Power system dynamics : stability and control

584 Pages·2008·17.364 MB·English

by  K R Padiyar

POWER SYSTEM DYNAMICS
Stability and control
Second Edition

POWER SYSTEM DYNAMICS
Stability and Control
Second Edition
K. R. Padiyar
Indian Institute of Science, Bangalore
SSP BS Publications
4-4-309, Giriraj Lane, Sultan Bazar,
Hyderabad -500 095 -AP.
Phone: [phone]
e-mail: [e-mail]
www.bspublications.net
Copyright © 2008, by Author
All rights reserved
No part of this book or parts thereof may be reproduced, stored in a retrieval system
I
or transmitted in any language or by any means, electronic, mechanical,
photocopying, recording or otherwise without the prior written permission of the
publishers.
Published by :
asp
BS Publications
4-4-309, Giriraj Lane, Sultan Bazal,
Hyderabad -500 095 AP.
Phone: [phone]
e-mail: [e-mail]
website: www.bspublications.net
Printed at :
Adithya Art Printers
Hyderabad.
ISBN: 81-7800-186-1
TO
PROF. H N. RAMACHANDRA RAO

Contents
1 Basic Concepts 1
1.1 General.......................... 1
1.2 Power System Stability . . . . . . . . . . . . . . . . . 1
1.3 States of Operation and System Security - A Review 3
1.4 System Dynamic Problems - Current Status and Recent Trends 4
2 Review of Classical Methods 9
2.1 System Model . . . . . .. 9
2.2 Some Mathematical Preliminaries [3, 4] 13
2.3 Analysis of Steady State Stability . . . 16
2.4 Analysis of Transient Stability . . . . . 29
2.5 Simplified Representation of Excitation Control 37
3 Modelling of Synchronous Machine 43
3.1 Introduction ..... . 43
3.2 Synchronous Machine. 44
3.3 Park's Transformation 48
3.4 Analysis of Steady State Performance. 58
3.5 Per Unit Quantities .......... . 62
3.6 Equivalent Circuits of Synchronous Machine 69
3.7 Determination of Parameters of Equivalent Circuits 72
3.8 Measurements for Obtaining Data . . . . . . . 85
3.9 Saturation Models . . . . . . . . . . . . . . . . 89
3.10 Transient Analysis of a Synchronous Machine 92
Vlll Power System Dynamics - Stability and Control
4 Excitation and Prime Mover Controllers 113
4.1 Excitation System ............ . 113
4.2 Excitation System Modelling. . . . . . . 114
4.3 Excitation Systems- Standard Block Diagram 119
4.4 System Representation by State Equations 125
4.5 Prime-Mover Control System. 131
4.6 Examples......... .. . . 141
5 Transmission Lines, SVC and Loads 151
5.1 Transmission Lines ........ . 151
5.2 D-Q Transformation using a - (3 Variables 157
5.3 Static Var compensators 160
5.4 Loads .......... . 167
6 Dynamics of a Synchronous Generator Connected to Infinite
Bus 177
6.1 System Model . . . . . . . . . 177
6.2 Synchronous Machine Model . 178
6.3 Application of Model 1.1 ... 181
6.4 Calculation of Initial Conditions. 188
6.5 System Simulation ....... . 191
6.6 Consideration of other Machine Models . 199
6.7 Inclusion of SVC Model ..... . 211
7 Analysis of Single Machine System 221
7.1 Small Signal Analysis with Block Diagram Representation 221
7.2 Characteristic Equation (CE) and Application of Routh-Hurwitz
Criterion . . . . . . . . . . . . . . . . . . . . . . . 229
7.3 Synchronizing and Damping Torques Analysis 232
7.4 Small Signal Model: State Equations . . . 240
7.5 Nonlinear Oscillations - Hopf Bifurcation. 252
8 Application of Power System Stabilizers 257
8.1 Introduction .......... . 257
8.2 Basic concepts in applying PSS 259
8.3 Control Signals ....... .. 263
Contents ix
8.4 Structure and tuning of PSS . . . . . . . . . . . 264
8.5 Field implementation and operating experience 275
8.6 Examples of PSS Design and Application. . . . 277
8.7 Stabilization through HVDC converter and SVC controllers 291
8:8 Recent developments and future trends 291
9 Analysis of Multimachine System 297
9.1 A Simplified System Model. 297
9.2 Detailed Models: Case I .. 306
9.3 Detailed Model: Case II .. 310
9.4 Inclusion of Load and SVC Dynamics. 318
9.5 Modal Analysis of Large Power Systems 319
9.6 Case Studies . . . . . . . . . . . . . . . 325
10 Analysis of Subsynchronous Resonance 333
10.1 SSR in Series Compensated Systems 333
10.2 Modelling of Mechanical System. . 338
10.3 Analysis of the Mechanical system. . 340
10.4 Analysis of the Combined System . . 348
10.5 Computation of Ye(s) : Simplified Machine Model. 350
10.6 Computation of Ye(s): Detailed Machine Model . . 354
10.7 Analysis of Torsional Interaction - A Physical Reasoning 356
10.8 State Space Equations and Eigenvalue Analysis 360
10.9 Simulation of SSR . 369
10.10 A Case Study . . . . . . . . . . . . . . . . . . . 369
11 Countermeasures for Subsynchronous Resonance 387
11.1 System Planning Considerations . 387
11.2 Filtering Schemes . . . . 390
11.3 Damping Schemes . . . . 391
11.4 Relaying and Protection 403
12 Simulation for Transient Stability Evaluation 407
12.1 Mathematical Formulation 408
12.2 Solution Methods ............... . 409