Transient stability analysis of integrated ac and dc power systems

275 Pages·2010·11.37 MB·English

by  K. S. Turner

TRANSIENT STABILITY ANALYSIS OF INTEGRATED
AC AND DC POWER SYSTEMS
A thesis
presented for the degree of
Doctor of Philosophy in Electrical Engineering
in the
University of Canterbury,
Christchurch, New Zealand
by
K.S. TURNER B.E. (HONS), M.E.
1980
i
CONTENTS Page
) List of Principal Symbols viii
Abstract xi
Acknowledgements xii
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 ELEMENTS OF TRANSIENT STABILITY ANALYSIS 5
2.0 INTRODUCTION 5
2.1 STEADY STATE STABILITY 6
2.2 TRANSIENT STABILITY 8
2.3 MULTI-MACHINE TRANSIENT STABILITY 10
2.4 MODELLING FOR TRANSIENT STABILITY STUDIES 11
2.4.1 Network Representation 12
2.4.2 Synchronous Machine Model 13
2.4.2.1 Algebraic equations 13
2.4.2.2 Differential equations 15
2.4.3 Speed Governor 16
2.4.4 Automatic Voltage Regulator 16
2.4.5 Loads 17
2.5 COMPUTATIONAL CONSIDERATIONS 18
2.6 SUMMARY 20
CHAPTER 3 MODELLING RECTIFIER LOADS 21
3.0 INTRODUCTION 21
3.0.1 Model Application 22
3.1 BASIC RECTIFIER MODEL 23
3.1.1 Commutation Reactance of Parallel
Bridges 24
3.1.2 Basic Assumptions 26
3.1.3 Basic Converter Equations 27
3.1.4 Per Unit System 28
3.1.5 Sequential Algorithm Formulation 29
3.1.5.1 Rectifier solution 32
3.2 DYNAMIC DC LOAD REPRESENTATION 33
3.2.1 Implicit Integration for Dynamic
DC Loads 34
3.2.2 Limitations of the Sequential
Algorithm 35
3.2 3 ~odel Limitations 36
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Page
3.3 ABNORMAL MODES OF OPERATION 37
3.3.1 Mode Classification 37
3.3.2 Equations for Abnormal Operation 38
3.4 UNIFIED ALGORITHM 39
3.4.1 Algorithm Proposal 39
3.4.2 Formulation of Equations for
Normal Operation 41
3.4.3 Formulation of Equations for
Abnormal Operation 43
3.4.4 Programme Implementation 44
3.4.4.1 Calculation of initial conditions 44
3.4.4.2 Choice of operating mode 46
3.4.4.3 Control specification 47
3.5 COMPARISON OF SEQUENTIAL AND UNIFIED
ALGORITHMS 47
3.6 RESULTS 50
3.6.1 System Studied 50
3.6.2 Discussion of Results 52
3.6.3 Rectifier Performance 55
3.7 CONCLUSIONS 56
CHAPTER 4 DERIVATION OF TRANSIENT STABILITY
COMPATIBLE EQUIVALENTS FROM TRANSIENT
CONVERTER SIMULATION WAVEFORMS 58
4.0 INTRODUCTION 58
4.1 TRANSIENT CONVERTER SIMULATION CONCEPTS 59
4.1.1 Formulation of Equations 60
4.1.2 Solution and Results 61
4.2 CONVERTER MODELLING FOR TRANSIENT
STABILITY 64
4.2.1 Transient Stability Requirements 64
4.2.2 Choice of Variables 65
4.3 ANALYSIS OF TRANSIENT CONVERTER
SIMULATION WAVEFORMS 68
4.3.1 Effect of Modulation 70
4.3.2 Effect of Frequency Mismatch 71
4.3.3 Fourier Transforms of Periodic
Waveforms with Noise 72
4.3.3.1 Spectral leakage reduction 74
4.3.3.2 Choice of window 76
4.3.3.3 Mainlobe width limitation 77
4.3.3.4 Algorithm to overcome mainlobe
width limitation 77
4.3.3.5 Algorithm tests 79
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Page
4.3.3.6 Significance 9f spectral
leakage in TCS waveforms 79
4.4 ALTERNATIVE TO SPECTRAL ANALYSIS 80
4.4.1 RMS Approximation for Voltage 81
4.4.2 RMS Approximation for Power 82
4.5 CONCLUSIONS 84
CHAPTER 5 MODELLING DC LINKS WITH TRANSIENT
CONVERTER SIMULATION INPUT 86
5.0 INTRODUCTION 86
5,1 QSS MODEL FORMULATION 86
5.1.1 Choice of Algorithm 87
5.1.2 Per Unit System 88
5.1.3 Quasi-Steady State Equations 89
5.1.3.1 Control equations 91
5.1.3.2 Series bridges 93
5.1.3.3 Including filters in the DC
link model 93
5.1.4 DC Link Control 94
5.1.4.1 Modification of control
characteristics 95
5.1.4.2 Implementation of control
mode changes 96
5.1.5 Calculation of Initial Conditions 97
5.1.6 Algorithm Performance 99
5.1.7 Programme Options 99
5.2 INCLUSION OF TRANSIENT CONVERTER
SIMULATION RESULTS 100
5.2.1 Solutions at the Link Node Using
TCS Input 100
5.2.2 Alignment of TCS Input with TS 102
5.2.3 Interactive Coordination Between
Programmes 104
5.2.4 System Equivalents for TCS 108
5.2.4.1 Obtaining time variant
equivalents 108
5.2.4.2 Algorithm for simultaneous
fault and link solution 109
5.2.4.3 Algorithm tests 110
5.3 CONCLUSION 112
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Page
CHAPTER 6 STUDIES WITH COMBINED. TCS AND QSS
DC LINK MODELS 114
6.0 INTRODUCTION 114
6.0.1 System Studied 114
6.0.2 Disturbances Examined 116
6.1 RECTIFIER AC SYSTEM FAULT 118
6.1~1 The Effect of Time Variant
Equivalents 118
6.1.2 Comparison of Results 120
6.1.2.1 Differences in voltage and 120
reactive power
6.1.2.2 Differences in real power 122
6.1.2.3 Coincidence at TCS end points 125
6.1.3 Approximations for TCS Equivalents 127
6.2 INVERTER AC SYSTEM FAULT 127
6.2.1 Fault Representation Using
TCS Equivalents 130
6.2.2 Low Voltage Mismatch 132
6.2.2.1 Second iteration 132
6.2.3 Comparison of Results 134
6.2.3.1 Differences in voltage and
reactive power 134
6.2.3.2 Differences in real power 136
6.2.3.3 Coincidence at TCS end points 138
6.2.4 Approximations for TCS Equivalents 138
6.3 DC FAULT STUDY 140
6.3.1 Link Performance During Fault 141
6.3.2 Matching QSS Restart with TCS 142
6.3.3 Termination of TCS 143
6.3.4 Comparison of Results 144
6.3.4.1 Recifier reactive power response 144
6.3.4.2 Differences in real power 145
6.3.5 Approximations for TCS Equivalents 147
6.4 CONCLUSION 147
CHAPTER 7 TRANSIENT STABILITY IMPROVEMENT USING
DC LINK CURRENT SETTING CONTROL 149
7.0 INTRODUCTION 149
7.1 BASIC PROPOSAL FOR TRANSIENT STABILITY
IMPROVEMENT 150
7.1.1 First Swing Stability Improvement 150
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Page
7.1.2 Full Damping Coritrol 152
7.1.3 Short Term DC Current Overload 152
7.2 POSSIBILITIES FOR TRANSIENT STABILITY
IMPROVEMENT 153
7.2.1 Classification of Systems 153
7.2.2 System for Study 155
7.3 THE EFFECT OF REALISTIC MACHINE MODELS 156
7.3.1 Summary of Results 156
7 3.2 Discussion 158
7.3.3 Effect on P-6 Curve 160
7.3.4 The Influence of Fault position 162
7.4 FACTORS AFFECTING TRANSIENT STABILITY
IMPROVEMENT 162
7.4.1 Magnitude of DC Current Increase 164
7.4.2 Period of DC Current Increase 167
7.4.3 DC Link position in the Network 168
7.4.4 Fault Resistance 169
7 4.5 Rate of DC Current Increase 170
7.4.6 Summary of Results 171
7.5 RESULTS WITH REALISTIC SYSTEMS 172
7.5.1 Two Generator SI System Equivalent 172
7.5.2 Full SI System 174
7.5.3 Full NZ System 174
7.6 CONSIDERATION OF FULL DAMPING CONTROL 177
7.6.1 Discussion of Controller 177
7.6.2 Results 178
7.7 ALTERNATIVE TS IMPROVEMENT SYSTEMS 180
7.7.1 Inverter End TS Improvement 180
7.7.2 DC Link Power Reversal 180
7.8 TRANSIENT CONVERTER SIMULATION RESULTS 182
7.8.1 Rectifier End Fault Case 184
7.8.2 Inverter End Fault Case 187
7.8.2.1 First Simulation 189
7.8.2.2 Second simulation 189
7.8.3 DC Link Reversal 191
7.9 CONCLUSION 194
CHAPTER 8 CONCLUSION 196
REFERENCES 198
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Page
APPENDIX A1 RELATIONSHIP BETWEEN AC AND DC
CURRENTS IN ABNORMAL MODES 205
APPENDIX A2 NEWTON-RAPSON SOLUTION METHOD 207
APPENDIX A3 FUNDAMENTAL EQUATIONS OF FOURIER
ANALYSIS AND CONVOLUTION 209
APPENDIX A4 EFFECT OF FREQUENCY MISMATCH BETWEEN
TCS AND TS PROGRAMMES 212
APPENDIX AS CONVERSION OF TCS SAMPLES TO A FORM
SUITABLE FOR USE IN AN FFT 213
APPENDIX A6 DATA FOR THE NEW ZEALAND PRIMARY
GENERATION AND 220KV TRANSMISSION
NETWORK 214
APPENDIX A7 DATA FOR TS IMPROVEMENT IN A RECTIFIER
AC SYSTEM - CASE 1 OF TABLE 7.1 219
APPENDIX A8 DATA FOR TS IMPROVEMENT IN AN INVERTER
AC SYSTEM - CASE 4 OF TABLE 7.1 221
APPENDIX A9 DATA FOR TS IMPROVEMENT USING DC LINK
POWER REVERSAL - CASE 2 OF TABLE 7.1 223
APPENDIX A10 PAPER PUBLISHED IN TRANS. IEEE, VOL.
PAS-99, NO.1, JANUARY/FEBRUARY 1980 225
APPENDIX All PAPER PUBLISHED IN PROC. lEE, VOL. 127,
PT.C, NO.5, SEPTEMBER 1980 234
APPENDIX A12 COMPUTATION OF AC-DC SYSTEM DISTURBANCES
- PART I INTERACTIVE COORDINATION OF
GENERATOR AND CONVERTER TRANSIENT MODELS 237
APPENDIX A13 COMPUTATION OF AC-DC SYSTEM DISTURBANCES
- PART II DERIVATION OF POWER FREQUENCY
VARIABLES FROM CONVERTER TRANSIENT
RESPONSE 246
APPENDIX A14 COMPUTATION OF AC-DC SYSTEM DISTURBANCES
- PART III TRANSIENT STABILITY ASSESSMENT 254
vii
THE AUTHOR
The author was born in New Zealand, in 1950 and began
'undergraduate studies at the University of Canterbury in 1969
as a bursar with N.Z. Electricity. He completed a B.E. (Hons)
degree in 1972 and an M.E. degree the following year. In early
1974 he joined the Dunedin staff of N.Z. Electricity and was
responsible over the next 3 years for the installation and
commissioning of Southward transmission on the N.Z. HVDC Link.
During this time he was also involved in developing partial
discharge testing for evaluating the aged condition of
generators and in transient fault location on AC lines.
He returned to the University of Canterbury as N.Z.
Electricity Power Fellow in 1977 to pursue investigations of
HVDC transmission.
viii
LIST OFl?RINCIPAL SYMBOLS
For convenience the symbols used throughout this
thesis are defined below. In some cases, symbols have
alternative meanings but if there is any ambiguity of
meaning this is clarified in the text or diagram.
Symbols
I Current
V Voltage
Synchronous Machine Field Voltage
Admittance
R Resistance
x Reactance
Commutation Reactance
Synchronous Machine Transient Reactance
X" Synchronous Machine Subtransient Reactance
L Inductance
C Capacitance
S Complex Power
P Real Power
Q Reactive Power
H Inertia Constant of Rotating Machine
Tq' o' Td' o Synchronous Machine Transient Open C~rcuit Time
Constant
Til T" Synchronous Machine Subtransient Open Circuit
qo' do
Time Constant
Vd DC Voltage
Id DC Current
VLlL Thevenin Source Voltage
E~ Converter Fundamental AC Terminal Voltage
I~ Converter Fundamental AC Terminal Current
ZthL1L : Thevenin Delay Angle
a Converter Delay Angle
u Converter Commutation Angle
o
a + u (converters)
o
Generator Rotor Angle (for synchronous machines)
y Converter Extinction Angle
Power Factor
~
7T 3.14159
t Time
h Integration Step Length
T Period of Power System Frequency
W Angular Frequency
SP
x Specified Value of x
x Derivative of x with t to Time
cos x + j sin x
j Complex Operator
f (x) Function of x
x Complex Variable x
x* Complex Conjugate of x
[ Matrix or Vector
.;
Square Root
f Integration
E Summation
a>b a greater than b
a <b a less than b
++ Fourier Transform Pair
x Convolution
Subscripts
a TCS Capacitive Nodes
S TCS Resistive Node with no Capacitive Connection
y TCS Inductive Nodes
o
TCS Converter Inductive Nodes
1 TCS Inductive Branches
r TCS Resistive Branches
k TCS Converter Branches
r,m Real and Imaginary Parts
r,i Rectifier and Inverter Variables
d,q Direct and Quadrature Axis Synchronous Machine
Variables
Abbreviations
N. Z. New Zealand
S.1. South Island of N.Z.
N.1. North Island of N.Z.
p.u Per unit