Preface xvii
Part I HVDC with Current Source Converters 1
1 Introduction to Line Commutated HVDC 3
1.1 HVDC Applications 3
1.2 Line Commutated HVDC Components 4
1.3 DC Cables and Overhead Lines 7
1.3.1 Introduction 7
1.3.2 Mass-impregnated Cables 7
1.3.3 Low-pressure Oil-filled Cables 7
1.3.4 Extruded Cross-linked Polyethylene Cables 8
1.4 LCC HVDC Topologies 8
1.5 Losses in LCC HVDC Systems 10
1.6 Conversion of AC Lines to DC 10
1.7 Ultra High Voltage HVDC 12
2 Thyristors 13
2.1 Operating Characteristics 13
2.2 Switching Characteristics 14
2.3 Losses in HVDCThyristors 18
2.4 Valve Structure andThyristor Snubbers 20
2.5 Thyristor Rating Selection and Overload Capability 22
3 Six-pulse Diode and Thyristor Converter 25
3.1 Three-phase Uncontrolled Bridge 25
3.2 Three-phase Thyristor Rectifier 27
3.3 Analysis of Commutation Overlap in a Thyristor Converter 28
3.4 Active and Reactive Power in a Three-phase Thyristor Converter 32
3.5 Inverter Operation 33
4 HVDC Rectifier Station Modelling, Control and Synchronisation with AC System 37
4.1 HVDC Rectifier Controller 37
4.2 Phase-locked Loop 38
4.3 Master-level HVDC Control 40
5 HVDC Inverter Station Modelling and Control 43
5.1 Inverter Controller 43
5.1.1 Control Structure 43
5.1.2 Extinction Angle Control 43
5.1.3 DC Voltage Control 44
5.1.4 DC Current Control at Inverter 45
5.2 Commutation Failure 45
6 HVDC System V-I Diagrams and Operating Modes 49
6.1 HVDC Equivalent Circuit 49
6.2 HVDC V-I Operating Diagram 49
6.3 HVDC Power Reversal 51
7 HVDC Analytical Modelling and Stability 57
7.1 Introduction to Converter and HVDC Modelling 57
7.1.1 Detailed Switching Transients Modelling 57
7.1.2 Modelling with Switchings 57
7.1.3 Analytical Dynamic Modelling of Converters 58
7.1.4 Phasor Modelling 58
7.2 HVDC Analytical Model 58
7.3 CIGRE HVDC Benchmark Model 60
7.4 Converter Modelling, Linearisation, and Gain Scheduling 60
7.5 AC System Modelling for HVDC Stability Studies 64
7.6 LCC Converter Transformer Model 67
7.7 DC System Including DC Cable 68
7.7.1 DC Cable/Line Modelling as a Single ?? Section 68
7.7.2 Controller Model 69
7.7.3 Complete DC System Model 69
7.8 Accurate DC Cable Modelling 70
7.8.1 Wideband Cable Model 70
7.8.2 Cable Higher-order Analytical Model in State Space 72
7.9 HVDC-HVAC System Model 76
7.10 Analytical Dynamic Model Verification 77
7.11 Basic HVDC Dynamic Analysis 77
7.11.1 Eigenvalue Analysis 77
7.11.2 Eigenvalue Sensitivity Study 77
7.11.3 Influence of PLL Gains 79
7.12 HVDC Second Harmonic Instability 80
7.13 100 Hz Oscillations on the DC Side 82
8 HVDC Phasor Modelling and Interactions with AC System 83
8.1 Converter and DC System Phasor Model 83
8.2 Phasor AC System Model and Interaction with DC System 84
8.3 Inverter AC Voltage and Power Profile as DC Current is Increasing 86
8.4 Influence of Converter Extinction Angle 88
8.5 Influence of Shunt Reactive Power Compensation 88
8.6 Influence of Load at the Converter Terminals 88
8.7 Influence of Operating Mode (DC Voltage Control Mode) 88
8.8 Rectifier Operating Mode 90
9 HVDC Operation with Weak AC Systems 95
9.1 Introduction 95
9.2 Short Circuit Ratio and Equivalent Short Circuit Ratio 95
9.2.1 Definition of SCR and ESCR 95
9.2.2 Operating Difficulties with Low SCR Systems 98
9.3 Background on Power Transfer Between Two AC Systems 99
9.4 Phasor Study of Converter Interactions with Weak AC Systems 101
9.5 System Dynamics (Small Signal Stability) with Low SCR 101
9.6 Control and Main Circuit Solutions for Weak AC Grids 102
9.7 LCC HVDC with SVC 103
9.8 Capacitor Commutated Converters for HVDC 104
9.9 AC System with Low Inertia 106
10 Fault Management and HVDC System Protection 111
10.1 Introduction 111
10.2 DC Line Faults 111
10.3 AC System Faults 113
10.3.1 Rectifier AC Faults 113
10.3.2 Inverter AC Faults 114
10.4 Internal Faults 115
10.5 System Reconfiguration for Permanent Faults 116
10.6 Overvoltage Protection 119
11 LCC HVDC System Harmonics 121
11.1 Harmonic Performance Criteria 121
11.2 Harmonic Limits 122
11.3 Thyristor Converter Harmonics 123
11.4 Harmonic Filters 124
11.4.1 Introduction 124
11.4.2 Tuned Filters 126
11.4.3 Damped Filters 128
11.5 Non-characteristic Harmonic Reduction Using HVDC Controls 132
Bibliography Part I: Line Commutated Converter HVDC 133
Part II HVDC with Voltage Source Converters 137
12 VSC HVDC Applications and Topologies, Performance and Cost Comparison with LCC HVDC 139
12.1 Application of Voltage Source Converters in HVDC 139
12.2 Comparison with LCC HVDC 141
12.3 HVDC Technology Landscape 142
12.4 Overhead and Subsea/Underground VSC HVDC Transmission 143
12.5 DC Cable Types with VSC HVDC 147
12.6 Monopolar and Bipolar VSC HVDC Systems 147
12.7 VSC HVDC Converter Topologies 148
12.7.1 HVDC with Two-level Voltage Source Converter 148
12.7.2 HVDC with Neutral Point Clamped Converter 150
12.7.3 MMC VSC HVDC Transmission Systems 151
12.7.4 MMC HVDC Based on FB Topology 153
12.8 VSC HVDC Station Components 155
12.8.1 AC CB 155
12.8.2 VSC Converter Transformer 155
12.8.3 VSC Converter AC Harmonic Filters 156
12.8.4 DC Capacitors 156
12.8.5 DC Filter 157
12.8.6 Two-level VSC HVDC Valves 158
12.8.7 MMC Valves and Cells 159
12.9 AC Inductors 160
12.10 DC Inductors 161
13 IGBT Switches and VSC Converter Losses 165
13.1 Introduction to IGBT and IGCT 165
13.2 General VSC Converter Switch Requirements 166
13.3 IGBT Technology 166
13.3.1 IGBT Operating Characteristics 167
13.3.2 Fast Recovery Anti-parallel Diode 171
13.4 High Power IGBT Devices 171
13.5 IEGT Technology 172
13.6 Losses Calculation 173
13.6.1 Conduction Loss Modelling 173
13.6.2 Switching Loss Modelling 174
13.7 Balancing Challenges in Two-level IGBT Valves 178
13.8 Snubbers Circuits 179
14 Single-phase and Three-phase Two-level VSC Converters 181
14.1 Introduction 181
14.2 Single-phase VSC 181
14.3 Three-phase VSC 184
14.4 Square-wave, Six-pulse Operation 185
14.4.1 180? Conduction 185
14.4.2 120? Conduction 188
15 Two-level PWM VSC Converters 193
15.1 Introduction 193
15.2 PWM Modulation 193
15.2.1 Multipulse with Constant Pulse Width 193
15.2.2 Modulating Signal 194
15.3 Sinusoidal Pulse Width Modulation 195
15.4 Third Harmonic Injection 197
15.5 Selective Harmonic Elimination Modulation 198
15.6 Converter Losses for Two-level SPWMVSC 198
15.7 Harmonics with PWM 201
15.8 Comparison of PWM Modulation Techniques 203
16 Multilevel VSC Converters in HVDC Applications 205
16.1 Introduction 205
16.2 Modulation Techniques for Multilevel Converters 207
16.3 Neutral Point Clamped Multilevel Converter 208
16.4 Half Bridge MMC 210
16.4.1 Operating Principles of Half-bridge MMC 210
16.4.2 Capacitor Voltage Balancing 212
16.4.3 MMC Cell Capacitance 214
16.4.4 MMC Arm Inductance 215
16.4.5 MMC with Fundamental Frequency Modulation 218
16.4.6 MMC with PWM Modulation 218
16.5 Full Bridge MMC 222
16.5.1 Operating Principles 222
16.6 Comparison of Multilevel Topologies 224
17 Two-level VSC HVDC Modelling, Control, and Dynamics 227
17.1 PWM Two-level Converter Average Model 227
17.1.1 Converter Model in an ABC Frame 227
17.1.2 Converter Model in the ABC Frame Including Blocked State 229
17.2 Two-level PWM Converter Model in DQ Frame 230
17.3 VSC Converter Transformer Model 231
17.4 Two-level VSC Converter and AC Grid Model in the ABC Frame 231
17.5 Two-level VSC Converter and AC Grid Model in a DQ Rotating Coordinate Frame 232
17.6 VSC Converter Control Principles 233
17.7 The Inner Current Controller Design 234
17.7.1 Control Strategy 234
17.7.2 Decoupling Control 234
17.7.3 Current Feedback Control 235
17.7.4 Controller Gains 236
17.8 Outer Controller Design 237
17.8.1 AC Voltage Control 237
17.8.2 Power Control 238
17.8.3 DC Voltage Control 239
17.8.4 AC Grid Support 240
17.9 Complete Two-level VSC Converter Controller 240
17.10 Small Signal Linearised VSC HVDC Model 242
17.11 Small Signal Dynamic Studies 242
17.11.1 Dynamics of Weak AC Systems 242
17.11.2 Impact of PLL Gains on Robustness 244
18 Two-level VSC HVDC Phasor-domain Interaction with AC Systems and PQ Operating Diagrams 247
18.1 Power Exchange Between Two AC Voltage Sources 247
18.2 Converter Phasor Model and Power Exchange with an AC System 249
18.3 Phasor Study of VSC Converter Interaction with AC System 252
18.3.1 Test System 252
18.3.2 Assumptions and Converter Limits 252
18.3.3 Case 1: Converter Voltages Are Known 253
18.3.4 Case 2: Converter Currents are Known 254
18.3.5 Case 3: PCC Voltage is Known 254
18.4 Operating Limits 254
18.5 Design Point Selection 255
18.6 Influence of AC System Strength 258
18.7 Influence of AC System Impedance Angle (Xs/Rs) 258
18.8 Influence of Transformer Reactance 258
18.9 Influence of Converter Control Modes 262
18.10 Operation with Very Weak AC Systems 262
19 Half Bridge MMC: Dimensioning, Modelling, Control, and Interaction with AC System 269
19.1 Basic Equations and Steady-state Control 269
19.2 Steady-state Dimensioning 272
19.3 Half Bridge MMC Non-linear Average Dynamic Model 275
19.4 Non-linear Average Value Model Including Blocked State 276
19.5 HB MMC HVDC Start-up and Charging MMC Cells 278
19.6 HB MMC Dynamic DQ Frame Model and Phasor Model 279
19.6.1 Assumptions 279
19.6.2 Zero Sequence Model 282
19.6.3 Fundamental Frequency Model in DQ Frame 282
19.6.4 Second Harmonic Model in the D2Q2 Coordinate Frame 284
19.7 Second Harmonic of Differential Current 286
19.8 Complete MMC Converter DQ Model in Matrix Form 286
19.9 Second-harmonic Circulating Current Suppression Controller 287
19.10 Simplified DQ Frame Model with Circulating Current Controller 290
19.11 Phasor Model of MMC with Circulating Current Suppression Controller 295
19.12 Simplified Dynamic MMC Model Using Equivalent Series Capacitor CMMC 296
19.13 Full Dynamic Analytical HB MMC Model 300
19.14 HB MMC Controller and Arm Voltage Control 301
19.15 MMC Total Series Reactance and Comparison with Two-level VSC 304
19.16 MMC Interaction with AC System and PQ Operating Diagrams 306
20 Full Bridge MMC Converter: Dimensioning, Modelling, and Control 309
20.1 FB MMC Arm Voltage Range 309
20.2 Full Bridge MMC Converter Non-linear Average Model 309
20.3 FB MMC Non-linear Average Model Including Blocked State 310
20.4 Full Bridge MMC Cell Charging 312
20.5 Hybrid MMC Design 313
20.5.1 Operation Under Low DC Voltage 313
20.5.2 Overmodulation Requirements 314
20.5.3 Cell Voltage Balancing Under Low DC Voltage 315
20.5.4 Optimal Design of Full Bridge MMC 315
20.6 Full Bridge MMC DC Voltage Variation Using a Detailed Model 318
20.7 FB MMC Analytical Dynamic DQ Model 320
20.7.1 Zero Sequence Model 320
20.7.2 Fundamental Frequency Model 321
20.8 Simplified FB MMC Model 321
20.9 FB MMC Converter Controller 322
21 MMC Converter Under Unbalanced Conditions 325
21.1 Introduction 325
21.2 MMC Balancing Controller Structure 326
21.3 Balancing Between Phases (Horizontal Balancing) 326
21.4 Balancing Between Arms (Vertical Balancing) 328
21.5 Simulation of Balancing Controls 330
21.6 Operation with Unbalanced AC Grid 332
21.6.1 Detecting Positive and Negative Sequence Components 332
21.6.2 Controlling Grid Current Sequence Components with MMC 336
22 VSC HVDC Under AC and DC Fault Conditions 339
22.1 Introduction 339
22.2 Faults on the AC System 339
22.3 DC Faults with Two-level VSC 340
22.4 Influence of DC Capacitors 345
22.5 VSC Converter Modelling Under DC Faults and VSC Diode Bridge 345
22.5.1 VSC Diode Bridge Average Model 345
22.5.2 Phasor Model of VSC Diode Bridge Under DC Fault 348
22.5.3 Simple Expression for VSC Diode Bridge Steady-state Fault Current Magnitude 351
22.6 VSC Converter Mode Transitions as DC Voltage Reduces 352
22.7 DC Faults with Half Bridge Modular Multilevel Converter 354
22.8 Full Bridge MMC Under DC Faults 356
23 VSC HVDC Application For AC Grid Support and Operation with Passive AC Systems 359
23.1 VSC HVDC High Level Controls and AC Grid Support 359
23.2 HVDC Embedded Inside an AC Grid 360
23.3 HVDC Connecting Two Separate AC Grids 361
23.4 HVDC in Parallel with AC 361
23.5 Operation with a Passive AC System and Black Start Capability 362
23.6 VSC HVDC Operation with Offshore Wind Farms 362
23.7 VSC HVDC Supplying Power Offshore and Driving a MW-Size Variable Speed Motor 365
Bibliography Part II: Voltage Source Converter HVDC 366
Part III DC Transmission Grids 371
24 Introduction to DC Grids 373
24.1 DC versus AC Transmission 373
24.2 Terminology 374
24.3 DC Grid Planning, Topology, and Power Transfer Security 375
24.4 Technical Challenges 376
24.5 DC Grid Building by Multiple Manufacturers - Interoperability 376
24.6 Economic Aspects 377
25 DC Grids with Line Commutated Converters 379
25.1 Multiterminal LCC HVDC 379
25.2 Italy-Corsica-Sardinia Multiterminal HVDC Link 380
25.3 Connecting the LCC Converter to a DC Grid 381
25.3.1 Power Reversal 381
25.3.2 DC Faults 382
25.3.3 AC Faults 383
25.4 Control of LCC Converters in DC Grids 383
25.5 Control of LCC DC Grids Through DC Voltage Droop Feedback 384
25.6 Managing LCC DC Grid Faults 385
25.7 Reactive Power Issues 387
25.8 Employing LCC Converter Stations in Established DC Grids 387
26 DC Grids with Voltage Source Converters and Power Flow Model 389
26.1 Connecting a VSC Converter to a DC Grid 389
26.1.1 Power Reversal and Control 389
26.1.2 DC Faults 389
26.1.3 AC Faults 389
26.2 Multiterminal VSC HVDC Operating in China 390
26.3 DC Grid Power Flow Model 390
26.4 DC Grid Power Flow Under DC Faults 395
27 DC Grid Control 399
27.1 Introduction 399
27.2 Fast Local VSC Converter Control in DC Grids 399
27.3 DC Grid Dispatcher with Remote Communication 401
27.4 Primary, Secondary, and Tertiary DC Grid Control 402
27.5 DC Voltage Droop Control for VSC Converters in DC Grids 403
27.6 Three-level Control for VSC Converters with Dispatcher Droop 405
27.6.1 Three-level Control for VSC Converters 405
27.6.2 Dispatcher Controller 406
27.7 Power Flow Algorithm When DC Powers are Regulated 406
27.8 Power Flow and Control Study of CIGRE DC Grid Test System 411
27.8.1 CIGRE DC Grid Test System 411
27.8.2 Power Flow After Outage of the Largest Terminal 413
28 DC Circuit Breakers 417
28.1 Introduction 417
28.2 Challenges with DC Circuit Opening 417
28.2.1 DC Current Commutation 417
28.2.2 DC Current Suppression and Dissipation of Energy 418
28.3 DC CB Operating Principles and a Simple Model 418
28.4 DC CB Performance Requirements 420
28.4.1 Opening Speed 420
28.4.2 DC CB Ratings and Series Inductors 420
28.4.3 Bidirectional Current Interruption 421
28.4.4 Multiple Open/close Operations in a Short Time 421
28.4.5 Losses, Size, and Weight 421
28.4.6 Standardisation 421
28.5 Practical HV DC CBs 422
28.6 Mechanical DC CB 422
28.6.1 Operating Principles and Construction 422
28.6.2 Mathematical Model and Design Principles 424
28.6.3 Test Circuit for DC CB Simulation 426
28.6.4 Simulation of DC Fault Clearing 427
28.6.5 Negative Fault Current Interruption 427
28.6.6 Multiple Open/close Operations in a Short Time 428
28.6.7 Mechanical DC CB for High Voltages 429
28.7 Semiconductor-based DC CB 430
28.7.1 Topology and Design 430
28.7.2 Self-protection of Semiconductor Valves 432
28.7.3 Simulation of Fault Current Interruption 432
28.8 Hybrid DC CB 434
28.8.1 Topology and Design 434
28.8.2 Hybrid DC CB for High Voltages 435
28.8.3 Simulation of Fault Current Interruption 436
28.8.4 Bidirectional Operation 437
28.8.5 Fault Current Limiting 438
29 DC Grid Fault Management and Protection System 441
29.1 Introduction 441
29.2 Fault Current Components in DC Grids 442
29.3 DC System Protection Coordination with AC System Protection 444
29.4 DC Grid Protection System Development 445
29.5 DC Grid Protection System Based on Local Measurements 446
29.5.1 Protection Based on DC Current and Current Differential 446
29.5.2 Rate of Change of Voltage Protection 447
29.6 Blocking MMC Converters Under DC Faults 450
29.7 Differential DC Grid Protection Strategy 452
29.8 Selective Protection for Star-topology DC Grids 455
29.9 DC Grids with DC Fault-tolerant VSC Converters 456
29.9.1 Grid Topology and Strategy 456
29.9.2 VSC Converter with Increased AC Coupling Reactors 457
29.9.3 LCL VSC Converter 459
29.9.4 VSC Converter with Fault Current Limiter 461
29.10 DC Grids with Full Bridge MMC Converters 461
30 High Power DC/DC Converters and DC Power Flow Controlling Devices 465
30.1 Introduction 465
30.2 Power Flow Control Using Series Resistors 466
30.3 Low-stepping-ratio DC/DC Converters (DC Choppers) 469
30.3.1 Converter Topology 469
30.3.2 Converter Controller 470
30.3.3 DC/DC Chopper Average Value Model 471
30.3.4 H-Bridge DC/DC Chopper 473
30.4 Non-isolated MMC-based DC/DC Converter (M2DC) 473
30.4.1 Introduction 473
30.4.2 Modelling and Design 474
30.4.3 Design Example and Comparison with MMC AC/DC 477
30.4.4 Controller Design 479
30.4.5 Simulation Responses 480
30.5 DC/DC Converters with DC Polarity Reversal 484
30.6 High-stepping-ratio Isolated DC/DC Converter (Dual Active Bridge DC/DC) 484
30.6.1 Introduction 484
30.6.2 Modelling and Control 486
30.6.3 Simulated Responses 487
30.7 High-stepping-ratio LCL DC/DC Converter 490
30.8 Building DC Grids with DC/DC Converters 492
30.9 DC Hubs 495
30.10 Developing DC Grids Using DC Hubs 496
30.11 North Sea DC Grid Topologies 496
Bibliography Part III: DC Transmission Grids 500
Appendix A Variable Notations 503
Appendix B Analytical Background to Rotating DQ Frame 505
B.1 Transforming AC Variables to a DQ Frame 505
B.2 Derivative of an Oscillating Signal in a DQ Frame 507
B.3 Transforming an AC System Dynamic Equation to a DQ Frame 507
B.4 Transforming an n-Order State Space AC System Model to a DQ Frame 509
B.5 Static (Steady-state) Modeling in a Rotating DQ Coordinate Frame 510
B.6 Representing the Product of Oscillating Signals in a DQ Frame 511
B.7 Representing Power in DQ Frame 512
Appendix C System Modeling Using Complex Numbers and Phasors 515
Appendix D Simulink Examples 517
D.1 Chapter 3 Examples 517
D.2 Chapter 5 Examples 517
D.3 Chapter 6 Examples 519
D.4 Chapter 8 Examples 521
D.5 Chapter 14 Examples 523
D.6 Chapter 16 Examples 524
D.7 Chapter 17 Examples 527
Index 535
