNECTIVITY Since wire always connect two poles, connectivity produces branch points at the position that pole and wire are connected. Therefore, for efficient recognition of wires, we should examine whether the wire that we want to recognize is within the branch points of two poles which are in the wire length boundary. Figure 7 shows search area for wire rccognition. In the drawings, thick solid line represents poles and wires, thin dotted line stands for search area for wire recognition. Search area consists of branch points of poles which are within the wire’s maximum length, pixels on the straight line connecting two branch points and pixels of left and right side of those pixels. Considering them, we minimize the error due to the conversion fkom real number system to natural number system, which makes it difficult to calculate the accurate position fi-om the image (While the equation for deriving straight line is about real number system, the position of pixels is of natural number system). Wire symbols that we want to recognize like high-voltage, low-voltage circuit and subsistence line of distribution facility map are represented as shown in table 1. HV circuit as thick solid line; LV circuit as thin dotted line and subsistence line as 3 thin solid lines or with 6 more short orthogonal lines. The first thing to do

pz

w

Fig. 7. Search area for wire recognition High-voltage circuit and subsistence line are direrent lkom the aspects of existence of thick solid line, thin solid line and orthogonal lines. Although line width can be considered as a feature for recognition, it is improper sincc it is ambiguous in many cases and varies from drawings. But as the orthogonal lines provide useful information, we can distinguish HV circuit and subsistence line from a gap between branch points formed by ortliogonal lines. Thus if tliere are 2-4 branch points with small width in search area, linc is considcrcd as subsistcncc line, and if not, line is treated as HV circuit. As LV circuit is represented as dotted line, there must be 2 or more connection line longer than predefined length. From the existence of this information, we can distinguish LV circuit and noisc. Thinncd imagc is rcfcrrcd in wirc rccognition process since it is much easicr to extract wires from tinned image. Table 2 shows the measurement of features for wire recognition. After the lines are recognized as wires, all the related pixels are deleted to avoid over-recognition by other candidate pole. Table 2. Features for wire recognition Features Ratio of Black pixcls

HV

circuit Morc than 86%

# of branch points with 2-8 0 Dixels gav Length of longest connected line The number of connected lines -: out of consideration

234

Subsistcnce Line Morc

circuit

than

60%

LV

86% 2-4 -

Larger than20 Larger than 2

Proposed method is shown in the form of algorithm in , and the results of this are saved in wire recognition result list RecogELine () { For (two poles (ij) within the length of wire) { For (all branch points k of pole i) { For (all branch points I of polc j) { Extract formation of straight line formed by k and 1 branch points; If (when extended line across near by the center of pole i and j) ( Calculate the ratio of black pixels, # of branch points with 2-8 pixels gap, length of longest connected line, the number of connected lines; If (ratio of pixels >= 85%) { If (2 >= number of branch points <= 4) Recognize subsistence line; Else Recognize as How-voltage line;) Else { If ((the ratio of black pixels >= 60%) AND (Length of longest connected line >=20) AND (the number of connected lines >= 2)) Recognize as low-voltage line; Else ignore; } If(not ignored) { cLine = new ELinc; Set the parameter value to eline, add to the wire recognition result list; Delete the pixels on branch point and the straight line; Modifji the hasELine value of ith and jth pole in candidate poles to TRUE;)

Input image was scanned with Vidar TruScan 500 of 300 DPI, and image size is 7568 x 5433 pixels with 256 colors.

Fig.8. Result ofAutomatic Recognition Figurc 8 shows rccognition rcsult of thc randomly selected image hom distribution facility map of Daejeon area. The threshold value 123 was obtained by histogram analysis. In this experiment, we focus on two aspects. First thing is the changes in performance with the quality of input drawings. We classi@ input drawings into "good", "normal", and "bad" groups and calculate average recognition ratio of each group. Secondly we evaluate recognition ratio with target facilities. Table 3 shows experimental results. Tablc 3 Statistics of rccognition ratio Quality

Good

1 As poles and wires are always connected, candidates with wire are recognized as real poles. But there are some cases that the wire is unrecognized in recognition process, so if the candidate poles without wire have large circularity (about 95%) is recognized as poles.

Normal

Bad

6. EXPERIMENTSAND PERFORMANCE EVALUATION In this section, we address the result of experiment pcrforrned and performancc evaluation. For the experiments, IBM-PCi586 with 450CPU is used and the program is coded with Visual C*.

Fsi$r: Pole HVC LVC

2.10 3.92 3.45

Unrec Recog ognize nition d ratio Ratio 1.02 96.88 1.85 94.23 11.70 84.85

SL

6.50

13.50

80.00

Subtotal Pole HVC LVC SL Subtotal Pole HVC LVC SL Subtotal

3.80 1.70 1.44 6.23 4.17 4.18 1.33 7.83 11.66 14.00 2.64

3.04 3.95 14.51 16.66 21.33 7.98 8.66 15.07 15.97 26.81 16.99

93.16 94.35 84.05 77.11 74.50 87.84 90.01 77.10 72.37 59.19 80.37

As shown in Table 3, while recognition ratio of poles is high with bad drawing quality, recognition ratio of HV circuit gradually declines as the quality get worse.

235

Table 4. Recognition ratio using probabilistic relaxation method (presented data) Drawings for experiment Symbols Lines

Dl

D2

D3

D4

92.8 98.8 96.9 94.9 80.1 92.1 86.6 87.4

Table 5. Recognition ratio using probabilistic relaxation method (experimental result) Quality of Drawings Good Normal Bad

Error Ratio 5.98 7.04 9.45

Unrecogni Recognitio zed ratio n Ratio 2.91 91.30 7.12 85.84 10.54 80.01

While recognition ratio which was got by using CREIPI tcchniqucs [8] is shown in tablc 4, the actual result from experiment with our distribution facility map is shown in table 5. Wc can notc thc followings from thc comparison of table 3 and table 5. The error ratio of our method was smaller than mcthod in [8], but unrecognized ratio of [8] is smaller than ours. 7. CONCLUSION AND FURTHER RESEARCH

In this paper we proposed a technique based on circularity and connectivity for recognizing clcctric poles, hi&-voltage circuits, low-voltage circuits and subsistence line in power distribution facility map. Experimental study of proposed method with 30 randomly sampled drawings. To evaluate the pcrformance, we examine the changes in recognition ratio related with quality of drawings and types of facilities. In case of poles and high-voltage circuit, recognition ratio appears good but in other cases, we did not get an accurate recognition result. Therefore, techniques for enhancing recognition ratio by extracting only facility drawings from input images efficiently can be proposed as a further research.

117, Jan. 1996. [3] Akio Okazaki, Takashi Kondo, Kazihiro Mori, Shou Tsunckawa, and Fiji Kawamoto, "An automatic circuit diagram reader with loopstructure-based symbol recognition," TEEE Transaction on Pattern Recognition and Machine Intelligence, Vol. 10, No. 3, pp. 331-341, May 1988. [4] S. H. Joseph and T. P. Pridmore, "Knowledge-Directed Interpretation of Mechanical Engineering Drawings," TEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 14, No. 9, pp. 928-940, Sept. 1992. [5] Wei Wu, Wei Lu, Masao Sakauchi, " A n Object-Oriented Model for Drawing Understanding and Its Ability of Noise Absorption", Proceedings of Third International Conference on Document Analysis and Recognition, pp, 261-264, 1995. [6] YUhong Yu, Ashok Samal, and Sharad Seth, "Isolating symbol from connection lines in a class of engineering drawings," Pattern Recognition, V01.27,NO.3, pp. 391-404, 1994. [7] Satoshi Suzuki and Toyomichi Yamada, "MARTS: Map recognition input system," Pattern Recognition, Vo1.23, No.8, pp.919-933, 1990. [Sl Osamu Hori, Shigeyoshi Shimotsuji, Fumlhiko Hoshino, and Toshiaki Ishii, "Line-drawing interpretation using probabilistic relaxation," Machine Vision and Applications, Vol. 6, pp. 100109,1993. [9] P. K. Sahoo, S. Soltani, and A. K. C. Wong,"A survey of thresholding Techniques" Computer Vision, Graphics, and Lmages Processing, Vol.41, pp. 233-260, 1988. [ 101 Louisa Lam, Seong-Whan Lee, and Ching Y. Suen, "Thinning Methodologies-A comprehensive survey," lEEE Transaction on Pattern Analysis and Machine Intelligencc, Vol. 14, No. 9, pp. 869-885, September 1992.

8. REFERENCES

[1] Gerd Maderlechner and Hclmut Mayer, "Conversion of high level information horn scanned maps into geographic information systems," Proceedings of the third international conference on document analysis and recognition, pp. 253-256, 1995. [2] J. E. Den Hartog, "Knowledge-based intcrprctation of utility maps," Computcr Vision and Images Processing, Vol. 63, No. 1, pp. 105-

236

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

SENSOR DYNAMICS COMPENSATOR FOR TEMPERATURE MEASUREMENT IN COMBUSTION CHAMBERS OF UTILITY BOILERS AND INCINERATORS

Igor Boiko", Vardan Mkrttchian"" *SNC-Lavalin, 909 5th Avenue SW, Calgary, Alberta, T2P 3G5, Canada, **All Armenian Internet (Jniversity, Armenia

Abstract A sliding mode compcnsation scheme for the dynamics of the sensors used for temperature measurements in the combustion chambers of utility boilers and incinerators is proposed. The proposed compensator can be used as a part of the electronics of temperature transmitters Analysis and design are carned out in the frequcncy domain with the use of the locus of a perturbed relay system (LPRS) method. Frequency-domain characteristics or the compensator dynamics are derived An example of design is provided Copyvzght 02006 IFAC Keywords sliding mode control, dynamic compensators, active sensing, dynamic observers

1. INTRODUCTION

Precise temperature measurements in the combustion chambers of modern utility boilers, incinerators, and Claus burners in various transient processes is an important technical problem. Accurate temperature measurement would allow one to know relatively fast fluctuations of this important internal process parameter and implement some more sophisticated control schemes to achieve a better quality of control. The same also applies to the measurement of water and steam temperature in utility boilers. However, unless the pyrometer measurements are used (which is an expensive option), the dynamics of the sensor due to the heat transfer in the thermowell and sensor matcnal would not allow one to read the process temperature instantaneously. The lag may be significant preventing the device rrom sensing rast temperature changes and fluctuations in a transient mode. The combined themowell-sensor time constant may range from a few seconds to a few minutes. A possible means or compensating for the sensor lag effect would be the application of the sliding mode (SM) principle (Utkin, 1992). This application can be

considered a special type of the SM observer, which would allow one to obtain the variable that cannot be measured directly, via matching the measured variablcs, subject to the sensor dyiiaiiiic model being available. This compensation would be used within the electronics of temperature transmitters. The theory of SM observers that can be utiliLed for the purpose outlined is presented in (Utkin, 1992; Edwards and Spurgeon, 1998). However, this theory does not provide any other than ideal quantitative characteristics of a SM observer in a transient mode, under harmonic excitation for example. It is assumed that once the SM is established an ideal observation occurs. With the recently developed frequency-domain method of analysis of real SMs (Boiko, 2005b), which considers parasitic dynamics and their effects being the "chattcring" phcnomenon and non-ideal response to external inputs and disturbances, one is able 10 do a quantilalive asessirienl of the compensator quality in various transient modes. The present paper uses the locus of a perturbed relay system (LPRS) method (Uoiko, 2005a) for analysis and design of thc SM compcnsator for the sensor

237

dynamics. The dynamical characteristics of the compensator can be assessed in the frequency domain as a response to the harmonic inputs at various frequencies. The paper is organued as follows At first the principle of the SM compensator is discussed, and it is shown that the SM compensator is essentially a relay servo systcm Thcn application of the LPRS method to the SM compensator along with the LPRS method fundamentals are given Finally, an example or analysis and design or a SM compensator is provided 2. SLIDING MODE COMPENSATOR

Let the dynamics of the temperature sensor be described by the following transfer function (Coughanowr and Koppel, 1965):

where TI is the time constant due to the thermowell heat transfer, T, i s the sensor time constant, T,(s) i s the temperature signal provided by the sensor (in the Laplace domain), Ti(s) is the true combustion temperature (in the Laplace domain). Let us design a SM compensator using the same idea as of the SM observer design (Utkin, 1992) The SM observer will include a model, which should be the same dynamics as the dynamics of the thermowellsensor This model will have a discontinuous control input that should enforce the output of the model to match the measured temperature This will be achicved on thc account of the discontinuous SM control, which will act in the direction of eliminating the mismatch between the measured temperature provided by the sensor and the output of the model

T,

=-

[*-(TI + T 2 ) i A-T,

TI T2

u={

+c

if

CT20

-c

if

o
(31

where f,is the output of the compensator internal model (which is supposed to match to the sensor reading Ty),u is the discontinuous control applied to the compensator internal model, c is the amplitude of this control, CT is the error signal for the SM compensator (mismatch between the sensor reading and the compensator internal model output) I he mode that occurs in the SM compensator can be characterised as an asymptotic sccond-ordcr SM (Anosov, 1959, Emelyanov et al., 1993), as the relative degree of the plant given by equation (2) is two. The variable that represents assessment of the true combustion temperature is the so-called

equivalent control u,,(t) (Utkin, 1992), which is the averaged discontinuous control u(t) subject to ideal sliding occurs. With the compensator model given by equations (2)(4) the mode that would occur in the compensator closed loop would be an ideal SM revealed as infinite frequency oscillations. Obviously such a mode cannot exist in a real system. Due to inevitable existence of some parasitic dynamics not accounted for in the compensator model the real mode would be high but finite frequency oscillations. This can be analysed with the use of the LPRS method (Boiko, 200%) if thc modcl of thcsc parasitic dynamics is available. A relatively precise model of the parasitic dynamics can be derived from the characteristics of the components of the SM compensator (limited bandwidth of the operational amplifiers, delays and hysteresis in the switching elements, etc.). For the purposc of the prcscnt analysis assume that the parasitic dynamics of the SM compensator is manifested as a hysteresis of the relay function given by formula (3). Therefore, the control function can now be rewritten as follows:

In the system (2), (4), ( 5 ) high frequency self-excited oscillations occur, which will be referred to as a real SM As a result of this, the averaged control will now be slightly different from the equivalent control The averaged control that is used as an assessment of the combustion temperature can be obtained by low-pass filtering of control u(t) For that purpose, a low-pass filter (I c second-order filtcr) must be includcd in the compensator model as follows

The resulting dynamic model of the senor and compensator can now be represented as a block diagram (Fig. I). It is worth noting here that the SM compensator is essentially a relay servo system. Therefore, all applicable methods of analysis that are used for relay systems can also be applied here.

I

I

Fig. I. Sensor dynamics SM compensator 3. ANALYSIS OF SLIDING MODE COMPENSATOR

Let us do two types of analysis of the compensator dynamics: under the ideal SM assumption and under non-ideal SM hypothesis. At first, we assume that thc

238

control is given by (3). Then the ideal SM occurs (Anosov, 1959). The averaged control uo in this case is equal to the equivalent control ueq.The latter can be obtained via replacement of the original relay nonlinearity (3) with infinite gain (Tsypkin, 1984):

u0 = K o , ,

K

(7)

+CO

Subscript “0” in (7) refers to the averaged values. ThereTore, Tor the averaged motion (3) and (4) can be rewritten as follows:

The equations of the averaged motions can be derived from (8) as follows Since u0 is always finite, the only possibility for (8) to hold is the equality of the variabler T, and f10 This in turn lead3 to the followmg equality.

periodic motions in the SM compensator can be found: nb ImJ(i2) = --

(12)

4r

where h and c are the hysteresis and the amplitude of the relay nonlinearity. After that the so-called equivalent gain of the relay, which relates the averaged values of the input to and the output of the relay, should be computed as follows:

With the equivalent gain value available, one can write the equations of the averaged motions in the compensator:

Therefore, uCq= T, . This conclusion is in accord with the theory of SM observation. However, this represents an ideal situation, which cannot exist in real applications. Let us carry out similar analysis - yet considering the hysteretic character of the relay nonlinearity. In accordance with the LPRS method (Boiko, 200Sa) a frequency-domain characteristic of the linear part of the system called the locus of a perturbed relay system (LPRS) must be computcd at first as follows:

One can see that the equations of the averaged motions are linear. This occurs due to so-called “chatter smoothing phenomenon” (Hsu and Meyer, 1968). Now via closing the open-loop equations find the transfer function of the compensator

W, (s)

= (TIs

1

+ 1XT2s + 1) 1+

1 ~

( T p + 1 p 2 s+ 1)

(17)

k,

k-l

1

. The (TIs + 1)(T*s+ 1) series ( I 0) converges very quickly and can be used for calculations. Alternatively, there are some other methods of LPRS computing presented in (Boiko, 2005b). For thc W,(s) given by the second order transfcr function the LPRS has an analytical formula:

where

W, (s) = W, (s) =

J ( w )= 0.5[1- Ti/(TI - T,) al cos ech a,

-T2 /(T2 - T , ) a 2 cosech a 2 ) ] - j 0 . 2 s n /(Ti - T,) x [ T , t h ( ~/2)-T,th(a, , /2)], where aI = n / ( T , w ) , a 2 = n / ( T , w ) .

(1 1)

Once the LPRS is computed, the following equation nee& to be bolved, from which the frequency of

Comparing (17) and (9) one can see that the real transfer function (17) of the compensator has an additional factor given by the fraction in (17) - in comparison with the transfer function of the ideal compensator (9). If k , + co this factor tends to unity and the real transfer function becomes equal to the ideal one. If the equivalent gain is high but finite value the factor in (17) represented by the fraction is a low-pass filter, which reduces the quality of compensation at high frequencies. Therefore, the bandwidth of the compensator depends on the value of the hysteresis. The value of the hysteresis b at given TI and T2 determines both the frequency of the pcriodic motion and the value of thc equivalent gain of the relay. This is illustrated below in the example of the compensator design. The low-pass filter, which serves to the purpose of suppressing the periodic component present in signal u(t) to obtain should be designed using conventional frequency-domain techniques and considerations of separating two signals of the frequencies that would differ by hundred or more times.

239

4. EXAMPLE OF COMPENSATOR DESIGN Let us design the SM compensator for the sensor, the dynamics of which are presented by the following two time constants: Tj=Ss, T2=2s. Let the frequency range of possible temperature variations be w E [0;0.2Hz].Thcrcforc, the rcquircd bandwidth of the designed compensator should be at least thc 1 samc. Dcnoic Ws((s)= . Thcn thc (5s + 1)(2s + 1) LPRS J( w) corresponding to this transfer function can be computed as per (1 1). It is presented in Fig. 11.

00

-0.2

2s

-0.4 -0 6

-0 x

-I 0 -0.I

00

0 I

02

03

04

05

(1.6

ReJ

frequencies are distanced far from each other select a two-pole Butterworth filter being the low-pass filter. Select the natural frequency of the filter to be by eight times higher that the upper frequency of thc bandwidth: un=lO.OSrad/s and calculate T, and T,. as follows: T3=1/~,=0.0995~,T, = f i l m , = 0.141s. Now Ict us run simulations of thc dcsigncd SM compensator. The Simulink model of the compensator is presented in Fig. IV. Run a few different simulations using this model. The output of the sliding modc controllcr (relay) is presented in Fig. V, which shows that self-excited oscillations of ihe predicted frequency indeed exist in the SM compensator loop. The response to a harmonic input T,.(t)=sin 0.51 is presented in Fig. V1. In this figure the horizontal axis represents T,(t), and the vertical axis is f r ( t ) .There is a small phase lag between the two signals, which is mainly due to the phase lag introduced by the low-pass filter. The use of higher-order filer would improve the quality of the compensator. The response of the compensator to the combination of a ramp input and a harmonic input is presented in Fig. V11. One can see from that figure that the output of the compensator Fc(t) tracks the true temperature T,(f) very closely.

Fig. 11. The LPRS J(w) for transfer function W(s).

5. CONCLUSION

If hysteresis b=O self-excited oscillations of infinite frequency would occur in the SM compensator loop of the system Fig. I. Assuming c=10 and a small value of hysteresis h=S. IO-'" (which represents the parasitic dynamics and is absolutely necessary in the model to obtain a finite frequency solution) calculate nb - _ =-3.93.10-". As per (12) compuie the

4c

frequency of self-excited oscillations in the SM observer loop: I2 = 12 18rad / s . Real part of the LPRS at this frequency is Re J(R)=-5.54~10~*. Now calculate the equivalent gain of the relay as per (1 3): k,=9.02.10'. The dynamic model of the averaged motions in the sensor-compensator system will be as in Fig. 111. Design the low-pass filter to filier out the frequency of self-excited oscillaiions.

A sliding mode compensator for temperature sensor dynamics is proposed in the paper. The compensator is capable of restoring the original temperature variations which otherwise are lagged. It can be used as a part of a temperature transmitter improving its dynamic response. Thc compcnsation is bascd on thc sliding modc observation pnnciple The sliding mode is generated in the compensator loop, which includes the model of the sensor dynamics and the SM controller It IS shown in the paper that if ideal sliding mode occurs then the equivalent control would be equal to the observed temperature signal. However, due to the parasitic dynamics presence ideal SM cannot occur, and real SM occurs instead. It IS shown that in this case the observed temperature signal is approximately equal to the averaged control signal Those conclusions are illustrated via example of design and simulations. REFERENCES Anoqov, D.V. ( I 959). On qtability of equilibrium points in rclay systems. Automution and remote control, 2, pp. 135-149. Boiko, I. (2005). Oscillations and transfer properties of relay servo systems - the locus of a perturbed relay system approach. Automatica, 41, pp. 677 - 683.

Fig. 111. Dynamics of averaged motions in SM compensator Considering the two frequencies: the upper frequency of the required bandwidth 2n0.2H2=1.256~*adhand the frequency of selfexcitcd oscillations R = 1218rud / s . Since the two

240

__ I-:*

1

_..=._. ,-.-. -.. I_.=_ .-, $

3..

1

-_ :I--

=.

_ _ I. _ ‘ -I

-. ==,-:

Fig. IV. Simulink model of sensor-compensator dynamics

1-

I

Self-excited oscillations in the SM Fig. compensator loop ~ ( t(Scope ) in Simulink model)

Boiko, I. (2005). Analysis of sliding modes in the frequency domain. International *J. Control, 78 (1 3), pp. 969 - 981. Coughanowr, D.R. and L.B. Koppel (1965). Process systems analysis and control, Ch. 25. McGrawHill, USA. Edwards, C. and S. Spurgeon (1998). Sliding mode control: theory and application, Taylor & Francis, London. Eirielyanov, S.V., S.K. Koroviri arid A. Levant (1993). Higher order sliding modes in control systcms. Diffcrcntial cquations, 29 (1 I), pp. 1627-1647. Hsu, J.C. and A.U. Meyer (1968). Modern control principles and upplicutions, McGraw Hill, New York. Tsypkin, Ya.Z. (1984). Relay control systems, Cambridge University Press, Cambridge, UK. Utkin, V.I. (1992). Sliding modes in oplimisation and controlprohlems, Springer Verlag, N.Y.

Fig. VI. Response of the SM compensator to the harmonic input (input-output dcpcndcncc)

/’

1

08 20

,

/21 22

23

T~~~

rS]

26

27

iS

29

Fig. VII. Response of the SM compensator to the combination of ramp and harmonic inputs

24 1

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

m ELSEVIER

PUBLICATIONS

SUB-SPACE PRINCIPAL COMPONENT ANALYSIS FOR POWER PLANT MONITORING

L. Pan, D. Flynn and M. Cregan The Queen 's University of Belfast, N. Ireland

Abstract: With increasing ease of access to plant-wide process signals in many power stations, operators face a growing challenge, particularly under alarm conditions, to monitor plant operations. However, recognizing that many of the signals are both highly correlated and collinear naturally lends itself to the adoption of data mining techniques. Typically, plant models are identified under normal conditions from historical data records. Subsequently, deviations from trained behaviour are used as indicators of poor plant performance and / or process faults. Both principal component analysis (PCA) and sub-space PCA have been applied to monitoring of a combined cycle gas turbine (CCGT). The capabilities of both approaches are demonstrated following a multi-block implementation, and the influence of external ambient conditions on CCGT performance are also examined. Copyright 02006 IFAC Keywords: performance monitoring, sub-space identification, principal component analysis, combined cycle gas turbines

1 . TNTRODUCTION In recent years, combined cycle gas turbines (CCGTs) have become a well-established technology for power generation. Compared with conventional fossil-fired generation they offer a significant improvement in thermal efficiency, a reduction in emissions and significant potential for unit flexibility. Essentially a CCGT utiliscs rotational cncrgy produced from a gas turbine to drive a synchronous machine. There is sufficient waste heat in the exhaust gases to produce steam through a heat recovery steam generator (HRSG). The steam drives a multi-stage turbine which is also connected to a synchronous machine. A number of CCGT configurations are possible consisting of multiple gas turbines and I or combined synchronous machines, giving rise to multi-shaft and single-shaft terminologies. Ballylumford power station is the largest power station in Northern Ireland and consists of 3 gas- / oil-firing thermal units, 3 x 200 MW. In addition, 500 MW and 106 MW CCGTs have recently been commissioned. The larger unit offers a multi-

shaft arrangement, consisting of two gas turbines supplying a steam turbine. In contrast, the smaller, but more efficient, unit instead provides a single-shaft arrangement driving only one electrical generator. Monitoring of power plant operations is clearly an important task both in terms of identifying equipment faults, pipe leaks, etc. within the generating units or confirming scnsor failurcs, control saturation, ctc. At a higher level, issues surrounding thermal efficiency and emissions production for each generating unit, as measures of plant performance, and the seasonal influence of ambient conditions will also be of interest. Fortunately, the frequency of measurement and distribution of sensors throughout a power station provides a great deal of redundancy which can be exploited for both fault identification and performance monitoring (Flynn et al., 2005). However, modem distributed control systems (DCSs) have the ability to monitor tens of thousands of process signals in real time, such that the volume of data collected can often obscure any information or patterns hidden within.

243

Physical or empirical mathematical models can be developed to describe the properties of individual processes. However, there is an assumption that faults are known and have been incorporated into the model. This can be a time-consuming exercise and requires the designer to have extensive knowledge of the application in question (Yoon and MacGregor, 2000). Alternatively, data mining i s a generic term for a wide variety of techniques which aim to identify novel, potentially useful and ultimately understandable patterns in data. The most successful applications have been in the fields of scientific research and industrial process monitoring, e.g. chemical engineering and chemometrics (Ruiz-Jimenez et al., 2004), industrial process control (Sebzalli et al., 2000) and power system applications such as fault protection in transmission networks (Vazquez-Martinez, 2003). In this paper it will be shown how using the principal component analysis (PCA) technique it i s possible to exploit data redundancy for fault detection and signal replacement, as applied to monitoring of a combined cycle gas turbine.

matrix by further considering past samples of individual signals (Ku et al., 199.5). However, the X matrix can soon become computationally inconvenient, while the time dependence of the signals is still not explicitly represented. Li and Qin (2001) also indicate that dynamic PCA relies upon the noise variance of all variables being identical. Alternatively, for subspace dynamic PCA, a dynamic process can be defined as follows: x(k+l)= A ~ ( k ) + B u ( k ) + p ( k )

where ~ ( R ) ER’, x ( ~ ) ER”, are the I system inputs and n state variables, and A and B are system state~ is a process space matrices. In addition, p ( k ) R“ noise term. In order to model the system dynamics, an extended state-space model is defined. For an arbitrary time sample k, taken as the current time, a future state vector, x f ( k ) and Hankel state matrix, X f , can be defined as follows:

2. PROCESS FAULT MONITORING Under normal operating conditions, a convenient way of monitoring individual process variables i s to assign upper and lower bounds to each sensor - univariate monitoring. However, such an approach ignores ‘stuck at’ faults, operating status of the plant / individual plant equipment, or even the impact of transient ‘system changing’ / load-lifting. Instead of treating each variable independently it is instead important that the validity of all sensors in relation to other variables is considered, which inevitably leads to multivariate techniques. Principal component analysis (PCA) has been used in a wide range or process monitoring applications. Here, linearly independent variables (principal components) are extracted from a highly correlated data source. Hence, a raw data matrix X ( m x n ) formed rrom m samples of n sensors, and subsequently normalised Lo zero mean and unil variance, can be decomposed as follows: X=TP’ + E

where T E and P E RnxA are the principal component score and loading matrices (Lewin, 199.5). Since the majority of the data variance is normally contained within the first A components it becomes possible to monitor the behaviour of the process by considering alone this reduced number of principal components. The residual matrix E represents the unexplained variance in the model. Although such an approach recognises, and takes advantage of, the correlation between neighbouring sensors the reduced order model developed is time independent, i.e. it does not recognize the dynamic relationships between individual process signals. A simple solution to this problem is to extend the X

X = [xf( k ) ,x f ( k + l ) . . . x f ( k+ rn - l ) ] RnjXrn ~ where f represents the number of future system states and rn 1s the number of samples. Similarly, the Hankel input matnx ,U j , is obtained as follows:

Uf

(k) =

u(k + 1)

... u ( k + f -1)

Now introducing an augmented data matrix, Z ,where

If it is assumed that measurement noise and process noise are not significant then p ( k ) = 0 . Subsequently, directly employing the PCA method, Z f can be decomposed into Z> = TPT+ TFr where T and P represent the score and loading are the associated matrices, as before, and ? and

244

residual matrices. Subsequently, the state-space A and B matrices can be obtained using a least squares approach (Wang and Qin, 2002). Having constructed the PCA model, it may then be used to determine whether recorded plant signals are consistent with historical values and neighbouring sensors. The squared prediction error (SPE) and Hotelling's T2 test provide univariate monitoring charts to quickly identiry difrerences between the actual and reconstructed value of individual signals (Sebzalli et nl., 2000). Plotting of t score plots, in combination with the above monitoring tools, also enables failing sensors to be distinguished from process faults. The relative cluster score positions can later assist in diagnosis (Kourti and MacGregor, 1995). 3. PCA TESTS AND RESULTS

Within Ballylumford power station data is archived from the DCS using a PI universal data server. Training data for PCA analysis was obtained by selecting periods of interest within the archive, and forming a snapshot of all DCS process variables. The

l i

v -1 5

~

I ~. 2

4 Time (hr)

Fig. 1 . Active power - PCA vs. sub-space PCA

I

-1 s

~

Dvnamic reconstruction

4 Time (hr)

Fig. 2. Turbine exhaust temperature - PCA vs. subspace PCA

Consequently, models were developed for one of the two gas turbines. Using process experience, 149 distinct signals were selected to create the models and training data was obtained in the range 100 - 160 MW, which is representative of normal operation. Both PCA and sub-space models were subsequently trained. For the sub-space model, the X matrix was augmented by 7 delayed rows, and the input U matrix was comprised of 25 control signals. The listed inputs include several bypass valves and (backup) fuel oil control inputs, which are normally inactive. Using the PRESS (predicted residual sum of squares) test (Wold, 1978), 10 principal components were selected for the PCA model, explaining approximately 90% of the data variance and 10 principal components for the sub-space model corresponding to roughly 95% of the data variance. In order to compare performance, Figures 1 & 2 illustrate a 5 hour test period, around a nominal operating point of 150 MW, during which the two models are separately applied to predict the gas turbine active power and the exhaust gas temperature, i.e. it is assumed that the respective sensors have failed. For reasons of confidentiality the vertical scales in the graphs have been normalised. I r a mulliple correlation coerficient, R, is defined as

1

I 2

500 MW CCGT was selected for study, consisting of a multi-shaft arrangement of 2 x 160 MW gas turbines and a 180 MW steam turbine. Although, it is clearly possible to design a single model for the entire unit there exists a natural hierarchical structure which encourages individual models to be constructed for each physical subsystem, e.g. gas turbine, condenser, heat recovery steam generator. Such a multi-block approach greatly assists in fault identification since only the model associated with that particular section will be affected, at least at first. Convenience and practicality also suggest that it is much easier constructing linking subsystems with tens or hundreds of sensors rather than a single model with, perhaps, thousands of sensors (Nomikos and MacGregor, 1994).

where y represents the raw (actual) data, j the reconstructed data and the moving average value of the signal, then it becomes possible to quantify the performance of ihe two models. A +3 minilie running average is computed for to accentuate any errors between the raw and reconstructed values. For the PCA model the observed errors are 15.5% for the active power and 20.3% for the exhaust temperature. In contrast, for the sub-space model these figures fall considerably to 1.6% and 3.1%, respectively. Although the PCA model performs reasonably well it is clear that particularly under dynamic conditions, when the power output of the gas turbine is ramping up and down that the PCA model introduces observable errors

245

with multiple correlation coefficient deviations of 4.6% and 6.7%, respectively.

5 biased data ~

I 4

b

8

time (hr)

Fig. 3. Reconstructed HP main steam temperature

9

As a final investigation of the properties of the developed sub-space model it is generally recognised that CCGT performance, and in particular gas turbine performance, can be affected by changes in ambient conditions (Lalor and O'Malley, 2003). For example, a fall in barometric pressure causes a reduction in air density and hence inlet compressor air flow. Similarly, an increase in ambient temperature causes a reduction in air density and inlet compressor air flow. Since the turbine inlet temperature is maintained constant, there is a subsequent reduction in turbine inlet pressure and hence cycle efficiency. Variations in other external variables such as relative air humidity and system frequency (affecting compressor rotational speed) can also impact on gas turbine performance.

'OI

Adopting a PCA model structure it is relatively straightforward to include the influence of such external signals into the plant model. Figure 7 illustrates the variation in barometric pressure, ambient temperature and relative humidity over an 8 hour

Fig. 4. SPE - HP main steam pressure bias in the predicted signal. These results are considered representative and consequently, the remainder of this paper will focus on the capabilities of the sub-space model alone. In order to confirm the fault identification capabilities of the PCA approach a 2% bias was introduced into the heat recovery steam generator high pressure (HP) main steam temperature signal, after 3 hours of operation while operating at approximately 130 MW, as can be seen in Figure 3. After 5 minutes the fault was detected by the unnormalised SPE indicator, Figure 4, assuming a 95% confidence limit, and after 15 minutes using the T2 test (not shown). Figure 3 also includes a (sub-space model) reconstructed version of the steam temperature signal. Given that a multi-block approach has been utilised here, and that the CCGT comprises of two identical gas turbines it is of interest to investigate whether the PCA model can be trained using &ah Gom one gas turbine and tested using data from the other. Figures 5 and 6 depict the reconstructed and actual HP main steam pressure and gas fuel flow over an 8 hour period around a nominal operating point of 100 MW, adopting the above approach. The two graphs both show that signal reconstruction has been successful,

I

2

2

6

4

8

Tlmc (h.)

Fig. 5. Multi-block - HP main steam pressure

-05

I-

I

'

'

I

'I

-2

4

2

Time (hi)

Fig. 6. Multi-block

246

-

gas fuel flow

8

period during a summer morning. It can be seen, for example, that the ambient temperature rises noticeably as the morning progresses, as would normally be expected. Figure 8 illustrates the contribution of each of the 149 variables in the X matrix to the variance observed in the direction of the first principal component of the sub-space model. This is a measure of how individual variables concord with the direction of greatest variation in the data. Amongst many signals, this principal direction tends to be associated with signals such as active power (variable 1 , variance explained 72%), gas lire1 flow (13, 78%) and inlet guide vane position (107, 92%). The environmental variables of relative humidity (125, 1 l%), ambient temperature (126, 32%) and barometric pressure (149, 14%) are highlighted in the figure, and although their contribution is less significant it can be seen that there is a measurable influence on the model (and hence gas turbine) performance.

irregularities, and identification of instrumentation errors and process faults. The PCA model is identified under normal operating conditions, and subsequently unusual deviations are highlighted and identified. The

1 ; I

(20°C)

~

~1

70%

(18°C)

__

Relative humidity %

......

Ambient temperature

5

0

100

xo

0

4. CONCLUSIONS

0

20

40

ffl

xo

loo

120

FCA vanablc

Traditionally, operator practice has been reactive, whereby actions are taken following the triggering of process alarms, often set over-responsive and mode insensitive - PCA methods enable a more proactive role for the operator, providing early warning of plant

;

Barometric p r e s s u r e

In order to better appreciate the impact of these environmental variables on the PCA model, Figure 9 illustrates a reconstruction of the active power signal with the barometric pressure, relative humidity and ambient temperature locked at the initial values shown in Figure 7. It can be seen that as time progresses during the morning that the error between the actual signal and the reconstruction gradually increases. This is predominantly due to the increase in ambient temperature. In fact the increase in barometric pressure during the same period tends to counteract the effects described, such that the externul vuriuble modelling errors largely cancel out. Much greater variations in ambient conditions could, of course, be seen by comparing midday timings with midnight, or even mid-summer conditions with mid-winter.

Distributed control systems provide many advantages in terms of improvements in productivity and plant manoeuvrability when introduced into power plants and other industrial processes. However, the ease of access to a range of plant-wide signals potentially introduces vast problems of scale, since the meaningful information contained within the collected data may be somewhat less than the volume suggests. The task remains, therefore, to identify normal operating regions and relationships within the historical data, and subsequently to apply the collated rules, reference cases, etc. Principal component analysis has received considerable interest as a method of reducing the effective ineasuremeiit space, and has been considered here for process monitoring of a combined cycle gas turbine.

5

Fig. 8. Sub-space PCA - variance explained

2

4

Time (hr)

Fig. 9. Non-environmental data reconstruction

247

6

140

developed model, however, does not naturally recognize time dependent relationships between variables. Consequently, when considering a power station application such static models generally work well under steady-state conditions but may struggle (perform less well) during changing or dynamic conditions. A sub-space PCA model was developed which inherently recognizes the dynamic nature of the CCGT plant under consideration. After confirming the capabilities of the model through reconstructing missing sensor signals, the sub-space model was alsodetect process faults through the creation of t-score plots (Flynn et al., 2005). A CCGT can naturally be split into a number of functional units. Consequently, a multi-block approach was adopted, with focus placed on a single gas turbine. In order to confirm the capabilities or the model, testing was successfully performed on an unseen second gas turbine. Finally, one of the particular benefits of the PCA approach is that it can provide insight into the process under study. It is recognised that CCGT performance is affected by variations in ambient conditions. So, by excluding these external parameters from the test data their influence on gas turbine performance can be easily examined. The primary objective of a PCA model is merely to introduce principal components in the direction of greatest data variance. Future work should, therefore, consider related techniques such as multiple linear regression and partial least squares where the objective is to introduce principal components in the direction of a defined quality variable(s). Suitable quality variables would include active power, unit efficiency, NO, and COPemissions. The year round impact of variations in ambient conditions and cooling water (sea) temperatures could further be investigated. ACKNOWLEDGEMENTS The authors wish to acknowledge the financial support provided for this work through the overseas research students awards wheme (ORSAS) and by Premier Power plc, and the access made available to Ballylumford power station

REFERENCES Flynn, D., J. Ritchie and M. Cregan (2005). Data mining techniques applied to power plant performance monitoring. 16" IFAC World Congress, Prague, Czech Republic. Kourti, T. and T.F. MacGregor (1995). Process analysis, monitoring and diagnosis, using multivariate projection methods. Chemometrics and Intelligent Laboratoiy Systems, 28, 3-2 1, Ku, W., R.H. Storer and C. Georgakis (1995). Disturbance detection and isolation by dynamic principal component analysis. Chemometrics and Intelligent Laboratory Systems, 30, 179-196. Lalor, G. and M. O'Malley (2003). Frequency control on an island power system with increasing proportions of CCGTs. IEEE Powertech, Bologna, Italy. Lewin, D.R. (1995). Predictive maintenance using PCA, Control Engineering Practice, 3,415-421 Li, W. and S.J. Qin (2001). Consistent dynamic PCA based on errors-in-variables subspace identification. Jozrrnal qf Process Control, 11, 661-678. Nomikos, P. and J.F. MacGregor (1994). Monitoring batch processes using multiway principal component analysis. AlChE ,Journal, 40, 13611375. Ruiz-Jimenez, J., F. Priego-Capote, J. Garcia-Olmo, M.D. Castro and M.D. Luque de Castro (2004). Use of chemometrics and mid infrared spectroscopy foor the selection of extraction alternatives to reference analytical methods for total fat isolation. Analytica Chimica .4cta, 525, 159-169. Sebzalii, Y.M., R.F. Li, F.Z. Chen and X.Z. Wang (2000). Knowledge discovery for process operational data for assessment and monitoring of operator's performance. Computers and Chemical Engineering, 24,409-414. Vazquez-Martinez, E. (2003). A travelling wave distance protection using principal component analysis. International Journal of Electrical Power and Energy System, 25 (6), 47 1-479. Wang, J. and S.J. Qin (2002). A new subspace identification approach based on principal component analysis. .Journal qf Piw.nres.s Contiwl, 12, 841-855. Wold, S. (1978). Cross-validatory estimation of the number of components in factor and principal components models. Technometrics, 20,397-405.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

COMBUSTION PLANT MONITORING AND CONTROL USING INFRARED AND VIDEO CAMERAS S. Zipscr*. A. Gommlich**.J. Matthes"**, H. B. Keller""" * Fruunhofer Institute for Transportation arrd Infru,strzcct.urc Systems, 01069 Dresden, Zeunerstr. 38 *+ 70'131 Kadsrdre. RiLdoljdv.15 *** IrmWute for Applied Computer. Science,

~'brsrh,unyszentrurnKu,rlsruh,e. 70'021 Kurlsmhe, P. 0. BOX 3640. Germany

Abstract: For an optimal combustion of fuels with changing properties advanced cont,rol slmtegies based on a continuous process monitoring are necessary. The monitoring is performed by canicras in conjunction with an aut,omatic image analysis t~oprovide additional information for t he adapt ion. In this papcr tvc discuss t,he capabilities and liniit,at,ionsof video and infrared camera for nionibring and cont,rol at the example of grate firing plant,s a.nd rot,ary kilns. The softawaresystcin INSPECT is introduced which provides the online image analysis for an camera, aided combustion control. Keywords: conibustion control, camera based control, image processing

1. INTRODUCTION

Diic t o cnvironmcntd ant1 cc oiio1nic a1 rmsonb conventional prirnarj fuel5 like fuel oil or coal will incieasingly be substitnted by secondary- fuels like biomass or waste. In contrast to primary fuels the secondary fuels are unfortimat,ely oft en characteri z d by +pIiicant IIiwnging fricl propc~rtw~ (. g heating \due). Fuels with approximately constant proprrt irs resiilt in a nrarhy stationary procrs5. This makes it easier to keep the pro optimal opcratiug point. While the combustion of fuels with changing propcrtics leads to a diffclent and non-itationary proces behavior and makes an environment-friendly and efficient 1.e. optimal coiiibustion a ckidlcnging task. A combustion mith changing fuel runs only optimally if the proccss control is adapted to the tiinc variant fuel properties and process state respectively. Coiiventiond control sysknis are not

atlapt,ive but, designed for avc:ragc fuel proport>ies and process condit,ions. The process control is sct up robust but t.liis is not opt.ima1 undcr ;dl conditions. Bc.caa.isc of following reasons only fcvv advanced ada,ptive control schemes are report,ed. - Combustions arc' dist,ribut.ed. time variant,,

nonlinear! a.nd niiilt,iva,riali)leprocesses. Ma t,hemat,icalmodels simulat,iiigt,he overall process or plant bchavior arc often not available. That a,pplies already for processes with time constant, and homogeneous fuels like fuel oil and even more so in case of time varying and het,crogcnous fuels like municipal waste.

- The dcvclopmciit of motlcls suitablc for a model-based control design without having an owrall proccss model is elaborat c, time consuming, and has t o be done a t the real plant. This usually prevents a systematic i.e.

249

I. e. they superpose or absorb the radiat,ion of interest, e.g. the IR emission of a solid fuel bed. Therefore we siiggest, a cornbinat,ion of short and long t,erin filtering which performs a detection and rcconstruct,ion of disturbed irn8g.e arms. This rcsults in a filt,ered image suit~ablefor the pa,ra.meter calculation. But. t,he recoiist,ruct,ion of disturbed image areas uses past image data. Obviously the validity of the filtered imagc and the succxxdiiig calculations d c creases if t,he dist,urbances effect a. la.rgeimage area and/or last long. Therefor, especially at closed loop coiit,roI,a proper aut,omat,icimage valitlat'iuii is required (Zipser et ul.? 2004).

model-based control design aiid leads to a more heuristic-int uitiv cont,rol. - The lack of rnodels describing t,he plant. r e x tion on fuel changes makes the development of ada.ptive control st,rat>egicsdifficult. - In most) cases the changing fuel propert,ies can not, be mea,surecl online (esp. solid fiiels). Furt,herrnore process variables charackizing the process condition like t.lie local oxygen coimntmtion or t,he temperature are riot known precisely. The missing knowlcdgc about, the current, and local different process state is one of the main reasons preveiiting the cleveloprnent of suitable niodcls arid advanccd control. Therefore as TV cameras and la,t!erinfrared cameras became available they were used for a det,ailed combust ion a,nalysis. This paper is locused on t.lie pot,ent,ialof VTS (visuell) a.nd TR (infrared) camera conibust,ion inoiiitoriiig wit,lirespect, to control. In dct,adl we tliscuss, prima.rily based on t he example of a grate firing, followiiig issues:

3. hlEASURING PRINCIPLE

- sclieme of camera aided combustion coiitiol, - measuring principle of VIS and IR cameras. - camera based temperature iiieasurernent,

- image parameters describing certain combustion features, aiid - camera aided combustion control with the

help of the sofLware system INSPECT. 2. CAMERA AIDED CONTROL Fig. 1 clepict,~a sket,cli of a camera. aided control. The control comprises an automalic part, whereas soloctd irnagc aiialysis rcsult>s(refcrrctl AS parameters) are used directly in t,he closed loop control and a inariual part whereas 1 he plant engineers adapt the contml s ings wit,h respect. to the displayed camera image and parameter charts.

0 Validation

I H I TI 4 Parameter

3

Display

Control

4

process Control System

I

For the combustion moiiit,oring in the VIS mostly single chip CCD (Charge Coupled Device) rolour video camera.s wit,h ail arialoge int,erface a.re used. Advant.ages are a good linearity? an approved and hexpensive t,ecliriology,arid a, high pixel resolution of c.g. 768x 576. Disadva,ntagcs arc tJhe low grey value resolut,ioii of only 8 bit, and the small exposure seiisit ivit,y rimge. Therefore 3-chip CCD sensors wit,h channel selective exposure or CMOS (Complementary Met a1 Oxide Serriicoiiductor) ca~merasbecoinc comiiion. 'I'hc latter liavc a 1ogarit.hiiiicchara,cterist.icand a wide serisitivit,y range. Hence t,hey enable lovv and high exposed irnagc areas without, saturation art>efrrcts. IR cameras are build with yuant,mn or bolometer sensors. Like the CCD sensors the quantuni sensors accumulate t,he charge carriers set free by the photons of t,lie IR irratlia,tion or iiicidcrit, light rcspcct,ivcly.To rcduce tlicrmic noisc IR quantum sensors need to be cooled. Bolomeler sensors m c k r the irradiat iori induced temperature increase of an absorber via t,liermo resistance or thermo voltage. Modern bolometer carncms operate with uiicoolcd bolometcr arrays, they are low-maiiit,enance, provide a resolntiori of 320x240 pixel, a measure rangc of 400-1500°C, and likc advaiiccd VIS camcras, a,digital intcrfxc. IR cameras for st,andard applications are sensitiv a.t a wavclcngt,hof 3-5 or 8-12 prn, t,hc rangc of thc so-called atmospheric transparency windows. For solid body t,eniperwt,uremea.siirenient,sin combustion chambers a band pass a t 3.8-4prn is required (Hoffniann et ul., 2005).

4. TEMPERATURE SIEASUREhIENT Cornhurtions arc' characterized cssciitially by the temperature level and distribution. Due to the limitations of therim couplc based measurcinents camera based approaches were iiivestigated rxtens i d y . After a skc>tch o€ thr. measuring principle the capnhilitim aiid limitations will be oiitliiiecl. Rvery horly with a icmperature T > O ° K m i i t 5

Fig. 1. Caniera a.ided coinbustion control scheme at. the exaniple of a grate firing plant After image capturing an image filtering is necessary, which minimizes t,hc influence of inevit.ably dist,iirbances likc whirlccl iip solid pxticles and flmnes. Pa,rt.iclesclist,url-,VIS or IR images siniilar.

250

with calculations bascd on c2 modcl describing the overall heat transfer including absorption and reflection effects (hlanca and Rovaglio. 2002). VIS based measurements are not reported because tlic light ciiiission rcquircs tciripcrat i r e s abovci 650°C and the light cmission of glowing fuel is oft eii superposed bv flames.

4.2 Gas and flame temperature measurement IS Wavclcngth ~nKin

Fig. 2. Black body emission vcrsus wavclcngth A: sensitivity of visuell and infrared canieias (ktromngnetic radiation. The Stcfan-Boltzmnnn law describes the emission (the spectral energy dcnsity L A ) of an ideal black body at thc wavelength X as a function of its temperature T , Fig. 2. Real bodies are often referred as grey bodies at least at certain tcmperatures and wavclcngths. Compared with the black body the grey body emission is lowcred by tlic mat crial dcpcndcnt emisqivity factor 5 with 0 < E < 1. For the grey body temperat lire rneasurenients usiially the W e n approximation

of the Stefan-Boltzmann law is used. The object tempcraturc. T can be t1cmvc.d from tlie emitted LA,] metered at the wavelength (spectral pyroinctcr), tlir ratio L A , ~ / L A at, two ~ wavclengths XI and A, (colour pyroineter) or the integral of L A between X I and A2 (band pyroriieter). 4.1 ,Wid furl tcrnpimtiirr rn~nsiircmrnt

The t,eunpcratjurcof solid bodies like the solid fuel or t,he boiler wall are measured with IR cameras scnsitiv at, 3.8-4pn (band pyroiii tra.nsparency window t,hc distjurbing absorpt>ion and emission from combust,ion ga.s comporieiits like carbon monoxide (CO), carbon dioxide (CO,) or water vapor (I3,O) are minimized. The other dominating gas components nitrogen (N,) and oxygen (0,)arc IR-transpa.rcnt. Unlike the gases with gas specific emission bands (H,Oz 2.9, CO,= 4.55! and C O z 4.8prn) soot has a continuous emission characteristic: (simi1a.r to l-he black body emission shown in Fig. 2). Therefore soot) is referred a.s grey body. If soot emission occurs it is present, in t,he camera images and requires image processing (whereat soot has a largcr cfftxtJin t,lic VIS tJhanin tlic IR). IR,-based kmperature measurement.s regarding a fuel bed of il waste combustion t,he relative error is despite disturbances and a changing emissivity less than 10%. The accuracy can be inc;reased 1

(7,

and

are constant,s,

Ro i s the solid angle

As mentioned abovt: hot) gases like CO, CO,, and H,O are visible at cert~airiwavelengths in the IR but. not- in tlic VIS. Flarncs arc visiblc bccausc they corit,aiii glowing soot, part,icles wit>h light emission. For flame temperature measurements it is a.ssumed t>ha.tt,hc gas and the soot, have t~he same temperature. Up to now it was implied that, the radiation is ernit,t,edhy a solid siirface. But in case of gases or flames the emission and the (re)absorption occurs in t>heMirnensional (3D) space. Therefor a point. of e.g. a. flame image represents the resultant, emission alorig a lim-of-siglit8across the fiamc. A t,empcraturo calculated Ixised on this is therefore called he-of-sight temperature. It describes t,he mean tempera,t,urealorig a, line approxima,tely because t,lic emission is relat,cd to both t,hc soot temperature and tlic soot, volume fraction. However t,he line-of-sight temperature of t,he flue gas (using an IR bolometer sensit.ive at the maximum cmissivit,y of CO,) providcs a fast signal for power control purposes. To determine t.lie 3D temperahre distribution regarding the 3D gas or soot c:oncent.rationrequires elaborate tomographic measurements and calculat,ions (hbel t~rnnsforniation).Applicat,ions work with colour \'IS carrieras (Cignolio et nl., 2005) or (Lu el ul., 2005) a d assume s~ableaxially symmet,ric soot flames (oil burner). Because a colow ca.niera,provides a mea.surement at 3 wavelengths barids coloiir pyrornctry can bo performed. Usually t,he red and the grcen cha.nnel are a.nalyzcd. Because of technical restrict~ionand the difficult,ies liandling t,hc fast changing fiaincs the VIS bascd t,einpera.turerneasurernent is past>ially1irnit)ed.Yet other non-tcinpcrsturc bascd information dcrivcd froin tlie VIS can be used cspccially for an enhanced gas burn out, cont>rol. For control purposes tlie t eniperature of' the burning solid fuel is of greater interest because t,his process dominates the combustion. Flames are in esseiice a result. of the solid firel c;oinbust.ion, alt hough flames themselves effect a.gabn t,he solid fuel combiistion via ratliat',ion. 5 . EXAMPLE GRATE FIRING PLANT

Fig. 1 dcpicts the consirlcrcd type of a grate fircd ( ombii\tion plant which rims typically with changing fiiels like hiomas5 or waste The file1

25 1

Table 1. Improwments due to IR-based process control

1200

3in

C

I process variable

1000

builer cEiciettcy steam variat.ion

900

iinproveinerit

+

2 7%. rcldlive -10 to -30 'lo, relative

800

-0,s 'it , absolute

700

variation Oa

600 500

-2 to -5 54,relative to -50 %, absolute to -80 % '

ture, ,..) Tor every line as well as the whole grate ase used (Schreiner aiid Jansen, 1997). The last, it,em implies a detect>ioiiof the burning zone a.s an object. 'Ibensure a reliable aut,onia.t,icburning zone det,ect,ioii an adaptjive approach has been developed arid patented (Zipser and Keller , 200.5). In detail the coiit,rol t,rics t,o achieve a proper shaped a,nd compact) ma,in burning zone a.t the grate middle, with a corist,ant' heat production, corresponding with t,licmain burning zonc properties. and a certain flue gas 0, content,. Manipulate variables are t,he fuel inass flow, the primary air flow and distribut>ion,the secondary air and t>he lrarisporl atiori speed. hlea.surenients from MARTIN GmbH Germany at different combustion plantis show tihe advant,uge of the IR-c,arncra based process control. In t,ahlc 1 the most import,ant, improvements a,rc summarized (Schreiner, 2005).

Fig. 3 . Top view inhared inmge of a grate firing fuel bcd; drawn in the gra,t,csegments aiid t,lic del ecled burning zones ent'ers the grat)eand pass t>lirougha drying, pyrolysis, arid igiiit,ion pliascs bcforc tlic birrriing down bcgins from tlic fucl hcd surfam Thc: gratc is subdivided into controllable zones and lines, see Fig. 3. The primary air flows t'hrougli the grate from below. Because t~heprimary air does not c~isurccomplclc gas burning out secondary air is injoct.c-:da,bove tho fuel bcd. The main cont,rol object,ives are: - an energy efficient combustion with low ex-

cess air, a.nd a constant heat production, - a complete solid fuel buriiing out. and a high

slag qiialit,y as well a.s - a complcte fluo gas burning oirt and a low polliit,nnt,fornia.t.ioni~.ndemission.

A VIS camera rrionnted at posit~iori( 3 ) is a standard configuration. It. monitors t'lie solid fuel burning out by the recognition of glowing or burning fuel after ti. given burning out, line. IR ca,nicra,sa,re not expedient at posit,ion ( 3 ) because the inforniat,ioii derivable are relat,ively small anyhow. To control the solid fuel burning out t,he transport,ation speed and primary air supply in t.he last grate segmenls a.re adapted.

Tlicsc objcct,ivcs are couiit,cra.ctcd by changing and heterogen fuel properties which lead to an local tliffercnt and non-stat,ionary conit)ust,ion.E. g. docs an incrcasc in t,he licat,iiig value causc a, cornbustion zone shift t,o the fuel feed. A drop causes a shift, t>othe fuel bed end. But. t,he process only operates properly if the main cornbustion takes place around t~liehalf grate length. In t~lie first case t.hc fuel can ignitc a,lrea,tlyin tlie fccder, iri (.he second case a, corriplek solid Tuel burriirig d. In both cases the pollritarit forriiat>ioriincreases. In case of niixecl liet~erogenous fuels several conihstion zones can emerge. From the cont-rolpoint, of vicw a, cl-iasactcrizatiori of t,he input fuel (on basis of the drying arid igriit,ionbehavior) is of great inkrest,, beeairse t.liis enables a prediction of combustion behavior. For that an IR camcra has t-o bc placed at position (1) in Fig. 1. Preliminary investigations for an IR irnage based heating value estima.tion are described in (1Llullc.r a,nd Keller, 1999). Placing a.n IR camera, on position ( 2 ) thc hirning zonc and depending on tlie plant geoniet,ry the ignition and the burning out) can bc monitored. For an opt,iniized process control up to 50 parameters likc (Fig. 3 ) t!hc nican sagmcnt, t,emperatiircs, t.hc longitudinal tc?mpcraturc profilcs, ;ml t,lic criicial hi.irning zone properf ies (areaj position, tempera-

G . EXAMPLE ROTARY KILN PLANT Fig. 4 shows a plant) sket,cli with t!he inclined rot8at,ingkiln for tlhe solid fuel coinbustlion and the post combustion cliamber to ensure a complete gas burning out. The solid fuel e.g. the hazardous wast,e enters the kiln via a chute. The combustion in the kiln can be controlled via the fuel and priinary air mass flow, perhaps the rotat,ional speed and tlie lieat, input. by a burnor. For t,he post, combirst,ioncontrol a secondary air input and again burners are provided. Rotary kilns work with solid fiicls a s wdl as licjiiids aiid gases. As will be discussed lat,er t,hey are also used for the conibust ion of high-calorific wwte in drums. Plant cont,rol object,ives arc' the same as ment,ioned above in case of grate firing. An additjiorial demand is to ensurc a prot,ect,ing slag layer on tlie expensive kiln lining snrfxe. Recaiise t.he sla,g

252

I

I Post combustion Oil burner

Oil burner

IR camera

I

Fuel bed

Rotary kiln

Slag

Fig. 4. Rotary kiln with IR camera monitoring fuel bed, kiln lining, and gaseous pliase (layer) behavior is closely relat.ed to t,he t.emperat,ure, an IR caniera monitoring the inner kiln temperat,ure is recomineizded. Of special int,erest, are longitudinal t,ernperature profiles m d hot, spot ion. An IR camera. ba 1 approach for lining t,ion is described in ( steen ct nl.. 2002). Wit,hin the scope of R&D projects at t,lie semiindustrial scalc rotary kiln plant. THERESA of the Research Centre Karlsruhe the fuel bed, the lining temperature, and t,he changes of t,lieg. pha.se in t,he rotary kiln were invest>iga,ted. Therefor a novel niultispectral IR camera was built up equipped wit11 bandpass filters at t.hc maxiniuni eniissivit,y of tlie gases I-120!CO,, and CO (2.9 i0.1; 4.55 f0.1, and 4.8i0.1pm) beside the coniinon filter a,t the akmospheric window for solid st,a . k t,emper at lire mea siir ement>s(3.9 i0.1pna ) . A result obtained rising wood chips as model fuel shows the t,emperature image of tlie kiln inside of Fig. 5. For a simpler analysis Ihe perspeclive

Y

1235 YinT

520

Fig. 5. Infrared temperature image of the kiln inside; right camera in Fig. 4 camera view was miippetl on basis of the geometric kiln model, Fig. G. The longitudinal temperatine profile (A) describes Ihe lining temperature, profile (B) the fucl hcat up drid ignition, and profile (C) the burning zone. The temperature charts sliow tlial hcrc tlic solid iiicl burning out is ( ornplete at = 40% of the kiln length. Investigations were also made with fuel oil filled drums as i-nodcl fuel for a rapid fucl change (Gommlich. 2005). Fig. 7 show the results of putting
Fig. 6. Mapped kiln inside (Fig. 5 ) ; drawn in t,hc t,erripera.t,ureprofiles and t,he burning zone tion is lour: and t,he background emission of the kiln surface (approximately a grey body with a continuous eiiiission characteristic) doinina.t,es. If

100

757

7 ~ 1

307

374

406

sfin

Fig. 7. combustion of oil filled drums; normalized rneaii intensity at X = 4.8i O . l / r m (CO)

the driim bursts the oil combustion starts and the IR. emission increa~sesas expected. But after a few seconds the oxygen provided is slot sufficicnt for a complete conihstion. The CO and soot, produced iiow (lamp t,he backgroirnd emission as tlie gas flows out to the post comhust,ion chamber. This can be seen from t,lie chart as well as from the diffuse images. Due to the air supply the view get,s clear again after about, 10 seconds. The l.emperat,ure change at a similar experiment is shown in Fig. 8. Due to t,he changed camera sensitivity now the CO emission is negligible. The chart shows the kiln surfxc temperaturc. iiicrciw . as a result of the addit,iorial oil combustion. Time n secons

300

400

500

Image Number

50

155

200

263

335

570

640

Fig. 8. Combustion of oil filled drums; normalized inem kiln temperature at X = 3.9 0.1pm

+

253

A new scheme adapling the post combustion air

t,eclinique for soot. diagnostics. Applied Optics 40(30),5370-5378.

cxccss to ensure d corriplctc gas burning out with reqpect to a n optical signal (analog to the CO signal of Fig. 7) is described in (Nolte et al., 2005).

Gonimlich, A. (2005). Kamerabasierfe Analyse ausyewiihlter Ga!skomponenten bei Verbrennungen. Diploma Thc , Univ. Karlsruhe.

7. INSPECT AND EXAMPLE OF USE

Hoffniaiin, M., 1\1. Zirniiicrhackl, K. Kcldcnich, G. Mollenhoff, G. Deutz and G. Hoven (2005). IR-Camera for Control of Cornbustioii Processes. 'WZIIW.dias-infrared. dc.

For an IR or VIS ranicra aidcd proccss control thc software systein INSPECT was developed. INSPECT is a c lieiit server system wliicli corrimunicates via a TCP/IP-based safety protocol. This the clients (e.g. the cainrra gatewav) may run distributed on different machines and allows a dynainical client log on and log off. A typical INSPECT configuration shows Fig. 9. Computer 2

Lu, G., G. Gilahert aiid Y. Yan (2005). Vision based moriit,oring a.nd characterisat>ion of coinbust,ion flamcs. .Journal of P/L?J/Y.~CS, Conf. Series 15, Sensors and their Applications XIII pp. 194-200. Manes, D, and h4. Rovaglio (2002). Infrared t>liermogra.pliic irnnge processing for the operation and cont'rol of hct,crogcneouscombustion cliambers. Comb. nnd Flame 130. 277-297.

Computer 1 GUI to adapt the

.-

image processing

Gateway IR Camera

I

1

Miiller, B. and H.B. Keller (1999). Neural Net,works for On Line Estimation of t,he Heat,ing Value in Tlicrmal Trcatmcnt of Waste. Proc. of a CIMCA-ht.. Wien 17.-19.2 1999

Display

lmaoe StoGge

pp. 68-75.

Gateway Process Control System

Nolte. &I.: hl. Eberhard, T. Kolb and H. Seifert (2005). Incineration of drums in a rotary kiln - a new control system for reduction of COemission. IT3V5 Conf., Galveston, Tex., 9.13. May. 2UM.

Fig. 9. Typical INSPECT configuration For tlir INSPECT tlevelopnient d iiiot1e1 tlrivcn approach was chosen. I3ascd on aii object oricntat ed UhlL-model (Unified hlodelling Language). describing the statical and dynamical system behavior. autonidic code generation to Ada was performed. Tlic niodcl based approach in conjunct ion nith Ada lend to u 24-hour operation system us well as an elficicnt development process.

Schreiner, R. (2005). Erfahrungen mit dein Inspect-System in der Industrie. Vortrag. CD z i m 1. INSPECT Workshop. INSPECT zur Optimierung der t.hermisc1ien Abfallbehaiidlung, 24.G.2005 Forscliungszcntrtini Karlsrulie.

By now INSPECT is running at about 15 plants in Enrope and Japan.

Schreiner, R. and A. Ja.nsen (1997). Infra.red carneras guide combiist,ion control. MPS Modern Poriuer Systesms, Vol. 17 Issue 9 pp. 45-39.

8. SUMhlARY

Vosteen, B.; J. Beyer arid Th. Bonkhofer (2002). Sirnult,aneous inner and outfer t~hermography of rotary kilns for hazardous wa.st,e incineration - controlled prot,ective slagging resiilt,s in a considerable prolonging of refractory life. VGB Power Tech Nr.9 pp, 71-77,

Combustion processes with clianging fiiols run only optimally if the control is adapted. The atlapt ion includes informat,ion itiit,oniatically derived by iiiiage processing from VIS or IR ca,merasmonitoring t,he c:onilr,ustiori.Regarding grate firing arid rotary kilni plants tlic pot,eritial for cuiiera a.idetl control is discussed. First) results of a novel mult>i-spectralIR camera inonit,oring a rotary kiln were presented. Finally, the software tool INSPECT was presenkd which was successfully applied as partr of the camera aided combustion control at several indust,ria,l phiits.

Zipser, S., A. Cornmlich, J. Mat,thes. H.B. Keller, Ch. Fo~icla and R. Schreirier (2004). On t.he optknizat,ion of intlust,rial combustion processes iisiiig infra,red t,hennography. Proc. 23rd IASTED eonf., 2.?.-25.2.2004 pp. 386391. Zipser, S. and H.B. Keller (2005). Verfahren zur Erkennung und Ident4fikation vvn Brennzoncn. gcriimn patent DE 103 02 175 A l , 712005; european palent applied for 8/2005.

REFERENCES Cignolio, F., S. De Liiliis and G. Zizak (2005). T~~r(~-dirnc.!nsioii~iI two-wavclcngth omission

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ENHANCEMENT OF ELECTRIC MOTOR RELIABILITY THROUGH CONDITION MONITORING Keith E. Holbert, Kang Lin, George G . Karady Department of Electrical Engineering, Arizona State University, Tenzpe, AZ, USA

Abstract: Diagnostic servicc offerings, such as condition monitoring (CM) of electric motors, for industrial customers are a potential market for electric utilities. This paper reviews the mechanisms of major motor component failures along with the existing techniques for detecting these defects. Whereas other researchers have focused on singular methods for fault diagnosis, we scck to develop an integrated CM systcm for induction motors. Our approach combines the diverse information from motor magnetic fields, vibration signals, and acoustic emissions into a more robust and comprehensive CM approach. Such a multi-faceted methodology using diverse measurement signals will allow inter comparisons of diagnostic information. Copyright 02006 IFAC Keywords: condition monitoring, failure detection, electric motors, motor bearing failure, predictive maintenance, online equipment health monitoring.

1. INTRODUCTION

I n the competitive, deregulated environment, electric utilities are continuing to expand their product line by offering value-added services to customers. For example, utilities are providing power quality monitoring for commercial customers and telecommunication services for residential consumers (Newbury, 1996). One potential market i s diagnostic services for industrial customers. Such diagnostics could include condition monitoring (CM) of electrical equipment such as motors. A CM program can reduce both costs and eqiiipment downtime, primarily by eliminating unnecessary maintenance and refurbishment actions. CM can also provide a technical basis for extending a motor’s qualified lifc, an advantagc that can provide very significant cost savings. Finally, CM can allow the utility to selectively focus attention on motors that, for reasons of loading conditions, operating patterns (is., onioff cycles, run time), or environmental considerations, are more susceptible to degradation.

Scientific literature is ripe with instances in which CM has been applied to equipment within power

plants and systems (McGrail, 1998) and other significant infrastructures (e.g., bridges). For example, Birlasekaran et al. (1998) review examples of condition monitoring applied to transformers, power cables, switchgear, bushings and insulators. Over the past 10 years. sophisticated online monitors, which are sensitive to many motor problems that can occur, have been developed. In particular, these methods include (Stone and Kapler, 1997): vibration monitoring to detect bearing problems, stator current harmonic analysis to detect induction rotor problems, and flux probes to detect synchronous rotor problems. These techniques have been applied to find various problems before catastrophic failure occurs, thereby enabling repairs to be made, often at a fraction of the cost that would be incurred if failure did happen. In one case, electric power plant operators reported avoided costs of $1.2 million over three years for -30 motors using prcdictive maintcnance techniques (EPRI, 1999a); in another plant, a cost savings of $182,000 was realized with four electric motors (EPRI, 1999b).

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2. TYPES OF ELETRIC MOTOR FAULTS AND THEIR DETECTION TECHNIQUES The major faults of electrical machines can be broadly classified as (Nandi and Toliyat, 1999): stator faults resulting in the opening or shorting of one or more of the stator phase windings; abnormal connection of the stator windings; broken rotor bar or cracked rotor end-rings: static and/or dynamic air-gap irregularities; bent shaft (akin to dynamic eccentricity) which can result in rubbing between the rotor and stator, causing serious damage to the stator core and windings; shorted rotor field winding; and bearing and gearbox failures. Industry reliability surveys suggest that ac motor failurcs may be divided into five categories, including (IEEE, 1997): bearing: 44%; stator winding: 26%; rotor: 3%; shaft: 5%; and others: 22%. Because bearing, stator, and rotor failure account for over 70% of all motor failures, much work has bcen done to identify ways to reduce operational conditions that may cause failure of these components. For instance, motor bearing failures would be significantly diminished if the driven equipment was properly aligned when installed and remained aligned regardless of changes in operating conditions. A motor coupled to a misaligncd pump load, or a load with rotational unbalance, will likely fail prematurely due to stresses imparted upon the bearings. Based upon the above information, bearing, stator turn, and rotor bar failures are the most prevalent ones and thus demand special attention. These faults and their diagnosis arc briefly discussed below. Subsequently, Table 1 provides a comprehensive comparison of the induction motor failure types and the existing techniques for their detection.

2.1 Bearing jkults. The majority of the electrical machines use ball or rolling element bearings. The main components of rolling bearings are the inner ring, the outer ring, and the rolling elements (see Fig. 1). Typically, the inner ring of thc bcaring is mounted on a rotating shaft, and the outer ring is mounted to a stationary housing. The rolling elements may be balls or rollers. The balls in a ball bearing transfer the load over a very small surface (ideally, point contact) on the raceways Radial ball bearings are simple in design, suitable for high and even very high speeds, and robust in operation and require little maintenance. Angularcontact ball bearings have an angle between the inner

and outer rings, as shown in Fig. 1 , which enables them to support both radial and axial loads.

Inner ring out& ring Fig. I Angular contact ball bearings (McInerny and Dai, 2003). There arc a number of mcchanisms that can lead to bearing failure, including mechanical damage, crack damage, wear damage, lubricant deficiency, and corrosion. Abusive handling can induce nicks and dents, which are especially harmfiil when located in areas trackcd by the rolling elemcnts. Even under normal operating conditions with balanced load and good alignment, fatigue failures may take place. These faults may lead to increased vibration and noise levels. Flaking or spalling of bearings might occur when fatigue causes small pieces to break loose from the bearing. Though almost 40%-50% of all motor failures are bcaring relatcd, very littlc has been rcportcd in literature regarding bearing related fault dctcction. Bearing faults might manifest themselves as rotor asymmetry faults (Kliman and Stein, 1990), which are usually covered under the category of eccentricity related faults. Otherwise, the ball bearing related defects can be categorized as (Devaney and Eren, 2004) outer bearing race, inner bearing race, ball, and train defects. The vibration frequencies to detect these faults are given by analytical expressions. Although bearing faults account for nearly half of all induction motor failures, Kliman et al. (1997) noted that a review of scientific literature reveals dozens of papers addrcssing rotor bars bul only a few papers employing motor current signature analysis to detect bcaring faults. Motor bearing damage detection using a stator current signal is a useful application area (Schoen et al., 1995; Yazici and Kliman, 1999; Lindh et al., 2002). In stator current monitoring, the condition is often scrutinized at pre-calculated characteristic frequencies at which faults are likely to cause changes. However, such information is not necessarily available or easily discovered and, thus, a generic method which can determine the significant frequencies of interest would be of considerable value. Ilonen et al (2005) have proposed a method and a general diagnosis tool The method can discriminate bctwecn two classes of signals using statistical discrimination measures for time-frequency features, I P , Gahor filter iesponses The method utili7es

256

global information, namely, power spectra of the filter responses. The tool is intended to bc uscd by engineering researchers to analyze differences between signals of normal and damaged motors and to identify the present condition. In experiments, the tool was successfully applied to detect bearing damage in 15 kW induction motors using measurements of the stator current or vibration.

2.2 Stator,faults. Bearings and rotors are only two of the main components of a motor. In a survey of over 7500 motor failures, 37% of significant forced outages were found to have been caused by the third major component: stator windings (Stone and Kapler, 1997). Stator faults are usually related to insulation failure. In common terms they are generally known as phase-to-ground or phase-to-phase faults. It is believed that these faults start as undetected turn-toturn faults that finally grow and culminate into major ones (Kliman et a/., 1996). Almost 30%-40% of all reported induction motor failures fall in this category (Kliman et al., 1996). Armature or stator insulation can fail duc to several reasons. Primary among these are (Nandi and Toliyat, 1999): high stator core or winding temperatures, slack core lamination, slot wedges and joints, loose bracing for end winding, contamination due to oil, moisture and dirt, short circuit or starting stresses, electrical discharges, and leakage in cooling systems. There arc a number of techniques to detect these faults. Turn-to-turn faults can be detected by analyzing the axial flux component of the machine using a large coil wound concentrically around the shaft of the machine (Penman et a/., 1994). Even the fault position could be detected by mounting four coils symmetrically in the four quadrants of the motor at a radius of about half the distance from the shaft to the stator end winding. The frequency components to detect in the axial flux component is given by [k* n (1 - s ) l ~ 1 . f ; (1) where p is the number of pole pairs, ,f; is the fundamental frequency, k = 1,3 and n = 1,2, 3, ...,(2p l), and s is the slip. Research beginning in 1977 indicated that patterns of features extracted from three-phase voltage and current phasors arc present during incipient stages of electrical-component deterioration. Research in these areas showed that a small voltage unbalance greatly reduces the effectiveness of the deteriorationdetection system because the unbalance alters the line currents and any subsequent features extracted from them. A result of the research in this area has been the identification of the effective negativesequence impedance as such an indicator. This impedance can be acquired easily, and has exhibited

a sensitivity to minor winding problems. The development of this indicator applied in the small motors (< 200 hp) that operate at low voltage (< 1000 V) is presented by Sottile and Kohler (1993). Stone and Kapler (1997) review the development of an expert system which analyzes all common on-line and off-line tests together with operating data to estimate an overall indicator of the risk of winding failure. They also examine an online partial discharge measurement system that can be used by plant personnel to detect most of the deterioration mechanisms that can occur in stator windings rated 4 kV and above.

2.3 Broken rotor bar and end ving faults. Cage rotors are of two types: cast and fabricated. Previously, cast rotors were only used in small machines. However, with the advent of cast ducted rotors; casting technology can be used even for the rotors of machines in the range of 3000 kW. Fabricated rotors are generally found in larger or special application machines. Cast rotors though more rugged than the fabricated type, can almost never be repaired once faults like cracked or broken rotor bars develop in them. The rotor bar and end ring breakage can be caused by (Nandi and Toliyat, 1999): thermal stresses due to thermal overload and unbalance, hot spots or excessive losses, and sparking (mainly fabricated rotors); magnetic stresses caused by electromagnetic forces, unbalanced magnetic pull, electromagnetic noise and vibration; residual stresses due to manufacturing problems; dynamic stresses arising from shaft torques, centrifugal forces and cyclic stresses; environmental stresses caused by for example contamination and abrasion of rotor material due to chemicals or moisture; and mcchanical strcsscs duc to loosc laminations, fatigued parts, bearing failure, and so forth. Motor current signature analysis is used to detect broken bar faults (Elkasabgy et al., 1992; Filippetti et ul., 1996). They investigate the sideband components,j,, around the fundamental frequency V;) for detecting broken bar faults .h,=(1 2s)fi. (2) While the lower sideband is specifically due to a broken bar, the upper sideband is due to consequential speed oscillation. In fact, broken bars actually give rise to a sequence of such sidebands given by (Elkasabgy et al., 1992) , ~ ~ = ( l i 2 k s ) f ; , k = 1 , 2,... ,3 (31 The motor-load inertia also affects the magnitude of these sidebands. Other spectral Components that can be observed in the stator line current arc given by (Nandi and Toliyat, 1999) ,fi= [(kiP)(l s) SIJi (4) where ,J, are the detectable broken bar frequencies, and kip = 1,3,5...

*

~

257

*

Table 1 AC Motor Faults and Techniques for Their Detection

Major Components Percent of failures (IEEE, 1997) Fault types

Bearing 44 % 0

0

Major cause of failure (Beck et a/., 1996) Techniques for fault detection

0

0

Structural defects (outer and inncr rings, rolling elements, and cage) Lubricant (high friction) Overheating Mcchanical damagc Acoustic emission (Miettinen et d., 2001) Current signature analysis (Benbouzid, 2000) Vibration monitoring (Thorsen and Dalva, 1997)

Stator Turn 26 ?/o

Rotor Bar 3

Phase-to-phase Phase-to-ground

0 0

0

0

0

Overheating Insulation breakdown Current signature analysis (Benbouzid, 2000) Magnetic flux (Sin eta/., 2003) Vibration monitoring (Trutt eta/., 2002)

0

Broken bar

0

Mechanical damage

0

Current signature analysis (Benbouzid, 2000) Magnetic flux (Sin eta/., 2003)

techniques will allow inter comparisons of diagnostic information. This strategy can be likened to the plugand-play modules of today’s computer industry as illustrated in Fig. 2.

3. AN INTEGRATED CONDITION MONITORING SYSTEM The capability to detect faults and to replace the components just prior to failure is desired by industry. By doing so, the consequences of unexpected equipment failures can be avoided. Online component monitoring can yield higher availability, extended life, and reduced costs. Incipient failure detcction not only serves to avoid catastrophic failure, but also to assist in planning corrective actions (e.g., predictive maintenance). Incipient failure detection has the ability to assist in achieving condition-based maintenance objectives.

I

I

Within the previous section a variety of fault detection techniques have been presented. Each of these approaches has advantages and disadvantages. Reliable commercial implementations favour those mcthods with low misscd and falsc alarm ratcs. In order to improve the overall reliability of motor CM, the use of various methods to address the diverse failure mechanisms (categories) and the implementation of multiple techniques within a failure category is promoted here to improve the fault detection (i.e., the robustness).

I

lnput Measurements I

I

Y Y Y $t $-

I

I

Y $-

Condition Monitor Decision Maker

Fig. 2 Architecture for integrated condition monitoring system, where the diverse measurements are input to the various signal processing modules from which thcir outputs arc assimilatcd into a decision regarding the electric motor health.

3.1 Diverse signals and fault detection techniques. Electric motor failures are a cause of critical system malfunctions and the interruption of large system operations. We propose the development of an integrated CM system for induction motors. In particular, other researchers have focused on singular methods for fault diagnosis. Instead, our monitor will combine the diverse information from motor magnetic fields, vibration signals, and acoustic emissions into a more robust and comprehensive CM approach. Such a multi-faceted methodology using diverse measurement signals along with novel or existing (Sin et a/., 2003) signal processing

As an example of utilizing diverse measurcments for integrated fault diagnosis, consider the use of magnetic field transducers. Vibration in the motor should be observable using magnetic field sensors placed at the peripheiy of the motor. In particular, consider lateral motor vibration with sensors mounted to the left and right; vibration-induced movement toward the right will result in a larger magnetic field in the right sensor, and a smaller measured field in the left sensor. A similar approach was successfully developed for nuclear reactor core barrel vibration

258

monitoring using neutron flux detectors, for which 0.02 to 0.06 mm motions were measured using detectors that were placed nearly 4 m from one another (Thie, 1981).

3.2 System simulation and testing

A salient feature of the approach presented in this paper is that it builds upon proven fault detcction and A challenge to the isolation (FDI techniques. integrated CM system is the combining of the diverse results from the signal processing modules into a final status decision. To accomplish this, we employ a rule-based fuzzy logic decision maker. The rules are established by first noting the failure mode(s) that a specific module is capable of detecting. Weights can be assigned to quantify the level of confidence that one has for a specific module in detecting a given anomaly type. By having multiple modules capable of detecting a given failure mode, we seek to decrease the missed alarm rate. Likewise, the rule-base is constructcd to dccrcasc thc falsc alarm ratc by using knowledge between modules. For example, from Table 1 we note that current signature analysis (CSA) is capable of detecting all three failure modcsbearing, stator, and rotor. Therefore, the rules are created such that the CSA module results do not falsely indicate a non-existent failure mode, while properly activating those rules pertaining to the failure mode which is truly occurring. In terms of motor health monitoring, this approach can be likened to the manner in which a physician employs multiple measures to diagnosis a patient’s illness. Over time, experience may demonstrate the need to remove a module due to poor performance, or if a new state-ofthe-art technique becomes available, then it can be inserted into the existing integrated health monitor.

Studies relating to the detection of electrical winding faults in rotating machines have normally been oriented toward the measurement and analysis of electrical parameters such as current, voltage and magnetic flux. Conversely, efforts to apply mechanical vibration technology in the CM of ac motors and generators have generally been focused on areas relating to unbalance, bearing condition, eccentricities, and other mechanical phenomena. However, theory predicts that current changes due to electrical winding deterioration in rotating machines will altcr intcrnal magnctic forccs which will thcn cause a modification in vibration characteristics. The monitoring of mechanical vibration should therefore be a useful indicator of electrical winding conditionyet another instance of employing diverse measurements for incipient fault detection through inter comparisons. While the application of these concepts in the protection of rotating machinery has been considered for many years, the major emphasis has been to study the relationships between winding faults and electrical parameters. However, an understanding of the relationships between mechanical vibrations and electrical winding deterioration could provide a means for supplemental monitoring of electrical winding integrity as well as information that might be used to discriminate between electrical and mechanical problcms.

In order to validate the developed methods for large motors, an clcctromechanical modcl of a largc induction motor for computer simulation of both fault-free and faulty conditions is nccdcd. Internal faults account for around 70% of the induction motor failures. A key challenge is to find a quantificational analysis tool for studying the diagnosis and protection of induction motor faults. Conventional methods make use of test machines; however, the machines must be damaged to orchestrate interior fault experiments. This is relatively easy for small motors, but difficult for repeated experiments and expensive to implement on larger capacity motors. Simulation models based on EMTDC (EMTP) in combination with internal faults, including both stator and rotor faults of induction motors, havc becn established to provide a virtual environment for researching induction motor interior faults (Cai et al., 2003). Such a computer model might be used to validate the developed signature analysis techniques.

Trutt et al. (1999) made a theoretical review of the relationships that should exist between electrical winding currents and the mechanical vibration of machine elements under normal and faulted operating conditions. Data from an cxpcrimcntal study that relates stator vibration and bearing vibration to selected winding faults in a synchronous machine were presented. Results demonstrated a measurable relationship between electrical deterioration and mechanical vibration and thus provide the motivation for additional study and a basis for monitoring applications.

In contrast to traditional acoustic emission (AE) analyses that simply examine wave peak amplitude, we propose to incorporate AE waveform analysis which makes use of information such as wave shape, arrival time and amplitude. For example, the high frequency components of waveforms originating from flexural events arrive first, whereas for extensional waveforms, the low frequencies are quicker to arrive at the detector. Modal AE analysis requires the use of broadband versus resonant sensors. Here we are referring to acoustic signals within both the audible and ultrasonic frequency ranges. Proper placement and monitoring of multiplc acoustic cmission scnsors provides the ability to perform three-dimensional source determination (i.e.,fault location).

REFERENCES Beck, C.E., B. Hussain, A.K. Behera, and A.J. Alsammarae (1996). Condition monitoring of 4 kV induction motors used in nuclear generating stations. Conference Record of IEEE Nuclear Science Symposium, 2, pp. 970-973. Benbouzid, M.E.H. (2000). A review of induction motors signature analysis as a medium for faults

259

Miettinen, J., P. Anderson, and V. Wikstroem (2001). Analysis of grease lubrication of a ball bearing using acoustic emission measurement. Proceedings of'the I MECH E Part J Journal of' Engineering Tribologv, 215(6), pp. 535-544. Nandi, S. and H.A. 'I'oliyat (1999). Condition monitoring and fault diagnosis of electrical machines-a review. IEEE Industry Applicutions Confkrence, Phoenix, pp. 197-204. Newbury, J. (1996). Development for the electric es networks towards the national information infrastructure. IEEE Trans. Power Delivery, 11(3),pp. 1209-1213. Penman, J., H.G. Sedding, B.A. Lloyd, W.T. Fink (1994). Dctection and location of interturn short circuits in the stator windings of operating motors. IEEE Trans. Energy Conv., 9(4), pp. 652-658. Schoen, R., T. Habetler, F. Kamran, and R. Bartfield (1995). Motor bearing damage detection using stator current monitoring. Applicat., 31(6), pp. 1274-1279. Sin, M.L., W.L. Soong, and N. Ertugrul (2003). Induction machine on-line condition monitoring and fault diagnosis A survey. Australasian Universities Power Engincering Conference, Christchurch, New Zealand. Sottile, J. and J.L. Kohler ( I 993). An on-line method to detect incipient failure of turn insulation in random-wound motors. IEEE Trans. Energy Conversion, 8(4), pp. 762-768. Stone, G.C. and J. Kapler (1997). Condition-based maintenance for the electrical windings of large motors and generators. Pulp and Paper Industry Technical Conference, Cincinnati, pp. 57-63. Thie, J.A. (1981). Power Reactor Noise, American Nuclear Society, pp. 1 1 5- I2 1 . Thorsen, O.V., and M. Dalva (1997). Condition monitoring mcthods, failurc idcntification and analysis for high voltage motors in petrochemical industry. Eighth International Conference on Electrical Machines and Drives, pp. 109-1 13. Trutt, F.C., J. Sottile, and J.L. Kohler (1999). Detection of A-C machine winding deterioration using electrically excited vibrations. IEEE 34'" Industry Application Conference, 3, pp. 19031907. Truii, F.C., J. Soitile, and J.L. Kohler (2002). Condition monitoring of induction motor stator windings using clcctrically excitcd vibrations. Conjerence Record of' the 37Ih Ind. Applicat. Conjkrence, 4, pp. 2301-2305. Yazici, B., and G. Kliman (1999). An adaptive statistical time-frequency method for detection of broken bars and bearing faults in motors using stator current. IEEE Tr*ans. Ind. Applicat., 35(2), pp. 442452.

detection. IEEE Trans. Ind. Electronics, 47(5), pp. 984-993. Birlasekaran, S., S.S. Choi, and A.C. Liew (1998). Overview of diagnostic and conditioning monitoring techniques for in-service power apparatus. International Conference on Energy Management and Power Delivery, 2, pp. 673-678. Cai, Z., A. Gao, and J. Jiang (2003). Modeling for interior faults of induction motors and its simulation on EMTDC. International Conference on Power Systems Transients, pp. 1-5. Devancy, M.J., and L. Eren (2004). Detecting motor bearing faults. IEEE Instrumentation & Measurement Magazine, 7(4), pp. 30-50. EPRI (1999a). Predictive maintenance tools and techniques help LG&E avoid costly motor failures. EPRIInnovators, IN-1 10285. EPRI (1 999b). Electric motor predictive maintenance tools and techniques increase motor reliability while reducing costs. EPRl Innovators, IN1 11769. Elkasabgy, N.M., A.R. Eastham, and G.E. Dawson (1 992). Detection of broken bars in the cage rotor on an induction machine. IEEE Trans. Ind. Applns., IA-22(6), pp. 165-171. Filippetti, F., G. Franceschini, C. Tassoni, and P. Vas (1 996). A1 techniques in induction machines diagnosis including the speed ripple effect. IEEEIAS Annual Meeting Con$', pp. 655-662. IEEE STD 493- 1997. IEEE recommended practice for the design qf reliable industrial and commercial power systems. App. H, Table XI. Ilonen J., J.-K. Kamarainen, T. Lindh, J. Ahola, H. Kalvianen, and J. Partanen (2005). Diagnosis tool for motor condition monitoring. IEEE Trans. Ind. Applicat., 41(4), pp. 963-971. Kliman, G.B., and J. Stein (1990). Induction motor fault detection via passive current monitoring. Intern. Con$ on Electrical Machines, pp. 13-17. Kliman, G.B., W. J. Premerlani, R. A. Koegl, and D. Hoeweler (1996). A new approach to on-line fault detection in ac motors. IEEE-IAS Annual Meeting Conference, pp. 687-693. Kliman, G.B., W.J. Premerlani, B. Yazici, R.A. Koegl, and J. Mazereeuw (1997). Sensorless, online motor diagnostics. IEEE Comp. App. Pwr.,10(2), pp. 39-43. Lindh, T., J. Ahola, and J. Partanen (2002). Evaluation of condition monitoring of bearings of 15 kW induction motor based on stator currcnt measurement. Proc. of' ICEM'O2, Brugges, Belgium. McGrail, T. (1998). Condition monitoring a user perspective. IEE Colloquium on HV Measurements, Condition Monitoring and Associated Database Handling Strategies, pp. 1 I1- 113. McInerny, S.A., and Y. Dai (2003). Basic vibration signal processing for bearing fault detection. IEEE Trans. Education, 46(1), pp. 149-156. ~

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PERFORMANCE OF HW-PSSS AS AFFECTED BY THE PARAMETERS OF THE BILINEAR TRANSFORMATION

K A Folly, K Mocwane Universily of Cape Town, Dept. of Electrical Engineering, Cape Town South Africa

Abstract: This paper investigates the effect of the parameters of the bilinear transformation on the performance of H,-PSSs. The bilinear transformation is used together with H, optimal control to design H, based Power System Stabilizers (PSSs) that are robust with respect to system's uncertainty. Two cases of the bilinear transformation are investigated. Namely, the Simple Case (SC) where only one parameter Cpl) of the bilinear transformation is used and the Complex Case (CC) where two parameters (PI and p2) are used. It is shown that for the controller to perform satisfactory in the Simple Case (SC), the absolute value of p i should be set high enough to give adequate damping without exciting the high-frequency modes. For the Complex Case (CC), a medium value of p 1 togcthcr with a rclativcly high value of p 2 should bc used to achieve a good performance of the controller. In this case, a trade-off is required in setting the values of p 1 andp2. Copyright 02006 IFAC Keywords: Power System Stabilizer (PSS), bilinear transformation, H m optimal control, robustness.

I . INTRODUCTION The bilinear transformation also known as the j w axis poles shifting transform technique (Chiang and Safonov 2001), has recently attracted a significant interest in power systems because of its ability to deal with the pole-zero cancellation phenomenon that is inherent with the H,-PSS (Folly et al., 1998). H, optimal control is a frequency-domain optimization and synthesis theory that was developed to explicitly address the problem of uncertainties. It deals with the minimization of the peak value of certain closed-loop system functions (Chiang ef al., 1990). A common design formulation in H, optimal control involves the so-called mixed-sensitivity weighting strategy where frequency dependent weighting functions are used to shapc thc various sensitivity functions such as the sensitivity function (8,the complementary sensitivity function (7) andor the input sensitivity function ( R ) (Chiang et al., 1990), (Chiang and Safonov, 2001). It is known that in the weighted mixed sensitivity problem formulation, the H, controller always cancels the stable poles of the

system (Chiang and Safonov, 2001; Bosgra and Kwakernaak, 1997). If lightly damped poles are cancelled, the closed-loop system will behave like an open-loop system. This issue becomes critical when designing power system stabilizers (PSSs), where the main objective is to add damping to the lightly damped electromechanical modes. Therefore, polezero cancellation phenomenon in H,-PSS design leads to poor robustness and performance (Folly, et al., 1998). To prevent this phenomenon, Chiang and Safonov (2001) have proposed the use of the bilinear transformation in combination with the H, optimal control. This approach has a number of advantages over the standard H m optimal control. First, it allows the designer to reassign dominant poles of the closed-loop system at desired locations in the s-plane. This means that time domain requirements such as the settling time, overshoots and rise time, which cannot be specified in the standard approach, can now be specified and achieved.

26 I

Second, it can remove the ill-conditioning inherent in some augmented plants (e.g., nominal system and weights). In other words, the bilinear transformation can deal with situations in which singularities arise in the equations that determine the state-space realization of the H, control law (Chiang and Safonov, 2001).

finite bus

e - p

'

,w

w-

Fig. 1 System model also vary. This variation is likely to affect the dynamic characteristics of the system.

Xu and Mansour (1988), Chiang and Safonov (2001); Folly et al. (2004) have shown the effectiveness of this approach. However, in the literature, the advantages and disadvantages of using the Simple Case (SC) bilinear transformation over the Complex Case (CC) and vice-versa is not discusscd. No clear guidelines can be found on how to choose the parameters of the bilinear transformation to achieve good damping at low frequcncics without scarifying thc robustncss of the system at high frequencies. While it clear that the parameters pl can be used to control the locations of the dominant poles, the role ofp2 is not clear.

2.2 Design Specijications

The objective in this study is to design a robust controller that stabilizes not only the nominal system G&) but also a set of system models that lie in the true plant G(s). Since the model of the true plant is not known exactly, the off-nominal conditions are used to model it. Table 1 shows the range of possible operating conditions considered in the design. The various operating conditions are obtained by varying the transmission line reactance Xe, the active power P, and reactive power Qe.

In this paper, we investigate the effect that the paramctcrs of thc bilincar transformation have on the performance of the Hm-PSS. Two bilinear cases are compared, i.e. the Simple Case (SC) where only one parameter (pi) of the bilinear transformation is used and the Complex Case (CC) where all the parameters (pi) and pz) are used. It found that the controller based on the Complex Case could perform better than the Simple Case if the parameters of the bilinear transformation are chosen such that the controller can attenuate disturbances at low-frequency without exciting high frcquency unmodelled dynamics.

The specifications of the design are: 1.

2.

3.

2 . SYSTEM MODEL AND DESIGN

Stabilization of the system despite the variations in the system's parameters (Folly el al., 1998; Travichandran, and Quintana 1996). Robustness in the presence of uncertainties such neglected high-frequency dynamics, unmodelled dynamics, noises, etc. (Chiang el a1 , 1998; Chiang, and Safonov, 2001, Folly et al., 2004) Settling time should be less than 2sec for the nominal closed-loop system, less than 3ec for off-nominal systems and acceptable maximum overshoot and undershoot (say bout 4.5%)

SPECIFICATIONS Specification 1 means that we should achieve a good disturbance attenuation at the frequency of oscillations, i.e., the sensitivity function S should be small at low frequencies.

2. I System Model

The system model used is a single machine infinite bus as shown in figure 1. The synchronous generator is modeled by a third-order differential equations (damper winding neglected), and it has a standard AVR which is modeled by a first order differential equation (Kundur, 1994; Folly el ul., 2004). To improve the stability of the system, a PSS is added to the excitation control (this is not shown in Fig.1). The nonlinear equations are linearized around the nominal operating condition and the system is rcprcscntcd in the frequency domain as:

where G, (s) = C, (SI - AO)-'B, + D o , y is the system output and ZI is the system input. A,,, Bo, C,, and Do are constant matrices of appropriate dimensions. It should be mentioned that ( 1 ) i s only valid for one operating condition (i.e., the nominal operating condition). As the operating point is varying, the matrices A,, B,,, C,, and D, will

Specification 2 means that the cornplerrieritary sensitivity function 7':= I-S and /or the input sensitivity R ;- KS (where K is the controller) should be small at high frequencies to prevent the highfrequency modes from being excited. This means a good roll-off of the controller Specification 3 is related to the damping of the dominant closed-loop poles. For the system that is considered in this study, this means a damping ratio of at least 0.25. This requirement can only be achieved by using the bilinear transformation. Table 1 Possible operating conditions Parameters

xe pe Qe

262

Minimum 0.25 0.80 -0.30

Nominal 0.50 0.80 0.30

Maximum 1.OO 1.04 0.40

It should be mentioned that uncertainty weighting functions are chosen by trial and error to represent the maximum multiplicative andior additive uncertainty. The disturbance weighting function should reflect the disturbance attenuation specification. During the design, these weighting functions are used to penalize the various sensitivity functions. Thc focus of this paper is not the weighting functions, so we will not discuss how the weights have been chosen. Interested reader can see Chiang and Safonov (2001), Chiang et al.. (1990), Folly et al. (1998, 2004).

3. BILINEAR TRANSFORMATION

-s = - s + p ,

(3)

S ~1

P2 where p l < 0 and p2< 0 arc the end-points of the diameter of a circle in the left s-plane as shown in Fig. 2 (b). Note that both the poles and zeros are affected by the transformation. With the Complex Case, we have two parameters to choose. This adds more flexibility in the design at the expense of complexity because the parameters interact with each other.

3.2 Simple Case (SC)

The bilincar transformation can be formulated as j l y axis polc shifting transformation. Let the pole-zero configuration of the nominal system Go@) be as shown in Fig. 2 (a). This system has a jo axis zero and a pair of lightly damped poles. If the standard H, approach is used to design the controller based on this model, the lightly damped poles will reappear as closed-loop poles due to the pole-zero cancellation phenomenon. Consequently, the damping of the closed-loop system will not be improved. This will lead to poor robustness and performance. To prevent this, we apply the bilinear transformation.

By simplifying the Complex Case, we obtain the Simple Case. The assumption made for the SC is that p 2 = m. Therefore, we are left with only one parameter y l which can take any value depending on the design requirements. Fig.3 illustrates this case.

In the following sections, we discuss the two types of the bilinear transformation: the Complex Case (CC) and the Simple Case (SC). Since the SC is a simplification of CC we start with CC.

a. Open-loop

4

s-plane

s--plane

x

............................................................

:.....................

.i..&jv\7L

x ....................................................................................................... b. Transformed open-loop

t

t

r--planc

s-planc

3.1 Complex Case (CC)

In the Complex Case, the two parameters of the p l and p 2 of the bilincar transformation of ( 2 ) are used to shift the poles of the nominal system G&) in the s-plane such that G,,(s) is transformed it into a tictitious unstable system Go(?) in the new F plane as shown in Fig. 2 (b). Because of the internal stability requirement in H, design, unstable poles cannot be cancelled; instead, they are shifted approximately to their mirror images once the fecdback loop is closed with the H, controller as shown in Fig. 2 (c). Thc controller K(s) corresponding to the original system is found by using the inverse bilinear transformation (3). It should be mentioned that K(s) is sub-optimal solution of the original H, control problem. When the original lightly damped nominal system GJs) is closed with this sub-optimal controller, the closedloop modes will move further in the left half s-plane as shown in Fig. 2 (d).

c. Closed-loop is s--plane

1 h, .

d. Closed-loop in s-plane

Fig.2 Bilinear Transformation- Complex Case (CC)

,

s--plane

.........................................................................................................

's-

1?2

x . .........................................................................................

a. Open-loop

c. Closed-loop is s--plane

+K

b. Transformed open-loop

d. Closed-loop in s-plane

Fig.3 Bilinear Transformation- Simple Case (SC)

263

4. POWER SYSTEM STABILIZER DESIGN

5.1 Time Domain Simulations

4.I Simple Case (SC) For all the simulations, a step response is applied to the voltage reference Vref Note that one could also apply a step response in the mechanical input, the results would have been the same. The responses shown in Figs. 4 and 5 are those of the output of the system (i.e., speed deviation). Thus, the input signal to the 11-PSS is thc speed deviation Aw.

For this design, we fixed p2 to infinity while p , is varied from -0.5 to -20. 'lhe rule-of-thumb for choosingpl is given as (Chiang and Safonov 2001):

I PI I

=

son

(4)

<

where is the damping ratio and u, is the natural frequency of oscillations.

Simple Case (SC)

Fig. 4. shows the performance of the controller under nominal operating condition for p i is -0.5, -10 and 20, respectively. It can bc seen that a s p , is increasing the system becomes more and more damped and the settling time decreases. F o r p l -0.5, the oscillations persisted after 5 sec., which clearly does not meet our design specifications (e.g., less than 2 sec). Porpl = 10 and -20 the settling time is about 1.25 sec and 0.5 sec, respectively. Clearly, a value of pI = -2 (not shown in the Fig. 4) would easily meet our design requirements. In terms of overshoot p 1 = -20 does not have any overshoot but the undershoot is quite large as compared to the case with pi = -10. We will see later in the frequency domain simulations the negative effect of arbitrary increasing the absolute value of pl. Note that the transfer functions of the PSSs for selected values o f p l andp2 are shown in the Appendix 1.

<

is strongly This means that the damping ratio related to P I . The higher the damping ratio the larger the absolute value ofpl. 4.2 Complex Case (CC) This case appears to be much more complex when compared to the SC as the two end points of the circle in Fig. 2(b) are varied. End-pointp, is fixed at -0.5, -1 and -2, respectively whilep2vary from -10 to -1000 as shown in Table 3. From the design point of view the choice o f p 2 is not straightforward, since p1 and p2 interact with each other as we will see in the next section. The role of p 2 and how to sclcct this paramcter is ambiguous in the literature. Chiang and Safonov (2001) suggested that it should be chosen to be much greater than the control bandwidth.

Complex Cnse (SC)

Table 2 Bilinear transformation: Siinple Case PI

Y2 -0.5

r*:

-1

-2...

-lo...

-20

Table 2 Bilinear transformation: Complex C ase PI -0.5 -1.0 -2.0

P2

-10 -10 -10

-20 -20 -20

-30

._.

-30 -30

._.

...

-1000 -1000 -1000

5. SIMULATION RESULTS

The performances and robustness of the controllers are analysecl by performing tiirie cloiriain simulations specifically looking into the time domain responses such as step responses and frequency domain responses such as Bode plots. The nominal open-loop system is poorly damped with dominant poles corresponding to the local oscillation modes at -0.430+8.2 18. This corresponds to a damping ratio of 5.23% and a frequency of For a good oscillations of about 1.31 Hz. performance of the system, this damping needs to be increased significantly by the Hm-PSS.

Figure 5 shows the responses of the system for the Complex Case. For this case we first fixed p2 to a specified value say - 10 and then vary p1. This process is repeated for all other values ofpz. However, only a handful of simulation results are shown in Fig.5. Fig. 5 (a) shows the case where p 2= - 10 and pl was varied from -0.5 to -2. If we consider the case forp2 = -10 and p i = -0.5, it can be seen that the system settled quicker than in Fig. 4. The settling time now is about 3 sec as compared to more than 5 sec in Fig. 4. This suggests thatp2 has contributed to the damping of the system. However, i n terms of overshoots and undershoots, Fig. 5 (a) is worst than Fig. 4. This problem can be solved by increasing the absolute value o f p 2 to -20 and -50, as shown in Fig 5 (b) and (c), respectively. For p z =-50 and pl=-0.5, the system settling time, overshoots and undershoots are smaller than for p 2 = cc and pl=-0.5in Fig. 4. This means that for a given value o f p i , we are able to achieve a better performance of the controller in terms of setting time, overshoots and undershoots by selecting a suitable value for p2 in the Complex Case than the Simple Case. From Fig. 5, it can be seen that for a fixed value of p2,the increase in the absolute value of p1would add more damping to system and reduce the overshoots as well as undershoots. As can be seen Fig. 5 (b) and (c), the value of pz that gives the best performance of the controller is not necessarily the

264

off when selecting the parameters of the bilinear transformation in the Complex Case.

Step Responce

I

1 i

1j 0

3

2

1

4

Time (5ecj

Fig.4. Step response- Simple Case

Step Responce

..... .. ... ... ..

. ,.. . .. ... ... . ..

1

=-0.5

1

Comparison of and Figs. 5 (a)-(c) shows that extreme values (e.g., very small and very big) ofpz will not in general give good results. The optimum value ofp2 is somewhere in the middle. Note that the transfer functions of the PSSs for selected values o f p , andpz are shown in the Appendix 2.

5.2 Frequency Domain Simulations The singular value Bode plots of the nominal closedloop system when pi is -0.5, -10 and -20 are shown in Fig. 6. The plots show a small peak (at the frequency of oscillations about 8 rad/sec) at low absolute values of p1. This means that there is not enough damping in the system. As pl is increasing from -0.5 to -10, the peak disappears and the gain at low frequency increases. This suggests that the controller will give good disturbance attenuation at low frequency (e.g., liiglier dc gain). However, as p1 continue to increase from -10 to -20, the gain at the low-frcquency rcmains almost constant, but a pcak appears at high frequency at around 110 radlsec. This shows clearly that the controller designed for the value of p1 = -20 will amplify noise (or unmodelled dynamics) at high frequencies. Therefore, in the SC, p I should not be selected to be too high.

I

-0 11 -0 151

i

1

0 02 m V

3 c -

0 01

The singular value Bode plots of the system for the Complex Case, i.e., p2= -10, and -100 are shown in Fig. 7 . For p2= -10, it can be seen that the high frequency gain of the system does not roll-off it stays constant but below 20 dB. This is the main problem that one encounters when using the bilinear transformation in the Complex Case. It makes the original strictly proper (more poles than zeros) system model to become proper (same number of poles and zeros). As a result, the high frequency gain of the controller is generally high when compared to the Simple Case. For example, for p2=-100, p l = -2, the high €requency gain increase froin 10 rad/sec to 100 rad/sec before remaining slightly above 25 dB. This is detrimental to the robustness of the system at high frequency (unmodelled dynamics). Bode plots ' I

0

r

-O O1 4 -002 -0 03 -0 04

-0 05

c

p2=-50

Time (sec)

-20

Fig. 5 Step Responses- Complex Case

-40 t IO-'

biggest value. For example, for p 2 =-20 and pl=-0.5, the overshoot of the system is significantly less than for p2 = -50 andpl=-0.5. This rises the issue of trade-

-

7

.---/-

lo

1

2

10'

~ = -0 1 5

,< i

1 ~ 2 ~

Frequency (radisec) Fig. 6 Singular value Bode Plots: Simple Case

265

Folly, K.A. Yorino, N. and Sasalti, H (1998). Synthcsis of two-input PSS based on the Ha-control theory. Trans. IEE .Japan, Vol. 118-B, N o h , pp. 699-

Bode plots

706. Folly, K.A. (2004). Robust controller design for small-

signal enhancement of power systems. In12004 IEEE Aflicon, 7'hAfvicon conjei+encein Ajiica. pp.631-636 Kundur K. (1 994). Power system stability and control. Mc.Graw-Hill 1994. Travichandran, T and Quintana V. H. (1996). Robust controller for iiiput disturbance attenuation of synchronous machines. In: 1996 Proc. IASTED Int conference. pp. 159-163.

Xu J. H. and M. Mansour. (1988). Hm-optimal robust regulation of MIMO systems. Int J. Control, Vol. 48, No.3, pp. 1327-1341

APPENDIX: CONTROLLER TRANSFER FUNCTIONS I,

-5c

- - - - - - - -- - - - - ' - - - - -r

:

P2 = -100 - 1 0'-

10'

- --- -

-

1on

---: ld ~

--- -

1. Simple Case

- -- --.

_ _

- ---_

-- - ~

1 o2

-

-

PI

= -0.5,

P2

-30

10"

Frequency (radlsec)

-0.98 (s-13.8) (s+l8) (s+3.8) (s' + 20.5s + 259.2) k(s)

Fig. 7 Singular value Bode Plots: Complex Case

=. .............................................................

(si-11) (s+l) (s'

+ 4.6s i-67) (s'

f

20,s -t 262.3)

This highlight the need of trade-off when using the Complex Case of the bilinear transformation.

6. CONCLUSIONS Thc effect of the parameters of the bilinear transformation on the performance of the controller has been investigated. In the Simple Case (SC) only one parameter p 1 of the bilinear transformation was used, whilc the paramctcrs p 1 and p 2 havc becn used for the Complex Case (CC). Simulation results show that when selecting the parameters for the Complex Case a trade-off is needed to guarantee that the controller can attenuate disturbances at lowfrequcncy without exciting high frequency modes. It is found that for the Simple Case, the value of P I should not be set too high. It is also demonstrated thatpz affects also to the damping of the system.

11880(s-1 10) ( s i 20) ( s l 10.43) (s' I 21s I 259.2) k(s) = ............................................................ (s+20) (s+ll) (s' + 53s + 1934) (sz+ 168s + 9783)

P,= -20, Pz = -K 94787373(~-7)(st20)(~130)(~' 121s t 273) k(s) = ............................................................ (s-13206) (s-t228)(s-t30) (si-20) (s2- 4s -120510)

2 . Complex Case Pi = -0.5. P: = -10 -5(s+36) (s+lO) (s+5) ( s + l ) (s' - I .4s + 91) k(s) = ........................................................ (s+19) ( ~ + l o (s+5.3) ) (s-6.1) (s+l) (s-0.04)

P, = -0.5,?'f

REFERENCES Bosgra H . 0 and Kwakemaak H. (1997). Design fbr control syxtem. Notes for a course of the

Dutch Institute of System Control, Winter term 1996-1997. Chiang, R. Y, Safonov, M. G. and Tekawy J. A. (1990). H, flight control Design with large paramctric robustncss. Was prcscntcd at Application of H , Control of The American Control Confirenee, San Diego, California FA14 11:15,pp. 2496-2501. Chiang, R. Y , Safonov, M. G. (2001). Robirst control

= -20

-0.3(s-159) (s+20) (s+7) (s+l) (s2 + 27s + 590) k(s) = .......................................................... (s+0.9) (s+l) (s+7) (s+20) (sz+ 38s + 416) f 1

= -0.5.

P..

= -100

-0.3 (s+~oo)(%+in)( ~ 7 (%+0.7) ) (2+2 i S + 259) k(s) = ...................................................................

(s+10) (s+l) (s2 + 11s + 60) (s2 + 19s + 278)

toolbox-user's guide. The Mathworks, Inc.

1992-2001.

266

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

DUAL INPUT QUASI-OPTIMAL PSS FOR GENERATING UNIT WITH STATIC EXCITATION SYSTEM

Zbigniew Lubosny The University of Edinburgh, School oj Engineering and Electronics, EH9 3JY Edinburgh, U K

Abstract: The paper considers dual input Power System Stabiliser (PSS) and Automatic Voltage Controller (AVK) for a generating unit equipped with synchronous generator and static excitation system. The control system uses analytically derived, quasi-optimal values of parameters (time constants) that cause the PSS to produce damping torque component only. Good dynamic properties of the plant equipped with the proposed dual input PSS and AVR are confirmed by simulation using a non-linear, multi-machine modcl of a powcr system (part of UCTE power system). Copyright 02006 ZFAC Keywords: adaptive control, control system design, power system control, power system stabilizers, stability.

I . INTRODUCTION Current power systems tend to get bigger and, due to commercial pressures, operate with relatively small stability margins. Both factors cnforce utilisation of effective control systems, especially control systems of synchronous generators. Today the basic tool for power system stability enhancement is the power system stabiliser (PSS). Researchers have been (and are) looking for various types of such control schemes too, e.g. PSS based on artificial intelligence (neural network, fuzzy logic), based on new techniques (LQG/LTR, Hl, H,, psynthesis), or based on adaptive schemes. Results of their investigations have been produced in numerous papers. An interested reader can be directed to papers (Larsen and Swann, 1981), books (Kundur, 1994; Machowski, et al., 1997), and reports (IEEE, 1981; CICRE, 1996; CIGRE, 2000). PSS design is usually based on the optimization of defined quality indices, fitting plant frequency characteristics to defined ones, or locating poles or the considered system in appropriate locations. In the casc of standard IEEE structures of the PSS, parametric optimization is widely used, while new techniques (LQG, HZ, H,, etc.) produce optimal controllers that minimise a given norm. Dynamic properties of plant equipped with such a controller can be, for example, shaped by their frequency

characteristics definition. In spite of the high amount of control schemes today in the real power systems, the single-input or twoinput time-invariant PSS are utilised - both usually of the IEEE standard structure (IEEE, 1981). This is a result of the utilities concerned about the adaptive and artificial intelligence based controllers utilisation in their systems. Usually, thc PSS design is separated from the AVR design. The PSS is designed then for the plant equipped with the “existing” AVR with the defined parameters. It can be the result of assumption that the AVR parameters cannot be changed because they allow the plant equipped with the AVK to fulfil the grid code requirements. Thc paper shows that the presented type of PSS - optimal in given bclow sense - enforces the AVK time constant correlation to their parameters. Rut the main aim of the paper is to show effectiveness of the derived PSS in the form of the dual input PSS, while one is applied to a model of the real multi-machine power system.

2. PSS AND AVR DESIGN PSS optimality can be defined in a various ways. In the paper it is assumed that the PSS is optimal when it produce, the damping electromagnetic torque component only, i.e. the PSS provides a component

267

of electromagnetic torque which is in phase with the rotor speed deviation.

parameters to achieve equality of the following coefficients:

a,= b, 2. I Quasi-optimal PSS and AVR design

a2= b,

T o achieve such definition, optimal PSS let us consider a linear model of the single-machine system (Kundur, 1994) presented in Fig. 1 . Let us assume also that the PSS input is the rotor speed d w Let us also neglect, at this stage of consideration, a way of the rotor speed measuring.

a3 = 6.1

For the considered plant, equipped with exciter, which transfer function is equal to ( S T I A excitation system without feedback loop, i.e. Kp- = 0):

,” and equipped with PSS, which transfer function is . .. initially - cqual to: vo1tege transducer

Fig. 1. Lincar modcl of single-machine system with AVR and PSS, (KO= 0). For such a model, the electromagnetic torque AT, can be described as a function of deviations of the rotor angle d6, the reference voltage dV,,f and the rotor speed Awin form:

by substituting equations (9) and (10) into (2) and by neglecting the voltage transducer, i.e. assuming that TR= 0, and assuming that the PSS time constant TcIis equal to the AVR time constant T( the lower equation (2) takes a form:

AT, = Ts (J ) . A 8 + T, (S) . AVrer + T p (J ) . A@ ( 1) where Ts(s), Tv(s), T,,,(s) are some transfer functions that depend on the plant parameters K,-K6, T3 (Kundur, 1994) and on thc control clement< transfer functions, defined by GJs) and Gps5(s). The transfcr ) Tp,,(s)have a form: functions T ~ Jand

By rearranging (1 1) to form of ( 5 ) wc can obtain thc gain K and the coefficient5 a,, a2, a?,b I ,b2, b?equal to:

K=

K 2 K 3 K A KP~S,5

1 + K,K,K,

a , = T,, + Tb + T, ,

a2= T,T, +To(Tb + T, )

The electromagnetic torque component produced by the PSS is equal to: = T[Jj,

’

(3)

The torque component will be in phase with the rotor speed deviation when the transfer function AT,,, will take form o f a gain:

i.e. the imaginary part of TP,(will become equal to zero. Thcn we will obtain the PSS, optimal in senw of the definition presented above. In general, the lower equation (2) can be wntten in form:

For such form of transfer function a one of the ways of fulfil requirement (4) is to define PSS and AVR

Then the next step of the optimal PSS searching is related to deriving the PSS time constants from conditions (6),(7) and (8). Condition (8) will be fulfilled when time constants T, and T, will be equal to: To = T,, T, = Tlj/(1+K3K,KA). Next, while assuming that Yh = Y> the condition (6) will be fulfilled when:

This requirement is in fact related to the voltage controller time constants T,, T c ~and to the plant’s field circuit time constant T,? but not directly to the PSS. This means that the optimal PSS requires modification of the AVR time constant values. Unfortunately, when the values of the PSS time constants have been chosen to satisfy (6) and (8), it is impossible to satisfy at the same time condition (7). But fortunately, for a typically small value of the voltage controller time constant TA , the difference

268

between coefficients a2 and hZlends to be small. This is because the absolute error is proportional here to a2-b2= TITA. This causes in fact that the imaginary part of the transfer function Tps5 is not equal to zero but fortunately it is very close to 7ero. In that senw the PSS can be named as the quasi-optimal one.

l=

0 9, computed for plant (described in Appendix) operating at rated load is presented in Fig. 2. 1.5

i

To makc the PSS defined by (1 0) implementable, thc transfer function GP5\has to be transferred to the following form: 0

1

2

3

Frequency (Hz)

Then the quasi-optimal PSS (and AVK) time constants can be defined as: m

T, = T, = T3 + T, Values of the time constants T, and Tl should be chosen small (i.e. T, = Tf = 0.005 s) so as to not introduce meaningful shift to the CP,)(s) transfer function phase, for frequencies in the electromechanical oscillation5 range, i.e. 0.1-2.5 Hz.

2.2 PSS gain design

Fig. 2. PSS gain and real Tcr, and imaginary T,, parts of transfer function T < i u ) - measure of the s ynchronising and damping torque. We can see here that for a given plant, keeping the PSS gain equal to 20 to allow us to keep the damping ratio not lower than 0.9 for the all range of frcqucncies of electromechanical oscillations. When reactive load of the plant decreases the Kpss required to keep the given damping ratio also decreases. That can suggests that KP,, can be defined as equal to the maximum value needed to keep given damping ratio computed for the plant's rated operating point. For simplification purpose the following equation was used for the PSS gain calculation:

The PSS gain definition, in a considered case, is a separate task, not related to the time constants definition. In general the PSS gain definition, especially for the multi-machine power system is not an easy task, but can be done by utilisation of various known methods. Below the simple way of the PSS gain definition is proposed. For plant from Fig. 1 the equation of motion, taking into account ( 1 ) and assuming that T,~,s.s(s) transfer function has only a real part (ix. the PSS is optimal), can be written in the form:

where 77 = 2.5, is a constant coefficient comprising nonlinearity of the synchronising torque component T
where Y'a and I'mare the frequency-dependent real and imaginary parts of transfer function T J defining synchronising and damping components of torque produced by the machine and AVK. Equation ( I 6) defines a standard oscillatory element. For such element the PSS gain, assuming (4) and first equation of (12), can be calculated as the function of the required damping ratio 6

Practical implementation of the proposed PSS requires the measuring component which at its output will be producing a signal which is in phase with the rotor speed. Simultaneously, the component should filter the higher (e.g. torsional) frequencies from the measured signal. The both functions can be realised by the component used in the standard dual input slabilisers with the rcal power and the rotor speed as inputs. In such a case, the final structure of the proposcd PSS takes a form as presented in Fig. 3, i.e. form of the IEEE standard dual input power system stabiliser type PSS2A. Such type of PSS has been used in the following tests. The filter time constant used was equal to TFi= 0. I s, while the wash-out time constant was equal to T, = IOxzH,,, where HJi is i-th element of plant's shaft inertia constant. The T, time constant value is not critical here and can be also equal to a few seconds.

The gain Kp\( is a nonlinear function of the plant parameters, state and frequency of oscillations. Example of the gain dependence from frequency, for

2.3 D u d input PSS

269

4a

Li

(1+sTa)(1+sTb)(1+ST,) Kpss (l+sTd)(l+sT,)(l+sTf)

I

I

here the time-invariant one. the real power oscillations are also extremely well damped in case of the plant operation at another than used for their parameters definition, states, e.g. at capacitive load. The responses show that the proposed PSS also increases the area of the plant stable operation. The plant equipped with the original PSS is losing stability after the last, presented in Fig. 4, disturbance while the plant equipped with the proposed PSS operates still stable and its response is similar to the previous. Utilization of the proposed PSS causes increase of the voltage settling time which is a typical effect of the electromechanical oscillations damping increase. The pant's responses presented in Fig. 4, allows us to conclude that the time-invariant control system (PSS and AVR), with parameters dcrived at the rated operating point, allows the plant to keep very good dynamic properties in the whole area of operating points.

" P g

Fig. 3. Dual input PSS.

3. CONTROL SYSTEM VERIFICATION It is well known that because of the power system non-linearity, and especially because of the plant's dynamic properties sensitivity on the operating point, the optimal controller of a synchronous generator should be adaptive - its parameters have to vary. The equations presented in the previous chapter confirm that fact because the plant parameters K2, K.j, Kh, and T3depend on the plant's operating point. In gencral, the PSS presented in the paper can be used as the adaptive one. In that case, their parameters should be sequentially updated. But, as it was said above, the utilities are worried about use of adaptive control schemes. Thereforc, the timeinvariant version of the PSS is considered further. In this case the PSS (and AVR) parameters, computed at the plant's rated operating point, are kept constant during the plant operation. The tests show that such a time-invariant control system still allows proper and very effective operation of the plant at the various operating points.

1 00 h

:0 9 0

v

z

080

Q $ 070

CT

0 60

0

2

4

6

8 1 0 1 2 1 4

Time (s)

Initial verification of the proposed PSS has been carried out by using a single-machine system. The 7 th order, Park's model of synchronous generator has been used. The shaft has been modeled as a multimass system. The gcnerating unit has been q u i p p e d 0 2 4 6 8 1 0 1 2 1 4 with turbine and governor. Data of Belchatow Power Time (s) Plant generating unit (located in Poland) has been Fig. 4. Plant response to sequence of the infinite-bus applied. The unit originally is equipped with static excitation system, AVR and a single input PSS (IEE voltage step changes AV, = 0.1 p.u. each. type PSSlA) with real power as input. Response of Figure 5. shows location of the plant oscillatory this plant (in Fig. 4 named as A) has becn compared modes of electromechanical swings range as a to the one equipped with the proposed dual input function of the PSS gain. Figure 5.b is related to the time-invariant PSS (and AVR) which parameters are plant equipped with the proposed time-invariant dual defined by ( 1 5 ) (named as B). input PSS, while Fig. 5.a, for comparison purpose, Fig. 4 shows response of the system to series of the shows modes of the plant equipped with the original infinite bus voltage step change equal AV, = 0.1 p.u. single-input PSS. Comparing the both Figs. we can each. The initial operating point was equal to the see that the proposed PSS in a single-machine system rated one, i.e. P, = 0.85 p a . , Qg = 0.53 p.u. introduces one additional oscillatory mode. One of Sequentially applied step increase of the infinite-bus the modcs, taking into account participation factors, voltage has caused changes of the operating point is related mainly to the rotor angle 6while another to (real and reactive power) as follow: (Pg,Q,) = the rotor speed W.The Fig. shows that the proposed (0.85,0.53)~(0.85,0.07)~(0.85,-0.39)~(0.85,-0.85) PSS increases damping of electromechanical modes p.u. This means that the final operating point was but simultaneously decreases frequency rotor swings. characterized by the leading power factor and was For example, in the case of a plant equipped with the located far behind limits defined by the stator current proposed PSS (and AVR) with gain equal to Kp,s,s= and the machine end region heating. 23.8 the damping ratio of electromechanical modes is Comparing responses of the original plant (A) to the equal to: (= 0.89 (f= 0.7.5 Hz) and (= 0.75 (f= 0.37 one equipped with thc proposed PSS (H) we can see Hz). While in the original system, with the single extremely high effectiveness of the proposed PSS. input PSS with gain Ks = -1.64 the damping ratio of What is very important, despite the proposed PSS is

270

electromechanical mode is equal to (= 0.33 (f= 1.3 HZ).

GTT

-r20

- 15

'+ ,

-20

-15

-

10

-5

1X-0.51

I I --1.5 I I 1--2 I I -2.5 I 1,-3 I I+-1

I

i0-4 O

-10

real(h) [-lis]

-5

I

I

IA2J

0

been computed at their rated operating point by using the single-machine model. Figs. 6 and 7 show responses of the chosen units to the short-circuit lasting IS0 ms applied at 220 kV busbar in the Belchatow substation. Units BEL2-01 and BEL4-06 are located in the Belchatow power plan1 but are connected to various busbars. Unit BEL2-01 is connected to 220 kV busbar while unit BEL4-6 is connected to the 400 kV busbar. Unit KOZ2-01 is located in the Kozienice power plant about 100 km (geographically) from Belchatow, while the unit TUR2-05 is located in the Turow power plant - about 300 km from Belchatow. 21

I

05 0 0

1

2

3

4

5

3

4

5

6

8

10

Time (s)

-20

-15

-10

-5

real(h) [-1/s]

Fig. 5. Plant's electromechanical modes as a function of PSS gain, a) original PSS, b) proposed PSS. To confirm good properties of the proposed control system the time domain simulations have been carried on the part of the UCTE power system model. The Polish power system was here fully modelled while the rest of the UCTE power system was equivalented. The model is consisted in 3529 nodes and 444 generating units. 1 10 generating units operating in the main power plants in the Polish power system were modelled in detailed form, i.e. with excitation systems (AVK and PSS), turbines and governors. 58 generating units were equipped with the static excitation systems, while the rest were equipped with the AC machine excitation systems. The generating units were equipped with single input PSSs with real power as input. This system is called further as original one, and response of the system in Figs. 6 and 7 is marked by letter A. To evaluate the proposed PSS cffcctivcness, the dual input PSSs have been implemented in control systems of the chosen units, while the control systems of the remaining units have been left unchanged. There have been chosen units equipped with static excitation system, and there were considered two variants: The proposcd PSS has been applied to all units of the Belchatow power plant (12x360 MW). This variant is marked in Figs. 6 and 7 by letter B. The proposed PSS has been applied to all units of thc Belchatow (12x360 MW), Opole (4x360 MW), Kozienice (8x220 MW), and Turow (7x200 MW) power plants which covers about half of the all units equipped with the static excitation system operating in the polish power system. This variant is marked by letter C. The AVR and PSS parameters for these units have

!

0.6

0

1

2

Time (s)

0 71 07 0 69 0 68 0 67 0 66 0

2

4

Time (s)

6. Generating units response to short-circuit lasting 150 ms, (a - BEL2-01, b - BEL4-06, c KOZ2-01, d - TUR2-05) (A - original system, B - PSS2A in the Belchatow power plant only, C - PSS2A in the Belchatow, Kozienice, Opole and Turow power plants).

Results of the time domain simulations show that: a Utilisation of the proposed PSS in control system of units in a single power plant (variant B) causes high increase of damping of electromechanical oscillation in case of units equipped with the proposed PSS (BEL4-06) and small positive effect in case of other units, e.g. KOZ2-01, TUR2-05. This erfect depends on many factors and, e.g. on distance of the generating units from the units equipped with the proposed PSS. Such a

27 1

positive influence on the other units is also resulted from the Belchatow power plant high capacity and location in the middle of the Polish power system. Relatively small positive influence of the proposed PSS on the unit BEL2-01 is resulted from fact that the unit is connected to a busbar at which the short-circuit was applied. Utilisation of the proposed PSS in a control system of higher amount of units operating in the power system (variant C) highly increases damping of electromechanical oscillation of these units (equipped with the proposed PSS) but also significantly increases damping of electromechanical oscillations in the whole powcr system. Utilisation of the proposed PSS slows down the process of the terminal voltage control. This effect is especially visible in case of unit BEL201 connected to a busbar at which the shortcircuit has been applied. In case of other units, located “far” from the disturbed busbar, the increase of voltage settling time is equal to 0.5 s and can be considered as acceptable. This increase is the typical cost paid for increase of the electromechanical oscillations damping.

The PSS time constants can be derived directly using a single-machine system model, without any optimization process. Simulations have shown that the parameters derived in a single-machine system are valid also in a multi-machine system. Gain of the PSS can be computed separately from lime constants by using any known method. The paper proposes a simple rule for the gain calculation, giving satisfactory results for units operating in single and multi-machine power system. Results o f simulations conducted in the real power system model have confirmed a high effectiveness of the proposed controller. The proposed method can be applied to the existing plants equipped with the static excitation system, AVR and dual input PSS without any modification of the control system hardware. ACKNOWLEDGMENT This research has been supported by EPSRC SupcrGcn grant GlUS28082101 “Future Nctworks Technologies”. REFERENCES

“I

0

2

4 6 Time (s)

8

IEEE Committee Report ( 1 98 1). Excitation System Models for Power System Stability Studies, IEEE Truns. Power Appar. Syst., vol. 100, pp. 494-509. Kundur, P. (1994). Power system stubility and control, p.76 I , (McGraw-Hill (Ed.)), New York. CIGRE Task Force 38.01.07 (1996). Analysis and Control of Power Systenz Oscillations, (CIGKE (Ed.)), Paris. Machowski, J., J. Bialek, and J. R. Bumby (1997). Power System Dynamics and Stability, p. 29 I , (John Wiley and Sons (Ed.)), New York. CIGRE Task Force 38.02.16, (2000). Impact of Interactions among Power Systems, (CIGRE (Ed.)), Paris. Larsen, E. V. and D. A. Swann (1981). Applying Power System Stabilizer, IEEE Trans. Power Appar. Svst., V O ~ .100, pp. 3017-3046.

10

Fig. 7. Gcncrating units rcsponsc to short-circuit lasting 150 ms, (a - BEL2-01, b - BELA-06) (A, B, C - like in Fig. 6). Summing up the above consideration one can say that utilisation of the proposed PSS (and AVR) values of time constants defined by ( I 5) - allows to increase damping of electromechanical oscillations in electric power system and, in it allows, to increase the power system stability.

APPENDIX Single-machine model data (in p u . , if not defined): generator: Pg,, = 360 MW, X d = 2.6, X ’ d = 0.33, X ” d = 0.235, Xc1= 2.48, X ’ , = 0.53, X ” , = 0.235, X i = 0.199, R , = 0.0016, T’,,(j= 9.2 S, T”,,(j = 0.042 S, T’,o = 1.095 S, T”,” = 0.065 S, S1 = 0.292, S12 = 0.883, Hix = 0.94 S, H j H p = 0.14 S, H j M p = 1.08~, H j i , p = 1.06 S, K r l H p = 0.014, KlIMP= 0.37, K,,, = 0.36; transformer: X , = 0.15, R, = 0.0034; system: X , = 0.09, R, = 0.007; original AVR (STlA): T, = 0.02 s, KA = 1170, T, = 0.01 S, T[<= 20.4 S , Tc = 2.4 S, VjVi,,JVt,,,,,, = 0.1510.1 5, Vr,nu,,/Vr,nin= 7.11-5.0, KC- = 0.06, K[,I<= 0.04; original PSS (PSSIA): Ti = 0, T2 = 0.02 s, T, = 0.55 S, T4 = 6.8 S, T 5 = Tn = 5 S, K,5 = - 1 .64, L,,,?,,/L,,,?i,, = 0.0541-0.054; proposed PSS: To = 1.74 s, Tb = TA,T, = 0.55 S, T,, = 1.75 S, T , = T f = 0.005 S, Kp.y.7 = 23.8; proposed AVR: T,.= T(,,the rest of data unchanged.

4. CONCLUSIONS The paper deals with synchronous generator control system consisted in the static exciter, dual input PSS and AVR. The PSS (and AVR) parameter value,, derived analytically, allow the PSS to produce damping torque component only. The PSS can be utilised as adaptive or time-invariant one without the plant, equipped with the PSS, dynamic properties significant change.

272

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

EXPERIMENTAL STUDIES ON A PROTO-TYPE POWER SYSTEM USING AN ADAPTIVE PSS G. Rainakrishiia * O.P. Malik **

*

Universztg oj Saskatchewan.SasXaloon. SK S7N 5AB. Canada ** The Uriruersrty of Culgury. Calgary. A B T2N i N 4 . Canada

Experimenhl st>udieswith an adaptive power system stabilizer (APSS) using radial basis function network as a system model identifier (RBF-Identifier) ant1 a liricar fcctlback pol(:!-shift, (PS) c:ontrollcr arc prcscntcd in t,liis pa.pcr. Tlic physicad model of the power system consists of a, 3lcVA. 220V synchronous microakernator antl a transmission line that simulates the perfornia,iice of a 500kV double-circuit transmission line. A comrncrical programmable logic cont.rollcr provides the AVR function and the APSS is inipleniented on a digital signal processing (DSP) board. The weights of the RBF-Ideiitifier are updakd on-line a.nd the net,work is linearized a t every sa.mpling interval to o h i n t~heARMA model paramekrs of the system. The PS controller uses the on-line updated ARAIA pa.rametcrs t,o obtain t,lic optimal control signal at. the given insl-ant..Ttic t,est,sdemonstrate that the proposed APSS is effective in damping oscillations and improving powcr system stabilhy. Keywords: Power System Stabilizer (I’SS), ARhIA Model, 13BF-Identifier, Pole-shift (PS) Controller.

1. INTRODUCTION

Power system stabilizers (PSSs) are widely nsed in power systems. They help damp low frequency oscillations in power systems (typically O.2H.z 2.0ZI.z) a.nd also iinprovc the dynamic performance of the generating unit. Compared to the cornmorily used lead-lag compensation type PSSs (CPSSs) (E.V. Larseri and D.A. Swam, 1981),the selhcljusting ability of adaptive PSSs (APSSs) ma.kes tliem very effective for power system stabilization (G.P. Chen and O.P. Malik and G.S. Hope aiid Y.H. Qiri and G.Y. Xu, 1993). Field tesk using APSS wit~hleast squares (RLS) identification and PS controller are reported in (A. Eichmann, A. Kohlcr, O.P. iClalik and J. Taborda, 2000).

In thii paper, a Radial Basis Function (RBF) network is used to idcwtify the syTtern parameters and ttic PS control techiiique (G.P. Chcn aiid O.P. hlalik and G.S. Hope and Y.13. &in antl G.Y. Xu, 1993) is used for control computation. The non-hnea functional mappiiig propel tie5 of the RBF network are the key to its use in identification. Its primary atlvantagcs arc: ability to store ’aprzom’ information and hence the ability to capture power system information. excellent approxiniatioii capability and tlic ability of cstdblishing a correspondence between the RRFIdentifier internal paranieters and the system paThe linear PS technique (G.P. Chen and 0.P. hIalik and G.S. Hope and Y.H. Qin and G.Y. Xu, 19%) is u d to compute tlic control signal using

273

the updated -4RAIA paramders. Linear fedback controllers have widespread industrial acceptance in addit ion to many tlicorclical and practical results about their performance charactcristics. With an ANN controller it is difEcult €or an lid the rontrol pro outside user to undt hccause of its %lack-bou" like naturc. In addition, it is difficult to prove stability of the closed-loop system. The PS-controller has tlic ability to resolve the ahove issues. Therefore, an APSS using a coinbindtion of RBF-Itlciitificr antl PS-Controller is presented in this paper.

The adaptive PSS is based on the self-tuning adaptive control in which an identifier is used to dctcrmiiic thc parameters o€ an ARLlA niodcl of tlic contrnllcd sv5tcm and tlic updated paraiiictcrs that track the system operating conditions are uscd in the controller to compute tlie control. The computation of the updated parameters and control is don(. on-line ('very sarnpling period. 3.1 RBF-Identzfier

The REF-Identifier and PS-Conlroller is implrmentetl on a. DSP board mounted 011 a PC. A CPSS is also implcmcntctl on tlic samc board in order to have a comparison bctwccn the two PSSs.

The power system is modeled as a third order AKRlA system (0.1'. Malik, G.S. Hope aiicl S.J. Clicng, 1991). A RBF network (Fig. 2) is used to determine the parameters o€the ARhlA model.

-+

A(zC1)g(t) = B ( z - l ) u ( f ) d ( t )

2 . POiVER SYSTEhl PHYSICAL AIODEL

Tlic physical moclcl consists of a. 3-phase SkVA micro-alternator connect,cd to a constant voltage biis tmhrougha doithle circiiitl transmission line, Fig. 1. The t.urbine i s niodeled by a 5.5 kW (7.5 1i.p.); 220 V, 30 A separat,ely excit,ed DC mot,or. The physical model of t,lie t,ransmissioii line consisting of six pl-sections simulates the performmce of a 500 k V , 300 k m long double circuit transmission linc. It has a frequency response which is close to t,liat of an actual line up to 500 H z . The pa.ramet,ers are given in Appendix A.

(1)

and g(b), u(t) and d ( t ) arc tlie system output, system input aiid white noise respectively. Equation (I) can be written in the form suitable for identification:

+

i ( t ) = F(L)*(L) d ( t )

A commercial ABB programmable high speed controller (PHSC2) provides automatic volt age regulator (AVR) funct,ion. Tliree phase RC volt,ages and ciirrents at, the generator I-erminal axe stepped down, rectified and filt,ered with a cutoff frequency of 8 H z t,o form six DC input signals to the -4VR. The PLC-based AVR computes thc required field cont,rol signd that is fcd to a, time-constant) r e g u h o r (TCR). The AVR also calculates t~lieact,ive power signal ( P , ) which is used as thc PSS input. Thc PSS comput,cs the required control signal, Up,,3.to be fed to the AVR. The APSS implernent,atioii details arc provided in Section 4.

(4)

is the paraniet,er vect,or (regression coefficients) and

*(t) = [-y(f - 1) - y ( t - 2 ) - y(t - 3 ) u(l - 1) u ( l - 2) u(t - 3)]*

(6)

is the measiirenient variable vect,or. The RBI? model shown in Fig. 2 aid as explained in (S. Haykin, 1994) is uscd to identify t>hcARMA parsmcters on-line (c.f. (1)).It consists of two layers: a. hidden layer consisting of radially syrnmet,ric basis functions aiid a. liiicar output layer. The hidden nodes consist, of REF ccrit,crsantl cadculnt~c the Euclidean distancc bctwccn t,hc ccrkcrs arid the network input vector. The result is passed through a Gaussian funct>ion,&(:rj>given by:

A variety of dist,urbanccs can be q p l i c d to t,lie system. Using t,he switch shown in t~heexcit,alion circuit of t.lie DC mot,or, Fig. 1, a st,ep change in input, torque of I,he generator can be applied. Similarly, t,lic input rcfcrcncc volt,itgc of t,hc -4VR can bc st,cppcd up or down. In addition, diffcrcnt, types of faults can be applied to simulate large dist,urbances. The faults are ximrilat,ed using relays cont,rolled by short circuit siniulat,ion logic (Fig. 1). The operating coiiditioii of the generator, i.c. active power and power fa.ct>or,can also be changed by changing the armature current of DC motor and terniinal voltage of the generator. rcspect.ivcly.

The overall input-output response of the network is given by

274

RBF

Transmission Line

W Circuit Tesf Three Interkkcked Breakers AdlirslahleTime Sequence

Manual

-

Fig. 1. St,ructurc of t,lic power syst,crn niodcl In ( 8 ) , x p is the input vector, w, is the biasing t,crni, w, is t,lic weight, bctwceii the hidden nodcs a.rid the out,put, c7&is t,he center of the hidden node, a is the widt,h of the hidden node, N is tho number of liitldcn nodcs aiid @(.)tlcriot,cs the Gaussian function. For on-line identification of a. power system using t8he RBF net'mrk t'lie centers have to suitably sample tho input domain. The n,-ineuns clustering t~cchniyueof pattern classification is an effectjive procedure t,o updat~ethe RBF centers. Because the response of t,he iiet>workis linear with respect, t>o its .i?leight,s.recursive least squares (RLS) inet,hod is proposed for atljust,ing t,hc mights. ~ 1 1 weight ~ : vect,or, I@, is c:rlculateti by t,he following RLS eqiiai-ions:

1 P(t + 1) = -[P(t)

dt)

W(t

+ 1)= W ( t )

-

KT(t)P(t)k(t)] (10)

+K ( t )[,y ( t )- Mir ( t )W (t)] ;I( t )

(11)

where p ( t ) is the €orgelting factor. P(t) is the covariance matrix and K(t) is the modifying gain vector. W ( t )is a vcctor consisting of tlic following elemenls (outputs of RBF-Identifier hidden layer)

13(t) a tracking constrained coefficient (G.P. Chen a r i d O.P. Malik and G.S. Hope imd Y.H. (tin aiid G.Y. Xu, 1993). The RBF represrnts a NARIVIAX modrl (S. Chen, S.A. Billings and P.M. Grant, 1992). '10 obtain the linear paramc~tcr~ (c.f. (5) ) of tlic standard ARlCIh model, the output of thc RBF, y(t) = f(z/(t- c), u(t - L ) ) . is liiieariaed using thc Taylor series expansion. Retaining only the linear t e r m

The partial derivative terms, [ay/i)x,] are the clerneilts ol' the RBF network Jacobian [.Iy] and are given by

iV rcprcscnts tlic total number of hidtien nodcs. is the node number.

12

The ARhIA model parameters are used in the PS coiit roller to calcula t c llic control.

9.2 RBF-Identifier Training A two-stage learning procedure is nsed for the proposed RBF-Identifier. The RBF-1dent)ifieris first. tra.ined off-line usiiig a. simulated model of t,he generating unit. The t,raining data set, coiisists of iiiput,-output tlat,a. for a. variety of operat,ing conditions asid disturbances. The operating condition changes iii the range of 0.3 p u to 1.1pu power output and 0.75 p f lag to 0.9 p f lead. The disturbances used are the voltage reference and input torque reference dist,urbances arid three phiise to ground fa,iilt. Scvciit>ccnRBF ccnt,crs arc obt,aiiicd duriiig offline training using the n-means clustering procedure a.s shown in Fig. 3. St,art>ingwit,h off-line w l -

275

ues for RBF centers, it requires small computation time to update tlie weights on-line.

.

.

0.05

-

"4.05-

Fig. 4. Stabilit,y proof for tJhe PS control: polepattern for T ( 2 - l )

0

To consider the time domain performance of t,lic cont,rollcd syst,cni, a pcrforrnancc index J is formed to measure the diEerence between the predicted system output, ?j(t+ I) and it~sreference. !h(t 1):

4.151

+

Fig. 3. Plot of y(t) k 7 4 t ) for training vectors and the centers

+

3.3 PS-Controller

The self-optimizing PS control algorithm (G.P. Chen arid O.P. Malik arid G.S. Hopc and Y.H. Qin and G.Y. Xu. 1993) is eniployed to generate tlie control signal. Assunie that the feedback has the form

From rqns. (1) and (15) the closrd-loop charactcristir polynomiaI T ( z - l ) ran h tlcrivctl as

A(z-')F(z-')

+ I?(z-')G(z-l)

= T(2-l). (16)

In the pole-assignment (PA) algorithm T(2-l) is prescribcd (PAL Mills arid Tadc, 1996). However, tlie PS control algorithm makes T ( 2 - l ) take tlie form of A(%-') but the pole locations are shifted by a factor a , i.c. T(z-') = A(~r2-l).

(17)

In tlie 1's algorithm, a , a scalar, is the only par to bc tlctcrmincd tLnd its value rcfl the stability of the closed-loop system. Suppose X is the absolute valuc of the largest cliaracteristic root of A ( z - l ) , then 0 . X is tlie largest characteristic root of Y'(2-l). 'lo guarantee the stability of the closed-loop system. a ought to satisfy the following inequality (stability constraint):

E is the expectation operator. G(t 1) is dctcrrniricd by system paramctcr polynomials A(.-'), B(2-l) and past ~ ( tand ) u ( t ) signal sequeiice. Coiisidcririg that u ( t ) is a fwiction of the pole shifting factor N , thc pcrformancc iiidcx J bccomes nzzn,J

= r [ A ( . ) ,El(.). u ( t ) , y ( t ) , yr(i

+ I)].

(20)

In (20) F[.] denotes function. The polc-shiftirig factor a is the only unknown variable in (20) and thus can be delerrniricd by minimizing J . The stabilizer must keep the closed loop system stable. It implies that all roots of the closedloop cliaracteristic polynomial (A(az-'))must lie within the unit circle in the z-planc (c.f. 18). Thcl pole-patterns of T ( 2 - l ) are shown in Fig. 4 for a tlrirecpliase fault.

4. DSP IMPLEMENTATION

Thc structure of the digital control system is shownin Fig. 1. Thc RBF-Idcntificr/PS-Controller is iniplcmcnted on a Texas Instruments (TI) ThIS320C30 Digital Signal Proccssing (DSP) Board mouiited on a Peiitium I11 PC. The DSP board provides requiiite computdtional power (33.3MHz) for iinplcmcntiiig the APSS. I/O signals are transferred between AVR and DSP througli A/D channels. A conimcrcial ABB PHSC (ABB Proqrammnblc Hzqh Speed Controller - System Dcscriptmn, 19'30) Excitation System providcs tlic AVR function. The ThIS320C30 DSP chip contains integer and floating-point arithmetic units. For data acquisition purposes. thc board is cquippcd with two 200 k H z . 16-bit analog 1/0 channel\ on h o x d to a11 4eria1 and parallel coiipled with direct ;1

It can hc seen that once T ( 2 - l ) is specified, F ( z P 1 )and G'(7-l) can be dctcrrniricd by (16), and thii.; thc control sigiial n(t)can br calciilatrd from ( I 5 ) .

276

T/O cha.rinels of DSP chip. The :32-bit, on-chip t,inier is programmed by soft,\varet,oa resolution of 120 ns. The board is mourit,ed inside Pentiuni 111 PC (Fig. 1) with tlic corresponding dcvclopnient software arid debugging applica.t,ionprogram. Comrniiiiicat~ioiibet,ween the DSP and t>hePHSCZ programmable logic controller is through analog signals, as sliown in Pig. 1. The AVR calculatcs (,lie gerierator a.ct.ive power, Pc, based 011 (lie measured instant,aneous voltages and current,s. The P, signal is t,lieii tra,nsferretl t,o DSP board t,hrough tlic A/D channel. This A/D channel samples tlic signal at 50 ms interval. The samplcd signal goes through a filt,er, which liinit,s the noise and provides ant,i-aliasingprot,cction. Tlic filtered signal is then stored in a. buffer. Thc DSP chip rends the buffcr and coinputcs the control signal, U,,,,. The coniput,ed U,,, is placed into the output D/A channel. This out,put signal is connect>edto the analog input of the PHSC2. The AVR receives thc PSS cont,rol signad as a supplcmcnt.ary input and adds it, to the volt,age reference signal. The combined signal Lhen goes tlirougli t,he AVR block in order t,o obtain the required field cont,rol signal. Dimensionality of t,he network can become a problem with t~heRBF-Identifier (S. Haykin, 1994). This problem is circiimvc:ntjed by sc;lec%ing the centers Erom the input, vector rather than using rantlonily init,ializcd ccnt,crs. Using t~liisprocetlurc 9 centers and linear weights were obt,ained from off-line computer simulations and are directly at1optc:d for t,he 1nbora.t~ory studies in t.his paper. Thr: ovcr;ill calculat,ion t,ima on t kit: DSP for R.BFIdent,ifier/PS-Controller is 24112s (with a maximum of 27ms during disturbance). This comput,at.ion time is within the 50m.s sampling interval chosen in t~heAPSS iniplenient,at~ion. For coinparison, a CI'SS wit,li t.lie following transfer fimct>ion(IEEE,Working Group on Sp bility Controls, Power System Engineering Committcc, 1087) was irriplcrncntod digit~ally.

was irnplemexit,ed in the same erivironnienl. Since t,he cont,rol environment is for the developmerit, of digital controllers; t.lic CPSS t,ransfcr function is discretized. Because of t>liecomputationa.1 simplicity of the CPSS, a sampling rate of T = 1ms is chosen in the st>utlies.

Fig. 5, AP, response for 0.20p.u. input torque reference Step change with APSS

4i

-"'I -"

5

10

15

iim.z

20

25

3

Fig. 6. AP, response for 0.1Op.e1. input torque refwence step clia.nge wit,h APSS in t!orque reference is applied at, 10s and removed at 20.7. Tlic AP, rcsponsc wit'li no PSS (OPEN), CPSS anti APSS is shown iii Fig. 5 . The pararnet>ersof t,he CPSS are tuned using t,he Zieger-Nichols rules for t,unirig PID cont,rollers (K. Ogaia., 1990) to givc t,hc hcst rcsponsc for t,hc operating conditions of this test.

To further test the performance of t,he APSS, the operating contlit,ion is ckiangctl to P = 0.6pu, p f = 0.92pi~(lend),V = 0.99pu. A 0.1Opu decrease in t,oryue reference is applied again and removed at, 20s. The genera.tor is operating at lower voltage (leading p f ) hence the stability margin is redimxi. Response is shown in Fig. 6. Alt,hough t>hcsta.bility niargiri is rcduccd in t,he new opera(irig coridiliori, (,lie APSS slill prwides a good performance.

5.2 Stnbility Maryin Tcsf

5. EXPERIMENTAL STUDIES 5.1 Input torque reference step churige

0

PSSs are primarily used to provide extra damping to gcncmting units to d a m p low frcquciicy oscillations, and thm increase the stability margin of t h e power system. JVith PSS in operation. a power

277

Ada.ptive Power Sysbem St>abilizerlor Damping of Activc Power Swings. Proceedings of The IEEE Power Engineering Society, Sumvier Meeting, Seattle, Washington. pp. 122126. ABB Pro,qrammable High Speed Controller - Systern Description (1990). IAR. Excitation System Training Manual, ABB 1ndust)rie AG, Turgi, Schweiz. E.V. Larsen and D.A. Swann (1981). Applying Power System Stabilizers, Part 1-111. IEEE Pans. on, Power Appuratzis and system..^. pp. 3017-3046. G.P. Chen and O.P. nlalik and G.S. Hope and Y.H. Qiri and G.Y. Xu (1993). An Ada,ptlivc Power Syst,ern Stabilizer Based on the SelfOptimizing Pole Shifting Control Strategy. IEEE Paas. on, Energy Contwxion. pp. 639-

OM

0 02

c

a‘

0

4 02

4 04

Fig. 7. Stability niargiiz tcst, APSS syst,em can operate at, higher levels of load even if it is not stahlc witliout a PSS or wit,li R poor PSS. The test) starts with t,he gencmting unit, operating at a stable condition wit.h APSS. The load is gradually incrcascd. At opcrating condition 0 . 9 7 ~ 7power, ~ 0.925p.f (lead) tlie APSS is st,able. The operating condition indicates approximat,ely t~liernaximurn stability rria,rgiri reached wit,h t~he APSS. At approximat,cly lOs, t,he APSS is replaced by tlie CPSS. Tlie systcin begiris to oscillate wit,hout,any ext,ernal tlist,urbance. This mea.ns that the CPSS is unable to maintain t.lie saine 1t:vcl of systmri st ability for tlic abovc opcrat.ing conditions. The APSS is switched ba.ck again and the system stabilizes again. The results are given in Figs. 7.

646. IEE,E W’orking Group on Special Stabilit,y Cunt,rols, Power System Engineering Committ,ee (1987). Bibliography on the Application of Discret,e Supy1ernent)ar.yControls to Improve Power System Stabilit,y. IEEE Trans. on Power Systems. pp. 474-485. K. Ogata (1990). 1VIodern Control Engzneerzng. Prentice-Hall. Englewood Cliffs, N.J. O.P. Madik, G.S. Hopo and S.J. Cliciig (1991). Some Issues on the Practical use of RLS Ident,ification in Self-Tuning Control. Inl. J. Control. pp. 1021-1033. P.M. Mills, A.Y. Zoinaya a.nd M.0. Tade (1996). Neuro-Adaptkue Process Control - A Pmcticul Appruuch. JuEiri Wiley & Suns. NY, U.S.A. S. Chen, S.A. Billings and l’.hl. Grant (1992). Re cursive IIyhrid Algorithm for Noii-Linea,r Syst e r n Ident,ifiic:ation Using Radial Basis Funct,ion Networks. h t . .J. &7i,tr01. pp. 1051-1070. S. Haykin (1994). Neural Networks: A Cornyehensiiie Foundation. klncniillan. New York.

6. CONCLUSIONS of APSS iisirig an RBF-Identificx Irriplernenl,i~.t,ion ant3 PS-Controller arid real-t,iine test resiiks on a. physical model of a power syst,emitre present,ed in this papcr. A conimcrcial ACB PIISC2 Excit,at,ion Syst,ern provided the AV-R function.

A. PHYSICAL MODEL OF POWER SYSTEM

The RBF-Ident,ifier is first, trained off-line. The RBF-Ident>ifieris furt,lier updated on-line at, every sampling interval to t,rack the dynamic coiidit ions. Tlie PS cont,rol iiscs tlic ARMA paramt t airiecl oil-line froni tlie lineurimtion of tlic ideritiiier Lo compute the control signal.

A . l Thc paramctcrs of tlic micro-altcrnator in p.u. arc 2,L - 1.20 1’,] - 1.20 r d - 0.0026 I’q = 0.0026 XTnd = 1.I 29 XnZq 1.129 T & = 1.25 xhq = 1.25 r’hd = 0.0083 rkq = 0.0083 xf = 1.27 rf = 0.000747 H = 4.75s A.2 Each transmission line consists of six 50 km equivalent rr-sections. For each i.r-vction, the parameters in p.u. are

Experimental results with the proposed APSS are comparcd t,o t~lioscof tlic CPSS. It- is dcmonstratal that APSS exhibits good performance over a wide rung; of operating condit,ions wit,hoiit requiring any taming unlike t,he CPSS. CPSS can provide similar performance as the APSS for the power system configurat~ioriarid operat,ing conditions for which it, is designed.

R = 0.036

X

= 0.0706.

Lz

= 18.779

A.3 Paranieters of the CPSS are

REFERENCES

K,

A . Eichniarni. A. Kohler. O.P. Malik and J . Tahorda (2000). h Prototype Svlf-Tuning

278

= -0.5

TI = 0.065s T3 = 0.065s

T2 = 0.08s T d = 0.08s

Copyright 8 Power Plants and Power Systems Control. Kananaskis. Canada 2006

PUBLlCATlONS

EXTENDED PHASE COMPENSATIONDESIGN OF POWER SYSTEM STABILIZER FOR BISOTOUN POWER PLANT G. Zafarabadi, It M. Parniani, M. Rasouli and P. Ansarimehr I . Power System Operation Department, Niroo Research Institute (NRI), 2. Sharij'University of Technology

Abstract: In this papcr, pcrformance of power systcm stabilizer (PSS) of a largc thermal power plant, as tuned by the manufacturer, is investigated. Then, the stabilizer is redcsigncd bascd on extended phase compensation of thc excitcr input - elcctrical torque transfcr function and root locus analysis; and its cffcct on local, intcrplant and intcr-arca clcctromcchanical oscillations is thoroughly analyzcd. As Bisotoun PSS has a special structure with two inputs, frequency and power, its performance is compared with power-speed PSS. The effect of PSS with existing and new tunings on transient stability is also studied. Simulation results are verified by experimental test records. Keywords: Electromechanical oscillations, Power system stability, Power system stabilizer, PSS tuning

1. INTRUDUCTION

YNAMIC stability is onc of the mosl important issues in powcr systcm opcration. Sufficicnt damping and stability margin is required to utilize maximum capacity of the system. Power system stabilizer (PSS) is a complementary controller installed on the excitation system to improve damping of electromechanical oscillations. In addition to the initial design and commissioning stages, PSS parameters may need to bc rctuncd after somc ycars of operation, bccausc of changes in thc structurc of powcr systcm and its paraincters. Bisotoun powcr plant has two 400 MVA stcam turbinc gcneraling units, and is located in the west area of Iran. This power plant is connected to electrical grid of Iran through six 230 KV transmission lines. Each generator is equipped with a PSS, connected to a static excitation system. In this paper, pcrformance of thc stabilizer is thoroughly invcstigatcd. Then, it is redcsigncd for ncar-optimal opcration under various conditions and in a widc range of oscillation frcqucncics. Excitation systcm and gcncrator data arc identified physically and experimentally during the work, and the whole Tran EHV system i s modeled for the analysis and design. PSS design is carried out based on phase compensation in a desired range of frequencies and root locus analysis eundur, et al., 1989, Kundur, 1999). Dynamic pcrformancc of the power plant and its cffcct on differcnt clectromcchanical oscillation modes, with and without PSS, is cvaluatcd. Also, as Bisotoun PSS has a special structure with frequency and power inputs, its performance is compared with a power-speed PSS. Besides,

D

influence of the PSS with existing and new tunings on transient stability is studied. On-sitc test results arc presented for cxpcrimcntal verification of the simulations, and showing the cffcctivcness of thc stabilizer on damping thc local and inter-area oscillations. 2. MODELING BTSOTOUN POWER PLANT AND THE INTERCONNECTEDPOWER SYSTEM

2.I Generalor Model Generator model parameters werc derived from identification cxpcrimcnts. DC currcnt decay tcst, according to IEC 34-4 standard was pcrformcd for thc idcntification. The gcncrator model used for dynamic stability studies is the 7th order twoaxis model (dqo) of IEEE standard. Generator data is given in Ref. (PSOD, 2002). 2.2 Excitation System Model Figure 1 shows a simplified modcl of the static excitation system at Bisotoun powcr plant. As shown in thc figurc, AVR is of PI typc. Its paramctcrs werc obtained from identification tests (PSOD, 2003). ".F'dllh

v, (PW

Fig. 1. Block diagram of Bisotoun excitation system

279

00471

P

I ~

1+0.0161S+2.48e4Sz

_I

1+0.086S ~

1 C0.018S t3 98e-5SZ

I

7.1s

1+7.1$

Fig. 2. Block diagram of thc PSS 2.3 PSS Model PSS of Bisotoun powcr plant has two inputs: active power and frequency. Figure 2 shows the block diagram of this PSS. PSS gains in either of the power and frequency paths arc tunable.

2.4 Modeling EHVPower Nehoork For modcling of Iranian EHV powcr grid, all lincs, transformers and compensators of transmission network are directly modeled. For modeling of gcncrators, according to thcir significancc in thc analyses, three kinds of models arc considered. Subtransicnt modcl is considered for Bisotoun gcncrators, which are of primc influcnce in the studies. Excitation systems of Bisotoun and ncarby plants arc also modelcd. Exccpt for Bisotoun generators, similar units in each plant are merged and an equivalent unit is replaced to represent them. For power plants near Bisotoun, transient model is used, and remote plants arc rcprcscnkd with classic model. With this approach, 48 generators arc rctained in thc system modcl. Plant parameters are taken from Ref. (Parniani, 2002).

3. DESIGNOF POWER SYSTEM STABILIZER For the PSS design, thc worst condition in which electromechanical oscillations have minimum damping should be considcrcd. This is known as "performance condition" and is accomplished in thc ratcd activc powcr and maximum equivalent impcdance of thc network (Larscn, 1981). Maximum anticipated impedance in the study system is obtained when two transmission lincs betwccn Bisotoun and East K e m s h a h buses are disconnected. 3. I Phase Compensation Thc basic principlc in PSS dcsign for incrcasing damping torquc is that the phasc lag of GEP(s) (transfer function between cxciter input and thc clcctrical torquc as a function of frcqucncy) in a

frcqucncy rangc including local, intcrplant and intcrarca modes should be calculatcd and compcnsated by proper selcction of PSS parameters. For this purpose, the two Bisotoun units were represented as a single equivalent generator having a large inertia, and the gcnerators at all other stations wcrc modeled as infinite buses (Kundur, et al., 1989). Phasc of PSS should bc as ncar as possiblc to thc phasc lag of GEP(s). It is important to avoid overcompensation, is.the phasc compensation of PSS should not bc more than phasc lag of GEP(s), sincc il results in a negative synchronizing torque, which is undesirable. With the above approach, in addition to improving the damping of local mode, thc stabilizer produces some positivc damping torquc at inter-area frcqucncics. Range of frequency that contains local, inlcrplant and intcr-tic oscillations in tbc study systcm is bctwccn 0.4 to 1.5 Hz. To calculatc the phase characteristic of the PSS depicted in Figure 2, with due attention to swing equation and considering ATm= 0, electrical power is: dt

-

2H

(AT,-AT,

-DAmr)

Thcrefore, noting the proportion of frcqucncy and rotor specd, block diagram of PSS is rcdrawn as Figure 3. Figurc 4 illustrates thc ideal phasc compensation characteristics in diffcrent operating conditions (curvcs 2-5) as well as actual phase compcnsation providcd by the designed PSS (curve 1). Curve 2 shows the phase lag of GEP(s) as a function of frequency, in

-

I+C 086s ~

Ix).018S+3.98c-SS

7.1s

I

lr7.lS

Fig. 3. Block diagram of PSS for calculating phase compensation

280

I

8,

84

8,.

~

8,

,

,

.

I :

11,

> /

1

Fig. 4. Phasc charactcristicsof PSS "performance condition". Curve 3 of the figure shows thc phase lag of GEP(s) at peak load and normal system condition. Curves 4 and 5 corrcspond to similar cascs as curves 2 and 3 with only onc unit of Bisotoun connected to the network. It is seen that curves 2 to 5 are all above curve 1, but the phase difference between them is less than 35" degrecs, which is acccptable. By the above phase compensation dcsign, the ratio of thc two PSS gains is obtained as: K, K,

=

0.2 15

(3)

For finding the absolute values of K, and K, root locus method is employed.

3.2 Determining the PSS Gain The gain of PSS has direct cffcct on damping of electromcchanical oscillations. It is desired to attain maximum damping of thcsc oscillations without destabilizing other modes. Since the ratio & is

Ic

constant, gains K, and K, arc increased from zero and root locus is drawn. The proccdure is carried out once for PSS with power and rotor speed inputs, and once with powcr and frequency inputs. Figurc 5 is thc root locus for thc performance condition. The root loci for another conditions is in (Zafarabadi, 2004). In this figurc, part "a" is for PSS with powerspeed input and part "b" is for PSS with powerfrcqucncy input. Arrows show thc direction of motion of some modes with increasing gains. Too much increase of K, and K, has a negative erfect on other modes (such as control modes). Based on these results, gain values of K, = 0.874 and K, = 8.625 arc selcctcd.

4.PLWORMANCE EVALUATION THROUGHSIMULATION The effect of Bisotoun Plant stabilizer on three types of oscillations (local, intcrplant and inter-area modes) is investigated. For identification of these modcs, mode shapes and participation factors associated with rotor speed and rotor angle arc employed (Kundur, 1994). To ease the demonstration, generators are numbered from 1 to 48, and Bisotoun is denoted by 3 . Moreover,

Fig. 5. Root locus with'two units connected to the network with full load and maximum impedance, (a) PSS with power-frequency input, (b) PSS with power-speed input. plants near Bisotoun are numbered from 1 to 14.

4.1 Effect of PSS on Damping of Local Oscillation Modes Local modes are associated with the swing of units at one generating station with respect to the rest of power system. State matrix of the system in performance condition comprises 110 complex eigenvalues. By studying these eigenvalues and the corresponding participation factors it is observed that 6 modes are affected by Bisotoun rotor speed. These modes (1 to 6 ) are depicted in Figure 5. Bisotoun generator speed has maximum participation in modes 2 and 5. Figure 6 shows mode shape components corresponding to the rotor ofthe turbine generators for mode 2. Local nature of this mode is evident from the figure. Investigation of participation matrix shows that after employing the PSS, (with the settings specified in the previous section) mode numbers which are most affected by Risotoun speed, change to modes 5 , 7 and 8. Among these modes, Bisotoun speed has the most participation in modes 5 and 7. The mode shapes also confirm this result. The mode shape components associated with the speed of all machines for mode 7 are depicted in Figure 7. It is observed that the effect and participation of Bisotoun on the oscillation modes also depends on PSS gain. This result is confmed in other conditions

281

Power uarizdtlon iou 8'

Fig. 6 . Mode shape components associated with speed of generators for mode 2 (without PSS) 1%

I

h

l

U

Fig. 8. Active power variations of one unit aftcr 2% change in voltage reference when 2 units working at full load are connected to the network.

r

1

Fig. 7 Mode shape components associated with the speed of generators for mode 7 (with PSS) (not presented here for the sake of brevity). Table I shows the effect of PSS with power-speed and powerfrequency inputs on damping of local mode in different conditions. It is observed from the table that the damping decreases as the impcdance or active power increase. Anotlicr result is that P-f PSS yields a little morc damplng than P-w PSS. Figures 8 and 9 show the variations of active power, when a 2% change in voltage reference IS applied to the generator. Each

"re

wax,

1.490

Min.

-0.944f 10.08i

1.605

figure contains thrcc curves: PSS off, P-w PSS and P-f PSS, with max and min impedance conditions shown in figurcs a and b respectively. It is observed that the PSS always has satisfactory performance, and P-f PSS slightly outperform the other type. 4.2 PSS Efects on Interplant Mode Damping Mode shape components corresponding to the rotor speed of 2 units arc in opposite direction for interplant mode and are unidirectional for local mode. PSS effect on damping of interplant mode is shown in Table 11.

PSS

0.066

P-W Eigenvalue of interplant mode -2.8721 12.24

1.955

0.093

-3.30+ 13.071i

2.080

Without PSS Eigenvalue of interplant mode -0,6171 9.3621

Impedance

Fig. 9. Active power variations after 2% change in voltage reference when 1 unit working at full load is connected to the network.

(

282

Freq. (Hz)

P-f PSS

0,228

Eigenvalue of interplant mode -3.781+ 11.08i

Freq. (Hz) 1.763

0.323

0.245

-4.251f 11.83i

1.883

0.338

Damping

Damping

The main result is alike local mode behavior: PSS improves the damping of interplant oscillation considerably and P-f PSS is a little better than P-w PSS. Also, it is obvious that the network structure and impedance has negligible effect on interplant damping. 4.3 PSS Ejfectson Inter-Area Modes Damping ContTibution of each power plant in inter-area oscillations mainly depends upon its situation in the network, its nominal power and inertia. Frequencies of these oscillations are less than local mode. In the analyses camed out on the study network, three interarca modcs wcrc idcntificd. Thcir frcqucncics arc 0.436,0.583 and 0.746 respectively. According to components of mode shapes associated with rotor speeds, Bisotoun is most effective on mode 2 and has no effect on mode 3. Investigations of the effect of Bisotoun PSS on theinter-area eigenvalues damping reveal that the designed PSS slightly improves damping of modes 1 and 2 but mode 3 remains unchanged. This result is confirmed by their mode shapes that are not shown (Zafarabadi, 2004).

5. MODELVALIDATION AND TESTRESLJJTS According to the results obtaincd from excitation system identification, present adjustments of the PSS gains set by the manufacturer were: K,=1.575 (4) K, =0.513 , The main result of this section is that unlike local and interplant modes, PSS is less effective on inter-area oscillations. Moreover, its effect on different inter-area modes depends upon the position and characteristics of a power plant. Figure 10 shows phase compensation of the existing PSS as compared to the desired compensation in different operating conditions. Notations of different curves are similar to Figure 4. Considerable overcompensation provided by the existing PSS is evident. So, these adjustments are expected to yield undesirable effects on synchronizing torque, and to decrease oscillation frequency. To investigate the performanccs of existing and designed PSS tunings, some safe disturbances like tap .,

.r>.,.

, . ?,...(,.”,

n:

Pm.m

r

III

pu 011 s j s t t i n base

1

‘ i

I Fig 11. Active power vanatlons of unit 1, PSS OFF

:r,

.,r.,

. ,. ,

r

changing of the generator transformer and turbine valve position changing (about 2%) were cc applied, and necessary signals like active power; frequency and PSS output were recorded using a Data Acquisition System (DAS). Figures 11 and 12 show active power variations of unit 1 without and with PSS. In both figures, unit 2 is paralleled and is operating at P=160 [MW] and Q=O [MVAR], while the operating point of unit 1 is P=310 [MW] and Q=130 [MVAR]. Also all transmission lines in the area are in service (normal condition). Applied disturbance in the simulations is voltage reference changing (1.7% of nominal value). Each figure consists of two signals: a- measured, and b- simulatcd activc powcr. It is evident from both simulation and test results that the existing PSS improves oscillation damping. However, as it was expected, oscillation frequency decreased considerably because of PSS operation. For example, in Figure 11, f= 1.33 [Hz] but in Figure 12, e0.75 [Hz]. Therefore, the present tuning is not desired from transient stability point of view. After implementation of the new adjustments, sufficient damping of the local mode was achieved without compromising transient stability (Zafarabadi, 2004). I-Iowever, somc higher frcqucncy (about 6 Hz), damped oscillations were observed. Therefore, a fine-tuning was performed to avoid these oscillations. Active power variations at P 3 2 0 [MW] and Q=l20 [MVAR] for both units with the final tuning are depicted in Fig. 13.

r,i

.s

.,

.”.

I

, .,

2

, I

,+

,~

1

,,,L,r:

Fig. 12. Active power variations of unit I, PSS ON (existing tuning)

Fig. 10. Desired and present phase characteristicsof the PSS

283

,

, / .

,

Fig. 13. Active power variations ofunit 1, PSS ON (final tuning) 6. CONCLUSION In this paper, extended phase compensation method and root locus analysis was successfilly used for PSS design. Experimental test results and nonlinear simulations verified lmearized eigcnvalue analyses. Participation factors and mode shapes were effectively employed to identify local, interplant and inter-area modes and their characteristics. The following observations were also made: Adjustment of PSS parameters set by the manufacturer possessed an overcompensation characteristic, and had negative impact on transient stability. The PSS designed with extended phase compensation improves the damping of local and interplant oscillation modes considerably, and has some positive damping effect on inter-area oscillations. Fine-tuning during on-site tests was necessary to achieve satisfactoryperformance. P-f PSS slightly outperforms P-w PSS in damping electromechanical oscillations. Participation of Bisotoun generators in the oscillatory modes also depends on PSS operation. ACKNOWLEDGMENT

This work was part OF the PONBROl projcct conducted by the Department of Power System Operation, Niroo Research Institute (NRI), Iran. Tavanir Organization and Bakhtar Regional Electric Company in Iran supported the project. The authors would like l o thank management and technical staff of Bisotoun Generating Station for their assistance.

REFERENCES

Kundur, P., M. Klein, G. J. Rogers, M. S. Zywno (1 989). Application of Power Systcm Stahilizcrs for

PSOD (power Systcm Operation Dcpartmcnt) (2002). Proper Model for Generators of Bisotoun Power Plant and Offering Proper Method for Its Parameters Identification, part of project PONBROl, Niroo Research Institute (NRI). PSOD (power System Operation Department) (2003). Modeling of Excitation System of Bisotoun Power Plant. part of project PONBROl, Niroo Research Institute (NRI) Parniani, M. (2002). Dala of Electrical Power Grid of Iran in Years 2004 and 2009. First Report of the Contract No. 275-76-lot3 with Tavanir, Sharif University of Technology. Larsen, E. V., D. A. Swan (1981). Applying Power System Stabilizers, Parts 1, TI and TTT. 1EIX Trans. Vol. PAS-100, pp. 3017-3046.6 Zafarabadi, G. (2004). Design of Power System Stabilizer for Bisotoun Power Plant. MS. Thesis, Sharif University of Technology. Kundur, P. (1994). Power System Stability and Control. McGraw-Hill. Gholambasan Zafarabadi received his B.Sc. degree in Electrical Power engineering from Mazandaran Univesity in 2001. In 2003, he received his MSc. drgree in Power Engineering from Sharif University of Technoloby, Tehran, Irdn. Since 2002, he has been with thc Department of Powcr Systcm Opcration at Nuoo Research Institute (NRI) in Tehran. He has been working for the Iranian Academic Center for Education, culture and Research (ACECR) Sharif Branch in Tehran since 2003. Mostafa Parniani (Senior Member, IEEE) reccived Ius B.Sc. degree from Amrkabir University of Technology in 1987, and the M.Sc. degree from Sharif University of Technology in 1989, both in Electrical Power Engineering. He worked for Ghcds-Niroo Consulting Engineers Co. and for Electric Power Research Center in Tehran during 1988-90. Then, he obtained the Ph.D. degree in Electrical Engineering from the University of Toronto, Canada, in 1995. Currently, he is an assistant professor at Lhe EE Dept., Sharif University of Technohgy, Tehau, ban. IIe also worked as a consultant for the Department of Power System Operation, NRI during 2002-2005. His research interests include power system dynamics and control, and power electronics applications in power. Mohammad Rasouli received his B.Sc. degree in Electrical Engineering fmm Power and Water Institute of Technology (P.W.I.T.) in 1997, and his MSc. degree in Control Engineering from Amii-kabir University, Tehran, Iran, in 2000. He worked in the Department of Power System Operation at NRI during 2000-2005 where he conducted or supervised several projects on dynamic model identification of large turbine -generators and tuning of their controllers. Currently, he is studying his PFID at Calgaq University. Pooya Ansarimehr received his BSc. degree in Control Engineeringand M.Sc. degree in Power System Engineering from the Sharif University of Technology in 1995 and 1998, respectively. Since 1998, he worked at Eleckical Power System Research Center, NRI. He has been head of Power System Operation Dcpartmcnt since 2000. His main research interests include power system operation, dynamics and control.

Enhancement of Overall Systcm Stability. IEEE Tram. Vo1.4, No.2, pp. 614-626.1 Kundur, P. (1999). Effective Use of Power System Stabilizers for Enhancement of Power System Reliability. Power Engineering Society Summer Meeting, IEEE, Vol. 1, pp. 96 - 103.

284

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

ROBUST CONTROL DESIGN OF PSS IN WIDE AREA POWER SYSTEM CONSIDERING INFORMATION RELIABILITY IIiroyuku Ukai *Goh Toyosaki * Yoshiki Nakachi "Surech Chand Verma **

* Nagoya Institute of Technology, Gokiso, Showa, Nagoya, 466-8555, JAPAN * * Electric Poiuer R&D Center, Chubu Electric Power Co. Inc., 20- 1 Kitasekiyama, Odaka-cho, Madori-ku, Nagoya 4 59-8522, JAPAN

Abstract: In recent years, electric power system becomes larger and more complex due to the enlargement of power flow in wide area, the deregulation of electric utilities and thc full-scale cntry of Power Product Companies. Utidcr the background both inter-area a i d local oscillations are significant. In order to cope with these problems, the advancement of the PSS(Power Stabilizing System) are expected. In this paper, we propose the control system on basis of the robust control theory, which can improve stability of power system in wide area. The proposed control system is based on the "hierarchical power and inforination network"; that is: the feedback control system is hierarchically constructed by using information of wide area system in correspondence with the level of reliability. In particular, we idcnt,ify the dynamic impedance niodel of large power system by measuriiig voltage and current at the interconnection node. Copyright (c) 2006 IFAC. Kcywords: power system stabilixr, wide area power system. systcm identification. PMU, reliability

1. INTRODUCTION

Power syst,ern stabilizer(PSS) has beeii a costefficient measure to improve stability in power systems. The conventional PSS is designed on the basis of classical control theory for the linearizcd modcl around a certain opcrating condition. Therefore, it is adequate only for a narrow range around a design point. Since a, wide area power system is highly nonlinear and the network operating condition frequently changes, it brings discrepancies between the mathematical

linearized model and the real nonlinear system. Moreover it. cannot compensate Tor t,he miltimodes of power oscillation in wide area power system. Under these backgrounds inany robust control techniques have been applied with incrcasing demands for high quality electricity supply(Qihua Zhao, 1995)(S.Chen, 1995)(S.Cui et al., 1999). However, niost, of these robust controllers are designed on basis of a single machine and a infinite bus model. Therefore, even if it i s robustly designed for uncertainties of oscillation modes, it is difficult to compensate for both the local and the

285

inter-area modes of power oscillation. Moreover, when t,he operating condition undergoes large variations, it is often impossible to achieve high perforinaiice over an entire operatiiig range.

duced for designing the control model. Lastly the effectiveness of t,he proposed met,hod is confirmed by soine numerical simulations.

On the other hand, in recent years, phasor ineasureinent unit(Pb1U) in power system by using GPS(Global Positioning System) was iiitroduced aiid applied to a, st,atic state estimation, various protections, and so on(R..O.Burnett. et al., 1994)(M.Hojoel; al., 2003). One of the authors is carrying 011 a research project among uiiiversities in Japan for dcvcloping an oiiliiic global monitoring system for power system dynamics by usirig llie PMU. Iri tlie iiear lulure, it is expecled applying the Pl\iIU based technologies to various fields in power system. In stabihing control of power system, power inforination which are ineasured or estimated at rmilti-points by using the PMU will be aggressively utilized.

2. HIERARCHICAL FEEDBACK CONTROL SYSTEM

In that case, however, it is iiriportaiit to consider the reliability of various power data measured in a wide area power system. In other words! it is necessary to properly use several information data in a wide area according the level of reliability. Reliability of inforination used in this paper implies two meanings. One is the measure of degratlat,ion of power data owing to the lack of data in acquisition systems, time delay of transmitted data, traiisrnission noise, aiid so 011. The other is parameter uiicertainties of mathematical model used for designing controllers. In this paper, the design method of the advanced PSS is proposed to coinpelisate for multiple oscillation inodes in wide area power system. The mathematical model representing the total system is constructed by the generator to be controlled, the local power system, and the large power systein connected to the local power system. It is inodeled by taking accouiit of the information reliability of data used iii tlie model. 111 this way, thc proposed method provides both the local and the inter-area oscillation inodes in the control design model. As the result,: the feedback control configuration is coiistructed by takiiig accouiit of reliability of power information. In the following chapter, t.hc concept, of the proposed design method of controllers based on the level of iiiforinatioii reliability is shown. In the third chapter, the constructioii of coiitrol model based oii this idea aiid the design iiiethod based on Ifm control theory are presented. In particular, in this paper, the dynainical impedance model for the interconnected large power system is intro-

In this section, the concept of the proposed control design method based on the hierarchical feedback cont,rol syst,em is explained. The configurai,ion of t,he system is shown in Fig. 1. The basic idea is to coiist,ruct feedback control loops according to reliability of iiiforinatioii fed back from inultipoints in a wide area power system. As mentioned before, the reliability of information used in this paper iinplies two meanings. One is tlie measure of degradation of power data owing to the lack of data in acquisition systems, time delay of transmitted data, transmission noise, and so on. The other is parameter uncertainties of inatheinatical inoclel used for designing controllers. The power information of the generator to be controlled is highly reliable, highly frequent, and has large data iiumbers in which generator speed, active power, teriniiial voltage, aiid so oii are iiicluded. Moreover almost parameters of the generator are able to be known in advance. The reliability, the frequency, and data number of power inforination in the local area belong to the inediuin level, and the parameters of generators, network impedance, and load are somewhat uncertain. Moreover, in case that, t,here are many generators and load in a local area, they should be aggregated. Therefore t,he local area power system is forced to include parameter uncertainty. On the other hand, the power information of a large power systeiii or ariothcr powcr system area connectcd to the intcrconnection node is poor, that is, at most only information at the interconnection node can be useful. Moreover, its reliability and frequency belong to the low level. As the result, the feedback data to be directly used for the PSS inputs are divided to thrcc categories according to the information reliability and acquisition frequency. Moreover, the model parameters to be used l o design the coiitroller are cat,egorized t,o three levels.

3. CONTROL DESIGN METHOD In this section, the control model is constructed based on the idea of the hierarchical feedback coiitrol system. hheover, the H O0 controller to stabilize the total power system is designed based on t,he a,ggregat,edcont,rol model.

286

with the governor and AVR as shown in Fig.2 and Fig.3 On the other hand, for othei generatois in

Fig. 2. Block diagram of the governor

(

Large Powersystem

)

Fig. 1. Hierarchical feedback control system

3.1 System model for control design First of all, let GI be a generator to be controlled, and let G2 Gk be geiicrators belonging a local area power system. It may be assumed that the generator group is aggregated in a local area power system. Then state space inodel for k generators is defined by

-

Fig. 3. Block diagram of AVR local power system the simplified models are used, where the same model of generator is used aiid the governor aiid the AVR are reduced to first order models.

These generator models are not connected to power network. In order to embedding the network iinpednnce a i d load in the local power syswhere tem to the above system models, it is necessary to give the impedance characteristics of both the local power system and the large power system connected to the local power system. The local power system is constriicted by appropriately aggreagted generaors and loads. The local oscillatioii modes are reprcsentcd in this way. On the other hand, thc large power systcrn includes many generators and loads. As mentioned above, however, the impedance characteristics of the large power where. Z L % is a stale variable for each generator, u,, is a control input froin PSS, and @.zdL, AzClIL system is uncertain. Thus it is necessay to model the inter-area oscillation inode between the genare d - q axis terminal currents of generator a. erators in the local power system and those in The percise model of the generator to be coiitroled the other large power system. In this paper, it is derived by linesrlidng the following nonlinear is proposed that the network impedance of the model. large power system is presented as the dynamical iriodel by applying the system identification = w n ( w - 1) method. Therefore, the effects from other power 1 ;j = - [T, - T, - D(u l)] systems coniiected to the considered local power 2H system c'm be cmhedded in t,hc c o n h l design model.

s

-

Let the sniall deviations of node voltage and cur, rent at the interconnection point be Avn, & a d the deviation of the frequency at this node be w ~ If .thcrc arc sevral nodes connected to the considered local power sgtern, the identification is done at, each connect,ion node. Then the dy-

287

nainical inodel for each connected power system is idcnt ificd as follows: Subst,itut,ing Eqs.(9) and (10) to Eq.(12), we have

+

AVL = K L Z L K R X R

(13)

and

Then the following relation is finally obtained.

whcrc, t>heinput signal for the identification is A7.R aiid the outJput signals the A ~ R and AWR at the interconnected iiode, respectively. hi this paer, the 4SID(SubSpace based State Space model IDentificatioii method) is used to identify the system model. This method is the effective identification algorithm to identify the state space niodel and is easily available using MATLAB "Identification Toolbox". Main features are as follows;

As the result, by substituting the above relation to (1) and (8), the control desgiii model of the

total power system is given by

+ [ B;'] ucz.

(15)

(1) It can be applied to unstable and/or closed loop systems. (2) It provides a high acciiracy by virtue of SVD and QR decomposition algorithm. (3) It provides simple iiurnerical algorit,hin (4) It is easy to extend to multi-inputs arid multioutput systems.

whcre, K 7 ,i = 1,. . . , 4 are suitable coefficient matrices constructed by network impedances.

In this way, it is possible to represent the t d a l systerri rriotlel iriclutliiig the inter-area oscillation mode.

Each output is fed back to PSS according to thier information levels. In this paper, the output to be controlled is defined by the generator power outputs ill local power system.

Now we embed the network equation to the system model. In this paper, loads are assumed to be coiist ant iinpedaiice for simplicity. The local power systcin is appropriately aggregated. T h a i the volt>agesand currents at generator nodes and the iiitercoiinectioii iiode are expressed b y network impedance as follows;.

where I L , VL are currents a d voltages at generator nodes aiid Y,, are aggregated admittances in the local power system, rcspcctivcly. On the other hand. the terrniiial currents AZL iii Eq.(1) are expressed by t eriiiirial voltages of aggregated geiierators ud,, uYZin the local system and the voltages Avdrz. Av,rz at the interconnection nodes. Coilsidered with the trsiisforinatioii of the phase angle froin the standard D - C2 axis to the geiirator d - 4 axis, the linearized equation is represent cd by

In the similar manner, the deviation of the terininal voli age VL are expressed by

On the other haiid, the ineaured output is defined by y = [Aw,, Aw2, . . . . A W k , Awn]

z

=

[AP,l, LIP,,,

' ' '

, Ar-',,I

(16)

(17)

3.2 Control design The controller is designed based on this mathematical model of the total system by applying the H W control theory. 111 this paper, tlie coiitrol problem is foriiiulated by the 1obust stabilization problem of HO" control. Thc weight functions are designed by considering the model errors due to the aggregation of generators iii local power system, the identification error, and tlie data error of frequency at each measuring point. The solution to this problem is obtained by using MATLAB "Robust control toolbox".

4. KUMERICAL SIMULATION RESULTS

In this section, the numerical simulation results are shown by applying the proposed method to the 1EE.J WEST10-inachiiies system in Fig.4, which consists of 10 machines and 30 nodes. It is generally known that the longitudinal structure produces t.he typical long term oscillat.ion a,nd local

288

Fig. 4. IEEJ WEST10-machines system generator oscillations. It is assumed that the generator to be controlled i s GI, and generators in the local area power system is aggregated to the generator G2. The iritercoiiriectsioiinode is the tie line bet,ween G2 and G3.

Bode Diagram From U l l r

0

-100

First of all: t,he identificatioii result is shown in F i g 5 The input and output data are used in case that the three phase-to-ground fault occurs at the transrriissioii line iieitr the generator 9. It. is found that the estimated frequency well coincides with the measured one. The order of t,he identified system model is five. In order to X10" 540

in

c 0.0 -1.5

10"

10

Frcwenry I H d

0

10

20 time [ s e c ]

30

40

Fig. 5. Identification rcsult confirm tlie effectiveness of the proposed method, the nonlinear simulation is done when the three phase-t>o-grouiidfault, occurs at t,he transmission line near the generator 1 as shown in Fig.5 The simulation is achieved under the conditions; (1) superimpose the random noise of inaxiinuiri &lo% to the frequencies of the generator G2 aiid the iiiterconncction node, (2) assume the time delay 80[msec]for the transmitted data, (3) and thin the data acyuisitioii of the freyuencies of G2 and the intercoiiiiection node coinparcd with thc oiic of gcncrator G1.

The bode diagrams from the control input to each generator active power are shown in Fig. 6. It is found that each transfer function has resonance

Fig. 6. Bode diagram from control input to each generator active power modes at 0 . 4 H ~and ~ H LThe . former corresponds to the inter-area oscillation mode, and the latter local mode. The controller is designed to suppress these resonance modes against modeling errors. The transient responses of the active power and the freqiieiiry of each generator are Show11 in Flg.7 aiid Fig.8. In both figures. tlie solid line represents the case of proposed controller and the broken line the case that only the frequency of G1 is fed back. In the latter case, the 11O0control iiiethod is applied to a single rriacliiiie arid irifiriite bus iriodel with respect to the generator 1. It is found that the proposed method improves the transient stability compared with the case of the conventional 11" control case against parameter uncertainty. Moreover, the frequency at the intcrconnection node is shown in Fig.9. It is also the oscillation of the frequency at the interconiiectioii node is well suppressed.

289

5. CONCLUSIONS

..__......_ COfl "en1 l O l l d l ad van ce

In this paper the design method of the advanced PSS is proposed to compensate for rnultiple oscillation modes in a wide area power system. The main ideas and results of the proposed method [lllne

the feedback cont;roller is designed by taking account of informatioil reliability in power system. To do this, tlie control sign model is derived in correspoiidarice with three levels of information reliability. The first is exact model of tlie controlled generator, the second is reduced model of the local generators, and third is the estiinatioii model of the large power system connected to t,he considered local power system. The dyiiainical iinpedaiice model of a large power system connected to the considered local power syst,ems is obt,ained by using the system identification method. The 4SID method is applied to obtain the dynninical iinpedaiice model. This inethod can be realized based on the PMU system. Tlic simulation results show the good performance of the proposed rncthod compared with the conventional H m applied to control design model b a e d on a single niachiiie and infinite bus system.

30

-0.0I

I

1 0 8 -

s

4

I

I

I -

-

.,: :. : , 1 0

,

20

30

40

I - Gl+ciP*Aw

1-

-

-

&. Zhm aiid J . .Jiaiig (1995), Robust Controller

ltimej

0

1

30

iiit.ercoiinectioii node REFERENCES

-

-0.15

I

20

0 2 -

-0 4

I

I

10

0 4 -

-0 7

-

0 . 15 I

.. .. ,

0 6 -

9 E

I

;

*

Fig. 8. Transieiit respoiises of the frequencies of G l j G2, and G10

I

0.1

.

I timc I

advance

- 0.05 -

40

I time I

. _ _ . . _c _ _ _ _I o n_ ventiona I

I

40

Itime I

Fig. 7. Transient responses of thc activc powers of G1, G2, and G10

Design for Generator Excitation Systems, IEEE Trans. on Energy Conv, Vol. 10, No.2, pp. 201-209. S. Cheii aiid O.P. Malik (1995),Power System Stabilizer Design Using p Synthesis, IEEE Trans. on Energy Conv. Vol.10, KO. 2 , pp.175181. S.Cui, H.Uk;ti. et al. (1999), Decent,ralized Control of Large Power System by H X Control Based Excitation Coiitrol System, Proc. of IFAC'99, Vol. 0 , pp.255-260. R.O.Burnett Jr, M.M.Butts, T.W.Cease, V.Centeno, G.Miche1, R..J.Miirphy, a i d A.G.Phadke (1994), Synchronized Phasor Measurements of a power system event, Trans. IEEE Powcr Syst., 9, No.3, pp.16431649. M.Hojo, T.Ohiiishi, Y.Mitani, O.Saeki, and H.Ukai (2003), OBservatin of Frequency Oscillation in Western ,Japan 6OHz Power System Based on Multiple Synchronized Phasor Measurement Proc. Powertech '03.

290

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ANALYTICAL INVESTIGATION OF THE EFFECT OF GENERATOR MODELLING ON ELECTROMECHANICAL MODE DAMPING Keren Kaberere’, Alexander Petroianu’, Komla Folly’ University of Cape Town, Dept ofElectncu1 Engineering, Cape Town, South Apicu ‘kkunulhu@ehe uct uc zu, 2upetvoiunu@ehe uct uc. zu, ‘kjolly@ehe uc.1 uc zu

Abstract: Power system analytical tools differ in their components modelling. The differences affect electromechanical modes damping. This paper investigates the effect of including rotor speed deviation in stator voltage calculation -with the stator transients neglected- and the modelling of turbine output, on electromechanical mode damping of a single machine infinite bus system. We use a sixth order generator model with different excitation control configurations. We analyse results obtained with EUROSTAG and compare these with results obtained with three other industrial-grade tools. Our results show that: (i) if rotor speed deviation is included in the stator voltage calculation, the results are more conservative than those obtained if speed deviation is neglected. (ii) if the turbine model output is torque, the results are more conservative than those obtained if the output model is power. Copyright 02006 IFAC Keywords: Eigenvalue analysis, electromechanical mode, speed deviation, turbine model output.

1

INTRODUCTION

The advancement of computer technology has facilitated the development of several power system analytical tools. Hence, decision makers increasingly rely on digital simulations for planning and operation. One important function of these tools is eigenvalue analysis. System stability is deduced from the eigenval tie resti It s. The analytical tools differ in their components modelling and numerical methodology; therefore, for the same benchmark network, different tools give different results. From experience (Kaberere, et al., 2005a; 2005b) the differences in results, obtained using different tools, are mainly due to differences in components modelling. The results obtained with different tools differ in damping but agree on frequency of oscillation (Kaberere, et al., 20053; Slootweg, et al., 2002). Kyriakides and Farmer (2004) acknowledge the need for carrying out studies to determine the modelling aspects that result in “damping errors”. Kaberere, et al. (2005a) highlighted the following generator modelling aspects as causes of variations in eigenvalue results obtained using different tools; i) Stator voltage calculation; include (rotor angular velocity, a, # 1) or neglect (q = 1) speed deviation. ii) Representation or turbine model output; mechanical torque, T, or mechanical power, P,.

aspects. We use a sixth order generator model with different excitation control configurations. With the tools at our disposal (PSS/E, PowerFactory, EUROSTAG, and SSAT), it was not possible to investigate the modelling aspects using only one tool. Only EUROSTAG and PowerFactory include rotor speed deviation in stator voltage calculation, but none of the two tools allows the user to neglect the speed deviation. The A matrix is therefore important for investigating the effect of speed deviation. The A matrix in PowerFactory is not accessible Therefore we use EUROSTAG and MATLAB to investigate the effect of including rotor speed deviation on the electromechanical mode We compare the EUROSTAGIMATLAB results with results obtained using PSSIE, PowerFactoiy and SSAT Our investigation reveals that: (i) if the stator transients are neglected, results obtained with rotor speed deviation included in the stator voltage calculation are more conservative than those obtained with speed deviation neglected, (ii) results obtained with T,,, turbine model output are more conservative than those obtained with P,, turbine model output. The paper is organisecl as follows. In section 2 , we discuss the linearised system equations; section 3, stator voltage calculation; section 4, turbine model output; section 5 , case study; section 6, conclusions.

We investigate the efrect of the two generator modelling aspects listed above on electromechanical modes. We use a single machine infinite bus (SMIB) system to demonstrate the effect of the two modelling 29 1

2

1979; TREE Std 1 1 10, 1991; Kundur, 1994). Moreover, the Power System Damping Ad Hoc Task Force (1999) reports that even if speed deviation is neglected in stator voltage calculation, it is important to include the effect of speed deviation in the value of terminal voltage fed back to the voltage regulator.

LTNEARTSED SYSTEM EQUATIONS

The dynamic behaviour of the power system is expressed through a system of non-linear differential and algebraic equations (DAE). To study the system's response to a small disturbance, these equations are linearised around an equilibrium point.

From the foregoing, various authors agree that it i s necessary to neglect stator transients and if stator transients are neglected, rotor speed deviation should also be neglected in stator voltage calculation.

For a S M B system with the generator on manual control represented using a 6'h order model, one form of expiessing the liiiearised system equations is 1' 3

1' 4

'15

a23

'24

a25 a2h

'33

034 ' 3 5

0

'VId

*VI~

'36

............................................. 043 044 045 046 ............................................. 0 5 3 '54 0 5 5 056

0 ru;, 0

One of the recommendations of the Power System Damping Ad Hoc Task Force (1999) is that research should be carried out to establish the effect on system damping, of neglecting stator transients without neglecting speed deviation in stator voltage calculation. From the available literature, little has been done in this respect.

"fd

'16-

. 4 2 ,

i

Aw, *b'

where: A

- denotes a small deviation

yffd

- field flux linkage

VJ/~

- d-axis amortisseur flux linkage

A study by Slootweg, et al. (2002) shows that the real part of the electromechanical mode is influenced by the inclusion or omission of rotor speed deviation in the stator voltage calculation. However, the authors do not state whether the influence is detrimental to damping or otherwise.

v2q- q-axis amortisseur flux linkage w, - rotor angular velocity 6 - rotor angle YJ,~,

.element

a,

of the A matrix for i , j =I, .... 6

- base angular velocity

wo

Johansson, et al. (2002) report that the inclusion of rotor speed deviation in stator voltage calculation results in conservative results. Their results were obtained using a 2"d order (classical) generator model.

The dimension of the A matrix increases as generator controllers are added. 3

All the tools that we use in our investigation neglect stator transicntc Table 1 gives a summary of thc representation of rotor speed deviation in four industrial-grade tools

STATOR VOLTAGE CALCULATION

Based on the dq-axis machine representation, the per unit (pu) stator terminal voltage, E, is expressed as E, = ed + j e ,

Table I : Representation of rotor speed deviation in stator voltage calculation in four industrial-grade tools Tool PSSIE PowerFactory EUROSTAG SSAT

where: ed, eq - d- and y-axis components of terminal voltage Y , Y, - d- and q-axis components of stator flux linkage - d- and q-axis components of stator current id, i, y - rotor angular velocity R, - stator resistance

Speed deviation Neglected Included Included Neglected

If rotor speed deviation is neglected, elements aI5,azi, equal to Lero.

u3irand ud5in (1 ) are all

4

In stability studies, network transients are neglected because they decay very l'ast. Therefore, for modelling consistency, the terms representing stator transients (d Y/dt terms in (2)) are also neglected.

TURBINE MODEL OUTPUT

From literature, it is not clear whether the turbine model output should be mechanical power Pm or mechanical torque T,. For example, Kundur (1994) represents the turbine model with T, output whereas IEEE Committee Report (1973) and Rogers (2000) represent the models with P,, output. Different analytical tools model the turbine output differently.

Several studies have found that in so far as low frequency oscillations are concerned, neglecting rotor speed deviation (co. = 1 in (2)) in stator voltage calculation counterbalances the el'fect of neglecting the stator transients (Dandeno, et al., 1974; Krause et al.,

If speed deviation is neglected (a. = 1 pu), then T, = P, pu; T,, and P,,, can be used interchangeably in the

292

Table 2 gives a summary of the turbine model output used in four industrial-grade tools.

swing equation. However, if speed deviation is considered (a,# 1 pu), T, # P, pu. The eigenvalue analysis results obtained with T, output are different from the results obtained with P,?,output.

Table 2: Turbine model output in four industrial-grade

tools

In section 4.1 and 4.2 we analyse the linearised swing equation with different turbine model outputs. We assume the following: i) Rotor speed deviation is neglected in stator voltage calculation. Thus electrical torque T, is a function of V J ~ , VIM, vlq,~2~~ and 6. ii) Rotor speed deviation is not neglected in the power-torque relationship (T,,?# P,,, pu). iii) The governor is not modelled

Tool

Turbine model output PSSE Pm PowerFactory P, T,,l EUROSTAG EUROSTAG’ P, SqAT p,,, SSAT~ T*,

5

Elernent uis ofA matrix

-&+ Pn&H -KD+ P d 2 H -KD/2H -(fG+ P,,o)I2H -(KO + P,,t0)/211 -KL>I2H

CASE STUDY - SINGLE MACHINE INFINITE BUS SYSTEM

4. I

Linearised swing equation T, turbine model output The linearised swing equation is

5.1

(3)

System model

We used the single machine infinite bus (SMIB) system as shown in Fig. 1 (Kundur, 1994) for our case study. For GI we used the 6‘h order generator model. We neglected saturation. vt

where: A - denotes a small deviation N - inertia constant (s) w,. - rotor angular velocity - turbine model mechanical torque output T, - electrical torque T, KD - damping torque coefficient.

P +

c!+ Figure I : SMIB system network representation

The mechanical torque is constant (AT,n = 0).

We sirnulaled the syskin with the following excitation control configurations: i) Manual control ii) AVR iii) AVR and power system stabiliser (PSS)

Equation (3) corresponds to row 5 , shown dotted in (1). From ( 3 ) , we deduce that element ass of the A matrix is equal to -K&2H.

Linearisedswing equation - P,x turbine model output Whenever the turbine model output is P,, and speed deviation is not neglected, equation (4) is used to calculate the turbine output torque.

4.2

Figure 2 shows the block diagram of the generator excitation system. We did not model the turbine-governor set.

(4)

System data are given in the appendix.

Lineansing (4),

(5) A l , = M,, t P,,,Ao, Subslituhng ( 5 ) in (3), the linearised swing equation becomes dAq I (hp, - A T - ( K O +P,,)Am,)

transducer

-

dt

2H

where P,, is the steady state mechanical power output.

Power system stablliset

Figure 2: Block diagram of excitation system with AVR and PSS

The mechanical power is constant (AP,, = 0). From (6), we deduce that element uJ5 of the A matrix is equal to -(K,,+Pm,,)/2H.

We used the following tools for eigenvalue analysis: (i) PSS/E, (ii) PowerFactory, (iii) EUROSTAG, (iv) SSAT.

Hence, from a theoretical viewpoint, we expect the electromechanical mode damping to be higher if the turbine model output i s PnIand rotor speed deviation is considered than with T, output.

’

The program’s default turbine model output is Kx. We modified the output for the purposes of this study. Power option - specd dcviation ncglcctcd (T,x= PM).

293

+

1Jsing ElJROSTAG and SSAT, we ran two sets o f simulations for each excitation control configuration: (i) T, turbine model output, (ii) P, turbine model output.

5.2

EUROSTAG results are more conservative than EUROMAT results.

Simulation results and discussion

To exclude the effect of speed deviation on stator voltage, we exported the A matrix from EUROSTAG into MATLAB and set elements uI5, uj5,and u45in ( I ) equal to zero. We set element a55equal to -KJ2H and -(K,+P,,)RH for T,, and P, turbine model output respectively. We calculated the eigenvalues of the resultant matrix.

<=328

c =31%

<=402 c = 6.1%

EUROMAT (pM,v)

Figure 4: Effect of including rotor speed deviation in stator voltage calculation and modelling of turbine output on damping ratio; manual control. Results obtained with EUROSTAG and MATLAB

Figures 3, 6, and 9 show the loci of the electromechanical mode on the complex plane. We obtained the results with four industrial-grade tools, for different excitation control configurations. The points labelled EUROMAT were obtained using EUROSTAG and MATLAB. In each figure, the turbine tuodel output and the speed voltage term are shown in parentheses beside the tool name.

The results in Fig. 4 show that the increase in damping ratio due to the change of turbine model output from T,, to P,,, is higher than the increase due to neglecting rotor speed deviation in stator voltage calculation.

Figures 4 and I show damping ratio results obtained using EUROSTAG and MATLAB with different excitation control configurations. Figures 5 , 8, and 10 show damping ratio results obtained using four industrial-grade tools with different excitation control configurations. c = 32%

In figures 4, 5, 7 , 8, and 10, the values next to the arrows show thc pcrcentagc increasc in damping ratio ( E ) if a modelling aspect changes e.g. in Fig. 4, neglecting the rotor speed deviation in a T,,, model results in a 9.3% increase in damping ratio.

c=-1.2%

Figure 5 : Effect of including rotor speed deviation in stator voltage calculation and modelling of turbine output on damping ratio; manual control. Results obtained with four industrial-grade tools

5.2.1 Manual control Figure 3 shows results obtained with the generator on manual control.

The results obtained using the four tools agree with the EUROSTAGEUROMAT results. However, the results obtained using PowerFactory (which includes the effect of speed deviation on stator voltage) have higher damping ratio than PSSIE and SSAT (which neglect the effect of speed deviation on stator voltage) results. EUROMAT (C,,, y ~ x)

5.2.2 Excitation system with AVR Figure 6 shows results obtained with the generator excitation system controlled by AVR.

EUROSTAG (P,, w'.yi)

639

1

-028

-026

-024

-022

-02

1

-0 18

0 (l/S)

Figure 3: Loci of the electromechanical mode in the complex plane; manual control. From Fig. 3 : + Results obtained with T,p2turbine model output are more conservative than those obtained with P, turbine model output.

294

7.4E

The results obtained using the four tools closely match the EUROSTAG/EUROMAT results.

7 44 7.42 u)

a

-F

EUROSTAG (P,,z,qt/)

5.2.3 Excitation control with AVR andPSS Figure 9 shows results obtained with the generator excitation system controlled by AVR and PSS.

7.4

3

7.3E EUROSTAG (Tnz.0 1 , ~ ) 7.3t O 8

0 52

0.5

0 54 0.56 0.58 G(l/s)

0.6

0.62

0.64

Figure 6: LOCIof the electromechanical mode in the complex plane; AVR.

3 673EUROSTAG (I,,, o,y) x

6.72 -

From figure 6: + Results obtained with rotor speed deviation included are the most conservative. + Results obtained using PowerFactory are very close to results obtained using EUROSTAG (P,,%, wry). + Results obtained with T, turbine model output are more conservative than those obtained with P,,l turbine model output.

7'

PowerFactory (Pk,m , ~ x)

'

hUROSTAG (P,,2,wvi)

X

-1.15

-1.2

-1 .I

-1.05

. 0 (l/s)

Figure 9: Loci of the electromechanical mode in the complex plane; AVR and PSS

From Fig. 9: + Results obtaiiied with rotor speed deviation included are the most conservative. + Results obtained with T, turbine model output are more conservative than those obtained with P,,, turbine model output.

I

FUROSTAG (7",,w, y) <=I56

E-7.1%

[c = 12%]

Figure 7 : Effect of including rotor speed deviation in stator voltage calculation and modelling of turbine output on damping ratio; AVR. Results obtained with EUROSTAG and MATLAB

E = 4.2% [c = 4.8%]

PSSE (P,<,~ $4 C = 17.4

[ I : = 7.4%]

l-17.5

The results in Fig. 7 show that the increase in damping ratio due to the change of turbine model output from T , to P,,, is lower than the increase due to neglecting rotor speed deviation in voltage calculation.

Figure 10: Effect of including rotor speed deviation in stator voltage calculation and modelling of turbine output on damping ratio; AVR and PSS. Results obtained with four industrial-grade tools.

6= -8.65

The results in Fig. 10 show that the increase in damping ratio due to the change of turbine model output from T, to P,,, is lower than the increase due to neglecting the effect of speed deviation on voltage.

I c - 12%

I

c = 11% [c=ll%]

rc

=22%~

c = I346 [ E = 13%]

Figure 8: Effect of including rotor speed deviation in stator voltage calculation and modelling of turbine output on damping ratio; AVR. Rcsults obtaincd with four industrial-grade tools.

We make the following general observations. i) The results obtained using PowerFactory with the generator on manual control do not agree with the findings of our investigation. ii) For each excitation control configuration, whenever rotor speed deviation is neglected in stator voltage calculation, the damping ratio increases. The highest percentage increase is observed in the configuration with AVR only. iii) The percentage increase in damping ratio due to the change in turbine model output from T,, to P,

295

i s highest with manual control and lowest with AVR and PSS. This may be attributed to the fact that the damping torque due to the excitation system is much higher than P,,,c/2H. Hence if the excitation system is modelled, the effect of the turbine model output on damping is reduced. iv) The differences in results obtained with different tools are most prominent with the generator on manual control and reduce as more controllers are modelled.

CONCLUSIONS

6

We compared the eigenvalues obtained directly from EUROSTAG (with the effect of rotor speed deviation on stator voltage included) with eigenvalues calculated using MATLAB (A matrix obtained from EUROSTAG); the results agree. Therefore we conclude that MATLAB does not introduce variations in the eigenvalues. In this paper, we have investigated the effect on the electromechanical mode of inclusion of rotor speed deviation in stator voltage calculation and turbine model output. We conclude: h The frequency of oscillation is marginally affected by both the inclusion of the effect of rotor speed deviation and type of turbine model output. For each excitation system control configuration, the change in frequency is less than 1%. P Therefore, the variations observed in damping ratio are mainly due to difrerences in damping (real part). h Inclusion of rotor speed deviation reduces the damping ratio. This effect is more dominant if an AVR is modelled than with manual control. P If the turbine is modelled with T, output, the damping ratio i s lower than that obtained with P,,, output. APPENDIX System data The network reactance i s in per unit on 2220 MVA, 241tV base. Generator rating: 2220 MVA, 24 kV X,= 1.81 X , =1.76 X'd = 0.30 Y q=0.65 X " d = 0.23 x'q= 0.25 T'& = 8.0 s T',,,=l.Os Y'{"= 0.03 s Yq" = 0.07 s

X,=0.16

R, = 0.003 N = 3.5 KD=O

We modelled the infinite bus with a short circuit reactance of 1 0-5p u on 2220 MVA, 241tV base.

Excitation control data KA = 200 r, = 0.02 s Tw= 1.4 s

T, = 0.154 s

K,yTAB = 9.5

T2 = 0.033 s

Operating condition P = 1998 MW V, = 1.OL36"

Q = 666 MVAr VH = 0.995L0"

296

REFERENCES Dandeno, P.L., P. Kundur and R.P. Schulz (1974). Recent Trends and Progress in Synchronous Machine Modelling in the Electric Utility Industry. Proceedings of the IEEE, Vol. 62, No. 7, July, pp.941-950. IEEE Committee Report (1973). Dynamic Models for Steam and Hydro Turbines in Power System Studies. IEEE Transactions on Power Apparatus and Systems, Vol. PAS-92, NovemberDecember, pp. 1904-19 15 . IEEE Std 1110 (1991). IEEE Guide for Synchronous Generator Modelling Practices in Stability Analysis. Johansson, E., J. Persson, L. Lindkvist and L. Soder (2002). Location of Eigenvalues Influenced by Different Models of Synchronous Machines, presented at the Sixth IASTED International Confcrcnce Powcr and Energy Systems, Marina del Rey, California, USA, May 13-15. Kaberere, K.K., M. Ntombela, K.A. Folly, and A.I. Petroianu (2005). Comparison of IndustrialGrade Analytical Tools Used in Small-Signal Stability Assessment, Proceedings of the AUPEC 2005, Hobart, Tasmania, Australia, September 2528, vol. 1, pp.147-152. Kaberere, K.K., K.A. Folly, M. Ntombela, and A.I. Petroianu (2005b). Comparative Analysis and Numerical Validation of Industrial-Grade Power System Simulatioii Tools: Application to SmallSignal Stability, Proceedings of the 15'h PSCC, Liege, Belgium, August 22-26. Krause, P.C., F. Nozari, T.L. Skvarenina, D.W. Olive (1979). The Theory of Neglecting Stator Transients. IEEE Transactions on Power Appuratus and Systems, Vol. PAS-98, JanuaryiFebruary, pp. 14I - 148. Kundur, P. (1994). Power System Stability and Control. McGraw-Hill, ISBN 0-07-035958-X Kyriakides, E. and R.G. Farmer (2004). Modeling of Damping for Power System Stability Analysis. Electric Power Components and Sy.stems, Vol. 32, NO. 8, pp.827-837. Power System Damping Ad Hoe Task Force (1 999), Damping representation for power system stability studies. IEEE Transactions on Power Systems, Vol. 14, No. 1, pp.151-157. Rogers, G. (2000). Power System Oscillations. Kluwer Academic Publishers, ISBN 0-7923-77 125 Slootweg, J.G., J. Persson, A.M. van Voorden, G.C. Paap, and W.L. Kling (2002). A Study of the Eigenvalue Analysis Capabilities of Power System Dynamics Simulation Software, Proceedings of the 14lh PSCC, Sevilla, 24-28 June.

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

COMPARISON OF METHODS FOR OSCILLATION DETECTION - CASE STUDY ON A COAL-FIRED POWER PLANT Peter Fogh Odgaard "Klaus Trangbaek'

*

Departrnmt of Control Engrneerang. Ralborg Unrverszty, Aalborg, Denmark. { odgaard,ktr) @control.aau,.dk

Abstract This paper compares a selecliori of methods for detecting oscillations in control loops. 'l'he methods are tested on nieasurenieiit da,ta from a, coal-fired power plant, where some oscillations arc occurring. Emphasis is p u t on being able to detect oscillations without having a system model and without using process knowledge. The tested methods show potential for detecting the oscillations, however, transient components in the signa.ls cause false detections as well, motivating usage of models in order t.o remove tlie expect.ed sigrials behavior. Copyright @ 2006 IFAC. Keywords: Oscillation Detection, Coal-fired Power Plants

1. INTRODIJCXION

In addition t,o optimizing controllcrs OF largcscale-closed-loop-controlled plants it, is as least as imporhnt to detect abnormalities in these closedloop-controlled plants. A special set of these abriorrnalities is oscillations. These are harmonic or quasi-liarrrioiiic corriporicrits ill the Irieasureiiicrit. signals. Different problems or faults in tlie plant call cause tliese oscillatioiis. A number of different methods have been suggested for detecting these oscillat.ions in the plant. measureinents. Some methods are better than others under certain conditions, hut this might- change for other conditions and applications. While an unexpected oscillation i s det,ected in the power plant, the subsequent task is to localize the cause of the oscillation, a,nd deal with the cause.

In this paper. six diflerent oscillation detection methods are conipa.red oii a (1at.a set from a. coalfired power plant. All these methods are nonmodel based methods, since models of these large scale plants can be problematic to achieve. 'lhe

detection rrietliod should fulfill the fbllowing requirements detect oscillations. not detect traiisients, detect oscillations during transients, be robust towards different frequencies. and qimple in terrns of tuning parametris In the following the different rnethods are shortly introduced, before the experiments are presented il'his leads to a comparison of the different oscillation dctcction methods on thc mcasurcmcnt data.

2. DESCRIPTION OF APPLIED hlETHODS

In this section six different oscillation detcctiori methods are introduced before they are tested in the following section.

2.2 Minimum Variance The minimuni variance (MV) method (Harris et al. 1999) compares the variance of the signal to tlie lowest achievable variance of tlie control loop.

297

depends on the window length a.nd definition of LF. Ideally, this method should be able to detect oscilla.tions even in the presence of tmnsients. 'The method is subseqiiently denoted DF'I'

'lhus, in order to set a threshold for detection, a.11est irr1a.t.e of t.he achieva.ble variance is needed. This estimate is hard to obtain, and as such. this method is not really snited for the detection of oscillations examined in this paper. 'lhe method is inc;luded oirly as a. reference. Ra.ther than estimating the achievable performance. the variance is taken directly on the signals. The signals are scaled with the maximum values of the sensor measuring the signals.

2.5 Auto Covanance E'unclton The method in (Miao and Seborg 1999) uses the Auto Covariance Function (ACF) of the control error for oscillation detection. Basically, an oscillation ill the control error with a period T will result in an ACF with the sa>meperiod. Furthermore, the damping of the oscillations in the ACF will reflect the damping of the original oscillations. 'l'he advantage is that the ACE' is less sensitive to noise. In the paper; poorly da,niped behavior is detected by looking at the decay rate over a period of the ACF. Selecting a threshold is a.ga.in signal independent. but i~nplerneritingthe scheme to work automatically is difficult sincc effects of tmnsients and noise must be taken into account. In this paper we find the two first peaks of' the ACF from zero crossings of the derivative arid compare thcir rnagnitudc. 1"hc rncthod is subscyuerilly derioted ACE'.

2.2 Knrhurnen Loerie This method uses the Karhunen-Loi.ve basis to approximate the oscillations arid other dornina,t.ing signal components. 'lhe method is described in (Odgaard and Wickerhauser 2005). It uses a set of data fiom different, sensors to conipiite a, basis, with the minimal linear error. If the row vectors in the matrix X are ineasiirements from the different sensors, arid t.he nuniber of samples are larger than the number of sensors. then the KarhunenL o h e basis can be computed as the eigeiivectors of the autocorrelation of X, see (Mallat 1 cornpnt.ed eigeriv-allies correspond to the energy in the signals supported by the related eigenvect,ors. In (Odgaard and Wickerhauser 2005) the variance of these eigenwlues is nsed to determine signal components with high energy level. In addition to detect oscillations and other signal components this niet,hod can as well locate these to specific mea.suremerits/ser~sors.'The method is subsequently denoted KL.

2.6 AZCR

('l'hornhill et al. 2003) uses the zero crossings of the ACF. By looking at the regularity of the period arid the power, a.n oscillation can be detected. The advantage of this in addition to the zero crossings of the signal itself is that the ACF in a, sense provides a filtering. Tn the a,hove paper this is used for detect,ing multiple oscillations a s particular frequency ranges can be separated. In this pa,per we will simply look at all the regularity o f the zcro crossings of t,hc ACF. Again, the t,hreshold selection is signal independent. The method is denoted A Z C X

2.3 Zero Crossing Regularity

A regular oscillation will cross the signal riiea,ii at regular intervals. In the zero crossing regularit,y method the deviation of the intervals between zero crossirigs a,re compased lo lhe mean int,erva,l length. A srnall deviat,iori indicates an oscillation. The threshold select ion is signal independent i t . there is no need for sca,ling the irrdividual signals. On the other hand, noise can causc '*false" crossiirgs a,nd drift, aird transients will destroy the notion of a signal mean. The rncthod will subsequently be denoted ZCK. ~

3 . EXPERIl\ilENTAI, RESTTITS

These different methods for detection oscillations in process data are siibseyuently cornpa.red on a. set of measurement data from a coal-fired power plant. In this applica.tion the following properties are required of oscillation detection methods: detect oscillations, be rion-sensitive to transients in the signals, robust towards change of the window length: and easy to time in terms of para-meters such a.s thresholds.

Detecting oscillations by looking for spikes in the frequency spectrum is an obvious approach that does not seem to have treated thoroughly in literature. In this paper the amplitude of the highest spike outside the low frequency (L1;) area is compared to the tot.al energy in the LF area. The detection threshold i s signal independent but,

In total the data set consists of 87 different measiirenierits sampled in intervals of 30 s. The different, rneasnrernents are scaled relative to their ma,xiinal sensor range. The data is plotted in Fig. I . The measi.irernents c m he segmented int.o a

298

number of parts. From sample 1 to 700 large transients in the signals are dominating, arid almost no oscillations occur. Bet.wcen sample 700 and sample 800 the signals contain neither oscilla.tions or t,ransients. j,F’Com sample 800 to the end an oscillation is occurring in the measurements. From sample 1400 to sa.mple 1800 the signals contain in addition to the oscillation some large transients. Subsequently the different methods’ responses to these test data are plotted, and discussed. ‘lhis leads to a closer inspection of two din’erent time intervals in the measurements. T h e first orre, Interval 1 (700-1100) starts wit,h no oscillatioris or transients and then develops an oscillation, see Fig. 2 . ’this can as a. consequence be used to validate the different methods ability to detect the oscillat~ion.‘Lhe second interval Interval 2 (16002000) contains tlie end of tlie transient area in tlie oscillations, which can be used to irivestigate how thc occurrciicc of tlie t)rarisicritsiriflucricc llic oscillatioris detectiori Tor. the diflererit rrietliods, see Fig 3 . Plo(,sof Interval 1 a,nd Inkrval2 a.re only sliowii fioin inethods in cases where they seem relevant. All the rrietliods have been optimized to given window lcngths and have as well been tcstcd on a window 4 times as long which again was dowiisampled 1o the “norniaY window length in order to validate the robustness of the methods towards diffcrcnt: window Icngths. All thc mclhods, cxccpt KL, are designed with a ”window” length at 256. Due to some properties ol KL it works fine with a “normal” window length al 14. 1.e. llie KL should detect the oscillations much faster. ‘l’he different methods are now tested in the order that they were present,ed in Sect,iori 2. In all t,he subsequent plots of the results of tlie methods, the lower plots show a detection signal, which takes the value 1 in d compared

The entire response to test da,ta of M V can be seen in Fig. 4. From this plot it can also be seen that both window lengths result in responses depending mostly on the transients in the signals, which are, however, expected. All in all it means t.liat, t,he M V cannot, be iiscd to det.cct oscillations in the set, of test dat.a.

299

I ,ma

5"O

1500

sampios ["I

2500

2W0

I

Normal Ir creared

08

B

07 6

10uo

500

zw0

im

s m p , e s I",

02

?son

1600

Figure 5 . Tlie response of KL applied to the test data.

1650

1700

1750

1800

Sampler ("1

Figure 7. The response of 2 of the test data.

18W

1'3W

KI,applied

1850

1

70W

to Interval

101

(0

d 10

(0'' 700

I::/

750

850

800

,

,

750

8on

;

,

9W

950

sampios ("1

,

~

1000

1050

,

,

loon

m50

07

1100

1

0

ni

700

850

OW

950

lion

sample3 ["I

Figure 6. The response of KI, applied to Interval 1 of the test data.

Figure 8 . The response of ZCR applied to tlie test data.

3.2 Il'rst of KL

10

The entire response to test data of' KL can be seen in Fig. 5 . From this figure it is seen that KI, responds stronger on the transients than the oscillation, but still significant enough on the oscillation to detect it. Another interesting observation to be made is that the window length seeiris to be of low significance for KL. 'l'he first zoom, see Fig. 6 and second zoom, see Fig. 7, support the observations froin Fig. 5 ; i.e. KL detects the oscillation fast, but reacts stronger on the transients. In additioii the KL is robust towards the change in window length.

3.3 Test of ZCR The entire response to test data of ZCR can be seen 111 Fig 8 From this plot it can he seen that ZCR detects the oscillation with a delay. It reacts on the trarisieiits as well IIowever, it does not respond strongly during the beginning and cnd of the transients In addition it is strongly depending on tlie window length The first zoom in Fig 9, ilhrstrates the delaycd dctection of the oscillation The oscillation i s dctected approximately at sample 850 whcrea\ thc nsrillation starti a t sample

$ in'

Figure 9. 'l'he response of ZCR applied to Interval 1 of thc tcst data. 800. A similar observation can be made from the second zooin, Fig. 10, in which the response slowly increases after tlie end of the tra.nsients approxiLJlakly ?it b?iIIJple 1800. 3.4 ilkst of DFY' Tlie entire response to test data of DFT can be seen in Fig. 11. This plot shows that, U F T detects the oscillat,ion arid does not. give a false a1a.rni on the transient. However. there is no dekction of the

3 00

Figure 10. The response of ZCR applied to Interval 2 of the test data.

Figure 13. The response of D F T applied t o Interval 2 of the test data.

Figure 11. The response of D F T applied t,o t,he test data.

Figure 14. The response of AZCR applied t o the test data.

3.6 l k s t of AZCR

Figure 12. The response of D F T applied to Interval 1 of t’he test’ dat’a. oscillation during t,he transient,. The response is clearly dependent on tlie window length. Similar observations can be drawn from t’he t’wo zooms, see Fig. 12 and Fig. 13. 3.5 Test of ACF

The test of the given irriplerrieritatioii of tlie method does riot work for this given data set. the response hardly seems correlated with anything in the data.

The response of AZCR 011 the t’est’ data can be seen in Fig. 14. By inspect,ing t,liis plot a number of inkresting observat,ions can be made. AZCR responds 011 the oscillat’ion, but as well 011 the t,ransient,s.Anot,lier observation which can be made is that t’he method depends strongly on the window length. Froin tlie zoom 011 the begiriiiiiig of t,he oscillat,ioii, see Fig. 15, it can be seen t,liat AZCR responds 011 t,he oscillation, but, with a delay. The plot of the second zoom, Fig. 16: shows that’ AZCR react’s 011 t’he transients but’ recovers fast t o the response of the oscillation when the transients have ended.

3.7 Summary of experiments Table 1 summarizes how well the crit,eria to t,he oscillat,ion det,ect,ion schemes have been fulfilled by t,he tested schemes. The first, column “Detect,s oscill.?” sinnmarizes t,he abilit,y of the individual methods t o detect oscillations, The coluinri “Det. dur. t,rans.” list,s if the individual methods can detect oscillations during transients. “Transients only” lists if transients tend t o cause false detections of oscillations, “Threshold” summarizes

301

n

11

Detects oscill.?

I

Det. dur. trans.

I

'L'ransients only

I

Threshold

I

Par. sensitivity

u

'l'a,k)le 1 . 'lk.hle snrnmarizing how well the diff'erent, methods fillfilled t h e reqiiiremenks to the oscilhtion detection method.

t

-02

700

1

150

800

850

9W

9M

1000

1050

liO0

banlples in1

Figure 15. The response of AZCR applied to lntcrval 1 ol the tcst data.

oscillations. Another drawback for this method is its strong dependency on the window length. 'l'he two remaining methods; ZCR and AZCR respond on thc oscillation wit,h a delay. They do not rcact as strongly on the t,rarisients a s KL does, but still too st,rong for separating transient responses from oscillations. ZCR and AZCK. do as well deperitl on t,hc window lcngth. Sincc all rncthotis havc problem with transients it. seems necessary to remove those from the data before the oscillation detection methods are applied. One way to do this is to compute a residual formed by measiirernents arid estimated signals from a system model. Oscillations can be difficult to detect in the magnitude of the residual since it would oscillate. Instead, one of the oscillation detection scheme can be applied to the residual. If obtaining a. model is not a realistic option, either KI, or I>FT methods appear most viable. The choice depends on the need for detecting oscillatiorw during transients versus avoiding false detections.

5 . ACKNOWLEDGMENI'

o.

-

~

'I'he authors acknowledge the Danish illillistry of Sciencc Technology and Innovation. for support to the research program CMBC (Center for Model Based Control), grant 110 2002-603/4001-93

~~~~~~~~~~~~~

REFERENCES Harris. T. J.: C . 'I?. Seppala and L. D. Desborough (1999). A review of performance monitoring a.nd assessment techniques for univariate and te control systems. Journal of Process Control 9(1)>1-17. Mallat, S. (1999). A mavelet tour of szgmd processing. 2nd ed.. Academic Press. Miao, 1'. and D.E. Seborg (1999). Automatic dctcctian of cxccssivcly oscillatory fccdhack control loops. In: IEEE Inlernational Conferen,ce o n Control Applications. Hawaii, 1JSA. pp. 359-364. Odgaard. P.F. and M V . Wickerhanser (2005). Karhunen-lo2ve based detection of multiple oscillations in multiple measurement signals from large-scale process plants. Submitted for publicat ion. 'I'honihill, N.F., B. Huang and H.Z21a.ng (2003). Detection of multiple oscillations in control loops. Journal o.f Process Control 13, 91-100.

4. CONCLUSION Thcsc cxpcrimcnts with thcsc diffcrcnt oscillation detection methods, have given sonie interesting results. Two methods could not in the given data set detect the oscillations, thrse are WIV and ACF KL responds strongly enough on the oscillation in the test data to detect it, hut responds even stronger on the transients Ilowevei. this method does as the only method give similar results for both window lengths DF'I' responds to the oscillation and not to the transients, However, as a consequence of t h e occi~rrenceof transients it cannot detect

302

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

LOW LOAD MODEL OF A ONCE-THROUGH BOILER WITH RECIRCULATION Klaus Trangbaek

Abstract: A dynamic sirnulation rnodel of a. once-t,hrough boiler in low to medium load is developed. When the syst.em is in low load; water from the evaporator is recirculated t-hrough a hott-lc. 'l'his recircnla,tion system is includcd in thc model, which is then shown to fit closed-loop data. from a real plant nicely. Copyright 0 2 0 0 6 IFAC Kcywords: Hydrothermal powcr systems, model approxiination, simulation.

1. INTRODUC?'ION The increasing liberalisation of the energy markets has led to a, grea,ter need for operating power pla.nts in ways for wliicli tlicy were not designed. For instance, plants designed to work a.t base load for most of the tirne are suddenly required to take part in 1oa.d regulation a.nd to operate at low 1oa.d for extended periods of t.irne. 'I% leads to a. rieed for i.econsidwing the cont,id strnctnre at, lorn 1oa.d. In order to do this it is nece simple dynamic model of the plant which is able to simulate 1oe.d hansients in low to niediuni 1oe.d. In this paper a model is developed for a 400 MW once-through boiler. When opera.ting this plant in low load, feed wat,er is recirculated leading to a, dynamic behaviour very different from tlie oiie in riiediurrr to high load, cspecially if t . 1 eritlialpy ~ of llie recircrrlated water is nirrch higher than (,hatof tile rresil reed water. Apart froin (Eitelberg and Boje, 2004), it seems t.liere are no dynamical models of this syst.eni described in 1it.erature. In this paper eniphasis is

' Supported by Eltra PSO grant 02-4114. The author would like t,o thank Babak hlataji et al. of Elsarn Erigirieering for kind support, and Prof. Edward Boje of U. of KwaZulu-Natal for useful advice.

put on acliieving a simple nonlinpar niodcl that will work in the range from low to medium load.

2. LOW LOAD OPERATION

'l'his section describes the system modelled in this paper. Some of the details are specific to the particiilar plant and may not hold in general for once-t,lirorigh boilers.

T h e boiler system considered is shown in Figure 1, where 3 syrribolises a hea,t input. In rriedium

to high loa.d, the boiler operates in once-through mode (O'ILI) meaning that the feed water passes through the high pressure pre-hea.ters (HPPH) and economiser to the evaporator where it fully evaporates int,o stearn. The stearn then passes to the superheaters: where it is 2iea.ted before passing t,hrough the (fully open) t,urbine valve to t,he high pressure turbine. and Loosely speaking, the outlet pressure, PhlL, temperature, 2 $ h , are controlled by the fuel flow ri?,fuei to t,he furnace and the feed water flow ri?fUl.

When tlie load and hence the Fuel flow is decreased, tlie feed water flow i s also decreased in order to maintain the desired stearn temperature and flow. However! a certain rninirnum Aow, rhmin! of' feed water is required in order to prevent dam-

303

some we,ter can be returned to the bottle throi.igh

m

--"(

lSh

s'h

5

To HP turbine "turb

'"out

&++ -x?- uperheater 2

~ R M F .

'l'here is a significmt difference in the dynainica,l bchaviours of the systcai in Ol'M and in RCM. In particuhr, if' tlie recirculated water is much warmer than the fresh feed water, non-minimum phase behaviour is iritrodnced, since iricreased recirculation in order to lower thc water lcvcl in thc bollle lends lo waririer ked waler (will] it larger specific volume); which in the short term increases the output flow from the evaporator, leading to an increased bottle level. Furthermore the systeni in H.CILI is less c o n t r o l l d e since the fresh water flow is bound by the minimum flow restriction, arid less obscrvablc since the cvaporator output temperature is given by the pressure and tlms contn.ins no informtition on thc st.cnm cnt.halpy.

3 . SIILIULATIO1v hlODEL

In this section the development of a simulation model of the above system is discussed. 'The aim is to obtain a simulator on which to examine different control stra.tegies for a pa.rticular plant. The pasarneters of the model are tuned using a. few easily obtn.ined physical parameters and measurement da.ta from closed-loop operation. Since the aim is controller design, the focns is on dymmic behaviour rat.her than stat.ic characteristics being exact. Furthermore, the model is required to be of rehtively low order and reasonably hst.

Feed water pump

'l'he model is required to operate from the lowest practical load (15%$)to aicdium load (50%) and to be able to handle transitions between RC'M and O1'1CI. Supercritical operation is not required.

Fig. 1. Y'he high pressure steam system. age t,o the evaporat,or tubes. Thus, at some point rj2pu, is mainhined a,t kmin even though the steam temperature is lower t,han desired. This also rneaiis that the stearn leaving the emporator is not. fully evaporated. The separator extracts the water, so that only saturated stenni is led to tlie superheaters. The ext,ract,ed wat,er is led t,o the bottle which acts as a srrrall buffer. In recirculation mode (RCM) t.he water in the bottle is recirculated to the feed water.

I f . '-

the

r,

I he main components of the recirculation system are the recirculation pump a.nd the recirculation valve wT. rl'he pump operates a t consta,nt speed and the valve controls the water level in tlie bottle through the recircula.tion flow fn,. Since the water leaving the bottle is close to saturation, it is irecessary to a.dd coolairt through w l y p s ~ , which is always fully open when t,he pump is on. Furthermore, in order to mainta.in a. suficient flow in the pump, when the required r j l , is low,

Fig. 2. A basic control volume.

The econoniiser, evaporator and superheaters are each modelled by a. lumped parameter control volume as shown in Figure 2. A control volunie IC has three state variables: steam mass AT,, steam enthalpy I/, , and wall temperature Ti,,,. The steam pressure P, and temperature 2; are determined by steam tables (Wagner. 2000) from the specific etitlia.lpy h, = f f , / h f , a,nd specific volume w, = K T / M , where KT is the steam volume. 'l'he niass flow between two volumes is determined by the pressure difference between them, i.e ~&-,+1 = c,,,+l(P, - 9,+1); where c is some constant. In a sense, this ineans that

3 04

the coiitrol volumes a.re split into a voluine with a inass and energy balance and a pipe across which the pressure drop occurs. 'l'he specific enthalpy of lhe steam flow oul of a. control volume is given by the specific enthalpy in that particular volume, whereas t,he input flow will have an eritlialpy specified by tlie preceding volume. This type of spatial discretisation has several advantages wlieii the objective is to rnodel dynarriic behaviour; it is simple a.nd leads to ordinary differential equations. Furtlieriiiore, using a biliiiea,r discretisation such as a ceiit.ra1 difference schenie tends t.o introduce unrealistic non-minirnuin phase bel-iaviour. This is not a problem when using a, backwards difference type scheme as the above. On the ot.lier hand, it may be difficult to obtain a good static fit in a. widc range of operating points, but this is considered as a minor problem here. A further simplification is the heat input from the furnace to the wall. 'l'he energy flow is simply modelled as the fuel flow multiplied by a coiist.ant gain for each control volume.

3. I Separator and bottle

Ideally, when steam in a 2-phase condition enters lhc (cyclone) scparalor, saturalcd water is separated and led to the bottle, whereas the reinainiiig saturdled steam IS led to the superheaters. To compensate for pressure differences, there is a lube from lhc lop of the botllc to tlic inlct of the superheater. as illustrated in Figure 3 I

r&hIe

= ritchtc

+ riJt,z.

(2)

In general? this results iii a steam flow from sepa.rator to bottle and then into tlie superheater. In steady state the resulting net flows are the same as with perfect separation, and the transient behaviour is almost the same! but this method tends to be softer on the eqimtion solver. Another issue is the output flow a.t the bottom of the bottle. When there is a flow of coolant through the L'RArJ7 valve to the bottom of the bot,t>le,the specific ent,halpy a.t the bottle out,let, can be considerably below saturation enthalpy. To model this properly it i s necessa.ry to split the bot,t,le model i1it.o a.t least t,wo control volumes. Here, we let the hott,le model consist, of t,wocorit,rol volnrnes, one at the top with the same steam volume a.s the actual bottle ha.ving steam inass a.nd eritlialpy as state variables, and a smaller oiie at the bottom with only enthalpy as the sta.te variable, liavirig a constant mass. Thus the mass flow from the top to the bottom volunie equals the net flow out of the bottom, i.e %r minus the coolant flow.

3.8 Parameter adjustment

I

i: separa

Fig. 3. T h e separator Assuming perfect separation, we would have (referring to Figure 3) m,h,

t,he pressure drop from evaporator to superhea,ter and bottle, respectively. The specific ent,halpies are then determined from he, i.e. if the dryness fraction a,t the evapora,tor outlet is higher than & / ~ c then the flow into the superhea.ter will have specific entha.lpy hz: and h, will be giveii by

+ m,hz,

= mlLhl

(1)

where hi and h~ are the saturation etithalpies at the appropriate pressure. Thus if for instance riz, or riz, 15 known, then the other two flows will be given. I'hus. one approach would bc to compute the evaporator outlet flow from tlir pressure drop from evaporator to superheater aiid then get mA or rkul from (1). However, this approach tends to be a bit rigid, inakiiig the differential equations hard to solve Instead, we will take a different approach letting the flows Ij%, or riz, be controlled by

The model is adjusted to fit a set of closed-loop data froin a 400 MW gas fired plant. 'l'he plant is a.n important part in compensa.ting for changes in elcctricity consumption on the nct,, nrcaning that there is a dearth of steady state data, especia.lly at low load. However: fitting the &tic characteristics acciirately is less important than getting the dynamic behaviour right.. A bigger problem is the closed-loop iiature of the data, but since no open-loop data are available, a choice mist be made on where to break the loop when simulating, i.e. which controllers should be included and what should act as exteriial sigiials when trying to make a siniula~tionfit the data.

In RCM the system is open-loop unstable, but is stabilised if a. feed water flow controller keeps r i z f w at rizman (or at some other reference, e.g. from a temperature control) and a bottle level controller keeps riz, proportional to the bottle level L. 'Therefore, all water flow controllers are applied in the simulation when tuning the parameters. As noted in (Eit.elherg and Boje; 2004), t.l-iese loops interact heavily and improper tuning can lead to insta.bility. However, since the ba.ndwidt1is of these

305

loops are fairly high, this issue is riot relemnt, in t,he frequency range or int,erest. In ot,her words, any sufficiently fast and stabilising flow loop controllers will do.

it is noted that the outlet, pressure follows the rnea.surernents nicely. The same goes for the evaporator outlet temperature, which is unsurprising, since it merely the saturation temperature in this mode. Thus, in order to evaluate the evapora.tor model it is necessary to look at the bottle level or the recirculation flow. Unfortunately these rneasurements are extremely rioisy, so it is bcttcr t,o look a t thc valvc positions vT and V R A I F . Note that. no effort has been put into a,djusting the valve models, so steady state levels should not be expected t.ofit. However, the general shapes fit nicely indicating t,hat t,hc evaporator and recirculation system are modelled correct.ly, The superheater outlet temperatures a.re not fully satisfact.ory. Achieving a, better fit would probably require a more thorough nonlinear model of he& tmiisfer from furnace to wall, or possibly splitting the superheater into several control volumes.

Essentially the fnel flow, feed water flow, a.iid turbine valve are nsed for controlling pressure, temperature, and flow at t,lie outlet. 'l'hese cont.ro1 signals contaiii both feedback p a t s from disturbarice corripcrisatiori arid feed-forward p a r k frorn load changes. When fitting to closed-loop data it is of course irnportant to kecp in mind that, some mcasurcmcnts, e.g. superheater outlet temperatures: are in reality controlled outputs. If' the controller is included in the simulation then of course the simulated out.put will fit the measurement. What should then he evaluated is if the control input, e.g. t.he feed water flow, looks like t,he rrieasiired input. If' the model is simulated withont the controller present, the simulated output should not be expected to fit the rneasnred outpnt nicely.

Figure 5 shows a siniula.tion in OThl at medium load. Here, the inputs to the simulator ase the measured fuel flow and feed water flow, where tlie latter is wed as a reference for the feed water flow control. Both the evaporator outlet temperature and the outlet, pressure fit very nicely. The SIIperheat.er t,emperat,iirt.s fit reasonably well. These a,re essentially coni.rolled oi.iiput.s, so a hei.ter fit) should probably not be expected from this openloop siniulation.

Since the objective is a model for controller design, it is chosen to let, the three signals act as openloop inputs in the simulation when fit,t-ingto data. Thus, the only part. of the cont,rol syst,cm, which h a s been included in the model is the water flow loops. Acting as inputs (boundary conditions) are feed water flow reference, fuel Row, injection flows, and turbine valve set,ting.

The transition between modes also works satisfactorily, but, it is difficult to do a direct comparison with nieasurement data, since the exact timing of achieving full evaporation is crncial to the overall bcliaviour .

The ma,in paraaiet,ers t,o adjust ade the hea,t input gains, pressure drop to flow gains, stea.m volumes, arid wall lieat capacities, where the first two are nia,irrly acljuslcd to fil stcady slate siluations arid llie l a t k two are irsetl lor i-tdju s h g (,lie tlyriairiic behavionr .

Finally! a few reinarks on experiences frorn the modelling:

Evaluating the evaporator model is somewhat difficult, sincc when in OTM the fccd water flow arid fiiel flow are heavily correlated. We can therefore not be entirely certadn that the model will work for inputs that are riot correlated in t,he same way. When in RCM, tlie measured ev-apora.tor out.let temperature is useless, sirice it is merely the satura,tion t,ernperature. There are no flow measnremerits showing the fraction of steam that flows to the superheater, so we have to rely on the bott.le level rneasnremerit, which is quite noisy.

r ,

1lie recirculation coolant flow can be large arid, since it is quite cold, significantly a.ffects the system behaviour. Getting the flow right in the simulation is difficult, since it has to be estimated from terriperaturr rneasurernents, and these tend to give unreliable estirnafes. Adding the small volume at the bottom of tlie bottle results in a correct outlet temperature most of the time, but perhaps splitting the bottle into a stearn volume and a wall with heat capacity would achieve the same, arid possibly even make the transient response more correct. The proposed model is not very flexible in terms of being a.blr to modify the dyiiamic behaviour by adji.isiing t h e parameters. Tf the xhieved behaviour is not acceptable, it is probably necessary to split the individual control volumes into two or more sma,ller volumes. This wonltl make it possible to motlify the transient behaviour without affecting

3.3 Sirnulutron model results

1 ' he tuned model is tested with dnt D sets not nsed for tlie tuning. Fignre 4 slio~vsa sininlation in RCM. where tlie input to the sirnulation model. shown in the first two plots, is the measured hie1 flow (scaled for confidentiality) and turbine valve setting (fully open). The remaining plots compare the simulation result to rneasurernents

3 06

fuel

bottle level [m]

turbine valve [0-I]

1.27 -1 I 4.5

0.8 25

O'g

I

recirc. flow [kg/s]

4

0.8

3.5

recirc. flow temp. [K]

bottle outlet temp. [K]

550

7

500 450 I

400 I

evap. outlet temp. [K] 595 I

superheater 1 outlet temp. [K] 800

700 0

I

50

100

150

superheater 2 outlet pressure [Bar] 1051

90' 0

Time [min]

50

100

'

150

superheater 2 outlet temp. [K] I

740' 0

50

Time [min]

100

I

150

Time [min]

Fig. 4. Siiniilation in RCM. Solid, blue: siinidation. Dashed, red: measuremriits. Ilhdtiple measurement lines are due to parallel superheater strings. Fuel measurernent scaled for reasons of confidentiality

feed water flow [kg/s]

fuel

evap. outlet temp. [K]

* 7 140

0.5 I superheater 1 outlet temp. [K] 900 1 -

700 I*--

I '

80' 550 superheater 2 outlet pressure [Bar] superheater 2 outlet temp. [K] 900 850

800 800 700 I 0

I

200 400 Time [min]

600

0

200 400 Time [min]

600

750

0

Fig. 5 . Simulation in O'lM. Solid, blue: simulation. Das'ried, red: measurements

307

200 400 Time [min]

600

r l

Ihis approach works very well in the small load range a.bove. Closed-loop simulation results with the EI'V inodel are practically iridistirigiiisha.hle from those of the nonli~iearmodel. However, extending the method to a wider load range causes problems. rna.inly in choosiiig a suitable scheduling pa.rameter. Using the reference pressure works fine for the above range and for O'lM, but the significant differences bctwccn the two modes makes it dificult t o perform a smooth transition. Another problem a.rises when moving to a lower load. Here, the pressure is kept above a minimum by pa,rtially closing the turbine valve. Thus, t,hc pressure is no longer useful a.s a scheduling parmieter. These problems remain a.s yet nnsolved. Employing ve1ocit.y-based 1inea)risations (Leit h and Leithead, 1999) may be part of' the solution.

the steady state performance. but would of course makc tlie model slower. The model has been verified with closedloop data only. There i s no way to tell if it will behave correctly if the control system is significantly altered

4. LINEARISEL) MODEL APPHOXII\/IA"lOn'

The niodel is of the 15th order and somewhat slow (approxirnately 4 times fa.ster than real- time). For extensive studies of cont,rol strategies a much faster model would be an a.dva.nta.ge.Possibly, it could be made faster rising singular pertrirba.tion techrriyues (Kokotovic et ul., 1976) or quasi steady statc modelling as dcscribcd i n (Eitclbcrg and Boje, 2003), but the slowness seems to be caused by the bottle, making it difficult to separate fast and slow dyirarrrics. A inore geireral nuinerically based nonlinear model order reduction method (e.g. (Fujinioto a.nd Schrrpen, 2004)) might be considered instead.

5 . CONCLUSIONS

A simple dynamic simulation riiodel of a oncethrough boiler has been developed to fit inea.suremerit data well both in recirculation and in oncethrough mode. Further work will focus on making the model execute faster, since the current speed is riot entirely satisfactory. A first step was taken by a local 1inea.risation approach, but it is unc1ea.r if' this will work i n general and how to perform rriode cliariges lo arid l'rurri OTM. Apart frorri the relative slowness, the model has already proven very useful in trying out new control methods.

As a first step on the way t o a faster model, a local lineasisation approach has been tested in a relatively sniall load range, where the system is in RCh.1 with a fully open turbine valve. 'lhe simulation model including flow controllers is liriearised at reference pressures 90,92,94.96:98.100, and 102 bar, resulting in 7 linear models with corresponding equilibrium points (zo.~, ~ 0 , ~ Even ) . for this relat.ively small load range, studying these linearisat ions show that there a.re significant nonlinearities.

REFERENCES

A linear time varying (LTV) niodel is now constructed from the linear models. 'I'he schedulr is chosen as tlie reference pressure

rather than the actual (simulated) pressure in order to avoid some of the problems of hidden feedbacks. For R given reference pressure P,. we will then select t,he two nearest linearisations A l l = ( A l . 5 1 ) and A12 = (Az,R2) given by their individual sta,te space matrices, a,nd a scheduling gain r ( t ) bet,ween 0 and 1, so t,hat we have the interpolated linearisation ( A ( t )B , ( t ) )= r ( t ) ( A lB,1) (1 - r ( t ) ) ( A 2H2) , with corresponding cyuilibrium point ( ~ g ( t ) . u g ( t ) ) = y(t)(.xg,l,ug.l) (1 ~(t))(x0,2 ~ ,0 . 2 ) .Note that this only inakes sense because the state variables have a specific meaning common to the two linearisations. The nonlinear model can now be approximated by the linear t.irne varying model

+

+

--

d2'(t) dt

~

+ B(t)(u(C)

A(t)zl(t)

-

uo(f))

-

dZo ( t ) $t'(")

where the state in global variables will be z ( t )= ~ [ ( +t ~) g ( t ) . Tlir last term in ( 3 ) niay have to be discretised in time ill order t o implement it.

Eitelberg, Eduard and Edward Boje (2003). Quasi steady state modelling of an evaporator. Proc. African Control Confe Eitelberg, Eduard a.nd Edward Boje (2004). Water circulation cont.rol during once-through boiler start-up. Control Engineering Practice 12(6), 677-685. Fujimoto, I(. and J.M.A. Scherpen (2004). Ralancing and model reduction for discrete-time nonlinear systems ba,sed on hankel singular value analysis. Proc. 16th Int. Syrnp. Malhem u t k a l yy~eoryof Networ.ks a d Systems. Kokol,ovic, P. V.: R.E. O'hlalley a i d I). Sannuti (1976). Singular perturbations and order reduct,ion in control theory. Autovimtica 12. 123-132. I,eit.h, D. J. and W. E. Lcithead (1999). Aiialyt.ic fra.mework for blended multiple model syst.cms using linear local modcls. Intcmationul Journal of Control 72(7-8), 605-619. Wagiier. W. et al. (2000). 'l'he IAPWS industrial formulation 1997 for the thermodynaniic properties of water and steam. A S M E Journal of Eng. Gas I'urbines and Power 122! 150182.

308

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

SEMICROUP BASED NEURAL NETWORK ARCHITECTURE FOR EXTRAPOLATION OF MASS UNBALANCE FOR ROTATING MACHINES IN POWER PLANTS Byoung-Hee Kim, John P. Velas, and Kwang Y. Lee

Department of Electi+icalEngineering, The Pennsylvania State IJniversity University Park, PA 16802, IJSA Abstract: In this paper we focus on an investigation of a mathematical approach to extrapolation, using a combination of a modified neural network architecture and the semigroup theory. Semigroup theory provides a unified and powerful tool for the study of differential equations, partial differential equations and combinations thereof. The target of this investigation will be the prediction (by way of extrapolation) of the mass unbalance of the rotating component in a power plant. Simple mass unbalance system is considered for the simulation purpose. A new technique is proposed for measurement of vibration directly from rotating component using extrapolation. Copyright 0 2006 IFAC Keywords: mass unbalance, vibration, neural network, extrapolation, power plant, semigroup.

1. INTRODUCTION Avoiding destructive vibration is of major imporlance in the lurbine-generalor in a power planl. Mass unbalance is the most common source of vibration in machincs with rotating parts. Balancing of rotors prevents excessive loading of bearings and avoids fatigue failure, thus increasing the useful life of machinery. There are many studies on the vibration subject and most of those studies are hased on linear modeling (Florjancic, et al., 1998; Selig and Ding, 2000; Ahmad, et al., 2001). It was found, however, that linear rotor dynamics cannot account for an unbalance as it had occurred. In addition, a linear model is not sufficient at high frequencies (Florjancic, et al., 1998). During transient loads, furthermore, extreme conditions have been observed and efficient methods and tools to analyze such cases are of primary interest to the industry. Vibration has been notoriously difficult to measure, and most reported measurements have used accelerometers attached to a stationary housing carried by a retrofitted bearing mounted on the shaft of interest. Thus, the theory may not well predict the coupling of rear axle motion and bending resonances in the drive shaft. Furthermore, it is difficult to take vibration measurement if a shaft is rotating. The objective of this research is to develop a method of estimating the rotational mass unbalance, which is the most common source of vibration as it pertains to the turbine portion of a power plant, by introducing a

system-type neural network architecture from a sparse set of test data. One of the most important applications of vibration analysis is the solution of balancing problcms. An unbalanced rotor or driveshaft will cause vibration and stress in the rotating part and in its supporting stmcturc. Balancing of a rotating part is therefore highly imperative in order to minimize structural stresses, minimize operator annoyance and fatigue, increase bearing life, or minimize power loss. In this paper, a new method of estimating vibration on a turbine-generator is proposed using mass unbalance extrapolation based on a system-type neural network architecture, i.e., the semigroup based neural network architecture. Essentially, rather than relying on inaccurate vibration measurements, this method extrapolates a set of reliable mass unbalance readings from a common source of vibration. Concerning the issue o f extrapolation, a global need for extrapolation exists in many diverse areas (which will be highlighted in Section 2). In the case of the power plant, the opportunity for extrapolation of temperature inside of boiler furnace (Kim, et al., 2005a) and enthalpy in steam delivery section (Kim, et al., 2005b) also exists in a unique way. In Section 2, the general approach for extrapolation will be presented and the newly proposed approach will be presented in Section 3. In Section 4, the proposed approach will be simulated on empirical data. Finally, we make some conclusions in Section 5.

309

2. BASIC THEORY 2.1. The General Problem of Extrapolation Concerning the general problem of extrapolation, there are two points to be made. One, the need exists for a universal type of extrapolation; two, at present, each extrapolation problem is solved by developing a tcchniquc specific to thc problem. For cxample, referring to (Jangamshetti and Guruparasada, 19991, the authors extrapolate a set of capacity factors (at the ground level) for a wind turbine generator in the altitude direction. In this case, the extrapolation is based partly on the assumption that the power law, which describes the distribution of capacity with height at low altitudes, also applies in a modified form at high altitudes. The extrapolation is also based partly on the use of the Weibull statistical distribution model. As a final example, in (He, et al., 1994), the authors develop a method for extrapolating in frequency a set of radar readings, based upon the use of the Papoulis-Gerchberg iterative method. In summary, there are numerous applications for extrapolation but, at present, there is no universal method. As a contrast, the proposed method can be applied generally; there is no need for individual customization (Kim, et al., 2005a, b). 2.2 The Specific Problem of Extrupolation Jbr a Turbine-generator in a Power Plant

Fin. 1. Simnle mass unbalance svstem. engine speed, Because of abnormalities in the normal manufacturing process, some irregularities in the mass distribution are always present, which become the origin of mass unbalance. As a result of the above, variable disturbing forces occur which produce vibrations. To remove these vibrations and establish safe and quiet operation, balancing becomes necessary.

3. PROPOSED METHOD

In this paper, a new mass unbalance extrapolation mcthod is developed. Very bricfly, the method is implemented with a new neural network ( N N ) architecture which consists of two cooperating NN’s, one of which develops a functlon space and the other one of which selects a particular function from within that space. 3.1. PhiluresiShortcomings of Conventional iVN k

There are various sources of vibration and there are various vibration models. The most common and the most important source of vibration for rotating equipment is mass unbalance, and to illustrate the proposed procedure, the most elementary physical model will be assumed. The physical system consists of a shaft carrying a mass at its midspan and having a small mass unbalance, as shown in Fig. 1 . In general, the resulting vibrations can be complex, depending primarily on the geometry of the system. In this case only the simplest forms of transverse vibrations along the longitudinal axis of the shaft are being considered. As one example of a more complex vibration that’s being ignored, mass unbalance can be coupled to shaft whirling. If a shaft, driven at constant angular spccd w, also deflects bccausc of shaft resonance, the centroidal axis of the shaft will break down. In general, it takes a long time to startup thc turbinc in a powcr systcm. That is, thc start-up proceeds in a series of steps, along each of which the speed is held constant. The total start-up time may take up to 18 hours. Therefore, if at any point during the start-up, we can anticipate the mass unbalance at a future step, we can balance it to avoid vibration.

Recently, a Shift has occurred in the overall architecture of neural nctworks from simple or component-type networks to system-type architectures. The most popular architecture seems to be the one advocated by Jacobs and Jordan (1 99 1j, called the “Modular Connectionist Architecture,” one example of which is shown in Fig. 2 (Atiya, et al., 1998). It consists of a collection of expert components, each being trained independently, tied together by a component called the “gating logic” element, whose function is to decide on the relative contributions to be made by each expert component, such that when they are added, they provide the correct output for a given input. The present proposed method represents an adaptation of Fig. 2. The most serious flaw in the design of system-type neural networks is the lack of a cohesive discipline in the architectural design and in the design of the

For simulation purposes, the simple mass unbalance system will be considered to be one integral mass, M, which represents the rotor mass, along with a small mass unbalance offset (mr) mounted on a stubby shaft and supported at the two ends by its own bearings which have nonlinearity, as shown in the Fig. I . The damping (C) is assumed linear.

L

“lt,llfI”f”

t --- j ‘

7-~”(I)YO)

Fig. 2. Modular connectionist architecture. The unbalance force presents itself as a harmonic forcing function with a frequency that matches the

learning algorithm. Virtually, the entire design is done on an intuitive basis. As a contrast to intuition, 310

the proposed method relies on semigroup theory for the design of the semigroup channel. To illustrate the lack of a cohesive discipline, in (Atiya, et al , 1998), the partitioning of components corresponds to the separation of variables, which works if the variables are separated and does not work if the variables are not separated (Lee, el al., 2004, Kim, et al., 2005a, b).

The similarity between the mapping F(co, A ) proposed architecture (Fig. 3) and that of Fig 2 anses from the fact that the function channel is implemented as N “expert” systems The function channel can have a Radial Basis Function (RBF) architecture (Haykin, 1999). It consist^ of n RBF networks, each one of which implements one orthonormal vector of an n-

3.2. lielationship qf semigroup theory to A I W design

IA

The semigroup approach begins by asserting that certain functions are to be re-interpreted as follows: under certain circumstances, the function F ( w ,A ) should be thought of not as one map, but rather, as one family of maps: ( F 9 ( A ) , uG[O,Q]} which, in turn, is produced by a second family of maps ( @ ( w ) } where the two families are related by the following:

I

!

1 -

Function Channel

Semi-group Channel (”2) I

I

!

Fig. 3. System-type architecture. dimensional basis set of vectors E ( A ) . The outputs of the orthonormal vectors are (internally) linearly summed so that the channel spans an n-dimensional function space. The coefficients which determine the linear sum and thereby define the specific function being implemented is supplied by the semigroup channel. Up to this point, the operation of the RBF channel parallels the idea used by Phan and Fmeh (1996).

where

This interpretation suggests that the mapping must be achieved with a pair of neural networks, one that selects a given function at each value of o and another that then implements the chosen function. This interpretation also places severe constraints on the “selecting” neural component, forcing it to take on the generic semigroup behavior (3).

One of the essential differences between their approach and the present proposed approach is that the former requires prior engineering knowledge for selecting the basis vectors, and the latter approach requires no such knowledge. One advantage that RBF networks have over other architectures is that their functionality can be given an explicit mathematical expression in which the neuron activation functions act as Green’s functions (Tikhonov, 1973). This makes these networks amenable to design rather than training. Another advantage is that they function as universal approximators (Haykin, 1999). Thc scmigroup channel can be adapted from the Diagonal Neural Network (DRNN) (Ku, et a/., 1992; Ku and Lee, 1995), the Time-Lagged Recurrent Network (TLRN) (David and Donald, 1992) or Simple Recurrent Netwrok (SRN) (Elman, 1990; Haykin, 1999), in which the input is split into a dynamic scalar component w and one static vector component, the vector C ( 0 ) .The output is a vector C ( W ) ,which is related to the dynamic input w and to the static input c‘(0) by the semigroup property.

If a given system behavior (expressed as a set of data) possesses a semigroup property, the extrapolation of that data set is achieved by a neural network (the semigroup channel) which itself acquires its own semigroup property. The semigroup property is ultimately achieved within the semigroup channel as a sequence of weight changes that occur after weight convergence has taken place.

3.3. Proposed N N Architecture Neural networks are being used for systems described by PDE’s (Padhi and Balakrishnan, 2002). Thc system-type attribute of thc neural network architecture is shown in Fig. 3, implementing an arbitrary function I.’(@,A ) . Unlike conventional neural network architectures that would attempt to achieve the mapping J(’(u,A) with one neural network, the proposed architecture reflects a systemtype approach using two neural network channels, a filnction channel and a semigroup channel, in an adaptation of the connectionist architecture (Fig. 2). During use, the semigroup channel supplies the function channcl with a coefficient vector C(w) as a function of the index OJ. The coefficient vector, when applied to thc basis sct E ( A ) of the function channel, causes the function channel to operate as one specific function from within a vector space of functions. Jointly, these two channels realize a semigroup-based implementation of the

3.4. Proposed Learning Algorithm

Since it is composed of RBF components, the first component of the system, namely the function channel, can be designed, rather than trained The second component, the semigroup channel, can be trained in the new way illustrated below. Dunng training, the scmigroup channel rcceives as input a preliminary coefficient vector C ( u ) and produces a 311

develop an analytic model for the data, and then extrapolate the model along one specific axis. System modeling is achieved through a technique referred to as algebraic decomposition. Algebraic decomposition is an operation which is applied to a given function F ( w , R ) , for the purpose of representing it in a form that contains a semigroup: F ( w , A ) = qJ( A ) = C(w)‘ E( A ) , where E( A ) providcs the algebraic basis for thc rcprcscntation of each member of the parameterized function {f.:u(24)j . The essential value of algebraic decomposition is that when it is applied to the class of functions that will be considercd in this paper, it always produces a semigroup property for the coefficient vector.

smoothened coefficient vector ? ( w ) . That is, the primary objective of training is to replicate (and, if necessary, to smoothen) the vector C(w) with a vector c ( w ) which has the following semigroup property: C ( w ) = CD(w)i;(O),

(4)

where C ( w ) = [E, ( w ) , Er (O)),

’..,En ( w ) ] ’

@(w) : an n x n matrix that satisfies (3).

However, there is a secondary objective of training; thc channel must also “replicatc” thc semigroup property of the trajectory by gradually acquiring a semigroup property of its own in the weight space. The existence of this acquired semigroup property in the weight space becomes the basis for extrapolation (Lee, et a/., 2004). In order to elicit this gradual acquisition of the semigroup property, it is necessary that the training in this second step (semigroup tracking) occur in a gradual manner, as shown in Fig. 4. It must be noted that there are two concepts of convergence that occur. First, to acquire a given weight, for example, weight W3, requires conventional training convergence, which in turn may require 500 training iterations. Second, after all . . ., W,) have been obtained, a search weights (W,, W,, begins for a convergence within this weight stream alone.

3.6. Extrapolation

Extrapolation involves only the coefficient vector and the recurrent neural network (the semigroup channel). At the uppermost level, the idea is to train the neural network to replicate the coefficient vector in such a way that it is additionally rcplicating the semigroup property. And this is responsible for generating the coefficient vector by acquiring a semigroup property of its own in weight space. As a comparison, some other recent extrapolation attempts are given in (Altman and Mittra, 1999). One current method, which also attempts to build a universal framework for extrapolation, occurs in various forms in nonlinear control theory and is collectively called “continuation methods.” These methods have been in existence for some time, but are only recently receiving attention (Richter and de Carlo, 1983). These “continuation methods,” however. require advanced mathematics. 4. SIMULATION RESULTS

data point

Fig. 4. Ovcrvicw of ncw training algorithm.

The following illustrates simulation results of the application of the proposed mcthod to thc prediction (extrapolation) of mass unbalance data. In its simplest form, assuming cubic nonlinearity in the spring, the vibration in Fig. 1. is expressed by the following equation:

Unlike conventional neural network training which would repeatedly present the entire trajectory as a target, the proposed method begins by slicing the entire trajectory into a nested sequence of trajectories. In the nested sequence a given trajectory includes the previous trajectory and adds one additional data point. Each sub-trajectory is trained by a conventional (batch) method, and the resulting weight is recorded. After all sub-trajectories have been trained (culminating in the last sub-trajectory being the entire trajectory), the sequence of resulting weights is examined for convergence. Again, unlike conventional neural networks which require large data sets for training, the proposed method has been applied to sparse data sets (Lee, et al., 2004; Kim, et a/., 2005a, b). If thc data contains noisc, this will be removed by the semigroup channel as part of the smoothing process.

M x + CX + Kx3= F ( t ) = nzrw’ cos wt

(5)

By scaling this last equation properly, the following equation is obtained, which is one of the classic Duffing equations: X+yX+((ax+,Bx3)= FW2cosWt

(6)

where w = engine speed, F = mr = normalized mass unbalance. It can be shown that Eq. (6) has the following approximate solution (Stoker, 1950).

3 5 Sy.yten? Modeling

The modeling and extrapolation problem is formulated as follows. Given a set of empirical data for which there is no analytic description, first

where, 312

w = engine speed, a,b,y = constant, and A

vibration magnitude. This will be simulated on the domain: w ~ [ 1 0 0 , 1 5 0 ] x 2 ~A~[0.01,0.10] ; , using the following pardmcter VdlUcs: a = 900; = 0.75; y = 0.75. (Vance, 1988). =

The extrapolation will be simulated in the region, which is assumed thcrc is no data. Thc results of the extrapolation will be compared to given raw data in that region. The mass unbalance raw data profile is shown in Fig. 5. The preliminary (rough) coefficient vector and the basis vectors produced by the RBF

I.

=

I

I1

I

160

01

140 0 02

Mass Unbalance Vlbiatlon Analysis alysls

Frequency (radisec)

0 06

0 04

120

loo

Vibration Amplitude

Fig. 8. Error between empirical and computed unbalancc profilc.

01 008 1

5

006

I

I

06

160

140

0

120

-

Frequency (radlsec)

006

, 100

0 02

0

0 04

01

on

0 595

..

0 59

V#biat#onamplitude

Fig. 5. Mass unbalance profilc

I

0 585

Coefficient vector

I

0 SR

l

100

105

110

120 125 130 Frequency (radsec)

115

135

145

140

150

Fig. 9. Comparison of original and smoothened coefficients.

--

Integral of lnpul Weight

x 10'

-p 4-

0 1958

Integral of weight conwrgence IS shown foithe first 15 weights 3~

o 1958 0 g,571ppppppppppI 100

105

110

115

125 130 120 Frequency (radlsec)

135

140

145

Fig. 6. Preliminary (rough) coefficient vector. Basis Vector I

I

r

I

1

r

r

I

1

150

:

1

2

0

5

10

15

20

25

30

35

5

40

Frequency (radlsec)

Fig. 10. Integral of input weights. Cnlrapoleled C1 coefficient 0 61

Extrapolallon Tesl

0 05 001

l pmpmpmp pmpmpmp p p

002

003

004

005 006 007 Vibration amplitude

008

009

01

1

Extrawlatlon

Observation

0 605

I

t-*

06

I

4 1

U

011

-

Fig. 7. Basis vectors. network arc shown in Fig. 6. and Fig. 7, rcspcctively. The use of this rough coefficient vector together with the basis set of vectors can produce the computed mass unbalance profile. The error between empirical and computed unbalance profile is shown in Fig. 8. The recurrent neural network then smoothens the prcliminary coefficicnt vector, as shown in Fig. 9. The possibility Tor extrapolation begins by checking for weight convergence as training is performed

0 595 0 59

o 585 0 58

. 100

105

110

115

120 125 130 Frequcnoy (mdlscc)

. 135

I 140

145

150

Fig. 11. Extrapolation. along the coefficient vector. In this case, weight convergence occurs as this training is repeated over 313

successively longer intervals (refer to Fig. 10). In this case, because of the smoothness, the possibility for extrapolation exists and the next step is to apply an extrapolation test in which the trailing end of the weight change sequence (produced by training) is replaced by an equivalent weight change sequence based on a rule that generates a semigroup. Based upon an observation of the weight change sequence on the interval from 125 radsec to 130 radsec, a semigroup-based rule for weight change is formulated and applied to the interval from 130 rad/sec to 135 r.ad/sec, as a test. Extrapolation, from 135 radsec to 150 radisec, consists of the autonomous continuation of the rule for weight change, which was derived during the extrapolation test. These results are shown in Fig. 1 1 . 5. CONCLUSIONS In this paper, a mathematical approach is investigated to extrapolation o f the mass unbalance which i s a common source o f vibration on a turbine-generator in a power plant, using a combination of a modified neural network architecture and semigroup theory. Given a set of empirical data with no analytic expression, we first develop an analytic description and then extend that model along a single axis. This can be achieved by using algebraic decomposition to obtain an analytic description of empirical data in a specific form, called the semigroup form, which involves the product of a coefficient vector and a basis set of vectors. The concept can also be tested in many other engineering and non-engineering problems. REFERENCES Ahmad, S. M., A. J. Chipperfield and M.O. Tokhi (2000). Modelling and control of a twin rotor multi-input multi-output system. Proceeding of American Control Conference, 3, pp. 1720- 1724. Altman, Z. and R. Mittra (1999). A tcchniquc for extrapolating numerically rigorous solutions of electromagnetic scattering problems to higher frequencies and their scaling properties. IEEE Transactions on Antennas and Propagation, 47, pp. 744-75 1. Atiya, A., R. Aiyad and S. Shaheen (1998). A practical gated expert system neural network. IEEE International Joint Conference on .Neural Nefivorks, 1, pp. 419-424. David, A. W. and A. S. Donald (1992). Handbook of Intelligent Control, Van Nostrand Reinhold, N.Y. Elman, J. (1990). Finding structure in time. Journal of Cognitive Science, 14, pp. 179-21 1. Florjancic, S. S., N. Livcly and G. R. Thomas (1 998). Mechanical behavior of an industrial gas turbine under fault conditions, a case history. Proceedings of ISROMAC- 7 Conference, A, pp. 373-382. Haykin, S. (1999). .Neural Networks, 2nd ed. Prentice Hall, N.J. He, S., W. Sun and G. Guo (1994). A new data extrapolation algorithm with application in

guidance and target recognition. Proceedings of the IEEE Aerospace and Electronics Conference, 1 , pp. 89-92. Jacobs, R. and M. Jordan (1991). A competitive modular connectionist architecture. Advances in Neural Information Processing Systems, 3, pp. 767-773. Jangamshetti, S. H. and R. V. Guruprasada (1999). Height extrapolation of capacity factors for wind turbine generators. IEEE Power Engineering Review, 19, pp. 48-49. Kim, B. H., J. P. Velas and K. Y. Lee (2005a). Development of intelligent monitoring system for fossil-fuel power plants using system-type neural networks and semigroup theory. IEEE Poiver Engineering Society General Meeting, pp. 2949-2954. Kim, B. H., J. P. Velas and K. Y. Lce (2005h). Semigroup based neural network architecture for extrapolation of enthalpy in a power plant. Proceedings ofthe ISAP, pp. 291-296. Ku, C. C. and K. Y. Lee (1995). Diagonal recurrent neural networks for dynamic systems control. IEEE Transactions on M w a l Networkr, 6, pp. 144-156. Ku, C. C., K. Y. Lee and R. M. Edwards (1992). Improved nuclear reactor temperature control using diagonal recurrent neural networks. IEEE 7kansactions on h'uclear Science, 39, pp. 22982308. Lee, I<. Y., J. P. Velas and 13. 11. Kim (2004). Development of an intelligent monitoring system with high temperature distributed fiberoptic sensor for fossil-fuel power plants. I Power Engineering Society General Meeting, 2, pp. 1350-1355. Padhi, R. and S. N. Balakrishnan (2002). Proper orthogonal decomposition based feedback optimal control synthesis of distributed parameter systems using neural networks. Proceedings c?f the 2002 American Control Conference, 6, pp. 4389-4394. Phan, M. Q. and J. A. Frueh (1 996). Lcarning control for trajectory tracking using basis functions. Proceedings of the 35th IEEE Conference on Decision and Control, pp. 2490-2492. Richter, S. and R. de Carlo (1983). Continuation methods; theory and applications. IEEE Transactions on Aulomatic Control, 28, pp. 660665. Selig, J. M. and X. Ding (2001). Theory of vibrations in stcwart platforms. Proceedings of 2001 IEEE/RSI International Conference, 4,pp. 2 1902195. Stoker, J. J. (1 950). Nonlinear Vibrations, Interscience, N.Y. Tahani, M. A. and C. Lucas (1991). Development of cxpcrt controller for steam temperature regulation in power plants. lEEE/R,SJ International Workshop on Intelligence fbr Mechanical Systems, 3, pp. 1333- 1337. Tikhonov, A. N. ( I 963). On solving incorrectly posed problems and method of regularization. Dokludy Akudenfmi iliauk USSR, 151, pp. 501-504. Vance, J. M. (1988). Rotordynumics of Turbomuchinery, Wiley, N.Y. 3 14

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

MGP: A TOOL FOR WIDE RANGE TEMPERATURE MODELING

Angel Fernando Kuri Morales * Luis VBzquez Seisdedos **

* Inslilulo Tecnolbgico Auldnomo de M&xico Rio Hondo No. I , Mekico 01000, D.F. Email: akuri@,itam. mx

** Departamento de Control Automatico, Universidad de Oriente Ave. Lus Americas S/N. Esq. Casero. 90400. Santiago de Cuba, Cuba. Email: L v a z q u e z ~ ~ e , u o . e d ~ i , c u Abstract. Superheated steam temperature dynamic is statically non linear. The steam enthalpy exhibits nonlinear dependence on both steam pressure and temperature. Also, the heat transfer process on superheaters and attemperators is strongly non linear and it was, reportedly, very difficult to find a synthetic expression (model). The so-called Genetic Multivariate Polynomials (GMP) solve this problem by finding the coefficients of a multivariate polynomial for an arbitrary set of data. Although this regression problem has been tackled with success using neural networks (NN) the ‘black box’ characteristic of such models is frequently cited as a major drawback. Despite the restrictions of a polynomial basis, GPMs compete favorably with the NNs without the mentioned limitation. Therefore, a practical tool is proposed for temperature modeling on a widc range rcal plant operation and its static parameter estimations. Based on advanced simulation tools, the polynomial expression of enthalpy (on a wide range) and the empirical heat transler equations in superheaters allow us to turn the static parameter estimation from a distributed to a lumped parameter system. Copyright 02006 IFAC Keywords: Mathematical models, dynamic modeling, process parameter estimation, thermal properties, lumped parameters system, temperature control.

1 . INTRODUCTION

In modern power systems’ control, eflicient power generation based on the thermal power plants must consider the control of the main frequency as well as the asqociated control of network qtabihty after hypothetical malfunctions. This is important since such events imply large and abrupt load changes which demand a large number of start-up and shutdown sequences. In order to be able to quantify the possible behavior of thermal power plants the dynamic properties of these plants must be known. In order to establish a mathematical model of an industrial process It i s often convenient to divide the process into a number of components. These components are treated separately. In this vcin, the large fossil drum boiler-turbinealternators units, from the methodological point of

view for mathematical modeling and for active power control proposal can be divided into two main dynamic regimes: a. Power dynamics. This model contains the major inputs and outputs which are needed for the overall plant control. As inputs we consider. a) Fuel mass flow rate, b) Feedwater mass flow rate and c) Control valve position; as outputs, we consider: a) Drum steam pressure, b) Drum water level deviation about the mean and c) Electrical output. In (Astrom & Bell, 1979) and (Working group, 1991) two analogous low order power plant modeling efforts are described.

b. Steam temperature dynamics. From the dome outlet to the valve control inlet, the steam jet passes through consecutive superheater sections. l o cool the steam temperature, water is injected into the steam flow. Certain sections are preceded by attemperators.

315

Each sct of attcmpcrator-supcrhcatcr should bc modelled in order to design temperature control mechanisms. As input we consider the cooling water mass flow on the attemperator control valve; as output we consider the steam maw flow at the superheater outlet. In (Eklund, 1971), (Usoro, 1977) and (Balchen and Larsen, 1997) three kinds of models when the power plant is based on boiler with dome are developed and, in (Moelbak and Mortensen, 2003) both modeling and temperature control are described. In this latter case, however, a once-through boiler power plant is considered. I . I Paper’s goal

For the wide-range control of Steam-Electric Power Plants it is neccssary to takc into account the plant manoeuvrability [see (Chen-Kuo, 1997)] and the optimal sensor locations, [see (Vande Wouwer, ct a1.,2000)]. The number or papers, research reports, MSc and PhD thesis treating different kinds of hcat exchangers is very large. The reported models, however, become very complex and usually lead to a set of nonlinear partial differential equations. It is required, therefore, that the dependence of heat transfer coefficients on physical variables such as flow and temperature is known a priori ‘I his paper is aimed at finding a practical procedure to build a lumped parameters model. The model assumes that the attemperator and the superheater display joint operation for temperature regulation when the steam mass is passing thiough them

The main paper’s contribution is to propose a way to build a single lumped parameters model for widerange tcmpcraturc control (for fossil fired power plants based in boiler with dome). To achieve this goal, a design procedure is being proposed: a) Use the enthalpy for energy balance, b) Apply the GMP approach for enthalpy curve fitting as a function of either temperature and/or pressure of the steam, and c) Systematically use a graphic simulation tool to make the fine and accurate model tuning when virtual (simulated) data and real plant data are compared.

SH:s3q&eatrr D:D e W

RH: re he ate^ A: Amupmior DST: D e W S t m a g e TmIi

H P : ~ F T e s mL P : L m v F T e s m IM:Mmdiate F T e s m CH:C a k a ~ l l

b> Sucesi-~ee n e r g y transformations

Fig.1 Fossil fueled generation unit The thermal energy transferred depends on the discrete and continuous combined control actions This process section can be identified as hybrid system The term “hybrid’, sec (Antsaklis, 2000), refers to the combination of continuous and discrete par15 In this w i s e a hybrid dyriarriical system is understood to mean a dynamical system where the bchaviour of intcrcst is dctcrmincd by thc intcracting continuous and discrete dynamics 2.2 The thermal sub process in the real plant. The physical thermal process to be modelled is shown in Fig. 11. S e n s o r locations

I

I

I

I

I

I

I

I

I

I

I

I

Cont.ro1 e

2. DYNAMIC MODELING

2.1 The real plant: review of jossil fired power plant based in boiler with dome. The heat generation process, see the section a) in Fig. I identifies parts functioning as discrete such as; the Induced Draft Fan (IDF), the Forced Draft Fan (FDF), the Regenerative Draft Fan (RDF) and the number of Burners. Also, the Soot Blowers (SB) are only activated when the fluid resistance increases due to the excessive soot.

De-vices for manoeurabikty Fig. I1 Theinid sub process c o n s i d e r e d .

Therc we have singled out the placement of sensor’s locations; ‘d’ stands for dome’s outlet, ‘1’ for Primary Atemperator inlet, ‘2’ for Primary SuperHeater inlet (coincident with Ap’s outlet), ‘3’ for Secondary Atemperator inlet (coincident with SHp’s outlet), ‘4’ for Secondary SuperHeater inlet

3 16

Heat suurces: Combustion gas +Flatne!flue! htion + comctlon , Metd + Sink:Superheated s t e . m Always convection

(coincident with A,’s outlet), ’v’ for control valve inlet (coincident with SH,’s outlet). We single out, as manoeuvrability or driving vanables, ‘(ILp’ and ‘qc,’ which are the cooling water mass flows on the attemperator primary and secondary control valves.

irlrirrirrii

2.3 Basic assumptions for temperature dynamic modeling

1

I

n Y

Superheaters (and also reheaters) are large heat exchangers with steam flowing into the tubes, and gas crossing the tube banks in cross flow. Thc following are some general properties (Maffeuoni, 1997) worth recalling:

Temperature profiles SOLTRCES

SINK (1) The hcat transfcr cocfficient on thc gas sidc is much smaller than on the steam side, so that steady state behavior is nearly independent of steam side coefficients. (2) The dynamics of these heat exchangers is essentially due to the considerable energy storage in the rnctal wall, because flue gas has negligible density and steam has much lower capacitance that the corresponding metal wall. (3) Mass storage determines much faster dynamics with respect to energy storage, because only steam is involved. (4) It is known that adequate modeling of superheaters and reheaters requires a distributed parameter approach. However, it turns out (Keflenz, 1986) that reasonable approximations by lumped parameters may be used. (5) The temperature dynamic is nonlinear, because the time constant is nearly proportional to the inverse of the load. (6) Temperature dynamics are affected by multiple lags, which vary with the load. In addition, the transducers for steam temperature are generally affected by a small (a few seconds) and a larger (some tens of seconds) time lag due to the thermal inertia of the cylinder where thc sensor is placed.

2.4 Practical considerations,for model building

I

x

t

Gradient of Temperatwe

I Fig. I11 Temperat.1.m profiles.

t x

For wide-range temperature modeling (for fossilfired power plants based in boiler with dome) as per the GMP approach, three temperature range arc defined (while keeping a wide prcssurc range). For cnthalpy polynomial curvc fitting, the following three temperature ranges arc considered Low range: [325 - 4001 “C Medium range: [460 - 4751 “C High range: [5 10 - 5401 “C Full range: [280 5401 “C ~

Polynomial curve fitting with GMPs is obtained for a wide pressure range as follows: Pressure range: [70 - 1401 Bar. The equations sets for lumped parameters temperature modcl for wide range pressure (power) operation are the following:

2.4.I Superheuter

The superheater is assumed to be a heat exchanger of the cross flow type. The tubes are represented by one tube with constant dimensions throughout the whole length. The main features for its modeling are revisited on Fig. 111

a. Empirical heat transfer equation in superheaters, see (Anderson, et. Al., 1968). b. Enthalpy polynomial curve fitting with GMPs:

c. Heuristic criteria (where, implicitly, the thermal energy loss factor is taken into account):

Where, ‘kcon,’can bc taken as, either

317

a) A constant. Which was implicitly taken to be k=1.8 in (Eklund, 1971). b) A load function.

superheater's ends. Thus, the heat transfer characteristics are implicitly included. Then, from the MGP approach, we may find an accurate polynomial which fits the whole operation range. We consider the Heuristic criterion, QMs = k,,,,. ( H s s ~ ,- Hss,+i) qs. Temperatures, pressure and steam mass rate are recorded on a central computer. The fuel calorific energy can be taken as Q G =~ kcombqf. Two possibilities on the simulated data (see Fig. IV) have been introduced. The reference is taken from real plant database (see, Table 3). Familiarity both on multivariate algebraic curve fitting and process modeling is assumed.

d. The superheater is divided into N sections (index 'n' refers to variables in section n); the equations governing heat dynamics for section n then are:

The pressure drop over a superheater can be taken according to the following momentum equation: p,, - pw= k,l%

1 Enthalpy polynomial curve fitting by MGP

2

2.4.2 Attemperator

A spray type attemperator is considered. The cooling of thc stcam is simply achicvcd by injccting water into the steam flow. The volume and material masses of such an attemperator are small (since the attemperator has a very small volume, storages in it are negligible). Therefore all dynamics of the attemperator are disregarded.

The algorithm and the corresponding software (see Kuri et Al., 1998) allow us to find the polynomial's coefficients according to any of the following three optimization criteria: The best minimax curve fitting (TRN) over the training set, the best (smallest) maximum absolute error (TSTM) over the test set or the best RMS error (TSTR) over the test set. In this paper, we report on the TRN results. We wish to point out, however, that the more stringent TSTR errors were also remarkably satisfactory. Table 1 shows the polynomial equations for different ranges.

Energy, mass and momentum equations yield:

'I'able 1: Enthalpv polvnomial curve fitting bv GMP. Range LR (fi)

The pressure drop is lumped to the end of the attemperator The drop is small and when it i s desirable to set it to zero, thc constant kp2 is made equal to zero The enthalpy of the coolant is assumed to be constant Often this is justified since the water supplied to the attemperators is feedwater taken at the outlet of the economiser For conveniencc wc present the nomenclature used in what follows in an appendix at the end of the paper

MR (f2)

HR (f3)

FR (f4) TSTR

3. EXPERIMENTS AND SIMULATION

Enthalpy obtained equation by MGP (h,,) 0.7581016 - O.5O798Pn,- 0.47261 P,: + 0.501973 T,, + 0.177947 T,, P,, + 1.189684 T,, P:, - 1.14979 Tn: P,: 0.09417 T:, - 0.00949 T:, P,, i 0.430308 T,,' P,: 0.780182 0.70817 P,, 0.06857P,: + 0.220623 T,,+0.047924 TnrPnr+0.018766 T,,,P,,,2-0.00348P,1,4- 0.00094 T,,,' 0.0073 1 T,: P:, + 0.0017 13 T,: P:, 0.0976-0.60736 P,,-0.041 59 P,: +0.406946 T,, - 0.00906 T,: P,, 0.00198 P,,' - 0.00035 T,: - 0.00025 T:, P,,, + 0.073059 T,,, P,,+0.014104 T,, P,,2 0.210735-0.2634 P,, - 0.67839P,: + 1.1 84068 T,, + 3.035704 T,, Pn:+ 0.27573 Tn: + 0.788859 T,: P,, - 4.15317 T,: P i - 0.35015 T:, P,, - 0.25692 Tnr Pnr- 0.67414 T,: + 1.775461 T,: P,; Table 2: Variable normahzation range.

In this paper, basically concerned with a primary superheater, thc following csscntial considerations hold:

Range LR

For the superheated steam, stating the energy balance by enthalpy thermodynamic property is the best way to include, implicitly, the heat transfer characteristic. Indeed, the quantity of calorific energy taken by the steam mass flow per time unit may be completely calculated by measuring temperature and prcssurc at both

MR HR

318

Normalization. T,, = 0.01333(T-325) P,,,= 0.1 1765(P-70) h= 560.026(hn,0.5018)+2880.13 T,, = 0.006666(T-460) P,,, = 0.1 1765(P-70) h= 168.65hn,+3181.55 T,,= 0.003333(T-510)

Coef. Error 0.0212

5.73 x 1 O-s 7.15

FR

P,, = 0.10526(P-60) h= 174.47hn,+3333.13 T,, = 3.84615x10 (T-280) P,, = 0.010526(P-60) h= 918.476(hnr0.224418)+2805.24

3.2 Simulation estimations

model for

21 T a ~ n , 358 TsSHo 470 TV, 495

Xl0j

4f

0.0249

static

U

Function Q M ~ (fs) TssHo (fc)

~

Once it is possible to describe analytically the static characteristic on a whole operation range, and knowing the dyiiaiiiic modeling aspects which were summarized in 2.4, a dynamic simulation on a wide range can be conducted. For example, Fig. V shows a TMOresponse when an 'qs' negative step forcing function (from 320 Tonlh to 322 Tonlh) excites thc simulation model (for Pd= 120 Bar and TISM,= 370 "C)

TSS1-l"

To illustrate the G M P approach a wide static range for temperature modeling data set was collected. When considering the the Primary SuperHeater from an Electrical Power Unit of 100 MWs we took advantagc of thc data recorded aftcr major maintenance procedures A special test was performed during these procedures. its temperature regulator was closed in the control loop with the basic purpose of recording the diagnostic variables listed on Table 4 A five MWs constant step on the active powcr was set and a range from 50 MW to 95 MW was swept.

Fig V

9s (If

T,,ix, ."._. TsSHo

TMo

Var.

75

MW Pd a.

112 300

'Tmo' dynamic r e s p o n s e w h e n t h e

simulation model is excit.sd by 'qs' .

Table 3: Primary superheater data report. 65 MW 95 247 18.7 350 470 495

Polynomial description. 0.960679q5,,- 0.820386 P d n l T \ ~ ~ l n r + 0.8586 Pdnr qsn? 0.941957 T,, + 0.001574 T s s ~TM,i 0.00136 Ts& + 2.6710~10"T,SH?Tuo - 1.lX10-j qs TM, - 0.75373 TsSHi+ 3.77 x 10.' qs TsSwl TMo 3.8 x qs T M ~ 6.0636q; - 621.0580 q: + 12.4995~10~ q; - 4.9361 x105 q: + 4.7869 x106qf13082 x107

QGM (f7)

Fig. IV Simulation model for data generation

Pd

27 374 470 495

Table 4: Wide range static functions for the Primary superheater.

4

qs_ IU l

55 60 MW MW 80 90 238 242 I6 17 345 347 470 470 495 495 Continued 80 85 MW MW 120 128 320 328

26 370 470 495

parameter

3.2.1 Simulation inodel for a superheater btep. The essential idea for the advanced simulation tool is bascd in Fig. IV.

50 MW 73 232 14 343 470 495

24.5 366 470 495

Wide range static functions obtained by GMP:

On the steam line between dome and control valve, the superheater modeling is much more complex than the attemperator's. Hence, the static parameter estimations by MGP (for the temperature modeling on a wide real plant operation) stem from data corresponding to this kind of thermoelectric subprocess.

Var.

23.2 362 470 495

4. CONCLUSIONS

70 MW 103 280 20 355 470 495

90

95

MW

MW

133 335

140 340

The application of thc reportcd mcthodology may bc very useful for the industrial and university sectors. In fact, a relative unified approach is now being proposed which will simulate and emulate the dynamic of steam temperature for each section's attemperator- superheater. Our methodology may be extended to the whole electrical generation unit. Indeed, its application can be applied to cach sub-process. As an 'off-line' approach, for 'real' plants, the functions should be updated periodically. At any rate, it can be a very useful software tool for both industrial and

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educational sectors which are interested in the design of control systems, the evaluation of dynamic performance on a day-to-day basis aimed at optimal plant maintenance, etc.

of Hybrid Systems. In: Proceedings ofthe IEEE, Vol. 88. NO 7, July 2000, pp. 879 - 887. Balchen, J. and Larsen G. (1997). Control of a steam boiler by elementary nonlinear decoupling (END). In: Proceedings of the NATO Advanced Study Institute on Nonlinear Model Based Process Control (Ridvan Berber and Costas Kravaris), pp. 749 - 779. Kluwer Academic Publishers. Bell, R.D. and Astrom K.J. (1979). ‘A Low Order Nonlinear Dynamic Model for Drum Boiler Turbine - Alierndior Uniis’. Repori LUTFD2 (TFRT-7162/1-039). Lund Institute of Tcchnology, Swccdcn. Chen - Kuo, W and Asok Ray, (1997). Robust Wide - Range Control of Steam - Electric Power Plants. IEEE Transactions on Control System Twhno/ogy, Vol. 5, No. 1, January 1997, pp. 74 88. Eklund K (1971). ‘Linear drum boiler-turbine models’. PhD thesis. Lund Institute of Technology, Sweeden. Klefenz, G. (1986). Automatic conlrol of steam powerplants. Bibliographisches Institut, Zurich. Kuri, A., Villegas, C., (1998) A Universal Genetic Algorithm far Constrained Optimization., EUFIP’ ?W, 6th European Congress on Intelligent Techniques and Sofi Computing, Aachen, Germany. Kuri, A, Alinaraz, F., (2005). Genetic Multivariate Polynomials: An Alternative Tool to Neural Networks. Lecture Notes in Computer Science, No. 3773, pp. 262-270, Springer-Verlag. Maffezzoni C, (1 997). ‘Boiler - Turbine Dynamics in Power - Plant’ Control. Control Eng. Praclice, Vol 5, No 3, pp 301 312. Elsevier Science Lid. Moclbak, T., and Mortensen, J. H.(2003): ‘Steam temperature control’ in Thermal power plant simulation and control, pp 131 - 160, edited by Flynn, D. IEE, London. Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies (1991). ‘Dynamic models for fossil fueled steam units in power system studies’. IEEE Transactions on Power Systems, Vo1.6, NO. 2, pp 753-761. Usoro P.B., (1977). ‘Modeling and simulation of a drum boiler-turbine power plant under emergency state control’. M.S. thesis, Massachusetts Inst. of Tech., USA. Vande Wouwer, A. et al. (2000). An approach to the selection of the optimal sensor locations in distributed paramctcr systems. .lournal of PROCESS CONTROL, Vol. 10 (2000), pp. 291 -

Appendix Nomenclature

LR, MR, LR and FR refer to Low, Medium, High and Full temperature’s range. SH, A, C: SuperHeaier, Aiiemperaior and Coolani. i, o: input and output rcspcctivcly. nr: normalized range. The symbols used are the following: T, P: Temperature [“C], Pressurc [bar]. C,: Heal capacitance for superheater tubes [kJikg “C]. M,: Mass of superheater metal tubes [kg] QGM:Heat flow from gases to superheater metal tubes [kJ/s]

QMs: Heal flow rrorn superheater meial lubes to steam [kJ/s]

Thl: Superheater metal tube temperature [“C] qs: Steam flow [kgis]

~

qc:Coolant flow in attemperator [kgis] qf: Fuel flow [kgis] Pd:

Drum pressure [bar]

Ps0: Steam pressure outlet [bar] hsSH1: Steam enthalpy at SH’s inlet [kJ/kg] hsSHo:Steam enthalpy at SH’s outlet [kJ/kg] hsA,:Steam enthalpy at A’s inlet [kJ/kg] hsAo: Steam enthalpy at A’s outlet [kJikg] h,: Coolant water enthalpy [kJ/kg] REFERENCES

300 Anderson, J. H., Kwan, H.W., Quallrough, G.H., Dynamic models for power station boilers. Item 9.1: The governing laws of fluid dynamics and some empirical heat transfer relationships. Paper presented at Third U.K.A.C. Control Convention, April 1968. Anisaklis, P.J (2000). Theory arid Applications. A brief introduction to the Theory and Application

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

SIMULATION AS A TOOL FOR PROCESS DESIGN AND DISTURBANCE ANALYSIS IN INDUSTRIAL POWER PLANTS

Yrjo Majanne

Tampere University of Technology, Institute ofAutomation and Control P.O. BOX692, FIN-33101 TAMPERE, FINLAND [email protected] Abstract: Industrial power plant is a large scale system. During evcry day operation thc plant is cxposcd to large load disturbanccs caused by trips and start ups of steam consuming processes. Pressure stability of the plant must be maintained also during the disturbances in order to ensure the trouble free and efficient operation of the production system. The required stability is achieved by using load leveling components for balancing the loads in the steam network. In large scale systems the dynamic simulation i s the only possibility to analyze the responses caused by the disturbances and design the process and control system to meet the requirements set for the plant. Copyright 02006 IFAC. Keywords: Dynamic simulation, Power plant control. Load level control

feed water tanks, auxiliary condensers, condensing turbines, and blow out valves (Majanne, 2005).

1. INTRODUCTION During the last few years the role of the dynamic simulation as a part of the process and control design has incrcascd rcmarkably. Benefits of thc dynamic simulation are the most evident in the analysis of the dynamic behavior of the large scale systems. An industrial power plant is a good example of a large scale dynamic system exposed large disturbances during an every day operaiion of ihe plani.

Modeling of the power plant process may be approachcd from different points of view dcpcnding on the purpose of the use of the model (Leva and Maffezzoni, 2003). For the disturbance analysis of the plant the simulation model should be valid for a rather wide range of operation (non-linear model) and should be based on the firsi principle phenomena (laws of conservation of mass, energy, and momcnium) and thc dcsign data. This spccification leads to a model structuring approach based on the representation of plant components and their interconnections with variables and parameters corresponding to well-defined measurements or physical entities. For simulation models representing an entire power plant, it is quite common to seek model accuracy over an intermediate time-scale, i.e. in the range from a few tenths up to a few thousands of seconds, (Leva and Maffezzoni ,2003).

Load charactcristics of thc industrial powcr plant differs remarkably from that of a condensing power plant producing electricity to nationaliintemational power grids or a CHP (combined heat and power) plant producing heat and electricity to the electric and district heating networks. The main output of the industrial power plants is process steam. These plants are typically exposed to large and rapid load changes caused by trips and start ups of steam consuming processes. Pressure disturbances in process steam network may lead to a trip of a large capacity production process causing great economical losses. E.g. a 30 min trip of a paper machine will cause about 8 000 € (10 000 USD) loss.

Modeling of the power plant process has a history dating back to the pioneering work of Chien et a!. (1958), the earlier engineering-oriented works of Caseau et al. (1970), McDonald and Kwatny (1970), Weber et ul. (1976), Lausterei et al. (1984), Maffezzoni et aE. (1984), and h t r o m and Bell (1988). In the boiler area, there are many well documcntcd models ranging from complex knowledge based models to experimental models

Besides steam generators and back pressure turbines the industrial power plants are equipped with load balancing components stabilizing the operation of the steam network during rapid load changes. Typical load balancing components are steam accumulators,

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denvcd from special plant tests In the middle of this range there are so-called interpretation models. These modcls are complex enough to capturc the essential physics whilst at the same time they have good control dcsign features. 2. DYNAMIC CHARACTERISTICS OF THE INDUSTRIAL POWER PLANT In process industry the steam generating units are typically dimensioned so that changes in production capacity (typically enlargement) lead also changes in cncrgy production cquipmcnt. To build a ncw boilcr results often to build a new turbine plant, and because of these modifications the structure and the dynamics of the steam network will be changed.

Fig. 1. Typical structure of the industrial power plant with three pressure level steam network.

The capacity of the boiler units does not tell directly how difficult or easy task it is to stabilize the steam network. That is because part of the steam generating units can be constant load boilers such as chemical recovery boilers or combined cycle plants without controllable supplementary firing. These constant load units reduce the control range of the steam generating power of the plant. The increasing capacity of the steam consuming processes leads to increasing size of the load disturbances caused by the trips of these units. E.g. a web break in a paper machine causes typically a 10 30 kgls load change within 1 - 2 minutes corresponding 20 - 40 YOof the controllable load capacity of the steam generation.

The boiler dynamics dominates the dynamic characieristics of the sieam network. Time constanis of the boilers are in the minute range whereas the time constants of the turbines and pressure reduction valvcs arc in thc range of a couple of seconds. Furthermore the boiler dynamics can be asymmetric; e.g. for a grate fired boiler and a fluidized bed boiler the ratio of the time constants for increasing load and decreasing load can be 1:2.

~

Typical load balancing components in the industrial power plant are a steam accumulator, a feed water tank, an auxiliary condenser, a condensing turbine, and a blow out valve. These components have different operation expenses and to optimize the efficiency of the plant the use of these components should be prioritized

The steam consumers are typically connected to the intermediate (IP) and low pressure (LP) networks and the boilers are connected to the high pressure (HP) network The networks are connected together by a back pressure turbine equipped with a required number of extraction outlets. The back pressure turbine controls pressures in consumer networks by manipulating steam flows from HP network to LP and 1P networks. The controlled load boilers stabilize steam pressure in the HP network by balancing steam generation and consumption in the network. This is possible only in a long run, because a typical control speed (inax.) of the boilcr is about 5%/iiiiii and the rate of the load change caused by the trip of the paper machine can be 10 20 % Imin or even more of the controllable power generating capacity. This unbalance between the generated and the consumed steam flows effects on the pressure of the HP network.

The most efficient load leveling components are the steam accumulator and the condensing turbine. The steam accumulator is typically charged from IP network and discharged to LP network. Both energy and process water are recovered. With the condensing turbine it i s possible to compensate the disturbances in the steam load by adjusting the generated electric power. The problem with these components is the investment cost. Steam accumulator is a 100 - 300 m3 pressurized tank which is not nomally included to the equipment of thc industrial power plant. Also the condcnsing turbine is not very often included in the industrial power plant. Thc problem with the use of the feed water tank for load leveling is the asymmetric leveling capacity. It can receive a good amount of excessive steam from the nctwork but it can not release extra steam to the network. Big changes in heating steam flow to the feed water tank may also effect on the deaeration of the condensate leading problems with the quality of the boiler water.

Pressure fluctuations in the HP network should not exceed 5 % of the nominal pressure of the header. Frequent pressure fluctuations exceeding this level may damage the boiler structures (pressure fluctuation -> temperature fluctuation) and even temporary fluctuations exceeding this level may trip the boiler due to the loss of the drum level. E.g. a tripping of a recovery boiler will disturb severely the opcration of both the pulp inill and the papcr mill.

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With the auxiliary condenser only the process water is recovered. Active use of auxiliary condenser for load balancing requires that the cooling pumpsifans must be running all the time causing energy losses. The blow out valve has the highest operation expenses as a load leveling component. Both energy and process water are lost. The effective use of ihe indusinal power plant requires an automatic scheduling of load leveling operations The use of different load levcling cornponcnts ahould be ataggered horn the rnoai economic one to the worst one In practice this is achieved by biasing the control errors for controllcrs controlling the operation of these load leveling components

Fig. 2. Staggered operation of the steam leveling components during a web breaks in a paper machine. 3. SIMULAI'ION BASbD ANALYSIS

The simulation study is especially useful when an exisiing production system is modernized and the production capacity, e.g. a capacity of a paper machine is increased, a new turbine-generator unit is installed, a boiler capacity is increased ctc. Reconstruction of any component of the process effects on the required capacity and control performance of the remaining components. With the simulation study it is possible to analyze the effects of the modernization to the remaining part of the system and design the possible changes and improvements needed for the rest of the process. Simulation study of a new, nonexisting plant gives a lot of valuable design information for process and control design, but the results are more suggestive than for the exisiing p h i , because the simulation model cannot be validated against the measured process data. The third case for simulation is to study the possibilities to improve the operation of the existing plant. Implemented studies have shown that it is possible to get annual savings about 200 000 1000 000 euros (250 000 - 1 200 000 USD) in energy costs by improving the control strategy of the existing plant. The savings are coming from the

reduced need of energy and make up water. This i q the case when the steam consumers are tripping frequently and the load balancing is carried out by blowing out the excessive steam during the trips. When designing the structure and the control concept of the industrial power plant, simulation is used to study, how the load disturbances should be handled. A portion of ihe load disturbance in IPiLP network will be transferred to the HP network by the turbine controller. The prcssure disturbance in HP network will be cornpensated by the controlled boilers. In the HP network the storage capacity of the boilers is utilized. Also the constant load boilers stabilize steam pressure in the HP neiwork because of the storage capacity of their steam and water volumes connected with the HP network. The operation of the turbine controller must be constrained so that the disturbance in the HP network will not exceed the +- 5% limit from the nominal pressure. The rest of the disturbance must be compensated with the load balancing components in the IP and LP networks. If the simulation study shows that the steam accumulator is needed, also the capacity (volumc and capacity of chargc and discharge lines) of the accumulator can be defined. Simulation results are also used for dimensioning the turbine parameters, capxity of extraction outlets etc., and properties of turbine controller unit.

4. POWER PLANT SIMULATOR The industrial power plant simulator is programmed in MatlabiSimulinkO environment. Modelling of the power plant components is bascd mainly on the first principle models. The dynamic models are based on the energy and the mass balances. The momentum balance is neglected and the flow dynamics is embedded into the actuator dynamics. The rcason for this is that physical parameters like friction coefficients for pipe lines are needed to parametrize the momentum balance equations, and this kind of information is typically noi available. The nonlinear thermodynamics is applied by using nonlinear lookup tables to determine the state variables of superheated and saturated steam. The model library consists of steam generators, turbines, load leveling components, stcam consumers, controllers, and miscellaneous components like valves for different media with different type of actuators (pneumatic, hydraulic, electric). 4.1 Boiler models

The mosi important features of the boiler model for the purposes of disturbance analysis are the load change rate and the storage capacity. The boiler model includes steam and water volumes and

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When charging the accumulator the 1P $team condenses into the saturated water in the tank increasing the temperature and the pressure in the tank The accumulator can be charged as long as the pressure in the tank is less than the IP network pressure When discharging the accumulator, tank pressure is dropped and saturated water is vaporized Pressure and temperature drops due to the required vaporization energy and the accumulator can be discharged to the LP network until the tank pressure equals with the LP pressurc

dynamic4 for fuel feeding (2 \eparate fuels, e g oil and bio mass), combustion, and heat transfer The dynamics of the heat transfer can be determined either by the mass of the heat transfer structures or by using experimental results measured from an existing boiler. Increasing and decreasing the load can be modeled with different combustion dynamics. Normally the drum level and the steam temperature controls are supposed to work ideally, and they are excluded from the model. Howevcr, thcrc IS an altcrnative model including drum dynamics and stcarn temperature control available, but it is not normally used

Auxiliary condenser and blow out valve are modeled as steam valvcs. Only the mass balance and actuator dynamics are modeled.

4.2 Turbine models

The main variables of the turhinc model arc the inlet and the outlet steam mass and energy flows. The inlet flow is modeled as a control valve operating under critical flow conditions. The flow dynamics is embcdded to thc actuator model. The energy balance of the steam expansion is modeled to determine the outlet steam enthalpy. The enthalpy is needed to calculate the amount of cooling water required to cool the steam to the set point temperature of the back prcssurc hcadcr. Stcam cooling is supposed to work ideally. In extraction turbines steam expansion is divided in stages, and each stage has been modeled as an individual turbine

4.4 Vulves

The main variable of the valve models is mass flow through the valve. Throttling has no effect on the enthalpy. The model library contains control valves for steam and water flows with the dynamics of pneumatic (1 order dynamics) or electric motor operated (constant velocity) actuators. The capacities of the valves can be determined by Cv or Kv values or by inlct and outlet prcssurcs and maximum flow. The flow models are referred from the Flow Control book by Neles Jamesbury. Pressure reduction valve is used to reduce the steam pressure and temperature to the next lower network level (HP -> IP, 1P -> LP). Pressure reduction valves are typically used to by pass the steam turbine if it is not available. The model of the pressure reducing valve includes both the mass and the energy balance equations. Energy balance is needed to calculate the cooling water amount nccded to cool the steam to thc desired outlet temperature. Temperature control is supposed to work ideally.

I

i

'.

4.5 Controllers The controller library contains a PID controller and a controller module with parallel connected PID controllers with the selection of the active controller according to the minimum or maximum selection of the controller outputs These parallel connected controllers are used in multi criteria control, where the actuator is connected with different controllers according to the operation state of the process In the steam networks e g the control of the charge and diqcharge valves of the steam accumulator requires this kind of controller structure

Fig. 3. Model library for turbine models and rcduction valvc models. 4.3 Load leveling component5

The controller outputs can also be forced to the predetermined positions and controllers can be forced to manual mode freezing the output to its present value. These options are needed e.g. in turbine controller where the operation of the controller must be able to be constrained if steam pressure in the HP network is disturbed too much (overriding control).

The main variables of the models of load leveling componcnts are mass flows to and from the component. In the models of the steam accumulator and the feed water tank also energy balance is included. The energy balance is needed to determine the pressure of the tank and further to calculate the charging or discharging flows to/from the tank.

3 24

4 6 Model huikding A simulation model is built by dragging model components from the library window to the application window. The components are connected together and parameterized according to thc initial state of the simulaied process. The model blocks are built so that the required parameters can be found easily from the technical documents of the plant. The initialization scnpts calculate initial values for the proccss states and the controllcr outputs and actuators so that the simulation can be starled horn d steady state without any transients In a typical project the customer fills up the coupons where the capacity and volume information of the examined process is determined. At the same time ihe control specialist of the consulting company drafts the proposed control scheme. After receiving the coupons the programmer sets up the simulator with the proposed control structure. Next simulation runs are executed and the performance of the controlled process during the load disturbances is analyzed. According to the simulation results it is evaluated if any changes to the process or control structure arc rcquircd.

operated by the frequency control of the electric network and turbine generator TG2346 (in practice 4 separate turbines) is controlling steam pressures in 12 bar (extraction outlet) and 4 bar headers (back pressure ouilet). Beside the turbines the headers are connected together with pressure reduction valves. A paper machine is connected to the 4 bar network. The operation of the process was studied during the disturbances originating from the steam load of the paper machine and from thc frequency control caused by the change of the eleclnc lodd At the rrioirienl there is no steam accumulator in process, but the rcsponse of thc proccss was simulated also with a 250 m3 accumulator connected between the 12 and the 4 bar headers Figures 5 and 6 show the simulated pressure stability in the 4 bar header during the load disturbance caused by the paper machine connecied to the 4 bar network. Fig. 5 shows the results without the steam accumulator and fig.6 with the accumulator. With the accumulator pressure fluctuations stay within 0.05 bar and no steam need to be blown out. Without accumulator fluctuation is -0.3 ... 0.1 bar and app. 1500 kg stcam is blown out

5 SIMULATlON CASE

A simulated power plant consists of 2 HP headers, 140 and 82 bar, 12 bar IP header, and 4 bar LP header. Steam is generated by two controlled power boilers controlling pressures in 140 (PB2) and 82 bar (PB1) headers and a constant load recovery boiler RB123 (actually 3 separate boilers) connected to 82 bar header. Turbine generators TGI and TG5 are

Fig. 4.

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important role when designing the process and the control structure to result a system with good disturbance attenuation.

4 t a r header [bar]

0

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20 30 Blmv oui [kgis]

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The simulation models included in the presented simulator are a compromise between the accuracy and thc complexity. Especially thc flow dynamics is simplified and embedded to the dynamics of the actuators. Compared with the accuracy achieved with more detailed model structures with a number of unknown model parameters which must be guessed, there is no big difference between the final accuracy achieved. However, the computational effort and the time required to tune up the simulator are minor compared with the more complex models.

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Load [kgis]

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The results gathered from over 20 simulation projects has shown the usability of this simulation bascd analysis concept.

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REFERENCES

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Time [min]

Astrom, K., Bell, R.: Simple Drum Boiler Models. Proceedings of the IFAC Power Systems Modeling and Control Applications. Brussels, Belgium, 1988, pp. 123 - 127. Caseau, P., Godin, P., and Malhouitre, G.: Numerical Simulation of a Steam Generator. Journees de I'AIM, Liege, 1970 (in French) Chien, K.L., Ergin, E l . , Ling, C., and Lee, A,: Dynamic Analysis of a Boiler. Trans. ASME, 1958 80, pp. 1809 - 1819 Flow Control Manual. Neles-Jamesbury, ISBN 95 195409-9-7. Helsinki 1992 Lausterer, G.K., Franke, J., Eitelberg, E.: Modular Modeling Applied to a Benson Boiler. Proceedings First IFAC Workshop on Modeling and Contiaol of Electric Power Plants. Pergamon, 1984 Leva, A., Maffezzoni, C. Modelling of Power Plants. Thermal Power Plant Sirnulation and Control. Damian Flynn (Ed.). IEEE Power and Energy Series 43. ISBN 0852964196,2003 Maffezzoni, C., Magnani, G., Marcocci, L.: Computer Aided Modeling of Large Power Plants. Proceedings First IFAC Workshop on Modeling and Control of Electric Power Plants. Pergamon, 1984ings Majanne Y .: Model Predictive Pressurc Control of Steam Networks. Control Eng. Practice, Vol. 13 (2005), FF. 1499 - 1505 McDonald, J., Kwatny, H.: A Mathematical model for Reheat Boiler-Turbine-Generator system. Proceedings of the IEEE PES Winter Power Meeting, January 25 30, 1970, New York, pp. 1 - 19. Weber, D.S., Konopacki, W.A., Massimo, F.M.: Modeling and Simulation of Hanfort K-Area Boiler-Turbine-Generator Sysytem. Technical report ERDA 76- 151, 1976

Fig. 5. 4 bar header pressure and blow out steam flow during the load disturbance without the steam accumulator. 4 t a r header [bar]

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----1 5 -

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6. CONCLUSIONS

~

Simulation is a good and pcrhaps thc only way to examine the cffects of load disturbanccs in a largc scale system having strong interactions between several process variables. Simulation has also an

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

Operator Guidance Simulator: A New Power Plant Training Tool Concept

Ulrich Tomschi Siemen:, Power Generation , E912 Plant Design, Erlangen, Germuny Horst Jackisch Siemens Industrial Solutions and Services, IS L B C Simulation Center, Lrlungeri, Germany Rainer Newald Siemens Power Generation , E912 Plant Design, Erlungen, Germany

Ahstract: The improvements and developments o f power plant automation syslems make operation easier. This comcs along with an increased tendency for the operator of losing knowledge about his plant. The consequential need for effective training possibilities led to the development of a new well-priced simulation tool "Operator Guidance Simulator" which combines early availability with high plant similarity. It is based on Siemens' longtime experience in simulation of power plant processes, which ranges from steady state performance simulations, dynamic plant and automation simulations to Operator Training Simulators. Copyright 02006 IFAC. Keywords: Simulators. Operation. Training, Power Generation. Automation

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1. NEED FOR TRAlNJNG

During the last years the market structures of electricity supply systems have been changing in many countries. Liberali7ation. in particular the scparation of gcncration and transmission of electricity. leads to increased challenges for the power plants regarding operational flexibility, e g. l‘requcnt fast plant start-ups and shut downs (cycling capability), often several times a week. lhere is a considerable economic benefit of such flexibility for the plant owner.

. . traininD

training at Site

training

courses

This development leads to a permanently increasing and optimiLed automation level covering these demands. Such highly automated processes ideally require only very few interaction with the power plant operator. As an extreme case he can start up the plant from cold condition to I‘ull output by pressing only one button. Nevertheless the operator should still be able to perform such procedures manually or react to disturbances, failures or any unexpected situations correctly.

Figure 1 : Effect of operator training

A description of the requirements and the characteristics of an OTS for fossil fuel power plants is given by ANSI/ISA [ 11. An OTS can therein be categorized into the following main types:

1) The “generic” simulator: A generic OTS, based on a generic process simulation model, instructs the trainee in the general process characteristics of the type of power plant he is going to work on (e.g. a steam power plant or a Combined Cycle Power Plant). Such an OTS can be used long before the operator starts working on -’his“ plant, but unavoidably it is generic not only in the process. but also in the automation and control system. Even if the simulated process is close to the real plant, there might be considerable differences in the automation and control concept. The familiarization with details of equipment. plant control and its graphical representation can be done only when he starts to operate “his” plant. Therefore such an generic OTS is applicable in particular for operators to be instructed in the fundamentals of the power plant process and - in case the HMl system is the same as used in the real plant in the principle handling of the system.

However, the lcss an operator has to intcract with his plant during undisturbed operation. the higher the probability that the detailed knowledge about the power plant process and the automation mechanism? gcts lost with time or ncvcr has bcen obtained comprchcnsively . Since critical damages to plant or personnel are avoided by several safety systems, the consequence of incorrect operator actions or reactions is not necessarily damage to the facility. What might happcn is an incorrect rcaction in situations which arc not covered by thc automation system. E.g. if by some reason a control loop has to be operated manually and the operator does not realize the impact of his actions, in the worst case the plant might trip. The negative effect of untrained personnel therefore is to the greatest extent on thc economical side. Unplanned outages lead to high opportunity costs as energy is not provided to the grid as contracted or the missing energy has to be bought on the control energy market on high tariffs. Additionally. any trip of the plant can lead to high thermal stress on critical plant components reducing their economical lifetime. This increases also the costs for the plant service and maintenance program.

2) The full scooc. high realism simulator At the other end, an OTS can bc developed individually for the specific plant, simulating the complete plant process and auxiliary systems together with the dynamic rcsponscs of any kind of normal and abnormal operation. Resides the laborious process modeling. this also requires representation of thc complctc functionality of the automation s j stem. One solution would be the use of the original automation hardware. This solution of course would be expensive due to thc hardware and space demand. An alternative is the emulation of the automation system which allows the use 01‘ the original application software or the simulation of the automation logic either in the process simulation tool or elseu here. Ideallj, the trainee should not see anj difference helween the sirnulator and the real plant in terms of‘

2. OPERATOR TRAINING SIMIJLATORS Operator Training Simulators (OTS) have been used for many years to train the power plant perxonnel iu operation of the plant and to avoid the negative effects as described above. The positive result of such training - if performed regularly - often is illustrated as shown in figure I .

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operation and behaviour. Such an OTS therefore needs to include the specific automation and control philosophy and the specific graphical HMI (human machine interface), embedded into the control room ambience, and requires a thorough model tuning once the plant has been put into operation. This kind of OTS, in combination with training features on the instructor side as e.g. programmed malfunctions, special scenarios, trainee monitoring and diagnosis tools is very useful for an effective training of the operator, but the main disadvantage beside the high expenses - is the long lead time which according to ANSIiISA indicatively is hvo to three years. Considering the present short lead time of the whole power plant, which in case of a Combined Cycle Power Plant during the last years could be reduced to less than 24 months, it is more than questionable that a customer would accept such an OTS lead time. In fact, in current power plant specifications. the availability of a training simulator is nften required even before the scheduled start of plant commissioning. in order to start operation with well trained personell.

3. OGS CONCEPT The targets of a contemporary power plant training tool can be summarized as follows:

. =

availability before handover of the plant to the customer same “look and feel” as in the real plant correct operation and automation philosophy affordable investment

In particular, the possibility to have a plant specific training tool allowing an effective initial operator training in due time appears to become more and more important, whereas the need for replication of the control room seems to be secondary since the control rooms themselves tend to be less representative and reduced to a few PC terminals. These requirements led to the development of a new concept of training tool, called Operator Guidance Simulator (OGS). The OGS is based on the project specific Automation System (AS) Plant Shop Test which is performed by Siemens Power Generation for virtually all new power plants, being an essential quality assurance for the process arid autornation engineering. This plant shop test integrates the complete original plant specific A S hardware and software (“hardware in the loop”), which will be used later in the real plant. with a process simulator reflecting the project specific power plant, see Fig. 2.

3) The reduced-scope. high realism simulator In this type of simulator thc simulated process arcas are limited to the major systems. Auxiliary systems are included only if relevant for the main operation. There is no complete replica of the control room required. However. the training effects should be similar to those of the full scope simulator. Price and lead time of such simulator of course depend a lot on the completeness. depth and fidelity of the simulation. The lead time of such a simulator is indicated by ANSILSA with one to two years. llcnce even with such a reduced scope simulator the above mentioned early availability can not be obtained.

Process Simulator

TXP AS

TXP HMl

Figure 2: Plant shop test with “hardware in the loop” As such it allows testing of the most important functionalities of the power plant, mainly in the f-leat Recovery Stcam Generator (HRSG) and wateristeam cycle areas: as slart-up, shul-down and normal operation. In case of a Combined Cycle Power Plant. (CCPP) in particular the unit control, i s . the integrating controls of the main components gas turhine, steam turbine and HRSG, is heing tested thoroughly. This test is done before the automation system will be delivered to site. The process simulation used for this plant shop test is based on the prqject specific P&IDs (Piping & lnstrumentation Diagrams), heat flow diagrams and equipment data sheets and hence shows a high consistency with the projected power plant. The OGS uses the automation software which was tested together with the process model in the plant shop test. In contrast to a conventional OTS, this OGS concept, making use of a direct high quality engineering output, allows early availability before PAC (Preliminary Acceptance Certificate) of a highly

In the ANSIiISA Standard there are only few indications given about the required representation of the automation and control system. Modern I&C systems allow effective engineering on a graphical interface with modular “drag and drop“ functionalities rather than building the logics from zero. The resulting functional diagrams do not always show all details of the correspoding internal logic. Therefore, a correct representation of the automation logics i n the simulation tool ofen is difficult or even impossible, if based only on the logic diagrams. In particular, simulated processes with a high automation lcvel bear thc risk of wrong responses even if the process itself is simulated correctly.

I n the view of the operator, the yardstick o f the quality o r the sirnulalor are riol onlj the correct process values but maybe rather the correct actions and messages he sees on the HMI in comparison to the real plant.

329

The focus of the simulation model in the OGS is the correct technological representation of the dynamic behaviour of the plant rather than compliance with all thermodynamic principles. which is necessary in other applications as e.g. process design or calculation of performance data. but would enhance unnecessarily the complexity of the model and might reduce the dynamic performance of the simulation. The simulation scope of the OGS comprises in the basic version the IIRSG and the wateristeam cycle with steam turbine (see Fig. 5 ) . The gas turbine is represented in a simplified way, but can also be simulated in detail if required.

consistent process model and automation and control software. PAC

Commissioning Plant Shop

,npvtto06s

Tested simulation model tested application s o h a r e

Figure 3 : Integration o f OGS in project handling

t,

4 '

The main components of the OGS system are (see also Figure 4): ,

..

.+.:

process simulation emulation/simulation o f the AS stimulated human machine interface (HMI)

d Automation

Figure 5: Example for a CCPP heat flow diagram This modular system of the OGS allows extension to other process areas and auxiliary systems as needed by the customer.

Simulation

The process simulation is implemented with the SIMIT test and simulation platform by Siemens I&S. SIMIT facilitates fine grained solutions for testing of automation software: from simple signal tests or tests on the actuator-sensor level to the entire automation system test with process models. It is widely used for Simatic automation testing in various industries. SIMIT either provides the electronic interface to the real automation hardware (CPUs). to emulated CPUs (SoTtPLCs in case or S 7 ) or it allows implementation of automation and control functions dircctly to thc simulation.

Emulation

Fig. 6 shows an example of the process oriented view of the simulatoriinstructor intcrface in the OGS:

HMI

Stimulated HMI

Figure 4: From plant to OGS

Process Simulation:

330

between the HMI in the training and the HMI in the plant. For the process parts which are simulated dynamically, all actions by the operator will have the correct effect on the process. Process signals which are not dynamically simulated appear as a static value. Other features which are part of the licensed HMI as e.g. trends are also available.

4. OGS CHARACTERISTICS IN COMPARISON ’1‘0 AN 0 1 S The OGS allows quite some of the functionalities which are known from an OTS:

Fig. 6: SIMIT simulation interface

.

Emulationisimulation of automation: One big advantage of the OGS is the high congruence with the automation used in thc real plant. Instead of the automation processors used in the real plant and in the Plant Shop Test, the OGS makes use of a software emulation of the AS which allows running the original plant specific automation software as if it was loadcd to the real system. This emulation communicates via a bus protocol with the process simulator using the signals defined in the P&IDs as liOs between process and AS Only in case when the emulation of some AS components is technically not possible, the relevant automation logics will be implemented into the simulator. In case ol‘ the Siemens power plant Automation System Teleperm XP, the emulation h as been used in many training simulation projccts, c.g. the OTS for Santa Rita Power Plant on the Philippines. Teleperm XP is based on S5 automation language and components and is used in virtually all large fossil power plants built by Siemens during the last years This automation system now is being followed by the new system SPPA-T3000, which is based on S7 components. The emulation software for S7 application code has been developed and proved successfully in several training simulator projects. The specifics for SPPA-T3000 are currently in a pilot phase. Here it is a big advantage to have the detail knowledge about the automation system within one company in ordcr to cmulatc thc complete functionality of the system.

.

The instructor h a access to all signals which are available in the simulator and hence has the possibility to manipulate them. Although this is not like a programmed malfunction or a scenario as known in an OTS, this allows training of the operator in detection. analysis and reaction to failures. Furthermore, in every moment during the training the instructor can make a “snapshot” of the current situation and reload it for Further training or analysis at a later time.

However, reflected at the AN SI/ISA standard, there are a couple of’differences, as e.g:

. .

Normal operation is limited to start up, shut down and load changes. Component or plant trips of course will happen according to the protective automation system. However. the plant dynamic response is not necessarily exactly the same as in reality in every case and it might not be available for a Fat restart. The initial conditions are limited to cold start and full load. No backtrack. slow time or fast time is foreseen in the OGS. Due to the early availability, no update to the real plant is part of the OGS scope. However, this could be supplied as an additional option i.e. after end of hot commissioning. Also due to the early availability. the issue of accuracy doesn’t apply as no data for comparison is available at that point in time.

The OGS therefore is close to a reduced-scope simulator within the ANSlilSA structure, with a limited scope of simulation and instructor features, but with a high realism automation representation. It has the same structure and is based on the same principles as an OTS. Therefore according to the needs of the customer, extensions to a full scale O’I’S are possible at any time and to any extend by implementing functionalities like malfunctioiis, scenarios or by applying a model tuning in order to

Stimulated HMI The I-IMI system and the graphical displays are identical to those used in the real plant. Thc information to be exchanged with the process i s obtained from and sent to the AS emulation (“stimulation”). Thcrcforc the training cffcct is maximized since the trainee sees no difference

33 1

Fossil Fuel Power Plant Simulators Requirements. ISA, North Carolina. May 1994

improve the dynamic representation and to implement later changes. as illustrated in figure 5.

t

Customer benefit

Malfunctions, scenarios, model tuning

PST Simulator

OTS

Complexity and cost

Fig. 7: OGS between Plant Shop Test (PSr) and 01s This staggered approach complies with the targets of a training tnol of being available already for initial training of the operator. being as realistic as reasonably possible and being extendable to a full scale OTS if required for a later extended and continuous training.

5 . SIJMMARY

The Operator Guidance Simulator was developed in order to meet the customer's demand for an early available and pro-ject specific training tool for initial and continuous training of the operational staff of a new power plant. The close linkage of the OGS to the project specific engineering of the process automation allows performing the training already at a time before hand-over of the plant to the client. Thus thc plant can be operated right from the beginning with well-trained personnel. Due to the same reason there is maximum congruence between OGS and the real plant regarding automation and HMI. This allows highest training efficiency. Since the development of the OGS i s highly integrated into the project execution. it can be offered at an attractive price together with the power plant. For further training quality the OGS can be upgraded to a plant specific 0 TS.

Rel'ercrices

ANSI/ISA-S77.20- 1993

332

-

Functional

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

APPLICATION O F AFFINE TRANSFORMATIONS T O REAL-TIME POWER SYSTEM EMS FUNCTIONS Emmanuel D. Crainic a ', Alexander 1. Petroianub de rheuux Inytitut de recherche d'Hydro-Que'hec, IRCQ, 1800 Blvd Lionel Boubt, Chrennes, QC, Cunudu,.J3X I SI Department ofElectrica1 Engineering, bniversity oJCape rown, University Private Bag, Rondebosch 7701, Republic of Soulh Africa

a Logicieh

Abstract: The paper introduces the concepts of affine transformations in the methodology and in the algorithms for real-time power system EMS functions. It demonstrates the advantages of this new conceptual approach. The advantages are: i) a new formulation of the state estimation problem and related applications. ii) a faster and more reliable solution obtained through direct. non-combinatorial techniques. Copyright 82006 IFAC Keywords: affine transformations, power systems, online applications, state estimation, bad data detection and identification, measurement and parameter validation.

I . AFFINE TRANSFORMATIONS: AN

Basically, the state estimation and the related E M S functions arc nonlinear problems; thcrefore. the algorithms used to solve them must be robust, fast, and ensure a feasible solution. The need €or improving the algorithms used in solving real time power system problems is very strong. In this paper, the authors introduce an affine geometrical approach for the solution of the state estimation and other functions related to it, like bad data detection and identification, and measurement and parameter validation.

INTRODUCTlON

Power systems are operating nowadays under much more difficult conditions than in the past. These difficulties are due to the following new factors: competitive operating conditions, higher fuel costs, environmental, institutional, and societal constraints. Even in the previous developed energy management systems (EMS), the state estimators were considered as suffering from the following major drawbacks (Handschin and Petroianu, 1991): i) slow response time i.e.: snapshot or static instead of 'tracking' or dynamic estimation, ii) poor quality of solution, especially with regards to reactive power flows, voltages, and tap positions. iii) lack o€ a strong local, busbar oriented validation.

Most of the physical quantities involved in the state cstimation modcl arc complcx numbcrs bclonging to the 1-dimensional complex space C'. This complex space is mapped into a 2-dimensional vector space 2, whose elements are involved in linear operations, i.e.: multiplication of a vector by a scalar and addition of two vectors. Of interest are not only the operations performed on these vectors, but also their mutual position and the geometric properties of the figures made of these vectors on the plane (Petroianu, 1969).

As of a result of such weaknesses, in some utilities the state estimator did not operate properly. results for reactive power being disregarded. In other utilities the state estimator was not really implemented. A large utility (Tokyo Electric Power-TEPCO) does not even have a state estimator; instead of it a double system control and data acquisition system (SCADA) hardware and software solution is utilized for obtaining the reliable real-time data base.

For this reason the aftlne space E. a space of points, is introduced and which is associated to a vector space ~. E of the same dimension. in the sense that: i) for each pair of points (u, h) E E, the difference (u-h) between them is a vector AB in the vector space E , ii) for each vector in the vector space and rhr each point in the affine space E, adding the vector to this point results in an anothcr point in the affine space E,

* Corresponding author: Emmanuel D. Crainic, E-mail address: c ra in ic.em man uel(@ req .ca

333

iii) every triplet of points (a, b, c) relationship fa-b) + (b-c) = fa-h).

EE

satisfies the

In the spirit of his 1872-Erlangen Programnz, Klein ( I 974) regarded any geometry as the study of those properties of figures on a given space which are invariant under all the transformations of a specified transformation. is any group. An @ne transformation that preserves parallelism of lines and the ratio of distances between colinear points. In matrix notation and using the homogeneous coordinates, first introduced by Mobius (1 827): the following main affine transformations in a 2dimensional space, i.e.: rotation by an angle cp counter clockwise about the origin (position of axes unchanged): I coscp -sin9 0 I R,= I sincp coscp 0 I (1) I 0 0 11

I:ig. 1 Electrical line II model representation 111the equations (5) and ( 6 ) the voltages a e complex numbers representcd by their modules V,, vk and by their angles 6,. fik with the difference: Omk = 6, - 61, (7) considered to be positive (all over this paper the hypothesis is made that m is the sending and k the receiving nodes of the active porn er). Analytically. the complex powers &,k and Skmare as follows:

reflection in the x axis:

M,=IO

-1

01 01

10

0

II

0

I1

0

scaling:

IL S1=l0

)y

01 01

10

0

II

I1 T,=IO 10

0

PXI

1

PSI

0

II

(3)

In (8) and (9) Pmk.Pk, are the active and Qmk, Qkm the reactive powers. They represent the real and the imaginary parts of the complex numbers Smk and &,:

trunslution: (4)

form the general affine group GA (2. R) which is a semi direct product of the general linear group GL ( 2 , R) and the translations in E by vectors o f E .Given a group G acting on elements o r an affine space E, a real value runciion I depending or1 these elernenls is called an invariant of G if, whenever a transformation g E G changes I into I*= f (g) I, where f is a function of g alone. i.e. does not depend on the element which is transformed. If f = 1, I is called an absolute invariant. In the case of the 2-dimensional space the general affine group GA (2. R) preserves the rutios (absolute invariants) between arias of subsets of E, or of E , while the arias themselves are relative invariants ofthe group (Olver, 1995).

From the above expressions, the active and reactive power5 in (5), (6) and in Figure 1 are: mk = Pm, (16) km = 'km (1 7) Q = Ql,,k- 0.5V',,,B'"'n,k (18) Q km = Qkm- 0.5V2~BCapmk (19) The module of voltage difference dYmk and, respcctively, the aria AVmkof the voltagcs triangle (Figure 2) are given by: dV,k

2. POWER SYSTEM LOAD FLOW MODEL

= (V2,

+ V*k - 2V,Vk cosO,k)

AVmk

2. I Power system loadflow equations

= 0.5V,Vk

sinemk

For an clectrical transmission line, the most common component ol' a power system (Figure l), the apparent power flows, expressed as complex numbers, are

Fig. 2 Electrical line voltage diagram

334

(20) (21)

The radius Pmk of the circle in Figure 3 is defined as: Pmk = (g*mk+ b * m d

()

'

cos2ymk= (g2,, - b 2 d 1 dnli sin2Ymk (2gmkbmk) / P2mL

(22)

By taking into account the equations (12)-(15) and (20). the active power losses for the line (rn, h) are. by definition: GPrn= ~ Plllk + Pkm= gmk dV2mr (23)

the angle (omk defined as: (Pmk = atan (vmk

+ Qkm= bmk

dV2mk

/V,ndVmk (32) cos (Ymk - (Pmk) = (V2m-vmvhcos~n,k) sin (ymk - q m k ) = V,Vk sinBmk/V,dV,k (33)

(24)

the angle (&,I

2.2 Electrical line base angles

defined as: (Pkm = atan (Qkm

In the next section the following electrical line angles and relationships between them will be extensively used: the angle &k between the voltages ym,&Three basic formulae (25), (26) and (27) allow evaluating it:

/ Pkm)

(34)

The following trigonometric functions may be derived for the difference of angles (qkm- ymk),i.e : (vkm - Ymk)

= (V'h

sin (qkm- ymk) =

tan%!,= (b,LP,L-g,hO~)/((P,,Lv~n)2;(g,hpmhfb~Vma)) ( 2 5 ) tanOnik= -(bnikPk,~-g,hVlm)i((Pnikv~) -(siii~Priii+bmhVhi,i)) (26)

-vmvh~Ose,,,,)/VhdVmk (35) V,Vk sinBmk/VhdVmk (36)

Iwo other points on the circle of radius Pn,k are of interest: the point g", at an angular distance equal to 0,k counter clockwise from the point gd. and the point gk,at an angular distance equal to 0,k clockwise from the point gd

tanemk = ( P m k Q k m - PkmQmk) 1( P m k P k m + QmkQkm) (27) the angle l/n& expressed as: Yink = atan (bmk / gmk)

(31)

The following trigonometric functions may be derived for the difference of angles (ymk - (Pmk), i.e.:

and the reactive power requirements are: K ? r n ~= Qmk

Pmk)

(29)

(30)

(28)

From (23) and (24) it may be seen that the vector

ci

3. AFFINE TRANSFORMATIONS ACTION

(oPmh,OQ,,,~)makes an angle Ymk with the x-axis: it is colinear with axis A A (Figure 4). The axis A' A

intersects the circle of radius P m k in two points (Figure 3). g"whose coordinates are (&k. bmk)and gd whose coordinates are (-gml,-hmk). These two points, together with the origin 0, are the fixedpoints and the line II'D (Figure 6). tangent in the point gd to the circle of radius P,,,k and which makes an angle with the x-axis equal to (yrnk-x), is the fixed line of some of the affine transformations used in the next section. The following trigonometric functions may be derived for the angle 2ymk,i t . :

where V, in (40) and (41) is given by the formula: vin= ((Pkin-v'kgmk)

f

(Qkm-V'kbnd ')" '/ PinkVk

(42)

The systems of linear equations (37), (38) and (40), (4 I ) represent afjne transformations, from one to another, of the electrical states (Plnh.Qmh,V,) and (PkmrV k m , Vk) at the extremities m and k of the line. With the matrix A defined as:

Fig. 3 Electrical line base angles

335

the equations (37), (38) and. respectively. the equations (40). (41) may be written as follows: Ik’km

IPm,

I

IQkml

A

I

Ik’km

(A) A-’ l Q k m l

IQmkl =

I l l

I l l

I (44) ‘The coefficients matrix Bgk of the right side of equations (48), (49) represents the af$ne transformation of point g”to point k (Figure 5), bcing the product of a rotation of angle (qkm-ymk) counter clockwise (see equations (35), (36)). followed by a scaling equal to (VkAVmk), i.e.:

I l l

The aria, taken counter clockwise. of the triangle formed by the points Omk (Figure 4) is an affine relative invariant, i.e.: %k=

0.5(pmk

Qkm

- Pkm

(45 1

Qmk)

Fig. 5 Fixed point to electrical transformation

Fig. 4 Electrical state to electrical state affine transformation

32

Fured

point transjornzation

to

electrical

slate

state

affine

I ( ~ ~ , - v ~ , V ~ c o s 0 , ~ ,-Vn,VksinBmk ) 01 Bgk = I VmVksinemk (V2,-VmVkcosAmk) 01 ( 5 2 ) 0 11 1 0

ajfine

?he systems of equations (12). (13) and (14). (15) may be rearranged as follows:

7 he matrix Bgk has the determinant = (vkAV,nk)* and it is invertible. Consequentlj, the equations (48), (49) may be written as follows:

Pmk= (V’, -VmVkcosOm,)gmk + VmVksinOm,bmk(46)

Om,= -VmV,sinem,gmh+ (V2m-VmVhcosBm,)b,,,h (47)

lPkm

I

lQkml

Pkn,= (V2k-VmVkCOS0mk)gmk - VmV,sinOn,,bm, (48) Qkm = VmVkSln0mkgmk + (V2k-VmVkCoS0,,,k)brnk(49)

I 1 I l l

lPkrn

lEnik

I (53)

= Bgk lbmk = (Bgk) B-’gk lQkml

I l l

I l l

The aria, taken counter clockwise. of the triangle Omg” (Figure 5 ) is given by the formula:

The coefficients matrix B,, o f the right side of’ equations (46), (47) represents the afine transformation of point g”to point m (Figure 5 ) , being the product o f a rotation of angle (Yd&mk) clockwise (see equations (32), ( 3 3 ) ) followed by a scaling equal to (V,nAVmk).i.e.:

d,g=

0.5(Pmkbmk-Qmkgmk)= O.jVmVkSitlt),kP’”k(54)

and the aria, taken clockwise, of the triangle Okg” (Figure 5 ) is given by the formula.

nkg= - o . s ( P ~ ~ =~ O~ . ~S -V Q~ V~ ~~ S~~ ~~( 5~~5 ),)~ P * ~ ~ 3 3 Electrical trunsforma tion Ihe matrix Bgmhas the determinant = (VmAVmk)’and it is invertible. Consequently, the equations (46), (47) may be cvrillen as hl~ocvs

state

to

parallel

line

affine

The systems of equations (12), (13) and (14), (15) may be rearranged a5 follows:

336

-VZrngm,) /VmVk (56) -CoSO,&nk +SlnOmrbmk = = (Qmk -VZmbm,)/VmV,(57) -sinOmkgmk -cosOmkbmk /VmVk (58) -cosBmkgmk-sinOmkbd = (Pkm-V2kgmk) Sinemhgmh-cosomhbrnk = (Qkm -VZkb,,,,)~VmVh(59) The right side of equations (56). (57) represents the .fine transformation of point m to point g" (Figure 6):

I glnmkl

I 'mk 1

I bmmkl= r m a I Qmkl I l l I l l

(60)

with the matrix Tmgdefined as:

Fig. 6 Electrical state to parallel line affine transformation 4.AN EXAMPIE In a large power utility, a transmission line 734.6 km long operates at 765 kV. The constructive parameters are as follous: 1) conductor type - Zebra, 2 ) number of conductors per phase - six, 3 ) distance between the conductors (bundle spacing) - 0.4 m.

Table I Line data

3.4 Relative and absolute invariants of the afine transformations The affine transformations approach to the power system load flow equations is an open subject; not all possible affinc transformations were treated in this paper, and for those selected, only a part of the relative and absolute invariants were presented. They play a major role especially in measurement and data validation. For instance, the ratio of the arias of the triangles Omg, Okg (Figure 5 ) , which is an absolute invariant: (Pmkbmk-Qmkgmk) 1(-Pmkbmk+Qmkgmk) 1 (66)

Table 2 AMine tramformation invariants VI, V,,

and links only the active and reactive power measurements. The following ratio, which is also an absolute invariant: (Amg Akg) /' (Amm Akk) = 1 (67) allows validating the voltage at one side of the line when the electrical state o f the other side is known.

337

=

1.00 [pu]

line. iii) the fact that in the affine space E, these triplets are afine transformations of each other (see matrix A, section 3.1)

Table 3 Aftine transformation in\ ariants Vk= 0,98 .V,,, = 1,02 [pu]

Lm

Qknl

Qknl

-3,33

1,78

Akk

Ak

U 2

15)

5.3 Parameter estimation

Pkni

If the triplets of measurements (P”’”,k, Q , k , Vmem) and ( P t n c k m . Q“2km. Vlllck)are consistent for a fair amount of time, one may proceed to better, or dynamic. parameter estimation. This may be done by using the matrices of type B-Imgor / and B-lkgwhich are matrices of electrical state to fixed point a f f i x transformations (section 3.2). This type of parameter estimation may be seen as a localized (per network elemcnt) dynamic or tracking statc estimation: potentially, it may be adapted or extended as parallel state estimation.

U 2

16

390,33 406,26

6. CONCLUSlON

In rablc I , the clcctrical parameters are calculated for Pbaie = 100 and Vbarc = 765 kV In Table 2 are presented the results that correspond to V,,, = Vk = 1 0 pu and in rable 3 those that that correspond to V,, = I 02 and Vk = 0.98 pu. All the formulae developed in the paper ma) be checked based on the information presented in these Tables

The affine transformations constitute powerful tools in dealing with and solving the linearized models of nonlinear problems encountered in power systems. ‘They are especially helpful in the context of on-line power system applications, where speed and robustness are critical constraints. This novel approach was shown to be adequate to various modern requirements of an EMS: state estimation, bad data detection and identification. measurement validation and parameter estimation and correction. Also new in this approach is the treatment of SCADA measurements. not as individual measurements, but as coherent triplets of measurements. dething a physical reality, i.e.: the electrical state of the extremities of a line,

5. ON-LINE POWER SYSTEM APPLICATIONS 5.1 State estimation for distribution networks In the affine approach solution to the state estimation problem the notion of topological spanning tree, which is a tree having (N-1) edges (lines. transformers, etc.) linking all the N nodes of the network plays a central role. In the case of distribution networks, which are predominantly radial, the topological spanning tree is self-evident. What is required to be known is one of the pairs (P,,, Qmk)or (Pkm.Qkm)of active and reactive power at the extremities m or k of each o i (N-I) edges of the spanning tree and one voltage at the arbitrary chosen reference bus. With this information, and starting from the refercncc bus, the formulae of type (39) or (42) are used to obtain the voltage module(s) at neighbouring node(s), and the formulae of type (43) to obtain its affine pair (Pkm,Qkm),respectively, (Pmk. Qmk). It is, basically, the same strategy as that developed in the first state estimator based on line flow measurement (Dopazo. et al. 1970), but instead of non linear systems of equations of type (12)-( H), systems of linear equations of type (37)-(38) or (40)(41) are used.

7. REFERENCES Dopazo, .1.1:., O.A. Klitin, G.W. Stagg and L.S. Van Slyck. (1970). State Calculation of Power Systems from Line Flow Measurements. IEEE Trans. Power App. Syst., Vol. PAS-89, No.7, 1698-1716. Handschin, E. and A.I. Petroianu. (1991). Energy Management Systems: Operation and Control o j Electric Energy Transmission Systenzs. Springer Verlag, Berlin Klein. F. (2004). Elementaipy Mathematics from an Advanced Standpoint: Geometry. Dover Publications. Mineola, New York. Mobius, A.F. (1827). Der harycentrische Calcul: ein news FlilJrmittel zur analytisrhen Hehandlung der Geonzetrie, Leipzig. Olver, P.J. (1995). Equivalence, Invariants and Symmetry. Cambridge University Press, Cambridge. Petroianu, P.I. (1969). A Geometrical Approach to the Steady State Problem of Electrical Networks. Rev. Roum. Sci. Techn.-Electrotechn. Et Energ., Vol. 14, NO. 4.623-630.

j . 2 Multiple bad data detection and identification It is known that grossly erroneous measurements and topological errors (e.g., breaker’s false status) cause state estimation‘s failure. The authors propose a direct method based on: i) the use of triplets of measurements (Pmemk, Q”lernk, V C m and ) (P”lekrn, Qmnekm, Vmck).defining the electrical state at the extremities of the line, ii) the fact that any one of these two triplets describes entirely the internal electrical state of the

338

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ELSEVIER

PU CATI BL o N SI AUTONOMOUS POWER NETWORKS BASED POWER SYSTEM A. Jokic, P.P.J. van den Bosch Eindhoven [Jniversity of Technolom, Department of Electrical Engineering, Postbus 513,5600 MB Eindhoven, The Netherlands Tel t 3 1 40 247 3307, e-mail A Jokic@tue nl

Abstract: I'he operation of future power systems will be more challenging and demanding than present systems owning to increased uncertainties (renewables, dispersed generation), less inertia in the system, replacement of centralized coordinating activities by decentralized parties and the reliance on dynamic markets for both power balancing and system reliability/security. The paper presents the concept of Autonomous Networks to cope with this increased complexity while enhancing market-based operation. Power balance problem and system reliability through provision of ancillary services are formulated as an optimisation problem for the overall autonomous networks based power system. Copyright Cj2006 IFAC Keywords: power systems, power distribution, renewable energy systems, reliability, economics

I . INTRODUCTlON Power systems are going through significant changes in many aspects. Central to the many of the changes are two major paradigm shifts occurring in the structure and operation of power systems. Major structural changes are caused by large-scale integration of privately owned Distributed Generators (DG) in all levels of traditional, vertically structured power system. In operational sense, there is a shift towards the use of competitive markets as rriechariisrris for both balaricirig power production and consumption and for ensuring system's rcliability. Indeed, these two major changes are coupled and one is supporting the other. Introduction of de-regulated, open-access markets should encourage investment in DG by creating new business opportunities. On the other hand, non-dependence on fossil fuels and environmental issues supporting renewable based DG together with high efficiency of some DG units, like for instance combined heat and power units, are introducing novel players having an impact on power system economics and creating a rich playground for existence of competitive markets. All this as well results in enormous changes on the more technical side of power systems. Network, as a dynamical system, is changing its characteristics on all time scales. Introduction of large amount of DG is a change towards the system with striking characteristics as large time and space heterogeneity, low inertia, extremely large uncertainties, and extreme increase in number of generators in comparison to traditional power systems.

Large variety of DG technologies (micro-turbines, fuel cells, wind turbines, photovoltaic (PV) arrays, to name a few) makes the system more heterogeneom with respect to the traditional power system that was completely relying on large-scale synchronous generators. Across the set of these different DG technologies, there is a huge variety of possible time responses to the changes in reference values for power outputs. Further more, many of the technologies, like fuel cells or PV, are inertia-less, and all the renewables, like wind turbines and PV, are practically uncontrollable in their power outputs and are introducing large production fluctuations and large uncertainties in any future system state predictions. It is the major challenge of managing the system of such an underlying technical complexity, even more since the solution has to enhance the major driving force causing the change - the existence of unbundled, competitive markets as central mechanisms for system operation and reliability. It is also evident that the efficient solution necessarily needs to be based on large amount of players capable of competition in all the markets. One of novel paradigms for defining the operation of distributed generation that has gained significant attention in power system society is the concept of microgrids (Lasseter, 2002; Venkataramanan, and Illindala, 2002). There is no simple or rather complete definition for a microgrid that in concise way presents its major characteristics and objectives. The papers of Lasseter (2002) and Venkataramanan and Illindala (2002), which are among the first references on the topic, present a microgrid as a

339

cluster of loads and microsources (DG units) operating as a single controllable system that provides both power and heat to its local area. To the utility the microgrid can be thought of as a controlled cell of a power system, while to the customer inside the microgrid, it can be designed to meet customers special needs; such as, enhance local reliability, reduce feeder losses, support local voltages, provide increased efficiency through use of waste heat, or provide uninterruptible power supply functions. As in those two papers, in most of the references dealing with microgrids (Lasseter, and Piagi, 2004; Kueck, e/ a/, 2003), the major emphasis is on microgrid’s internal objectives, problems and their solutions. One of those objectives that has been widely studied (Pecas Lopes, e/ al, 2003) is the possibility of a microgrid to efficiently operate in an island mode, i.e. disconnected from the rest of the power system. Much less attention has been paid to the relationship between the microgrid and the local utility, and the main feature of this relationship is often summarized in the statement that a microgrid is a well behaved, “good citizen” or “model citized” (Lasseter, et al, 2002) in the overall power system. By “good” behaviour, it is in most cases thought of a low impact, or more importantly on absence of a negative impact, that a microgrid has on the electricity network, despite a potentially significant level of generation by intermittent renewable sources (AbuSharkh, e t a / , 2004). This low impact is attained by a good match between generation and load inside microgrids, even for a faster time scales (seconds). What is however less clear is the reward that would encourage the microgrid to behave in this way, especially in the case when the outside system is rather strong and the microgrid’s total installed capacity is relatively small so that even the worst case, sudden internal imbalances would have rather low impact on the outside system. In the case of a significant number of microgrids in the system, their mutual and overall system impacts will indeed become significant, and “good citizen” behaviour would not only be desirable but is also a necessity. To the best of our knowledge, some more detailed elaboration of the overall system’s operation in such a microgrids-based system has not yet been presented. Still, several references are addressing this topic. I n (Dimeas, and Hatziargyriou, 2005) the operation of a multiagent system for control of microgrids in a market environment is presented. Only the real power market has been considered, and the emphasis of the paper is on the details of an auction algorithm and the operation of negotiations agents. In (Abu-Sharkh, et al, 2004) the possibility of the creation of local ancillary services markets has been addressed as an important issue. Similarly (Kueck, et al, 2003) refers to provision of ancillary services from microgrids as a future research need. The purpose of this paper is to take one step further from the microgrid concept. It presents the concept of autonomous power networks as a realistic approach to dealing with increased complexity and uncertainty of the future power systems while enabling markets-based operation for both dispatch (economic) and ancillary services (reliability).

2. AUTONOMOUS POWER NETWORKS Although it shares many of the objectives and characteristics with the microgrid, an Autonomous power Network (AN) has an additional property: it is a major building block of a power system in all of its layers, i.e. physical, economic and reliability. The idea of the overall system being a network of ANs is crucial. With the strong emphasis on this, which is the central idea to the AN concept, in this section we continue with presenting the concept of AN. I n a more formal and detailed way, this is further continued in the next section. An AN is the aggregation of networked producers and consumers in a relatively small area with respect to overall system, whose operation is coordinatedicontrolled with one central unit acting as an interface in between internal producerslconsumers and the rest of the power system. The goal of such a unit is efficient deployment of internal recourses and active involvement in overall system competitive markets where it reflects the preferences of its owners, i.e. of its internal producersiconsumers. In the physical as well as in the economical layer (power and ancillary service markets) each AN is presented as one producerlconsumer. It is this requirement for the active involvement in all of the layers of the system that defines AN to be a major building block. For power balance and reliability issues (ancillary services) this implies that AN is obliged to provide, in an appropriate form, the information of its own actions and to take the responsibility for those actions. Note that the “good citizen” behaviour, if defined as within the microgrid concept, implies high uniformity of microgids in some of their characteristics, e.g. each microgrid has well controlled power exchange with the rest of the network, even for the time scale of seconds. In the AN concept, there are no such a priori characterizations (constraints) of an AN, and different ANs can have significantly different characteristics. However, it is crucial that all those, possibly different and time varying characteristics are taken into account on the global level, so that the overall system will operate efficiently and reliably. Good citizen behaviour for an AN is therefore defined by the requirement for its active and responsible involvement in the energy and ancillary service markets, as well as for following a set of predefined rules in provision of the commodities sold in those markets. Energy and ancillary services markets provide global coordination and time synchronization of ANs actions. They have a central role in keeping the power balance in between ANs, and in ensuring the overall system’s reliability by accumulating sufficient levels of ancillary services, e.g. regulation capacity, spinning, non-spinning or operational reserves, etc. As presented in the next section, ANs can be both producers and consumers of ancillary services. This is a novel and unique feature, and is in the line with the driving forces for the power system restructuring since it introduces a large amount of well defined players in ancillary service markets. In

340

AN based power systems, spare capacities for ancillary services are treaded in a equivalent way as energy in energy markets. As a result, the operational structure of ancillary service markets becomes analogous to energy market. With the increase of uncertainties in the future power systems, e.g. due to the increased penetration of renewable sources, it is expected that the value of transactions in those markets will increase as well. To summarize, an AN is seen as an intrinsically local co-operative venture. Each of its internal members accepts the AN as its operational authority and in return shares the benefits of this co-operation. The AN is therefore the highest authority for those members. Each unit (producericonsumer) can also act as an isolated player, but it is then required to take responsibilities in all layers of the system, i.e. it iq preqented in the overall syqtem as an AN. This especially holds for large-scale synchronous generator based producers or large-scale costumers, e.g. large factories, that are by themselves capable of efficient involvement in markets. For a price inelastic consumers inside some AN (e.g. residential loads), AN becomes a market agent acting on their behalf. Furthermore, for those consumers, an AN offers a possibility of their efficient involvement in ancillary service markets if they agree on a certain level of interruptions in power supply. In contrast to the microgrids, that are usually associated with a "small community", like for instance typical housing estate, isolated rural communities, academic or public communities such as universities and schools, commercial areas, trading estates and similar, what implicitly defines a microgrid as a very small cell of a power system, we do not restrict to any particular sizes of networks candidates for AN. Possible different sizes of coexisting ANs are a result of their efficiency in a competitive market environment. For existence of efficient overall markets, it is important that large amounts of ANs are mutually interconnected. A well-meshed topology of transmission networks fits well for this purpose. In that network topology the candidate areas for ANs are all medium and low voltage networks with aggregated DG units and corresponding loads. An illustration of an AN-based power system is presented in Fig. 1 .

3. POWER BALANCE AND RELIABILITY By treating ancillary services (regulation capacity, spinning, non-spinning or operational reserves, etc.) as market commodities, the objectives of the corresponding markets are to ensure a required reliability level of power system. This required level of reliability is prescribed by the required total accumulated amount of each of the commodities. For instance, hourly spinning reserve requirements are usually defined to be the grater of a fixed percentage of total forecast demand and the largest on-line unit. To simplify mathematical formulations we will consider only one ancillary service and denote it with A, but other ancillary services B, C, ... could easily be included. Generally, A is a capacity that is available as a power injection, or load reduction, in the system within some specified time interval. The systems required reliability level at some time t is then defined with

1A, ( t ) 2 Afey( t ) ,

(1)

I

where A, is available capacity at bus i, and A""(t) is required capacity that has to account for an uncertainty in power productionldemand and can be different for different t. Assume that for a certain autonomous network n it is required to have AF1(t) for a reliable operation of that AN. For simplicity, further in the text we will leave out time dependence i n the notation, although we will consider all the quantities being time dependent. Then for some autonomous network n it is necessary to have 4,

A,,

-

2 A,yq

A:

(2)

r=l

where A,,l is capacity [W] available from unit i inside AN,

mrz

is total number of units inside '41

autonomous network n, so

.4,,

is total capacity

1-1

available in the AN, and A,:* is the capacity that the AN sells to the outside system, i.e. to other ANs. Note that if A>: is negative, the AN is buying that amount from the outside system. Now, for the overall system we can write

11=1

i=1

,,=I

11=l

Since we assume the overall system being a network of ANs (i.e. any consumer or producer is in some AN), we can take A'"'" =CAT' , i.e. required n

overall system capacity is sum of required capacity levels for each AN. From (3), for the reliability of the overall system, one of the goals for the outside A: = 0 . market is to achieve I?

Fig. 1. Autonomous networks based power system

Note that with this formulation, capacity from ancillary services is traded in an equivalent way as real power. All ANs are either "producers" or "consumers" of spare capacity for ancillary services and the overall balance has to be achieved. This is in contrast with today's power systems where the 341

required capacity for system's reliability is determined by ISO. In an AN-based power system, trading with ancillary services capacities is closer to the trading in PX. Attaining the required overall system reliability level becomes a decentralized decision and each AN contributes. This decentralisation is desirable due to the overall system's complexity and its large-scale, since for AN it is easier to assess its internal required capacity level based on local predictions and on generally better insight into its internal situation. The power balance within some autonomous network n is given with

c m,,


,=I

-

e:

Our next goal is to present the real implementation of solving this problem by assigning one optimisation problem to each AN market agent, and defining the goal of the overall system markets. For that purpose we use Lagrangian relaxation, but dualize only coupling constraints (1 0) and ( 1 1) to form a partial Lagrangian

The dual problem is now given with = 1%

(4) mn

where P,,/ is the power of unit i in AN n, so

P,,, /=-I

where t(Al,,AA) is concave function defined with

is total power produced inside AN, L, is total internal load of AN, and 4:'" is power that AN sells to the outside system (it has negative value if AN buys power from the outside system). Obviously, from (4), for the overall system power balance, one of the goals of the real power market is to achieve = 0 (no exporthmport assumed on the level

c elex n

of overall system). With the abbreviations A,

-

[A,, , ..., A,,

11,,,

1,

we

e2= [P,, ,, ..., Pn m,, I , can

formulate

the

following optimisation problem for the system:

subject to

(1 4)

subject to (6)' (7), (8)' (9). The optimal solution 16,A; of ( 1 3) has economical interpretation: those are the overall system spot prices for power exchanges and ancillary services. Therefore, the task of the overall system markets is the solution of (13). Note that for coupling constraints that actually account for the transmission network connecting all ANs, we have used the simplest possible form, i.e. (1 0) and (1 1). Including real physical constraints coming from transmission network would result in possibly different spot prices Tor different buses in the network (nodal pricing), i.e. the dual solution has a physical-economical intcrprctation. It is also possiblc to includc thc costs paid to transmission network owners, or constraints on distribution of ancillary service capacity over the overall network, i.e. nodal pricing of ancillary service. Now that we have defined the goal of overall system markets in a rather general way, we can define objectives for each AN. Given some Ap and A d ,minimisation problem in (14) subject to (6)-(9) has a nice property that it can be decomposed per AN. So, for autonomous network n ( n = I, ..., V ) we have

where j,,(e?, A,?) denotes the costs associated with f:, and A,, while (6)-(9) denote all constraints defined for ANs (note these constraints are decoupled for each AN), and (10) and ( I I ) are coupling constraints. In more general formulation, we can reformulate (5) to be maximisation problem where fn(P,.A,) denotes the benefit for each AN. The solution of optimisation problem (5-1 I ) presents exactly the goal that would be achieved with an efficiently designed overall markets with the assumption of perfect competition. So above formulated optimisation problem is the "ideal" that we would desire in the real-life system operation.

rn..

This is nothing else than minimising AN costs while respecting all AN'S physical constraints (like for instance constraints in units level), including AN

342

power balance ( I 6), constraint on AN reliability ( 1 7), while maximising the profit from trading with the outside system in the case of spot prices A,, and LA . This optimisation problem is assigned to each AN market agent. The set of AN'S constraints (19) accounts for the coupling between real power and ancillary service capacity. This coupling implies that for attaining the actual optimum, real power and ancillary services markets should be coupled as well. This would however lead to more complex market operation and is not a usual practice. For completeness of the presentation and because of the novel way of trading with ancillary service capacity in AN-based power systems, we shortly address this possibility. Assume that there is one combined market for P and A, and that it has announced the prices Ap and A A . With these prices each AN market agent solves its local optimisation problem (15)-( 19) and announces the values P" and Aex for that AN. From (12), the values of sums in (10) and (11) give us a subgradient for (1 3). Knowing this sub-gradient, outside market is able to make a correction in the prices. With proper price updates, this iterative process results in optimal solution. For more detail we refer to (Conejo, and Aguado, 1998) where such an approach was used in optimal power flow problem in multi-area system. A more practical and commonly used solution is the decoupling of the markets and replacing the iterative process with the solution based on bids provided by cach markct playcr. Each AN markct agcnt is from ( I 5)-( 19) capable of determining its incremental cost (gradient) for provision of [P". A " ] . Since outside markets are decoupled, each AN is facing the trade-offs in the decision of making optimal independent bids for both markets. Apart from this trade-off in decoupling, optimal bids would be based on some profit maximising strategy, e.g. prices in a competitive environment do not need to correspond to the costs. In real operation, AN optimisation problems (1 5)-( 19) will probably include the whole variety of weighted terms in the AN'$ benefit function. For instance, it can include local heat needs to optimise the operation of combined heat and power units. Close proximity of generation and loads, its relative small size and rather good insight into its internal situation makes an AN capable of accounting for many of its internal needs and reflecting them into the overall system markets. The operation of the decoupled overall system markets is similar to current operation practice. However, one of the differences is that received bids will not be aggregated in demand and supply curves since each AN makes bids for the whole intervals of P" and A'" that generally range from negative (buying offers) to positive values (selling offers). A solution for market clearing is however equivalent to current practice: for each spot price market aggregates the received curves. The price for which the total aggregated curve fulfils (11) (or (10) in

case of the capacity market) is the market-clearing price. This general operational formulation of AN-based power system is valid for both forward time and realtime markets. Usually forward time markets have a horizon of one day and result in a unit commitment solution for the overall system. For the AN-based power system we can still expect the existence of markets with day-ahead horizon, due to daily repetitive nature of accumulated loads in the overall system and since for large-scale units this long horizon is also necessary for solution of unit commitment. However, DC units have much shorter up and down minimum times, and can quickly be brought back on-line once they where shut down. Further more, increased uncertainties (renewables) make the future AN'S state badly predictable. Therefore it might be beneficial, or even necessary, for an AN to perform a dispatching and unit commitment in a receding horizon manner with much shorter time horizon (e.g. several hours) that is properly adjusted with respect to the ANs internal characteristics. In this way, an AN can efficiently adopt to novel situations what results in its efficiency in real-time markets. The re-dispatching in receding horizon will be based on more accurate predictions of both internal demand and renewable sources and of market prices for real power and ancillary services. What is important is that the way each AN schedules its resources can be completely independent of other ANs, i.e. there is no need for synchronisation. The only synchronisation of actions is made in day ahead and real-time markets. 4. EXAMPLE The simulation of optimal AN dispatching in the day ahead markets, based on predicted spot prices for real power, and two ancillary services, named A and H, has been performed. The simulated AN consists of 12 generating units, out of which 8 are controllable and the remaining 4 are wind turbines. The considered trading period was half an hour. Required levels ( B'"4 ,A"Y ) of capacities for ancillary services are presented in Figure 2. Predicted spot prices of real power ( P ) and ancillary services A and R are presented in Fig. 2, while Fig. 3 presents corresponding optimal results for Y" , A" and Be" . The set of constraints that accounts for the coupling between real power and ancillary service capacity (i.e. corresponding to (19) in the general formulation), is taken in the following form:

t,,,,

0 5 Al 5 min( Al,mm,4 - t,,,ln,- 4 ) i = 1, ...,8 i = I .....8 0 2 B, I min(B, ,.P, lllax -

e)

i.e. ancillary service A denotes capacity available for both up and down movements in power production, while ancillary service 5 denotes (slower) available capacity for up movements in power production (power injection). The values of prices, internal AN'S loads, and production from renewable generators are chosen in 343

such a way that the trade-offs induced by coupling of commodities ( P , A , and B ) is easily observed, rather than taken to have some realistic daily profile. Internal loads, as well as the production from wind turbines, are taken to be constant. Costs for power production of controllable units are taken to be quadratic functions of produced power.

5. CONCLUSIONS Large changes occur in a power systems structure and operation, most of them adding to the uncertainty and complexity of the system. The introduced concept of an autonomous power networks based power system is a realistic and consistent approach to formulate and operate a market-based dispatch of both power and ancillary services. The market guarantees, within physical constraints, the optimal price for power and the optimal allocation of spare capacities. ACKNOWLEDGEMENT This research has performed within the framework of the research program 'Intelligent Power Systems' that is supported financially by Senter Novem. Senter Novem is agency of the Dutch Ministry of Economic Affairs. REFERENCES

Fig. 2. Required capacities B"" and ATeYfor AN 's reliablity t PRIC'ESt

hn,, 40

45

Fig. 3. Spot prices ( Ap,A,, A, ) of real power ( P ) and ancillary services A and B

Fig. 4. Optimal results for P" , A" and B"

18

Abu-Sharkh, S., R.J. Arnold, J. Kohler, R. Li, T. Markvart, J.N. Ross, K. Steemers, P. Wilson, R. Yao (2004). Can microgrids make a major contribution to UK energy supply?. Renewable (I; Sustainable Energy Reviews. Conejo, A.J., J.A. Aguado (1998). Multi-Area Coordinated Decetralized DC Optimal Power Flow. IEEE Transactions on Power Systems, Vol 13. No 4., November 1998. Dimeas, A.L., N.D. Hatziargyriou, (2005). Operation of a Multiagent System for Microgrid Control. IEEE Transactions on Power Systems, Vol. 20, No 3. Kueck, J.D., R.H. Staunton, S.D. Labinov, B.J. Kirby (2003). Microgrid Energy Management System. CERTS report, ORNLITM-20021242. Lasseter, R.H. (2002). MicroGrids. Proc IEEE Power Engineering Society Winter Meeting. Lasseter, R.H., A. Akhil,C. Marnay, J. Stephens, J. Degle, R. Guttromson, A.S. Meliopoulous, R. Yinger, J. Eto (2002). The CERTS MicroGrid Concept. CERTS report, LBNL-50829 2002. Lasseter, R.H., P. Piagi (2004). MicroGrid: A Conceptual Solution. PESC '04. Pecas Lopes, J.A., J. Tome Saraiva, N. Hatziargyriou, N. Jenkins (2003). Management from of MicroGrids, avai I able microgrids.power.ece.ntua.gr1 Venkataramanan, G., M. Illindala (2002). Microgrids and sensitive loads. Proc IEEE Power Engineering Society Winter Meeting.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

IMPORTANCE OF THE SELFREGULATING EFFECT WITHIN POWER SYSTEMS

M. Kurth and E. Welfonder Department for Power Generation and Automatic Control, n7D, University ojstuttgart Pfaflenwrddring 23, 70550 Stuttgar, Gernzany Tel +49 711 685-6210, Fax +49 711685-6590 kurthaivd. mi-stuttgart de

Abstract: The selfregulating effect of power systems consists on the one hand on the frequency dependence of the load - caused by the speed dependent torque characteristics of asynchronous motor driven working machines and on the other hand on a hidden selfregulating influence of speed controlled municipal heating and industrial process power plant units. The hidden influence of these mostly smaller power plant units is proved in this paper quantitatively by measurements concerning the whole European power system as well as by three special experimental investigations. Further on, there are pointed out the advantages of the in practice quite higher selfregulating effect than expected by the transmission system operators. The advantages concern the dynamic behaviour of power systems as well as saving costs on the power plant side for keeping ready less spinning reserve power. Copyright 6 2006 IFAC Keywords: self regulating effect, asynchronous motors, working machines, power plant units, speed governors, power system, dynamic behaviour, spinning reserve power, cost savings

I . INTRODUCTION

According the Transmission Code 2003 [l], based on [2] and [3], a spinning reserve power of 3 GW has to be kept ready within the European power system at any time. Network based this means a percentile spinning reserve power for peak load of 3GWl300GW + 1% and for peak-off load of 3GWIl50GW 2%, see Fig. I , curve Ia and Ib. From the power plant view the 3GW accord to a possible simultaneous outage of two nuclear power plants, 1250 MW net power each, and a 500 MW fossil fuelled steam power plant. The frequency behaviour based on this defaults is shown in Fig. 2a and is related to the DVG guideline [2], [3] under consideration of a system selfregulating effect of kpf(s)= 0,5%1%. Furthermore there is assumed that small power plant units with a nominal power of PG,Nom< 100 MW do not participate on the primary control. However, in the reality they do participate too by means of their underlaid acting speed control.

a) 3 e q u . r e d spinni-,g r e s e v e po’gei

AF’!~,j

C u r v e ! since 1997 C u r v e !I un:il ’396

[s]

2,s 2.0

1.25 1.0

e

.

3

.

51

311 5

‘5n.,r:

t

b) S i m p l i i ’ e d power system model f o r simula:ing r h e f-equency Sebavior

Fig. 1 : Spinning reserve power, to be kept ready within the European power system

345

I light load

1

Af

\PI

frequency

AF

= 3GW/300GW 4 1%

Af [mHzI

power

74

bHz1

" I

I1 peak load

= 3GW/150GW 1 2 %

frequency

-800

1

I)-0,5%

0

-6OOJ

-

IO.-600 -

0

JO

t

60 [s:

Fig. 2: Reduction of required primary reserve power when regarding the system self-regulating effect [4] => fulfilling further on the DVCAJCTE requirements with Af(m) 1- 1SO mHzl behaviour according to the DVG guideline [ 6 ] , concerning the spinning reserve power to be kept rcady from 1980 to 1996, scc Fig. I , curvc 11, and thc measuring points ten to 22 refer to the present guideline [I]-[3], in force since 1997, comp. Fig. 1, curve I and 11. The corresponding measuring values are also listed up, see Fig. 3b. As to be seen by Fig. 3a the expected frequency drops according to the DVG guidelines as well as to the Transmission Code, each time considered for kpt(s)= 0,5%/%, are significantly bigger than the real frequency behaviour. The reason for this is founded in the fact that on the one hand the effective consumer selfregulating effect with kppl 0,6 in winter and kpf(c) 1,l in summer, as extensive experimental investigations have shown [ 7 ] ,is higher than it is assumed by the DVG. On the other hand a further hidden selfregulating effect is noticeable, which is based on the fact, that usually smaller industrial and municipal power plant units are operated with underlying speed governors, which are even then active, when their setpoints - t o compensate the p-governor related control deviation - are adjusted to e.g. n, = 3050 rpm. This fact is shown in Appendix A1 in conformity with [S] for an industrial power plant unit with process steam extraction as well as for a municipal power plant unit with district heat extraction. Both influences lead to a quite higher system selfregulating effect according to the following implication:

The costs for keeping spinning reserve power ready are enormous. They are traded on the control energy market with 100 EUR per KW and year. Also the requirement to fulfil the power gradient for the activation of the spinning reserve power exactly is expensive under certain circumstances. Therefore, if the system selfregulating effect will be quite higher than assumed by the DVG and UCTE, less spinning reserve power would be required, as to be seen by Fig. 2b and due to this considerable amounts of costs could be saved! The simple dynamic model for simulating the frequency behaviour in dependence of possible power outages AP*z and varying selfregulating effects kDf(s)is shown in Fig. 1 b.

11. REAL FREQUENCYiPOWER BEHAVIOUR OF THE EUROPEAN POWER SYSTEM REVIEW STAGE Considering the real frequencyipower behaviour of the European power system, it can be seen that the frequency drops Af,,, caused by the corresponding power outages are significantly smaller than expected according to the DVG guideline. This fact is illustrated graphically in Fig. 3a on the hand of a comparison between the occurred and the expected frequency behaviour, based on [5]. The peak points of the frequency drops Af,, are drawn in dependence of the corresponding referred disturbance power AP*L = APL/PN, therein the measuring points one to nine belong to the frequency

~

346

~

A

a) Graphical presentation

b) Tabulated presentation disturbance

NO

drops

,

,

I

date

=

3 "1 pN

frequency COllaPS

remark

%, ImHzl

MI

15041975

251150=166

M2

03 02 1984

1 251200 = 0 63

-58

M3

15.021985

51190

=2.63

-380

M6

31.05 1991

2 71250

= 1.23

~105

M7

04.07 1992

1 251205 = 0 61

M8

19101994

1251175 = 0 7 1

-72

M9

09 09 1995

1 251200 = 0 63

-80

MIO

08.052004

I171201 '0.58

-54

Nogent2

MI1

11 052004

1.21270 -0.44

-52

Golftech2

M12

12052004

0.91171 =0.53

-43

St.Laurenf2

M?I

14 ns ?on4

n w ? 7 n = n ?fi

-fi5

ARC"

MI4

16.05 2004

I081270 = 0.4

-50

Canenom

Cruas

-192

France

-76

1

M I5

16 05 2004

0 891253 = 0.35

-48

MI6

21 052004

0.851197 =0.43

-42

BoxbergQ

MI7

28.05 2004

0.971270 = 0.35

-42

Temelin 2

Mi8

06 06.2004

0 951212

= 0.45

-43

ASCO 2

MI9

2506.2004

141212 =0,66

-53

GKN2+HN7

M20

14062004

261280

= 093

-95

St.Alban I+il

M21

22 062004

091272 = 0.33

-43

Blayais 3

M22

23062004

131241 = 0.54

-58

Paluel2

,

3

system

selfregulating efl'eci k(s)

=

consumer seifregulating + emeel

-

Pf

k(") Pf

+

influence speed governed power plant units k(lnd+inunlclpalppu)

Pr

AP

Po - AP' _ Af -

Af* k(') pf

=

0,6 ...1,I

+ 2 1,0

r/d%]

~

f k$)

>

1,s

[WYO]

This quantitative equation agrees with the real frequencylpower behaviour of the European power system as proved by the lot of measurements in Fig. 3a. As to be seen there, all measuring points are laying above the maximal frequency dropioutage power characteristic for kpp)= 2,O %I%. 111. EVIDENCE OF THE HIGH SYSTEM SELFREGULATING EFFECT The exiqtence of the hidden - induqtrial and municipal - selfregulating effect, based on the speed control of the corresponding steam power plants, is documented in the following on the hand of three examples.

Exaniple 1: Comprehenbive experimental investigation, concerning a real power system Before the East European Centre1 power system together with the East German VEAG power system was connected to the West European power system thc cvidcncc of thc controllability of thc ncw accessory power systems had to be provided. For that, the in synchrony operating Centre1 and VEAC power systems performed comprehensive experimental investigations, which, as can be seen in Fig. 4e2, induced a much higher controllability as expected during the test planning [91.

This was based in the fact that not only the 500- and 200-MW power plant units, which were upgraded with up-to-date primary control equipment, kept spinning reserve power ready during operation, but also the older 100-MW power plant units, s. Fig. 4el, as well as further municipal and industrial power plant units, s. Fig. 4d2, which were equipped with simple speed governors. Based on this, the system selfregulating effect summed up to:

347

system selfregulating effect

k $)

This lead to a system selfregulating effect of

consumer influence speed selfregulating + governed power plant effect units )k: + k(lnd PP) + k(’OOMW PP) =

Pf

sy stem

selfiegulating effect

Pf

consumer =

selfregulating + effect

influence speed governed power

plant units

fl

=> Above parameter values see also Fig 4 d l , d2, el 3)

a) Pump storage power plant Forbflch

Seconoary controlled power p l u n k of VEAG

A K’( i )

V5

V6

area

b) ?ice

Murqtal”

7 c ) V o l t o g e dependence o f t h e lood

A K’(i)t

v7

v7

v5

Vh

v1

v3

vs

:

v

c

consumer

v4

d l ) Frequency deoeqdence of t h e lood

02) S p e w c o i r r o l l e d

P ) Speed cnnrrolleC 100 UW u o ta e 2 ) P r n o y controlled 506 MLll ond 210 N S un i s

i

6,4

I L2 VL

VG

VI

l

l

vs V9

I VR

1

industrial power plant (paper mill)

Fig. 5: Control tests during isolated operation

tndustrzal paver plants

AK’(i)‘

v7

u

I b4

I

c

J

lest runs ( V )

Fig. 4: Representation of shares of the power plants, consumers and power system in the normalized power-frequency characteristic derived from test run (“yersuch”) V1 - V9.

Example 2: Industrial procesJ power plant, generating steam j o r a paper nzill During tests of isolated operation within the part system “Badenwerk”, situated in the South West of Germany, initially two pump storage driven generators supplied the service area “Murgtal”, s. Fig 5. After disconnecting the smaller second generator the frequency dropped quite less than expected. Instead of an expected consumer selfregulating effect of k(c)pi= I%/% a system selfregulating effect of k(s)pf = 4,4%/% resulted. A s aimed inquiries have shown, a speed governed industrial power plant, build to supply a paper mill with process steam, fed in the running isolated power system as well.

Example 3: Industrial process power plant, generuting steanz for a sugar refinery A comprehensive study carried out by the University of Stuttgart assigned by the DVG to determine the consumer selfregulating effect k(‘lpi seven load areas nearly equally distributed over the West German power system were equipped with numerous automatic data logging systems [ 7 ] . 1his had been carried out mainly in substations on the 110- and 220-kV level, supplying sub-systems, whereby in cases of distributed feed-ins more than one datalogging system were required. Within the underlying 150-MW load area of the EVS with two feed-ins in the sub-stations “Heilbronn” and “Kupferzell”, situated in the South of Germany, an unexpected high consumer selfregulating effect of k(C)p,{Jan I)ec = 1,6 %I% resulted as annual average value, which had been determined by the lot of measurings. Aimed investigations have shown that during I 5th September and 23th December of the considered year an industrial power plant unit with PG, = 15 MW, equipped with a speed governed turbine valve, was in operation to supply a sugar refinery with process steam. Also the operation times within the two M o w i n g years were clearly fixed €or evaluation. For this duration the measurements had been recorded by the two data logging systems. The carried out semi-annual analysis of the acquired measurements APc(t) and Af(t) yield to the results shown in Fig. 6db. When the industrial power plant

348

was out of operation the alone effective consumer selfregulating effect yields to kpf(L)= 0,9 %I%. In the other case the resulting system selfregulating effect yields to kpf(s) = 3,4 %I%. As can be seen, the speed governed power plant unit contributed with k(lndPP)pf = 2,5%/% to the effective system selfregulating effect. This fact looks feasible because it applies: 15MW 100 2.5 150MW 4 with 6,: drop of the speed governor. ppp

Pf

- PG,N 100 --.-=-.-=

PCN 6,

This result is essential for the spinning reserve power to be kept ready qualitatively and quantitatively not only concerning the power plants but also concerning the whole power system.

In addition no agreement between transient measurements and corresponding simulations can be achieved without regarding the existing system selfregulating effect in full size (e.g. [ 101). A. Advantages,for the power system

Assuming a system selfregulating effect according to the Transmission Code [ 11 of sq stem

consumer

selfregulating effect

=

influence speed

selSregulating + governed power eSfect plant units

0.0

0.5

U ) 2IDec.

13.SFPJ

2'1 Dec

i

1 4 Sepi

_I

i

a) ldentiiicction o i load scliqulatinq eiiecr

i

b) loer!ificalion

3i

sysierri selfrequlatinq eliec!

0.9 t

2.5

Fig. 6: Long term evaluation ofthe consumer and system selfregulating effect

Example 4: Global Estimation Assuming an amount of only 5% of smaller speed controlled industrial and municipal power plant units, which feed in additionally into the interconnected power system having a speed controller gain of V, = 1000//5% = 20, then the hidden selfregulating effect already results to k p t n dpp) = I ,O%/%.

1V. ADVANTAGES OF THE EFFECTIVE SYSTEM SELFREGULATING EFFECT As proved in Chapter 2 by means of measurements in the interconnected power system and underlined in Chapter 3 by experimental investigations carried out on the example of individual part syqtems behaviour, the existing system selfregulating effect of the European power system must be in practice at least equal kpf(s)= 1,5 %I%.

the system frequency will arduously decrease in the case of disturbances greater than the spinning reserve power of 3 GW to be kept during operation. This theoretically bad behaviour can clearly be seen in Fig. 3a. Thus the lower frequency border from 49,O Hz, i.e. the first step of load shedding, would already be reached with an outage power of AP*z = 2,2% 2 3,3 GWII5O GW during peak-off time, as shown by the dotted line5 in Fig. 3a. However, in practice, where a realistic selfregulating effect of system selfregulating

consumer =

eSSect

k(") Pf

-

influence speed

selfregulating + effect k(C)

Pf

+

governed powcr plant units k(PPu) Pf

AP ~

+ 2 l,o

L"/dYO]

will be effective, the lower frequency border of 49,O Hz will still be reached at a disturbance power of AP*Z=3,7%; 5,s GWIISO G W . A corresponding worst case consideration was carried out in [ I l l . Assuming a system self regulating effect of kpf(i)= kpf(L)+ kPf('"') = 1 ,O + 0 = 1 ,O %I% the lower frequency border of 49,O Hz will be reached at a disturbance of AP*z= 3%; 6,O GWI200 GW. Thiq rewlt agree4 almo4t with the eqtimation in Fig. 3.

349

The reason is that the system selfregulating effect caused - on the one hand by a greater frequency dependence of the load and - on the other hand by smaller, not regarded municipal and industrial power plant units being operated with underlaying speed controllers is much higher as assumed by the transmission operators when deriving the guide lines for the required spinning reserve power to be kept ready by the primary controlled power plant units. The advantages of the higher existing selfregulating effect are - on the power system side the frequency will decrease much smaller in emergency cases when the outage power will be higher than the spinning reserve power to be kept ready, and - on the power plant side the steam power plant units have not to be throttled so much any more. As they have not to hlfil the Transmission Code guide lines dynamically exactly they can be operated more economically.

B. Advantagesfor power plants

For fulfilling the requirements of [ I ] also dynamically, a relatively high throttling of the turbine valve is continuously necessary in case of a system disturbance of AP*z = 2% and a participation of kp, 2 50% of power plants at the mimary control. The reason for this is, that during the considered time space of 0 < t I 30s nearly only the high pressure turbine-parts of the primary controlled thermal power plant units are active with a power share of about clHp = 40%. With proceeded time the low pressure turbine power share delayed up to 50s through the reheater -becomes active, too. However, as the steam storage capacity is limited with a storage time constant of up to 80s, the live steam pressure decreases, until the fuel-sided increased heat supply becomes effective after some minutes. As both influences are pointed in contrary and almost compensate each other, an uneconomically high throttling of the turbine valve of Ay*7 2 10% is needed round the clock. ~

6. REFERENCES

Neglecting this only transiently acting fact, that during the first minutes only the high pressure part of the steam turbine is effective, the throttling of the turbine valves can be reduced from Ay*l = 10% to A Y * ~= 4%. Doing this, the resulting frequency behaviour has been simulated in Fig. 8 by means of a simplified system model, sketched in Fig. 7. There all primary controlled power plant units are gathered to one equivalent steam power plant unit of corresponding size. Furtheron in both simulation cases a power outage of PZ= 2% has been considered.

VDN (2003). ‘Transmission Code 2003: ,.Network and Sjstem Rules o f the German Transmission System Operators“. Berlin, August 2003. DVC (1 996). Anforderungen an die Primarregelung im UCPTr-Verbundbetricb. I lcidclbcrg. UCTE (1998). Ground rules concerning primary and secondary control of frequency and active power control within the UCTE. Paris Welfonder (2002). Interaction o f power plants and power systems within the deregulated energy market. VGR PowerTech (82) 2002, Issue 3 and 4. Welfonder, k.(1997). Lcast Cost Dynamic Interaction of‘ Powcr Plants and Power Systems. 13th IFAC World Congress. June 30 - July 5, 1996, San Francisco, IJSA. Control Engineering Practice, Vol. 5, NO. 9, pp. 1203-1216, 1997. DVG ( 1980). Leistungsregelung im Verbundnetz. Heidelberg Welfonder, E.. Hall, B.. Glaunsinger, W.. Heueck, R. (1994). Study of the Dependence of Consumer Subsystems on Frequencq and Voltage CIGRE 1994 Session, 28.08.-03.09 1994, Paris. VDI/VDE 3508 (2003). Unit control o f thermal power stations. Reuth Verlag, Berlin. [lo] WelFonder, E.; NeiFer, R.; Sattinger, W.; Spanner, M. and Tillmann, H.-B.; Kranhold. M. and Svarc, L. (1996). Control Behaviour of the VEAG and CENTREL Power System determined by comprehensive experimental investigations and additional simulation. CIGRE 1996 Session; 25.31.08.1996, Paris [ I l l Kurth, M. and E. Welfonder (2005). Oscillation Rehaviour of the Enlarged European Power System under Deregulated Energy Market Conditions. Control Engineering Practice, Special Section on Power plants and Power Systems Control, Volume 13, Issue 12. pp. 1455-1558, December 2005. [12] Asal. 1I.P.; Bath, P.; Grebe. E.; Quadflieg, D. (1998). Dynamic System Studies of new Requirements and Strategies for the Primary Control in the UCP‘TE/CENTREL, Power System. ClGKE 1998 Session, 30.08.-05.09.98. Paris.

As to be seen by Fig. S1 the frequency will strongly drop by -1200 mHz to less than 49 Hz in case of a system selfregulating effect of only k,?) = 0,s %I% as assumed by [6] and [I] up to now. However, in the real case, where - as pointed out - a selfregulating effect of kpJs)2 1,5 %/% exists, the frequency will only decrease by -360 mHz to > 49,6 Hz, as shown in Fig. SI1.That means, the frequency will clearly remain within the permitted system operation range of 49,O 5 f 5 5 1,0 Hz [ l]! Therefore keeping the necessary system dynamics further on, the steam power units have not to be throttled so much any more and can be operated much more economically.

5. SUMMARY Within the European power systerri the frequency drops resulting in reality in the case of power outages are much smaller than expected by the transmission system operators [ 1,3].

350

a Grid

............................ b) Equivalent steam pawer plant unit

Fig. 7: Simplified summary model of the power system under consideration of the steam generation dynamics I) kb;' = 0,5%/%

II) k$'

a) DisturbanceAP;

= I$%/%

a) Disturbance AP*,

.....................................................................

i

b) Frequency

49

c) Generatooutput&

c ) Generator output

P,

PGsDI,~

PG '

0.96--

0.96-

d) Fuel mass flow

e) Fuel mass flow

0,96

e) Valve position

i) Valve position 1.04

ll::i1T**

A

f) Live steam pressure p * " q

09d

09d h) Turbine steam flow live steam flow difference

g) Turbine steam flow live steam flow difference 1 04 m*, I ~ I [

1 04

.-

,----

by---.

o,g5--

................................................ _ ..i......-..'-.......... ->........... ,

,

t

[S]

0,961- .-",., 2000

Fig. 8: Simulation results for kpE(S)= 0,5 %/% and kpf(s)= I 1,5 %I%

351

......*,............

........................................................ t [S]2000

7. APPENDIX : INDUSTRIAL AND MUNICIPAL POWER PLANT UNITS

I

I n the appendix the block diagrams of industrial and municipal power plant units are illustrated. The dynamic behaviour of the overlaid process pressure control or heatwater temperature control respectively is normally slow in comparison to power system caused actions of the underlaid speed controllers, which will last only a few minutes, until the normal primary controlled steam power plant units will have increased their generator power already to their enlarged reference values.

Psir*

A 1 Industrial process power plunt unit with underlaid speed control

'-1

,. , I

I

1.... I

I

I

Turbine valve

'----I-' apenurecontml

Q

Fig. A111 : Unit control of steam power in a process steam network

Figurc A111 shows an cxamplc of thc control of a unit, generating process steam. The steam pressure in the process steam network, pPSt, is the back-pressure of the turbine pBp. This pressure is adjusted to a specified value; the turbine valve aperture yI is the assigned manipulated variable. By adding the actuating signal of the turbine speed controller to that of the back-pressure controller, the unit also temporarily contributes to frequency drops in the electrical power network. As the process steam network is very inert, steam generation is at first adapted to steam consumption by adjusting the live steam pressure prsr to a fixed setpoint pLSlset, see left side of Figure A 111.

I

A 2 Municipal heatingpowerplant unit with underluid speed control retwn

FigureA211 shows an example of the control of a unit generating district heat. The district heat supply temperature QDll is set to the setpoint QDLise, by adjusting the turbine valve aperture y r . The actuating signal of the turbine speed controller - added to that of the heating-water supply temperature controller - causes the unit to contribute to the frequency control in the electrical power network, utilising the large storage capacity of the district heat network. Steam generation is adapted to steam consumption by adjusting the live steam pressure pLst to a fixed setpoint pLStset.The thermal output Qb of the fuel

Fig. A211 : Unit control of a combined heating and power station using hot water as heat carrier

mass flow m g is the manipulated variable. The control response to changes in output is improved using the PD-TI feedforward signal derived from the turbine steam mass flow m, .

352

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

OPTIMAL POWER SYSTEM MANAGEMENT VIA MIXED INTEGER DYNAMIC PROGRAMMING Harry G. Kwatny * Edoe Mensah * Dagmar Niebur ** Carole Teolis *** * Department of Meclmnical Engineering arid Mechan,ics, Drezcl UrriversitzJ, Philadclphiu. PA 19104. USA ** Department of Electrical an,d Computer Engineering.

Dyezel [Jniuersity. Philadelphia, PA 19104, USA *** Tech,no-Sc,lences. Inc..lOOOI Derekwood Lane Lunham, M D ,20706, USA

Abst,ract: Power systems involve both continuous and discrete acting components and subsyst,erns.In this work a logical specification is used to define the traasit,ion dynamics of the discrete subsystem. A computational tool that. reduces t,he logical specification to a set of' incqualities and tlic use of t,he transforrned inodel in a dyiiarnic progrnrnining approach to the design of optimal feedback controls are described. An example of optinial load shcddiiig for a power system with aggregate induction motor and const,aiit>admit t,a,iiceloa,cis is g,'wen. Keywords: power syst,em mantgerncnt., liybritl systems, dynamic: progra.mmiiig, mixcd intcgcr progmnming

1. INTRODUCTION In thib papei we seek to design poivci inailagement systems that optimize tlie discrete actions of protcctivc device5 in order to insure continuity of service to vital loads. lye describe a modeling approach that captures both the discrete and continuous aspects of the power syskm and show how dynamic prograrnniirig can be applied to derivcl optimd control 5trdtcgic5. Tlic coiiiputational tools iire summarized and an example is given.

A power systeni's continuous and discrete dynamics can be iiitcgratcd in ct hybrid nulornaton rnodcl thnt i b coinposrd of a deswiption of the discrete transition behavior from one discrete state (or mode) to another along with model5 of continuoub This rcscarch was supported by tlic Office of Naval Rcseilrcli Contrxt Number N00014-04-LI-0285 mid the No.-

behavior wit>liincach iiiodc. It has provccl to be an important theoret,ical t,ool and is a key coiicept,ual devicc for modcl building. However, ot,licr forms of models are far more convenient for coiitrol system design. Such models include the 'mixed logical dgiiamic systcin' (MLD) (Bcmpor8.d and hlomri, 1999: Geyer eC a,l., 2003). The ability t>o corivcrt, from one form of iriodel t,o another are import tint.

In our approach, we model the transition dynamics by a logical statement (or specification). We have developed a tool in hfuthernuticu, that) converts any logical specification into a set of niixcd-int,cgcr forrriulas (IP formulas). Thus, t,hc transition specificat,ionfor the automaton is converted into a set of iiieyualities involving Boolean variables. The IP formulas iire used in comput,iiig the opt>imalcontrol strat'egy.Our approach derives

tional Science Foundation Contract Nuinher ECS-0400391.

353

a feedback policy based on finite horizon dynamic programming.

events and p to represent uncontrollable events. Thus, C = S x P where s E S and p E P. A g i i ~ r dis a siibset, of the continuoils &ate space X that. enables a transit,ion. A transition enabled by a guard might rcprcsent a, prot,cction device. Not, all t,raiisitions have guards and some transit,ions might require simultaneous satisfaction ol a guard antl the occurrence of a.n event. The gua.rd assignment function is G : E 4 2x.

The basic idea was out.lined in (Kwatny et al.. 2005) where we gave several simple rxa.mples that illustrated t.he conversion of logical specifications to IP formulas. We also gave im cxaniple of 01)I.irria1 periodic corilrol o r sirrrple power elechiiic device. In this paper we design an opt,imal load shedding coiitmller for a power system with aggregated induction motors and const.ant admittame loatis. Because this simple syst,ern ex1iibit)s typical power syst,ein nonlinear dyna.inics, it has h.xpicnl~lybccn used to articula1,c behaviors associat,ed with volt,age collapse, e.g., (Ohtsuki et al., 1991; Pal, 1993; Bao et al.; 2000).

We consider each discret,e state label, q E Q , and each event,.(T E C , t,o be logical va.ria.blest>ha.tt,a,ke the values True or Fa,lse. Guards also a.re specified as logical conditions. In t,his way t he transition system, iiicluding gua,rds, can be defined by a. logical specification (€ormula) C.

In Sect>ion2 we provide a specific definit,ion of the problems considered herein. S ions 3 antl 4 describe t,he comput,ational tools. The opt,imal load shedding example is given in Sectlion 5.

For computa,t,ionalpurposes it is useful to a,ssocia.t,ewit,li each logical Val-iable, say a , a, Boolean variable or indica.t,or function, ha, such t,ha.t 6, aSsiinies tlie values 1 or 0 corresponding respectively t,o 0 being True or False. It is convenient to define t.he discret~est,a.t,evector 6, = [6,, , . . . 6,,n]. tlic cont,rol event, vector J , ~ = fi,, , . . . ,h.3wls],and

2 . PROBLEM DEFINITION

[

bpL,.

t,he exogenous event vector 6, = . . ,6 ? h P ] . l’rccisely one of the clenients of 6, will be unity and all others will be zero.

2.1 Modeling

The class of hybrid systems t,o be consitlcrcd is defined as follows. The syst,em operates in one of m modes denoted ql, . . . , qm,. We refer t,o the set^ of modes Q = (91. . . . , q m } as t,lie cliscrete state space. The discrete time diEercncc-algebraic equalioii (DAE) describiiig opcratiun iri motle q,

Notice t1ia.t with the int.rodiict,ionof the Boolem variables we can replacc the set of dynamical cquations (1) with t,hc single rclat.iori

is

iii cont,innous st nt,c,

y EY

2 Rp is the vector of algebraic variables and

u E U Rrnis the continuous cont,rol. Transitions caii occur only Mween cert,adn modes. The set of admissible transitions is E C (2 x Q. It, is convcnient, to view the rnotle transition systom a,s a graph with elements of t,he set Q being the nodes and t,he elements of E being the edges. We assume that^ transit~ionsare instant,aneous a.nd t,akeplace at thc beginning of a t,imeinlerval. So, if a, syst.em transitions from mode ql to 92 at)time k we would writ>eq ( k ) = 41%q(k+) = q 2 . m7edo allow resek. State traject,ories are assumed cont,inuous t,lirough cvcnts, i.c., x ( k ) = x(k+), unlcss a rcsct’ is specified.

2.2 The Control problem

FVc asunic hat, t,he syst cin is observed in operat’ionover some finit.et , i m horizon T that is divided into N discrete t,irne intervals of equal length. A cont,rol policy is a. sccpcncc of functions 7i-

= {PO (To. 6,o)

3..

.

1

P X - 1 (%-I,

6y(N--l))}

such that, [Uk.6d.3 = pk. (Xk,6&)

Transitions are triggered by ext>ernal events and grcards. We dcwote the finit convenient to part,ition the those tha.t, are conlrollable (t,hey can be assigned a value by the cont,roller), and t,hosc that arc not. The lat,terare exogenous and occur spont,anc>ously. Such an cvcnt rniglit corrrspond t,o a. component, failiire>or a. high level change of opera.tiona1mode. We will use the symboIs .s t,o represent!cont,roIIabIe

354

Thus, p~k.genera,tsesthe continuous cont.rol U k and t,he discrete control 61, t,hat. are to be applied at. i-imc k , based on the st,at,c (xl;,h41;)obscrvcd at. t,inie k .

Consider tlie set of m-tuples (0: 1}ln. Let, A,,,, denot,e the subset of elements S E { O . l } r r L that. satisfy 61 . . . S, = 1. Dcnot,c by II t,hc set. of sequences of fii /“k ; x + u x isc. con1,inuous on X. (0,.I}”” t.hat. are p

+

+

x a,,,

Now, given the init,ial st,a,t,e ( 2 0 , h,o) t,he pi-ohlem is to find a policy, T* G n, that minimizes tlic cost functional J7r

(xo, 6,o) =

+

G,v (rn;? 6,~)

E56,++Eed 5 E0+Eiz+~~'26,+E~6,+E~~~ (6)

(3)

Specific ally, the Optancal Feedbad Coritr 01 Problem is defincd a5 follows. For e;icli .xg E X , Sqo E A,, determine the control policv T* E TI that minirni7cs tlie cost ( 3 ) subject to tlie constraints (I) and thc logical spccification. i.c>.,

A* (zo. 6,o) 5 J ,

exogenous events. They also involve a set of auxiliary Boolean variables; d. introduced during the t,raiisforination process, and t,he contiiluous st,ate variables, T . The general form is

( T o . 6,o)

wherc t,hc matrices havc appropriate dimensions. As we will see in examples below, wit,h x,6,, 6,, 6, given these inequalities typically provide a unique solubion for t
VT E rI

(4) Notice t h d if a receding horizon optimal control is ctc%retl, once the optimal policy i5 determined, we need only implement the state feedback control

A. CONSTRUCTING THE OPTIMAL SOLUTION

(5)

The optimal policy 7r* is one that satisfies (4). Now a.c ale in J, position to apply rlellnim's principle of optirnality: suppose T* = { p ~. ., . is an optimal control policy. Then the sub-policy T,* = { p r , . . . , j~;--~}, 1 5 L 5 :v - 1 is optimal wit11 respect to the cost function ( 3 ) .

The first, step in solving the optimal control problem is to lhansform the logical specification L into a. set, of inequalities involving integer (in fa,ct, Boolcm) variables and possibly r e d variabl called IP-for.muias. The idea of forniiila.ting o p tiniizat>ionproblems using logical constraint,s and then converting t,hem to IP formulas has a long history. This conccpt was recentslyused as a mca,ns t,o incorporate qiialit,atJiveinformation in pro conf,rol a.nd monit.oring (Tyler a.nd nTora,ri, 1999): and generally iiit~roducedint>ot>liest,udy of hybrid systems in (Benipora,d and Morari, 1999).

Let 1.15 dcnotc the optimal cost of the trajcctory begiririing a t 1,.6,, a h J,* (xZ.cjqz). 11 folluws florn the principle of optimality that

[w,, 65LI

= P o ( Z k , 6,k)

3 . LOGICAL SPECIFICATION TO IP FORMULAS

McKinnori ancl Williams (1989) proposed the inclusion of logical const,raint,s in optimization methods. They suggested a sequence of transformat~ionsthat, brings a logical specific:at~ioninto a set, of IP-formu1a.s. Li et al. (2000) present, a syslerriatic algorit lirri lor traiislorrnirig logic lorrnulas inlo IP forniulas. 1% havc modified and uxtended t,heseriietliocls in order to obtain simpler and more compact IP formulas with other modifications to cnhance thcir a.pplicabilit,yt,o hybrid systems.

The basic funct,ion iii our Math,ematica implrnent,at,ion is GenIP which t,akes as t,wo arguments, tlic spccificatsioii and a list, of variablcs, cit.licr proposit,ional variables or bounded real or integer varia,bles. The lat,t.erare specified in the form a 5 J: 5 h. GenIP performs a. sericjs of tmnsformntioiis and simplifica,t8ionsand &urns t8heIP formulas. If all of the guards are linear (set, boundaries arc coniposecl of linear segmeilts), then the IF' formulas are system of linear const,raints involving t he Boolcan variables 6, , 6,+ ,6, , &, rcspcctivcly, t,ho tliscrc%e state before transit>ion,the cliscrcte state after trmsition, t.he controllable event.s, the

4-1 ( Z % - d q ( % - L ) ) =

{LL ( z ~ - ~ , ~ ~ ( ~ - I ~ +J,* , P - I( )~ , 6 ~ ~ ) }

in111 !J-1

(7)

Equation (7) provides a mcchaiiism for backward recursive solution of the optimization problem. To begin the backward recursion, we nccd to solve tlic single stage problern with z = N . The elid point ZN.b q i5~ free, 50 wc begin at a gencml terminal point

Once the pair pi--l, JAr-l is obtaincd, wc com.Ti,-,. Coiitiniiing in this way we obtain piite

for 2

2 i 2 N.

VTe need t.o solve (9) recimively backward, for i = 2 . . . . , 1V aftcr iriit>ializingwit>h(8). We begin by construct,iiig a discrete grid on the continuous slat,e space. The tliscrele space is denoted Atj each it>crationthe optimal control arid the optimal cost are evaluated at, discrete poiilts in Q x 2. To cont inuc with the next, sta,gc we need to set, up an interpolation function to cover a.11points in Q x X .

x.

We exploit the fact that, the syst,em is liiglily constrained and almost all of the constraint,s are linear in Boolean varia.bles. The basic approach is a s follows:

355

(1) Identify the binary and real variables and separate the inequalities into binary and real sets, biiiary equations contain only binary variables, real equations can contain bot.11 binary and real variables. ( 2 ) Usc the Ilfathernaticn function Reduce to obtain all feasible solutions of the binary inequalities: a list of possible solutions of pairs (Sq+, d ) . Reduce is a very efficient solver, espccisllg- wlieii thc inequalitics are linear although it is not limited to linear inequalities. In gerieral, if there A r c N binary variables then t2icrc arc ZN corntinations tliat need to I)e evaluatcc1if one were to attempt to optimize by enumeration. But the feasible combinations are almost certainly much fewer. ( 3 ) Use Reduce to solve the real inequalities for tlie real variables for every feasible combination of binary variables. Many of tliese conilinations of binary variables will not admit feasible real variables. so they can be dropped. The reinailling combinations typically produce unique values for the real variables. (4) Enumerate the values of the cust for cach feasiblc pair uf binary and real variables and select the ininirnuin.

Fig. 1. System configimtion. impedance depends on the aggregate induction motor slip. The ncl work equut ions are cwsily obtainrd. Suppose 61.62denote thc voltage anglcs at bus 1 aiid 2. Define the relative angle iictwork equations arc I'dJ03 = r.,

-

0 2 = 62 - 61. The

cv,2

0 = ( u / n )E f i sin 82 + cV; 0 = ( ( ~ / / tEV2 ) cos 02 dV; From the last two equation5 we obtain

+

5. EXAA1PLE: OPTlAlAL LOAD SHEDDLNG In this section we provide a simple illustration of t he formu1;ttion ;tnd solution of a powcr managcinent opt,imal control problem. 'L'he primary mechanism for w h g e cont,rol is the corit,inuousvariation of field vokage wit)hinit,s bounds. 111 addition, we consider load shedding as a discrele control means, specifically for acconmlotla.til?g.~ini~[la~t,iiigtransinission line faaults.

The power absorbed by the load is PL = -v, 2 c.

(2,

= V,"d

Now, let 11s t u n to t'he induct,ioii motors. An equivalent circuit for a.n induction motor is shown in Figure 2. Here, l.he parameters R,, X , dciiote the resistance and inductance of t,he stator, X , denotes the magnet>izinginductance, and R,, X , t,he rotor resistance ;tiid inductance. Thc rcsist a.nce R, (1. - s) / s represents the motor electrical output. power. We will neglect, t,hc small stator resist>anceand inductance. We also assume t,he a,pproximat,ionof large magnetizing inductance is accept'able.

5.1 Network and Load D ~ ~ n a m i c s

A rc1at)ivoly simple tcin that) is known to cshibit. interesting vohage stability charxteristlcs is a single generator feeding an aggregated load composed of constant iinpedance loads a.nd induction motors. The syst.erii lias beer1 used to study thr: offcct of tap changing transformers antl capacitor banks in voltage control, e.g., (Ohtsuki et al., 1991; Pal, 1993: Bao et al., 2000). Considcr t,lic system shown in Figure 1. Tlic syst,em consists of a generator, a transmission line, an on-load t,ap changing transformer (OLTC) and an aggregat)ed load. The generat,or is c1iaract)erized by a 'const>antvoltage behind reactance' model. Tlic gcIicrat,or interrial bus voltage E is used t,o maintairi the voltage at bus 2 ; so long as E remains within the liniits iniposed by [,heescit,a,t,ion cnrrent, limits. The OLTC ordinarily rrioves in smdl discrete steps over a narrow range. The load is an aggregate coiiiposed of parallel induction 1110tors antl constant impeda,nce loads. An induction motor can be characterized as an impedance with slowly varying rcsist,ancc; conscxpmit,ly.t,hc aggmgate load is represent,ed hy const,a.ntinipcda.iico actually, a slowly wrying irnpedance, where t h e

jx,

jx,

R,

R,

Fig. 2 . Induction niotoi equivalent circuit. Undm Lliesc toridit ions we obt ain t lie following. Thc real power tlclivcrctl to the rotor, Pd, and thc power delivered to the shaft, P?. are

r, =

R,S If:

R; + s 2 X ?

p, = r d (1- S )

The dynamic a1 equation for tlic motor (Newton's law) is 1

(P,- Pn,) I,, iU'0 Introducing the slip, s, s = ( L U ~- wff,)/wo, tlie motor dynamics take the form Gm =

356

______

5.2 System Operation

In t,he following, we allow for shedding a fraction, I', of the loatl. In the present example, we allow three different values of q including zero, so E (0, r l l , ria} . ConseqiientJy, there is normal operat,ioii a.nd two priorit,ized blocks of load that, can bc droppcd in wcorde.ncc with tlic tmnsition behavior defined in Figure 3. The corresponding logical specificat>ionis = eXactl?J (1, {41 ( t ) ,(Z" ( t ) ,43 ( t ) } A) P r a 4 Y (I, (41 ( t i - ) ,42 ( t + ) > ( I 3( t ' ) } )

(M

A

( t ) A (51 v 7 3 2 ) =+ r12 ( f ' ) ) A ( t )A 32 + ~a ( f ' ) ) A (43 ( t )A 7

(43

V2. Wc will assume that it. is dcsirctl to niaint,ain V2 = 1. If we ignore tlie exciter dyna.rriics, t.lieri (11) allows Ihe delemiination of Lhe field voltage that, yields the desired load bus voltage. However, the field voltage is st-rict>lylimit,ed, 0 < E < 2 . If we assume tliat, only t hc uppcr limit is a binding const,raint,,there are two possibilities for sat,isfying (11):

752

+ 43 (t'))

Equation (12) represents the aggregated 1110tor tlvnaniics. and tlic load atlinittancc is givcn by the last t\+o equations. The system data is RL = 2, R, = 0.25, X , = 0.125, u = 1 (nominal) Imcji = 4.

.

5.3 The Oplimal Control Problem WLL~OUL OLTC. TL = 1

Fig. 3 . Transit ion diagram €or load shedding optimization. In the present case. n7e asslime the blocks are sized sucl1 that 41

*

= U,

41

* 7 = U.4,

q3

+ rl = 0.8

Wc <~siiiiic that thc OLTC ratio is hxcd, i.c.. tlic OLTC is not being used for control, so n = const. If the OLTC is to be employed, tlie dynamics of tap change must be added. IIU& = r, - cv;

e = ( I - q ) q , , cg=

(10)

'")

1 (%+ R: + sax:

(13)

(R: + s2X?)

(14)

d = (1 - q ) d o , do =

xrg2

Equation (10) rcprcscnts tur biiic-generator dynamics. Ordinarily, the power input P, is adjusted to regulate the speed w' which is to be niaintained at the value wu. We assiiine that regulation is fast and accurate. It is possiblc to invcstigatc the impact of frcqiiency varint ion on syst ciii behavior. I f it were assumed that frequency variations mere small, then the enect on all impedances could be approximated. a i d this is often done. That has not been included h e , $0 there is no apparent toiipling betwcen (10) and t he remaining equations, $0 it can Ise dropped. Equation (11) represents the network voltage characterist ic The field to (ontrnl tlw loatl h i 5 voltagc

The problem is formulated as an N step moving horizon opt,imal control problem, in which they slip dyna,mics arc writ,ten in discrctc time form. The control mriables are E ( k ) .rl ( k ) . The goal is lo keep tlie load volhge V2 close lo one, specifically, we require 0.95 < V, < 1.05. Our intent is to use t,he field voltage, E , to regulate the tersiiiiial volt,age, V2 to 1 p.u. Bccausc 0 < E < 2 is const,rained, we specify that solut,ions must satisfy

(V2 = 1 A 0 < E < 2) v (E= 2 ) If the field voltage saturat.es, the only reniaining option is to shed some load. We seek an oytima1 control policy: i.e.; a sequence of cont,rols ,71 ( A T - 1) . 'II ( I ; ) = 17 ( k ) , t>hat,minimizes the cost, function

subject to the system constraints. \Ve can make some rough assessments of appropriaic weighting constants r1 . Load shcdding should bc avoided with respect to regulating rJ, unless the V2 tolerance is violaicti. Hem(. we want rl > o.252/0.052 = 1/25. In summary, we have slip dynamics in discrete tlnlc fornl SL+1

= f ( S k ?v2.rl)

The transition specification in IP for in 1 - 6,, - bq2 - 6,? 2 0, 1 - 6, ' 2 0, 1";- 6,, 2 0, 1 - 6q, hq; - 6,, 2 0, -6q1 dq; -6,, (r4: 6,, 2 0,

s4:

b,, +

-1 -1

+ + 6,2 + S?, 2 0 + "t + Sq; + Sq; 2 0

1 - 6,, + ";- S,, 2 0 1 - 6,, + ($2 - cs,, 2 0 68,? 0 -6q7 + (IqT cs,, 2 0 0 I6q1 5 L O IS,,I1,0Id,,I 1 0 Id,+ L 1 , o 5 6*; 5 l , o csq+ 5 1

+ +

+

+ +

+

016, 11,016, < I 3

357

The IP formulas for the logical constraint

+

+

3 - dl - E > 0 , 1 - d l E > 0, -2d2: l3 -2d1 v2 2 0. -2 dl 50 0 5 dl,d2: 5 1, 0 5 E,V2 5 2

+

+ + v,

20

Arid the IP forniulas for the load shed parameter rl -0.4d4 17 2 0. -0.8d5 77 2 0, d3 - h,, 2 0, d d - 6,; 2 0, d5 - (54’, 2 0 -1 d3 7 5 0, - 1 0.6 d.i r] 5 0, -1 i 0.2d5 i r ] 5 0 0 < & < 1 , 0
+

+

4 +

+

+

One result is shown in Figure 4. It, illustrat~es the optimal load shedding st.rategy follon-ing a, line failurc rcprcscntcd as a reduct,ion of a. ‘I’tic feedback control is given as a. funct,ion of the state - the latter composed of the coiit.inuous slip a.nd t>hethree discre at>es.At) each st>at,e.the valises of t,he cont~rolactions h,5, h,, are given. Thc cont,rollcd txarisitions arc also indicat,cd. 0

o<

to line faults. The example also ilhistrates how logical constraints involving systciii real variablcs - in this case excitation voltage - can be incorporated in the problem via transformation to IP formulas.

02

03

a4

REFERENCES Dao, L., X. Duan and TY. IIe (2000). Aiialysis of voltage collapse mechanisms in state space.

IEE Proceedings - Gerrernt.ion. Dansmission and Distribution, 147(6), 395-100. Bcinporad, Albcrto and Rlanfrcd Rlorari (1999). Control of systems iiit>egratiriglogic, dynamics, and constraints. ~4ulomalicn35(3), 407427. Branicky, _\I. S., 1’. S. Borkar and S. K. hlit,ter (1998). A unified framework for hybrid control: L’lodcl and optimal cont.ro1 thory. IEEE Tra,risaclions on Automatic Control 43(1), 31-45. Geyer, T., hI. Larsson and M. Morari (2003). Hybrid emergency voltage cont,rol in power systems. In: European Control Conferenm. Ca.mbridge. Kwatny, H., E. nlensah, D. Niebur antl C. Teolis (2005). Opt,imal shiphoa.rd power syst cni management via dynamic mixed integer programming. In: IEEE Electric Ship Technoloyies Symposiu.m. Philadelphia. Y. ~ 1 1 0and T. Ida (2000). hIodclling inLi, t>egerprogramming with logic: Lalippage and iinplenient ation. IEICE Transactions on Fundamentals o,f Electronics, Cornmimicatioris an,$ Computer Sciences E83-A(8), 16731680. McKinnon, K. aiid H. Williams (1989). Construct.isig int~egerprogramming models by the predicatc calculus. Annals o j Operations Research 21, 227-246. Ohtsuki, H., A. Yokoyama aiid Y. Sekine (1991). Reverse action on-1oa.d tap changer in association wit,h vohage collapse. IEEE Tnnsnction,s on Power Systems 6(l ) , 300-306. Pal, h1. K. (1993). V o h g e sta,biliby: Analysis needs, modelling reqiiirerrient, and modelling adequa.cy. IEE Proceedings - C 140(4), 279286. Tylcr, M. L. and M. Morari (1999). Propositional logic in cont.rol and monit>oriiig problems. Automatica 35(4), 565-582. Williams, H. P. (1993). Model BuildLrig 271 Mathenzntical Programming. Johii IViley and Sons.

o5

b.,

Fig. 4. Depiction of the feedback law obtained with a = 0.25, t k + l - t k = 0.5, antl N = 20. Supposc nnniediat cly post-falure, tlic system is in modc q l , with a rcduccd slip of 0.1, thcn tlic system will respond as follows. Given a mechanical power lcvcl of 0.7, the eqiiilibriuni slip is about 0.47. As slip increase. the first block of load 05 dropped at dboist 5 = 0.3 dnd the second at about

s = 0.4.

6. CONCLUSIONS W e have described an approach to modeling power m s as hybrid tlyriarnical 1111ousand discret>esubs

fcaturc of t,hc model is a charnctcriznt,ion of the tliscret,esubsyst,rm in terms of a set,of IP formulas. The application of this mo opt isnal feedhck control sy programming has also bccn described. Compiit,atioiial tools for perforiiiing the trarislat,ioii of the logical spc?cification to IP fornmlas ttnd for solving a limited form of the dynamic programming problcm Iiavc bccn asscniblctl iii Mnthernnticn. An exa.mple is given t,hat, illust,ra,tes the problem of optimal load shedding as a means of responding

358

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

STATIC CHARATERISTICS ANALYSIS OF POWER SYSTEMS THROUGH A HERMITIAN APPROACH J u n Zhou *J Yasuhara Ohsawa** * Department of Electricul Engineering, Kgoto lin,%.uersity Department of Electrical Engineering, Kyoto Uniiiersity

x*

Abstract: This p p e r forniulates the power equations of power syskms into t.he Hermitian power equa.t,ions in terms of act ive/rea.ctive power inrlicc.~,based on tvliich we complete t,wo tasks: (i) constriict,ing novel Newt,on-Raphson ikrative iilgorit,lims for compiit'ing power flows of tjhepower systeiiis t,liat, include ajdjust&le weighting coefficieiits; (ii) deriving possible eigeiivalue/singular-~~alue ineqnalities for riodal voltage evaluat,iori with or without power flow computations. The results itre sigiiificmt in evtalunt ing volt,a,gesta.bilii>yof the power syskms. Kelworcls: static characteristics: Hermitiail power equation; power systein.

1. INTRODUCTION

It) i s a,n iinavoidable task for power syst.cni opcrators and engineers to frequent>lyevaluate steady st,ate operating characterkkics such as voltage stabilily- and seiisit,ivi(,y ol power incrernenk wit.11 respect, to nodal volt.age variations in t>hepower systems (Hasegawa, ef al., 2002: Nagata, 2002; Nejdawi, et al.. 2000; Taylor, 1994: Tirariuchit and Thornas, 1988). Unlortunately, however, there are II a i d applicable tools to co r e k i i i i g (lie opcratiori ne tentative discussions about st,at.icvoltage stability through power flow computations are suggcxtetl. One citn say thal power flow computations are indispeiisihle in many aspectasof practical power system opcratioris. Newtori-Ra.plisori niet,liods are seeinirigly the best) choice at) hand! which usually involve tirne-consumiiig riunieric coinputations. La.k:ly grc:a(.

coIIcI-:rIIs

I1a.ve bt:er1 ra

s t a i ic voltage stability, power network security arnong electricity engineers a.ntl resexhers thie

t o several voltage drop crises or severe blackout,s a,roiind the world, Indeed, various stabi1it)ies in power syst,ems ;are tackled by Pavella a r i d Murtliy (1994) and inlluences ol harmonics on vol1,age stnbilit,y has been examined hy Acha, and Matlri-

gal (2001). To attack the static volt,age stabiliLv, t,he P-V and/or &-V sensit.ivity curves inet,hods (Taylor. 1994), singular-value inequalities (Zhou and Ohsav-a,2003) aiid convex analysis (Zhou and Olisawa, 2003) have been consitleretl by means of power flow computations. However, since the polar power equations are iionlinear and of high order, their solution, that is, t.lie power flow, can only be det>erininedapproximat,ely t,hrough such numeric algorithms as the Newton-Raphson method and it,s various modifications, Therefore, the P-V and/or Q-V seiisit,ivit,y curves iiietliotls are not very helpful in vokage stability analysis before power flows are available. In the paper we write the power equat,ions of ms in the st,eady s t a k into Herrr1itia.n forms in terms of active/react,ive power indices, based on which we consider t,he following problems: (i) coiist,ructirig novel Newton-Raphson iterative algorit,hmsfor computing power flows of the power systems that contain adjustable weighting coefficients, whicli play an importmt role in iniproving algorithm convergence rate; (ii) deriving possible eigen~.aliie/singular-value inequalities for iiodal voltage stability eva1ua.tion with or wit h u t , power flow compiitations. It is expected that^ result~sdeveloped by iiieaiis of t~hesest,atic st~ructurad characteristics can be iiscful in eiduating voltage st,ability of power systems.

Correspoiidirig Author: Kyotodaigaku Katsura. Nisliikyo-ku, Kyoto 615-8510, JAPAN. Email: z hoiij@,kuee.k yot 0- ti.ac .j p

359

PL,8,. For our later arguments, we recall that

2 . I’RELIA1INARIE;S TO €’OI.Z’E;R SYSTEMS

yC7k =

2.1 Power Equattons oJ Power Systems

yckz,

gsrk =

admittance matrix

Finally, we define the

&I,&?.

Y of tlic power systcm by

In a power systcizi that is in the steady state, its nodal power equations are defined a i follows.

-

where I = 1 , 2 , . . ,M with the intc.ger N being the number of all the nodes. V, and I , are the ( ouiplex expr cssioris 01 t lie. iiocl~l volt <16c)a r i d current, respectively. of the Ith node while yk ii t h e a t l m i t t a n c ~hetwem t h e nodes I aiitl k.. Tn particular, Y,, is callcd the self-admittanc c> of the 6-tli node. P, and Q,defined in (1) are the slim of all active and rcdctivc powers input and outpnt dt the i-tli node of the power system, respectively. We tcrin (1) the nodal power cqu< t’ions. i 2.2 Hermitian Expression of Power Equations iVodal Powers

2.3 Hermitian Expression of Power Equations via Power Indices Let 11s define ilr active power indices a.nd N reactive power indices, respect,ively,given by

ilia

Herc, rLli.and rrLii; ( i . k E ( 1 , 2 , . . . , A T } ) arc p r e scribed real numbers as weight,ing coeificient~st~o indicate t,lieimport,ance of each nodal acivc/rea.ctive power with rcspcct, to otlicr power indices.

Write (lie complex nodal voltage V, arid Llie atlmittance Y r k of (I) in the power system as follows.

By t he dcfiiiit,ionsof

P,a.iid Q+, wc can mrritc

r, = VTYp,V,

[“I

]p]

with 2 , k = 1 , 2 , . . . ,X. In the sequel, vCZand Y,, are tcrmctl the nodal rcal and imagiiiary voltagt. factors at the 2-th node of the power system, respectively. Now siibitituting V,and I’LL give in ( 2 ) for (I), we observe

(7)

QN

&, = VTYQ,V

(3)

In thc following R := { r , k } and AT =: ( m 7 k } will be called thr. weighting vocfficicnt imtric-cs. In otlier words. t he active and reactive power indiccs Pt and Q,are linear combinations of the nodal active and reactive powers, rcspcctivcly. It follows readily from ( 3 ) that

Aiid siiiiilarly, we liave from ( 5 ) that Clearly, Yp, and Yc27ilre determined by ihe power system pcrtaining to tile r-th node. while V collects all the nodal voltage factors of the power system. Rorn ( 3 ) and the facts that P, and Q,are scalars, it follows readily that

+

Eq. (8) is called t,he qiiadrat,ic power equat,ions in tcrnis of the power indices Piand Qz,while (9) the Hermitiail powcr equations iii t,crms of t 1ic powcr indices Pt a.nd Q i .

+

Notc that Y p c Y g a i ~ dY Q ~ Y$,are rral aiid Hcrrnitiari. This is thc reason why wc call ( 5 ) tlic Hcri-nitian power equations of the powcr system in tcrms of {lie iiorhl artivc and rcadivr powers

Now wc list some special caws in the p o w r intliccs Pi nnrl Qf. If the weightj&, coefficient. mat.rices sat,isfy R = M = 1 ~ 7 ;t h i P,anel Q, arc t hc

3 60

norla 1 act ive/rear t ive powers t hemselves, a 11 d t hi is

(8) m d (9) reduce to ( 3 ) and (5) immediately. Another interesting case is mhen all tlie sralar entrirs in R and A 1 are equal to 1. In this case v,rc actually dcfiiw onlv two powcr in& Q k ! which are the net active and reand Err=, active p w r r inpiit into thc powcr syytcm. Tt is interesting to note by (9) that

act,ive and reactive power increment, vect,ors, respectively. Siiiiilarly wc denote by ap,& and AQ, tlie active and reactive power index increments, respectively, corresponding to the a.ctive/reactive power indices Pf and Q,. Hence, we call A P and AQ the act.ive/reactive power index iiicrernerit, vectors, respectively. In the obvious fashion, the nodal volt,age vect,or AV is written as follows.

AV

=:

[Av,, . AY,, I

* * '

I A7',,V,

AlI,'\T]T

Based on the discussions, we obtain by (12) that

whcrc y( and Y5are givcn in (6).

3 . COhlPUTING POWER FLOWS VIA HERhIITIAN POWER EQUATIONS JFV

In t.liis section, we develop sonic Newton-Raplisoii algorithms for powcr flow computations in thc power syst,erii tlirougli t,lie Herniitiaii power eqmLions (9) ill terms of t hc powcr indices Pi and Q,. Thcreaft.cr, we s11ow how to evaluate t,hc nodal voltage through (8) and (9). Generally speaking, if t,he node number 1V 2 2, there are no closed-form forinulas t.o determine the solut,ioiz V of ((3) sincc (9) is qutatlratic. Therefore, numeric solutions for the Hermitian powcr cquat,ions (9) is gcncrally ncc:dc:d. To coiist,ruct riurncric algorit,hrns for power flow coiiiputat>ioiisvia (9) t,hroiigh t.he Newton-Raplison met,tiod, we riot,e that ~ f = r , k= ( ~,p i Y,',) arid Cr='=, m2k-(Y~i + YZi)are Hermitian. This implies by Property 10.3.2(10) of that

+

=

I

I

k=l

By means of (14), wc arc in a position to construct ail iterative algorithni foi solving the nodal voltage factors u,, and v Y l .To this elid, we modify (14) as follows.

wlicrc 111 = 0 , 1 , ~. ... and (.)(I,') incans tlic 772-th ewlutation of a vector or matrix (.) and thus which leads us: in particular, to a Jacobiaii equa.tion in terms of the incremental variations APi, AQ,&, Av,i and Av,, associated wit,li the active/reactive power indices Pi, Qiand the nodal voltage fact,ors vri am1 il,i. Note t,liat, R and Al a,re conshnt mat,rices. It is evident by (7) that

A general Newton-Raphson algorit hrn for power flow coinput a t ions dcvelopcd tlirougli the Jawtian equation (16) arid (17) can be as follows.

Step 1. Choose tlic weighting factor matrices R and A[; take initial d i e s for aiitl for ear11 7 = 1 . 2 , . f . .N ailti form ~ ( 0 )= [ti!:). I . . , I 7icnr, ( 0 ) t i (s0N)] T; take specified nodal powers P;" and Qf with i = 1 , 2 , . . . ,N and form P S = [Pi?.. , r ; ] T and Q S = [ Q f , .. . , Q%]*; choose convergence tolerance error E > 0:

06:)

ti::)

'

Stcp 2. Sutx,titutc v(")for ( 3 ) or (5) to compute p ( n ~ )= [P:"', ... aIic1 ~ ( 7 1 2 ) =

where AP, a.nd AQ7, denot,es t,lie nodal act ive/react,ive power iiicrerrieiih, respeclively, corresponding to tlie nodal act,ive/react,ive powers P, a n d (2,. Hence we call AP a.nd AQ t h e nodal

,pg)l*

[Qj""'*.. . , Q$"]', and tlicn i i 5 ~R. A1 and V('") in (17) to compute J$$ and J)$: then determine A ~ ( . J=) p s - p(7n) and ~ ~ ( n=t (2 )s - ( ~ ( m ) ;

361

rminc the solution AV('".'') by siibst,itutiiigR, A P ( ~ ~ALQ)(,~ T&~) ) , and for 1,he first, ecpiatjionof (16) as appropriately;

.~g)

nr,

Step 4. By the second equat>ioiiof (16), compute V("'+') = V('") + AV(mi-*) and t,est if I lAV("'+') I I 5 c: i f the tolerance inequality condition is satisfied, talienstop; ot,herwise,let, ni = ,rn+ 1 and return to Step 2. In t,lic Jacobian eynations (16) and (17), an underlying assumplion is that, all tlie nodal act,ivc/rcact ivc powrs a.rc spccifictl. Howcvcr, t his is not the case a.s always. If there are nodes in t.he power syst,em either (or both) of whose nodal active and reactive powers is (or are) not given but whose nodal voltages are specified, t.he NewtonRaplisori algorithm must be modified.

4. VOLTAGE EVALUATION VIA QUADRATIC EXPRESSIONS Here we develop eigen~.alue/signLilar vahe inecliialities between the nodal voltages L$, (or t,he nodal voltage vect,or V and t,he nodal voltage increment vector LV) and tlie ac:t,ivc/rea.ctive power indices Pt%Qi (or the nodal act,ive/rea.ctive power index increment. vectors A P , LQ).Tliese inequalities allow us t,o evaluate nodal voltage st,a.lr,ility wit,h or withiit, power flows.

One can assert a similar result on YgY&. Using tliese facts back to (18). we obtain lPfI

Secondly, we est ablisli inequalities by working or1 t,he Hermitian power eqiiat,ion (9). Obviously, we can have from (9) and the C'auchy-Scliwarz inequality that .

+

N

Since Y p k YFk and U,, eack k , it follows that

+Y& are Hermitian for

(i). Inequalities &(.ween V, (or V) and P,i, Q,

First,ly, we establish inequalit,ies by working on t.he quadratic power equat,ion (8). By the specific , obt aiii from niat,rix cxpressioiis of lip, and Y ; J ~we the well-known Caucliy-Schwarz inequality that

0twioiisly, we can cla.irn some sirnilas results on IICr=lmi,,(Y~k+Y$k)l I. By thcso iiiequalitics, we can verify t,lic following two iiiequalit,ics.

Note that Ypl; and

are square. Then,

miix k

Now assiimc that R = Af = IL\r.In this spwiitl case of R and A f . we have that

Now let) 11s consider the case when all t,he entries 01 1,he weiglil irig coefficierit irialrices R arid A 1 are 1. H,ecalling the discussions around (10) and (1 1) a,nd t h e eigenvalue rules a,hout, Kronecker

362

prodiirts of matrices (see Propertv 2.4(1 l)(e) of Lukkcpohl (1996), we are led by (20) tliat

+

Thirdly, again by tlie [act that Ypk Y& and Y Q ~Y& are Hermitian for eack k , tlie following inequalitics can bc clainicd by applying RayleighRitz tlieorrin (Lutkepohl, 1996) to (9).

+

s

claim that t,he IIerniitian power equations reveal t,lie statsic structural cliaractreristics of power systerns better than t,he coiiventional polar power equa.tion.

(b). In vicw of (20) and ( 2 2 ) : it should also be poiritxd out) t,liat by choosing R a.nd AP in ccrt,ain ways one can evalmtc nodal volt,age stability through tlie cliiatlra.tic a n d 1Ierinitia.n power equations (8) arid (9) but, in tcrrns of diffcrcnt, lowcr/upper bounds. (ii). Inequalities bctwccri Au,~,Av,, (or AV) and

AP,A Q

Now we develop inequalities between nodal voltage fact>orincrements Au,i and A.U:,, (or t,lie nodal volt age increment, vector AV) and power index incrcrncnt vcctors AP and A Q by mcans of thc Jacobian eqiiat,ion (14). Different, from t,he inequalities (18). (20) and ( 2 2 ) , these inequalities involve t,lie power flow knowledge. To derivc these inequalities, assume t,hat the Jacohian mahrix J defined in (14) i s non-singular. By t,he definitions of the infinite vector norms 1 1 . I I m and the EL^clidean vect,or norm I I 11, it is evident, t,ha.t, 11 . [ I m I1 1 . 1 1 for any vector (.).

-

Firstly, we obt.ain by (14) t,hat From Properly 5.3.2(2) of Lutkepohl (199G). ( 2 2 ) yields that

Sccondly, if J is non-singular, we obtain from the

+

generahed matrix inverse theory that [ J & J p v J & , J ~ V ] I [&,. J,&]J = 12x, wlicrc (.)+ is tkic

generalized matrix inverse of tionship in (14), we obtain

(A).

1Jsing this rela-

Again let us consider the case when all the entries of the weighting coefficient matrices R and A1 arc 1. Repeating some discussions similar to those around (21), T.VP are led by (22) that

Suriiniarizing tlic above argunicnts. wc liitvc tlic following results.

Theorem 1. Assume that the power system is in the steady stat?. Thcn, the eigcrivalue/singularvalue inequalities (I$), (19), (20). (21), ( 2 2 ) . (Z), and (24) are always satisfied. Also under the non-singiilarity assuniption on JpvJ&/ and J Q ~ ~ J Q ' ,it. . is clear to see that Sornc rcmarlis about the rcsults of Thcorcm 1. .J&<Jp,, J&JQv is also non-singular. Hence, (a). From the above arginiicnts, we can scc that the generalized matrix inverse theory yields that il fioultl be hard lo tlrrivr (lie irieqiiali~irsol Theoreiii 1 witliout the Hcrniitian power equation (9) Tn a mathematical sense it i i reasmahle to

+

363

(b). Since the iiieqiialities in Theorem 2 can be expresied also through the nodal active/reactive power incrcment vectors A P and Ad) via (Is), the inequalities of Theorem 2 can be used for estimating nodal voltage variations quantitatively through eigenvalues and/or singular values of Ja cobian matrices at a givcln working point V and with prescribed weighting coeIGcients matrices R and ill, wlieii nodal iiiput active and/or reactive powers arc changed minutelv.

Now we obscrve by tlic singular valucs thcory (Zhou, K and J. C. Doyle, 1998) again that

5. CONCLTJSIONS

In t,he pasper we suggest a Hermit>ia,iiapproac,h in power systems t,hat are running in t,hc steady &ate through quadrat,ic funtion forms in terms of iiodal v o h g e factors. This brings us theoretic and niinieric advantages in dealing with probleins of power syst,einsover the coiivciit,ioiial po1a.r power equations can provide. In particular, we have paid our a,ttent,ioiit~o:(i) suggest.ing Newt~onRaplison iteralive a.lgoritlims four powcr flows Ihal include adjust~ableweighting coefficieat,s; (ii) deriving c:igc~nvitIiir./singiilas-valii~? incqiialities for nodal voltage stability evaluat,ion wit.h or without power flows.

+

Lel us define A x . = Ai;, ~ A 1 - 1which ~ ~ . means tlicx nodal voltage incrcment of V , at tlie i-th iiodc in thc polar expression scrisc. It i s obvious that niax,=1,2, ,L%r{lA&I} 5 IlAVll. This, together with (23) and (as), yields the following resiilts.

Theorem 2. In the power system that is in the steady statc with the nodal voltagc vector V . Assuinc that the Jacohiaii mdtrix J = [J&, J&IT defined in (14) is rloli-5i11gUh' at V . Then

REFERENCES

Furt lierrnore, if J ~ non-singular . then

~ ~ - I ,and T,

Aclia, E. bi: M. Ma.drigal (2001). Power Systems Ha.rmonic.s, Wiley. Hasegawa, J. k e t al. (2002). Pozrier Systems Enqineerzng, Denkigakkai (in Japaness). Horn, R. A. & and C. R. Johnson (1985). Mo,tyi:r An,a,ly.sis, Ca.mbridge Uiiiv. Press. Lulkepohl, I1 (1996). fIa7idbocik: of Mutr-ices, John

JQ\/JQT, are also

(in Japsness). Pavella,, 11.& P.C. I\;lurtrhy(1994). Transient Sta.bilitg of Power Syslems- T h e o ~ yarid Praclice, John Wiley & Sons, Chichest,er. Taylor, C. W. (1994). Po,uier System Voltage Slabilit?~, McGrew-Hill, Inc., New York. Tiranuchit, A. bi: R. J . Tliornas (1988). A posturing st~rategyagaiiist voltage instabilities in eleclric: power syslerns, IEEE Truns. orb Power. Systems, vol. 3, pp. 87-93. Rockafellar, R. T. (1 970). Conrier Annlysis, Princeton Universky P r Nejdawi, K.A. Clements An efficient interior poiiit method for sequeiitial quadratic programming based optimal power flow, IEEE Tram. on Power Systems, vol. 15, 111). 1179-1183. Zhou, J. & Y. Ohsawa (2003). Iterative singu1a.r inequalit,y evaluation of stat,ic voltage stability in power systems, Proc rtuiccd Rleetirry o'ri Pvuier Systems Engineering. IEE Japan, pp. 25-30 (in Japaiiess). Zhou, J. bi: Y. Ohsawa (2004). Volt>agestability evaluation of power systems under convex analysis fra,mework. Proceedi.n.ys oef Intcrnatiorid Corifereiice on Pomer Systern.s (ICPS2004). K:rthmunthi, Ncpal. pp. 125-130. Zhoir, K. 6c J. C. Doyle (1998). E.ssentials of Robust Control, Prentice Ball.

Sonic rcniarks a.bout (26) and Tlinorcm 2 .

(a). Eq. ( 2 6 ) indicaaes t,lia.t,bot>liact,ivo a~iitlreactive power variations have irnpactJs 011 the nodal v o h g e s . The struct,ural fca.tures in the qmlitative a.spects of tliese impacts a,re t,lie same, while tlie quantit,alive aspects of 1hese inipacts may be di€ferent,. In ot,lier -words, struct>ural;i.djust~~iient~ nieasiires in order t.o improve the active (respectively, reactive) power performance in a power system bring a similar a,ffcct on llie react,ive (respectively, adive) power perlorrriawe, iii the seiise ol 111erelationship between AP and AV a i d that, between A Q and AV.

364

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ECONOMIC DISPATCH ALGORlTHM BY 2.-P TABLES REFLECTING ACTUAL FUEL COST CURVES Kyung-11 Min, Jong-Gi Lee, Suk-Joo Kim, Hyo-Sik Hong, Young-Hyun Moon Dept. of Electrical Engineering, Yonsei Univ., Seoul, 120-749, Korea

Abstract: This paper presents a new approach to economic dispatch (ED) problems with actual fiiel cost curves using a L P table method. Conventional ED algorithms are developed on the basis of approximated fuel cost function, which cannot be adapted to actual fuel cost curves properly. In this paper, a A-Ptable method is proposed to improve accuracy of ED solution. It is noled that the proposed algorithm is very simple and has some advantages in considering the must-run condition and modifying the ED solution associated with generator addition/elimination. Numerical results of the proposed algorithm are compared with those of the conventional algorithms. Copyright 0 2006 IFAC Keywords: generalion cosl runclion, h-P table meihod, P-h LdbleS, aclual rue1 cosl curve, nonlinear cost function, economic dispatch (ED), unit commitment (UC), must-run condition

1. INTRODUCTION

Power industries are faced with rapid renovations in the whole world. Past power industries characterized by monopoly, excessive regulation and public property have been transferring to a new paradigm characterized by competition, deregulation and structural reform, and participation of private funds. It needs new economic dispatch (ED) algorithm for transitional systems of which concepts of economic operation is changed as compared with the rormer. Due to introduction of power market systems ED should be able to admit various types of fuel cost curves with frequent alteration by power market bidding. Conventional ED algorithms cannot apply to actual fuel cost curves because they have to use approximated cost functions such as second ordcr polynomial, piecewire linear function, and so on For accuracy, nonlinearity of fuel cost curves should be considered NLP (Nonlinear Programming) (Kuhn and Tuckcr, 1951) may allow using nonlincar cost functions, but it has reliability problems in convergence which make it complex to implement ED In order to overcome the reliability problem, LP (Linear Programming) (Waight, et al., 1981) has

been widely applied to solve the ED problem. Thc LP algorithms allow adopting only piecewise linearized functions, and it is necessary to divide fuel cost curve into so many linear sectors in order to rcflect fucl cost function accurately. However, the more linear sectors create the more inequality conditions, which significantly degrade the merits of LP algorithms. Recently, it has been attempted to apply ANN (Artificial Neural Network) and GA (Genetic Algorithm) based on AI(Artificia1 Intelligence) to ED problems. Some of the interesting methods are GA (Walter and Sheble, 1992), SA (Simulated Annealing) (Wong and Fung, 1993) and PSO (Particle Swarm Optimization) (Park, et al., 2005), which are considered the most advanced. These methods have a severe defect that drastic increase in the number of genes or particles with the system size increasing guarantce neither optimality nor convergence. Up to date, ED algorithms havc developed on the basis of smooth continuous fuel cost functions. However, due to introduction of power market systems, the fuel cost functions presented by electric power company at bidding may be artificially manipulated different from the actual. In this reason, it is necessary that the ED algorithms

365

be able to accept various types o f the fiiel cmt functions, that is, step, linear, piecewise linear, and smooth function as well. On the othcr hand, it is supposed in the power market systems that gencrators are subjected to frequent onioff switchings Some generator maintains minimum output with must-run condition, while some generators are shut off when the market price goes down under a certain value This situation can be well treated by using the proposed h-P table method This paper proposes a new ED algorithm using a h-P table which is obtained by inverting the P-h curve. Hcre it is noted that the h-P tablc accommodates any kind or rue1 cost function and enables us to adopt the actual cost data obtained in the field test.

Especially, as Fig. 1 (h) depicts, discontinuities due to valve switchings makc the error larger. In order to reduce the approximation error, the cost curve is approximated to one-piece or two-piece linear functions, or higher order polynomials in economic dispatch. In order to obtain a precise incremental cost function close to the actual, one may use linearization of five or ten sectors or higher order of polynomials for approximation. Main idea of the proposed algorithm by h-P tables is to use sampling data of the incremental fuel cost curves instead of approximatcd ones, and to utilize the h-P table, which is obtained by inverting thc P-h table Details will be examined further in the next section Fig 2 illustrates the sampling and inverting process of the incremental fuel cost function.

2. THE P-h TABLES REFLECTING ACTUAL FUEL COST CURVE Conventional ED algorithms have been developed on the basis of incremental fuel cost functions which arc approximated to Iincar, piccewisc linear and/or higher ordcr polynomials However, adopting approximated cost functions always involves some approximation error? The errors are illustrated in Fig I(a>

I L ‘1‘ \ Inverting

Fig. 2. Curve Data Sampling and Inverting process P-h data can be obtained by table sampling from the field measurement data. This h-P table reduces the approximation error. Sampling error can be minimized by selecting properly small sampling interval. Here, it should be noted that the proposed approach is developed under a premise that each of the incremental fuel cost curves must be nondecreasing. Actual incremental fuel cost may show decreasing trend in very low generation but keeps nondecreasing trend for regular generating interval. Since minimum of generation is assumed for each generation, this premise can be generally accepted in the ED problem. If the P-h table are inverted to the h-P table for the same interval and values, generation output is determined by the function of h, pG,(A).

Poweroulput. M W

(a) Actual and approximatcd curvcs 14.006

5 13.000

8

E 12wo g,

-

2’- 11000

3. ED ALGORITHM USING THE h-P TABLE WlTHOUT LOSS CONSIDERATlON

z

-P

10000

50

60

70

!XI Net generation (mw)

90

1W

In order to develop a new ED algorithm, we utilize thc fact that each output power of all gencrators is determined by the incremental cost h. The total generating power is given by summation of each generating power. That is, total generating power, PGttl, is a function of h given by

110

(b) Including discontinuities due to valves Fig. 1. Incremental fuel cost curves

3 66

where PD is the total demand including estimated system loss. Since PGI,,(A)is nondecreasing, we can solve (1) to obtain A* with bisectional or linear interpolation methods, etc. In this method, it is noted that KuhnTucker conditions need not be considered since PGz(A)provides all information for minimum and maximum generation outputs (Madrigal and Quintana, 2000; Moon and Park, 2000).

optimal output is determined by substituting A*,that If generator 2 is added or eliminated, is, PG!(A*). PGIIi (A) is modified by adding or subtracting PG2(A) from P~,,, (A).

3.3 Proposed ED algorithm In this section, the proposed ED algorithm will be explained by using the main idea described in the previous section. The proposed algorithm is composed of the following 5 steps roughly. Siep 1) Take sample data for the incremenial fuel cost curve and construct the P-h table for each generator. Step 2) Establish h-P tables by inverting the P-h tables. Step 3) Consiruct the total generation function PGrr,(A)by summing up the h-P tablcs for all generators. Step 4) Calculate optimal A* by solving (1) by using the bisectiondl method andor linear inierpolation. Step 5 ) Calculate optimal dispatch for each generator with PG,(A*).

Fig. 3 shows an illustrative example with a 3generator system.

In the subsequent sections, the detailed implementation strategies of the proposed method are described.

Fig. 3. The summation of three generators’ ouiput power 3.I Must-run condition

Fig. 3 shows graphical analysis for three generators. Generator 1 and generator 3 are operated in the must-run condition which must generate its minimum output, while generator 2 is stopped for economical elkiency below a certain marginal cost. Conventional methods have no efficient algorithm to deal with this situation including must-run or not conditions. However, the condition can be easily applied into h-P tables by filling actual generator output below the minimum marginal cost for both cases.

In step 1, the measurement data obtained from field test can bc directly used without approximation. If the measured values are discrete, those values can be direcily used to construct P-h tables. In step 3, linear interpolation can be applied to obtain generation power for every generator at arbiirary h. In step 4, the optimal A- can be calculated by the bisectional method. Generally, this method is known to degrade the computational specd. However, the bisectional algorithm does not take much time to find Abecause it finishes within only n times for 2“ points of h. The proposed algorithm can be efficiently applied to the modules which need repeated ED computations as in UC. In step 5 , it calculates power generation for each generator with A* obtained in the previous step. Interpolation is also adopted for calculaiing the exact generation. Remarks

i) It can be applied to any type of incremental fuel cosi curves which may have nonlinearity, high order terms or discretc jump points as long as each of the Pc,(A) satisfies the nondecreasing assumption.

3.2 Arbitrary generator’s addition and elimination

The proposed algorithm can also be applied to ED associatcd with UC(Unit Commitmcnt) assuming rrequent onioff operations Tor each generator Total ), summation of generating power, P ~ ~ ~ ! (isAsimple three generators.

Afier selecting arbitrary

11) Once

A:,,,,,,

&,!(A) is constructed, modification of

P‘,,!(A) can bc pcrformcd with simple process in association with addition or elimination of arbitrary generators.

optimal incremental cost, A*,can be easily obtained by bisectional or linear interpolation method Each

367

iii) Arbitrary changcs in PG,(A) can bc casily takcn into account with the simple modification of

In this case, modified P-h table should be used instead

4. ED BY h-P DATA TABLE REFLECTING SYSTEM LOSS In thc previous scction, thc system loss has bcen neglected to explain the concepts of the main idea. Howevcr, thc system loss i s considcrcd to be an important factor in the ED problem in practice. The ED problem with losses can be also solved by using the h-P table? with slight modification The total generating power with losses is expressed as

.

.*-.--

Modify

,.

...- -...~ ., ,

,

Inverting

Fig. 4. Construction process of modified h-P tables considering losses

5. EXAMPLES

The loss-considered optimal condition is given by

PF, , IC, = PF, . IC, = 6 = PF, . IC,, = A" (3 )

Test is executed by using the proposed h-P table method. It is assumed that actual fuel cost curve is third order polynomial because it is difficult to gather thc data and obtain real solution. Actual fuel cost curve is assumed as ( 5 ) and its coefficients arc given in table 1.

where

F ( 4 )= A + B e

+ Ce' + D e 3 (5)

Table 1 Coefficients of actual fuel cost curves assumed by third order polynomial

The penalty coefficient for generator I , PF , can be calculated by the power flow calculation. The penalty factors can be slightly changed by the results or ED. However, this study uses approximated penalty factors calculated in the similar previous operation condition. By substituting (3) into (2), the total generating power is rewritten as

1

320

XO0

74955

695

9 6 8 E 04

127r 07

2

300

1200

12x5

7 051

738E-04

h 4 5 k 08

3

275

1100

1531

6 531

104E-03

998E-08

The h-P table is constructed by sampling actual incremental fuel cost curve from ( 5 ) by lambda interval o r 0.01. LineariLed incremental fuel cost function is one-line approximated as (6). Table 2 represents its coefficients.

(4) Table 2

Each of the optimal generating power is determined by A* divided by Pe . In this facts, modified h-P tables, P p d ( A ) ,can be obtained. Once PFd(/l)is constructed, optimal h can be found out by bisectional or linear interpolation methods in the same manner of the neglecting loss case. Fig. 4 illustrates the construction process of

e;,'"d (A).

First, P-h tables are modified by multiplying each penalty factor to h. And then, modified P-h tables arc invcrtcd to h-P tables. Process of thc considering loss case is the same as the neglecting except step 2.

One-line approximated incremental fuel cost function coefficients

I

320

800

6.837879

0.002363

2

qno

I200

6955216

0no176s

3

275

1100

6.40653

0.002492

5. I Comparison ojresults of each method

The results of the conventional and the h-P table mcthod are compared to the actual results. Total demand for test is set as 2300MW, 2500MW and 2700MW. Results are represented in Table 3.

368

Table 3 Generating Dowers and costs (Demand=2300MW) [MW] (;en, No.

Actual curve

Linearized h.

h-P ldbk

1

1j64.6849

667.2822

1j64.6849

2

828.0756

826.8844

828.0756

3

807 2395

805.8334

807 2395

Coat

21,033 4659

21,033 4779

21,033 4659

generators respectively. The system demand is set as 8000MW. In this problem, must-run condition considering case is compared with not considering case. Must-run condition is applied to 14 generators. Results are shown in Table 7 Table 7 Generations and costs in 50-generator system (Demand=XOOOMW) 1h8w1

Must-run-not-considered

(;en. N,\

Table 4 Generating powers and costs (Demand=2500MW)

1

2 3 4

r ~ w i Gen.No.

Actual cuwe

Linearized th

1-P table

5

1

724.9915

728.1 272

724.9915

2

910.1533

908.3442

910.1 533

3

864.8552

863.5287

864.8552

Cost

22.729.3246

22.729.3421

22.729.3246

6 7 8 9 10 I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 13 14 35 36 17 38 39 40 11 42 43 44 45 46 47 48 49

Table 5 Generating powers and costs (Demand=2700MW) Gen. No.

Actual curve

1,inrarred h.

h-P table

1

785.1824

788.9721

785.1824

2

992.1608

989.8040

992.1608

3

922.6568

92 1.2239

922.6568

Cost

24,455 1679

24,455 1940

24,455 1679

The conventional method results in some errors. On the contrary, the h-P table method shows exact results in all c a m . Results o f Cost also show that the h-P table method remarkablely improvcs the solution accuracy. 5.2 1-P table method considering losses

The h-P table mcthod is also tested in the lossconsidered case. In the test, the power demand is 2S00MW and losses are set to be 7SMW, 3 percent of the total demand. Penalty factors are given in Each generating powers are also Table 6. represented in Table 4. Generator 3 is taken as the slack bus. Table 6 h-P table method with losses (Demand=2300MW, Losses=75MW(3%))

5. 0 .

lMWl

Gen No

q

A,(= IC, PF,)

Total

PF,

I

764 5398

8 6529

10450

2

846 2951

8 6529

10255

1

758 I 6 5 0

8 6529

I 0000

Cost

21,629.0986

aldck

5.3 Example with 50-generator considering various types of incrementalfuel cost jiinctions

The proposed method has also been applied to the ED problem with SO-generator system which has various incremental fuel cost function types. The type of second order incremental fuel cost function is from generator I to 20. From generator 2 1 to 50, the function types are third order polynomial, two-piece linear function, and step function every ten

Must-run-considered

Genera11on

Cost

Cieneralioll

cost

130 130 460 465 160 455 455 470 80 80 0 300 162 I62 0 100 0 0 0 0

2884.66 2884.66

130 130 460 465 160 455 455 470 80 0 0 0 0 162 0 0 1x o 210 210 210 0 0 100 100 155

2884 66 2884 66

lll29.91 I1 120.36 4066.02 8544.62 8887.28 11205.19 2197.37 2720.1 I 7704.60 4253.40 3741.25 3041 .SO

0 0

100 100 155 I55 197 197 197 400

2077.89 2088.77 1902.56 1905.94 4867.75 4887.96 4908.19 3460.00

0

0 80 80 0

197 136 0 400

1112036 4066 02 854462 888728 11205 19 2197 37

0 0 0 0 0

3741.25

5702.75 6616.67 6648.07 6490.40

0 0 0 0

2077.89 2088.77 1902.56 1905.94 4867.75 3438 23 3460.00

0

0

0 3112.88 3076.57

0 0

300 300 335 70 70 120 120 120 210 210 210 2x0 3x5 8000

I55

1112991

MI1

10x14 63 11202.98 15990.35 1868.71 3868.74 2774.20 2774.20 2774.20 51 17.33 5177.33 5177.33 6584.94 9717.21 198577.60

80 80 0 0 0 300 300 425 70 70 120 120 120

210 210 210 2x0 385 8000

3 112.88 3076.57

10x1463 11202.98 18291.59 1868.71 1868.74 2774.20 2774.20 2774.20 5 117.33 5 177.33 5177.33 6584.94 9717.21 202259.20

0 0 0

0 0

From Table 7, it is known that the proposed algorithm can efficiently deal with must-run condition and mixed types of incremental fuel cost in the ED problem. In comparison with considering must-run condition case, not considering case is a little cheaper.

6. CONCLUSIONS This paper has presented a new approach to the ED problem bascd on a h-P table mcthod reflecting actual fuel cost curve. In order to apply actual fuel cost curve to the ED problem, the h-P table method uses sampling data obtained fioni field tests or

3 69

Programming S/ati,stir.s und Prohahility, University of California Press, Berkeley Park, J. B., Lee, K. S. (200.5). A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Transaclions on power systems, Vol. 20, No. 1, pp. 34-42 Madrigal, M., Quintana, V. H. (2000). An analytical solution to the economic dispatch problem, IEEE Power Engineering Review, Vol. 20, pp. 52-55 Moon, Y. H., Park, J. D. (2001). A new economic dispatch algorithm considering any higher order generation cost functions, International Journal ojElectrica1 Power & Energy System, Vol. 23, pp. 113-1 18 Waight, J. G., Bose, A., Shcblc, G. B. (1981) Generation dispatch with reserve margin constraints using linear programming, ZEEE Transaction on Power Apparatus and Sjntems, Vol. PAS-100, NO. l,pp252-258 Walter, D. C., Sheble, G. B. (1992). Genetic algorithm solution of economic dispatch with valve point loading, IEEE PAS summer meeting, Seattle, paper 92 SM 4 14-3 PWRS Wong, K. P., Fung, C. C. (1993). Simulatedannealing based economic dispatch algorithm, IEE Proceedings. C, Vol. 140, issue 6, pp. 509-

operations. Main idea of the proposed algorithm is very simple and very easy to apply to the ED problem. The proposed method has some advantages in must-run condition and arbitrary generator’s additionielimination. Test shows that the proposed method provides much-improved calculation results very close to the optimal solution compared with the conventional methods. It has been shown that the proposed method can nicely handle the lossconsidered case with slight modification in algorithm. REFERENCES

Allen J Wood, Bruce F. Wollenberg (1996). Power generation, operation, and control, John Wilcy & Sons John J Grainger, William D Stevenson, Jr (1994) Power system analysis, chapter 13, McGrawHill. Leon K. Kirehmayer (1958) Economic operation oJ power systems, chapter 2, John Wiley & Sons, New York Kuhn, H. W , Tucker, A. W (1951). Nonlinear Programming, in Second Berkeley Symp0.c rum on Mathematical Progruinming Statistics and

5 15

3 70

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

POWER SYSTEM MAXIMUM LOADABILITY WITH GENERATION CONSTRAINTS C. E. M. Fernandes* R. S. Salgado* L. V. Barboza**

*

Uni~~er.siclaile Federal rle Santa Catcmna

CTC - EEL - LARSPOT Flot ioaripolas. SC. Brnzzl * * Un,*ioer.s.irladeCato'lica cLc relotas Gentro Federal de Educnpio Tecnolbyica Pelotas, RS, Brazil

Abstract: Thc control of reactive power aims at bot>h iiicroasing tlic limit of power t,ra.nsfer between areas ant1 monitoring the bus volt,a,ge ma,gnitiide. In order to increase tlie amount, of' energy transfer, suppliers must, produce reactive power close t,o t,lic p1;~ccwhere it, is nccdcd. Additionally, extra reactive power capacity niust, be kept to protect, the int,egrity of the system against, unforeseeable corihgencies and sitdden cliariges of powcr load levels. Tlie present work is addressed to the cletermination of operational solutions (that is, t>hosesatisfying all operat,ioiial h i t s ) of iiiaxiiiium loadability considering the reactive power reserve. A constraint) related to tlic quadratic dcviat,ioii of a pre-spccificd level of reac:tive power generation is included in h e stal.ic opt~imizat,ionproblem t,haf, models f he computation of t>liemaxiinurn loaclabilit,ysolution. This iiiodified problem is solved t,hrough t,he nonlinear version of t,lie Interior Point met,hod. It is shown how the crit,ical loadability arid the reactive power margins are modified as the priority of reactjive powcr rcscrvc changcs. Numerical rcsults obt,aincd .with a 57-biiscs system ilhistrat,e the app1icat)ioiiof the proposed approach. Keywords: Maxirnurri loadability, rcnct,ivc power gcnoration rcscrvc, opt,irnizabion.

1. INTRODUCTION

Ovcr tlic. last decadcs, economic prcssurc ha,i led to the continuous interconnection of bulk power systems and full use of existing facilities. This brought about more complexity to the power networks. such as to require theni to operate closer to thc limits. It also contributed to incrcasc the importance of problems associated with the maximum loadability of power systems, traditionally limited by transient stability or thermal condi-

tions. Besides. the problems of voltage stability and voltage collapse faccd by
371

The determination of the critical power demand consists of computing the maxiiiiuni value of the load parameter. such the power balance at each bus is satisfied. In (Ajjarapu and Christy, 1991; Cafiizxrcs and Almrado, 1993), a scqucncc of power flow solutions is determined through the Continuation Method described in (Seydcl, 1994). Although these approarlies allow to determine the static bifurcation point of the power flow equations, t h y do not take into xcount some opcrdtional limits (such as the voltage magnitude limits at the load buses). Thus, a number of solutions of this scqiiciicc can not be used for practical purposes. Besides, there is 110 svsteniatic wdy to adjust tlic power gcncratioii as the dcniantl increase$, that is, the load supply is the only objective considered to establish the power generation.

Several studies concerning technical arid economical aspects of t,he reactjive power in t>heoperation of power netrworkscan be foiincl in the literatiire. Approaches such as (Alvarado and Overbye, 1999) a.rc fociwcd on t,l-ie issues related to tlic rcactivc power ma.rket. Reference (Hao and Papalexopoulos, 1997) proposes mea,sures relating tlie reactive power requirements of the el( ric ixkwork t,o the cliange in the power demand. A few studies found in the 1it)cratiu-cconsidcr t>liciiiflueiicc of the rcactive power margins iii t.he critical operational power demand. This compromise provides addit.ional argument>sfor understanding t,he react,ive power c1ist)ribution;which is essent,ial t.o the assessment of tlic rcquiremcnt,s of power transactions. The loadability ma.rgin a.nd the reactive power reserve can be seen as very mance indexes whicli can be s efficient,QV cont,rolnieasurement.s. The guara,ntee of miiiimurn values t,o these aiiiount,s reduces the risk of 1oa.d shedding in t,he normal opera.t>ioiia.nd under cont,iiigencyconditions (Bao et al., 2003).

If' all operational coiistraink are considered, the optimimtion tcclmiqucs arc tlic iiiost suitablc strategy to solvc this problem. The predictorcorrector dlgorithin of the Interior Point Method is applied in (Irisarri cf al., 1997) to obtain the operational solution corresponding to the critical opcrational demand. The problem to bcl solved is analytically expreqsed as Mar p 3.t. pv, - (p,g P A p d , ) - PJ(v.6,a ) = 0

The research described in this paper is focused on the applicatjioii of sta.t,ic optimization met>liods t,o deterniine the critical opera,t,ional 1oa.dabilit~yof a power system, increasing simultaneously t,hc rcactivc power magins. Analytically, the proposed strategy consists of iiicluding an addit iond inequ;rlit,y constraint, relat,etl indirectly t~ot,he react,ive power reserve. This const,raJnt is expressed in tcrins of t,hc squascd deviation from a pre-specified levcl of reactive power gciieration. The new aspect of the proposed approach is the use of a variable limit to t,he definition of this inequality const,raint. The proposed methodology provides stcady statc powcr network solutions in which the power demand is maximized together with the reactive power reserve. Numerical resnits obtaiiicd wit.h t,he IEEE 57 buses lest-system arc iised to illustrat>etrhe applicat,ion of the proposed met liodologp.

+

- (62:J 4- PAQd, I - Q3 Pg","5 Pg, 5 P ; OgJ

v,"' 5 v,5 by)'

&I

a;i: 5 a k j 5 akJ (1) where the optirnimtion variables are: the voltage magnitude at all buses (K), the voltage angle at all buses except the reference bus (&). the transforines taps of tlic Load T,ip C h a n g ~trcinsforniers ( o n [ ) and the load parameter p. The equality wiislrairils represeiil the power balnrict. equdtioii at the load buses. The inequalities represent the upeiatioiial constraints on the power generation, voltage magnitudc dnd transformcr tap of thc LTCs. The power generation is represented
PROBLEM To formulate tlie problem of the maxirnum loadability supplied in a power system operating in steady state, tlie power demand is parameterized by a scalar p and analytically expressed as (Ajjarapu and Christy, 1991; Irisarri et d., 1997) $-

U d A=

+ PA&dZ

0

Q;;F Q q J F QiJ1

2. THE hIAXIhIUhI LOADABILITY

pd, =

(v.6,a )

The solution or the problem expressed b> equation (1) provides:

whcrc, Pj6 and QO,, are the active and rcactivc power load at the bus z, respectively, for a base caw: APdt arid AQd, rcprescnt the tliicction of activc and reactive power load change and p is t h e w-rallrd load p a m m P f w

0

372

t he opcr ational solution of t lie power nci work in steady state corrrsponcling to the maxii-nurn 1mwc.r load supply (voltage angle

0

0

and iriagiiitude at each bus. tap of the UI’C translormers and load parameter p, wkli all the ineqiialit,y constradnts satisfied; t,he Lagrange mult,ipliers corresponding t,o t,hc active a.nd rcxt,ivc powcr balance cquat>ionsat, the load buses, which are iilterpret)ed as instant,aneous sensitivity relationships bet>weeiithe load para.mct,er ziiid tlie power iiijeclions at the load buses; t>hc dual multipliers corresponding to tlic act,ive inequality constraints, which represent^ t,he instantaneous sensitivity rela.tions1iip of t>hcload parameter wit,li respect to the limit that, was reached.

In (Dai et al., ZOOO), the first order optimalit,y condit,ions of the optimization problem solved to determine the critical power loadability are simplified, providing a reduced and efficient. model which providcs thc critical power demand and/or the minimal load curtailment and the available transfer capability between t>he producers aid the costlimes. In these approaches the iiiaximuin power demand t.o he supplied is the only ta.rget. taken into account to establisli t,he tlispatcli of tlie power generation. The comhina.t,ionof t,he Continuation Method with the iionlinear version of the primal-dual int,erior point, algorit,hm is proposed in (Almeida and Salgado, 2000) to the determi1i:rtion of a sequence of opt,imnl solut,ions from a, base case t,o t,he point) of maximuin operat,ioiial loadabilit,y. Although ail act,ivcpower distribution of minimum cost, is cieterminecl for ea.ch solution, a high cornpittatiorial effort is required to determine this sequence.

3 . I\IAXTkKJkT T,OADARTT,TTY WTTH GENERATION CONSTRAINTS The modified version of the problem of the inaxinium operational powcr demand proposed in the prcsc~~t work consists of tlic inclusion of a constraint related to the squared deviation of the rcartive power generation from a pre-specified geiieratioii level. It is analytically expressed as 2

Q;‘) 5 Pq 1=1

wlicrc cyq, is t,lic pcnalty fa,ctor corrcspondiiig t,o the deviation of t,he react,ive power generat’ion from the prc-spec:ified value QiLaiid pq is the liiiiit of t,he t>otalweighted sum of the reactive power dcviat ion. Several alternatives are available to specily Ihe generation level a i d the associated penalty factors. The guarantee of a power margin is related to the prc-spccificd \ d u e s of t,l-ic powcr gcmcration. For exa.mple, if QE:” = Qby is selrrt,ed, t,he rve corresponding i.o t,he upper

limit is maximized. Thus, in order to liave these margins accordingly with the gencration capacity, tlie penalty factors are selected as

(3) Therefore, the optimization problem considering tlic iiiclusion of tlic constraint associated to tlie rcactivc powcr tlcviation is cxpresscd as 1Zla.7

-3.f.

wop - +pq

Pg3- (P:? f p a P d J ) - Pj(v, 6. 0,) d?gJ -

(@fJ

+ Pad?,

-0 3

=0

(v,fi, a ) = 0

i=l

(4) where, pq is the limit. associa,tedto the constraint, t,o be included; wo is the weight,ing factor assigned t,o t>lie1oa.d parameter aiitl wq represent,s the weighting faclor ributed to the power deviation const.raint,s. c ncgativc signal in the term of the objective fuiict,ion ensures that the non-negat,ive variable prl is minimized. The weigliting factors i~()and u4a,redirectly associat,cd tmothc im,por.tance of t8herespectlive performance indexes. They allow to obt aiii solutions favorable t,o t,he loadability margin or t>ot,he reasctfivepower reserve. Equation (4) could be also interpreled as a niult,i-objcctivc optimization problem, wlicro the a.im is to maximize the power demand and sirriultaneously to rriiriirnize t.he deviation of a prespecified power generation level. The iiiodeling of tliis problem can be seen as a conibinatAon of tlic rnct,kiodologicswhich iisc vvc:igkitjingfactors as well a.s inequality const mints to deal hierarchically with tlie performance indexes t>obe optimized. Observe that fixed values selected wrongly could make impossible to satisfy the constraint on the deviation of t,lic power gcncration. Tlius, in order t,o faci1itat)ethe scarch for t,he optimal solut,ion of blem expressed by equat,ion (4), the papq is coiisiciered im opt irnization mriable. hdditiona.lly, in order to limit tlie incursions of tliis ~iewvariable, a rion-riegativity coristrainit is a.dded to the opt~imizationproblem. 4. KUMERICAL RESULTS

In order to illustratc the application of the proposed methodology, numeriral results obtained with thc IEEE 57 buscs systcrn arc prcscntctl in this section. The Predictor-Corrector of the Primal-Dual Tnterior Point mrl hod WRS iisc~lto

373

l'able 2. Variation of the weighting factor d q - powcr demand and power inargins.

solve the optirnization problem r epresentecl by equation (4). In all casc5, the prc-spccificd valuc of the reactive power generation was Q6pJ' =

w.

The main objectives of tlicsc tests wcrc:

css t,lic sohitjions obtaincd t,lirougli t~lic at,tribut,ion of different, weighting fa,ct'or to the loadabilit8yand reactive power devia,tion; to vcri& t,he margins of rcact,ivc power rcserve determined with different penaky factors; to observe the coniproinise beheen t,he critical operational demand and t,he maintenance of a prc-specified rcactivc power margin: t,o assess the effect, of the transformer tsapsiri the constrained loadability problem proposed here; to observe the coInput,ational effort. added to the it.crat>iveprocess of tlie ma,ximurn loada,bility problem due to the inclusion of the reactive power constraint.

30 f

\

m

Unity Weighthg Factor Tablcs 1 and 2 sumniarizc t,hr: rcsults obt,a,inctl with cvq = 1 for five values of uq = 0. The s o l u h n oblainecl wit,h wq = 0 corresponds l,o the conventional maximum loadability problem of equa,t,ioii(1). The increase of the factor wq (I, 10, 100 and 1000) means tliat, a liiglicx priority i s given to the minimum deyiat ion Gorri the reactive power level. This results in sniallcr critical loadability (1612.43 t.o 1300.12 MW and 433.16 ho 349.25 hfvar), reactive power geiieratiori levels (391.02 to 249.69 kIvar) and deviations (148.53 to 7.20 M w r ) and 1a.rger reactive power masgins (93.97 t,o 235.30 Mvar).

[

Total generation

Po

100 1000

I 1

111:3 51 1311.40

]

I

302.02 249.69

I I

I I

I

800

1wo

In this ca.sc, the weighting factors aqi are as cxpressed by equation ( 3 ) . Nunierical rcsuks prcsented in tables 5 and 6 show the active and rcact,ivc power generation, t,he active and reactive power margin arid tlic pcrccnt 1oa.dabilitv (wit,li rcspcct to thc uppcr powcr gciicration limit) of each generating unit. It can be observed that, if the capacity of t,he gcmerat'or is t,aken into account t,o assign the weighting factor, as the priority of the minimum reactive power deviation increases (w,) t,he loadability of each generating unit knds to be more proportional to the capacity of the generator. wit,h a better distribution of t.lie reactive power margin.

Power deviation

182.19 50.35

€00 weights

upper power generation limit) of each generating unil. Since the capacity of llic generator is not taker1 irito accoiiiit to assign tlic weighting fxtoib the reactive power deviation (aq= I ) , some units opciatc at the upper ieactive power limit without any power margin (units 2. 3, 9 dnd 12).

I

I

400

P"

Fig. 1. Variation of the parameters p and prl

Table 1, Varia.tion of the weighting factor uq - power generation a,nd deviation from it. prc-spccificd level. Weight

-x-

59.53 7.20

~

Figure 1 shows the parameters associated to tlie 1oa.d ( p ) and t,o t'he reactive power deviation (p,). As t>hef x t o r wq beconies higher, one of t.liese two parameters increases ( p q ) as the ot,her dccrcascs ( p ), showing the compromise bctwccn the inaxiiiium loadability and the ma.intenaiice of a reactive power margin.

4.3 Effect of the Transformer Taps Tables 7 and 8 shows the influence of the transformer taps in t.he critical loadability- arid reactive power reservc. These resiilts were ohtaincxl by fixing a,i1 transfoririw ta,ps iii t,he valiie corresponding

Tablcs 3 and 3 show Ihc activc and reactive power generat,ion, t,he act,ive arid react.ive power margin and the percent loadw,bility (wit.h respect to t h e

3 74

d C iari , =

Table 4. Variation of

d4,

Generation 71.97 49.99

50

Margin 27.03 0.01 0

1.0

uq = 1.0.

w q - 100

BUS

1 2 3

Table 3. Variation of

up- 1000

% Load. 72.7 100.0 100.0

Generation 73.18 49.99

50

Margin 25.82 0.01 0

%) Load.

Q""

Qerp

73.9 100.0 100.0

99

99 50 50

50 50

Table 5. Variation o f d q , a4 = Q"'1-9". 1

Bus ~~

1 2 3 6 8 9 12 Total

1

= 0. i Margin 32.61 0.02 0.01 8.03 52.31 0 0 92.08

I

Wn

Generation 66.39 49.98 49.99 26.07 47.60 80 70 391.02

96 Load. 67.1 100.0 100.0 77.1 47.7 100.0 100.0

=1 Margin 32.57 0.06 0.01 8.03 52.3 0

I

*'n

Generation 66.43 d9.94 49.99 26.97 47.7 80 70 391.03

n 92.97

Table 6. Variation of

to the conventional maxiinurn loadability problem. It can be observed that the reactive powcr margins are modified with some generating units rcacliing tlicir reactive power limits. Tlic total amotmt of' reactivc powcr dclivcrcd by the generators is bigger, indicating that there is a larger ainount of reactive powcr circulating in tlie power network and how effective the transformers are to better dislribut e the reactive power margins.

% Load.

aq =

dJq.

67.1 99.9 100.0 77.1 47.7 100.0 1no.o

= 10 Margin 24.13 0.07 1.66

I

Wn

Generation 74.87

49.93 48.31 27.65 60.6 62.02

m i l

386.81

7.55 39.4 17.98 6. Ci 97.19

'% Load. 75.6 99.9 96.7 79.0 60.6 77.5 90.6

6.

tlie reactive power deviation. The values presented in this table correspond to thc coniputatiorial time in seconds. Tliese results were obtained in a personal computer AMD ATHLON 1.2 GHz. In both cabes, an incrcase in the computational effort is noted, mainly for d J q2 100. However. as previously pointed out, there is no considerable changes in the maximum power demand to the solutions obtained to d q 2 100 and thus. the computational effort addcd by the inclusion of the reactive power constraint is relatively small, as can be observed by coniparing ~ o w s2 and 5 of tablc 9.

Table 9 shows the computational effort required bv the iriclirsion of the inequality const rairit 011

375

Table 7. Results for fixed tra.risforrrier taps, a,* = &.

Table 8. R,esults for fixed transformer t,a,ps,ctq = &. Bus 1 2

(Jq

Gencration 81.79 -49.98

= 100 Margin 17.21 0.02

1000 Ma.rgin 17.15 0.02

dq =

'X Load.

Gencration 81.85

82.6 100.0

-49.98

'X Load. 82.7 100.0

Q" 99 50

Qesp

99 50

Table 9. Computational effort.

I

100 1000

1

1.792 1.542 1.932 3.224

1.392 1.782 1.452 2.914 5.237

I

dit>ions. IEEE Transactions on Power Sgsterns 15(4), 1204-1211. hlvaratio, F. and T. Ovcrbyc (1999). Mea,suring reactive power mahket. In: Proceedings o,f the IEEE/PES Winler Meeting. Vol. 1. pp. 294296. Bao, L., Z. H~iarigand W. Xu (2003). Online volt,age st>abilit,ymonitoring using va,r reserves. 1EEE Transactions on, Po,wer Systems 18(4), 1461-1469. Ca.nizares, C. A. and F. L. Alvarado (1993). Point of collapse and cont,iriuat,ioriniet,liod for large ac/tlc systems. IEEE Trunsactions o n Power Systems 8(1), 1-8. Dai, Y., J. D. McCalley and V. Vittal (2000). Sirnplificatioii, expalision and enliaiiceiiieiit of tlircct iiit>eriorpoint algorit hnr for powcr system maximum lodabilily. IEEE Transnckions on Power Systcms 15(3), 1014-1021. Hao, S. and A. hpalcxopoulos (1997). Rcactivc power pricing a.nd management. IEEE Truri.9acb,ions on Power Sysbem,s 12(1), 95-104. Trisarri. G. D., X. Wang, J. Tong arid S. Mokhtari (1997). hfaximum 1oadahilil.y of power t,crns using noii linear iiit,crior point, rriethod. IEEE Transactions on Power Syst r r / ~12(1), s 162-172. SeycM, R. (1994). Pmrtacd Bifurcation i d Stobility Analysis - From Epu,il?;briumto Chaos. Springer - Verlag New York Inc.

5. CONCLUSIONS Alt'ernat,iveoperat'ional solutions can be obtained t-odifferent levels of crit>icaldemand. Ea.ch of these solutions sabisfies the power balance a i d bhc operat,ional const,raint>s.The use of tliese solutions depends on the desi.red operational condition of the power system. If the choice for the adequate operational solution t,akcs into a.ccount not only the conventional criteria like the volt,age magnitude level, powcr loss in the traiisniission system etc, the proposed met,hodology can he useful t.o take int,o account the react,ive power margin as the tlccisioii c,rit>cria.The a,ddit,ionof a const,ra.int related to the reactive power deviation, represerikd by an inequality: rcsrilt,s in an increase in t.he cornput,at,ioiialeffort, to reach the convergence ol the ikralive process, mainly i i high values are attributed to thc a-cightiiig fa.cturs. Future works ilecl arialysis of (,lieileralive prucess.

REFERENCES Ajjarapii. V. aiicl C. Christy (1991). The coiitinuation power flow: A tool for strady state volt-

age stability analysis.. IEEE Transactions on Poapr S y s t e m s 10, 30;1-310. Almcitla, K. C. and R. Salgado (2000). Optimal power flow solutions under variable load con-

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

OPTIMAL ALLOCATION OF STATIC VAR COMPENSATORS USING MODAL ANALYSIS, SIMULATED ANNEALING AND TABU SEARCH Somayeh Ebrahimi", Malihe Maghfoori Farsangi*, Hosien Nezamabadi-Pour", and Kwang Y. Lee**

"Department of Electrical Engineering, Kerman University, Kernzan, Iran ""Departnzent of Electrical Engineering, The Pennsylvania State University, Uriiversily Purk, PA 16802, USA

Abstract: This paper investigates the ability of tabu search (TS) and simulated annealing (SA) optimization methods to deal with optimal placement of Static Var Compensators (SVC) in a large power system based on its primary function, where the optimization is made on two parameters: its location and size. 'I'he primary function of an SVC is improving transmission system voltage, thereby enhancing the maximum power transfer limit. Modal analysis is used to place several SVCs in the power system and the results obtained are compared with the results of applied TS and SA techniques. The results show that SA can give a good suboptimal placement while TS gives an optimal solution. Since by using the modal analysis alone SVCs may not be placed optimally in the power system, the study is carried out in two steps. In the first step, by using the modal analysis, the critical area of the power system is identified in view of the voltage instability. In the second step, once the weak area is identified, the SA technique is applied to get the level of compensation by the SVCs. Copyright 02006 IFAC Keywords: S v c , modal analysis, simulated annealing, tabu search, voltage Stability.

1. lNTRODUCTlON The daily operation of a power system requires that the voltage protile be within pre-specified limits. Due to a continuous growing on demand for electricity and system interconnections, and also due to economic and environmental considerations to expand the generation and transmission capacities, power systems worldwide are operating closer to their transfer capability limits that results in a higher possibility of voltage collapse. Due to several major blackouts that have happened around the world, voltage collapse phenomena in power systems have become one of the important concerns in the power industry over the last two decades. In the last decades, efforts have been made to find the ways to assure the security of the system in terms of voltage stability. It is found that FACTS devices arc good choices to improve the voltage profile in

power systems that operate near their steady-state stability limits and may result in voltage instability. Many studies have becn carried out on thc use of FACTS devices in voltage and angle stability. Taking advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size. In a practical power system, allocation of the devices depends on a comprehensive analysis of steady-state stability, transient stability, small signal stability and voltage stability. Moreover, other practical factors such as cost and installation conditions also need to be considered. A great deal of work has been carried out to develop analytical and control synthesis tools to detect and avoid voltage instability. In the literature a tool has been reported based on the determination of critical modes known as modal analysis. Modal analysis has

377

been used to locate SVCs and other shunt compensators to avoid voltage instability. The work carried out by Mansour, et al. (1994) is one of the works about using of modal analysis. Over the last decades there has been a growing interest in algorithms inspired by the observation of natural phenomenon. It has been shown by many researches that these algorithms are viable candidates as tools to solve complcx computational problcms. For example, various heuristic approaches have been adopted, including genctic algorithm, tabu search, simulated annealing, ant colony, particle swarm, etc.

power in a power system. For this, several SVCs are placed in a large power system based on their primary function, which is the voltage stability. To locate SVCs based on the voltage stability, modal analysis is used. However, using the modal analysis, the SVC cannot be placed in the power system optimally due to the unknown optimal size of SVC. For this reason, to place SVC efficiently, two heuristic methods are used; simulated annealing and tabu search, that are considered as global optimization tcchniques. A bricf description about the modal analysis, SA and TS are given in the next section.

Tabu search (TS) and simulated annealing (SA) has been paid attcntion on different applications in powcr systems since 1995 and 1990, respectively. Among these applications a few work has been done on FACTS devices. Bhasaputra and Ongsakul (2003)proposed a hybrid tabu search and simulated annealing approach to determine optimal settings of the FACTS parameters for different loading levels, and then find the optimal placement of the multi-type FACTS devices by solving optimal power flow to minimize the total generator fuel cost. Cerbex, et al. (2003) used three heuristic methods, simulated annealing, tabu search and genetic algorithm, to locate FACTS devices in a power system to enhance the power system security. Parallel tabu search was applied by Mori and Goto (2000) for the optimal allocation of UPFCs to maximize the available transfer capability. Mori (2UUI) placed SVC in distribution system using parallel tabu system. Tabu search was used by Kim, et al. (2001)to tune the input and output gain of a Fuzzy Logic Controller (FLC) for thyristor controlled series compensator (TCSC) for a low frequency oscillation in a power system. Similar study was done by Hwang, et al. (2004). Simulated annealing was used by Chen, et al. (1998) to design output feedback controllers for TCSCs in a power system to damp the critical modes. A twostage optimization method using an expert system and simulated annealing to solve the SVC placement problem is carried out by Jwo, et al. (1999). Hsiao, et al. (1994) developed a computer package based on SA for multiobjective SVC planning of large-scale power systems. In the above methods, the attention has been focused upon 1R2 losses. Relatively little effort has been directly involved with voltage stability improvement. Similar study was carried out by Chang and Huang ( 1 998). Simulated annealing algorithm was used by Abido (2000) for robust power system stabilizer (PSS) design to get optimal settings of the PSS parameters. Also, tabu search and simulated annealing have been applied to several power systcm problcms such as planning, economic dispatch, unit commitment, network reconfiguration, ete., which can be found in the literature. In this paper, SVCs are used to maintain the nodal voltage magnitudes. The problem formulation is how to place SVCa that provide compensation for reactive

2. VOLTAGE STABILlTY ANALYSIS Voltage stability is the ability of a power system to maintain acceptable voltages at all buses in the system under normal operation as well as following disturbances. Voltage stability can be categorized to large-disturbance and small-disturbance voltage stabilities. Large-disturbance voltage stability is the ability of the system to control the voltage after being subjected to large disturbances such as system faults, loss of load or generation. Small signal voltage stability is the ability of the system to control voltage after being subjected to small perturbations, such as gradual changcs in loads. In this paper three techniques are used for analysis of voltage stability, which are briefly explained.

2. I Placenzent Lking Critical Modes of Instability (Modal Analysis)

Voltage

Modal or eigenvalue analysis of the system Jacobian matrix near the point of voltage collapse can he used to identify buses vulnerable to voltage collapse. When modal analysis is used, there is no need to drive the system precisely to its “nose point” to ensure that a maximum level of stress is reached. The eigenvector of the critical eigenvalue gives information about the loads responsible for the voltage collapse. The main conclusion from this is that voltage collapse is actually the collapse of a modal voltage. In which case, the power system cannot support a particular combination of reactive power loads.

2.2 Siniulated Annealing

Simulated annealing is a derivative-free optimization technique that simulates the physical annealing process in the field of combinatorial optimization. Annealing is the physical process of heating up a solid until it melts, followed by slowly cooling it down by decreasing the temperature of the environment in steps to obtain a perfect structure corresponding to a minimum energy state. SA is a global search strategy, which tries to avoid local minima by accepting worsc solutions with a

378

probability. The probability to accept a solution is defined according to the Metropolis distribution:

I' where x and y are an initial and new solutions, respectively, and A,) is the evaluation of the objective function at a solution. SA starts from an initial solution x and then a solution y is generated. If y has been improved from x, it will be accepted; otherwise, y will be accepted as the current configuration with a probability proportional to the difference in the value of the objective function,f(x)fcv), on temperature Tas shown in (1). 2.3 Tabu Search

Tabu search (TS) algorithm is used to solve combinatorial optimization problem (COP). This mechanism is somewhat similar to SA, but the main difference between the two search algorithms is that TS uses a flexible memory to store the information and data of the solutions in each iteration. This is to get to the lower objective function values with the hclp of the information stored, whilc spccial features are added to escape from being trapped in the local minima. TS searches the neighbourhood of the current solution to find the next solution with more improvement in the value of objective function. In order to avoid returning to the local optimum, TS uses a list which is called Tabu List. The elements of the tabu list are called tabu moves. Tabu list stores the moves in a data structure such as finite length and restricts the local search algorithm in reusing those moves for some iteration. The number of iteration a move is kept in the list is called tabu list size. Since the tabu list may forbid certain worthy or interesting moves found so far, this tabu moves will be accepted as the next move and will be released from the tabu list if they are judged to be worthy. This override of the tabu list is called aspiration criterion.

regions of the solution space so far to diversify the search solution. If there is a better solution in the outer spaces of the local search the search space changes it's place to that new region. It should be mentioned that a frequency counter denotes the number of times the solution having been visited throughout the solution process. 3. STUDY SYSTEM A 5-area-16-machine system: The system shown in Fig. 1 consists of 16 machines and 68 buses. This is a reduced order model of the New England (NE) New York (NY) interconnected system. The first nine machines are the simple representation of the New England system generation. Machines 10 to 13 represent the New York power system. The last three machines are the dynamic equivalents of the three large neighboring areas interconnected to the New York power system.

Modal analysis, simulated annealing and tabu search are used to locate SVCs optimally in the power system shown in Fig. 1. Starting from an initial load, the SA is applied. All loads are increased gradually ncar to the point of collapse. To locatc SVC by simulated annealing, suitable buses are selected based on 30 test runs. Thc obtaincd rcsults by SA arc as follows: 27% of results show that the first SVC should be placed at bus 48 with 156 Mvar (the bestso-far), 13% of results show that a 186 Mvar SVC should be placed at bus 47, and 7% of results show that the first SVC should be placed at bus 40 with the size of 145 Mvar. Bus voltage magnitude profile of stressed system after placing SVC at buses 40, 47 and 48 are shown in Figs. 2-4, respectively. Using modal analysis, it is found that the weakest area in this power system is in the N Y system near bus 40, as illustrated in Fig. 5. Fig. 6 shows the profile of the voltage when system is heavily stressed and is reached to the point of collapse. Based on modal aidysis, bus 40 is a good candidate to place the first SVC. Using the modal analysis, only the weak area can be determined. However, it cannot give any information regarding the size of SVC.

The Tabu search algorithm used in this paper follows a rather straight forward pattern. As soon as a trial solution is generated, it is checked to see if it's in the tabu list or not. If so, the search algorithm will then searches for the frequency counter related to this trial solution. If the frequency counter is smaller than a threshold, it will add up the frequency counter by one, and starts to search for the next move from the neighbourhood of the current solution. This mechanism is called intensqication. And if the frequency counter was more than the threshold the move will be penalized for some iteration and the search will therefore be directed to unexplored

Fig. 1. Single line diagram of a 5-area study system.

3 79

Fig. 2. Bus voltage magnitude profile of stressed system after placing SVC at bus 40 with the size of 145 Mvar.

Fig.

5. The critical eigenvector corresponding bus number.

and the

Fig. 6. Bus voltage magnitude profile when system is heavily stressed. Fig. 3. Bus voltage magnitude profile of stressed system after placing SVC at bus 47 with the size of 186 Mvar.

Fig. 4. Bus voltage magnitude profile of stressed system after placing SVC at bus 48 with the size of 156 Mvar. Since the size is playing an important role for the SVC to be effective, simulated annealing is used to find the Mvar size needed for SVC. To find the optimal compensation level, first, the SVC is placed in the power system at bus 40, and then using simulated annealing, the Mvar size of SVC is obtained, which is 145. The obtained level of compensation is the same as the 7% of the results obtained by simulated annealing when bus 40 was selected. After placing the first SVC at bus 40, once again the loads are gradually increased. Based on Figs. 2-4, the best recovery of the voltage profiles is when SVC is

located at bus 40. On the other hand the obtained Mvar size of the SVC when located at bus 40 is less. It means that SA is a good tool to get promising suboptimal results. Therefore, since the SA failed to identify bus 40, which is vulnerable to voltage collapse, only the modal analysis is used to place the second SVC. Then SA is used to find the level of compensation for the SVC. Using the modal analysis, as shown in Fig. 7, the second worst bus is identified which is bus 50. Fig. 8 shows the voltage profile when system is under stress. Again simulated annealing is used to find the optimal size of the SVC at bus 50. The obtained Mvar size is 155 Mvar. Now, tabu search is applied to find the best place of SVC in the power system shown in Fig. 1. Once again, all loads will increase gradually near to the point of collapse. As in the case of simulated annealing, to locate SVC by tabu search, suitable buses are selected based on 30 test runs. The obtained results by tabu search are as follows: 86.66% of results show that the first SVC should be placed at bus 40 with 138 Mvar, 6.66% of results show that a 136.4 Mvar SVC should be placed at bus 48, and 6.66% of results show other buses to place SVC. The results show that tabu search has the ability of finding the optimal location better than SA. The fitness and the level of compensation are shown in Figs. 9-1 0. Also, by applying modal analysis and then placing SVC at bus 40, TS finds the level of compensration to be 138 Mvar.

380

Fig. 7. The critical eigenvector and the corresponding bus number.

Fig. 9. Convergence characteristics of TS in finding the solution, 145 Mvar SVC at bus 40.

Fig. 8. Bus voltage magnitude profile when svstem is heavilv stressed.

Fig. 10. Search process for finding the level of compensation.

4. CONCLUSIONS In order to take of the advantages of the FACTS devices in the power systems, two SVCs are placed optimally in a large power system. For this purpose, the location and size of SVCs are obtained using modal analysis, simulated annealing and tabu search. In finding the best place based on their primary function, both modal analysis and tabu search give the same results. While simulated annealing gives a suboptimal solution. The work carried out by other researches with simulated annealing as reviewed in section 1 reported promising results, but in this study, although choosing of the objective function was done carefully, simulated annealing did not identify optimal place of SVC. In placing the SVC by simulated annealing, the results are not the same as those obtained by modal analysis and tabu search, and it was shown that the result obtained by SA is not the best. However, SA gives a good suboptimal result (choosing bus 48), and the best sizes of SVCs can be found by SA (by placing SVC at bus 40 and 50). Although, the obtained size of SVC by SA and TS are not the same but they are close. This inconsistency is due to the tuning of parameters in SA and TS. Taking the advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size. Therefore as shown in the results, by

placing SVC based on the modal analysis and then finding the level of compensation by simulated annealing or tabu search, SVC can be placed optimally (sub-optimally) in the power system. REFERENCES Abido, M.A. (2000). Robust design of multimathchine power system stabilier using simulated annealing. IEEE. Trans. Power Systems, 15 (3), pp. 297-3043. Bhasaputra, P. and W. Ongsakul, (2003). Optimal placement of multi-type FACTS devices by hybrid TSISA approach. Proceedings of the 2003 International Symposium on Circuits and Systems, 3, pp. 285-290. Chang, C.S. and J.S.Huang (1998). Optimal multiobjective SVC planning for voltage stability edhancement. TEE Proc.-Gener. Transm. Distrib., 145 (2). Chen, X.R, N.C. Pahalawaththa, U.D.Annakkage and C.S.Kumble (1998). Design of decentralized output feedback TCSC damping controllers by using simulated annealing. TEE Proc.-Gener. Transm. Distrib., 145 (5), pp.553 558. Gerbex, S., K.,Cherkaoui, and A.J Germond (2003). Optimal location of FACTS devices to enhance ~

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power system security. Power Tech Conference Proceedings, 3. Hsiao, Y.T. , H.D Chiang, C.C. Liu, and Y.L. Chen (1994). A computer package for optimal multiobjective VAR planning in large scale power systems. IEEE Trans. Power Sys., 9 (2), pp. 668-676. Hwang, G.H., J.H. Park; K.J. Mun and H. T. Kang (2004). Design of fuzzy logic controller for firing angle of TCSC using real-type tabu search. The 30th Annual Conference of IEEE Industrial Electronics Society, 3, 2-6 Nov. 2004, pp.2182-2187. Jwo, W.S. , C.C. Liu and Y.T. Hsiao (1999). Hybrid expert system and simulated annealing approach to optimal reactive planning. 1EE €‘roc.-Gener. Transm. Distrib., 142 (4), pp.381-385. Kim, W.G.; G.H. Hwang; H.T. Kang; S.O. Lee and J.H. Park (2001). Design of fuzzy logic controller for firing angle of TCSC using realtype tabu search. IEEE International Symposium on Industrial Electronics, 1, 12-16 June 2001, pp. 575 - 580. Mansour, Y., W. Xu, F. Alvarado and C. Rinzin( 1994). SVc placement using critical modes of voltage instability. IEEE Trans. Power Systems, 9 (2), pp. 757-763. Mori, H. and Y. Goto (2000). A parallel tabu search based method [or determining oplimal allocation of FACTS in power systems. International Confcrcncc on Powcr Systcm Tcchnology, 2, pp. 1077 1082. Mori,H. (2001); Optimal allocation of FACTS devices in distribution systems, IEEE Power Engineering Society Winter Meeting, 2, pp.936 - 937. ~

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

DISTRIBUTED MPC STRATEGIESFOR AUTOMATIC GENERATION CONTROL Aswin N. Venkat * James B. Rawlings *

Ian A. Hiskens **,I Stephen J. Wright ***

* Dcrpartment of Chemical and Biological Engineering,

University of Wisconsin, Madison, WI-53706

** Drpartinerz f of Electrical and Computer Engineering, ***

University of Wisconsin, Madison, WI-53706 Computer Sciences Department, University of Wisconsin, Madison, WI-53706

Abstract: The paper considers distributed model predictive control (MPC)strategies that are appropriate for controlling large-scale systems such as power systems. The overall system is decomposed into subsystems, each with its own MPC controller. To achieve performance equivalent to centralized MPC, these distributed regulators must work iteratively and cooperatively towards satisfying a common, systemwide control objective. Automatic generator control (AGC) provides a practical example for contrasting the performance of centralized and decentralized controllers. Keywords: Distributed model predictive control; automatic generation control; power system control.

1. INTRODUCTION

Model predictive control (MPC) is emerging as a sophisticated, yet practical, control technology. This model-based control strategy uses a prediction of system behaviour to establish an appropriate control response. A number of benefits follow from using MPC, including the ability to account systematically for process constraints. The effectiveness of MPC depends on models Of

accuPacy and 'On the

ity of sufficiently fast computational resourcesrequirements that limit the application base for MPC' Even so/ abound in the Process industries, and are becoming more wide2003; Carnacho and spread (Qin and BadP"ellf Bordons, 2004).

often perform poorly when the subsystem interactions are significant. Centralized MPC, on the other hand, is impractical for control of largescale, geographically expansive systems, such as power systems. A distributed MPC framework is appealing in this context, but must be designed to take account of interactions between subsystems. Interaction issues are crucial to the success of distributed MPC, and are discussed further in Section 3. Automatic generation control (AGC) provides a topical example for illustra ting the performance of distributed MPC in a powep syqtem setting. The purpose of AGC is to regulate the real power output of generators, with the aim of controlling system frequency and tie-line interchange (Wood and Wollenbere, 1996). AGC must account for various limits, including restrictions on the amount and rate of generator power deviations. VI

Traditionally, control of large, networked systems is achieved by designing local, subsystembased controllers that ignore the interactions between the different subsystems.These controllers Correspondingauthor. Email : hiskens@ e n g r .wisc .e m

Flexible AC transmission system (FACTS) devices allow control of the real power flow over selected paths through a transmission network

383

(Hingorani and Gyugyi, 2000). As transmission systems become more heavily loaded, such controllability offers economic benefits (Krogh and Kokotovic, 1984).However FACTS controls must be coordinated with each other, and with AGC. Distributed MPC oflers an ellective ineaiis ol achieving such coordination, whilst alleviating the organizational and computational burden associated with centralized control. 2. MODELS Distributed MPC relies on decomposingthe overall system model into appropriate subsystem models. A system comprised ol hl interconnected subsystems will be used to establish these concepts.

2.1 Centralized model The overall system model is represented as a discrete, linear time-invariant (LTI) model of the form .r(k

+ 1) = AT(L)+ B u ( k ) dk)= W k ) .

(1)

in which I; denotes discrete time and

3. DISTRIBUTED MPC FOR POWER SYSTEM CONTROL 3.1 Preliminaries Given the PM for each subsystem 1 = I , . . . , A l , we consider two formulations for distributed MPC: communication-based MPC and cooperationbased MPC. The suitability of either distributed MPC framework for systemwide control is assessed in the sequel. In both approaches, an optimization and exchange of variables between subsystems is performed during a sample time. We may choose not to iterate to convergence. The set of admissible controls for subsystem z. [it C R”&% is assumed to be a non-empty, compact, convex set containing the origin in its interior. The set of admissible controls for the whole plant I1 is defined to be the Cartesian product of the admissible control sets of each of the subsystems. For subsystem / at time k, the predicted state vector at time t > k is denoted by ~ ~ ( t l k ) . We havex.,(klk) = r L ( k ) . The cost function for subsystem 1 is defined over an infinite horizon as follows: & (G,,%,T?,(k)) =

2

2k(tlk)’Q,(t).&(tlk)

+ ut(tlk)’Rz(t)u,(tlk),

(4)

t=k

where Q7 > 0, R,> 0 are symmetric weighting matrices and xt(k)7 [ z , ( k + l l k ) ’ , z , ( k . . .]‘, u,(I;)= [u,(I;lI;)’, .,(I; + Ilk)’, . note the infinite horizon state and input trajectories, respectively, for subsystem L. C .

=

[21‘

2Af’]

22‘

‘

z/ = [VI‘

1/2’

7J\J‘]

‘

For each subsystem 7 = l . . . .,AP, the triplet ( u z2, , . g l ) represents the subsystem input, state and output vector respectively. 2.2 Decentralized model

3.2 Communication-based MPC For communication-basedMPC, the optimal stateinput trajectory (z$(k),uf(k)) for subsystem i at iteration p is obtained as the solution to the following optimization problem

In the decentralized modeling framework, the effect of the external subsystems on the local subsystem is assumed to be negligible. The decentralized model for subsystem i , 7 = 1,.. . , M is written as ct(k

+ 1) = A t r t ( k ) + Bttut(k) uz(k) = C d % ( k ) .

+

(2)

2.3 Partitioned model (PM) The PM for each subsystem z incorporates the eflect ol the local subsystem variables as well as the effect of the states and inputs of the interconnected subsystems. The PM for subsystem 2, as the name suggests, is obtained by consideringan appropriate partition of (l),as follows: xz(k

J f 7

u,(tlh) E R,,k 5 t 5 I, ut(tlk)= 0, k N 5 t.

+ n.- 1 (5)

The integer N denotes the control horizon. For notational simplicity, we drop the time de en dence of ( z p ( k ) .uf(A))and represent it as (2,. $ uf-). For each subsystem i at iteration p, only the subsystem input sequence uf is optimized and updated. The other subsystems’ inputs are not altered during the solution of (5); they remain at their values from iteration p - 1. The objective function is the one for subsystem i only. In the communication-based MPC framework, each subsystem’s MPC has no information about

+ 1) = & & ( k ) + Bttut(k) + C ( A % J Z J +( ~B)‘ J ~ ’ J ( ~ ) ) Jf r

Yz(k) = Ct%G(k).

Similar strategies have been proposed by (Jia and Krogh, (3)

2001; Camponogara r i ni., 2002)

384

the objectives of the interconnected subsystems’ MPCs. Convergence of the exchanged state and input trajectories must therefore be assumed-a drawback of this formulation. Not uncommonly, this MPC formulation leads to unstable closedloop behavior, so i t is an unreliable strategy for systemwide control.

a),(.) is obtained by eliminating the state trajectory 2,from (4), using (3). For this case, the FC-MPC optimization problem for each subsystem z = 1... . , 111 can be explicitly written as the finite horizon optimization

in which each cost function

FC-MPC, A

3.3 Feasible cooperation-basedMPC (FC-MPC) To arrive at a reliable, distributed, systemwide MPC framework, we modify the objectives of the subsystems’ MPCs to provide a means for cooperative behaviour among the controllers. Each local controller objective b, is replaced by one that measures the systemwide impact of local control actions. Here, we choose the simplest such measure - a strong convex combination of the individual subsystems‘ objectives z.e., 4 = C7uto,, where tit, are the weights. We set w, = l / A 1 for all z = 1.. . . ,111 in our discussion below, but our results hold for any combination of weights satisfying ui, > 0, C u‘, = 1. In large-scale implementations,the system sampling interval may be insufficient for the convergence of the iterative, Cooperation-based algorithm. In such cases, the algorithm has to be terminated prior to convergence of the state and input trajectories and the last calculated input trajectories used to compute a suitable control law. To facilitate intermediate termination, it is imperative that all iterates generated by the cooperation-based algorithm are systemwide feasible (i.e., satisfy all model and inequality constraints) and the resulting distributed control law is closed-loop stable. We define the finite horizon state and input trajectories for subsystem I as Z,(.k)’ = [x,(k + Ilk)’, . . . , ~ ~ ( k + ~ V l andu,(k)’ k)’] = [u,(klk)’.u,(k+ 1I k)’ , . . . u, (A + 11: - 1I k ) ’ ] .For convenience, we in thei follow, drop the k dependence of Z7and % ing discussion. It is shown in Appendix A that for each L = 1. . . . .M , Z, can be expressed a s follows:

.

+ S L L ~ L (+k :C[Ez3uJ ) + ft3zJ(k:)] (6)

% = EZ,%

3fZ

The infinite horizon input trajectory u,is obtained by augmenting u,with the input sequence u t( tlk) = 0 for all t 2 k + K . The infinite horizon state trajectory z,is derived from Zzby propagating the terminal state r , ( k + iVlk) using (3) and u,(tlk) = 0, t 2 k + N , ti z = 1,.. . , M . For subsystem (, the FC-MPC optimization problem is uf‘*)(k)g

in which FC-MPC,

arg(FC-MPC,)

(7a)

in which

j=1

s# j

j=1

=diag(Q,(l) , . . . ,C2i(N-1),aZ)>

Q%

M,,] = diag ( 0 , . . . , O,aij) , R, = diag (R,(O),R c ( l ) ,. . . , R,(N

-

1)) ,

nr j=l

while

is a suitable terminal penalty matrix. Restricting attention to open-loop stable systems simplifies the choice of Q.For each i = 1,.. . , M , let Q L ( 0 = ) Q t ( l ) = ... = Q,(,V - 1) = Q,. The terminal penalty can be obtained as the solution to the centralized Lyapunov equation

~’o~-(re=-~

(10)

in which Q = diag(Q1,( 2 2 . . . . ,CJ-bf).

3.4 FC-MPC algorithm and properties The state trajectory for subsystem i generated by the set of subsystem input trajectories u1,. . . ,Z L L ~ and initial state z i s represented as 2,( u ~. .,,ul1~ ; 2). For notational simplicity, we drop the functional dependence of the state trajectory and write z,+ z , ( u l , .. . ,ulxf; z ) . The following algorithm is employed for cooperation-based distributed MPC.

.

Algorithm 1. Given (u:, xL(k)), Q, 2 0, R, 2 0. L = 1,.. . M pmax(k)L 0 and E > 0 p + i , p , +rE,r >> 1 while p, > f for some i = 1,. .. , 111and p 5 pmax for I = 1,.. . . A l uF(*)E arg(FC-MPC,),(see (7), (8)) I’ - 1 P ( * ) (1 - &) uf-1 21, - xut p 1 . -- lluP1 - uP-l L II

+

385

end (for) Transmit up, i = 1,.. . , M to interconnected subsystems. Calculate zz(u:',. . . ,ugl;t(kj), I = 1,.. . , ?il. P+P+l

in which 1L(2(k))

= [tL:'("(k;;,:(k))':... ,,u;r)(k:z(k))t] '

forallx(kj ~ X a n d a n y p ( k ) =1 , 2,...

end (while)

Remark 4. If ( A ,Qij is detectable and Qz 2 0 for After p iterates, denote the cooperation-based . . ,u : ~~;( k ) The ) . followcost functionby @(uy,. ing properties ciin be estiiblished for the FC-MPC formulation (8) employing Algorithm 1.

.

all i = 1,. . . M , then the closed-loop system is asymptotically stable under the distributed MPC control law.

4. EXAMPLES Lemma 1. Given the distributed MPC formulation FC-MPC, defined in (7), (8), V i = 1,.. . AI, the sequence of cost functions {@(uy,. . . , u : ~~; ( k ) ) }4.1 Performance comparison generated by Algorithm 1 is a non-increasing

.

function of the iteration number p. Using Lemma 1and the fact that a(.)is bounded below assures convergence with iteration number p.

The examples use the cumulative stage cost as an index for comparing the performance of different controller paradigms. Accordingly, define

k=O

z=1

Lerrirm 2 . All limit points ol Algorithm 1 are optimal.

4.2 Two area power system network

Lemma 2 implies that the solution obtained at convergence of Algorithm 1is Pareto optimal i.e., the solution at convergence is identical to the centralized MPC solution.

We consider an example with two control areas interconnected through a tie line. For a 25% load increase in area 2, the load disturbance rejection performance of the FC-MPC formulation is evaluated and coinpared against the performance of centralized MPC (cent-MPC), decentralized MI'C (decent-MK), communicationbased MPC (comm-MPC) and the standard automatic generation control (AGC) with anti-reset windup. The load reference setpoint in each area is constrained between 1 0 3.

3.5 Distributed MPC control law Let X represent the constrained stabilizable set for the system under the set of input constraints x x . . . x Rbr. At time I;, let the FC-MPC algorithm (Algorithm 1)be terminated after p ( k ) = I iterates, with u',(.(k)) =

+ l,.L(k))', . . ,] 0

[UE(k,L(k))/,UI(k

z=l..

(11) ,PI

representing the solution to Algorithm 1 after I cooperation-based iterates. The distributed MPC control law is obtained through a receding horizon implementation of optimal control whereby the input applied to subsystem L at time k , u , ( k ) , is & ( k ) = uf(k,.c(k))

(12)

The relative performance of standard AGC, centMPC and FC-MPC (terminated after just 1cooperation-based iteration) is depicted in Fig. 1,where the transient responses of the tie-line power flow and the area 2 load reference setpoint are shown. Under standard AGC, the system takes more than 400 sec to drive the tie-line power flow deviation to zero. With cent-MPC or FC-MPC (termninated after just 1 ileration), the tie-line power flow disturbance is rejected in less than 100 sec. The closed-loop performances of the various control formulations are compared in Table 1. Table 1. Performance of different control formulations w.r.t. cent-MPC,

Lemmas 1and 2 lead to the following theorem on closed-loop stability of the nominal system.

=

standard AGC decent-MPC comm-MPC FC-MPC (1iterate) FC-MPC (5iterates) cent-MPC

Theorem 3. Let Algorithm 1, the distributed MPC formulation (7), (8) with N 2 1, and the distributed control law defined in (12) be given. If A is stable, is obtained from (lo), and Qi(0) = Qi(1) = . . . = Q i ( N - 1) = Qi > 0 &(0) = Ri(1)= . . . = R I ( N - 1)= R,

>0 . . . .M

i=1,

then the origin is an exponentially stable equilibrium for the closed-loop system .(k

+ 1)= Az(k) + B u ( z ( k ) )

hioiifxg-'~cent h n t

x 100.

A 39.26 17683 17.42 15.24 N

15.2

15.2

Ah% 158.32 164 1462 0.24 N

0

-

In practice, such a large load change would result in curtailment of AGC, and activation of other, more drastic controls such as load sheddhig. This exaggerated disturbance is useful, however, for exploring the influence of constraints on the various control strategies.

386

~.

0.2,

cent-MPC =point-

----

0.1

~

-I r"i

----0.05O :

-0.1 1 , 0

20

40

60

80 100 120 140

I

10

0

Time (sec)

I

20

I

I

I

30

40

50

I

Time (sec)

comm-MPC - - - -

0.2

..--.--

,--._

,'

0

20

target cent-MPC .......~. standard AGC - - - FC-MPC (1iterate) ------

_,-.__--

40

-0.5j1;

-1 0

60 80 100 120 140 Time (sec)

i

,

,

,

~

...

10

20

30

Time (sec)

40

50

Fig. 1. Change in tie line power flow (LIP,',,") and load reference setpoint (APrCt2).

Fig. 3. Change in tie line flow (LIP,',,"), and load reference setpoint (APrcfl).

4.3 Four arm power system netwovk

4.4 True men power system with FACTS device

An example with four control areas is shown in Fig. 2. Power flows through tie-line connections 1 - 2, 2 - 3, and 3 - 4 are the sources of interactions between the control areas. The relative performance of cent-MPC, comm-MPC and FCMPC is analyzed for a 25% load increase in area 2 and a simultaneous 25% load drop in area 3. In the comm-MPC and FC-MPC formulations, in each area is the load reference setpoint (Pref) manipulated independently to reject the load disturbances and drive the deviations in frequencies (Aw,) and tie-line power flows ( A P i i )to zero. In the cent-MPC framework, a single MPC controls the entire power network. The load reference setpoint for each area is constrained between il.

This example returns to the two area network. In this case, the interconnection between the two areas incorporates a FACTS device that is employed by area 1 to manipulate the effective impedance of the tie line. We investigate the relative performance of the cent-MPC, comm-MPC, and FC-MPC formulations, in response to a 25% increase in the load of area 2.

Fig. 3 shows the performance of cent-MPC, commMPC and FC-MPC (terminated after 1cooperationbased iterate.) Based on calculated closed-loop control costs, the performance of comm-MPC is worse than that of cent-MPC by about 25%. The closed-loop performance of the FC-MPC formulation, terminated after just 1 cooperation-based iterate, is within 3.2%) of cent-MPC performance. Perforinance of the FC-MPC framework can be driven to within any pre-specified tolerance of cent-MPC performance by allowing the cooperation-based iterative process to converge.

Under the comm-MPC formulation, the system takes about 300 sec to reject the load disturbance. The comm-MPC formulation incurs a performance loss of 192.51% relative to cent-MPC. Under the FC-MPC formulation, terminated after 1 iterate, the performance loss is only 6.2% compared to cent-MPC. The system rejects the load disturbance in less than half the time required by comm-MPC. Fig. 4 shows the relative phase deviation in the two areas, and the change in impedance due to the FACTS device, for the different MPC frameworks. 5 . CONCLUSIONS

Centralized MPC is not well suited for control of large-scale, geographically expansive systems such as power systems. However, the performance benefits obtained with centralized MPC can be realized through distributed MPC strategies. Such strategies rely on decomposition of the overall system into interconnected subsystems, and iterative exchange of information between these subsystems. An MPC optimization problem is solved within each subsystem, using local measurements and the latest available external information. Various forms of distributed MPC have been defined. Feasible cooperation-based MPC (FCMPC) assigns a common, system-wide objective

Fig. 2. Four area power network.

387

in which 0.05 comm-MPC - - - FC-MPC (1 iterate) ------

O -0.01

-I

...................

I--

0

20

40

[

0

-'J 9 .I

1

- 4 zN1 - 2

60 80 100 120 140 Time (sec)

:I'

0 0

...... 0 0 ... 0

;

.... .

A,, Azl-3A,, . . . . . . 0

Combining the models in (A.1)/b' i = I,... , M , gives the following system of equations A;c = E u + Bz(k)

(A4

in which ,

-0.1 0

20

40

,

I

60

80 100 120 140 Time (sec)

. . ......

Fig. 4. Relative phase difference (A& - A&)/ and change in FACTS impedance (AX,,).

Thc papcr has prcscntcd a numbcr of powcr system examples that have applied distributed MPC to automatic generation control (AGC).MPC outperforms standard AGC, due to its ability to account for process constraints. FC-MPC achieves performance that is equivalent to centralized MPC, and superior to other forms of distributed MI'C. The FC-MI'C framework also allows coordination of FACTS controls with AGC. In this case, the cooperative aspect of FC-MPC was very important for achieving acceptable response. 6. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of the industrial members of the TexasWisconsin Modeling and Control Consortium, and NSF through grant #CTS-0456694. Appendix A. MODEL MANIPULATION To simplify the development of the FC-MPC algorithm, it is convenient to eliminate the states z t ,2 = 1 , , 91 using the PM (3). Propagating the model for each subsystem through the control horizon ,V gives

=EtZuP +??,~zZ(k) + C[ZZJZJ+gLJzJ+?,~xCj(k)] J#L

V7=1>...,AI

u=

xM

I

UbT

(A.3)

to all subsystem problems, and has the property that the converged solution is identical to centralized MPC. In addition, the FC-MPC algorithm can be terminated prior to convergence without compromising feasibility or closed-loop stability of the resulting distributed controller. This feature allows the practitioner to terminate the algorithm at the end of the sampling interval, even if convergence is not achieved.

%

x=

.

(Al)

388

Since the system is LTI, a solution to the system (A.2) exists for each permissible RHS. Matrix A is therefore invertible and consequently, we can write for each i = 1,.... M ZL= &,Ti,

+ j i i z i ( k ) + c [ E i j . U j+ fijxJ(k)].

(A.4)

I.#<

REFERENCES Camacho, E.F. and C. Bordons (2004).Model Predictive Contuol, Second Edition. Springer Verlag, New York, NY. Camponogara, Eduardo, Dong Jia, Bruce H. Krogh and Sarosh Talukdar (2002). Distributed model predictive control. IEEE Ctl. Sys. Mag. pp. 44-52. Hingorani, Narain G. and Laszlo Gyugyi (2000). UizdePvstanding FACTS. IEEE Press, New York, NY. Jia, Dong and Bruce H. KPogh (2001).Distributed model predictive control. In: Proceedings of the American Control Conference. Arlington, Virginia. Krogh, Bruce and Petar V. Kokotovic (1984). Feedback control of overloaded networks. In: IEEE Transactions on Automatic Control. Vol. AC-29, NO.8, pp. 704-711. Qin, S. Joe and Thomas A. Badgwell (2003). A survey of industrial model predictive control technology. Control Eng. Pruc. 11(7),733764. Wood, A.J. and Bruce F. Wollenberg (1996).Power Generation Operation and Confrol. John Wiley and Sons, New York, NY.

Copyright 0Power Plants and Power Systems Control, Pananaskis, Canada 2006

ELSEVIER

MODELLING AND OPTIMIZATION OF A MICRO COMBINED HEAT AND POWER PLANT

Damien Faille', Christian Mondon', Laurent Henckes2 ( I ) Electriciti de France R&D 6 Quai Watier, 7800 Chatou 13.ance (2)Europeanlnstitutefor Energy Research (EljER) hW1y NOi.?the?' Stf'USSi.?, 1 1 - 7613 1 KUU.lSI'Uht!- Dt.UtSc/l~Und

Abstract: Most electrical power in developed countries today is produced by large centralized power plants. With the technology progress, micro combined heat and power generators (ranging from 1 to 10 kW) are becoming available. Tomorrow, they will produce electricity and heat at home, locally. This paper presents a method of handling these new kind of power plants. The solution based on dynamic programming schedules the use of the micro CHP and of the hot water tank in order to minimize the operating costs. An on-line iinplenientation of the algorithm is proposed and tested on a validation model. Copyright 02006 1FAC Keywords: Dynamic programming, dynamic modcls, Energy managcment systems, Energy control, Non linear control, On-line Control, optimal control, Power generation, Predictive Control

EdF is an integrated energy company with activities stretching from power plant generation to gas and electricity commercialization for industrial and residential customers. CdF has studied the O&M improvements of its centralized power plants and is now investigating how to optimke the distributed resources. In Mondon (2005), the problem of an isolated mCHP fleet is addressed. The system consists of 200 houses equipped with mCHP, thermal and electrical storage devices, and is not connected to the grid. Compared to a reference case with electricity generated by centralized combined cycles and thermal needs satisfied locally by traditional gas boilers, the studied systcm, once optimized, reduces the ycarly gas consumption by more than 6%. Apart from the mCHP tleet optimization, t d b is investigating the benefits of an optimal control to meet the thermal and electrical needs of a single dwelling by the means of a mCHP and a support boiler. This kind of system is likely to appear sooner than the inCHP network solution because of the lower investment cost. Priority we ofmCHP is adopted generally but Entchev (2003) suggests a solution based on fu77y logic to improve the performance of such a system.

Recent progress in technology has made possible the development of micro Combined Heat and Power (mCHP) for dwellings and small buildings. These systems, which produce electricity, heat and hot water, might soon replace the traditional boilers. Internal combustion engines are already available, and more efficient technology will be available in the near future. Stirling engines and Rankine cycle could be marketed in two or three years while fuel cell technology could appear afier 201 0. The two main drivers for the development of mCHP arc (i) the liberalization of the gas and electricity markets (utilities could propose commercial packages including mCHP to attract customers) and (ii) the increasing importance of environmental policies aimed at reducing greenhouse gas emissions. Peacock (2005), for instance, shows how the use of the mCHP can contribute significantly to the reduction of the C 0 2 emissions. In parallel, the technology has improved enough for mCHP to be reachable (better reliability and lower prices).

389

valve located at the boiler output. The volume of the tank is 250 1.

In the present paper, we propose a predictive control based on the dynamic programming to optimize the operations. The dynamic programming is indeed a very general method that can accept nonlinear models, logical and continuous description, and is suited for small systems.

Tor

The section 2 presents the process we want to control and thc simulation model that has bcen developed to test our optimization scheme. The scction 3 presents the optimiration problem itsclr. It involves a design model whose dynamics are simpler than the dynamics of the simulation model and a set of equations corresponding to the constraints. The results of the optimization and a validation on the detailed model are discussed in the section 4 before a conclusion that will indicate the further investigations

2.

f:ig. 2 : classical mCHP control strategy 2.2 C alidation Model A model of the process has becn developed to test our control law. This validation model is based on physical laws (pump, valve, pipe, tank, radiator, boiler). This model is useful because it allows easier testing of the control at the design stage. Indeed, as the model runs much faster than real time (some of the dynamics involved in our problem are rather slow), the use of a model Saves plenty of time. The validation model has been built using SIMBAD, a Matlab-Simulink library for Building and HVAC (Heating Ventilating Air Conditioning) systems. SIMBAD is available at the address http://so~~rc.cstb.fri.

PROCESS DCSCKlPTlON & VALIDATION MODEL

2. I Process Description Thc sludicd syslcm is shown in Figure 1. I1 consists of a dwelling equipped with a mCHP and a support boilcr fcd with gas. Thc mCIHP produccs hcat to meet the thermal needs and electricity. When the thermal power is not enough, a support boiler is activated. The heat produced by the machines is ured to warm the water that circulates in the pipes and is sent either to the radiator or to the water tank. According to the electric consumption, the electricity is either consumed in the house or sold to the electrical network. I T the electricity production is not sufficient, the missing amount can be bought. An electricity meter is supposed to measure the purchased and the sold electricity

The first level of the Matlab-Sirnulink validation model is given in Figure 3.

Weekly w a t h e r data CSTB - ciry of T w w

Weekly clock generator

i z h Building Gershwn House

[Ii;;

Tr,

Display & Post processing

Fi

w-inp

Distribution

W_dep P o w r Production &Tank

Fig. 3 : SimulinkTM Validation Model The first module provides the weather at Trappes. a citk near Paris. 'The Control block contains the regulations presented in the previous paragraph. The parameters of the regulations have been tuned using the software EaspPIDTuning presented in Faille (2003). The Building block contains the simplified equation of a house. The Distribution block simulates the circulating pipes and the radiator as presented in Figure 1. The Module Power Production &Tank contains a model oi' a mCHP. This model is a black box developed with data obtained on machines (Stirling Engine. Fuel cell, ...) tested in EiER and EdF Laboratories. The static parts of thcsc modcls arc functions of thc

Fig. 1 : Process Description The system is regulated by several loops represented in Figure 1. The room temperature Tr is regulated by the thermostatic valve and the hot water temperature Thw by the mixing valve. The temperature at the boiler output To is controlled at a set-point To, which depends in general on the outside temperature. The regulation uses in priority the mCHP following the scheme proposed in Figure 2. The tank water temperature Tt is maintained between 60°C and 80°C by the 3-way

390

load X , the water flowrate Q. and the temperature at the input Ti. E:or instance, the elcctrical power is given by a polynomial function of 2nd order Pel = F ( X . Q, Ti) .

thermal power Pthk can be used to warm the tank water (Eq. 2 ) or the heating circuit (Eq. 3), by controlling a k the opening of the 3-way valve. The inertia terms Ci and C‘t in these equations are identified with experimental data. Pdhwk and Pdhk in Equations ( 2 ) and (3) are, respectively, the hot water and heating demands. Equation (2) is an energy model of the water tank. In reality, there is stratification in the tank, which is represented in the validation model, and the water at the top of the tank is in general warmer than the temperature 7tk calculated with Equation (2).

3.OP17MJZA7’10N AND CONI ROL

In this section, we formulate the problem of optimization more precisely. The cost function is roughly the bill with additional terms for the startup and shutdown transients, which are supposed to take into account the maintenance expenditures. The global problem described below contains continuous and logical variables and belongs to the class of hybrid problcm. A lot of work has been done recently in the field of hybrid control (see Bemporad 1999), particularly with the Mixed Integer Predictive Command (MIPC) scheme. This approach is very powerful (see Davelaar 2005 for an application to the start up transient of a combined cycle) but require\ heavy computation and high-tech solvers like XPRESS-MP or CPLEX, for instance. For our purpose, we need a solution that can be cmbeddcd in a low-cost microprocessor running in real time. We are, therefore, investigating the feasibility of a solution based on dynamic programming. In this section, we present the optimization problem, give a brief theoretical overview on the dynamic programming, and finally present its application to our optimiLation problem.

Ti,,, - T L ~=---Pdh, 1 At I

The sought solution must respect domain constraints for the input temperature Tik at the entrance of the mCHP and for the water temperature in the tank Ttk (Equations 12 and 13). There are also limitations on the machine loads corresponding to constraints on the gas consumption ofthe mCHP Qgmk and of the support boiler Qgsbk (Equations 15 and 16).

The Equation (1) gives the objective function J. ‘V

=

C

~

g~k

g + ,Cse, Pse,

k=O

C’Juk

+ Cbe, Pbe,

(3)

Besides the start-up and shutdown costs, the optimization manages a stock of working hours hk and can force thc solution to respect a maximum number of operating hours Ifmax (Eq. 14).

3 I Optimization Problem

J

+(I-a,).Pth,]

(1)

+ Csdk

The sample period k is chosen equal to I hour in the numerical application. The horizon IV is the number of samples considered in the optimization problem and chosen equal to 24. In Equation ( I ) , Cg, and Cbek are, respectively, the prices of the purchased gas and electricity, and Csek is the price of the excess electricity sold to the electrical network. Qgk (Eq. 11) is the sum of the gas consumed by the mCHP Qgmk and by the support boiler Qgssbk. The bought and sold electrical power Phek and P w k are calculated knowing the electricity demand Pdek and the electricity generated by the mCHP Pemk (Eq. 9-10). Pemi is calculated by a nonlinear function F , obtained by experiments (Eq. 5). The last terms in the objective function are the costs corresponding to the start-up C F U ~and , shut-down CJdk (expressions are given in Eq. 18 and 19, where Csd and Csu are constant).

3.2 Dynumic Progrumming

Dynamic programming is a well-known mathcmatical technique to find the optimal trajectory of a time-evolving system. Finding the short& path in a network is a simple illustration of this method, hut the formalism of dynamic programming first documented by Rellman (Rellman 1957) is much more general. Briefly :

The thcrmal energy produced by thc mCHP PthnZk and the support boiler Pthsbk are given by nonlinear functions F2 arid F3 (Eq. 6-7). The global

39 I

1. the system is considered over a finite numbcr N of steps t 2 . at each step t, the state of the system x(t) takcs a value in a finite set X, 3. at each step t, the set U of possible commands u(t) is finite 4. at each step 1, the system evolution is fully dctined knowing (t,x(t),u(t)} by a transition equation. X(t+ 1 )=f(t,x(t),u(t)) 5 . at each step t, a cost c(t,x(t),u(t)) is associated with each transition. 6 . a termination cost CF(x(N)) is associated with each final state.

already computed Bellman Value of the arrival state (sce Pig. 4). When gridding continuous statcs and commands, a possible outcome is that the arrival state of a transition could be outside the grid. Interpolation of the Bellman values can be done to overcome this difficulty. Dynamic Programming ha5 several advantages as a tool for solving optimal control problems. I'he rcsolution code is short and simple to write, it can handle difficulties such as non linearity or mixed integerlcontinuous elements and, nevertheless, find the global optimum. Another important advantage is that we not only compute one single solution but one solution for each step and each state of the problem. Hence, re-optimization can be done with no extra work when a perturbation occurs to the condition that it does not affect the knowledge of the future. This feature has been used in our predictive command. 1here are, however, some drawbacks. To begin with, it can be very difficult to make a problem compatible with the formalism of Dynamic Programming. But the biggest issue concerns the computation time, which grows exponentially with the dirncnsion of the state or space ("the curse of dimensionality").

The associated optimization problem is : N

mlnJ(z) = C c ( t , x ( t ) , u ( t ) ) + C, ( x ( N ) ) 77

ILO

x,vt E { L N }

x(t)E

x(c + I ) = f ( l J ( t ) . U ( l ) ) Y t E {o...w - 1) x(0) = x, where x ={(xO,u(0)),...(x(t),u(t)).. .,x(N)j is a command policy of the system.

To solve this problem, Dynamic Programming is based on the so-called principle of optimality, dewibed by Bellman (Bellman 1957) with these words "An optimal policy has the property that, whatever the initial state and decision are, the remaining decisions must constitute an optimal policy with regard to the state resultingfronz the Jirst decision". The underlying idea is to define a recursive relation which can simply be solved. For a given step k and for a given state xk E &, one can consider the same optimization problem starting from this state : A'

Step k

m i n J ( z k ) = C c ( t . x ( t ) . u ( t ) ) + ~( ~, ( I v ) )

Grid ofthe state space

t-k

x(t)E

x,vt E j k ,

Cnunieration of thc states and the commands to compute Hellman Value?

A}

x ( t + 1 ) = f(t,x(t),u(t))Vt E {k,&I] x ( k ) = x/(

Grid ofthe state space

Bellman Values are alrcady cornputcd

Fig. 4. Principle of Dynamic Programming

If n-;(xk) is the solution of this problem and Anyway, for systems with a low dimension, such as the mCHP optimization problem given in Q 3.1, Dynamic Programming is an efficient and easy solution to develop.

vi(xk) = . / ( n ; ( x k ) ) defines the Bellman Value, the principle of optimality leads to the following recursive relation called the Bellman equation : v i ( x k ) = m i n C ( k . x k . u k ) + ~;+~(f(k,~~,zi(k)) I4k)

=

and%&)

w,,ut 1+ v;+, ( f ( k , Xk

= ~,xk,zL;)]"z;+i

X k , ut

1)

3.3 Application to the mCHP optimization

(f(k,xk.U;))

After the theorctical presentation of the Dynamic Programming, we now present how to adapt this method to our problem. The state space is discretized and supposed to belong to the set X defined below. The command is supposed to belong to the set 1J defined below. x = (h, { I , T t ) with h E {o,I..... II max) Tt E {Tt min, Tt2,..., Tt ma,) ~i E j7i min, Ti2..... ~i ma,)

Starting from the end ( k h ] , it is possible to compute the Bellman values step by step for each state and finally find the solution for the first-step. Practically, Dynamic Programming can be used to solve the optimal control of a process. For this purpose, evcry continuous part of the systcm (state, command, or equation of evolution) must be discretizcd. Then, for each time step, a matrix of Bellman values is built lor each slate of the grid. Eor a givcn state, the Bellman equation is solved by enumerating each possible command, taking the minimum value of the transition cost plus the

392

from the real transient, we propose adjusting the command at each stcp to take into account the real state that is supposed to be measured. If the forecasted prices and demands are not modified, it is indeed possible to use the command obtained during the off-line optimization providcd it has been saved. As we mentioned before, an advantage of the dynamic programming is that we calculate all the optimal trajectories fi-om each point on the grid to thc final state. If wc want to update the demands or use a receding horizon, a new uptimiration is however necessary.

wzth Qgm E {O. Qg min .....Qg ma,) Qgsb E [o, Qgsb ma,] cr E [O.1] The sketch of the algorithm is given below. At each step k, we calculate the Bellman values at each node xi. The command u is calculated to minimize the transition between this state and a final state xf belonging to X. To achieve that, we test every possible value of Qgm and calculate for each of them exactly the valuc of Qgsb and a by inverting the Equations (2-3,543). The command u is re-jected if the solution doesn't respect the conditions (Eq. 16-17). With this manner the state remains on the grid and no interpolation is needcd. 21

k

= (Qgm, Qgsh.a)

4.

APPLICATIONS AND RESIJLTS

4.I OJjLine optimization

= LV

To test the algorithm, we consider the demands for mid-season represented in Eigure 6. The mCHP is supposed to work in ONIOFF mode. The inertia for the water tank and for the heating system are equal to 0.46 kWh1"C and 0.06 kWh/"C, respectively. The gas price is equal to 2c€kWh and the electricity is equal to 5 c€lkWh during the low demand hours and 11 cElkWh during the high demand hours (7 am to I0 pm).

'dx E X , J ( k , x ) = 0

while k > 0 k=k-l foveuch xi E X foreuch x j

E

X.

F(xJ) = min, v(xi.xf)

r ( x J ) = m i f uisnotadmissible end J ( k , x i ) = minXf( F ( x f ) + J ( k + l , x f ) )

Electrical Power Demand I

suve u ( k , x i ) end

I

Heatina Power Demand

end

'-1

Once the optimal schedule has been calculated offline, it has to be applied to the process. But generally the design model used for the optimi~ationdiffers from the real plant. To mitigate the effect oT this error, we propose the closed loop scheme givcn in Figurc 5 , that takcs into account on-line measurement on the process.

I

Drinking hot water Demand 1.5i

I

time In hour

Fig. 6. Power demands in kW on a day. In Figure 7, we present the results of the optimization when there are no penalties for startup and shutdown. mCHP gas consumption (Qgm)

support boiler gas consumption (Qgsb)

Qgsb-opt

I

-I

"I

Forecast (prices, demands)

3-way valve opening (alpha)

Fig. S : On-line optimization Only a part of the command (the mCHP gas flowrate Qgm-opt and the 3-way valve opening a-opt ) is applied, and the support-boiler gas flow rate Qgsb is kept free to compensate for the prediction errors. Moreover, because the transient calculated during the optimization can bc different

time in hour

Fig.7. Optimized command without start-up cost (C'su =Csd =O). J=3e54

393

but a more precise optimization might lead to better results.

When we take a start-up and shut-down cost equal to 6 c'2, thc optimizcd control sequence is quite different, as we can see in Figure. 8. We observe that the optimization limits the mCHP running hours to the most valuable period between 7 am and noon. The pricc to pay for this lower solicitation is a gas-consumption increase of more than 7%. A lot of other ca5e studies can be treated with the developed model playing with different sccnario of pricc and demand to find the best situation for the mCI-IP development.

Tank Temperatures predicted (-) and measured (--) Rn

-Temperature at mCHP entrance : predicted (-) and measured (--)

mCHP gas consumption (Qgm)

228

Room Temperature : measured (-) and setpoint (--) ...................

0 20~ .L ..

18

0

5

10

15

20

support boiler gas consumption (Qgsb)

Fig. 10. On-line optimization validation.

3-way valve opening (alpha)

0

'I

5 . CONCI,USlON

-

The presented paper has proposed a new scheme to optimize the operations of a mCHP. The solution minimizes a cost function that takes the bill and the maintenance expenditure into account. Dynamic Programming has been used to solve the problem. The algorithm has been adapted to run on-line and has been tested on a validation model. The results are good and promising. The future steps are the improvement of the design model to include demand forecasting. The scheme will be next implemented and tested on a real-time environment.

nn

0.51

rL----IuL-r'LL

I

5

OO

10 15 time in hour

20

Fig. 8. OptimiLed command with start-up cost (Csu=Csd=h&) 5=3'292 (3630 for the gas) 4.2 On-line Optimization The control designed has been tested on the validation model presented in the $2.2. We can see in Figure 9 that the new control avoids startup and shutdown without a loss of efliciency. The gas consumptions for the classical control (described in Figure 2) and for the new scheme are almost the same (3'257 vs. 3E60).

RCrCRCNCCS

Bellman R.E. (1957), Dynamic Programming, Princeton, NJ:Princeton University Press Demporad A,, Morari M. (1999) : Control or Systems integrating logic, dynamics and constraints, Automalica, 3.5 ( 1999) 407-427. Davelaar F., Faille D., Girard A. (2004). Hybrid Modeling and Control of a Combined Cycle during start-up transient, ISA Conference, Nashville, June 2004. Entchev E. (2003) Residential fuel Cell energy systems performance optimization using soft computing techniques, Journal of power Sources I18 (2003) 212-217 Faille D., Hire1 A., Davelaar F. (2003) Integrated interface for power plant modeling", IFAC PPS 2003, Scoul ,2003 Mondon C.,Faille D. (2005) Optimiiation of a micro Combined IIeat and Power Fleet, TASTED, June 2005. Peacock A.D., Newborough M (2005) lmpact of micro-CHP systems on domestic sector C 0 2 emissions, Applied I'hermal Engineering 2.5 (2005) 2653-2676.

Classical Control Strategy

0,

off-line optimization

on-line optimization scheme

'~

0 0

r u - I 5

10

15

20

Fig.9. mCIIP solicitations: ON (1) OFF (0) ~

Ihe evolution of the main temperatures (tank, heating circuits, room air) are shown in Figure 10. The responses are globally satisfying. Nevertheless, there are some discrepancies between the trajectories obtained with the orf-line optimiation (predicted) and the reahation (measured). The online optimization scheme compensates this error,

394

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

THE WAY OF DISTRICT HEATING OUTPUT CONTROL BY MEANS OF HYDROTHERMAL POWER SYSTEMS - THREE MODlFlCATIONS Jaroslav BalatC’, Petr Jenik’, Bronislav Chramcov’, Pave1 Navratil’

Faculty o f Applied Informatics, Tomus Bata University in Zlin, Czech Republic 211nitedEnergy, Join Stock Company, Most - Komofany, Czech Republic

Abstract: District Heating Systems (DHS) are being developed in large cities in accordance with their growth. The DI-IS are formed by enlarging networks of heat distribution to consumers and at the same time they interconnect the heat sources gradually built. DHS is used in larger cities of some European countries e.g. in Germany, France, Denmark, Finland, Sweden, Austria, Czech Republic, Poland and others. Production technology of heat by means of combined production of power and heat (CHP) is an important way to increasing of thermal efficiency of closed thermal loop. The paper shows the system access to the control of extensive DI-IS controlled plant. It concerns automatic control of technological string “production, transport + distribution, consumption” of extensive district heating and that is the contiibution of this paper. Control by means of advanced contiol algoiithms is a tool (up to now neglect) for decreasing consumption of energy and increasing the level of environment protection. I’he paper deals with brief description of’ three modifications of the way of control of hot-water piping heat output at simultaneous operation of qualitative and also quantitative parts of control. Copyright 0 2006 IFAC Keywords: District Heating, Control Algorithms, Control System, Hierarchical Control, Combined I Ieat and Power - CI IP, I Iydrothermal Power Systems.

1. INTRODlJCTION Cogeneration of Power and Heat i s an important way to increasing of thermal efficiency of closed thermal loop. The experiences in design of Control Strategy for Extensive District Heating System in the towns Bmo, Prague and Most-Komofany in Czech Republic are summarised in the paper. It involves the connection of main author’s operational experiences gained during many years of his work in the Power and Heating Plant and his further scientific - research activities on the technical university in co-operation with his colleagues, PhD students and with his students. The design of control strategy shows the basic concept of control methods of the district heating system of specific locations in town Brno, Prague and Most-Komohny. Each district heating system has its specific features and therefore it is

necessary to create a philosophy of control for each of them. From the point of view of control, this philosophy consists of both general regularities and special features of a specific locality. The idea of a system approach to design of technological string control “production, transport + distribution, consumption” resulted from the specific solution of the way of control in real time and also fi-om shorttime preparation of district heating operation in region of’ Bimo, Czech Republic during the last decade of 20th century. The knowledge of operation and experience motivatcd the author to creating the methods and conception of control of this technological string. At present it is known from the literature that the problems of optimum control of combined heat and power production (CHP) in sources and also systems of automatic heat consumption control are solved

395

only separately. Very few attentions is paid to analysis of static and dynamic behaviour of heat networks and utilization of these features for operation control of these networks. There are no any works dealing with elimination of transport delay in transport of hcat in heat networks. Publications dealing with system approach to control of the technological string as a controlled plant are missing at all. This fact was the motivated cause for solving a new problem.

accumulation and enables to eliminate influence of transport delay between the source of heat and relatively Concentrated heat consumption by all consumers. At combined production of heat and electric energy it enables to use heat accumulation for heat supply for combined heat and power purposes aside from the time interval of peak supply of electric energy. It is created for the case of heat supply from power and heating plant exchanger at the source of heat but with the configuration according to Fig. 3. 111 Modification when hot-water boilers with grate are sources of heat: .4lgorithm o f qualitative-quantitative method of output control with grate hot-water boilers as sources qf heat The algorithm enables the method of control of technological string “production - transport+ distribution” of heat in radial or circular hot-water network. It enables to eliminate the influence of transport delay between the source of heat (hot-water grate boilers) and relatively concentrated heat consumption by all consumers (see Fig. 4).

2. DEFINITION OF THE PROBLEM

District heating system has to ensure supply of energy to all heat consumers in qiiantity according to their requirements variable in time. Energy supply has always to comply with prescribed quality index (Reetz and Halmdienst, 2002), (Linderberger and Bartels, 2002). In case of hot-water piping it means to maintain prescribed temperature of hot water in intake piping. Algorithm of so called qualitative-quantitative method of control using prediction of the course of heat supply daily diagram in hot-water systems of district heating enables to eliminate influence of transport delay between the source of heal and consumption of heat by relatively concentrated consumcrs. Transport dclay dcpcnds on thc spccd of flow of heat-carrying medium (hot water) and on the length of feeder piping. The new method of hotwater piping output control consists in simultaneous and continuous acting of two manipulated variables influencing transferred heat output and in utilization of required heat output prediction in the specific locality. I’hc newly designed method of control was considered for a specific case when the transport delay was supposed to be in the range of six up to twelve hours depending on consumed heat output by all consumers. The following three methods of application of qualitative-quantitative method of hot-water piping output control are elaborated at present namely according to technologic equipment of the source of heat. I Basic method - it is crcatcd for the case of heat supply from the exchanger at power and heating plant as the source of heat - the principle: Qualitativequantitative method qf control of hotwater .piping heat output using prediction o f the course of heat supplv dailv diagram in district heating systems It is created €or the case of heat supply from the exchanger at power and heating plant at the source of heat. Technologic scheme is presented on Fig.1. It enables to eliminate the influence of tmnsport delay between the source of heat and relatively concentrated heat consumption of all consumers. 11 Modification of the basic method: Adaptation o f qualitative-quantitative method o f control o f heat supply b y hot-water Diping for the case using part ofthe piping for heat accumulation The method of control is created for the case when part of the feeder piping can be used for heat

3. THE PRINCIPLE OF CONTROL METHOD

Algorithm of so called qualitative-quantitative method of control with utilization of prediction of the course of heat supply daily diagram in hot-water systems of district heating enables to eliminate the influence of transport delay between power and heating exchanger at the source of heat and relatively Concentrated heat consumption by all consumers (Balattir, 2003). The transport delay depends on the speed of flow of heat-carrying medium (hot water) and on the length of feeder piping. The new method of output control of hot-water piping consists in simultaneous and continuous acting of two ntariipulated vuriables influencing transferred heat output and in utilization of required heat output

prediction in the Jpecijk locality The new designed method of control was considered for a specific case when the transpod delay was supposed to be in the range of six up to fourteen hours depending on consumed heal ouiput by consumers. The designed method is a solution of heat output control method at the source of heat. The present common method of heat output control of heat supply by hot-water piping utilizes usually dependence on water temperature in intake piping of the heat feeder or also even dependence on outdoor air temperature. Two manipulated variables are available for the control of hot-water piping heat output from the source of heat: - the change of water temperature difference in intakc and rcturn piping of hot-watcr piping rcalizcd in practice by changing heat input at intake into power and heating plant exchanger, so called qualitative method of heat output control; - the change of mass flow of hot-water by means of changing speed of circulating pump, so called quantitative method of heat output control.

396

I he above mentioned manipulated variables are usually uscd a5 scparately acting, namely only one of them. If both are used it would be a case when qualitative method of control is the main method of control and quantitative method is used by starting and stopping pumps with different transportcd mass flow. These quantitative changes have been used once at changc of season (summer, transient season, winter). For this purpose usually two or three sizes of circulating pumps have becn used. Disadvantage of the described methods of control is thc fact that thcy do not covcr complctcly dynamic properties of the controlled plant. rransport delay in the intake branch of heat feeder and delay oS inertial members of power and heating plant exchanger are omitted. If the output consumed in Some places of the hot-water network changes, then the corresponding output of sources (production) controlled by the classic qualitative method adiusts ithelf though with considerable delay even if there occurred self-controlled change of hot-water mass flow due to self-controlling properties of static characteristic of transport pump caused by the change of operating point of the pump. The changc of heat output consumption is realized by acting of autonomous controllers of temperature in secondary nctworks or c~nsumcrs'trdnsrer sktions. Thus some of the requirements on the prescribed quality indcxcs of hcat-carrying mcdium arc not fulfilled. 3 I Analysis of dynamic properties of the hot-water piping. Technologic scheme of hot-water piping equipment is principally presented on Fig.1. On the displayed case the circulating (transport) pump is included at the end of return piping before the exchange station. 3

,r

Behaviour of controlled plant at qualitative method of control At qualitative method of control the hotwater piping behaves as a proportional system with inertia of higher grade with transport delay, expressed by transfer function (2)

where: TI, T, and T3 are parameters of transfer function describing the behaviour of heat exchanger situated in heal exchange station, TU' - transport delay. Uehaviour of controlled plant at quantitative method of control Quantitative method of control realizes thc changc of circulating watcr mass flow by converter of speed of circulating pump and thus also the change of supplied heat output (I). It includes inertia of speed converter and contains also a time constant of piping, which affects the time necessary for acceleration or possibly deceleration of circulating m a s of incompressible heat carrying medium. The hot-water piping itself behaves as a proportional system without inertia. The specified properties can be expressed by transfer function

G\kl.unr(S)

where inertia time parameters of speed converters T, and T, are defined by the kind of convcrter (hydraulic clutch, electric speed-changing device), time conshnt T3 is defined by the length or piping, speed of heat-carrying medium and transport height of circulating pump. Thcy arc gcncrally much smaller (seconds, tens of seconds) than time parameters in the relation ( 2 ) i.e. than time constants of heat exchanger in power and heating plant (tens oS minutes). T3 is the time which hot-water needs for achievement the speed c,, from zero speed. This speed corresponds to maximum mass flow .U,,,axby acting of the transport height Hmmof the pump.

3.2 Elimination of transport delay at heat output control of hot-water piping.

51 -

Fig.1 Principal scheme of hot-water piping I-Ieat output is supplied according to the Sollowing rclation:

It is possible to eliminate influence of transport delay at control of heat output of hot-water feeder by siriiultaneous and uninterrupted control by two manipulated variables. This algorithm is shown on the l'ig.2

Key to Fig2 c- specific heat capacity, I- lcngth of intake branch of heat feeder, RT- real time (time in which manipulated variable of qualitative method of control is acting on exchanger in power and heating plant), S cross section of intake branch of feeder, rtime in which acting of manipulated variable of quantitative method of control shows itself at locally concentrated consumers, T d - transport delay, T: presupposed transport delay, Zij,.- time advance, Tpreeih-time of transition of exchanger in power and

f t) Pr = M ; c . A $

Quantitative metod of control

Qualitative metod of control

where: PI (W] is heat output of hot-water piping, MJkg F 'J is mass flow of heat-carying medium, A$(.r] i q temperature difference, c (.I kg I K '1 i\ specific heat capacity.

397

Fig. 2 Algorithm of qualitative-quantitative method of control of heat supply by heat supply by hot-water piping heating plant at action of manipulated variable, Tlz period of sampling (approx. 15 minutes), M,- mass flow of circulating water, M ; - real mass flow of circulating water in time RT, lu,A, - real mass flow of circulating water in time T, PT - heat output of hotwater piping, P," - presupposed heat output read from predicted daily diagram of heat supply (DDIIS), p,![- presupposed heat output in time T, p;, - real

accumulation in intake branch of heat feeder for the purpose of utiliting economically justified combined production of electric energy and heat in power and heating plant. In this case for qualitative part of control it is necessary to utili7e mixing of hot water from piping determined for heat accumulation and cooled water in return branch of hot-water piping (scc Fig. 3). Presupposed heat output in time T (see analogically to the key to 1:ig. 2) is

,~~

measured (calculated) heat output in time T, $;> real temperature in intake branch of feeder at consumers in timc 7, $1 - real temperaturc in return ~

PF

~

branch of feeder at consumers in time r, APT,, deviation between presupposed and real consumed heat output in time 7, AM,, 7- quantitative correction, i.e. change of mass flow of circulating water, AQchange of heat content in intake branch of feeder causcd by quantitative corrcction, A$; - real temperature difference at consumers in time T, A$! presupposed temperature difference on exchanger in power and heating plant in time Twhich is calculated from pr1 and which is manipulated variable of

+

..............................................................

:

qualitative method of control, A$; c' - presupposed temperature difference on exchanger in power and heating plant in time 7 which includes correction of heat content in intake branch of feeder AQ. I t is necessary to lxing i n this heat or possibly to decrease heat admission by it in dependence on sense (sign) of quantitative correction AM, /, p,- specific mass of circulating water in intake branch of feeder.

* $,,,,,,,

= Mv,l,,XT * c * A$:

................................................... ...... :..................... A4,.",R, = f ( Apmin)i i . .j A$: = j

:

!A$;

(4)

......................... -t9z11r I ~

= f(M:E.s,/')

Fig. 3 Principal scheme ofheat output control of hot-water piping by mixing

5. ALGORITHM OF QUALITATIVE QIJANTI'I'AI'IVE METHOD OF OllTPlJT CONTROL OF HOT-WATER PIPING WITH HOTWATER BOILERS AS HEAT SOURCES

4. MODlFlCATlON OF THF: A1 GORlTHM OF CONTROL AT LJTILIZATION OF A PART OF HEAT FEEDER FOR HEAT ACCUMULATION

The algorithm enables control method of technological string production - transport+ distribution of heat in radial or circular hot-water nctwork (Balatg, et al., 2003).

It is necessary to adapt the above described algorithm at possibility of utilizing a part of piping for heat

398

f~

Aufamatic combustion contmi Of bollem

I

Variants of heat network configuration a) Each heating plant has separate heat network

b) Both boller houses collaborate in one heat network

0

Vig. 4 Algorithm of qualitative - quantitative method of output control of hot-water piping with hot-water grate boilers as heat sources Thc philosophy of the mcthod of control utilizes prediction (of part) of daily diagram of heat supply in particular locality (DDHS) at simultaneous and continuous acting qf two manipulated variable i.e. qualitative part of control (by controlling temperature gradient at intake and return branch of hot-water piping or poSSihly at hot-water boiler) and quantitative part of control (by controlling mass flow oj heat carrying medium hot water by means of circulating (transport) pumps) so that it would be enabled to eliminate transport delay of really consumed heat output by consumers from really produced heat output at hot-water boiler, which has been produced in advance. The presented method of control enables supply of heat output with Vdriabk temperaturc at intake into hot-water network in dependence on presupposed heat consumption. Prediction of the course of DDHS is based on the analysis of development history oftime series (Box Jenkins method). Sequence (algorithm) of qualitative quantitative method of output control of hot-water piping with hot-water grate boilers as heat sources is described by rcalization of thc following stcps according to Figure 4: -

-

1. Calculation of prediction of DDHS 2. Covering of predicted heat supply daily diagram produced heat output p; selection of operational assembly of collaborating boiler houses and determination of separate boilers of these boiler houses for separate time pcriods of the daily diagram of heat supply in the course of 24 hours. It concerns 4 time periods: u = 1,2,3,4

3. Optimization of operation of sources for p ; F in current time period of DDHS (time period is denominated by u) 4. Dividing the load into collaborating sources: Qualitative part of control: U I , R T 5. Measurement (or possibly completed by calculation) of immediate heat consumption i.e. in time 7':

Cpztr

6. Determination of working point of hot-water is pressure network ApDly=f(Apref)where Ap"' diffcrencc in refercnce point of circular hot-water network. 7. Calculation of transport delay in reference point hot-water network yp{ in time 1'. 8. Calculation of time back-prediction (is. prediction to the past), i.e. output of production units i n time RT. 9. Quantitative part of control: U Z J It concerns correction of mass flow of hot water in time T at circulating pumps A kf,I : 10. Correction of qualitative part of control i.e. of boilers output Au, in time T (correction of original output adjustment U I K I ). Calculation of individual steps is not so complicated but it is assumed right knowledge of function (operation) and behaviour of technolog. equipments. Key to big 4 c - Fpecific heat capacity, l - length of intake branch of feeder between power and heating plant and concentiated consumeIs, R7 - teal time (time in which manipulated variable of qualitative method of control at hot-water boiler is acting), S cross section of intake branch of feeder, T - time in

399

which acting of manipulated variable of qualitative mcthod of control shows itsclf at locally concentrated consumers, i(, transport delay, r;/ transport delay at reference point of hot-water network in time T, dt7- time o f prediction to the past (time by which it is necessary to change manipulated variable of boilers in advance so that change of heat output of hot-water boiler by qualitativc method of control shows itself in time T), tK- transition time o f output control of boiler, tk - medium transition time of output control of the whole boiler house, T L Z - period of sampling, p;/)(J/)- prediction of daily diagram of (produced) heat oulput supply - DDHS, u - number of the time period of DDHS, p;/Fz1 ~

-

RI

predicted heat output of hot-

water boilers of boiler house No j in time RT, p,f,&Y’- piedicted heat output pioduced in time R7, - predicted heat output of boiler Yo i of P:Kl>111 boiler house No KJ, M ; -~ prcdictcd ~ mass flow in time RT, A$/<’ correction of heat input in delivered fuel at hot-water boilcr in timc T including correction of heat content in intake branch of feeder and at the same time also in fuel on grate of hottemperature of hot water in water boiler, :$ intake piping in consumers’ network, 9,”’ temperature of hot water in return piping in consumers’ network. ~

~

presupposed supplied (produced) heat output in time RT and in time period h%, ti, P~ ;, K? - heat output of boilcr house No j in time RT in time period No u, p, K / , heat output of hot-water boiler No i in ~

heating plant 12/0 j , A 9 = 81. - 9~ - temperaturc difference in intake 8,. and return piping of hotI ,- heat output in fuel 01 heating water network, b’p~po/ temperature difference predicted plant No j , A$;/ in time RT corresponding to predicted produced - heat output consumed output of boilers, ~

C

by all consumers in time R/’, ApceJp- pressure difference of circulating pump in hot-water network, A M , I - correction of mass tlow of hot-wa into being which enables to iitilire parts of intake piping of feeder for accumulation of heat. Modification 111 was initiated by the requirement of application of qualitative-quantitative method of heat output control of hot-water piping on hot-water system of district heating where hot-water boiler houses are sources of heat and thercforc on the basc of good equipment of hot-water system by information system for measuring heat at consumers it is possible to control the technological string production - transport+distribution of heat as the whole. It is the matter ofcomplex access to solution ofgiven task and the solution is original and quite uniquc. REFERENCES

6. BENEFITS

minimization of primary fuel consumption by adjustment - control of heat output of sourccs on the base of knowledge of immediate heat consumption by consumers, minimi7ation o f pumping work of circulating pumps for transport of hot water at hot-water piping with continuous control Ap lerP minimization of heat losses of hot-water piping with continuous control of temperature in feeder intake branch 8,in dependence on predicted course of DDHS. 7. FINAL SUMMARY 1 hree presented ways of application of qualitativequantitative method of output control of hot-water piping gcneralizc the original idca described in chapter 1 Qualitative-quantitative method of heat output control of hot-water piping with utilization of prediction of the course of heat supply daily diagram in district heating systems. This access to solution of control, so called ADVANCED CONTROL ALGORITHMS, is quite unique in the field of district heating. In the course of timc further requircments appeared on the algorithm namely according to technological equipment of the source of heat. Thus the modification JI came

Balatt6, J. (2003). The way of district heating output control by means of hydrothermal power systems (Design principle). In: Proceedings of IFAC Symposium on Power Plants Ce Power Systems Control 2003 KIEE - The Korean Institute of Electrical Engineering, page 240245, Seoul, Korea. BalatE, J., Chramcov, B., Princ, M. (2003). Strategy of control of extensive district heating systems. In: Proceedings of IFAC Symposium on Power Plants & Power Systems Control 2003 KIEE The Korean Institute of Electrical Engineering, page 762-767, Seoul, Korea. Balrit6, J. (2005). The way of district heating output control by means of hydrothermal power systems. In: Proceedings of 16Ih IFAC World Congress 2005 Prague,CZ. Lindenberger, D. and Bartels, M. (2002). Perspektiven der Kraft-W2rme-Kopplung im europaischen Strombinnenmarkt. In: Proceedings of 7 Dresden FernwarmeKolloquium, AGFW, Dresden, Germany. Reetz, B. and Halmdienst, Ch. (2002). Witschaftliche Einsat~grenzen kombinierter Kraft-WarmeKalte-Kopplungsanlagen. In: Proceedings of 7 Dresden Ferm~1ai”me-Kolloquiaim, AGFW, Dresden, Gennany.

400

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

WEIGHTED FOULING MODEL FOR POWER PLANT CONDENSER MONITORING M. Cregan and D. Flynn The Queen’s University o f Belfast, United K,ingdom

Abstract,: Operating a powcr station i b much more t1ia.n underst,a.nding the functional relationship between its ninny parts. In today’s market, rlrivcn ec:ononiy it, requires a mnlt,i-disciI>liiied approach to balaiice t,lie t,echnical, economic, environmcntal and oft.cn times political forces! that influence the decision making process. This paper presents a method for quantifying the economic impact of condenser maintenance based on plant thermodynamics, condenser modelling arid market forces in the form of power purchase agreernent,s. An opcrat,ing cost. function is forrnu1at)cd which is ablc to cst,imatc opcratiiig costs based on current plant da,t,a and opemting paramet purchase cont>racts.The results highlight the financial iniplic ions. Due t,o t,lic coniplcx, mult~i-modaland discont,inuous nature of tlric: cost funchion, conventional optimisation techniques struggle with this scheduling problem. However, using genet,ic algorithms, it is possible to search arid iderkify a range of feasible least cost maintenance schedules. As a result, key sclieclules arid their associated costs are quickly liigliliglitetl. allowirig the user to make a more informed decision regarding future maintenance. Kcymwds: genetic algorithms, stcani plants. physical rnodc4s

1. INTRODUCTION The environment in which nmny power stations opcrahe has changed considerably over the past t,wo decades. No longer is t,lie pursuit. of unit, cfficioncy the sole arbiter. In its place is a multit ride of economic and environmental forces which only exacerbat,ethe already difficult ta.sk of power st~ationoperation. On one side t.here may be shareholders anticipating a. profit~ableret,iirn on investment,, and on t,he other, new legiskion enforcing capital investment in emissions reducing plant. It, is within this compctitive environment, that mana,genientjcont~inuallyendeavour t,obalance t,he opposing economics of gcncrat,ion and niaint,c> naiicc. While producing electricity is funtlaancntal to generating revenue, maintenance can not be ignored, as the physical healill of‘ the plant) is

paramount, to both t,he ability t,o generate electricity arid also rclia,bility. It is oftcn the case t,hat,unt,irnely pla.nt failures ca.n have drama.t,ic financial penakies, especially if t>lieyoccur at t,iines when thc systcni dcnianil for clcct,ricity is high.

At tjhc heart of a, convent,ional power plant, are the boiler and condenser, whose respective tasks govern the efficiency of the generating unit, as represented by t,he Rankine steani cycle. This paper preseilts a. methodology to improve unit efficiency and profitability for a steam turbine genera,t,or. by targeting tlic largcst, single cncrgy loss wit,hin the Rarikine cycle, t,lie condenser.

It. is in t,hc condcnscr t,liat, latent heat from t2hc st,ca.ni is lost t,o the cooling water, arid where inefficiencies in the heat transfer process impact on t.he overall efficiency of the generating unit.

40 1

Unfort,unat~ely,process control on the condenser

--

is usually limited t,o the number of cooling water

o,9.

feed pumps in operation and the rate of air ext,raction, neit>lierof which have a major impact on heat t,ra,nsfer, except, when t,hey fail t.o operate. Consccpently~condenser performance relics heavily on rout,ine maintenance such as cleaning and t,ube repair. Present>edin this paper is a novel method for modelling condenser losses. This is a.chiewd by idcnt,irying t hc fouling processes at work within tlie condenser a,nd motlelliiig their non-1inea.r variat,ion over t,ime. In so doing, previously uiiaccounted variations in seasoiial and eiivironrnc+iit,al conditions are incorporated, as well as time of ycar dependent cont,rac:t,u;tlc:onst,rairit,s.This combination of operating rosts permits accrirate performance estiniat,es for any specified time period. The resiilts highlighted in this paper are a development, of work originally presented by Cregan and Flynn (2003). Sincc t,licii t,he focus 1ia.s been on pra.ctical implementation, dealing with issiics sucli a.s computer interfacing, graphical uscr int,crfa.ccdcvclopiiimt~and physical niotlcl custoniisaliori. Decisions regartlirig sollware desigri arid inil.)lementat,ionwere t,aken in consultation with plant operators and engineering staff. The result of t,his was that complex GA and costing parameters have been hidcleii from the operator, model t,uiiing has been simplified and where appropriate simplc: graphics havc rcplacc: text, in t,hc user inter face.

2 . CONVENTIONAL hIAINTENANCE APPROACH Tra,dit,ionally, condenser ma,intena,nce has been based on simple thermodynamic perforriia.nce estimaks, as presented by BE1 (1991). hIaiiit,enance schedules based on these techniques, as described by Put'maii (2000), liave ignored non-linear seasonal variations in performmce as well a.s cont.ractual cost s and constrabnts. This conventional approa.ch is liniit,cd tjo cfficiciicy rcla.t>ctlcosts. which for a modern power station are only one of a multitude of different costs which may influence the maintenance planning program. In the t,echniyue described by Putman a simple linear relat,ionship between condenser fouling and t,ime is a.ssmned. Hence, the c:urriulat,ive fuel costs are calculat~edby int.egraling with respect to lime. Subsequently, t,lie specific cost of n sclietluletl out,ages at, times tl to t , are added t.o the cumulative addkional hiel cost). A typical graph, Figure 1, plots t,he cumulat,ive costs stret,ching over twelve months and iiichdes three planned outages at tiiiics 11 to t 3 .

0.8-

Zero Maintenance

- - One Outage - TWO Outages

Zero Maintenance

,'

Fig. 1. Operating Cost for Lineu Fouling TypicaJly, t.he aim is to find tlie least. cost solution to t,he problem by 'experimenting' with various maintenance schedules. Figure 1 demonstrat,es this by highlightzingthree possible schedules. The first, and most, expensive opt.ion is to ignore maint,ena,iicewit,h a subsequent, coiit iiiiial incrcasc in plant fouling. Hcrc, thr: cxponcntial increase in cost indicates that this is not a sensible approach. Also plotted a,re two other schedules, with one a.nd two o i h g e s respect~ively,where two outages represent's t>hebet>t'eror least cost scliedule. This graph is only illiistrative and does not necessarily show t8hebest, solution.

To find tlic lr:ast, cost solut,ion, as tlcmonst3ra,t,cd by Putman, t,lie maintenmce window is recursively divided into equally spaced periods, wit,li thc nurnbor of outages incrcasing by one diiring each iteration. Eventually, a series of schedules are calciilat ed am1 from t,hese a. least cost,maintenance plan may be det,ermined. This simple costing technique however does not provide a triie representation, because ra,rely is condenser fouling liiiear - inst,ead it vxies wit,li tirric of ycar, unit loading, ctc. In itddition many of (he o(,lier market -driven economic a r i d conlritcl iial costs have been cornplet,ely ignored. This simple approach may have been sufficient when the economics of' operating a geiierat>iiigunit were limited tfo unit efficiency, but. in today's competit,ive environment,, gcncra~t>ing conipanics ncctl a. new and morc comprchcnsivc approach. 3. COhlPOSITE FOULING MODEL

The composit.e fouling inotlel presenkd here l.enipls to a.dtlress the weaknesses of the linear model by ideiitifiing t,lie various fouling processes act,ive and iiiodelling their non-linear beliaviour. One of the early attenipk at modelling the thermal resistance due t.o fouling ( r f) was proposed by Kern and Seaton (1959), using t~hefollowing simple mat>crialbalancc cyuat>ion,

402

%

where the rate of fouling, is the difference bet.ween, &> t,he rate of deposit.ion and, $,, the rate of removal. The composite model contends tha,t,a I ogicr?1 tievc:loprnent of t,his si ni ple foi 1 I irig ni ode1 is tlie ide1it)ification and analysis of individual incchanisms at, work wit,liin tlic contlcnscr. Thcsc would be represented a s sub-models for particulat,e fouling, bio-fouling, scaaiag/crystalliza.tion, tube blockages?etc. Most recent work by Putriiaii (2000) and Zubair (2000) identified various fouling mecha.nisins,which are listed in Table 1 t,ogether with a brief description. Table 1. Coniposit>eFouling Sub-Models Sub Model sml

Dcscription

= Altl/"l

Power law

r1

Asymptotic Falling rat,e Linear

r g = r,(l - e-61'2 r:i = A 3 log( R3t)

smg

Exponential

rs = A;,tB5

rq

= Aqt

1

+ Bq

Ai and Bzare constants, r s = Sat,uration fouling limit. t = t,ixne.

where:-

0 < IVi

< 1,

where i is t,he nuniber of sub-models and t is time. It is also assumed that, t,liere are no ext,crna.lt,herinal resisCances impeding heat transfer. Therefore, rf = r,, whcrc rf is t,hc tot.al fouling r~sist~aiicc.

3.1 Composite Sub-Models

Format

sirs2 sm,g smg

The weights. I f / , . allocated to the sub-models may vary between zero and one, to reflect the changes in seasoiial and environmental conditions. Hence. the coiiiposite fouling resistance, rc, is the sum of is the fouling all weighted sub-models, u hile rate for each sub-model.

In ortlcr to highlight the rclntis-e time dependent properties for ~ a c hsub-model, cach has bcen norrn~disedand plotted on a single axis, spalining twelve months, in Figure 2. It IS notcd that thc falling rate inodel (rg),and power law model ( T I ) , look similar. However, with the falling rate model is always decreasing, the rate of deposition, ~6 hich is not true of the power law model.

9.

('Omel

Each of the sub-models 1ist.ed in Table 1 has been ideiit.ifiec1as representing a, particular type of fouling found in heat, exchangers and condensers. The following is a. brief description of cach, highligliting t,hcir particular chara.cteristics.

Power Law n/Iodel (sm

Documented hy Klian,

cb al. (199G) whilc investigating t.hc deposit,ion of

CaC03 in heat exchangers operating at, relatively high temperatures (2 50°C). Consequently, this may be employed t.o represent, the build up of crystalline deposits, commonly associa.ted with condensers opera.t,ingat, high ai-nbient, temperat,ures. Asymptotic Model (.sm2) It was obsc:rvcictl by Zubair (2000) that hea.t, exchanger fouling from cooling water at, t,einperatures 5 25°C caii be represented as an a.symptot~icmodel. This is because at lower temperat>uresthe deposition of different shaped salt crystals and suspended pa.rt,iclescreates a,relatively weak layer. As the thickness of the deposit, lwpr incrcascs so docs thr: rt:moval rnto, and cvciitmlly t,lie reizioval rat,e approaches that of t.hc deposit ion ratc arid sat.iiration is reached. Such a modcl may bc used to represent the condenser deposits encountered during the cooler seasons in both coastal arid inland power stat,ions.

0

60

120

180

240

300

360

Time (days)

Fig. 2. Coniposit,c Fouling Sub-Modcls In practice, siiriulating the non-linear fouling processes requires a collection of sub-models, tailored to each condenser or power st,atioii. Each of the sub-models is chosen to reflect, t,he fouling niechanisms act,ive in the condenser ant1 weighted according to their relativc eflcct.

Fa,lling Rate Model (srn,y) The falling rate curve represenh a process where t,lie deposition mte is always greater tfliatst>lieremoval rat>e. Bot,h nluller-Steinhaga.n (1988) and Bansal (1993) have iclc~it~ified this fouling proccss. In thc lattcr it was representative of tallisa.tion: while in the former it was pa,rt.iculat,efouling. Putman (2000) highlighted t,he process as being typical of that observed in coastal power stat,ioiis. It represents the particulat~enature of organic fouling deposit,s that, build up in coa.st,al condensers, especially problematic during tbc sunirncr montbs.

403

Li.n,cti,r Model (‘qrn.1) T,inea.r foiiling i - r q be included to represent unidentifiable deposits that arc not represented by the otlrcr sub-models. It may also be employed when the operat,or is unavare of what fouling processes are a.t work. Even wit,h the simple linear sub-model t,he composite niodcl can wary its weighting to rcprc sonal changes in fouling, which is still a dramatic improvement over the conventional linear fouling model.

Exponential Model (sms) An exponential model m a y be employed t>orepresent, air ingress int>othe midcnscr. It is lrnown that trhc prcscncc of a.ir can drast>icallyreduce condtmser performance by reducing lieat) ixmsfer t>ot>liecooling wat,er. For examplc, an air blanket of 1 mm is equivalcnt~t,o a slab of copper 16.5 In thick. It was remarked by Putmari (2000) that the thernial resistance of entrapped air in t.he condenser has an almost exponmt,id effect on heat traiisfer.

3.2 Pal-anreter. Selection Given t,hat there a,re several sub-models each with their own unknown parameters a i d weight~s it is initially assumcd that, all the sub-modcls arc cqually wcig1it)cd. antl tlrc cocfficicnts for each sub-model, A, and B,, are chosen so tjliat, each sub-model produces zero foiding at, zero t inic, ~ ~ & ~,. , In and a, thermal resistance, T ~ ~ ,at,. tirnc Figure 2 t,he target end point is represented by point. A , where rtargetis the annual accurnulat~ed fouling under normal operat,ing condit~ions.

t,o derrioiist,rate the strengths of t,he composite modelling process. Visual inspect,ion of t~liecondenser during routine cloaning idcntified t,wo scpa.rat,e fouliiig t,ypcs as beirig pretloinina.rit, Duriiig the waruier rrioiit,lis, organic fouling due t>osea mussels restricts cooling wat,er Bow, an(l during the wint,er, silt.ing on condenser tubes reduces heat, iransfer. In t,he composite model, these fouling mechaiiisms are represented by submodels s7n2 and s n ~ ,3 m-here sm,2 corrcsponds t,o the t,licrmal rcsistsncc of a weakly boiidecl low temperature deposit. In submodel s m 3 the depositmionrate is alm-ays greater that>t hc rcmoval rate, a result of thc parliculat,e nat.urc of organic fouling.

Is was determined, based on recorded LhITD (log mean temperat,ure difference) data, €rom t,he power st,at.ion and extrapolated over t,welve mont,hs, that the fouling resistance increased by almost. t,wo thirds in a year. Assuming, r,leala.the therante of t,lic coiiticnscr whcii clean is m’K/W, the target)re 40 x m’K/W. Figure 3 plots tpheestimated thcrnial rc;sist,anccsfor thc: t,wo sub-models over a. Lwelve riiori(,h period.

p is t,o allocate weights t,o each submodel. Aga.in t>osimpli€y select>ion,weigh1.s are either maiiitaincd constant, or varicd t,o reflect. sc~sorialvariations. It) was ,judged that a gaussian funct,ion, g ( l ) , or t,he form,

Fig. 3. Coastal Power Station Sub-Models where, cj, is the centre of t!he function, antl, F ? , is t,he spread or width of the function, would allow summer or aut,umn peaks t,o gent,ly fade with t,inic and rise again t,hc following year. In the following soct,ioii, this process of paramct,cr selection is illustmted by employing t,lie cxcmple of a costal power station.

The A a,nd B coefficients €or t>hethermal resist.ancc curves in Figure 3 were calculated bascd on t>hcassiimptjion that. the condcriscr is iiiit,ially clean. Ilence, both curves pass through t.he origin. Additionally, the target time was set at twelve mont,hs. T h e weights applied to each of the sub-models re-

flect,sthe impwt ca.ch has on t,he condenser. Sincc 3.3 Composite Model for Coa,stcrl Potucr Station,

This example utilises data froin a coastal power station on the north cast coast of Ireland. For commercial reasons, the specific plant performance details are not disclosed. This, however, docs not detract from tlic potential of tlic example

organic fouling. rcprcseiitctl by 57113, is afkxt~etl by sea water temperature then the sub-model weight., 7113, should reflect variations in t,he cooling wat,er inlet t,emperature. Dat.a collected from the plant, indicated t,hat, t,he cooling water t,emperat.ure peaked in late September, followed by a gradual decrease until a low in March. However, in the winter pcriocl of Novcnibcr tjo February,

404

- w3 Parltculate

o,9

-

0.7 3E 0.6 I

wliere C,, are performance relat,ed costs, C, are contract, related costs and C,, are direct ma,interiance costs. The negative sign applied to C, indicates an iiiward flow of revenue, compared t,o the remaining terms which m e all out,wa.rd expenditures. A full description of t,hese costs is dcscri1)ed by Crcgan and Flynri (2003).

-

0.3. 0.2.

Fig. 4. Coastal Power Station Sub-hlodel Weights Finally. c.orrhining the fouling resistance, r, . from Figure 3, aiid sub-model viieiglit5, wZrin Figure 4. rcsults in tlic wciglitcd fouling plot cli,r in Figure 5. This graph liigliliglits tlic strength of tlicl composite rriodcl bv dciiioiistiat iiig the nun-liiicar fouling cxpcctcd in t hc condenser.

The effect of the non-linear coniposit e fouling model is expressed in C, as the cost, of addit>ional fuel required to conipensat>efor condenser fouling. Thc comp1cxit.y of t,hc cost function is furthcr coinpouiitled by t.he many tliscoiitiiiiious regions int,roduced by restrictions and fluctuations in the contract cost,s, Cc. For example, imit,s are given an availability payment and during a winter wcck day tlie payment. during peak t,irnes (4-7 pm), is foiir times greater t.han that, al; riiglit t.irne. The aim of the cost function is to determine the operating cost, based on a specific maintenance schedule. Many of the parameters assocjat,ed wit,h arc fixed, for examplc, the physical dimensions of the condenser, heat load, etc. while others arc wsiable - fouling rate, opera.ting times, niaint,onancc tinics, ctc. In ordcr to find a lmst, cost rriaiiileriarice scliedule only (,lie rriairileria.rice t,inies should he perrnit,ted t>ovary while t,lie ot,her parameters reiiiain constant. This will allow ail optimisat,ion routine to utilise the cost funct,ion in it,s search for least cost solutions.

5. MAINTENANCE SCHEDULING

2006

Fig. 5. Coastal Power Station Sub-Model Fouling The umisual ‘hump’which occiiis during Februaiy niid LIarcli is prirri
4. OPERATING COST FUNCTION

From a, qualit~ativcanalysis it, has kxen det,crmined that, a contiensor’s operating cost,, C C o T l d . is t>lie s l i m of three distinct wmponents such that,

Advnnces within the domain of condenser ma.intenance have been very limited Ma & Epnteiri (198l),and more recently, Wolff, et. al. (1996) approached the problem by applying mixed integer linear programming (hIILP). This technique, like most others, breaks down when large discontinuities are encountered in tlie cost function. Alternatively. tlie success of genet,ic a1gorit)hms (GA) with NP (noii-d rrninist,ic polynomial) t>ypcsr:hcduling problniiis such a.s t,hc ‘t,ra,vclling salesman’ is well documented. The GA eiiiploys an intdligent, search of a h r g e hut firiit,e soliition space, wliich converges towards minima.. Nonlinearities or discontinuities in the cost. funct,ion do not significant>lyhinder the search. Using hlatlah’s graphical interface and toolboxes: a n integrated software package was creat>edfor the power shlion. By employing a s l a n d a d binary encoding chromosome t,o represent, rnairit,enance schedules. Each schedule evaluatsed by tlie cost function would return an estimate for the operat.ing cost over a specific period such t,hat, maintenance cost. = f ( t 1 , t 2 .

405

where N is tlie niiiiiber of oiitages and t is the time between maintenance outages.

The GA optimisation routine u.oiild search for soliit,ioiis using tlic cost, function and presentj t,o tlie operator a raiige of kmt, cost, solutixis a s illustra,ted in Figure 6. The bar chart, presented in this grap1iic:al user interrace liiglilight~st-he t o t d cost for each schedule by combining the maintenance, contract and perforniance costs. For this example the least cost soliition generat,ed by the CA rccommcnds a iivc out~agcschcdulc. b'.. ,'

A

d

HmtenmnrL S*Ldulmm

approaches, where many of t,hese subtle differences would go iinrecognised, the composite model can identify the significant, effect. of changing sea and air temperatures on condeiiser fouling. Wlien planiiing future rna.iiiteriarice scliedules identifying variations in condenser fouling can especially wlien iiit,egrated into an overall cost^ function. By combining cont,ra.c:tual, performance and rriaintenance costs into a single function, it is then feasible to search for minima. Howcvcr, thc process of opbimisation, wl-lerc. least, cost so1ut)ioiisare located, tlepends great,ly on the complexit,y of t,he cost) funct,ion.

.

It hiis been denionstrat ed t,liat dcspitc the cornplexities of the cost fimct>ion,stja.ndardGA algorithms are able t,o effectively search and return valid, least, cost,, condenser niaint,enance schedules. T&%h these solutions the key times and schedules are quickly highlighted. permit.ting a well informed decision on fiitlture maintenance.

REFE,RENCES Fig. G. Scheduling Costs Operator Display By selecting onc of the schcdulcs in Figure 6 tlic opcraior is ihlc? to analysc in detail a.ny of the range of possible solutions. In this example Figure 7 plots a breakdown of component costs against time for the five outage schcdulc. - Combined (Cmo,) o.5.

- - Performance(cJ (CJ - - Contract Maintenance(Cm) ,

Feb. Mar. Apr. May h 11

i2

e July pug. Sap. Oct. Nbv. Dec. Jan. 2o06

t3

14

t5

Fig. 7. Component Cost,s for Opt,irniim Schcdule Furtlier opt.ions in software permit. existing planned oiitages to be incorporated by fixing t,he time of one or more outages. In each instance t,he program highlights a range of opt,irnal scheduling solut,ions.

6. CONCLUSIONS The composite fouling model presented enables the noii-linear antl time dependent variations in condenser fouling to be reprotliiced antl quant ificd. Compared with convcntional linear modelling

BiLnsal, B. a n d H. Midlcr-St.einliagac1??ii(1993). C:rystallizat,ioiifouling in plate heat, exchangers. ASWE +J. Heut Trmsfer. 115, pp. 584591. BET (1991). Modern Power Sta.tion Practice. Perganion Press, London, UK. Crcgan, nl.and D. Flyrin (2003). Condenscr maintenance cost optimisation using genetic algorit,lims. IFAC Puuier Plants and Power Syst e m Control Con~fSeoul, Korea. Kern, D.Q. and R.E. Scaton (1959). A t.heoret'ica1 analysis of tlierrrial surface foiiling. Cli,errrical ETLY.,4(6). pp. 258-262. Kha.n, M.S., SAL. Zuba.ir, M.O. Biida.ir, A.K. S1ir:ikh and A. Qutidus (1996). Fouling r e sist~mcemodel for prediction of C n C 0 3 scaling in AIAI 316 t.ubcs. Heat Muss Tmn.sfer, 32, pp. 73-80. 1CIa, R,.S.T. and W. Epstein (1981). Opt,imum cycles for falling rate Ixocesses. Cu,nadinn J . Chemical Eng.. 59, pp. 631-633. h/ruller-St,eirihageri, H., F. Reif, N. Epsteiri arid A.P. Watkinson (1988). Influeiice of operating conclit,ionson particiila.trefouling. Can,. JUYT. Cficrri. Erg., 66, pp. 42-50. I'utman, R (2000). Steam Surjnce Condensers. ASME. Wolff, P.J., P.A.March and 1I.S. Pearson (1996). Using condenser performance measurements to optimise condenser cleaning. EPRI Heut Rute Con,! Dallas,USA. Zubair. S. hl.. A. K. Sheikh, hl. Younas and M.O. Biidair (2000). A risk based. lieat exchanger analysis subject, t,o fouling - part 1 - performa~nccevaluation. Errer

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Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLlCATlON$

A MULTI-AGENT SYSTEM-BASED REFERENCE GOVERNOR FOR MULTIOBJECTIVE POWER PLANT OPERATION

Jin S. Heo and Kwang Y. Lee

Department of Electrical Engineeuing, The Pennsylvania State University, University Park, PA 16802, U.S.A. (email:juh [email protected]) (email: kwunglee@jpsu,edu)

Abstract: A large-scale power plant requires optimal set-points, namely references, for optimal operation. In a 600 MW oil-fired drum-type boiler power unit, the set-points considered are for the main steam pressure and reheaterhperheater steam temperatures. Thc set-points should bc mapped with varying unit load dcmand and satisfy the conflicting operation requirements of the power plant. The conflicting requirements are tackled by multiobjective optimization problem to produce the optimal mapping. In general, the set-points obtained by using a fixed nonlinear function cannot provide optimal power plant operation. This paper presents a methodology, Multi-Agent Systembased Reference Governor (MAS-RG), to realize the optimal mapping by searching for the best solution to the multiobjective Optimization problem. In searching for the optimal set-points, a heuristic optimization tool, Particle Swarm Optimization (PSO), is utilized to solve the multiobjective optimization problem. Moreover, the approach provides the means to specify optimal set-points for controllers under a diversity o f operating scenarios on-line. Copyright 02006 IFAC Keywords: Reference governor, multi-agent system, multiobjective optimization, power plant control, set-points, particle swarm optimization.

1. INTRODUCTION While the demand in power is increasing, powcr plants are getting more complex and expansive to run. Power plant is a large-scale system consisting of many subsystems. It is no longer the best solution to manage the large-scale system by using only strictly centralized or loosely decentralized schemes. The data processing and operational requirements of the large-scale system have been excessive, especially for optimal operation. Moreover, it has been challenged to generate power while minimizing loadtracking error, fuel consumption, heat loss rate and

pollutant emission, and maximizing duty life on equipment. Recently, there has been a growing interest in MultiAgent System (MAS) to deal with the complexity and distributed problems in power systems. Each agent system has special functions to solve the distributed problems. Moreover, in the multi-agent system the agents can work together to solve problems, which are beyond the capabilities or knowledge of an individual agent (Woodridge, 2002). On ilie other hand, a modern heurisiic method, Particle Swarm Optimization (PSO), has become a favorite topic for multiobjcctivc optimal power plant

407

Fig. 1. The large-scale power plant model and MAS. operation (Heo, et ul., 2005). The PSO provides high quality solution with simple implementation and fast convergence as reported in many references (Kcnncdy and Eberhart 1995: Lce and El-Sharkawi, 2002; Park, et al., 2003). In the power plants, the optimal operation can be achieved by various approaches such as optimal control, optimal set-points scheduling, and other optimal techniques for the power plant (Ghezelayagh and Lee, 2002). In a small-scale power plant, which is a low-order system, the optimal set-points can be obtained by analytical approaches (Gaduno-Ramires and Lee, 2001). However, a large-scale distributed powcr plant rcquircs gcncrating optimal sct-points using an intelligent method such as MAS. The MAS is described as a group activity of individual distributed intelligent agents (Wittig, et al., 1994). This paper presents a methodology, Multi-Agent System-based Reference Governor (MAS-RG), to realize the optimal mapping between set-points and varying unit load dcmand by searching for the best solution to the multiobjective optimization problem. The set-points considered are for the main steam pressure and reheated superheater steam temperatures in a 600 MW oil-fired drum-type boiler power unit. The optimal set-points are determined by solving the multiobjcctive optimization problem with conflicting requirements such as load following, fuel conservation, life extension of equipments, reducing pollution, etc. Following the introduction, the power plant and Multi-Agent System (MAS) are described in Section 2. Section 3 describes the Multi-Agent System-based Reference Governor (MAS-RG). Section 4 shows simulation results to demonstrate the feasibility of the proposed approach. The final section draws some conclusions. 2. POWER PLANT AND MULTI-AGENT SYSTEM

2. I

Description oJ'Power System (Usoro, 1977)

The power plant is a 600 MW oil-fired drum-type boiler-turbine-generator unit It is a balanced draft, controlled recirculation drum boiler capable of delivering 4 . 2 ~ 1 0Ib/hr ~ of steam at a pressure of 2600 psig and at 1005°F. Six recirculation pumps supply the required recirculation flow to provide sufficient flow for full load operation. Two forced draft fans supply the primary air, and two induced draft fans are controlled to maintain a furnace pressure at a desired pre-set value. Two condensate pumps, a combined booster and main boiler feedpumps handle the feedwater flow. The turbine is a tandem compound triple pressure steam turbine. It consists of three parts: a highpressure turbine, an intermediate pressure turbine, and low twin pressure turbines rotating on a common shaft at a ratcd spced of 3600 rpm and exhausting pressure at a 2 inch Hg absolute. The generator is coupled with the turbine and has a 685,600 kVA, 3 phase, 60 Hz, 22 kV, with a power factor of 0.90. In this paper, the model has twentythree state variables and twelve control valves ( u,,u2,...,u12) associated with physical processes. The control valves are named as following: u i : fuel flow, u2: gas recirculation, uj: induced draft fan, uq: forced draft fan, u5: combustor gun tilt, u6: superheater spray flow, u7: reheater spray flow, ux: governor control valve, u9: intercept valve, uI0: deaerator valve, u I I : feedwater valve, u/z: feedpump turbine flow. The model is reorganized into four main modules, which are boiler system, turbine-generator system, condenser system, and feedwater system. The proposed MAS-RG is one of the functional systems based on multi-agent sysieiri which is inlercoiinected with the distributed subsystems that are components of thc four main modules. Fig. 1 shows thc largcscale distributed thermal power plant model and MAS. The proposed scheme will be applicable to other types of plants, including nuclear and fuel cell plants.

408

2.2

Multi-Agent System

An agent is a computer software program that is autonomous and situated in some distributed environments to meet its design objective (,Padgham and Winikoff, 2004). Since the agents are faced with different environments, they are designed differently and properly for the given environment. Moreover, the agent is intelligent because it is reactive, proactive, social, flexible, and robust. In a large-scale distributed complex system, the agent's autonomous and intelligent properties can reduce the complexity by reducing the coupling problems between the subsystems (Gupta and Varma, 2004). Furthermore, the proactive, reactive, and robust properties can be well suited for applications in a dynamic and unreliable situation (Hossack, et al., 2003, McArthur and Davidson, 2004, Zhang, et al., 2004). In order to design the MAS-RG, design of architectures for a single agent system and an organization for multi-agent system are required in advance. First, the architecture of a single agent system is shown in Fig. 3. Since the agent is situated in an environment that is the power plant, it needs a perceptor and effecter to act and react (Junpu, et al., 2000). First, thc senscd raw data arc processed and mapped into a scenario, and then an objective, which is a sub-goal, is initialized under the situation to achieve the main goal that is the optimal operation. The initial objective is sent to other agents through the communicator for eliminating redundancy and conveying the mission of the agent to others. After confirming the objective, the best plan i s chosen for the objective (sub-goal) in decision-making. Depending on the plan, an algorithm module is selected to launch the plan. Finally, the action made by the algorithm module effects through the effecter into the environment. Most decisions are made in the decision-making process, which i s like in a human brain (Heo and Lee, 2005a). A Multi-Agent System (MAS) can be defined as a loosely coupled network (organization) of problem solvers (agents), which interact with each other to solve problems that are beyond the individual capabilities or knowledge of each problem solver (agent). In order to perform the cooperative works, it is presented to build multiple hierarchical structures for the multi-agent system organization as shown in Fig. 4. The organization has low level, middle level,

Fig. 3. Single agent architecture.

Fig. 4. Organization of MAS.

Fig. 5. Composition of MAS for the power plant. and high level, and agent iii each level has a specific role in the society so that the agents pursue their tasks by the proactive property. In this paper, the high level agent is the task delegation and interface agcnt, thc middlc lcvcl agcnts arc thc mcdiatc and monitoring agents, and the low level agents are intelligent agents. The hierarchical structure that has three levels gives advantages for dynamic organization and autonomous systems (Kosakaya, et ul., 2003, Velasco, et ul., 1996). Moreover, the idea of multiple hierarchical structures is well fitted for the large-scale distributed system. Although there are multiple hierarchical structures, each hierarchical structure has a different formation from the others becausc thc structurcs arc constructed to fit for operating each real physical subsystem so that the organization is better optimized for the given power plant.

3 . MULTI-AGENT SYSTEM-BASED REFERENCE GOVERNOR With the proposed architectures of single agent and multi-agent system, the MAS-RG is developed to obtain the optimal mapping between set-points and varying unit load demand. The composition of MAS for the power plant is shown in Fig. 5 , where the functionality of individual agents is explicitly defined. In this paper, the reference governor cluster system will be mainly discussed. However, the functionality of individual agents is introduced in other paper [Heo and Lee, 2005al. Although all agents are connected with network, the reference

409

governor cluster, which is made of set-point generation agent and steady-state model agent, performs mainly for the MAS-RG. However, the refercnce governor cluster will cooperatc with the monitoring system, knowledge processing system, and reinforcement system clusters to obtain better performances. An operator will command and monitor the preference and status through the interface agent toifrom the reference governor delegation agent who has all access for the MASRC. In order to realize the MAS-RC, first, all feasible operating points, which satisfy all imposed constraints, need to be found using the on-line performance monitoring agent and virtual simulation agent. The virtual simulation agent simulates the power output responses with various set-point conditions. Since system response is in steady-state, the constant control inputs and static power, pressure, and temperature outputs become a pair of operating points. However, the admissible power outputs can be obtained within an appropriate steam pressure and reheaterisuperheater temperature ranges. Fig. 6 shows the power output responses with different steam pressure and reheaterisuperheater temperature values for 450MW power set-point. This implies the same power output can be obtained with different steam pressure and reheatedsuperheater temperatures. During the simulation by the virtual simulation agent, the on-line performance agent evaluates the operating points in order to find the admissible power, steam pressure, and reheated superheater temperature operating points. The power-pressure operating window is obtained in Fig. 7. The reheaterisuperheater temperature operating range is 1359.67"R-1459.67"R (900°F-1000°F) for all power ranges. Since the design and operation of reheater are essentially the same as the superheater, we decide that the reheater and superheater temperature setpoints arc equal. Fig. 8 shows thc powcr-control input operating windows. When pressure and temperature are changed, control inputs ( ul,u*,..., uIZ ) are varied to produce the desired power output. The gap between the upper and lower limit is obtained by changing the pressure and temperature within the operating windows.

Power plant condition might change as the plant agcs, in which case, the updating o f MAS-ISSMs 500 480 460 440

5 420 400

4 0

100 200 300 400 500 600 700 800 900 1000 time (sec)

Fig. 6. Power output responses with various set-point conditions for 450MW set-point. 3000 -

-

2800 -

~

~

-

2600 -

p 2400v)

4 2200 -

5

g a

2000-

1800-

~

1600-

-

-

-

1400} 1200 I

1

upperlimit lower limit 150 260 2kO 300 350 400 i 5 0 500 550 600 Power (Id1W) ~

-

looo'

-

Fig. 7. Power-pressure operating window.

In order to find the set-points of power, pressure, and temperatures, the next step is the development of the steady-state model using the steady-state model agent. The main algorithm module of the steady-state agent is Neural-Network (NN), which is the best approximator for nonlinear systems. The steady-state models are called Multi-Agent System based Intelligent Steady-State Models (MAS-1SSMs) (He0 and Lee, 2005b) and expressed as follows: Powev: Ed =$, ( u , , u2,...,u12)

(1 ,a)

Steam pressure: pd = $2 ( u , ,u 2 ,...,u 1 2 )

(Ib)

Re heater / Superheater temperatures: ) RT, =STd = & ( U , , U ~ , . . . , U ~ ~ (1,c)

Fig. 8. Power-control input operating windows. 410

I

I

takes place after checking the difference between previously obtained operating data and current output data that are generated under the same condition. With the operating windows and MAS-ISSMs, the multiobjective Optimization problem can be tackled by the set-point generation agent and the cooperation of other agents. In this paper, the objective functions are accounting for the minimization of load-tracking error, fuel consumption, heat loss rate, pollutant emission, and extension of duty life on the equipment. Thus, the objective functions are J,(u)=lE,,,,

-EJ, J, =ul, J, =-u2, J , = u 3 ,

J, = - u ~ , J , = -us, J, = u,, J , = u,, J , = -u*, (2)

J9 =-u9, J 10 =-u 10'

Jll

=-%I,

J12 = -12

'

where, Euklis the unit load demand and the decision variables ( u ) are control variables as shown in Fig 1. When the unit load demand, Ezt,dis given from a central dispatch centre, the set-point generation agent creates the solution space, R,,R2,..., R,,, using the power-control input operating windows, Fig. 8. An operator commands the objectives and their preferences for the multiobjective optimization problem through the interface agent. The reference governor delegation agent adjusts the preference values by investigating the condition of power plant with historical data. After confirming the preference values, the multiobjective optimization problem i s solved by Particle Swarm Optimization (PSO), which is one of the algorithm modules in the setpoint generation agent. During the search for the solution, one of the MAS-ISSMs, Ed = 4, (u,,u, ,..., u,, ) , is utilized to evaluate the load-tracking error. The PSO algorithm is well suited for the reference governor because of the simple implementation, quality solutions, and the fast convergence. The performance monitoring agent evaluates the performances produced from the setpoint generation agents which utilize different optimization techniques. The detail comparison of the performances are shown in other references (Heo, et al., 2005).

Unit load demand E,,

I

Objective and preference

Fig. 9. Configuration of MAS-RG Casc 2: minimize J,(u),J,(u),J 2 ( u ) Case 3: minimize J,,(u),J,(u),J 2 ( u ),..., J,,(u) The objective functions are given in (2) and a vector of preference values is given as p = [1, 0.25,0.25,0, 0,0,0.25,0.25,0.25,0,0.25,0.25,0.25]. The demand power ( E,, ) is almost the same as the unit load demand as shown in Fig 10; however, the conflicting requirements cause slight difference between the demand power and the unit load demand. The demand pressure set-points ( Pd ) mapped for different number of objective functions are quite different as shown in Fig. 11. This is because the power-pressure operating window is quite large and the same amount of power can be produced on a wide range of pressure as shown in Fig. 7. Similarly, the demand reheaterisuperheater temperatures are shown in Fig. 12. As additional objective functions are added in the optimization, the plant is operating more conservatively in lower pressure and temperatures. Thus, all simulation results show that the MAS-RG can perform well in the multiobjective optimization problem and also in the on-line implenieniaiion since the pressure, ieniperatures setpoints need to be updated only when the unit load demand i s changed during the load cycle. Unit load deman

580

~

1

After finding the optimal solution,

U;

u ; , . . ., u;*

0

using

the PSO, the MAS-ISSMs are applied to map the optimal solution into demand power ( Ed ), steam ), reheater temperature ( RT, ) and pressure ( superheater temperatures ( ST, ) using (1). The setpoint scheduler block processes the task under the observation of set-point generation agent. Fig. 9 shows the configuration of MAS-RG.

100

200

case? - Case3

300 400 500 time (sec)

600

700

Fig. 10. Demand power set-point trajectories.

Case1

case:

2600

- - Case3

- 2500 m

-$

~

0 m ~

2400:

m

2? a

4. SIMULATION RESULTS

2300

2200 -

In the following, thc results of the MAS-RG will be shown. Simulations deal with three different cases:

2100 0

I

100

200

300

400

t 500

600

700

time (sec)

Case 1 : minimize J,(u) only

Fig. 11. Demand pressure set-point trajectories.

41 1

13901

0

100

200

300

400

500

600

700

time (sec)

Fig. 12. Demand reheatedsuperheater temperature set-point trajectories. Morcovcr, distributcd computing, which is thc advantage of the MAS, rcduces the computing time for on-line implementation. 5. CONCULSION

The Multi-Agent System (MAS) reduces the coupling problems of subsystems by intelligent dnd dsynchronous computation The MAS-RC gcncratcs the optimal mapping by searching for the best solution to the multiobjective optimization problem. The optimal mapping? between the varying unit load demand and the power, steam pressure and reheatedsuperheater temperature set-points are realized in an on-line implementation with the help or MAS. As one or the algorithm modulca, PSO is well suited for finding optimal solution in the multiobjcctivc optimization problcm In thc largcscale distributed power plant, the MAS-RG methodology shows good performances REFERENCES Decker, K. S. and Sycara, K. (1997). Intelligent adaptive information agents. Journal of Intelligent Information Sys., 9, pp. 239-260. Garduno-Ramirez, R. and Lee, K. Y. (2001). Multiobjective optimal power plant operation through coordinate control with pressure set point scheduling. IEEE Trans. on Energy Conversion, 16, (2),pp. 115-122. Ghezelayagh, H. and Lee, K. Y. (2002). Intelligent predictive control of a power plant with evolutionary programming optimizer and neurofuzzy identifier. Proc. Congress on Evolutionary Computation, 2, pp. 1308-1313. Gupta, R. P. and Varma, R. K. (2004). Agent based software integration at distribution control center. IEEE PES General Meeting, PESCM2004000930.PDF. Heo, J. S., Lee, K. Y. and Garduno-Ramirez, R. (2005). Multiobjective optimal power plant operation using particle swarm optimization technique. Proc. IFAC Congress, paper code: 04833.pdf, Tu-M06-T0/4, Prague. Heo, J. S. and Lee, K. Y. (2005a). Multi-agent system-based intelligent control system for a

power plant. IEEE PES General Meeting, CD,PESGM2005-000858.~df. Heo, J. S. and Lee, K. Y. (200Sb). Multi-agent system-based intelligent steady-state model for a power plant. Pvoc. the 13'" International Conference on Intelligent System Application to Power Systems (ISAPOS), Washington D.C.. Hossack, J. A,, Menal, J., McArthur, S. D. J. and McDonald, J. R. (2003). A multiagent architecture for protection engineering diagnostic assistance. IEEE Trans. on Power Systems, 18, (2), pp. 639-647. Junpu, W., Hao, C., yang, X. and Shuhui, L. (2000). An architecture of agent-based intelligent control systems. Proc. the 3"' World Congress on htelligent Control and Automation, pp. 404-407. Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. Proc. of IEEE internutional Confkrence on Neurul Networks (ICNN'95), LV, pp. 1942-1948, Perth, Australia. Kosakaya, J. Kobayashi, A. and Yamaoka, K. (2003). Cooperative multi-agent-based control technology for supervisory control and dataacquisition systems. Proc. Emerging Technologies and Factory Automation Conf:, pp. 19-26. Lee, K. Y. and El-Sharkawi, M. A. (Editors). (2002). Tutorial on modern heuristic optimization techniques with applications to power systems, IEEE Powcr Engincering Socicty, IEEE Catalog Number 02TP160, Piscataway, NJ. McArthur, S. D. J. and Davidson, E. M. (2004). Multi-agent systeins for diagnostic and coiidition monitoring applications. IEEE PES General Meeting, PESGM2004-000972.pdf. Padgham, L. and Winikoff, M. (2004). Developing intelligent agent systems. John Wiley & Sons, New York. Park, J.-B., Lee, K.-S., Shin, J.-R. and Lee, K. Y. (2003). Economic load dispatch based on a hybrid particle swarm optimization. Proc. International Conference on Intelligent Systems Application to Power Systems, CD ISAP03070.pdf, Lemnos, Greece. Usoro, P. B. (1977). Modeling and simulation gf a drum-turbine po wer plant under emergency state control, M.S. Thesis, Massachusetts Institute of Technology. Velasco, J. R., Gonzalez, J. C., Magdalena, L. and Iglesias, C. A. (1996). Multiagent-based control systems: a hybrid approach to distributed process control. Control Engineering Pmctice, 4,(6), pp. 839-845. Wittig, T., Jennings, N.R. and Mamdani, E.H. (1994). ARCHON: framework for intelligent cooperation. IEEE Trans. on Intelligent Systems Engineering, 3, (3), pp. 168-179. Wooldridge, M. (2002). An introduction to MuEtiAgent systems. John Wiley & Sons, Chichester, UK. Zhang, Z., MaCalley, J. D., Vishwanathan, V. and Honavar, V. (2004). Multiagent system solutions for distributed computing, communications, and integration necds in thc power industry. IEEE His' General Meeting, 1, pp. 44-47. 412

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ADAPTIVE GOVERNOR CONTROL AND LOAD SHEDDING SCHEME FOR AN INCINERATOR PLANT

Y. D. Lee"", C. S. Chen"",C. T. Hsub3' aNationalSun Yat-Sen University, Kaohsiung, Taiwan bSouthern Taiwan University of Technology, Tainan, Taiwan

Abstract: This paper presents an adaptive control strategy for the governor system of an incinerator cogenerator to maintain the steam pressure and system power frequency. Due to the unstable steam generation in incinerator plants, the turbine valves have to be controlled adaptively to keep the boiler steam pressure constant for normal operation. After tie-line tripping caused by utility faults, the governor system must be operated with constant frequency control for the islanding system. By this way, the surplus steam supply to turbines will be bypassed effectively. For the islanding operation, the deficiency of steam generation is then supplemented by boilers. To maintain thc system stability after transient disturbance for the isolated system, the load shcdding scheme is designed by considering the under steam pressure protection. According to the transient stability analysis, the system frequency can be restored successhlly after tie-line tripping with the adaptive change of governor control system from the constant steam pressure mode to the constant frequency mode. Copyright 020061FAC Keywords: Governor control system; boiler; cogeneration system; load shedding; transient stability

1 . SYSTEM DISCRIPTION

T

o study the effectiveness of governor controller

for cogenerators with unstable steam system, an incinerator plant in Taiwan with three sets o f boilers and an extraction-condensing type of turbine gencrator as shown in Fig. 1 was selected for computer simulation using CYMSTAB sortware package. Different from conventional cogeneration systems of industrial customers, all steam generated from the incinerator boilers is exhausted by the turbine generator, and then condensed as the feed water for boilers. The power output of the incinerator cogenerator varies with the steam generation according to the amount o f refuse burned. Due to the variation of heat value in the trash, the steam flow generated by incinerator cogeneration will fluctuate very seriously. Therefore, the governor control system of the turbine has to be operated with

constant pressure control to maintain the boiler steam pressure for normal operation. For the severe fault contingencies of external Taipower system, cogeneration systems are normally isolated by opening the tie-line breakers, and the governor systems of cogenerators are adaptively changed to the constant frequency control to prevent the isolated power system from collapsing. With the unstable steam generation, it becomes very difficult to control the stearn pressure arid system frequency for the isolated cogeneration. In this paper, an adaptive governor control system for the turbine generator has been presented to maintain the stable operation of the incinerator cogeneration system.

"Corresponding author.

I l l

Tel: 886-7-5256436; fax: 886-7-5256436. E-mai 1 address : D93X 1001 3(as t uden t . n s y s u . edu . tiv

ydl ccl216@yahoo. corn. t n ' Member, IEEE.

Fig. I . Incinerator cogeneration system.

413

2. GOVERNOR SYSTEM MODEL WITH BOILER DYNAMICS

3. THE MATHEMATICAL MODEL OF THE INClNERATOR COGENERATlON SYSTEM

The governor system model with boiler dynamics for the incinerator cogeneration system is represented as shown in Fig. 2. The dynamic change of steam flows generated by boiler systems affects the power output of the cogenerator, which can be calculated as the product of the valve flow area x2 and the throttle pressure x4 of steam inlet. The valve flow area can be controlled by the governor system so that the turbine inlet pressure will be proportional to the integral of the net inflow passing through the tube of distributed superheater. Ksir is the friction coefficient of the tubes in the superheater, and KDis the overall storage volume coefficient of the boilers. Both parameters dominate the time response of incinerator boiler systems. The steam pressure drop from drum to inlet turbine is represented as the square of mechanical input power P,,,. The steam generation of boiler Qn is determined by the heat release in waterwalls depending on the amount of trash burned. Instead of considering the fuel dynamics and the boiler control systcm, thc stcam flow Qn directly controllcd by operators can be considered as the input variable of this model. The turbine power output can be derived according to the dynamic steam flows measured by the distributed control system (DCS). T I , T2, TCHare the time constants of the speed relay, servomotor and steam chest of the turbine, respectively. For constant pressure operation of the governor controller WOODWARD505, the PID frequency controller is cascaded by the PID pressure controller. By this way, the speed reference Q , ,can ~ be adjustcd to maintain the constant steam pressure of header according to the variation of steam flows, and the power output of cogenerator is independent of the system frequency fluctuation. For constant frequency operation, the PID pressure controller and the frequency droop controller R1 are deactivated as shown in Fig. 3. The speed reference is then set equal to the actual speed, and adjusted automatically to reach the synchronized speed with rate change of 2rpm per second.

Table 1 lists the parameters of the incinerator cogeneration unit, which were provided by the manufacturer, or obtained from performing the field test. The typical values were used for the time constants of the servomotor of govcmor systcm and the steam chest of turbine. The coefficient of steam pressure drop KSM was estimated based on the calculation of fluid dynamics for the incinerator boiler systems. The parameter KU was derived from the dynamic relationship between steam pressure of header and total steam generation. The parameters of PID frequency controller of the governor system were tuned for the possible maximum load rejection to maintain the stable operation of the incinerator cogenerator. To develop the better system analysis with the above parameters of the cogeneration unit, the governor system model with constant pressure control in Fig. 2 is linearlized as shown in Fig. 4. The output u of the controller is calculated in Eq. (1). The transfer function is expressed as Eq. (2), and the corresponding parameters H are solved by Eq. (3), (4), (5) and (6), respectively with constants A, B, C, D calculated as follows. By the same way, the mathematical model of the isolated-incinerator cogeneration system with constant frequency operation is linearlized as shown in Fig. 5. The corresponding state equation of the system can be represented as Eq. (7). Table 1 Parameters of the cogeneration unit

Gen

kV MW 1 1 9 54 X.' q

and Boller ~~~~~~~~~

ZdO

H Xd X, Xd 8 1 9 6 4 1 0 8 0257 &,I 0 z,o U, dU 1 5 0031 008 0 1 2 TCH Vnlax V,,, RI 02 10 0 005

X, 06 SGI 2

02

654

TI 005

Tz 005

Dl

R2

p2

I2

D2

KD

KSH

04

0

4

01

0

001

025

06 PI

4

X d

0 169 D 1 11 1

I

Fig. 4. Linearlized governor system model for constant pressure operation. mnom NIW

Fig. 2. Pressure control of governor system model.

., I'IIl1n !\

l r l l l l \I111

k, '

1,111

,,I,,,

111,1

rT,

1

Fig. 3. Frequency control of governor system model.

414

Fig. 5 . Linearlized governor system model for ation.

For an actual remote fault of external Taipower system without causing the tripping of tie-line, the dynamic rcsponse of systcm frcqucncy has bccn monitored as shown by line 1 in Fig. 6. To maintain a constant steam pressure, the speed reference of governor controller has been adjusted accordingly with the change of system frequency as shown by line 2. Figure 7 shows the steam flow of the header and power generation of the cogenerator. It is found that the power generation of the incinerator cogeneration system can be adaptively controlled by constant pressure operation o r the governor system with the variation of system frequency and steam flow.

[

I . System frequency 2.Speed reference setting

58.6Hz and 61.5Hz, the governor system is operated with constant pressure control to maintain the steam pressure for the unstable cogeneration system. The rotor speed of cogenerator is varied with the system frequency because of rather large inertia of the external Taipower system. To prevent the cogenerator from operating with undesired speed to cause the damage of the turbine, an over frequency relay 81H with setting at 62.5Hz and an under frequency relay 81L with setting at 58.6Hz are installed at the tie-line. The electrical signal for turbine tripping is also used with frequency setting at 63Hz to coordinate with the over frequency protcction for tic-linc tripping. Additionally, thc governor control strategy is designed to adaptively change to the frequency control when the incinerator plant exports the surplus power to Taipower with system frequency operation over 61.5Hz. After tie-line tripping, the power output of cogenerator has to be adjusted rapidly to accommodate the in-plant local load by frequency control of the governor system. At the same time, the fluctuated steam pressure of boiler header is controlled by bypassing the excessive steam, or activating the load-shedding scheme proposed in Table 2. The turbine bypass valve is controlled with setting at 1.08 times of the normal operating steam pressure for thc boilers. On the other hand, the loadshedding scheme is designed to maintain the boilcr steam pressure to be higher than 0.92p.u for the normal operation of the turbine. The total amount o f load to be disconnected is determined by the minimum generated steam flows and the maximum electrical load served by the incinerator plant.

Table 2 Load shedding schemc Steam pressure (PA) 0.98

0.96

1

0.95 0.94

Time delay (sec) 0. I 0.1

0. i For every 10 second

Load shedding 3M W

2MW 2MW 1MW

5. EFFECTIVENESS OF THE GOVERNOR CONTROL SYSTEM Time (mm )

Fig. 6. Actual system frequency and speed reference sctting. h

2

8k1xo

I

1 Steam flow

2 Power generation

v

3

2165

2

'150

Ti e mi )

Fig. 7 . Steam flows ,?the Reader and power generation.

4. GOVERNOR CONTROL STRATEGY WITH LOAD SHEDDING DESIGN When the cogeneration system is connected to Taipower with system frequency fluctuation between

To demonstrate the effectiveness of the proposed governor control strategy and load-shedding scheme, the tie- line was disconnected intentionally to test the islanding operation of the incinerator plant with different operation scenarios. Before tie-line tripping, three sets of incinerators arc operated with in-plant load of 8MW. The power output of cogenerator fluctuated between 2SMW and 32MW due to the unstable steam generation. By adding an extra heavy load of 27MW in the plant, the maximum power flow over the tie-line will be changed from exporting by 24MW to importing by IOMW. With the deficiency of power gcneration in the plant, the load shedding has to be cxecuted to maintain the steam prcssurc o f cogeneration system with constant frequency operation after tie-line tripping. Three different operation scenarios have been selected for computer simulation to solve the system response of the islanding incinerator cogeneration system.

415

C h e A. Small amount ofpower jlow,y over the tieline In this case, the power output of incinerator cogenerator is varied with the reduction of steam generation as shown in Fig. 8. The tie-line power flow is assumed to be changed by k3MW. Figure 9 shows the system frequency response of the incinerator cogeneration system with constant steam pressure operation after intentionally tie-line tripping. For the cogeneration system with exporting 3 MW to Taipowcr systcm beforc tic-linc tripping, thc isolated system frequency will be increased lo 61 H L , and then gradually decreased to 60.6Hz due to the governor control action. On the other hand, the frequency will be decayed to he less than 58Hz within a very short time for the operation condition of importing 3 MW from Taipower before tie-line tripping. It is found that the fluctuation of system frequency could result in the unnecessary load shedding or generator tripping if the constant pressure operation is implemented for the isolated incinerator cogeneration system. If the constant frequency control mode of the governor system is adaptively applied after tie-line tripping, the system frequency can be restored to 60Hz effectively as shown in Fig. 10 despitc of the dynamic fluctuations of power generation of cogenerator and steam pressure of boiler. Case 13 Steam generafionsurplus of the cogeneration system In this case, the power output of incinerator cogenerator is 32MW, and the total load demand for

the auxiliary boiler systems is 8MW, which implies that the imbalance of power generation and load demand will be 24MW. Figure 12 and 13 show the responses of system frequency and power output of cogenerator by applying the constant frequency control aftcr tie-line tripping for the islanding operation of incinerator plant. With such a large power generation surplus for the isolated system, the system frequency is increased to 62.8Hz during the reduction of power generation from 32MW to 8MW. The surplus steam is bypassed effectively to limit the steam pressure of boilers at 1.08p.u, and the system frequency was restored to 60Hz in 30 seconds. Case C. Steam generation dejiciency of the cogeneration system The power output of cogenerator and total in-plant load are 26MW and 35MW, respectively. Eigure 14, 15 and 16 show the system responses of the cogeneration system after tie-line tripping. Due to the dcficicncy of powcr generation in the plant, thc system frequency of the isolated system has dropped to the minimum value of 59.2Hz. The steam valve is opened to increase the power output of cogenerator to restore thc systcm frequency around 60112 by constant frequency operation. With proper control of the steam valve, the decay of steam pressure will result in the limitation of the turbine power output. By activating the load shedding scheme proposed in this paper, the steam pressure can be controlled to be stable at 0.94p.u, and the power output of cogenerator will be reduced to 25MW after one and half minutes.

20

40

T i ole( S

60

XO

I00

~ C )

Fig. 11. Frequency response of cogeneration system in Case B. -

-+3MW

GMW

-3h4W

35 + +

58

20

40

- --60

2 XO

25

2

--

20 15 1 0

5

-

0

100

I 1 mc ( 5 c < )

Fig 9 Frequency response for constant pressure operation in Case A 60.51

I-

SY.7

+3MW

- - GMW

-3MW

[

' , , ' ;,\

59.5

20

40

<

m

T i me sec 1

xn

58.51 100

Fig. 10. Frequency response for constant frequency operation in Case A.

20

40

hn

Ti n i d s c c )

xo

Fig. 13. Frequency response in Case C

41 6

I

inn

34r

---_ 24

20

40

80

60

350cr 0

100

_. 75

ii3

Fig. 14. Power output of cogeneration system in Case C.

,>

Fig. 17. Three different specd reference settings.

~~

0.921

20

80

40 60 Timc(scc)

i.i

100

Fig. 15. Steam pressure of cogcneration system in Case C.

6. TRANSIENT STABILITY ANALYSIS OF THE INCINERATOR COGENERATION SYSTEM To investigate the transient stability of the incinerator plant, the cogeneration system with the neighboring Taipower network in Fig. 17 has been used for computer simulation of transient stability analysis. The 161kV tie-line is connected to Taipower Nankung substation which also serves other large customers in the heavy industrial park. The Talin power plant of Taipower provides 420MW to serve the load of Linyuan substation which is connected to Kaokang EHV substation. The rest of Taipower system has been represented as the equivalent generator unit connected to Kaokang substation. The mathematical models with two damping coils along the p and q axes by taking into account thc magnctic flux saturation cffcct arc considered for all generators. The governor and exciter systems of Taipower generators are also included to simulate the transient response more accurately for the fault contingency of external Taipower system. I7t.iiliilv

ha, ~IwngIlil I\\

-1f

11111

7 -

I ItllC (\CCI

T I IIK( x c 1

l,i,lllf

Fig. 16. Onc linc diagram ofthc study powcr systcm.

T i

-.I

511 Timr (sc‘c k

~

r-,

1111)

Fig. 18. Frequency response in Case D. Case D. Nearby,fault of external power system For the nearby power contingency, a bolted ground fault on the 161kV transmission line in Fig. 17 has been assumed for computer simulation. By the operation of circuit breaker to clear the fault, the Nankung substation becomes an isolated system. With large industrial loads to be served, the cogeneration system frequency has been dropped to be below 58.6Hz to activate the tie-line tripping by under frequency relay to result in the islanding operation of the incinerator plant. At the same time, the governor system was changed from constant pressure operation to constant frequency operation by the governor controller. With three different speed rcfercnce settings as shown in Fig. 18, the corresponding system frequency of the islanding system during the transient period has been illustrated in Fig. 19. It is found that the over shooting of system frequency has been reduced to 62Hz by setting the initial speed reference as the actual speed with ramping rate of 2rpmisec after tieline tripping. Case E. Severejuult of external power system For the severe fault, such as the tripping of EHV 345kV transmission line, the whole Taipower system is separated to form the southern and northern subsystcms. Bccausc of thc largc amount of powcr flows carried from the south to the north, the tripping of transmission lines will introduce serious unbalance between power generation and load demand in each subsystem. With such large amount of power generation surplus in southern Taiwan, the system frequency increases dramatically in a short time period. To test the over frequency protection of the cogeneration system, the load tripping at Linyuan bus and the constant power generation of Talin power plant have been assumed in the study system for computer simulation by transient stability analysis. Figure 20 and 21 show the system responses of cogeneration system with different timing to change the governor control strategy.

417

When the fault occurs, the system frequency is increased to activate the tie-line tripping of the incinerator cogeneration system. The change of governor system from the constant steam pressure to the constant frequency control has to be made at the system frequency of 61.5Hz to reduce the power output o f cogcnerator in timc as shown by line 1 . On the other hand, the isolated cogeneration system will collapse if the constant frequency control of governor system is applied at the system frequency of 62.5Hz due to the turbine over speeding.

I

581

2

Preq c m t d at 61 5 H z

2

-Freq

. 60 TIIIIC(SLC)

ccmbol at 62 S H z

I

46

I00

80

Fig. 19. Frequency response with different models of governor system in Case E 1

&Prea oanhol at 61 5 H z

-7-

FPO o m h o l

st

62 5Hzl

I 20

40

60

RO

100

T I inlei w c )

Fig. 20. Turbine power output with different models of govcrnor systcm in Case B

concluded that the proper load shedding and the adaptive governor control by changing from constant steam pressure to constant frequency are very critical for the incinerator plant to maintain power system stability after tie-line tripping. REFERENCES C. S. Chen, Y. L. Ke, and C. T. Hsu (2000). Protcctive rclay setting of the tie line tripping and load shedding for the industrial power systcm. IEEE Trans. on Indmtrial Applirutions, Vol. 36, No. 5, Sep. /Oct., pp. 1226-1234. CYME International Inc. (199 1). CYMESTAB/UDM User’s Guide and Reference Manual. Canada. F. P. de Mello (1991). Boiler models for system dynamic performance studies. IEEE Tvcms. on Power Systems, Vol. 6, No. 1, pp. 66-74. M. E. Flynn, M. J. 0’ Malley (1 999). A drum boiler model for long term power system dynamic simulation. IEEE Trans. on Power Systems, Vol. 14, NO. I , pp. 209-217. Woodward Governor Company (1997). 505 Digitul governors j’br steam tuvbines with single of splitiwnge uctzratovs Munzral85017Vl.

Y. D. Lee received the B.S. and M.S. degrees in electrical engineering from National Taiwan University of Science and Technology, Taipei, Taiwan in 1997 and 1999. He has been an electrical engineer at the Southern Incinerator Plant, Kaohsiung, Taiwan since 1998. He is currently pursuing the Ph.D. degree in electrical engineering at National Sun Yat-Sen University, Kaohsiung, Taiwan.

7. CONCLUSION The adaptivc control stratcgy of govcrnor system for the incinerator cogeneration has been demonstrated by transient stability analysis. The design of load shedding scheme based on the under steam pressure protection has been proposed to maintain the system frequency and boiler steam pressure for the incinerator cogeneration system after tie-line tripping. For the external system disturbance, the fluctuation of steam pressure, the governor control system and the boiler control system or the cogenerator will affect the system response. To maintain the boiler steam pressure by considering the unstable heat value of trash bum in the incinerator plant, the PID controllers of the governor system for the constant frequency operation and constant pressure operation are coordinated with each other. The power output of the turbine generator fluctuates with trash heat value by applying the constant steam pressure control for normal operation. After tie-line tripping to isolate the fault contingency of external system, the constant frequency control will override the constant pressure control loop so that the system frequency of the islanding system can be maintained. The frequency response and power output of cogenerator for different case studies have been simulated. The transient stability analysis of incinerator cogeneration system by considering the unstable steam generation due to dynamic change of heat value of trash has been performed. It is

C. S. Chen received the B.S. degree from National Taiwan University, Taiwan in 1976 and the M.S. and Ph.D. degrees from the University of Texas, at Arlington in 1981 and 1984 respectively, all in electrical engineering. From 1984 to 1994, he was with National Sun YatSen University as a professor. From 1993 to 1997, he was with the Kaohsiung Mass Rapid Transit Department as the Deputy Director to be in charge of electrical and mechanical system planning. From 1997 to 1998, He was a professor at the National Taiwan University of Science and Technology. He is currently a full professor of Electrical Enginecring Department at the National Sun Yat-Sen University. His research interests include thc distribution automation, cogeneration systems, electrical and mechanical system of mass rapid transit networks. He is a member of IEEE and a registered professional engineer at Taiwan.

C. T. Hsu was born in Taiwan, 1963. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan in 1986, 1988, and 1995, respectively. From 1990 to 1992, he was with Phoenixtec Power Company Limited as a Power Electronics Engineer, developing USP equipment. He is currently a Professor of Electrical Engineering at Southcm Taiwan IJnivcrsity of Tcehnology, Tainan, Taiwan.

41 8

Author Index Abu-Ayyad, M. Amracc, T. Andersen, P. Ansarimehr , P. Arakawa. h1. Bai. X. Balate, J. Barboza, L.V. Bathaee, S.M. Befekadu. G.K. Bendtsen, J.D. Boiko, I. Casolino, G.M. Caux, S. Cha, .J.S. Chawla, G. Chen. C.S. Cho, S.K. Choe, C.Y. Choi, M.S. Choi, S.Y. Chrarncov, B. Crainic, E.D. Cregan, hf. Ding, J . Duhay, R. Ebina, H. Ebrahimi, S. Erlich, I. Fadel, MI. Faille, D. Fang, Z. Fa rsangi , hl .i\f . Fernandes. C.E.M. Fernando, I.T. Flynn, D. Folly, K.A. Fusco, G. Givehchi, A.H. Golc, A.M. Gommlich, A. Giidat, R. Haake, D.

17, 35

Haase, T.

65

Haniachcr, T.

171 279 189 195 395 371 83 23 171 29, 237 213 95 219 125 413 231 143 207 219 395 101, 333 243, 401 195 17, 35 153 377 23 95 389 195 377 371 147 243, 401 41, 261, 291 107 71 147 249 183 183

Han, S.S. Hankache. W. Hashiguchi, T. Henckes, L. Heo, J.S. Hikiliara, T. Hiskens. I.A. Hissel. D. Hojo, M. Holbert, K.E. Hong, H.S. Hsu. C T. Hur, D. Jackisch, H. Jang. B.T. Jenik, P. Jeong, Y.W. Joergeriseri, C. Jokic, A. Jung, G. Kaberere, K. Karady, G.G. Karrari, 1c1. Kawai, K. Keller, H.B. Kezunovic, hl. Kim, B.H. Kim, H.H. Kirn, S.J. Kuri-Morales. A. F Kurth, M. Kwatny, H.G. Lee, C.J. Lee, H.J. Lee. J.G. Lee, J.I. Lee, J.W. Lec, K.W. Lee, K.Y. Lee, S.J. Lee, Y.D.

419

59 59 207 95 77 389 407 153 383 95 77 255 365 413 113 327 143 395 47 20 1 339 143 29 1 255 71, 83 189 249 137 309 131 365 315 7, 183, 345 353 131 113 365 231 47 119 309, 377, 407 207 413

Li, Z.

171 Pedersen, T.S. Petroianu, A.I. 101, 159, 291.333 Qahrarnan, B. 147 131 Radoj wic , Z . Rarnakrishna, G. 125, 273 Raiijbar, A. M. 65 Rasouli. W'. 2 79 Rawlisigs. J.B. 383 Rosehart, W. 71, 83 107, 213 Russo, hll. Sachdev, A!LS. 125 Saeki, 0 . 77 Saied, S.A. 83 Salgado, R .S. 371 Scisdcdos, L.V. 315 Shin. J . H . 231 Shin. J.R. 47, 131 Shin. M.C. 219 Shirakawa, M. 189 So&-Yome, A. 119 Song, J.I. 231 Susiiki. Y. 153 Teolis, C. 353 Torrisclii, U . 327 Toyosaki, G. 285 Trangbaek, K. 297, 303 Ukai, H. 77, 285 van den Bosch, P.P.,J. 339 309 Velas, J.P 383 Venkat. A.N. Verrna, S.C. 285 59 Wpher, H. Wcissbach. T. 183 Welfonder, E. 7. 183, 345 Wright. S.J. 383 Yariagihara, J . I. 165 Yang, K.M. 47 Yi, B.J. 231 Yoon, C.D. 219 2 79 Zafarahadi. G. 137 Zhang, Y. 195 Zhao, W. Zhou, J . 359 249 Zipser, S. Zoby, M.R.G. 165

195 159 207 255 213 267 hlajanne,Y . 32 1 Malik, O.P. 71, 83 273 Maruo. T. 53 hlataji, B. 89 Mataji, B. 177 hlatsurnoto, I(. 53 Matthes, J. 249 Mensah, E. 353 Miii, K.I. 365 hlritani, Y. 77 hlithulananthan, N 119 iliIkr t tcliiari, M. 237 Mocwane. K. 26 1 Moelbak, T. 201 Alondon. C. 389 Moon, Y.H. 365 Mori, N. 53 hlort ensen, J .H . 171, 201 Mozafari, A. 65 hlozafari, B. 65 Nakachi, Y. 285 Nakayama, H. 189 Navratil, P. 395 Newald. R . 327 Nezamabadi-Pour, H. 377 Nichur, D. 353 Niclscii. E.O. 201 Nielsen, R.J. 171 Odgaard. P.F. 177 Odgaard. P.F. 89, 297 Ohsawa, Y . 359 Ota, Y. 77 Pan. L. 243 Pandey, R.K. 1 Park, D.H. 207 47,131 Park, J.B. Park, J.K. 225 Park, J.Y. 225 Pariiiani, M. 2 79 Lilje, P. Lirn, S.I. Lin, I(. Losi, A. Llshosny, Z.

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