About the Authors xiii
Preface xv
1 Modular Multilevel Converters 1
1.1 Introduction 1
1.2 MMC Configuration 2
1.2.1 Converter Configuration 2
1.2.2 Submodule Configuration 2
1.3 Operation Principles 3
1.3.1 Submodule Normal Operation 3
1.3.2 Submodule Blocking Operation 5
1.3.3 Converter Operation 6
1.4 Modulation Scheme 8
1.4.1 Phase-Disposition PWM 9
1.4.2 Phase-Shifted PWM 10
1.4.3 Nearest Level Modulation 11
1.5 Mathematical Model 12
1.5.1 Submodule Mathematical Model 12
1.5.1.1 Switching-Function Based Model 13
1.5.1.2 Reference-Based Model 13
1.5.2 Arm Mathematical Model 14
1.5.2.1 Switching-Function Based Model 14
1.5.2.2 Reference-Based Model 15
1.5.3 Three-Phase MMC Mathematical Model 16
1.5.3.1 AC-Side Mathematical Model 17
1.5.3.2 DC-Side Mathematical Model 17
1.6 Design Constraints 18
1.6.1 Power Device Design 18
1.6.1.1 Rated Voltage of Power Devices 19
1.6.1.2 Rated Current of Power Devices 19
1.6.2 Capacitor Design 21
1.6.3 Arm Inductor Design 23
1.7 Faults Overview of MMCs 24
1.7.1 Internal Faults of MMCs 24
1.7.2 External Faults of MMCs 25
1.8 Summary 25
References 26
2 Control of MMCs 29
2.1 Introduction 29
2.2 Overall Control of MMCs 30
2.3 Output Control of MMCs 31
2.3.1 Current Control 31
2.3.2 Power and DC-Link Voltage Control 33
2.3.3 Grid Forming Control 36
2.4 Centralized Capacitor Voltage Balancing Control 38
2.4.1 On-State SMs Number Based VBC 39
2.4.2 Balancing Adjusting Number Based VBC 39
2.4.2.1 Capacitor VBC 40
2.4.2.2 SM Switching Frequency 40
2.4.3 IPSC-PWM Harmonic Current Based VBC 42
2.4.3.1 IPSC-PWM Scheme 42
2.4.3.2 High-Frequency Arm Current 43
2.4.3.3 Arm Capacitor Voltage Analysis 46
2.4.3.4 Voltage Balancing Control 47
2.4.4 SHE-PWM Pulse Energy Sorting Based VBC 53
2.4.4.1 MMCs Analysis with Grid-Frequency Pulses 53
2.4.4.2 Charge Transfer of Capacitors in Lower Arm 56
2.4.4.3 Charge Transfer of Capacitors in Upper Arm 57
2.4.4.4 Voltage Balancing Control 59
2.4.5 PSC-PWM Pulse Energy Sorting Based VBC 65
2.4.5.1 MMC with PSC-PWM 65
2.4.5.2 Capacitor Charge Transfer Under Linearization Method 67
2.4.5.3 Capacitor Voltage Analysis 70
2.4.5.4 Voltage Balancing Control 72
2.5 Individual Capacitor Voltage Balancing Control 79
2.5.1 Average and Balancing Control Based VBC 79
2.5.1.1 Average Control 80
2.5.1.2 Balancing Control 80
2.5.2 Reference Modulation Index Based VBC 81
2.5.2.1 Analysis of Capacitor Voltage 82
2.5.2.2 Control of i cdc by modulation Index m 83
2.5.2.3 Voltage Balancing Control by m 84
2.5.3 Reference Phase Angle Based VBC 86
2.5.3.1 Control of i cdc by Phase Angle θ 86
2.5.3.2 Voltage Balancing Control by θ 87
2.6 Circulating Current Control 94
2.6.1 Proportional Integration Control 95
2.6.2 Multiple Proportional Resonant Control 97
2.6.3 Repetitive Control 98
2.7 Summary 100
References 100
3 Fault Detection of MMCs under IGBT Faults 103
3.1 Introduction 103
3.2 IGBT Faults 104
3.2.1 IGBT Short- Circuit Fault 105
3.2.2 IGBT Open- Circuit Fault 105
3.3 Protection and Detection Under IGBT Short- Circuit Faults 106
3.3.1 SM Under IGBT Short- Circuit Fault 106
3.3.2 Protection and Detection Under IGBT Short- Circuit Fault 107
3.4 mmc Features Under IGBT Open- Circuit Faults 109
3.4.1 Faulty SM Features Under T 1 Open- Circuit Fault 109
3.4.2 Faulty SM Features Under T 2 Open- Circuit Fault 110
3.4.2.1 Operation Mode of Faulty SM 110
3.4.2.2 Faulty SM Capacitor Voltage of MMCs in Inverter Mode 111
3.4.2.3 Faulty SM Capacitor Voltage of MMCs in Rectifier Mode 112
3.5 Kalman Filter Based Fault Detection Under IGBT Open- Circuit Faults 115
3.5.1 Kalman Filter Algorithm 117
3.5.2 Circulating Current Estimation 118
3.5.3 Faulty Phase Detection 119
3.5.4 Capacitor Voltage 120
3.5.5 Faulty SM Detection 121
3.6 Integrator Based Fault Detection Under IGBT Open- Circuit Faults 127
3.7 STW Based Fault Detection Under IGBT Open- Circuit Faults 132
3.7.1 MMC Data 132
3.7.2 Sliding- Time Windows 133
3.7.3 Feature of STW 134
3.7.4 Features Relationships Between Neighboring STWs 137
3.7.5 Features Extraction Algorithm 137
3.7.6 Energy Entropy Matrix 138
3.7.7 2D- CNN 138
3.7.8 Fault Detection Method 140
3.7.9 Selection of Sliding Interval 141
3.7.10 Analysis of Fault Localization Time 142
3.8 IF Based Fault Detection Under IGBT Open- Circuit Faults 145
3.8.1 IT for MMCs 145
3.8.2 SM Depth in IT 146
3.8.3 IF for MMCs 147
3.8.4 SM Average Depth in IF 147
3.8.5 IF Output 147
3.8.6 Fault Detection 149
3.8.7 Selection of m p 150
3.8.8 Selection of k 151
3.9 Summary 156
References 156
4 Condition Monitoring and Control of MMCs Under Capacitor Faults 161
4.1 Introduction 161
4.2 Capacitor Equivalent Circuit in MMCs 162
4.3 Capacitor Parameter Characteristics in MMCs 164
4.3.1 Capacitor Current Characteristics 164
4.3.2 Capacitor Impedance Characteristics 167
4.3.3 Capacitor Voltage Characteristics 167
4.4 Capacitor Aging 169
4.5 Capacitance Monitoring 171
4.5.1 Capacitor Voltage and Current Based Monitoring Strategy 172
4.5.2 Arm Average Capacitance Based Monitoring Method 172
4.5.2.1 Equivalent Arm Structure 172
4.5.2.2 Capacitor Monitoring Method 173
4.5.3 Reference SM based Monitoring Method 179
4.5.3.1 Principle of the RSM- Based Capacitor Monitoring Strategy 179
4.5.3.2 Capacitor Monitoring- Based Voltage- Balancing Control 180
4.5.3.3 Selection of RSM 182
4.5.3.4 Capacitor Monitoring Strategy 183
4.5.4 Sorting- Based Monitoring Strategy 189
4.5.5 Temperature Effect of Capacitance 195
4.6 ESR Monitoring 195
4.6.1 Direct ESR Monitoring Strategy 196
4.6.2 Sorting- Based ESR Monitoring Strategy 196
4.6.3 Temperature Effect of ESR 203
4.7 Capacitor Lifetime Monitoring 204
4.8 Arm Current Optimal Control Under Capacitor Aging 205
4.8.1 Equivalent Circuit of MMCs 205
4.8.2 Arm Current Characteristics 207
4.8.3 Arm Current Optimal Control 208
4.9 SM Power Losses Optimal Control Under Capacitor Aging 212
4.9.1 Equivalent SM Reference 213
4.9.2 SM Conduction Losses 215
4.9.3 SM Switching Losses 216
4.9.4 SM Power Losses Optimal Control 217
4.10 Summary 225
References 226
5 Fault-Tolerant Control of MMCs Under SM Faults 229
5.1 Introduction 229
5.2 SM Protection Circuit 229
5.3 Redundant Submodules 230
5.4 Fault- Tolerant Scheme 231
5.4.1 Cold Reserve Mode 232
5.4.2 Spinning Reserve Mode- I 233
5.4.3 Spinning Reserve Mode- II 235
5.4.4 Spinning Reserve Mode- III 235
5.4.5 Comparison of Fault- Tolerant Schemes 235
5.5 Fundamental Circulating Current Elimination Based Tolerant Control 236
5.5.1 Equivalent Circuit of MMCs 236
5.5.2 Fundamental Circulating Current 238
5.5.3 Fundamental Circulating Current Elimination Control 239
5.5.4 Control Analysis 241
5.6 Summary 247
References 247
6 Control of MMCs Under AC Grid Faults 249
6.1 Introduction 249
6.2 Mathematical Model of MMCs under AC Grid Faults 250
6.2.1 AC- Side Mathematical Model 250
6.2.1.1 MMC with AC- Side Transformer 250
6.2.1.2 MMCs without AC- Side Transformer 252
6.2.2 Instantaneous Power Mathematical Model 253
6.3 AC- Side Current Control of MMCs under AC Grid Faults 254
6.3.1 Positive- and Negative- Sequence Current Control 255
6.3.1.1 Inner Loop Current Control 255
6.3.1.2 Outer Power Control 256
6.3.2 Zero- Sequence Current Control 257
6.3.3 Proportional Resonant Based Current Control 259
6.4 Circulating Current Suppression Control of MMCs under AC Grid Faults 261
6.4.1 Circulating Current of MMCs Under AC Grid Faults 261
6.4.2 Single- Phase Vector Based Control 262
6.4.3 αβ0 Stationary Frame Based Control 264
6.4.4 Three- Phase Stationary Frame Based Control 266
6.4.4.1 Positive- and Negative- Sequence Controller 267
6.4.4.2 Zero- Sequence Controller 268
6.5 Summary 269
References 270
7 Protection Under DC Short-Circuit Fault in HVDC System 273
7.1 Introduction 273
7.2 MMC Under DC Short- Circuit Fault 274
7.2.1 System Configuration 274
7.2.2 AC Circuit Breaker 274
7.2.3 Protection Thyristor 275
7.2.4 Protection Operation 276
7.3 DC Circuit Breaker Based Protection 281
7.3.1 Mechanical Circuit Breaker 282
7.3.2 Semiconductor Circuit Breaker 283
7.3.2.1 Semi- Controlled Semiconductor Circuit Breaker 283
7.3.2.2 Fully Controlled Semiconductor Circuit Breaker 284
7.3.3 Hybrid Circuit Breaker 285
7.3.3.1 Conventional Hybrid Circuit Breaker 285
7.3.3.2 Proactive Hybrid Circuit Breaker 286
7.3.4 Multiterminal Circuit Breaker 287
7.3.4.1 Assembly CB 287
7.3.4.2 Multiport CB 288
7.3.5 Superconducting Fault Current Limiter 289
7.3.6 SFCL- Based Circuit Breaker 289
7.3.6.1 SFCL- Based Hybrid Circuit Breaker 290
7.3.6.2 SFCL- Based Self- Oscillating Circuit Breaker 291
7.3.6.3 SFCL- Based Forced Zero- Crossing Circuit Breaker 292
7.4 Fault Blocking Converter Based Protection 293
7.4.1 FB SM and HB SM Based Hybrid MMC 294
7.4.2 Fault Blocking Control 296
7.4.3 FB SM Ratio 298
7.4.4 Alternative Fault Blocking SMs 298
7.5 Bypass Thyristor MMC Based Protection 299
7.5.1 Bypass Thyristor MMC Configuration 299
7.5.2 SM Control 302
7.5.3 Current Interruption Control 303
7.5.3.1 Three- Phase Rectifier Period 304
7.5.3.2 One- Phase Current Interruption Moment 304
7.5.3.3 Single- Phase Rectifier Period 305
7.5.3.4 Three- Phase Current Interruption Moment 306
7.5.4 Protection Operation 307
7.6 CTB- HMMC Based Protection 311
7.6.1 CTB- HMMC Configuration 312
7.6.2 SM Operation Principle 313
7.6.3 Operation Principle for DC Fault Protection 314
7.6.4 DC- Side Current Interruption Operation 315
7.6.5 Capacitor Voltage Increment 317
7.6.6 AC- Side Current Interruption Operation 318
7.6.7 MMC Comparison 321
7.6.7.1 Comparison with Current Blocking SM Based MMCs 321
7.6.7.2 Comparison with Thyristor Based MMCs 323
7.7 Summary 328
References 329
Index 333
