FACTS: Modelling and Simulation in Power Networks
Enrique Acha, Claudio R. Fuerte-Esquivel, Hugo Ambriz-Pérez, César Angeles-Camacho.
John Wiley & Sons, 1 edition, 2004
This book presents a general introduction to the modeling of Flexible Alternating Current Transmission Systems (FACTS) for use in power system simulations in steady state, spiced with other topics such as Three-phase Power Flow, and Optimal Power Flow (OPF).
FACTS mentioned include Thyristor-controlled Reactor (TCR), Static Var Compensator (SVC), Thyristor-controlled Series Compensator (TCSC), Voltage Source Converter (VSC), Static Compensator (STATCOM), Solid State Series Compensator (SSSC), Unified Power Flow Controller (UPFC), and High-Voltage Direct-Current Voltage Source Converters (HVDC-VSC). Their mathematical modeling is given relating currents, voltages, and firing angles of individual components. Then the models are presented in matrix form, relating currents and voltages through corresponding admittance matrices, which permits including the devices in a general power flow formulation to be solved by Newton-Raphson techniques.
Though the book includes the description and modeling of the conventional power flow problem, it does not attempt to be an introductory text, and so many explanations are rather terse. A previous understanding of the power flow problem, by reading other books, should be required.
The greatest controversy regarding this book is in the amount of Matlab code that is provided.
Even if plagued by typos and formatting horrors, most of the code given in small amounts is fairly easy to "fix" by those with some knowledge of the power flow problem.
The exception is the appendix which includes a complete Optimal Power Flow (OPF) program to minimize power generation costs. This is a big block of code which becomes totally unreadable. The code, if used exactly as is, will not work because there are several undeclared variables and errors which may be hard to spot. If you've done any serious programming before, you'll be pulling your hair out.
The code lacks enough commenting and the chapter discussing the OPF problem does not explain with enough detail the algorithm implemented.
The last chapter, concerning Power Flow Tracing, doesn't really fit within the rest of book, and only seems like an attempt to fill more space.
With that said, this book is extremely short, and it does not justify a price over USD $100, being barely 420 pages long, all the code included.
Over all, it seems like the authors wanted to be extremely brief when presenting the topics.
It would have been better if this same book, covering the same topics, was expanded to be 100 pages longer in order to include better, more elaborate treatment of the subjects, more worked out examples, and nicely formatted and working code.
Author(s): Enrique Acha, Claudio R. Fuerte-Esquivel, Hugo Ambriz-Pérez, César Angeles-Camacho
Edition: 1
Publisher: Wiley
Year: 2004
Language: English
Pages: 420
Team LiB......Page 0
Cover......Page 1
Contents......Page 8
Preface......Page 14
1.1 Background......Page 17
1.2 Flexible Alternating Current Transmission Systems......Page 18
1.4 FACTS Controllers......Page 19
References......Page 22
2.1 Introduction......Page 25
2.3 Controllers Based on Conventional Thyristors......Page 27
2.3.1 The Thyristor-controlled Reactor......Page 28
2.3.2 The Static VAR Compensator......Page 32
2.3.3 The Thyristor-controlled Series Compensator......Page 34
2.3.3.1 Thyristor-controlled Series Capacitor Equivalent Circuit......Page 35
2.3.3.2 Steady-state Current and Voltage Equations......Page 36
2.3.3.3 Thyristor-controlled Series Capacitor Fundamental Frequency Impedance......Page 40
2.4 Power Electronic Controllers Based on Fully Controlled Semiconductor Devices......Page 44
2.4.1 The Voltage Source Converter......Page 45
2.4.1.1 Pulse-width Modulation Control......Page 46
2.4.1.2 Principles of Voltage Source Converter Operation......Page 49
2.4.2 The Static Compensator......Page 50
2.4.3 The Solid State Series Compensator......Page 51
2.4.4 The Unified Power Flow Controller......Page 52
2.4.5 The High-voltage Direct-current Based on Voltage Source Converters......Page 54
2.5 Control Capabilities of Controllers Based on Voltage Source Converters......Page 56
References......Page 57
3.1 Introduction......Page 59
3.2 Transmission Line Modelling......Page 60
3.2.1.1 Calculation of Lumped RLC Parameters......Page 61
3.2.1.3 Internal Impedances......Page 63
3.2.1.4 Ground Return Impedances......Page 64
3.2.2 Ground Wires......Page 66
3.2.3 Bundle Conductors......Page 67
3.2.4 Double Circuit Transmission Lines......Page 70
3.2.5 The Per-unit System......Page 71
3.2.6 Transmission-line Program: Basic Parameters......Page 72
3.2.7 Numerical Example of Transmission Line Parameter Calculation......Page 75
3.2.8 Long Line Effects......Page 76
3.2.9 Transmission Line Transpositions......Page 78
3.2.10 Transmission Line Program: Distributed Parameters......Page 79
3.2.11 Numerical Example of Long Line Parameter Calculation......Page 82
3.2.12 Symmetrical Components and Sequence Domain Parameters......Page 83
3.2.14 Numerical Example of Sequence Parameter Calculation......Page 85
3.3.1 Single-phase Transformers......Page 86
3.3.2 Simple Tap-changing Transformer......Page 88
3.3.3 Advanced Tap-changing Transformer......Page 89
3.3.4 Three-phase Transformers......Page 91
3.3.4.1 Star–Star Connection......Page 92
3.3.4.3 Star–Delta Connection......Page 94
3.3.5 Sequence Domain Parameters......Page 95
3.4 Rotating Machinery Modelling......Page 98
3.4.1 Machine Voltage Equation......Page 99
3.5 System Load......Page 102
3.6 Summary......Page 105
References......Page 106
4.2 General Power Flow Concepts......Page 109
4.2.1 Basic Formulation......Page 110
4.3.1 Early Power Flow Algorithms......Page 113
4.3.2 The Newton–Raphson Algorithm......Page 114
4.3.4 Generator Reactive Power Limits......Page 117
4.3.5 Linearised Frame of Reference......Page 118
4.3.6 Newton–Raphson Computer Program in Matlab® Code......Page 120
4.3.7 The Fast Decoupled Algorithm......Page 127
4.3.8 Fast Decoupled Computer Program in Matlab® Code......Page 128
4.3.9 A Benchmark Numerical Example......Page 131
4.4.1 Load Tap-changing Transformers......Page 135
4.4.1.1 State Variable Initialisation and Limit Checking......Page 137
4.4.1.2 Load Tap Changer Computer Program in Matlab® Code......Page 138
4.4.1.3 Test Case of Voltage Magnitude Control with Load Tap-changing......Page 143
4.4.1.5 Control Coordination between One Load Tap Changer and One Generator......Page 146
4.4.2 Phase-shifting Transformer......Page 148
4.4.2.1 State Variable Initialisation and Limit Checking......Page 150
4.4.2.2 Phase-shifter Computer Program in Matlab® Code......Page 151
4.4.2.3 Test Cases for Phase-shifting Transformers......Page 156
4.5.1 Sparsity-oriented Solutions......Page 160
4.5.2.1 Test Case of Truncated Adjustments Involving Three Load Tap-changing Transformers......Page 161
4.5.3 Special Load Tap Changer Configurations......Page 163
4.5.3.1 Test Case of Sensitivity Factors in Parallel Load Tap-changing Operation......Page 164
4.6 Summary......Page 165
References......Page 166
5.1 Introduction......Page 169
5.2 Power Flow Solutions Including FACTS Controllers......Page 170
5.3.1 Conventional Power Flow Models......Page 171
5.3.2 Shunt Variable Susceptance Model......Page 174
5.3.3 Static VAR Compensator Computer Program in Matlab® Code......Page 175
5.3.5 Static VAR Compensator Firing-angle Computer Program in Matlab® Code......Page 178
5.3.6 Integrated Transformer Firing-angle Model......Page 182
5.3.7 Nodal Voltage Magnitude Control using Static VAR Compensators......Page 183
5.3.8 Control Coordination between Reactive Sources......Page 184
5.3.9 Numerical Example of Voltage Magnitude Control using One Static VAR Compensator......Page 185
5.4.1 Variable Series Impedance Power Flow Model......Page 187
5.4.2 Thyristor-controlled Series Compensator Computer Program in Matlab® Code......Page 189
5.4.3 Numerical Example of Active Power Flow Control using One Thyristor-controlled Series Compensator: Variable Series Compensator Model......Page 194
5.4.4 Firing-angle Power Flow Model......Page 196
5.4.5 Thyristor-controlled Series Compensator Firing-angle Computer Program in Matlab® Code......Page 198
5.4.6 Numerical Example of Active Power Flow Control using One Thyristor-controlled Series Compensator: Firing-angle Model......Page 203
5.4.7 Numerical Properties of the Thyristor-controlled Series Compensator Power Flow Model......Page 205
5.5.1 Power Flow Model......Page 207
5.5.2 Static Compensator Computer Program in Matlab® Code......Page 208
5.5.3 Numerical Example of Voltage Magnitude Control using One Static Compensator......Page 214
5.6 Unified Power Flow Controller......Page 216
5.6.1 Power Flow Model......Page 217
5.6.2 Unified Power Flow Controller Computer Program in Matlab® Code......Page 219
5.6.3 Numerical Example of Power Flow Control using One Unified Power Flow Controller......Page 229
5.7 High-voltage Direct-current-based Voltage Source Converter......Page 232
5.7.1 Power Equations......Page 233
5.7.2 High-voltage Direct-current-based Voltage Source Converter Computer Program in Matlab® Code......Page 234
5.7.3.2 HVDC-VSC Full Model......Page 241
5.8.3 Controllers Represented by Series Reactances......Page 243
5.9 Summary......Page 244
References......Page 245
6.1 Introduction......Page 247
6.2 Power Flow in the Phase Frame of Reference......Page 248
6.2.1 Power Flow Equations......Page 249
6.2.2 Newton–Raphson Power Flow Algorithm......Page 250
6.2.3 Matlab® Code of a Power Flow Program in the Phase Frame of Reference......Page 252
6.2.4 Numerical Example of a Three-phase Network......Page 260
6.3 Static VAR Compensator......Page 265
6.3.1 Variable Susceptance Model......Page 266
6.3.2 Firing-angle Model......Page 267
6.3.3 Numerical Example: Static VAR Compensator Voltage Magnitude Balancing Capability......Page 268
6.4.1 Variable Susceptance Model......Page 269
6.4.2 Firing-angle Model......Page 271
6.5 Static Compensator......Page 273
6.5.1 Static Compensator Three-phase Numerical Example......Page 276
6.6 Unified Power Flow Controller......Page 277
6.7 Summary......Page 280
References......Page 281
7.1 Introduction......Page 283
7.2.1.1 Variables......Page 284
7.2.1.3 Equality Constraints......Page 285
7.2.2 Application of Newton's Method to Optimal Power Flow......Page 286
7.2.3 Linearised System Equations......Page 287
7.2.5 Conventional Power Plant Modelling in Optimal Power Flow......Page 288
7.2.5.1 Transmission Lines......Page 289
7.2.5.2 Shunt Elements......Page 290
7.2.6.1 Handling of Inequality Constraints on Variables......Page 291
7.2.6.2 Handling of Inequality Constraints on Functions......Page 293
7.3 Implementation of Optimal Power Flow using Newton's Method......Page 294
7.3.2 Active Power Schedule......Page 295
7.3.5 Conjugated Variables......Page 296
7.3.6 An Optimal Power Flow Numerical Example......Page 297
7.5.1 Load Tap-changing Lagrangian Function......Page 299
7.5.2 Linearised System of Equations......Page 300
7.5.3 Load Tap-changing Transformer Test Cases......Page 301
7.6.1 Lagrangian Function......Page 302
7.6.2 Linearised System of Equations......Page 303
7.6.3.1 Case 1: No Active Power Flow Regulation......Page 305
7.6.3.2 Case 2: Active Power Flow Regulation at LakePS......Page 306
7.7.1 Lagrangian Function......Page 307
7.7.2 Linearised System of Equations......Page 308
7.7.3.1 Firing-angle Model......Page 309
7.7.3.2 Susceptance Model......Page 311
7.8.1 Lagrangian Function......Page 312
7.8.2 Linearised System of Equations......Page 313
7.8.3 Thyristor-controlled Series Compensator Test Cases......Page 315
7.9.2 Direct-current Link Lagrangian Function......Page 317
7.9.4 Linearised System of Equations......Page 318
7.9.5 Unified Power Flow Controller Test Cases......Page 321
7.10 Summary......Page 323
References......Page 324
8.1 Introduction......Page 327
8.2 Basic Assumptions......Page 328
8.3 Mathematical Justification of the Proportional Sharing Principle......Page 329
8.4 Dominions......Page 331
8.4.1 Dominion Contributions to Active Power Flows......Page 333
8.4.2 Dominion Contributions to Reactive Power Flows......Page 335
8.4.3 Dominion Contributions to Loads and Sinks......Page 336
8.5 Tracing Algorithm......Page 337
8.6.1 Simple Radial Network......Page 338
8.6.2 Simple Meshed Network: Active Power......Page 340
8.6.3 Meshed Network with FACTS Controllers: Reactive Power......Page 345
8.6.5 Tracing the Power Output of a Wind Generator......Page 347
8.6.5.1 The Wind Generator Model......Page 351
8.6.5.2 Numerical Example......Page 352
8.7 Summary......Page 355
References......Page 356
A.1 Tap-changing Transformer......Page 359
A.2 Thyristor-controlled Series Compensator......Page 360
A.4 Unified Power Flow Controller......Page 361
A.5 High-voltage Direct-current-based Voltage Source Converter......Page 363
B.1.1 The Gradient Vector......Page 365
B.1.2 The Matrix W......Page 366
B.2 Phase Shifter Transformer......Page 368
B.3 Static VAR Compensator......Page 371
B.4 Thyristor-controlled Series Compensator......Page 372
B.5 Unified Power Flow Controller......Page 373
Appendix C: Matlab® Computer Program for Optimal Power Flow Solutions using Newton's Method......Page 381
Index......Page 415
