IEE Power and Energy Series - AC-DC Power System Analysis

328 Pages·1998·13.92 MB·English

by  Arrillaga

IEE Power and Energy Series
AC-DC
P O W ER
SYSTEM
ANALYSIS
Jos Arrillaga
and Bruce Smith
The Institution of Electrical Engineers
Published by: The Institution of Electrical Engineers, London,
United Kingdom
© 1998: The Institution of Electrical Engineers
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British Library Cataloguing in Publication Data
A CIP catalogue record for this book
is available from the British Library
ISBN 0 85296 934 1
Printed in England by Short Run Press Ltd., Exeter
Preface
Although the early decision to generate electric power at 50/60 cycles and
three phases is practically irreversible, the transmission and utilisation of
energy is not necessarily tied to these conditions. The choice between
transmission alternatives is made on the basis of cost and controllability.
The original justification for HVDC transmission was its lower cost for
long electrical distances which, in the case of submarine (or underground)
cable schemes, applies to relatively short geographical distances. At present,
the controllability factor often justifies the DC alternative regardless of cost,
as evidenced by the growing number of back-to-back links in existence.
The merits of HVDC over AC transmission have been explained in
several books by Adamson and Hingorani, Uhlmann, Kimbark, Arrillaga,
and Paddiyar, listed in chronological order.
In earlier days, the dynamic performance of the DC link was assessed with
the help of scaled-down physical simulators. These provided a reasonable
representation of the converter control and protection functions, but were
very restricted in AC-network representation.
With the expansion of HVDC transmission throughout the world, and
particularly the increasing numbers of interconnections between different
countries, few power systems can continue to escape the effect of this
technology in their planning and operation. Such expansion has encour-
aged the development of analytical models to represent the behaviour of the
AC-DC power system.
An early attempt to describe the HVDC link as a power system component
was made in the book 'Computer modelling of electrical power systems'.
Although the book's main objective was conventional power-system analysis,
it did propose algorithmic modifications for the incorporation of HVDC
transmission. Since then the experience of many years of HVDC operation
has produced more advanced models to represent the behaviour of both the
AC and DC systems.
In particular, the availability of the EMTP (electromagnetic-transient
program) with detailed representation of power-electronic components and,
more recently, its implementation in the RTDS (real-time digital simulator)
xii Preface
has practically eliminated the need for physical simulators. Consequently,
the impact of the EMTP techniques is given prominence in this book.
Although steady-state waveforms and their harmonic components can also
be derived using the EMTP method, such information can be obtained
more accurately and efficiently in the frequency domain. Therefore, the
present book also contains several chapters describing frequency-domain
techniques with reference to the AC-DC converter.
The primary object of this book is the incorporation of HVDC converters
and systems in power-system analysis, but the algorithms described can
easily be extended to other industrial components such as drives and
smelters, and to the FACTS (flexible AC transmission systems) technology.
Conventional AC power-system concepts and techniques are only in-
cluded in as much as they are required to explain the incorporation of the
HVDC link behaviour.
The book only deals with system studies, influenced by converter control,
whether steady state or transient. Fast transients, such as lightning and
switching events (in the ns or fj,$ region) are not considered, as they are
beyond the influence of HVDC controllers and can be analysed by conven-
tional power-system methodology.
Contents
Preface
XI
Introduction 1
.1 Basic AC-DC configuration 1
.2 AC-DC simulation philosophy 2
.3 Steady-state simulation 3
.4 Fault analysis 4
.5 Harmonic analysis 4
.6 System stability 5
The AC-DC converter in steady state 7
2.1 Introduction 7
2.2 Power frequency—symmetrical operation 8
2.2.1 Analysis of the commutation circuit 10
2.2.2 Rectifier operation 12
2.2.3 Inverter operation 14
2.2.4 Power factor and reactive power 15
2.3 Power frequency—unbalanced operation 17
2.3.1 Terminology and waveforms 17
2.3.2 Variables and equations 18
2.4 Characteristic harmonics 23
2.5 The converter as a frequency modulator 26
2.5.1 The modulation process 27
2.6 Harmonic transfer generalisation 29
2.6.1 From the AC to the DC sides 30
2.6.2 From the DC to the AC sides 31
2.6.3 Effect of switching-instant variation 32
2.6.4 Transfer across the DC link 33
2.7 Harmonic instabilities 36
2.8 Generalised harmonic domain converter model 41
2.8.1 Analysis of the commutation 41
Star-connected bridge 41
Delta-connected bridge 43
2.8.2 Valve-firing control 44
Current control 45
Commutation margin control 46
vi Contents
2.8.3 Direct voltage 48
Star-connection voltage samples 48
Delta-connection voltage samples 49
Convolution of the samples 51
2.8.4 Phase currents 54
Converter side 54
System side 54
2.9 Summary 59
2.10 References 60
The power flow solution 61
3.1 Introduction 61
3.2 Specification of the operating condition 61
3.3 Formulation of the algorithm 63
3.4 Decoupled Newton techniques 66
3.5 Incorporation of AC-DC buses 70
3.6 DC-system model 71
3.6.1 Converter variables 72
3.6.2 DC per unit system 74
3.6.3 Derivation of equations 74
3.6.4 Incorporation of control equations 77
3.6.5 Control of converter AC terminal voltage 78
3.6.6 Inverter operation 78
3.7 Unified AC-DC solution 78
3.7.1 Multiconverter systems 83
3.7.2 Programming considerations 84
3.8 Convergence properties 86
3.9 Modification of the power flow for use with the unit connection 87
3.9.1 An equivalent inverter model 90
3.10 Components-related capability 92
3.10.1 HVDC test system 93
3.10.2 Type of HVDC constraint loci 94
3.10.3 Constraint equations 95
3.10.4 Loci of operating constraints 98
3.10.5 Complete capability chart 100
3.11 System-related HVDC capability 102
3.11.1 Converter power—current characteristics 102
3.11.2 Converter power limits 104
3.11.3 DC link power-transfer capability 106
3.12 Summary 107
3.13 References 108
The harmonic solution 109
4.1 Introduction 109
4.2 Basic AC-DC system 109
4.3 Functional notation of the converter equations 110
4.4 Mismatch equations 113
4.5 Newton's method 116
4.5.1 The Jacobian matrix 117
Numerical differentiation 117
Analytical derivation 121
Contents vii
With respect to AC phase-voltage variations 122
With respect to direct current ripple variation 123
With respect to end-of-commutation variation 123
With respect to firing-instant variation 124
4.5.2 Sequence-components model 124
4.6 Computer implementation 128
4.6.1 Initialisation 130
4.6.2 The switching system 130
4.6.3 Harmonic solution 132
4.6.4 Convergence tolerance 133
4.7 Validation and performance 134
4.8 Summary 141
4.9 References 141
Three-phase power and harmonic flow 143
5.1 Introduction 143
5.2 The three-phase power flow 143
5.2.1 Mismatch equations 145
5.2.2 The power-flow Jacobian 146
5.2.3 Newton's method 153
5.2.4 Performance of the power flow 153
5.2.5 Zero-sequence blocking 158
5.3 Converter harmonic model 161
5.4 Combined solution 162
5.4.1 Sequential method 162
5.4.2 Unified Newton method 165
5.4.3 Test system 167
5.4.4 Convergence characteristics 167
5.4.5 Power flow/converter interaction 169
5.5 Summary 171
5.6 References 172
Electromagnetic transient simulation 175
6.1 Introduction 175
6.2 The state-variable solution 177
6.2.1 Structure of TCS 178
6.2.2 Integration method 180
6.2.3 Choice of state variables 181
6.2.4 Forming the network equations 182
6.2.5 Valve switchings 184
6.2.6 Effect of automatic time-step adjustments 186
6.2.7 TCS converter control 189
6.3 The EMTP method 192
6.3.1 Discretisation of system components 193
6.3.2 Error analysis 199
6.3.3 Switching discontinuities 201
6.3.4 Voltage and current chatter due to discontinuities 204
6.4 Subsystems 209
6.5 The EMTP program 215
6.6 The NETOMAC program 216
viii Contents
6.7 The PSCAD/EMTDC program 217
6.7.1 Program structure 217
6.7.2 DC valve groups 220
6.7.3 Transmission-line model 223
Frequency-dependent transmission-line models 225
Curve fitting for Z and ,4(0 228
c
Line constants 229
6.7.4 Converter-transformer model 230
Single-phase UMEC model 230
UMEC Norton equivalent 233
UMEC implementation in PSCAD/EMTDC 235
Three-limb three-phase UMEC 237
6.7.5 Future developments 241
6.8 Examples of PSCAD/EMTDC simulation 241
6.9 Modelling of flexible AC transmission systems (FACTS) 258
6.9.1 Simulation of the SVC in PSCAD/EMTDC 259
6.9.2 Dynamic voltage control at an inverter terminal 262
6.10 Real-time digital simulation 263
6.11 Summary 269
6.12 References 271
Electromechanical stability 275
7.1 Introduction 275
7.2 Dynamic model of the synchronous machine 276
7.2.1 Equations of motion 276
7.2.2 Electrical equations 278
7.2.3 Synchronous-machine controllers 280
7.2.4 Generator representation in the network 282
7.3 Load representation 285
7.4 The AC transmission network 286
7.4.1 System faults and switching 287
7.5 Static power conversion models 287
7.5.1 Single-converter loads 288
Abnormal modes of converter operation 290
Converter representation in the network 293
7.5.2 DC links 296
DC power modulation 298
DC link representation in the network 301
7.6 , AC-DC transient stability programs 301
7.6.1 Program structure 301
7.6.2 Trapezoidal integration 301
7.6.3 Initial conditions 304
7.6.4 Test of operating mode 306
7.6.5 Converter program interface 307
7.6.6 Test for commutation failure 309
7.7 Test system and results 312
7.7.1 Minor disturbance 315
7.7.2 Major disturbance 316
7.8 Summary 320
7.9 References 320
Contents ix
8 Electromechanical stability with transient converter simulation 323
8.1 Introduction 323
8.2 Description of the hybrid algorithm 324
8.2.1 Individual program modifications 326
8.2.2 Data flow 326
8.3 TS/EMTDC interface 328
8.3.1 Equivalent impedances 329
8.3.2 Equivalent sources 331
8.3.3 Phase and sequence-data conversions 331
8.3.4 Interface variables derivation 332
8.4 EMTDC to TS data transfer 335
8.4.1 Data extraction from converter waveforms 339
8.5 Interaction protocol 343
8.6 Interface location 346
8.7 TSE hybrid algorithm 351
8.8 Test system and results 355
8.8.1 Electromagnetic transient response 356
8.8.2 TSE hybrid response 356
8.9 Summary 361
8.10 References 362
Appendices
I Newton-Raphson method 363
1.1 Basic algorithm 363
1.2 Techniques to make the Newton-Raphson solution more efficient 364
Sparsity programming 365
Triangular factorisation 365
Optimal ordering 366
1.3 References 366
II The short-circuit ratio (SCR) 367
Definitions 367
Derivation of short-circuit ratios 368
Reference 370
III Test systems 371
III. 1 CIGRE HVDC benchmark model 371
111.2 Simplified test system 371
111.3 Test systems used in the stability chapters 373
System A 373
System B 375
IV State-space analysis 379
V Numerical integration 383
VI Curve-fitting algorithm 387
Index 391
Chapter 1
Introduction
1.1 Basic AC-DC configuration
The three-phase bridge, shown in Figure 1.1, is the basic switching unit
used for the conversion of power from AC to DC and from DC to AC. The
valve numbers in the Figure (1, % 3, 4, 5, 6) indicate the sequence of their
conduction with reference to the positive sequence of the AC-system phases
(R, Y, B).
Two series-connected bridges constitute a 12-pulse converter group, the
most commonly used configuration in high-voltage and large-power appli-
cations. Figure 1.2 illustrates schematically the main components involved
in a typical AC-DC converter station and Figure 1.3 shows the standard
circuit of a monopolar high-voltage direct-current transmission scheme.
Although the analysis described in this book relates specifically to the
12-pulse converter and a point-to-point DC link, the proposed algorithms
can easily be extended to higher pulse converters and multiterminal
AC-DC interconnections.
.z _
iM A^ 3 ii 5
n
ik 4 i^ 6 'f 2
Figure 1.1 Three-phase bridge configuration