CONTENTS
1. Introduction 1
1.1 Background 1
1.2 Electrical Transmission Networks 1
1.3 Conventional Control Mechanisms 3
1.3.1 Automatic Generation Control (AGC) 3
1.3.2 Excitation Control 4
1.3.3 Transformer Tap-Changer Control 5
1.3.4 Phase-Shifting Transformers 5
1.4 Flexible ac Transmission Systems (FACTS) 6
1.4.1 Advances in Power-Electronics Switching Devices 7
1.4.2 Principles and Applications of Semiconductor
Switches 8
1.5 Emerging Transmission Networks 12
References 13
2. Reactive-Power Control in Electrical Power Transmission
Systems 16
2.1 Reactive Power 16
2.2 Uncompensated Transmission Lines 18
2.2.1 A Simple Case 18
2.2.1.1 Load Compensation 18
2.2.1.2 System Compensation 19
2.2.2 Lossless Distributed Parameter Lines 19
2.2.2.1 Symmetrical Lines 21
2.2.2.2 Midpoint Conditions of a Symmetrical
Line 22
2.2.2.3 Case Study 23
2.3 Passive Compensation 33
2.3.1 Shunt Compensation 34
2.3.2 Series Compensation 34
2.3.3 Effect on Power-Transfer Capacity 35
2.3.3.1 Series Compensation 36
2.3.3.2 Shunt Compensation 37
2.4 Summary 39
References 39
3. Principles of Conventional Reactive-Power Compensators 40
3.1 Introduction 40
3.2 Synchronous Condensers 41
3.2.1 Configuration 41
3.2.2 Applications 42
3.2.2.1 Control of Large-Voltage Excursions 42
3.2.2.2 Dynamic Reactive-Power Support at
HVDC Terminals 42
3.3 The Saturated Reactor (SR) 43
3.3.1 Configuration 43
3.3.2 Operating Characteristics 45
3.4 The Thyristor-Controlled Reactor (TCR) 47
3.4.1 The Single-Phase TCR 47
3.4.2 The 3-Phase TCR 52
3.4.3 The Thyristor-Switched Reactor (TSR) 56
3.4.4 The Segmented TCR 56
3.4.5 The 12-Pulse TCR 56
3.4.6 Operating Characteristics of a TCR 59
3.4.6.1 Operating Characteristics Without Voltage
Control 59
3.4.6.2 Operating Characteric With Voltage
Control 61
3.5 The Thyristor-Controlled Transformer (TCT) 62
3.6 The Fixed Capacitor–Thyristor-Controlled Reactor
(FC–TCR) 63
3.6.1 Configuration 63
3.6.2 Operating Characteristic 64
3.6.2.1 Without Step-Down Transformer 64
3.6.2.2 With Step-Down Transformer 65
3.7 The Mechanically Switched Capacitor–Thyristor-Controlled
Reactor (MSC–TCR) 70
3.8 The Thyristor-Switched Capacitor (TSC) 71
3.8.1 Switching a Capacitor to a Voltage Source 71
3.8.2 Switching a Series Connection of a Capacitor and
Reactor 72
3.8.2.1 The Term Involving Fundamental
Frequency, q0 73
3.8.2.2 The Terms Involving Natural Resonance
Frequency, qn 74
3.8.2.3 Practical Switching Strategies 75
3.8.3 Turning Off of the TSC Valve 78
3.8.4 The TSC Configuration 78
3.8.5 Operating Characteristic 81
3.9 The Thyristor-Switched Capacitor–Thyristor-Controlled
Reactor (TSC–TCR) 82
3.9.1 Configuration 82
3.9.2 Operating Characteristic 83
3.9.2.1 A Practical Example 83
3.9.3 Current Characteristic 84
3.9.4 Susceptance Characteristic 86
3.9.5 Mismatched TSC–TCR 87
3.10 A Comparison of Different SVCs 89
3.10.1 Losses 89
3.10.2 Performance 91
3.11 Summary 91
References 91
4. SVC Control Components and Models 93
4.1 Introduction 93
4.2 Measurement Systems 93
4.2.1 Voltage Measurement 94
4.2.1.1 ac/ dc Rectification 95
4.2.1.2 Coordinate Transformation 95
4.2.1.3 Fourier Analysis 96
4.2.1.4 Measurement of Squared Voltage 97
4.2.2 The Demodulation Effect of the Voltage-
Measurement System 98
4.2.2.1 Addition 98
4.2.2.2 Modulation 101
4.2.2.3 Fourier Analysis–Based Measurement
System 101
4.2.2.4 Coordinate Transformation–Based
Measurement Systems 104
4.2.2.5 ac/ dc Rectification–Based Measurement
Systems 104
4.2.2.6 Filtering Requirements 104
4.2.3 Current Measurement 106
4.2.4 Power Measurement 109
4.2.5 The Requirements of Measurement Systems 110
4.2.5.1 Phasor Transducers 112
4.2.5.2 Optical Sensors 112
4.3 The Voltage Regulator 112
4.3.1 The Basic Regulator 112
4.3.2 The Phase-Locked Oscillator (PLO) Voltage Regulator 118
4.3.2.1 The Basic Single-Phase Oscillator 118
4.3.2.2 The 3-Phase Oscillator 120
4.3.3 The Digital Implementation of the Voltage
Regulator 121
4.3.3.1 Digital Control 122
4.4 Gate-Pulse Generation 123
4.4.1 The Linearizing Function 124
4.4.2 Delays in the Firing System 125
4.4.2.1 Thyristor Deadtime 125
4.4.2.2 Thyristor Firing-Delay Time 126
4.5 The Synchronizing System 127
4.6 Additional Control and Protection Functions 128
4.6.1 The Damping of Electromechanical Oscillations 128
4.6.2 The Susceptance (Reactive-Power) Regulator 129
4.6.3 The Control of Neighboring Var Devices 131
4.6.4 Undervoltage Strategies 132
4.6.5 The Secondary-Overvoltage Limiter 132
4.6.6 The TCR Overcurrent Limiter 133
4.6.7 TCR Balance Control 133
4.6.8 The Nonlinear Gain and the Gain Supervisor 133
4.7 Modeling of SVC for Power-System Studies 134
4.7.1 Modeling for Load-Flow Studies 134
4.7.1.1 SVC Operation Within the Control Range 134
4.7.1.2 SVC Operation Outside the Control Range 135
4.7.2 Modeling for Small- and Large-Disturbance Studies 136
4.7.3 Modeling for Subsynchronous Resonance (SSR)
Studies 137
4.7.4 Modeling for Electromagnetic Transient Studies 137
4.7.5 Modeling for Harmonic-Performance Studies 137
4.8 Summary 138
References 138
5. Concepts of SVC Voltage Control 142
5.1 Introduction 142
5.2 Voltage Control 142
5.2.1 V-I Characteristics of the SVC 142
5.2.1.1 Dynamic Characteristics 142
5.2.1.2 Steady-State Characteristic 145
5.2.2 Voltage Control by the SVC 145
5.2.3 Advantages of the Slope in the SVC Dynamic
Characteristic 147
5.2.3.1 Reduction of the SVC Rating 147
5.2.3.2 Prevention of Frequency Operation at
Reactive-Power Limits 148
5.2.3.3 Load Sharing Between Parallel-Connected
SVCs 148
5.2.4 Influence of the SVC on System Voltage 149
5.2.4.1 Coupling Transformer Ignored 149
5.2.4.2 Coupling Transformer Considered 151
5.2.4.3 The System Gain 152
5.2.5 Design of the SVC Voltage Regulator 154
5.2.5.1 Simplistic Design Based on System Gain 155
5.2.5.2 Design That Considers Generator
Dynamics 163
5.3 Effect of Network Resonances on the Controller Response 163
5.3.1 Critical Power-System Parameters 166
5.3.2 Sensitivity to Power-System Parameters 166
5.3.2.1 Response Variation With Regulator-
Transient Gain, KT 170
5.3.2.2 Response Variation With System Strength,
ESCR0 170
5.3.2.3 Voltage-Sensitivity Transfer Function 170
5.3.3 Sensitivity to TCR Operating Point 172
5.3.4 Choice of Transient Gain 175
5.3.5 Certain Features of the SVC Response 176
5.3.6 Methods for Improving the Voltage-Controller
Response 177
5.3.6.1 Manual Gain Switching 177
5.3.6.2 The Nonlinear Gain 177
5.3.6.3 Bang-Bang Control 178
5.3.6.4 The Gain Supervisor 178
5.3.6.5 Series-Dynamic Compensation 180
5.3.6.6 ac-Side Control Filters 183
5.4 The 2nd Harmonic Interaction Between the SVC and
ac Network 186
5.4.1 Influence of the 2nd Harmonic Voltage on the TCR 186
5.4.2 Causes of 2nd Harmonic Distortion 191
5.4.2.1 Fault Clearing 191
5.4.2.2 Reactor/ Transformer Switching Near an
SVC 193
5.4.2.3 Geomagnetically Induced Currents 195
5.4.2.4 Noise or Imbalance in the Control
Systems 195
5.4.3 TCR Balance Control 195
5.5 Application of the SVC to Series-Compensated ac Systems 199
5.5.1 ac System–Resonant Modes 199
5.5.1.1 Shunt-Capacitance Resonance 199
5.5.1.2 Series-Line Resonance 201
5.5.1.3 Shunt-Reactor Resonance 201
5.5.2 SVC Transient Response With Series-Compensated
ac-Transmission Lines 203
5.5.2.1 Reactor Switching 204
5.5.2.2 Fault Application and Clearing 207
5.5.3 Effect of the Shunt-Reactor Mode on the SVC
Voltage Controller 209
5.5.3.1 Effect of the TCR Operating Point 211
5.5.3.2 Filtering of the Shunt-Resonant Mode 211
5.6 3rd Harmonic Distortion 214
5.7 Voltage-Controller Design Studies 217
5.7.1 Modeling Aspects 217
5.7.2 Special Performance-Evaluation Studies 217
5.7.3 Study Methodologies for Controller Design 217
5.7.3.1 Impedance-Versus-Frequency Computation 217
5.7.3.2 Eigenvalue Analyses 218
5.7.3.3 Simulation Studies 218
5.8 Summary 218
References 218
6. SVC Applications 221
6.1 Introduction 221
6.2 Increase in Steady-State Power-Transfer Capacity 221
6.3 Enhancement of Transient Stability 224
6.3.1 Power-Angle Curves 225
6.3.2 Synchronizing Torque 226
6.3.2.1 Uncompensated System 227
6.3.2.2 SVC-Compensated System 228
6.3.3 Modulation of the SVC Bus Voltage 229
6.4 Augmentation of Power-System Damping 232
6.4.1 Principle of the SVC Auxiliary Control 233
6.4.2 Torque Contributions of SVC Controllers 235
6.4.2.1 Effect of the Power System 235
6.4.2.2 Effect of the SVC 236
6.4.3 Design of an SVC PSDC 239
6.4.3.1 Controllability 240
6.4.3.2 Influence of SVC Sites and the Nature of
Loads 240
6.4.3.3 Selection Criteria for PSDC Input Signals 242
6.4.3.4 Input Filtering 243
6.4.3.5 General Characteristics of PSDC Input
Signals 243
6.4.3.6 Performance of PSDC Input Signals 244
6.4.3.7 SVC PSDC Requirements 245
6.4.3.8 Design Procedure for a PSDC 248
6.4.3.9 Case Study 249
6.4.4 Composite Signals for Damping Control 252
6.4.4.1 Frequency of Remotely Synthesized
Voltage 252
6.4.4.2 Case Study 254
6.4.5 Alternative Techniques for the Design of SVC
Auxiliary Controllers 256
6.5 SVC Mitigation of Subsynchronous Resonance (SSR) 257
6.5.1 Principle of SVC Control 257
6.5.2 Configuration and Design of the SVC Controller 260
6.5.3 Rating of an SVC 262
6.6 Prevention of Voltage Instability 263
6.6.1 Principles of SVC Control 263
6.6.1.1 A Case Study 263
6.6.2 Configuration and Design of the SVC Controller 265
6.6.3 Rating of an SVC 266
6.7 Improvement of HVDC Link Performance 268
6.7.1 Principles and Applications of SVC Control 269
6.7.1.1 Voltage Regulation 269
6.7.1.2 Suppression of Temporary Overvoltages 269
6.7.1.3 Support During Recovery From Large
Disturbances 269
6.7.2 Configuration and Design of the SVC Controller 271
6.7.2.1 Interactions Between the SVC and the
HVDC 272
6.7.3 Rating of the SVC 272
6.8 Summary 272
References 272
7. The Thyristor-Controlled Series Capacitor (TCSC) 277
7.1 Series Compensation 277
7.1.1 Fixed-Series Compensation 277
7.1.2 The Need for Variable-Series Compensation 277
7.1.3 Advantages of the TCSC 278
7.2 The TCSC Controller 279
7.3 Operation of the TCSC 280
7.3.1 Basic Principle 280
7.3.2 Modes of TCSC Operation 281
7.3.2.1 Bypassed-Thyristor Mode 282
7.3.2.2 Blocked-Thyristor Mode 283
7.3.2.3 Partially Conducting Thyristor, or Vernier,
Mode 283
7.4 The TSSC 284
7.5 Analysis of the TCSC 285
7.6 Capability Characteristics 290
7.6.1 The Single-Module TCSC 292
7.6.2 The Multimodule TCSC 294
7.7 Harmonic Performance 295
7.8 Losses 298
7.9 Response of the TCSC 301
7.10 Modeling of the TCSC 304
7.10.1 Variable-Reactance Model 304
7.10.1.1 Transient-Stability Model 305
7.10.1.2 Long-Term-Stability Model 308
7.10.2 An Advanced Transient-Stability Studies Model 309
7.10.2.1 TCSC Controller Optimization and TCSC
Response-Time Compensation 310
7.10.3 Discrete and Phasor Models 311
7.10.4 Modeling for Subsynchronous Resonance (SSR)
Studies 311
7.11 Summary 312
References 313
8. TCSC Applications 315
8.1 Introduction 315
8.2 Open-Loop Control 315
8.3 Closed-Loop Control 316
www.Techbooksyard.com
CONTENTS xiii
8.3.1 Constant-Current (CC) Control 316
8.3.2 Constant-Angle (CA) Control 317
8.3.3 Enhanced Current Control 319
8.3.4 Constant-Power Control 319
8.3.5 Enhanced Power Control 320
8.3.6 Firing Schemes and Synchronization 321
8.4 Improvement of the System-Stability Limit 321
8.5 Enhancement of System Damping 322
8.5.1 Principle of Damping 323
8.5.2 Bang-Bang Control 325
8.5.3 Auxiliary Signals for TCSC Modulation 325
8.5.3.1 Local Signals 325
8.5.3.2 Remote Signals 325
8.5.4 Case Study for Multimodal Decomposition–Based
PSDC Design 326
8.5.4.1 Selection of the Measurement Signal 326
8.5.4.2 Selection of the Synthesizing Impedance 327
8.5.5 H∞ Method–Based PSDC Design 330
8.5.6 Alternative Techniques for PSDC Design 334
8.5.7 Placement of the TCSC 334
8.6 Subsynchronous Resonance (SSR) Mitigation 334
8.6.1 TCSC Impedance at Subsynchronous Frequencies 335
8.6.2 A Case Study 340
8.6.2.1 Transient-Torque Minimization 342
8.6.2.2 Criteria for SSR Mitigation by the TCSC 342
8.7 Voltage-Collapse Prevention 343
8.8 TCSC Installations 345
8.8.1 Imperatriz–Serra da Mesa TCSCs in Brazil 346
8.8.1.1 TCSC Power-Oscillation Damping (POD)
Control 348
8.8.1.2 Phasor Estimation 350
8.8.1.3 Performance of Both TCSCs 352
8.8.2 Stode TCSC in Sweden 353
8.9 Summary 355
References 355
9. Coordination of FACTS Controllers 359
9.1 Introduction 359
9.2 Controller Interactions 359
9.2.1 Steady-State Interactions 360
9.2.2 Electromechanical-Oscillation Interactions 360
9.2.3 Control or Small-Signal Oscillations 361
www.Techbooksyard.com
xiv CONTENTS
9.2.4 Subsynchronous Resonance (SSR) Interactions 361
9.2.5 High-Frequency Interactions 361
9.2.6 The Frequency Response of FACTS Controllers 362
9.2.6.1 The Frequency Response of the SVC 362
9.2.6.2 The Frequency Response of the TCSC 364
9.3 SVC–SVC Interaction 364
9.3.1 The Effect of Electrical Coupling and Short-Circuit
Levels 364
9.3.1.1 Uncoupled SVC Buses 364
9.3.1.2 Coupled SVC Buses 365
9.3.2 The System Without Series Compensation 366
9.3.3 The System With Series Compensation 371
9.3.3.1 Shunt-Reactor Resonance 373
9.3.4 High-Frequency Interactions 374
9.3.5 Additional Coordination Features 379
9.3.5.1 Parallel SVCs 379
9.3.5.2 Electrically Close SVCs 380
9.4 SVC–HVDC Interaction 381
9.5 SVC–TCSC Interaction 382
9.5.1 Input Signal of the TCSC–PSDC With Bus
Voltage 384
9.5.2 Input Signal of the TCSC–PSDC With a System
Angle 387
9.5.3 High-Frequency Interactions 387
9.6 TCSC–TCSC Interaction 393
9.6.1 The Effect of Loop Impedance 393
9.6.1.1 Low-Loop Impedance 393
9.6.1.2 High-Loop Impedance 394
9.6.2 High-Frequency Interaction 394
9.7 Performance Criteria for Damping-Controller Design 399
9.8 Coordination of Multiple Controllers Using Linear-Control
Techniques 401
9.8.1 The Basic Procedure for Controller Design 401
9.8.1.1 Derivation of the System Model 401
9.8.1.2 Enumeration of the System Performance
Specifications 402
9.8.1.3 Selection of the Measurement and Control
Signals 402
9.8.1.4 Controller Design and Coordination 402
9.8.1.5 Validation of the Design and Performance
Evaluation 403
9.8.2 Controller Coordination for Damping Enhancement 403
www.Techbooksyard.com
CONTENTS xv
9.8.3 Linear Quadratic Regulator (LQR)–Based
Technique 405
9.8.4 Constrained Optimization 405
9.8.4.1 Techniques Without Explicit Robustness
Criteria 405
9.8.4.2 Techniques With Explicit Robustness
Criteria 405
9.8.5 Nonlinear-Constrained Optimization of a Selective-
Model-Performance Index 405
9.8.6 Global Coordination Using Nonlinear-Constrained
Optimization 407
9.8.7 Control Coordination Using Genetic Algorithms 408
9.9 Coordination of Multiple Controllers Using Nonlinear-
Control Techniques 409
9.10 Summary 409
References 410
10. Emerging FACTS Controllers 413
10.1 Introduction 413
10.2 The STATCOM 413
10.2.1 The Principle of Operation 415
10.2.2 The V-I Characteristic 417
10.2.3 Harmonic Performance 419
10.2.4 Steady-State Model 421
10.2.5 SSR Mitigation 425
10.2.5.1 A Study System 425
10.2.5.2 STATCOM Performance 426
10.2.6 Dynamic Compensation 428
10.2.6.1 A Multilevel VSC–Based STATCOM 428
10.2.6.2 A Selective Harmonic-Elimination
Modulation (SHEM) Technique 431
10.2.6.3 Capacitor-Voltage Control 431
10.2.6.4 STATCOM Performance 433
10.3 The SSSC 437
10.3.1 The Principle of Operation 437
10.3.2 The Control System 440
10.3.3 Applications 442
10.3.3.1 Power-Flow Control 442
10.3.3.2 SSR Mitigation 443
10.4 The UPFC 444
10.4.1 The Principle of Operation 444
10.4.2 Applications 448
www.Techbooksyard.com
xvi CONTENTS
10.5 Comparative Evaluation of Different FACTS Controllers 449
10.5.1 Performance Comparison 450
10.5.2 Cost Comparison 452
10.6 Future Direction of FACTS Technology 453
10.6.1 The Role of Communications 455
10.6.2 Control-Design Issues 455
10.7 Summary 456
References 457
Appendix A. Design of an SVC Voltage Regulator 462
A.1 Study System 462
A.2 Method of System Gain 464
A.3 Eigenvalue Analysis 465
A.3.1 Step Response 466
A.3.2 Power-Transfer Studies 471
A.4 Simulator Studies 472
A.4.1 Step-Response Studies 472
A.4.2 Power-Transfer Limits 474
A.5 A Comparison of Physical Simulator Results
With Analytical and Digital Simulator Results
Using Linearized Models 475
References 477
Appendix B. Transient-Stability Enhancement in a Midpoint
SVC-Compensated SMIB System 478
Appendix C. Approximate Multimodal Decomposition Method
for the Design of FACTS Controllers 481
C.1 Introduction 481
C.2 Modal Analysis of the ith Swing Mode, li 483
C.2.1 Effect of the Damping Controller 485
C.3 Implications of Different Transfer Functions 486
C.3.1 Controllability 486
C.3.2 Observability 486
C.3.3 The Inner Loop 486
C.4 Design of the Damping Controller 486
C.4.1 The Controller-Phase Index (CPI) 487
C.4.2 The Maximum Damping Influence (MDI)
Index 487
C.4.3 The Natural Phase Influence (NPI) Index 488
References 489
www.Techbooksyard.com
CONTENTS xvii
Appendix D. FACTS Terms and Definitions 490
D.1 Definitions of Basic Terms 490
D.2 Definitions of Facts Controller Terms 490
Reference 492
Index 493
www.Techbooksyard.com
