Analysis of Subsynchronous Resonance in Power Systems

271 Pages·1999·8.358 MB·English

by  K. R. Padiyar (auth.)

ANALYSIS OF
SUBSYNCHRONOUS
RESONANCE IN
POWER SYSTEMS
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
Power Electronics and Power Systems
Consulting Editors
Thomas A. Lipo and M. A. Pai
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ANALYSISOF
SUBSYNCHRONOUS
RESONANCEIN
POWER SYSTEMS
by
K. R. Padiyar
Department ofE lectrical Engineering
Indian Institute ofS cience
Bangalore 560 012, India
~.
"
Springer Science+Business Media, LLC
ISBN 978-1-4613-7577-7 ISBN 978-1-4615-5633-6 (eBook)
DOI 10.1007/978-1-4615-5633-6
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available
from the Library of Congress.
Copyright © 1999 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint ofthe hardcover Ist edition 1999
AII 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, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC .
Printed on acid-free paper.
To my sister, Manorama
Contents
Preface
1. INTRODUCTION 1
1.1 General 1
1.2 Definitions of SSR 4
1.3 Interactions with power system controllers 7
1.4 FACTS Controllers 8
1.5 Methods of Analysis of SSR 12
1.6 Chapter outline 16
2. MODELLING OF TURBINE GENERATOR 17
2.1 Introduction 17
2.2 Synchronous machine model 18
2.3 Park's transformation 22
2.4 Per unit quantities 30
2.5 Operational impedances and equivalent circuits 35
2.6 Modelling of excitation control system 41
2.7 Modelling of turbine generator mechanical system 43
2.8 Modelling of turbine and governor 55
2.9 Modelling and analysis of the mechanical and prime mover system 56
2.10 Synchronous generator modelling for transient simulation 59
3. MODELLING OF THE ELECTRIC NETWORK 63
3.1 Introduction 63
3.2 Transmission lines 64
3.3 Transformation using a - f3 variables 68
3.4 State equations 70
3.5 Interface between the network and generator 74
3.6 Impedance functions 75
3.7 Simulation of electromagnetic transients 78
4. ANALYSIS OF SSR WITH FIXED SERIES COMPENSATION 83
VII
Vlll ANALYSIS OF SUBSYNCHRONOUS RESONANCE IN POWER SYSTEMS
4.1 Introduction 83
4.2 Analysis of induction generator effect: frequency scanning method 83
4.3 Analysis of torsional interaction(TI) 87
4.4 State equations and eigenvalue analysis 96
4.5 An algorithm for computing torsional modes 108
4.6 Countermeasures for SSR III
4. 7 Torsional oscillations in parallel connected turbine generators 120
5. INTERACTIONS WITH POWER SYSTEM STABILIZER 121
5.1 Introduction 121
5.2 Basic concept in the application of PSS 122
5.3 Design of PSS 126
5.4 Torsional interaction with PSS 130
5.5 A case study 132
6. INTERACTIONS WITH HVDC CONVERTER CONTROL 137
6.1 Introduction 137
6.2 HVDC converters and control 138
6.3 Modelling of HVDC system for study of torsional interactions 147
6.4 Analysis of torsional interactions - A simplified approach 153
6.5 A case study 156
6.6 A simplified damping torque analysis 161
6.7 Control of torsional interaction 167
7. INTERACTIONS WITH SHUNT COMPENSATORS 169
7.1 Introduction 169
7.2 Static Var Compensator 171
7 .3 Torsional Interactions with SVC 186
7.4 Static Condenser(STATCON) 189
7.5 Torsional interactions with STATCON 196
7.6 A simplified analysis of torsional interaction with voltage controller 200
8. INTERACTIONS WITH SERIES COMPENSATORS 205
8.1 Introduction 205
8.2 Thyristor Controlled Series Compensator 206
8.3 Modelling of TCSC for SSR studies 216
8.4 Mitigation of SSR with TCSC 223
8.5 Static Synchronous Series Compensator (SSSC) 229
8.6 Torsional interactions with SSSC 234
Appendices 239
A- Data on IEEE Benchmark Models 239
A.1 IEEE First Benchmark Model ( FBM ) 239
A.2 IEEE Second Benchmark Model ( SBM ) 241
B- Calculation of Initial Conditions 245
Contents IX
c-
Abbreviations 249
References and Bibliography 251
Index
261
Foreword
In addition to the power flow at and around the nominal power frequency, all electrical
and electromechanical power systems involve a wide range of resonant oscillatory
modes which are excited during disturbances and switching events. Most of these
oscillations are harmless and die out because of net positive damping. However, under
some circumstances, a specific oscillation may have unacceptably high magnitude, rise
or sustain for a long period, and result in damage due to insulation, mechanical aging
or breakdown, or system instability. Given the natural parameters of lines and
equipment, power system oscillations that involve only the passive electrical
components, their resonance frequencies are substantially higher than the main power
frequency. However, when the oscillations involve both the electrical and rotating
mechanical equipment coupled through the magnetic flux, frequencies lower than the
power frequency appear. These oscillations that involve mass and inertia of the
complete turbine-generator have inter-machine or inter-area electromechanical
oscillation frequencies in the range of 0.1 Hz to several Hz.
Sub synchronous oscillations in the range of 10-50Hz result from mechanical
oscillations among individual turbine masses and the generator coupled into a long
shaft, and these mechanical oscillations, electrically coupled with the electrical system
via the generator. Subsynchronous Resonance (SSR) was unheard of until the
catastrophic damage to the turbine-generator at Southern California Edison's Mojave
Power Plant in 1970.
It has since been recognized that all high speed active controls of a power system such
as HVDC, FACTS, excitation control, etc., have a potential of mitigating as well as
causing damage or loss of life in large multi-machine generators. Even high speed
reclosing after fault clearance has been recognized as having a potential of causing loss
of life of turbine-generator shafts
There are simple rules of thumb that convey whether or not such possibilities of SSR
exist and, if so, there are available computational tools and expertise. Also, a large
number of papers have been published which are available in scattered form.
Analytically, SSR is a very complex subject matter, and it is gratifying to see Professor
Padiyar bring together complicated analytical and practical material into a monograph.
This monograph will be of great value to engineers and post-graduate students who
wish to learn about the details and find solutions for SSR problems.
Narain G. Hingorani
Los Altos Hills, CA
Preface
Modern power systems are large and complex syst.ems and pose challenges to
their secure and economic operation. The regulatory and resource constraints
have resulted in power transmission networks operating under stressed condi
tions. The problems of system stability are further complicated by recent trends
towards deregulation and restructuring of electric utilities. The system plan
ners are increasingly relying on existing and new solid-state controllers based
on high power semiconductors such as thyristors and GTO's. HVDC links
and Static Var Compensators based on thyristor controls have contributed to
system stability and prevent system collapse. New Flexible AC Transmission
System (FACTS) controllers are presently under development and have the po
tential of overcoming many of the control problems.
The problem of Subsynchronous Resonance (SSR) was encountered in the sev
enties when fixed series compensation was us~d in long radial lines connecting
turbine-generators to load centres. This involV!~s interaction between the elec
trical network and the torsional system of t.he turbine-generator leading to
self-excitation. The torsional oscillation modes, generally have frequencies in
the range of 10 to 50 Hz. Such torsional interactions were also discovered with
Power System Stabilizer (PSS), HVDC cOllvert.er controller and SVC voltage
controller.
While the SSR problem had discouraged syst.~1lI planners from introducing se
ries compensation, the recent development of Thyristor Controlled Series Com
pensator (TCSC) has demonstrated that the SSR problem can be mitigated.
New FACTS controllers based on Voltage Source Converters (VSC) such as
Static Compensator (STATCOM) and Static Synchronous Series Compensator
(SSSC) for voltage and power flow control ar~ expected to minimize the SSR
problem.
While there are a large number of papers published on SSR with fixed series
compensation, there is hardly any book that gives a comprehensive coverage of
the various aspects of the SSR problem. The modelling and analysis of SSR is
more complex than the analysis of small signal stability involving low frequency
oscillations. The system simulation for SSR studies, cannot be performed using