Fujin Deng, PhD, is a Professor and Head of the Department of Power Electronics at Southeast University, China. He is a Senior Member of the IEEE. Chengkai Liu, PhD, is a PhD student who studies coordinated fault diagnosis and fault tolerant operation for flexible direct current transmission systems at Southeast University, China. Zhe Chen, PhD, is a Professor and the leader of Wind Power System Research program at the Department of Energy Technology, Aalborg University, Denmark. He is a Fellow of IEEE, a Fellow of IET and a Chartered Engineer in the U.K.

• About the Authors xiiiPreface xv1 Modular Multilevel Converters 11.1 Introduction 11.2 MMC Configuration 21.2.1 Converter Configuration 21.2.2 Submodule Configuration 21.3 Operation Principles 31.3.1 Submodule Normal Operation 31.3.2 Submodule Blocking Operation 51.3.3 Converter Operation 61.4 Modulation Scheme 81.4.1 Phase-Disposition PWM 91.4.2 Phase-Shifted PWM 101.4.3 Nearest Level Modulation 111.5 Mathematical Model 121.5.1 Submodule Mathematical Model 121.5.1.1 Switching-Function Based Model 131.5.1.2 Reference-Based Model 131.5.2 Arm Mathematical Model 141.5.2.1 Switching-Function Based Model 141.5.2.2 Reference-Based Model 151.5.3 Three-Phase MMC Mathematical Model 161.5.3.1 AC-Side Mathematical Model 171.5.3.2 DC-Side Mathematical Model 171.6 Design Constraints 181.6.1 Power Device Design 181.6.1.1 Rated Voltage of Power Devices 191.6.1.2 Rated Current of Power Devices 191.6.2 Capacitor Design 211.6.3 Arm Inductor Design 231.7 Faults Overview of MMCs 241.7.1 Internal Faults of MMCs 241.7.2 External Faults of MMCs 251.8 Summary 25References 262 Control of MMCs 292.1 Introduction 292.2 Overall Control of MMCs 302.3 Output Control of MMCs 312.3.1 Current Control 312.3.2 Power and DC-Link Voltage Control 332.3.3 Grid Forming Control 362.4 Centralized Capacitor Voltage Balancing Control 382.4.1 On-State SMs Number Based VBC 392.4.2 Balancing Adjusting Number Based VBC 392.4.2.1 Capacitor VBC 402.4.2.2 SM Switching Frequency 402.4.3 IPSC-PWM Harmonic Current Based VBC 422.4.3.1 IPSC-PWM Scheme 422.4.3.2 High-Frequency Arm Current 432.4.3.3 Arm Capacitor Voltage Analysis 462.4.3.4 Voltage Balancing Control 472.4.4 SHE-PWM Pulse Energy Sorting Based VBC 532.4.4.1 MMCs Analysis with Grid-Frequency Pulses 532.4.4.2 Charge Transfer of Capacitors in Lower Arm 562.4.4.3 Charge Transfer of Capacitors in Upper Arm 572.4.4.4 Voltage Balancing Control 592.4.5 PSC-PWM Pulse Energy Sorting Based VBC 652.4.5.1 MMC with PSC-PWM 652.4.5.2 Capacitor Charge Transfer Under Linearization Method 672.4.5.3 Capacitor Voltage Analysis 702.4.5.4 Voltage Balancing Control 722.5 Individual Capacitor Voltage Balancing Control 792.5.1 Average and Balancing Control Based VBC 792.5.1.1 Average Control 802.5.1.2 Balancing Control 802.5.2 Reference Modulation Index Based VBC 812.5.2.1 Analysis of Capacitor Voltage 822.5.2.2 Control of i cdc by modulation Index m 832.5.2.3 Voltage Balancing Control by m 842.5.3 Reference Phase Angle Based VBC 862.5.3.1 Control of i cdc by Phase Angle θ 862.5.3.2 Voltage Balancing Control by θ 872.6 Circulating Current Control 942.6.1 Proportional Integration Control 952.6.2 Multiple Proportional Resonant Control 972.6.3 Repetitive Control 982.7 Summary 100References 1003 Fault Detection of MMCs under IGBT Faults 1033.1 Introduction 1033.2 IGBT Faults 1043.2.1 IGBT Short- Circuit Fault 1053.2.2 IGBT Open- Circuit Fault 1053.3 Protection and Detection Under IGBT Short- Circuit Faults 1063.3.1 SM Under IGBT Short- Circuit Fault 1063.3.2 Protection and Detection Under IGBT Short- Circuit Fault 1073.4 mmc Features Under IGBT Open- Circuit Faults 1093.4.1 Faulty SM Features Under T 1 Open- Circuit Fault 1093.4.2 Faulty SM Features Under T 2 Open- Circuit Fault 1103.4.2.1 Operation Mode of Faulty SM 1103.4.2.2 Faulty SM Capacitor Voltage of MMCs in Inverter Mode 1113.4.2.3 Faulty SM Capacitor Voltage of MMCs in Rectifier Mode 1123.5 Kalman Filter Based Fault Detection Under IGBT Open- Circuit Faults 1153.5.1 Kalman Filter Algorithm 1173.5.2 Circulating Current Estimation 1183.5.3 Faulty Phase Detection 1193.5.4 Capacitor Voltage 1203.5.5 Faulty SM Detection 1213.6 Integrator Based Fault Detection Under IGBT Open- Circuit Faults 1273.7 STW Based Fault Detection Under IGBT Open- Circuit Faults 1323.7.1 MMC Data 1323.7.2 Sliding- Time Windows 1333.7.3 Feature of STW 1343.7.4 Features Relationships Between Neighboring STWs 1373.7.5 Features Extraction Algorithm 1373.7.6 Energy Entropy Matrix 1383.7.7 2D- CNN 1383.7.8 Fault Detection Method 1403.7.9 Selection of Sliding Interval 1413.7.10 Analysis of Fault Localization Time 1423.8 IF Based Fault Detection Under IGBT Open- Circuit Faults 1453.8.1 IT for MMCs 1453.8.2 SM Depth in IT 1463.8.3 IF for MMCs 1473.8.4 SM Average Depth in IF 1473.8.5 IF Output 1473.8.6 Fault Detection 1493.8.7 Selection of m p 1503.8.8 Selection of k 1513.9 Summary 156References 1564 Condition Monitoring and Control of MMCs Under Capacitor Faults 1614.1 Introduction 1614.2 Capacitor Equivalent Circuit in MMCs 1624.3 Capacitor Parameter Characteristics in MMCs 1644.3.1 Capacitor Current Characteristics 1644.3.2 Capacitor Impedance Characteristics 1674.3.3 Capacitor Voltage Characteristics 1674.4 Capacitor Aging 1694.5 Capacitance Monitoring 1714.5.1 Capacitor Voltage and Current Based Monitoring Strategy 1724.5.2 Arm Average Capacitance Based Monitoring Method 1724.5.2.1 Equivalent Arm Structure 1724.5.2.2 Capacitor Monitoring Method 1734.5.3 Reference SM based Monitoring Method 1794.5.3.1 Principle of the RSM- Based Capacitor Monitoring Strategy 1794.5.3.2 Capacitor Monitoring- Based Voltage- Balancing Control 1804.5.3.3 Selection of RSM 1824.5.3.4 Capacitor Monitoring Strategy 1834.5.4 Sorting- Based Monitoring Strategy 1894.5.5 Temperature Effect of Capacitance 1954.6 ESR Monitoring 1954.6.1 Direct ESR Monitoring Strategy 1964.6.2 Sorting- Based ESR Monitoring Strategy 1964.6.3 Temperature Effect of ESR 2034.7 Capacitor Lifetime Monitoring 2044.8 Arm Current Optimal Control Under Capacitor Aging 2054.8.1 Equivalent Circuit of MMCs 2054.8.2 Arm Current Characteristics 2074.8.3 Arm Current Optimal Control 2084.9 SM Power Losses Optimal Control Under Capacitor Aging 2124.9.1 Equivalent SM Reference 2134.9.2 SM Conduction Losses 2154.9.3 SM Switching Losses 2164.9.4 SM Power Losses Optimal Control 2174.10 Summary 225References 2265 Fault-Tolerant Control of MMCs Under SM Faults 2295.1 Introduction 2295.2 SM Protection Circuit 2295.3 Redundant Submodules 2305.4 Fault- Tolerant Scheme 2315.4.1 Cold Reserve Mode 2325.4.2 Spinning Reserve Mode- I 2335.4.3 Spinning Reserve Mode- II 2355.4.4 Spinning Reserve Mode- III 2355.4.5 Comparison of Fault- Tolerant Schemes 2355.5 Fundamental Circulating Current Elimination Based Tolerant Control 2365.5.1 Equivalent Circuit of MMCs 2365.5.2 Fundamental Circulating Current 2385.5.3 Fundamental Circulating Current Elimination Control 2395.5.4 Control Analysis 2415.6 Summary 247References 2476 Control of MMCs Under AC Grid Faults 2496.1 Introduction 2496.2 Mathematical Model of MMCs under AC Grid Faults 2506.2.1 AC- Side Mathematical Model 2506.2.1.1 MMC with AC- Side Transformer 2506.2.1.2 MMCs without AC- Side Transformer 2526.2.2 Instantaneous Power Mathematical Model 2536.3 AC- Side Current Control of MMCs under AC Grid Faults 2546.3.1 Positive- and Negative- Sequence Current Control 2556.3.1.1 Inner Loop Current Control 2556.3.1.2 Outer Power Control 2566.3.2 Zero- Sequence Current Control 2576.3.3 Proportional Resonant Based Current Control 2596.4 Circulating Current Suppression Control of MMCs under AC Grid Faults 2616.4.1 Circulating Current of MMCs Under AC Grid Faults 2616.4.2 Single- Phase Vector Based Control 2626.4.3 αβ0 Stationary Frame Based Control 2646.4.4 Three- Phase Stationary Frame Based Control 2666.4.4.1 Positive- and Negative- Sequence Controller 2676.4.4.2 Zero- Sequence Controller 2686.5 Summary 269References 2707 Protection Under DC Short-Circuit Fault in HVDC System 2737.1 Introduction 2737.2 MMC Under DC Short- Circuit Fault 2747.2.1 System Configuration 2747.2.2 AC Circuit Breaker 2747.2.3 Protection Thyristor 2757.2.4 Protection Operation 2767.3 DC Circuit Breaker Based Protection 2817.3.1 Mechanical Circuit Breaker 2827.3.2 Semiconductor Circuit Breaker 2837.3.2.1 Semi- Controlled Semiconductor Circuit Breaker 2837.3.2.2 Fully Controlled Semiconductor Circuit Breaker 2847.3.3 Hybrid Circuit Breaker 2857.3.3.1 Conventional Hybrid Circuit Breaker 2857.3.3.2 Proactive Hybrid Circuit Breaker 2867.3.4 Multiterminal Circuit Breaker 2877.3.4.1 Assembly CB 2877.3.4.2 Multiport CB 2887.3.5 Superconducting Fault Current Limiter 2897.3.6 SFCL- Based Circuit Breaker 2897.3.6.1 SFCL- Based Hybrid Circuit Breaker 2907.3.6.2 SFCL- Based Self- Oscillating Circuit Breaker 2917.3.6.3 SFCL- Based Forced Zero- Crossing Circuit Breaker 2927.4 Fault Blocking Converter Based Protection 2937.4.1 FB SM and HB SM Based Hybrid MMC 2947.4.2 Fault Blocking Control 2967.4.3 FB SM Ratio 2987.4.4 Alternative Fault Blocking SMs 2987.5 Bypass Thyristor MMC Based Protection 2997.5.1 Bypass Thyristor MMC Configuration 2997.5.2 SM Control 3027.5.3 Current Interruption Control 3037.5.3.1 Three- Phase Rectifier Period 3047.5.3.2 One- Phase Current Interruption Moment 3047.5.3.3 Single- Phase Rectifier Period 3057.5.3.4 Three- Phase Current Interruption Moment 3067.5.4 Protection Operation 3077.6 CTB- HMMC Based Protection 3117.6.1 CTB- HMMC Configuration 3127.6.2 SM Operation Principle 3137.6.3 Operation Principle for DC Fault Protection 3147.6.4 DC- Side Current Interruption Operation 3157.6.5 Capacitor Voltage Increment 3177.6.6 AC- Side Current Interruption Operation 3187.6.7 MMC Comparison 3217.6.7.1 Comparison with Current Blocking SM Based MMCs 3217.6.7.2 Comparison with Thyristor Based MMCs 3237.7 Summary 328References 329Index 333

Fujin Deng, PhD, is a Professor and Head of the Department of Power Electronics at Southeast University, China. He is a Senior Member of the IEEE. Chengkai Liu, PhD, is a PhD student who studies coordinated fault diagnosis and fault tolerant operation for flexible direct current transmission systems at Southeast University, China. Zhe Chen, PhD, is a Professor and the leader of Wind Power System Research program at the Department of Energy Technology, Aalborg University, Denmark. He is a Fellow of IEEE, a Fellow of IET and a Chartered Engineer in the U.K.

• About the Authors xiiiPreface xv1 Modular Multilevel Converters 11.1 Introduction 11.2 MMC Configuration 21.2.1 Converter Configuration 21.2.2 Submodule Configuration 21.3 Operation Principles 31.3.1 Submodule Normal Operation 31.3.2 Submodule Blocking Operation 51.3.3 Converter Operation 61.4 Modulation Scheme 81.4.1 Phase-Disposition PWM 91.4.2 Phase-Shifted PWM 101.4.3 Nearest Level Modulation 111.5 Mathematical Model 121.5.1 Submodule Mathematical Model 121.5.1.1 Switching-Function Based Model 131.5.1.2 Reference-Based Model 131.5.2 Arm Mathematical Model 141.5.2.1 Switching-Function Based Model 141.5.2.2 Reference-Based Model 151.5.3 Three-Phase MMC Mathematical Model 161.5.3.1 AC-Side Mathematical Model 171.5.3.2 DC-Side Mathematical Model 171.6 Design Constraints 181.6.1 Power Device Design 181.6.1.1 Rated Voltage of Power Devices 191.6.1.2 Rated Current of Power Devices 191.6.2 Capacitor Design 211.6.3 Arm Inductor Design 231.7 Faults Overview of MMCs 241.7.1 Internal Faults of MMCs 241.7.2 External Faults of MMCs 251.8 Summary 25References 262 Control of MMCs 292.1 Introduction 292.2 Overall Control of MMCs 302.3 Output Control of MMCs 312.3.1 Current Control 312.3.2 Power and DC-Link Voltage Control 332.3.3 Grid Forming Control 362.4 Centralized Capacitor Voltage Balancing Control 382.4.1 On-State SMs Number Based VBC 392.4.2 Balancing Adjusting Number Based VBC 392.4.2.1 Capacitor VBC 402.4.2.2 SM Switching Frequency 402.4.3 IPSC-PWM Harmonic Current Based VBC 422.4.3.1 IPSC-PWM Scheme 422.4.3.2 High-Frequency Arm Current 432.4.3.3 Arm Capacitor Voltage Analysis 462.4.3.4 Voltage Balancing Control 472.4.4 SHE-PWM Pulse Energy Sorting Based VBC 532.4.4.1 MMCs Analysis with Grid-Frequency Pulses 532.4.4.2 Charge Transfer of Capacitors in Lower Arm 562.4.4.3 Charge Transfer of Capacitors in Upper Arm 572.4.4.4 Voltage Balancing Control 592.4.5 PSC-PWM Pulse Energy Sorting Based VBC 652.4.5.1 MMC with PSC-PWM 652.4.5.2 Capacitor Charge Transfer Under Linearization Method 672.4.5.3 Capacitor Voltage Analysis 702.4.5.4 Voltage Balancing Control 722.5 Individual Capacitor Voltage Balancing Control 792.5.1 Average and Balancing Control Based VBC 792.5.1.1 Average Control 802.5.1.2 Balancing Control 802.5.2 Reference Modulation Index Based VBC 812.5.2.1 Analysis of Capacitor Voltage 822.5.2.2 Control of i cdc by modulation Index m 832.5.2.3 Voltage Balancing Control by m 842.5.3 Reference Phase Angle Based VBC 862.5.3.1 Control of i cdc by Phase Angle θ 862.5.3.2 Voltage Balancing Control by θ 872.6 Circulating Current Control 942.6.1 Proportional Integration Control 952.6.2 Multiple Proportional Resonant Control 972.6.3 Repetitive Control 982.7 Summary 100References 1003 Fault Detection of MMCs under IGBT Faults 1033.1 Introduction 1033.2 IGBT Faults 1043.2.1 IGBT Short- Circuit Fault 1053.2.2 IGBT Open- Circuit Fault 1053.3 Protection and Detection Under IGBT Short- Circuit Faults 1063.3.1 SM Under IGBT Short- Circuit Fault 1063.3.2 Protection and Detection Under IGBT Short- Circuit Fault 1073.4 mmc Features Under IGBT Open- Circuit Faults 1093.4.1 Faulty SM Features Under T 1 Open- Circuit Fault 1093.4.2 Faulty SM Features Under T 2 Open- Circuit Fault 1103.4.2.1 Operation Mode of Faulty SM 1103.4.2.2 Faulty SM Capacitor Voltage of MMCs in Inverter Mode 1113.4.2.3 Faulty SM Capacitor Voltage of MMCs in Rectifier Mode 1123.5 Kalman Filter Based Fault Detection Under IGBT Open- Circuit Faults 1153.5.1 Kalman Filter Algorithm 1173.5.2 Circulating Current Estimation 1183.5.3 Faulty Phase Detection 1193.5.4 Capacitor Voltage 1203.5.5 Faulty SM Detection 1213.6 Integrator Based Fault Detection Under IGBT Open- Circuit Faults 1273.7 STW Based Fault Detection Under IGBT Open- Circuit Faults 1323.7.1 MMC Data 1323.7.2 Sliding- Time Windows 1333.7.3 Feature of STW 1343.7.4 Features Relationships Between Neighboring STWs 1373.7.5 Features Extraction Algorithm 1373.7.6 Energy Entropy Matrix 1383.7.7 2D- CNN 1383.7.8 Fault Detection Method 1403.7.9 Selection of Sliding Interval 1413.7.10 Analysis of Fault Localization Time 1423.8 IF Based Fault Detection Under IGBT Open- Circuit Faults 1453.8.1 IT for MMCs 1453.8.2 SM Depth in IT 1463.8.3 IF for MMCs 1473.8.4 SM Average Depth in IF 1473.8.5 IF Output 1473.8.6 Fault Detection 1493.8.7 Selection of m p 1503.8.8 Selection of k 1513.9 Summary 156References 1564 Condition Monitoring and Control of MMCs Under Capacitor Faults 1614.1 Introduction 1614.2 Capacitor Equivalent Circuit in MMCs 1624.3 Capacitor Parameter Characteristics in MMCs 1644.3.1 Capacitor Current Characteristics 1644.3.2 Capacitor Impedance Characteristics 1674.3.3 Capacitor Voltage Characteristics 1674.4 Capacitor Aging 1694.5 Capacitance Monitoring 1714.5.1 Capacitor Voltage and Current Based Monitoring Strategy 1724.5.2 Arm Average Capacitance Based Monitoring Method 1724.5.2.1 Equivalent Arm Structure 1724.5.2.2 Capacitor Monitoring Method 1734.5.3 Reference SM based Monitoring Method 1794.5.3.1 Principle of the RSM- Based Capacitor Monitoring Strategy 1794.5.3.2 Capacitor Monitoring- Based Voltage- Balancing Control 1804.5.3.3 Selection of RSM 1824.5.3.4 Capacitor Monitoring Strategy 1834.5.4 Sorting- Based Monitoring Strategy 1894.5.5 Temperature Effect of Capacitance 1954.6 ESR Monitoring 1954.6.1 Direct ESR Monitoring Strategy 1964.6.2 Sorting- Based ESR Monitoring Strategy 1964.6.3 Temperature Effect of ESR 2034.7 Capacitor Lifetime Monitoring 2044.8 Arm Current Optimal Control Under Capacitor Aging 2054.8.1 Equivalent Circuit of MMCs 2054.8.2 Arm Current Characteristics 2074.8.3 Arm Current Optimal Control 2084.9 SM Power Losses Optimal Control Under Capacitor Aging 2124.9.1 Equivalent SM Reference 2134.9.2 SM Conduction Losses 2154.9.3 SM Switching Losses 2164.9.4 SM Power Losses Optimal Control 2174.10 Summary 225References 2265 Fault-Tolerant Control of MMCs Under SM Faults 2295.1 Introduction 2295.2 SM Protection Circuit 2295.3 Redundant Submodules 2305.4 Fault- Tolerant Scheme 2315.4.1 Cold Reserve Mode 2325.4.2 Spinning Reserve Mode- I 2335.4.3 Spinning Reserve Mode- II 2355.4.4 Spinning Reserve Mode- III 2355.4.5 Comparison of Fault- Tolerant Schemes 2355.5 Fundamental Circulating Current Elimination Based Tolerant Control 2365.5.1 Equivalent Circuit of MMCs 2365.5.2 Fundamental Circulating Current 2385.5.3 Fundamental Circulating Current Elimination Control 2395.5.4 Control Analysis 2415.6 Summary 247References 2476 Control of MMCs Under AC Grid Faults 2496.1 Introduction 2496.2 Mathematical Model of MMCs under AC Grid Faults 2506.2.1 AC- Side Mathematical Model 2506.2.1.1 MMC with AC- Side Transformer 2506.2.1.2 MMCs without AC- Side Transformer 2526.2.2 Instantaneous Power Mathematical Model 2536.3 AC- Side Current Control of MMCs under AC Grid Faults 2546.3.1 Positive- and Negative- Sequence Current Control 2556.3.1.1 Inner Loop Current Control 2556.3.1.2 Outer Power Control 2566.3.2 Zero- Sequence Current Control 2576.3.3 Proportional Resonant Based Current Control 2596.4 Circulating Current Suppression Control of MMCs under AC Grid Faults 2616.4.1 Circulating Current of MMCs Under AC Grid Faults 2616.4.2 Single- Phase Vector Based Control 2626.4.3 αβ0 Stationary Frame Based Control 2646.4.4 Three- Phase Stationary Frame Based Control 2666.4.4.1 Positive- and Negative- Sequence Controller 2676.4.4.2 Zero- Sequence Controller 2686.5 Summary 269References 2707 Protection Under DC Short-Circuit Fault in HVDC System 2737.1 Introduction 2737.2 MMC Under DC Short- Circuit Fault 2747.2.1 System Configuration 2747.2.2 AC Circuit Breaker 2747.2.3 Protection Thyristor 2757.2.4 Protection Operation 2767.3 DC Circuit Breaker Based Protection 2817.3.1 Mechanical Circuit Breaker 2827.3.2 Semiconductor Circuit Breaker 2837.3.2.1 Semi- Controlled Semiconductor Circuit Breaker 2837.3.2.2 Fully Controlled Semiconductor Circuit Breaker 2847.3.3 Hybrid Circuit Breaker 2857.3.3.1 Conventional Hybrid Circuit Breaker 2857.3.3.2 Proactive Hybrid Circuit Breaker 2867.3.4 Multiterminal Circuit Breaker 2877.3.4.1 Assembly CB 2877.3.4.2 Multiport CB 2887.3.5 Superconducting Fault Current Limiter 2897.3.6 SFCL- Based Circuit Breaker 2897.3.6.1 SFCL- Based Hybrid Circuit Breaker 2907.3.6.2 SFCL- Based Self- Oscillating Circuit Breaker 2917.3.6.3 SFCL- Based Forced Zero- Crossing Circuit Breaker 2927.4 Fault Blocking Converter Based Protection 2937.4.1 FB SM and HB SM Based Hybrid MMC 2947.4.2 Fault Blocking Control 2967.4.3 FB SM Ratio 2987.4.4 Alternative Fault Blocking SMs 2987.5 Bypass Thyristor MMC Based Protection 2997.5.1 Bypass Thyristor MMC Configuration 2997.5.2 SM Control 3027.5.3 Current Interruption Control 3037.5.3.1 Three- Phase Rectifier Period 3047.5.3.2 One- Phase Current Interruption Moment 3047.5.3.3 Single- Phase Rectifier Period 3057.5.3.4 Three- Phase Current Interruption Moment 3067.5.4 Protection Operation 3077.6 CTB- HMMC Based Protection 3117.6.1 CTB- HMMC Configuration 3127.6.2 SM Operation Principle 3137.6.3 Operation Principle for DC Fault Protection 3147.6.4 DC- Side Current Interruption Operation 3157.6.5 Capacitor Voltage Increment 3177.6.6 AC- Side Current Interruption Operation 3187.6.7 MMC Comparison 3217.6.7.1 Comparison with Current Blocking SM Based MMCs 3217.6.7.2 Comparison with Thyristor Based MMCs 3237.7 Summary 328References 329Index 333

Fujin Deng, PhD, is a Professor and Head of the Department of Power Electronics at Southeast University, China. He is a Senior Member of the IEEE. Chengkai Liu, PhD, is a PhD student who studies coordinated fault diagnosis and fault tolerant operation for flexible direct current transmission systems at Southeast University, China. Zhe Chen, PhD, is a Professor and the leader of Wind Power System Research program at the Department of Energy Technology, Aalborg University, Denmark. He is a Fellow of IEEE, a Fellow of IET and a Chartered Engineer in the U.K.

• About the Authors xiiiPreface xv1 Modular Multilevel Converters 11.1 Introduction 11.2 MMC Configuration 21.2.1 Converter Configuration 21.2.2 Submodule Configuration 21.3 Operation Principles 31.3.1 Submodule Normal Operation 31.3.2 Submodule Blocking Operation 51.3.3 Converter Operation 61.4 Modulation Scheme 81.4.1 Phase-Disposition PWM 91.4.2 Phase-Shifted PWM 101.4.3 Nearest Level Modulation 111.5 Mathematical Model 121.5.1 Submodule Mathematical Model 121.5.1.1 Switching-Function Based Model 131.5.1.2 Reference-Based Model 131.5.2 Arm Mathematical Model 141.5.2.1 Switching-Function Based Model 141.5.2.2 Reference-Based Model 151.5.3 Three-Phase MMC Mathematical Model 161.5.3.1 AC-Side Mathematical Model 171.5.3.2 DC-Side Mathematical Model 171.6 Design Constraints 181.6.1 Power Device Design 181.6.1.1 Rated Voltage of Power Devices 191.6.1.2 Rated Current of Power Devices 191.6.2 Capacitor Design 211.6.3 Arm Inductor Design 231.7 Faults Overview of MMCs 241.7.1 Internal Faults of MMCs 241.7.2 External Faults of MMCs 251.8 Summary 25References 262 Control of MMCs 292.1 Introduction 292.2 Overall Control of MMCs 302.3 Output Control of MMCs 312.3.1 Current Control 312.3.2 Power and DC-Link Voltage Control 332.3.3 Grid Forming Control 362.4 Centralized Capacitor Voltage Balancing Control 382.4.1 On-State SMs Number Based VBC 392.4.2 Balancing Adjusting Number Based VBC 392.4.2.1 Capacitor VBC 402.4.2.2 SM Switching Frequency 402.4.3 IPSC-PWM Harmonic Current Based VBC 422.4.3.1 IPSC-PWM Scheme 422.4.3.2 High-Frequency Arm Current 432.4.3.3 Arm Capacitor Voltage Analysis 462.4.3.4 Voltage Balancing Control 472.4.4 SHE-PWM Pulse Energy Sorting Based VBC 532.4.4.1 MMCs Analysis with Grid-Frequency Pulses 532.4.4.2 Charge Transfer of Capacitors in Lower Arm 562.4.4.3 Charge Transfer of Capacitors in Upper Arm 572.4.4.4 Voltage Balancing Control 592.4.5 PSC-PWM Pulse Energy Sorting Based VBC 652.4.5.1 MMC with PSC-PWM 652.4.5.2 Capacitor Charge Transfer Under Linearization Method 672.4.5.3 Capacitor Voltage Analysis 702.4.5.4 Voltage Balancing Control 722.5 Individual Capacitor Voltage Balancing Control 792.5.1 Average and Balancing Control Based VBC 792.5.1.1 Average Control 802.5.1.2 Balancing Control 802.5.2 Reference Modulation Index Based VBC 812.5.2.1 Analysis of Capacitor Voltage 822.5.2.2 Control of i cdc by modulation Index m 832.5.2.3 Voltage Balancing Control by m 842.5.3 Reference Phase Angle Based VBC 862.5.3.1 Control of i cdc by Phase Angle θ 862.5.3.2 Voltage Balancing Control by θ 872.6 Circulating Current Control 942.6.1 Proportional Integration Control 952.6.2 Multiple Proportional Resonant Control 972.6.3 Repetitive Control 982.7 Summary 100References 1003 Fault Detection of MMCs under IGBT Faults 1033.1 Introduction 1033.2 IGBT Faults 1043.2.1 IGBT Short- Circuit Fault 1053.2.2 IGBT Open- Circuit Fault 1053.3 Protection and Detection Under IGBT Short- Circuit Faults 1063.3.1 SM Under IGBT Short- Circuit Fault 1063.3.2 Protection and Detection Under IGBT Short- Circuit Fault 1073.4 mmc Features Under IGBT Open- Circuit Faults 1093.4.1 Faulty SM Features Under T 1 Open- Circuit Fault 1093.4.2 Faulty SM Features Under T 2 Open- Circuit Fault 1103.4.2.1 Operation Mode of Faulty SM 1103.4.2.2 Faulty SM Capacitor Voltage of MMCs in Inverter Mode 1113.4.2.3 Faulty SM Capacitor Voltage of MMCs in Rectifier Mode 1123.5 Kalman Filter Based Fault Detection Under IGBT Open- Circuit Faults 1153.5.1 Kalman Filter Algorithm 1173.5.2 Circulating Current Estimation 1183.5.3 Faulty Phase Detection 1193.5.4 Capacitor Voltage 1203.5.5 Faulty SM Detection 1213.6 Integrator Based Fault Detection Under IGBT Open- Circuit Faults 1273.7 STW Based Fault Detection Under IGBT Open- Circuit Faults 1323.7.1 MMC Data 1323.7.2 Sliding- Time Windows 1333.7.3 Feature of STW 1343.7.4 Features Relationships Between Neighboring STWs 1373.7.5 Features Extraction Algorithm 1373.7.6 Energy Entropy Matrix 1383.7.7 2D- CNN 1383.7.8 Fault Detection Method 1403.7.9 Selection of Sliding Interval 1413.7.10 Analysis of Fault Localization Time 1423.8 IF Based Fault Detection Under IGBT Open- Circuit Faults 1453.8.1 IT for MMCs 1453.8.2 SM Depth in IT 1463.8.3 IF for MMCs 1473.8.4 SM Average Depth in IF 1473.8.5 IF Output 1473.8.6 Fault Detection 1493.8.7 Selection of m p 1503.8.8 Selection of k 1513.9 Summary 156References 1564 Condition Monitoring and Control of MMCs Under Capacitor Faults 1614.1 Introduction 1614.2 Capacitor Equivalent Circuit in MMCs 1624.3 Capacitor Parameter Characteristics in MMCs 1644.3.1 Capacitor Current Characteristics 1644.3.2 Capacitor Impedance Characteristics 1674.3.3 Capacitor Voltage Characteristics 1674.4 Capacitor Aging 1694.5 Capacitance Monitoring 1714.5.1 Capacitor Voltage and Current Based Monitoring Strategy 1724.5.2 Arm Average Capacitance Based Monitoring Method 1724.5.2.1 Equivalent Arm Structure 1724.5.2.2 Capacitor Monitoring Method 1734.5.3 Reference SM based Monitoring Method 1794.5.3.1 Principle of the RSM- Based Capacitor Monitoring Strategy 1794.5.3.2 Capacitor Monitoring- Based Voltage- Balancing Control 1804.5.3.3 Selection of RSM 1824.5.3.4 Capacitor Monitoring Strategy 1834.5.4 Sorting- Based Monitoring Strategy 1894.5.5 Temperature Effect of Capacitance 1954.6 ESR Monitoring 1954.6.1 Direct ESR Monitoring Strategy 1964.6.2 Sorting- Based ESR Monitoring Strategy 1964.6.3 Temperature Effect of ESR 2034.7 Capacitor Lifetime Monitoring 2044.8 Arm Current Optimal Control Under Capacitor Aging 2054.8.1 Equivalent Circuit of MMCs 2054.8.2 Arm Current Characteristics 2074.8.3 Arm Current Optimal Control 2084.9 SM Power Losses Optimal Control Under Capacitor Aging 2124.9.1 Equivalent SM Reference 2134.9.2 SM Conduction Losses 2154.9.3 SM Switching Losses 2164.9.4 SM Power Losses Optimal Control 2174.10 Summary 225References 2265 Fault-Tolerant Control of MMCs Under SM Faults 2295.1 Introduction 2295.2 SM Protection Circuit 2295.3 Redundant Submodules 2305.4 Fault- Tolerant Scheme 2315.4.1 Cold Reserve Mode 2325.4.2 Spinning Reserve Mode- I 2335.4.3 Spinning Reserve Mode- II 2355.4.4 Spinning Reserve Mode- III 2355.4.5 Comparison of Fault- Tolerant Schemes 2355.5 Fundamental Circulating Current Elimination Based Tolerant Control 2365.5.1 Equivalent Circuit of MMCs 2365.5.2 Fundamental Circulating Current 2385.5.3 Fundamental Circulating Current Elimination Control 2395.5.4 Control Analysis 2415.6 Summary 247References 2476 Control of MMCs Under AC Grid Faults 2496.1 Introduction 2496.2 Mathematical Model of MMCs under AC Grid Faults 2506.2.1 AC- Side Mathematical Model 2506.2.1.1 MMC with AC- Side Transformer 2506.2.1.2 MMCs without AC- Side Transformer 2526.2.2 Instantaneous Power Mathematical Model 2536.3 AC- Side Current Control of MMCs under AC Grid Faults 2546.3.1 Positive- and Negative- Sequence Current Control 2556.3.1.1 Inner Loop Current Control 2556.3.1.2 Outer Power Control 2566.3.2 Zero- Sequence Current Control 2576.3.3 Proportional Resonant Based Current Control 2596.4 Circulating Current Suppression Control of MMCs under AC Grid Faults 2616.4.1 Circulating Current of MMCs Under AC Grid Faults 2616.4.2 Single- Phase Vector Based Control 2626.4.3 αβ0 Stationary Frame Based Control 2646.4.4 Three- Phase Stationary Frame Based Control 2666.4.4.1 Positive- and Negative- Sequence Controller 2676.4.4.2 Zero- Sequence Controller 2686.5 Summary 269References 2707 Protection Under DC Short-Circuit Fault in HVDC System 2737.1 Introduction 2737.2 MMC Under DC Short- Circuit Fault 2747.2.1 System Configuration 2747.2.2 AC Circuit Breaker 2747.2.3 Protection Thyristor 2757.2.4 Protection Operation 2767.3 DC Circuit Breaker Based Protection 2817.3.1 Mechanical Circuit Breaker 2827.3.2 Semiconductor Circuit Breaker 2837.3.2.1 Semi- Controlled Semiconductor Circuit Breaker 2837.3.2.2 Fully Controlled Semiconductor Circuit Breaker 2847.3.3 Hybrid Circuit Breaker 2857.3.3.1 Conventional Hybrid Circuit Breaker 2857.3.3.2 Proactive Hybrid Circuit Breaker 2867.3.4 Multiterminal Circuit Breaker 2877.3.4.1 Assembly CB 2877.3.4.2 Multiport CB 2887.3.5 Superconducting Fault Current Limiter 2897.3.6 SFCL- Based Circuit Breaker 2897.3.6.1 SFCL- Based Hybrid Circuit Breaker 2907.3.6.2 SFCL- Based Self- Oscillating Circuit Breaker 2917.3.6.3 SFCL- Based Forced Zero- Crossing Circuit Breaker 2927.4 Fault Blocking Converter Based Protection 2937.4.1 FB SM and HB SM Based Hybrid MMC 2947.4.2 Fault Blocking Control 2967.4.3 FB SM Ratio 2987.4.4 Alternative Fault Blocking SMs 2987.5 Bypass Thyristor MMC Based Protection 2997.5.1 Bypass Thyristor MMC Configuration 2997.5.2 SM Control 3027.5.3 Current Interruption Control 3037.5.3.1 Three- Phase Rectifier Period 3047.5.3.2 One- Phase Current Interruption Moment 3047.5.3.3 Single- Phase Rectifier Period 3057.5.3.4 Three- Phase Current Interruption Moment 3067.5.4 Protection Operation 3077.6 CTB- HMMC Based Protection 3117.6.1 CTB- HMMC Configuration 3127.6.2 SM Operation Principle 3137.6.3 Operation Principle for DC Fault Protection 3147.6.4 DC- Side Current Interruption Operation 3157.6.5 Capacitor Voltage Increment 3177.6.6 AC- Side Current Interruption Operation 3187.6.7 MMC Comparison 3217.6.7.1 Comparison with Current Blocking SM Based MMCs 3217.6.7.2 Comparison with Thyristor Based MMCs 3237.7 Summary 328References 329Index 333