Static Compensators (STATCOMs) in Power Systems (eBook)

Dr. Farhad Shahnia received his Ph.D. in Electrical Engineering from Queensland University of Technology, Brisbane, Australia. He is currently a Lecturer in Curtin University, Perth, Australia. His professional experience includes three years at Research Office-Eastern Azerbaijan Electric Power Distribution Company, Tabriz, Iran. Prior to joining Curtin University, he was a research fellow in Queensland University of Technology, Brisbane, Australia. He has published 5 book chapters, 8 journal papers and 55 conference papers.Dr. Sumedha Rajakaruna received his Ph.D. in Electrical Engineering from the University of Toronto, Ontario, Canada. He was a Lecturer at University of Moratuwa, Sri Lanka until 2000 and then an Assistant Professor at Nanyang Technological University, Singapore until 2007. Since 2007, he is at Curtin University, Perth, Australia. He is the founding Director and Lead Designer of Green Electric Energy Park at Curtin University, a state of the art renewable energy laboratory built at the cost of over $1.2 million in 2012. He is the supervisor of more than 10 PhD graduates and has published 2 book chapters and over 40 research articles.Dr. Arindam Ghosh received his Ph.D. in Electrical Engineering from University of Calgary, Canada in 1983. Currently, he is a Professor of Power Engineering at Curtin University, Perth, Australia. Prior to joining the Curtin in 2013, he was with Queensland University of Technology, Brisbane, Australia from 2006 to 2012 and with the Department of Electrical Engineering at IIT Kanpur, India, for 21 years. He is a fellow of INAE and IEEE. He has published 1 book, 6 book chapters and more than 350 papers in international conferences and journals.

Preface 6
Contents 9
About the Editors 12
Reviewers 13
Abbreviations 14
1 Converter and Output Filter Topologies for STATCOMs 19
Abstract 19
1.1 Introduction 20
1.2 Multi-pulse Converters 23
1.2.1 Six-Pulse Converter 23
1.2.2 12-Pulse Converter 26
1.2.3 24-Pulse Converter 28
1.2.4 48-Pulse Converter 29
1.3 Multilevel Converters 31
1.3.1 Diode Clamped MLC 32
1.3.2 Flying Capacitor MLC 33
1.3.3 Cascaded H-Bridge MLC 35
1.4 Filter Topologies 36
1.4.1 Passive Filters 37
1.4.1.1 L Filters 37
1.4.1.2 LC Filters 39
1.4.1.3 LCL Filters 41
1.4.2 Active Power Filters 42
1.5 Control Methods of STATCOM Converters 44
1.5.1 Sinusoidal PWM (SPWM) 44
1.5.2 Space Vector PWM (SVM) 46
1.5.3 Selective Harmonic Elimination PWM (SHE-PWM) 47
1.5.4 Hysteresis Band PWM (HB-PWM) 48
References 49
2 Multilevel Converter Topologies for STATCOMs 53
Abstract 53
2.1 Introduction 54
2.1.1 Multilevel Converters: Basic Concepts and Features 59
2.2 Monolithic Multilevel Converters 62
2.2.1 Diode-Clamped Multilevel Converter (DCMC) 62
2.2.1.1 DCMC 63
2.2.1.2 Dual CSC Structure of DCMC 70
2.2.2 Flying Capacitor Multilevel (FCM) Converter 72
2.2.2.1 FCM VSC 72
2.2.2.2 Dual CSC Structure of FCMC 79
2.3 Modular Multilevel Converters 81
2.3.1 Chain-Link Multilevel Converters Based on Bipolar Cells 81
2.3.2 Modular Multilevel Converters Based on Half-Bridge Cells 88
2.3.2.1 Modular Multilevel Converter (MMC) with DC Connection 88
2.3.2.2 Modular Multilevel Converter (MMC) with AC Connection 90
2.3.3 Modular Current Source Converters (MCSC) 92
2.3.3.1 Modular CSCs Using H-Bridge Cells 93
2.3.3.2 Modular CSCs Using Cells with Common DC Connection 94
2.3.3.3 Current Source M2LC with Half or Full-Bridge Cells 94
2.4 Future Trends in Multilevel Converter Topologies 96
References 98
3 Analysis and Implementation of an 84-Pulse STATCOM 101
Abstract 101
3.1 Introduction 102
3.2 84-Pulses STATCOM 104
3.2.1 Reinjection Configuration 104
3.2.2 Total Harmonic Distortion 106
3.2.3 STATCOM Arrangement 109
3.2.4 Phase-Locked-Loop 110
3.2.5 Firing Sequence 111
3.2.6 Seven-Level Generator 111
3.2.7 Angle Control Circuit 111
3.3 Control Strategy 113
3.3.1 Segmented PI Controller 113
3.3.2 Study Case 116
3.4 Experimental Results 117
3.4.1 VSC Based on Multi-pulse Strategy 118
3.4.2 STATCOM Synchronized to the Grid 119
3.4.3 STATCOM Based on Energy Storage and Capacitors on the DC-Link 120
3.4.3.1 Notching 121
3.4.3.2 Harmonics 121
3.4.4 STATCOM Reference Voltage Tracking Through a PI Controller 124
3.4.5 Load Imbalance 124
References 126
4 Mathematical Modeling and Control Algorithms of STATCOMs 129
Abstract 129
4.1 Introduction 129
4.2 STATCOM Mathematical Model 130
4.2.1 Three-Phase Mathematical Model 131
4.2.2 Mathematical Model in the alpha - beta Coordinate System 132
4.2.3 Mathematical Model in the d-q Coordinate System---Balanced Conditions 134
4.2.4 Mathematical Model in the d-q Coordinate System - Unbalanced Conditions 136
4.2.4.1 Harmonics Compensation Due to the Unbalanced Switching Function 138
4.3 STATCOM Control Algorithms 140
4.3.1 Frequency Domain: d-q Control Algorithm for Balanced Conditions 140
4.3.2 Frequency Domain: d-q Control Algorithm for Unbalanced Conditions 142
4.3.2.1 Control Algorithm Simulation 144
4.3.3 Time-Domain: Predictive Control Algorithms (PC) 145
4.3.3.1 STATCOM Model---Discretization 147
4.3.3.2 Current, Voltage Predictions 149
4.3.3.3 TOCC---Time-Optimal Current Control 151
4.3.4 Resonant Controller 155
4.3.4.1 PR-Controller Transfer Function 156
4.3.4.2 Control Algorithm 158
4.3.4.3 DC-Bus Voltage Control 159
A.0. Appendix 160
References 162
5 STATCOM Control Strategies 164
Abstract 164
5.1 Introduction 165
5.2 Space Vector Model of a VSC Connected to the Grid 165
5.3 Power Delivered by the VSC to the Grid 168
5.4 Block Diagram of the Control System 170
5.4.1 Determination of the PI Regulator Constants 171
5.4.2 Space Vector Modulation 174
5.4.3 Synchronization with the Grid: PLL Algorithm 175
5.5 STATCOMs Operating as Nonlinear Current Source 176
5.5.1 Variable Switching Frequency Controllers with Two-Level and Multilevel Converters 179
5.5.2 Constant Switching Frequency Controllers 182
5.6 Advanced Functions of STATCOM Systems 182
5.6.1 Selective Harmonic Compensation 183
5.6.2 Active Power Filter 186
5.7 The Unbalanced Case 194
5.7.1 Grid Voltage Decomposition into Symmetrical Components 194
5.7.2 Calculation of the Power Delivered to the Electrical Grid 197
5.8 DC Voltage Determination 198
References 201
6 Robust Nonlinear Control of STATCOMs 204
Abstract 204
6.1 Introduction 205
6.2 STATCOM Mathematical Model 206
6.3 Feedback Linearization 210
6.3.1 Input--Output Feedback Linearization for Single-Input Single-Output Systems 210
6.3.2 Input--Output Linearization of STATCOM System 213
6.3.3 Input--Output Linearization with Damping Controller 215
6.3.4 Input--Output Linearization with Modified Damping Controller 217
6.3.5 Controllability and Observability Analysis for STATCOM System 220
6.3.6 Stability Analysis Based on Lyapunov Theorem 222
6.3.7 Performance of the Nonlinear Feedback Controller 224
6.4 Passivity-Based Control 226
6.4.1 Euler-Lagrange Formulation 227
6.4.2 Passivity-Based Controller for STATCOM 228
6.4.3 Additional Nonlinear Damping-Based PBC 230
6.4.4 Numerical Approximation of Desired Dynamics 231
6.4.5 Performance of the PBCND Method 232
6.5 Advanced Control Strategy 233
6.5.1 Dynamic Extension of STATCOM System 234
6.5.2 Desired Control Input 236
6.5.3 Port-Controlled Hamiltonian Method 237
6.5.4 Performance of PCH Method 238
References 239
7 Versatile Control of STATCOMs Using Multiple Reference Frames 241
Abstract 241
7.1 Introduction 242
7.2 Fundamentals of the Control of a STATCOM 244
7.2.1 Park's Transformation 244
7.2.2 Active and Reactive Power Control in a STATCOM 246
7.2.2.1 Decoupled Control of P and Q in a STATCOM 248
7.2.2.2 DC-Voltage Control 250
7.2.2.3 More Complex Connection Filters 252
7.3 Harmonic Control in a STATCOM 253
7.3.1 Selective Harmonic Control 255
7.3.2 Repetitive Control 256
7.3.3 Grid-Frequency Variations 258
7.4 Efficient Use of Multiple Reference Frames in STATCOM Control 259
7.4.1 Design and Stability Analysis 261
7.4.2 Description of a Case Study 264
7.4.3 Investigating the Computational Burden of the Proposed Algorithm 266
7.4.4 Experimental Results Using an EMRF Controller for a STATCOM 268
7.5 Voltage Support in Unbalanced Power Systems 272
7.5.1 Problem Description 272
7.5.2 Voltage Unbalance Compensation Using EMRF Controller 274
7.5.3 Experimental Results of Voltage Unbalance Compensation 275
References 276
8 Control of Multilevel STATCOMs 280
Abstract 280
8.1 Introduction 281
8.2 Multilevel STATCOMs Modeling 282
8.2.1 Cascade H-Bridge Topology 282
8.2.1.1 Steady State Analysis 284
8.2.2 Neutral Point Clamped Topology 288
8.2.2.1 Steady State Analysis 291
8.2.3 Multilevel Current Source Topology 294
8.2.3.1 Steady State Analysis 296
8.3 Control Requirements for Multilevel STATCOM Topologies 298
8.3.1 Cascade H-Bridge 300
8.3.2 Neutral Point Clamped 300
8.3.3 Multilevel Current Source Converter 301
8.4 Linear Control Strategies 302
8.4.1 p-q Theory Based Control 302
8.4.2 dq Frame Based Control 304
8.4.3 Power Distribution Strategies 306
8.4.3.1 Power Distribution Strategy for the dq Frame 307
8.4.3.2 Power Distribution Strategy for the abc Frame 308
8.5 Non-Linear Control Strategies 313
8.5.1 Input/Output Linearizing Control 313
8.5.2 Hysteresis Control 317
8.5.3 Predictive Control 318
References 324
9 Adaptive Observer for Capacitor Voltages in Multilevel STATCOMs 327
Abstract 327
9.1 Introduction 328
9.2 System Description and Modeling 328
9.2.1 Modeling of Cascaded H-Bridge Multilevel Converters 329
9.2.2 Modeling of Flying Capacitor Multilevel Converter 331
9.3 Observer Design 333
9.3.1 Interconnected Observer for the Cascaded H-Bridge Multilevel Converter 336
9.3.2 Adaptive Interconnected Observer for a Flying Capacitor Multilevel Converter 337
9.3.3 Extended Adaptive Interconnected Observer for a Cascaded H-Bridge Multilevel Converter 339
9.4 Simulation and Experimental Results 341
9.4.1 Validation of the Interconnected Observer Using Simulation Experiments 341
9.4.2 Validation of the Extended Adaptive Interconnected Observer for a Flying Capacitor Converter Using Experimental Data 343
References 350
10 Modeling and Control of STATCOMs 352
Abstract 352
10.1 Introduction 353
10.2 STATCOM Implementations and Models 354
10.2.1 Angle and Magnitude Controlled Converters 354
10.2.2 Current Controlled Converters 356
10.2.2.1 Active and Reactive Current Control 357
10.2.2.2 Resonant Controller 357
10.2.2.3 Unbalance Mitigation 358
10.3 STATCOM Control Requirements 358
10.3.1 Transmission Level Applications 359
10.3.1.1 Power Transfer Capability Enhancement 359
10.3.1.2 Transient (Angle) Stability Enhancement 359
10.3.1.3 Small Signal (Dynamic) Stability Enhancement 360
10.3.1.4 Voltage Stability 361
10.3.2 Distribution Level Applications 362
10.3.2.1 Similarities and Differences Compared with Transmission 362
10.3.2.2 Customer Site Location of STATCOMs 363
10.4 Distribution System Modeling for Instantaneous Control 364
10.4.1 Model Derivation 365
10.4.2 Application to Sub-cycle Control 367
10.4.3 Scalability to Large Systems 368
10.5 Sub-cycle Voltage Regulation 368
10.5.1 Non-minimum Phase Nature of the Voltage Regulation Problem 369
10.5.2 Linear Control Design 370
10.5.3 Non-linear Control Design 371
10.5.4 Controller Comparison via Simulation 372
10.5.5 STATCOM Control Design 373
10.5.6 Integrated System Performance 377
10.6 Conclusion 379
A.0. Appendix: Stability of the Zero Dynamics 380
References 381
11 Study of STATCOM in abc Framework 383
Abstract 383
11.1 Introduction 384
11.1.1 PV-Curves 386
11.1.2 Voltage Stability Margin 388
11.2 STATCOM at Steady State 390
11.3 Embedding a STATCOM into the Power Flow Formulation 392
11.4 Case Study 395
11.4.1 Analysis of the Reference Case 396
11.4.2 Analysis of Three-Phase Unbalanced Cases 399
11.4.3 Results 401
11.4.3.1 Single-Phase Analysis 401
11.4.3.2 Voltage Stability Margin Calculation 401
11.4.3.3 Modal Analysis 403
11.4.3.4 Unbalanced Three-Phase Cases 409
References 414
12 Modeling of STATCOM in Load Flow Formulation 416
Abstract 416
12.1 Introduction 417
12.2 Operation Principles and Equivalent Circuit of STATCOM 419
12.2.1 STATCOM 419
12.2.2 The Shunt Compensation Concept on STATCOM 420
12.2.3 STATCOM Equivalent Circuit 422
12.2.3.1 Power Equations 422
12.3 NR Load Flow Formulations 423
12.3.1 NR Current Injection Load Flow Formulation (Version-1) 423
12.3.2 NR Current Injection Load Flow Formulation (Version-2) 425
12.4 Recent NR Power-Current Injection Load Flow Formulation 426
12.4.1 Representation of PQ Buses 427
12.4.2 Improved Representation of PV Buses 430
12.4.3 Current Mismatches for PQ Buses 432
12.4.4 Power Mismatches for PV Buses 433
12.4.5 Bus Voltage Corrections 433
12.5 Developed STATCOM Model 434
12.6 Load Flow Solution Process with Developed STATCOM Model 437
12.7 Numerical Examples 437
12.7.1 IEEE 14 Bus Test System 437
12.7.2 Performance Characteristics 439
12.7.3 Robustness of the Developed STATCOM Model in Many IEEE Test Systems 439
12.7.4 Execution Time and Numbers of Iterations 441
A.0. Appendix 441
References 445
13 Optimal Placement and Sizing of STATCOM in Power Systems Using Heuristic Optimization Techniques 447
Abstract 447
13.1 Introduction 448
13.2 STATCOM Placement and Sizing Using Optimization Techniques 449
13.2.1 Evolution Strategies (ES) 450
13.2.2 Genetic Algorithm (GA) 450
13.2.3 Particle Swarm Optimization (PSO) 452
13.2.4 Harmony Search (HS) Algorithm 453
13.2.5 Hybrid Artificial Intelligence Techniques 454
13.2.6 Comparison of Various Heuristic Optimization Techniques 455
13.3 Optimal Placement and Sizing of STATCOM Using GHS Algorithm 456
13.3.1 STATCOM Modelling 456
13.3.2 Modal Analysis for Determining STATCOM Placement 458
13.3.3 Problem Formulation for Optimal Sizing of STATCOM 460
13.3.4 Global Harmony Search Algorithm 463
13.3.5 Application of GHS Algorithm for Optimal Placement and Sizing of STATCOM 467
13.3.6 Case Studies and Results 470
A.0. Appendix 1 474
A.0. Appendix 2 476
References 485
14 Optimal Placement of STATCOMs Against Short-Term Voltage Instability 487
Abstract 487
14.1 Introduction 488
14.2 Problem Descriptions 490
14.2.1 Basics of STATCOM 490
14.2.2 Load Modeling 492
14.2.3 Transient Voltage Severity Index 493
14.2.4 Risk-Based Criterion 494
14.2.5 Candidate Bus Selection 494
14.3 Mathematical Model 495
14.3.1 Objectives 495
14.3.2 Steady-State Constraints 496
14.3.2.1 Dynamic Constraints 496
14.4 Solution Method 497
14.4.1 Pareto Optimality 497
14.4.2 Decomposition-Based MOEA 498
14.4.2.1 Step (A) Initialization 499
14.4.2.2 Step (B) Updating 499
14.4.2.3 Step (C) Termination 499
14.4.3 Coding Rule 499
14.4.4 Computation Process 500
14.5 Numerical Results 501
14.5.1 Parameter Settings 502
14.5.2 Short-Term Voltage Stability Assessment 503
14.5.3 Candidate Bus Selection 505
14.5.4 STATCOM Placement Results 506
A.0. Appendix 1 509
A.0. Appendix 2 509
A.0. Appendix 3 511
References 512
15 STATCOM Application for Enhancement of Available Power Transfer Capability in Transmission Networks 514
Abstract 514
15.1 Introduction 515
15.2 Available Transfer Capability 516
15.3 Modeling of Power System Components 518
15.3.1 Generator Model 518
15.3.2 Excitation System 520
15.3.3 Network Equations 521
15.3.4 Load Model 522
15.3.5 STATCOM 523
15.4 Optimal Placement of STATCOM 525
15.4.1 Structure Preserving Energy Function 526
15.4.2 Computation of Energy Margin 529
15.4.3 Energy Margin Sensitivity 530
15.5 Evaluation of Dynamic ATC 530
15.6 Case Studies 535
References 539
16 STATCOM Application for Decentralized Secondary Voltage Control of Transmission Networks 540
Abstract 540
16.1 Introduction 541
16.2 Partitioning Based on Graph Theory 544
16.2.1 Spectral K-Way Partitioning 544
16.2.2 Case Study I (Graph Partitioning for IEEE 39-Bus) 546
16.2.3 Case Study II (Graph Partitioning for IEEE 118-Bus) 548
16.3 Location of STATCOM 551
16.4 Controller Design Using STATCOM 555
16.4.1 Partitioning Model Estimation 555
16.4.2 Decentralized Voltage Control Design by STATCOMs 558
16.4.3 Decentralized Voltage Control Design 560
References 564
17 Analysis and Damping of Subsynchronous Oscillations Using STATCOM 566
Abstract 566
17.1 Introduction 566
17.2 SSR Phenomenon 567
17.3 Modelling of Electomechanical System 569
17.3.1 Synchronous Generator 570
17.3.2 Modeling of Excitation Control System 572
17.3.3 Power System Stabilizer (PSS) 573
17.3.4 Electrical Network 573
17.3.5 Turbine Generator Mechanical System 574
17.4 Analytical Tools for SSR Study 576
17.4.1 Damping Torque Analysis 577
17.4.2 Eigenvalue Analysis 580
17.4.3 Transient Simulation 580
17.5 A Case Study 581
17.5.1 Results of Damping Torque Analysis 582
17.5.2 Eigenvalue Analysis 582
17.5.3 Transient Simulation 584
17.6 Modelling of STATCOM 584
17.6.1 Modelling of a 2-Level Converter Based STATCOM 587
17.6.2 Equations in D-Q Reference Frame 588
17.7 Controller Structures for STATCOM 589
17.7.1 Type-2 Controller 589
17.8 Case Study with STATCOM 590
17.8.1 Damping Torque Analysis 591
17.8.2 Eigenvalue Analysis 592
17.8.3 Transient Simulation 593
17.9 Design of SubSynchronous Damping Controller (SSDC) 595
17.10 Analysis with SSDC 596
17.10.1 Damping Torque Analysis with SSDC 596
17.10.2 Eigenvalue Analysis 597
17.10.3 Transient Simulation 598
A.0. Appendix 599
A.0. IEEE FBM 599
References 601
18 STATCOM Application for Mitigation of Subsynchronous Resonance in Wind Farms Connected to Series-Compensated Transmission Lines 603
Abstract 603
18.1 Introduction 604
18.1.1 SSR in Wind Farms 604
18.1.2 Subsynchronous Resonance 607
18.1.3 Subsynchronous Resonance Study Techniques 608
18.1.3.1 Frequency Scanning 608
18.1.3.2 Eigenvalue Analysis 608
18.1.3.3 Transient Torque Analysis 609
18.2 System Modelling 609
18.2.1 Wind Farm 610
18.2.1.1 Drive-Train System 610
18.2.1.2 Aggregation of Drive Train System 612
18.2.1.3 Induction Generator 613
18.2.1.4 Aggregation of Induction Generators 617
18.2.1.5 Shunt Capacitor at Generator Terminal 619
18.2.2 AC Network 619
18.2.3 Complete System Model 621
18.3 SSR Analysis 622
18.3.1 Small-Signal Stability Analysis 622
18.3.1.1 Eigenvalue Analysis 622
18.3.1.2 Participation Factor Analysis 627
18.3.2 Electromagnetic Transient Analysis 631
18.3.2.1 Steady State SSR 631
18.3.2.2 Transient SSR 634
18.4 SSR Mitigation Using STATCOM 640
18.4.1 Power Circuit Modeling 642
18.4.2 Steady State Performance of the STATCOM 645
18.4.3 Modeling of STATCOM Controller 645
18.4.3.1 Controller-I 646
18.4.3.2 Controller-II 647
18.4.4 Complete System Model 649
18.4.4.1 Complete System Model with Controller-I 649
18.4.4.2 Complete System Model with Controller-II 651
18.5 Small-signal Stability Analysis 651
18.6 Electromagnetic Transient Analysis 653
18.6.1 Steady State SSR 653
18.6.2 Transient SSR 656
18.6.2.1 Variation in Wind Farm Size 656
18.6.2.2 Variation in Wind Farm Output 660
18.7 Discussion 662
A.0. Appendix 663
References 664
19 STATCOM on the Mexican Power Systems: Two Case Studies 668
Abstract 668
19.1 Introduction 669
19.2 Mexican Electrical System Features 669
19.2.1 Electric Generation 670
19.2.2 The Mexican Network 671
19.2.3 Operating Conditions of the MES 672
19.3 Benefits of FACTS Devices 673
19.3.1 FACTS Applications in Mexico 674
19.4 STATCOM Projects 675
19.4.1 STATCOM Model Description 677
19.5 STATCOM Application in the MES 680
19.5.1 STATCOM Application in Northeast Region 681
19.5.1.1 Consideration of Various Values of the Coupling Transformer 684
19.5.2 STATCOM Application in the Southeast Region 687
19.5.2.1 Considerations of STATCOM Simulations 688
References 691
20 Stability Analysis of STATCOM in Distribution Networks 693
Abstract 693
20.1 Introduction 694
20.2 DSTATCOM 694
20.2.1 Simplified Representation of the DSTATCOM 697
20.2.1.1 Ideal Sources 697
20.2.1.2 Smooth Hysteresis Band Approach 697
20.2.2 DSTATCOM Operating in Current Control Mode 698
20.2.2.1 Compensation Algorithm and Control 699
20.2.2.2 Simplified DSTATCOM Model 700
20.2.2.3 Comparative Analysis of Models for the DSTATCOM in Current Mode 701
20.2.3 DSTATCOM Operating in Voltage Control Mode 702
20.2.3.1 Simplified DSTATCOM Model 703
20.2.3.2 Comparative Analysis of Models for the DSTATCOM in Voltage Control Mode 705
20.2.4 Comparison of the Simplified Modeling Approaches 706
20.2.4.1 DSTATCOM Operating in Current Mode 706
20.2.4.2 DSTATCOM Operating in Voltage Mode 708
20.3 Stability Analysis of Periodic Steady State Solutions 709
20.3.1 Stability Analysis of the DSTATCOM in Current Control Mode 710
20.3.1.1 Stability Regions in the Ls-Rs Plane 710
20.3.1.2 Stability Regions in the Gains Plane 711
20.3.1.3 DC Capacitor Impact on the Stability 713
20.3.1.4 AC Capacitor Impact on the Stability 713
20.3.2 Bifurcation Analysis for DSTATCOM in Voltage Control Mode 714
20.3.2.1 Stability Regions in the Rs -- Ls Plane 714
20.3.2.2 Stability Regions in the Gains Plane 715
20.3.2.3 DC Capacitor Impact on the Stability Region 718
20.3.2.4 AC Capacitor Filter Impact on the Stability Region 719
References 719
21 Network Protection Systems Considering the Presence of STATCOMs 721
Abstract 721
21.1 Introduction 721
21.2 The Power System 723
21.2.1 The STATCOM 723
21.3 Analytical Study of Impedance Seen by Distance Relay 726
21.4 The Simulation Results 728
21.4.1 Performance of IDMT Overcurrent Relay 728
21.4.2 Performance of Mho Relay 729
21.4.2.1 Performance During Balanced Fault 730
21.4.2.2 Performance During Unbalanced Fault 730
21.4.2.3 Performance of Mho relay with fault location 731
21.4.2.4 Performance During High Resistance Fault 733
21.4.2.5 Performance with fault location variation 734
21.4.3 Performance of Distance Relay with Quadrilateral Characteristic 734
21.4.3.1 Performance during unbalanced fault 735
21.4.3.2 Performance with variation in fault location 735
21.4.3.3 Performance with close-in fault and load angle variation 736
21.4.3.4 Performance with STATCOM located at the end of line I 737
21.5 The Adaptive Distance Relaying Scheme 738
A.0. Appendix 1 739
A.0. Appendix 2 740
A.0.0 System Data 740
A.0.0 STATCOM Specifications 741
References 741