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NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
The K1uwer International Series on ASIAN STUDIES IN COMPUTER AND INFORMATION SCIENCE
Series Editor Kai-Yuan Cai
Beijing University 01 Aeronautics and Astronautics, Beijing, CHINA
Editorial Advisory Board Han-Fu ehen, Institute ofSystem Science, Chinese Academy ofSciences Jun-Liang Chen, Beijing University ofPost and Telecommunication Lin Huang, Peking University Wei Li, Beijing University of Aeronautics and Astronautics Hui-Min Lin, Institute ofSoftware Technology, Chinese Academy ofSciences Zhi-Yong Liu, Institute ofComputing Technology, Chinese Academy of Sciences Ru-Qian Lu, Institute ofMathematics, Chinese Academy ofSciences Shi-Tuan Shen, Beijing University of Aeronautics and Astronautics Qing-Yun Shi, Peking University You-Xian Sun, Zhejiang University Lian-Hua Xiao, National Natural Science Foundation ofChina Xiao-Hu Vou, Southeast University Do Zhang, Tsinghua University Da-Zhong Zheng, Tsinghua University Ding-Kun Zhou, Tsinghua University Xing-Ming Zhou, Changsha University ofTechnology
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NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
by
Qiang Lu
Yuanzhang Sun
Shengwei Mei
Tsinghua University, Beijing, China
Springer-Science+Business Media, B.V.
.... " Electronic Services <http://www.wkap.nl>
Library of Congress Cataloging-in-Publication Data
Lu, Qiang, 1936-Nonlinear contral systems and power system dynarnics / Qiang Lu, Yuangzhang Sun,
Shengwei Mei. p. cm.-- (Kluwer international series on Asian studies in computer and information
science; 10) Inc1udes bibliographical references and index.
ISBN 978-1-4419-4885-4 ISBN 978-1-4757-3312-9 (eBook) DOI 10.1007/978-1-4757-3312-9
1. Automatie contra!. 2. Nonlinear control theory. 3. Electric power system stability. 1. Sun, Yuanzhang, 1954- 11. Mei, Shengwei, 1964- III. Title. IV. Series.
TJ213.L72 2001 629.89--dc21
Copyright © 2001 by Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001. Softcover reprint of the hardcover 1 st edition 2001
2001016020
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, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-Science+Business Media, B.V
The Publisher offers discounts on this book for course use and bulk purchases. For furlher information, send email to<[email protected]>.
To Dur Alma Mater
---- Tsingbua University
SERIES EDITOR'S ACKNOWLEDGMENTS
I am pleased to acknowledge the assistance to the editorial work by Beijing University of Aeronautics and Astronautics and the National Natural Science Foundation of China
Kai-Yuan Cai Series Editor Department 0/ Automatie Control Beijing University 0/ Aeronauties and Astronauties Beijing 100083 China
Contents
Preface ............................................................................................... xxi
Chapter 1
Introduction ......................................................................................... 1
1.1 Overview ................................................................................................ 1
1.2 Outline ofthe Development of Control Theory ..................................... 3
1.3 Linear and Nonlinear Control Systems ................................................ 12
1.4 Modeling Method of Approximate Linearization ................................ 16
1.5 Stable and Unstable Equilibrium Points .............................................. 19
1.6 References ........................................................................................... 22
Chapter 2
Basic Concepts of Nonlinear Control Theory ................................ 25
2.1 Introduction .......................................................................................... 25
2.2 Coordinate Transformation ofNonlinear Systems ............................... 26
2.2.1 General Concepts of Coordinate Transformation ..................... 26
2.2.2 Coordinate Transformation ofLinear Systems ......................... 28
2.2.3 Nonlinear Coordinate Transformation and Diffeomorphism .... 29
2.2.4 Mapping .................................................................................... 30
2.2.5 Local Diffeomorphism .............................................................. 30
2.2.6 Coordinate Transformation ofNonIinear Control Systems ....... 32
2.3 Affine Nonlinear Control Systems ....................................................... 33
2.4 Vector Fields ........................................................................................ 34
2.5 Derived Mapping of Vector Fields ....................................................... 36
2.6 Lie Derivative and Lie Bracket ............................................................ 38
2.6.1 Lie Derivative ........................................................................... 38
vii i NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
2.6.2 Lie Bracket. ............................................................................... 41
2.7 Involutivity ofVector Field Sets .......................................................... 45
2.8 Relative Degree of a Control System ................................................... 47
2.9 Linearized Normal Form ...................................................................... 50
2.10 Summary ............................................................................................. 56
2.11 References ......................................................................................... 58
Chapter 3
Design Principles of Single-Input Single-Output Nonlinear Control Systems .............................................................. 59
3.1 Introduction .......................................................................................... 59
3.2 Design Principles of Exact Linearization via Feedback ....................... 60
3.2.1 Linearizing Design Principle as Relative Degree r
Equals n for an nth-order System .............................................. 61
3.2.2 General Linearization Design Principle .................................... 70
3.2.3 Conditions for Exact Linearization ........................................... 72
3.2.4 Algorithm ofExact Linearization ............................................. 80
3.3 Zero Dynamics Design Principle ......................................................... 90
3.3.1 First Type of Zero Dynamic Design Method ............................ 91
3.3.2 Second Type ofZero Dynamic Design Method ........................ 97
3.3.3 Discussion ofSome Problems ................................................. 101
3.4 Zero Dynamics Design Method for Linear Systems .......................... 104
3.5 Design of Disturbance Decoupling .................................................... 109
3.6 References ......................................................................................... 120
Chapter 4
Design Principles of Multi-Input Multi-Output Nonlinear Control Systems ............................................................ 121
4.1 Introduction ........................................................................................ 121
4.2 Relative Degrees and Linearization Normal Forms ........................... 122
4.2.1 Relative Degree ........................................................................ 122
4.2.2 Linearization Normal Form ...................................................... 125
4.3 Zero Dynamics Design Principle ....................................................... 136
4.4 Design Principles ofExact Linearization via State Feedback ............ 147
4.4.1 Conditions for Exact Linearization via State Feedback .......... 148
Contents IX
4.4.2 Algorithm of Exact Linearization via State Feedback ............ 151 4.5 References ......................................................................................... 164
Chapter 5
Basic Mathematical Descriptions for Electric Power Systems ................................................................... 165
5.llntroduction ........................................................................................ 165
5.2 Rotor Dynamics and Swing Equation ................................................ 166
5.3 Output Power Equations for a Synchronous Generator ..................... 170
5.4 Output Power Equations for Synchronous Generators
in a Multi-Machine System ................................................................ 179
5.4.1 Output Power Equations for a Generator in
a One-machine Infinite-bus System ....................................... 179
5.4.2 Practical Output Power Equations for Synchronous
Generators in a Multi-machine System .................................. 181
5.5 Electromagnetic Dynamic Equation for Field Winding ..................... 185
5.6 Mathematical Description ofa Steam Valving Control System ......... 186
5.7 Mathematical Description of a DC Transmission System ................. 191
5.7.1 Dynamic Equations ofa DC Transmission Line ..................... 191
5.7.2 Mathematical Model of a DC Control System ........................ 196
5.8 References ......................................................................................... 198
Chapter 6
Nonlinear Excitation Control ofLarge Synchronous Generators ....................................................................................... 199
6.1 lntroduction ........................................................................................ 199
6.2 Development ofExcitation Control ................................................... 200
6.3 Nonlinear Excitation Control Design for
Single-Machine Systems .................................................................... 208
6.3.1 Exact Linearization Design Approach .................................... 209
6.3.2 Discussions on the Implementation of
Nonlinear Excitation Control ................................................. 217
6.3.3 Effects ofNonlinear Excitation Contro!.. ................................ 219
6.4 Nonlinear Excitation Control Design for
Multi-Machine Systems ..................................................................... 223
x NONLlNEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
6.4.1 Dynamic Equations of Multi-Machine Systems ..................... 223
6.4.2 Exact Linearization Design Method
for Excitation Control ............................................................ 225
6.4.3 Practical Nonlinear Excitation Control Law ........................... 234
6.4.4 Discussion on the Nonlinear Excitation Control Law ............. 235
6.4.5 Effects ofthe Nonlinear Excitation Control... ......................... 237
6.5 References ......................................................................................... 244
Chapter 7
Nonlinear Steam Valving Control ................................................. 245
7.1 Introd ucti on ........................................................................................ 245
7.2 Nonlinear Steam Valving Control in a
One-Machine Infinite-Bus System .................................................... 246
7.2.1 Mathematical Model ............................................................... 246
7.2.2 Exact Linearization Method .................................................... 249
7.2.3 Physical Simulation Results ofNonlinear Valving
Control in a One-Machine Infinite-Bus System ..................... 256
7.2.4 Digital Simulation Results ofNonlinear Steam
Valving Control in a One-Machine Infinite-Bus System ....... 259
7.3 Nonlinear Steam Valving Control in a Multi-Machine System ......... 261
7.3.1 Mathematical Model ............................................................... 261
7.3.2 Exact Linearization Method .................................................... 263
7.3.3 Effects ofNonlinear Steam Valving Control in a
Multi-Machine System ........................................................... 271
7.4 Discussion on Some Issues ................................................................ 273
7.5 References ......................................................................................... 276
Chapter 8
Nonlinear Control of HVDC Systems ........................................... 277
8.1 Introduction ........................................................................................ 277
8.2 Characteristics and Conventional Control of Converter Stations ...... 278
8.2.1 Voltage-Current Characteristics on Rectifier Side .................. 278
8.2.2 Voltage-Current Characteristics on Inverter Side .................... 279
8.2.3 Conventional Control with Constant DC Current at
Rectifier and Constant Extinction Angle at Inverter .............. 280
Contents xi
8.2.4 Conventional Control with Constant DC Current at
Rectifier and Constant DC Voltage at Inverter ....................... 282
8.2.5 Power Modulation in DC Transmission Systems .................... 284
8.3 Nonlinear Control of Converter Stations ........................................... 285
8.3.1 Nonlinear Control with Constant Current
and Constant Extinction Angle .............................................. 285
8.3.2 Nonlinear Control with Constant Current at
Rectifier and Constant DC Voltage at Inverter ....................... 297
8.4 Nonlinear Control ofDC Systems and Stability
of AC/DC Systems ............................................................................ 302
8.4.1 Modeling for Nonlinear Stabilizing Control Design
of AC/DC Systems ................................................................. 302
8.4.2 Nonlinear Control Design for Stabilizing
AC/DC Systems ..................................................................... 304
8.4.3 Effects ofNonlinear Control for Stabilizing
AC/DC Systems ..................................................................... 306 8.5 References ......................................................................................... 308
Chapter 9
Nonlinear Control of Static Var Systems ...................................... 309
9.1 Introduction ........................................................................................ 309
9.2 Fundamentals ofReactive Power Compensation ............................... 310
9.2.1 Reactive Power Flow in a Transmission System .................... 310
9.2.2 Two Basic Types of Reactive Power Compensators ............... 312
9.2.3 Effects ofthe Midpoint Compensator
on the Stability Limits ............................................................ 314
9.3 Configuration of Static Reactive Compensators ................................ 319
9.3.1 Thyristor-Controlled Reactor (TCR) ....................................... 319
9.3.2 Thyristor-Switched Capacitor (TSC) ...................................... 325
9.4 Conventional Control Strategies of SVS ........................................... 330
9.5 Nonlinear Controller Design for SVS ................................................ 333
9.5.1 Modeling of SVS Control Systems ......................................... 333
9.5.2 Exact Linearization Design Approach .................................... 335
9.5.3 Effects ofthe Nonlinear Control ofSVS ................................ 339
9.6 References ......................................................................................... 342
xii NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
Chapter 10
Nonlinear Robust Control ofPower Systems ............................... 343
10.1 Introduction ...................................................................................... 343
10.2 Basic Concepts ................................................................................. 344
10.2. I L2 -space ................................................................................. 344
10.2.2 L2 -gain .................................................................................. 345
10.2.3 Penalty Vector Function ........................................................ 348
10.2.4 Dissipative Systems .............................................................. 348
10.3 Nonlinear Robust Control ................................................................ 350
10.3.1 Description ofNonlinear Robust Control ............................. 350
10.3.2 General Form ofthe Nonlinear Robust Control Law ............ 351
10.3.3 Hamilton-Jacobi-Isaacs Inequality ........................................ 355
10.4 HJI Inequality of Linear Control System - Riccati Inequality ....... 358
10.5 Nonlinear Robust Excitation Control (NREC) ................................. 359
10.5.1 Introduction ........................................................................... 359
10.5.2 Regulation Output Linearization ........................................... 361
10.5.3 Analysis ofRobustness ofthe Closed Loop System ............. 363
10.5.4 Nonlinear Robust Excitation Control .................................... 365
10.5.5 Simulation Results ................................................................ 368
10.5.6 Summary ............................................................................... 369 10.6 References ....................................................................................... 371
Index ................................................................................................. 373
List of Figures
Figure 1.1 Structural diagram of linear optimal control system ..................... 8
Figure 1.2 R-L-C Circuit ............................................................................. 12
Figure 1.3 A one-machine infinite-bus system ............................................ 14
Figure 2.1 a, b, C coordinates and d, q, 0 coordinates
of a synchronous generator ........................................................ 27
Figure 2.2 Mappings between X coordinate system and
Z co ordinate system ................................................................... 30
Figure 3.1 Diagram iIIustrating the design principle of
exact linearization via feedback .................................................. 68
Figure 3.2 Relations among the coordinate transformations of
the spaces X , W and Z ............................................................... 85
Figure 3.3 Structural diagram of a system with
outputs decoupled from disturbances ......................................... 112
Figure 5.1 Relationship between different reference axes
used to measure the motion of a generator' s rotor .................... 167
Figure 5.2 Coordinate axes a, band c fixed on the stator and
coordinate axes d, q and 0 fixed on the rotor............................ 171
Figure 5.3 A one-machine, infinite-bus power system ............................... 180
Figure 5.4 A 6-generator power system and its equivalent circuit ............. 182
Figure 5.5 Electric potential vector diagram of
an n-generator power system .................................................... 183
Figure 5.6 Positive directions of the current and voltage of
a field winding .......................................................................... 185
Figure 5.7 Physical configuration ofthe steam valving control system
for a large generator set with reheater ....................................... 187
Figure 5.8 Transfer function block diagram ofthe control system
for a steam turbine with reheater .............................................. 188
x i v NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
Figure 5.9 Transfer function block diagram ofa steam valving
control system with reheater ..................................................... 189
Figure 5.10 Transfer function block diagram of a steam
valving control system with reheater ........................................ 190
Figure 5.11 Transfer function diagram for a steam valving control system. 190
Figure 5.12 Basic configuration of a OC transmission system ..................... 191
Figure 5.13 Equivalent circuit of a OC transmission line ............................. 192
Figure 5.14 Converting loop of the rectifier side ......................................... 193
Figure 5.15 Converting process of a rectifier ............................................... 193
Figure 5.16 Equivalent circuit for a rectifier ................................................ 193
Figure 5.17 Converting loop of an inverter .................................................. 194
Figure 5.18 Converting process of an inverter ............................................. 194
Figure 5.19 Equivalent circuit for an inverter when Vdi is
expressed by the inverter firing angle ß .................................... 194
Figure 5.20 Equivalent circuit for an inverter when Vdi is
expressed by the extinction angle y ........................................... 195
Figure 5. 21 Schematic diagram of a rectifier's a -regulator ....................... 196
Figure 5.22 Schematic diagram of a inverter's ß-regulator .......................... 197
Figure 6.1 The structure of generator self-shunt excitation ........................ 200
Figure 6.2 The block diagram oftransfer function of
single variable excitation control .............................................. 201
Figure 6.3 A single-input single-output c1osed-loop system ...................... 202
Figure 6.4 The excitation regulator transfer function dividing the
amplification into static and dynamic amplifications ................ 204
Figure 6.5 The transfer function block diagram of PSS ............................. 205
Figure 6.6 Schematic diagram ofa generator LOEC (analogous)
in a one-machine, infinite-bus system ...................................... 207
Figure 6. 7 The schematic diagram of
microcomputer nonlinear excitation controller ......................... 219
Figure 6.8 The one-machine, infinite-bus system diagram
and its parameters ...................................................................... 219
Figure 6.9 The generator power-angle curve under
nonlinear excitation contro!... .................................................... 221
Figure 6.10 The structure diagram ofthe 6-machine system ....................... 238
List 0/ Figures xv
Figure 6.11 The comparison of generator small disturbance response
curves under various excitation controls strategies ................... 239
Figure 6.12 The system's dynamic response curves with PSS ..................... 241
Figure 6.13 The system's dynamic response curves with LOEC ................ 241
Figure 6.14 The system's dynamic response curves with NOEC ................. 242
Figure 6.15 The system's dynamic response curve with PSS ...................... 242
Figure 6.16 The system's dynamic response curves with LOEC ................ 243
Figure 6.17 The system's dynamic response curves with NOEC ................. 243
Figure 7.1 The structure diagram of transfer function for
nonlinear control of steam valves .............................................. 255
Figure 7.2 A one-machine, infinite-bus system ......................................... 256
Figure 7.3 Physical simulation results for improving transient stability by
using nonlinear steam valving control under temporary faults. 257
Figure 7.4 Physical simulation results for improving the transient stability by
using steam valving nonlinear control under permanent faults. 258
Figure 7.5 Computer simulation results of
nonlinear steam valving control... ............................................. 259
Figure 7.6 Computer simulation results with permanent fault.. .................. 260
Figure 7. 7 Oynamic responses under three-phase fault.. ............................ 272
Figure 7.8 Oynamic response curves under three-phase fault ................... 273
Figure 7.9 Oynamic responses und er three-phase fault.. ............................ 274
Figure 7.10 Physical testing results of re-synchronizing by
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
using the nonlinear steam valve control .................................... 275
Vdr-Idr characteristic of rectifier with various firing angles ....... 278
Vdi-Idi characteristic of rectifier with various firing angles ....... 279
Vdi-Idl characteristic of inverter with various extinction angles 280
Converter controller characteristic with constant
current and constant extinction angle ...................................... 281
Figure 8.5 Converter controllers with constant current
and constant extinction angle .................................................... 281
Figure 8.6 Converter controller characteristic with
constant current and constant voltage ....................................... 283
Figure 8.7 Inverter controllers with constant OC voltage ........................... 283
Figure 8.8 The transfer function block diagram of
the power modulator in a converter.. ......................................... 284
xv i NONLINEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
Figure 8.9 A 6-machine ACIDC power system .......................................... 294 Figure 8. 10 System dynamic response under conventional controllers
with constant current rectifier control and constant extinction angle inverter control ................................ 295
Figure 8.11 System dynamic response under nonlinear controllers
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
with constant current at rectifier and constant extinction angle at inverter .......................................... 296
System dynamic response under conventional controllers with
constant current at rectifier and constant voltage at inverter. .... 300 System dynamic response under non linear controllers with constant current at rectifier and constant voltage angle at inverter. ............................................. 301
An ACIDC power system .......................................................... 302
System dynamic response under nonlinear controllers
for AC/DC system stability ....................................................... 307
Reactor and capacitor treated as load ........................................ 310
Reactor and capacitor modeled as power supply ....................... .311
Anode with three branches ....................................................... 312
Simple circuit and its vector diagram ........................................ 312
The circuit with the capacitive compensator ............................. 313
The equivalent diagram oftransmission system ....................... 314
Effects of reactive power compensation on the
transmitted power of symmetricallossless line ........................ 319
Single phase diagram ofTCR and its waveforms ..................... 320
Current and voltage waveforms at different gating angle ......... 321
Figure 9.10 The control characteristic of BreR ............................................. 322
Figure 9.11 The configuration of TCR-FC type compensator ..................... 323
Figure 9.12 Voltage/current characteristics of Thyristor-Controlled
Reactor-Fixed Capacitor (TCR-FC) type SVS ........................ 324
Figure 9.13 Bsvs characteristics of Thyristor-Controlled
Reactor-Fixed Capacitor (TCR-FC) type SVS ........................ 325
Figure 9.14 TSC type .................................................................................... 326
Figure 9.15 TSC applied structure ................................................................ 326
Figure 9.16 Effects of n2 ( n2 -Ion natural frequency ................................... 327
Figure 9.17 The configuration ofTCR-TSC type SVS compensator .......... 328
Figure 9.18 Equivalent circuit of SVS .......................................................... 331
Figure 9.19 The fundamental control system ofTCR-FC type .................... 332
List 0/ Figures XVI I
Figure 9.20 The conventional PID control structure ofTCR-FC type SVS. 332
Figure 9.21 Single-machine, infinite-bus system with SVS ......................... 334
Figure 9.22 The block diagram ofthe nonlinear controller of SVS ............ 339
Figure 9.23 The block diagram ofSVS conventional control system .......... 339
Figure 9.24 Effects of different types of
controllers on system performance ........................................... 341
Figure 10.1 Dynamic response ofthe system with PSS ............................... 370
Figure 10.2 Dynamic response ofthe system with LOEC ............................ 370
Figure 10.3 Dynamic response ofthe system with NOEC ........................... 370
Figure 10.4 Dynamic response ofthe system with NREC ........................... 370
Figure 10.5 Dynamic response ofthe system with NREC
under the values ofparameters having 50% errors .................. 370
List of Tables
Table 6.1 Comparison of Transient Stability Limit.. ..................................... 222
Table 6.2 Generator parameters ofthe 6-machine system ............................ 237
Table 6.3 The critical clearing time under
different excitation control mode .................................................. 240
Table 6.4 The critical transmission power under
various excitation controls ............................................................ 241
Table 7.1 Dynamic simulation results under temporary short circuit fault ... 256
Table 7.2 Dynamic simulation result under permanent faults ....................... 258
Table 7. 3 Critical clearing time for different control strategies .................... 271
Table 8.1 Operating parameters of the DC transmission system ............... 293
Appendant Table 9.1 Errors with approximate linearization of SVS ............ 330
Table 9.1 Characteristic values of SVS with three types compensators ........ 340
Preface
We may agree with the opinion that in operating an electric power system the top priority should be given to the dynamic security and stability before pursuing other targets, such as economical operation, optimal load flow and fair deregulation (power market), etc. However, in the past decade, quite a number of power systems, both in China and abroad still suffered from too many collapses, most of them affected a large area and lasted even over 10 hours, which caused grievous damages not only to the economies of the nations, but also to the residents' comforts and the public order. These facts show c1early that it is of paramount importance for us to greatly improve the operation security, more precisely, the dynamic stability and especially the transient stability of power systems.
The development of science and technology calls for belief that the stability of power systems can be decisively enhanced by adopting new and advanced control theories, approaches and the corresponding control schemes.
Now the question is: what should we do to achieve that goal? The first step is to build a bridge over the big gap between the mathematicians, the theorists and the engineers, the technicians; to build a bridge over the big gap between the profound theorems, the abstruse mathematical notations and the industrial designs, the engineering implementation. We have tried, in our small way, to do just this and come to write this book. We wish that this volume could become a small impulse to the purpose mentioned above and set a small example to show that the endeavor which the scientists and engineers of the world will make along this way could lead to something new and berter for modern electric power systems, as weil as for other nonlinear control systems.
This book presents a comprehensive description of non linear control of electric power systems using nonlinear control theory which is developed by the approach of the differential geometry and the notions of the dissipativity and the differential game.
It is intended as a text for undergraduate seniors and graduate students, as weil as a reference to engineers and researchers, who are interested in the application of modern nonlinear control theory to practical engineering
NONL/NEAR CONTROL SYSTEMS AND POWER SYSTEM DYNAMICS
control designs. While readers in the area of power systems may feel a great interest in the chapters which deal with power system control problems; readers in other engineering disciplines may use some of these chapters as examples of application to facilitate their own control designs.
For readers' convenience, this book is organized in a self-contained way to introduce, in sufficient detail, the essences of modern nonlinear control theory as weil as the corresponding developed algorithms to the readers in practical engineering control areas, and to explore how these theory and algorithms work in practice. Mathematical preliminaries in ordinary differential equations and modern linear control principle are required for reading the book.
The book consists of five parts, and the organization has been influenced by the objective of this book.
Part I (Chapter land Chapter 2) starts with the characteristics and special problems associated with nonlinear systems by comparing nonlinear systems with linear ones. In this part some elementary notions of nonlinear control theory are introduced, emphasizing on differential geometric approach. These notions provide the necessary background for subsequent discussions.
Part 2 (Chapter 3 and Chapter 4) presents a comprehensive discussion of the design principles and methods for single-input single-output and for multi-input multi-output non linear systems. The discussion involves the design principles and approaches associated with exact linearization via state feedback, zero dynamics, and output-disturbance decoupling. The design principles and methods presented in this part constitute the tool kit, which will be used to solve practical engineering control problems. In this book they are used in power system control designs.
Part 3 (Chapter 5) serves as the connection between non linear control theory and power system control designs. This part addresses the modeling of power systems. In particular, non linear mathematical models of power systems are given in this part.
Part 4 (Chapter 6 through Chapter 9) discusses the application of non linear control theory to various power system control designs, which include non linear excitation control of large generators, nonlinear steam valving control of turbine-generator units, nonlinear control of HVDC transmissions systems, and non linear SVS contro!. All the mathematical models, design methods, control strategies, and effects of nonlinear controllers are given in this part.
The last part (Chapter 10) deals with the nonlinear robust control theory, which is mainly based on the notions and principles of dissipativity and differential game, and its application to multi-machine systems. This part presents a rich collection of new results on nonlinear control of power systems. Each chapter in Part 4 and the last part is virtually a research
Preface
monograph.
At the moment of completing the book, I cherish the memory of Jingde Gao more than ever before. It was he who first propounded the subject of power systems nonlinear control, and benefited me significantly for my research work and in my academic career.
I wish to express my sincere gratitude to Professor T. J. Tarn, to Professor J. Zaborszky, to Professor Y. N. Yu, to Professor T. Mochizuki, to Professor Felix Wu and to Professors Daizhan Cheng, Huashu Qin from whom I learnt many of the methods and methodologies which have been applied in the book. I wish to thank Professor Kaiyuan Cai for his encouragement. I am indebted to Dr. Zheng Xu, Dr. Xin Jiang, Professors Gengshen Hu, and Dayu He who reviewed the manuscript and made many valuable suggestions. Finally, my thanks go also to my graduate students Wei Hu, Yusong Sun, Wencong Wang, Feng Liu, Hua Xie, Baoping Mao, Jin Ma, Juming Chen, Tianqi Guan, Zhitao Wang et al., the manuscript preparation would not have been possible without their assistance.
On behalf of the authors I wish to express our gratitude to KLUWER ACADEMIC PUBLISHERS for affording the opportunity to publish this book.
The work presented in this book mostly grew out of the projects supported by Chinese National Key Basic Research Fund under grant G 1998020300, by NSFC under grant 59837270, and by Chinese National Key Science and Technology Tackling Project under grant No. 97-312-01-lI-la. The work is also supported partly by NEDO International Joint Research, Japan under grant 99EA 1.
Qiang LU
Beijing, May 2000
