Table Of ContentPower System Wide‐Area
Stability Analysis and Control
Power System Wide‐Area
Stability Analysis and Control
Jing Ma
State Key Laboratory of Alternate Electrical Power
System with Renewable Energy Sources
North China Electric Power University
Beijing, PR China
This edition first published 2018 by John Wiley & Sons Singapore Pte. Ltd under exclusive licence
granted by Science Press for all media and languages (excluding simplified and traditional Chinese)
throughout the world (excluding Mainland China), and with non‐exclusive license for electronic
versions in Mainland China.
© 2018 Science Press
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, except as permitted by law. Advice on how to obtain permission to reuse material
from this title is available at http://www.wiley.com/go/permissions.
The right of Jing Ma to be identified as the author of this work has been asserted in accordance
with law.
Registered Offices
John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA
John Wiley & Sons Singapore Pte. Ltd, 1 Fusionopolis Walk, #07‐01 Solaris South Tower,
Singapore 138628
Editorial Office
1 Fusionopolis Walk, #07‐01 Solaris South Tower, Singapore 138628
For details of our global editorial offices, customer services, and more information about
Wiley products visit us at www.wiley.com.
Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some
content that appears in standard print versions of this book may not be available in other formats.
Limit of Liability/Disclaimer of Warranty
While the publisher and authors have used their best efforts in preparing this work, they make
no representations or warranties with respect to the accuracy or completeness of the contents
of this work and specifically disclaim all warranties, including without limitation any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created or
extended by sales representatives, written sales materials or promotional statements for this work.
The fact that an organization, website, or product is referred to in this work as a citation and/or
potential source of further information does not mean that the publisher and authors endorse the
information or services the organization, website, or product may provide or recommendations it
may make. This work is sold with the understanding that the publisher is not engaged in rendering
professional services. The advice and strategies contained herein may not be suitable for your
situation. You should consult with a specialist where appropriate. Further, readers should be aware
that websites listed in this work may have changed or disappeared between when this work was
written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or
any other commercial damages, including but not limited to special, incidental, consequential, or
other damages.
Library of Congress Cataloging‐in‐Publication Data
Names: Ma, Jing (Electrical engineer), author.
Title: Power system wide-area stability analysis and control / Dr. Ma Jing,
State Key Laboratory of Alternate Electrical Power System with Renewable
Energy Sources, North China Electric Power University, Beijing, China.
Description: First edition. | Singapore ; Hoboken, NJ, USA : Wiley, [2018] |
Includes bibliographical references and index. |
Identifiers: LCCN 2017013166 (print) | LCCN 2017039657 (ebook) |
ISBN 9781119304876 (pdf) | ISBN 9781119304869 (epub) |
ISBN 9781119304845 (cloth)
Subjects: LCSH: Electric power system stability. | Electric power system–Control.
Classification: LCC TK1010 (ebook) | LCC TK1010 .M328 2017 (print) | DDC 621.319–dc23
LC record available at https://lccn.loc.gov/2017013166
Cover design by Wiley
Cover images: (Powerline) © Trudy Fletcher / EyeEm/Gettyimages;
(Wind Turbines) © Nicolas Balcazar / EyeEm/Gettyimages
Set in 10/12pt Warnock by SPi Global, Pondicherry, India
10 9 8 7 6 5 4 3 2 1
v
Contents
About the Author ix
Preface xi
1 Basic Theories of Power System Security Defense 1
1.1 Introduction 1
1.2 Power System Reliability and Stability 2
1.2.1 Reliability of Power System 2
1.2.2 Stability of Power System 4
1.3 Three Defense Lines in the Power System 7
1.3.1 Classification of Disturbance in the Power System 7
1.3.2 Power System Operation State 8
1.3.3 Three Defense Lines in Power System Stability Control 10
1.3.4 Functions of Defense System 12
1.4 Summary 15
References 15
2 Power System Analysis and Control Theory 17
2.1 Introduction 17
2.2 Mathematical Model of Power System 17
2.2.1 Mathematical Model of Synchronous Generator 17
2.2.2 Mathematical Model of Excitation System 22
2.2.3 Mathematical Model of Prime Mover and Speed Governor 24
2.2.4 Mathematical Model of Load 27
2.3 Power System Stability Analysis Method 29
2.3.1 Time‐Domain Simulation Method 29
2.3.2 Eigenvalue Analysis Method 31
2.3.3 Transient Energy Function Method 33
2.4 Automatic Control Theory 33
2.4.1 Classical Control Theory 34
2.4.2 Modern Control Theory 35
2.4.3 Large System Theory and Intelligent Control Theory 36
2.5 Summary 38
References 38
vi Contents
3 Wide‐Area Information Monitoring 41
3.1 Introduction 41
3.2 Test System 41
3.2.1 Four‐Generator Two‐Area System 41
3.2.2 Sixteen‐Generator System 42
3.2.3 Western Electricity Coordinating Council 43
3.3 Optimal Selection of Wide‐Area Signal 44
3.3.1 Wide‐Area Signal Selection Method Based
on the Contribution Factor 44
3.3.2 Simulation Verification 48
3.4 Optimal Selection of Wide‐Area Controller 57
3.4.1 Mathematical Background 57
3.4.2 Example Test System 62
3.4.3 GPSS Based on Collocated Controller Design 63
3.4.4 Testing Results and Analysis 64
3.5 Summary 70
References 71
4 Stability Analysis of Stochastic System 73
4.1 Introduction 73
4.2 Stability Analysis of Stochastic Parameter System 74
4.2.1 Interval Model and Second‐Order Perturbation
Theory‐Based Modal Analysis 74
4.2.2 Power System Small‐Signal Stability Region Calculation Method Based
on the Guardian Map Theory 82
4.3 Stability Analysis of Stochastic Structure System 102
4.3.1 Model‐Trajectory‐Based Method for Analyzing the Fault System 102
4.3.2 Angle Stability Analysis of Power System
Considering Cascading Failure 119
4.4 Stability Analysis of Stochastic Excitation System 137
4.4.1 Model of Multiple Operating Conditions System Considering
the Stochastic Characteristic of Wind Speed 137
4.4.2 Simulation Analysis 146
4.5 Summary 152
References 153
5 Stability Analysis of Time‐Delay System 155
5.1 Introduction 155
5.2 Stability Analysis of a Non‐Jump Time‐Delay System 156
5.2.1 Stochastic Stability Analysis of Power System with Time Delay Based
on Itô Differential 156
5.2.2 Stochastic Time‐Delay Stability Analysis of a Power System with Wind
Power Connection 168
5.3 Stability Analysis of a Jump Time‐Delay System 182
5.3.1 Jump Power System Time‐Delay Stability Analysis Based on Discrete
Markov Theory 182
Contents vii
5.3.2 Time‐Delay Stability Analysis of Power System Based on the Fault
Chains and Markov Process 196
5.4 Summary 208
Appendix A 209
References 210
6 Wide‐Area Robust Control 213
6.1 Introduction 213
6.2 Robust Control for Internal Uncertainties 214
6.2.1 Multiobjective Robust H /H Control Considering
2 ∞
Uncertainties for Damping Oscillation 214
6.2.2 Robust H /H Control Strategy Based on Polytope Uncertainty 221
2 ∞
6.3 Optimal Robust Control 226
6.3.1 Wide‐Area Damping Robust Control Based on Nonconvex
Stable Region 226
6.3.2 Wide‐Area Damping Robust H /H Control Strategy
2 ∞
Based on Perfect Regulation 236
6.4 Error Tracking Robust Control 243
6.4.1 Control Algorithm 245
6.4.2 Simulation Verification 248
6.5 Summary 251
References 252
7 Wide‐Area Adaptive Control 253
7.1 Introduction 253
7.2 Adaptive Control Considering Operating Condition Identification 254
7.2.1 Federated Kalman Filter Based Adaptive Damping Control
of Inter‐Area Oscillations 254
7.2.2 Classification and Regression Tree Based Adaptive Damping Control
of Inter‐Area Oscillations 268
7.3 Adaptive Control Considering Controller Switching 288
7.3.1 Dual Youla Parameterization Based Adaptive
Wide‐Area Damping Control 288
7.3.2 Continuous Markov Model Based Adaptive Control
Strategy for Time‐Varying Power System 303
7.3.3 Discrete Markov Model Based Adaptive Control
Strategy of Multiple‐Condition Power System 318
7.3.4 Adaptive Controller Switching Considering Time Delay 327
7.4 Summary 339
References 340
Index 341
