Multi-terminal Direct-Current Grids

Nilanjan Ray Chaudhuri received his Ph.D. degree from Imperial College London, UK. His research interests include power system dynamics and control, application of power electronics in power systems, online system identification, FACTS, HVDC, and renewable energy systems. He serves as an Associate Editor of the IEEE Transactions on Power Delivery. Nilanjan is a member of the WECC’s HVDC modeling Task Force, multiple CIGRE’ subcommittees, a member of the IEEE, IEEE PES, CIGRE’ and Sigma Xi.Balarko Chaudhuri is a Senior Lecturer in the department of Electrical and Electronic Engineering at Imperial College London, UK. His areas of expertise include electric power transmission systems, control theory, smart grids and renewable energy. He is an associate editor of the IEEE Systems Journal and Elsevier Control Engineering Practice. He is a Senior Member of the IEEE.Rajat Majumder did his PhD in Power Systems at Imperial College London, UK. He specializes in power system analysis, modeling and control design, with special emphasis on dynamic stability issues in large interconnected power grids involving HVDC and FACTS. He is serving as an editorial board member of Institute of Engineering Technology’s (IET) Proceedings of Generation, Transmission and Distribution. He is a Senior Member of the IEEE.Amirnaser Yazdani is an Associate Professor with Ryerson University in Toronto, Canada. From 2006 to 2011, he was an Assistant Professor with the University of Western Ontario in London, Canada, and prior to that he was with Digital Predictive Systems (DPS) Inc., Mississauga, Canada, active in the design and production of power converters for wind energy systems. Dr. Yazdani has extensive industry and academic experience in design, modeling, and analysis of switching power converters and railway signaling systems, and has served as an Associate Editor of the IEEE Transactions on Power Delivery. He is a Senior Member of the IEEE, a Professional Engineer in the Province of Ontario, Canada, and a co-author of the book Voltage-Sourced Converters in Power Systems, published by IEEE/Wiley Press, 2010.

• Foreword xiiiPreface xvAcronyms xixSymbols xxi1 Fundamentals 11.1 Introduction 11.2 Rationale Behind MTDC Grids 51.3 Network Architectures of MTDC Grids 61.3.1 Series Architecture 61.3.2 Parallel Architecture 71.4 Enabling Technologies and Components of MTDC Grids 91.4.1 LCC Technology 91.4.1.1 Control Modes in LCC-based MTDC Grid 101.4.1.2 Examples of Existing LCC MTDC Systems 101.4.2 VSC Technology 121.5 Control Modes in MTDC Grid 141.6 Challenges for MTDC Grids 151.7 Configurations of MTDC Converter Stations 161.8 Research Initiatives on MTDC Grids 191.9 Focus and Scope of the Monograph 212 The Voltage-Sourced Converter (VSC) 232.1 Introduction 232.2 Ideal Voltage-Sourced Converter 242.3 Practical Voltage-Sourced Converter 282.3.1 Two-Level Voltage-Sourced Converter 282.3.2 Three-Level Voltage-Sourced Converter 312.3.3 Multi-Level Voltage-Sourced Converter 352.4 Control 382.4.1 Control of Real and Reactive Powers 382.4.2 Design and Implementation of Control 392.4.2.1 Space Phasors 392.4.2.2 Space-Phasor Representation of the AC Side 422.4.2.3 Current Control in the Stationary Frame 432.4.2.4 Current Control in a Rotating Frame 442.4.2.5 Phase-Locked Loop 522.4.3 Control of the DC-Side Voltage 562.4.4 Control of the AC Grid Voltage 582.4.5 Multi-unit Control of DC Grid Voltage and/or AC Grid Voltage 592.4.6 Control of Islands 612.5 Simulation 652.6 Symbols of the VSC 753 Modeling, Analysis, and Simulation of AC–MTDC Grids 773.1 Introduction 773.2 MTDC Grid Model 783.2.1 Modeling Assumptions 783.2.2 Converter Model 813.2.3 Converter Controller Model 833.2.3.1 Outer Control Loops 833.2.3.2 Inner Current Control Loop 873.2.4 DC Network Model 873.2.4.1 Algebraic Equations 893.2.4.2 Differential Equations 913.2.5 State-Space Representation 913.2.5.1 Dynamic Equations of Converters and Controllers 923.2.5.2 Output Equations 933.2.5.3 Control Modes 933.2.5.4 Dynamic Equations of DC Network 953.2.5.5 Output Equations of DC Network 963.2.6 Phasor from Space Phasor 963.2.6.1 Base Values and Per-unit Systems 973.2.6.2 Phase Angle of Space Phasors 973.3 AC Grid Model 983.3.1 Generator Model 993.3.1.1 State-Space Representation of Synchronous Generator (SG) Model 993.3.1.2 Inclusion of Generator in the Network 1013.3.1.3 Treatment of Sub-transient Saliency 1023.3.1.4 State-Space Model of Excitation Systems for SGs 1043.3.1.5 State-Space Model of Turbine and Governor 1043.3.2 Load Model 1053.3.3 AC Network Model 1063.4 AC–MTDC Load flow Analysis 1083.4.1 AC Grid Load flow Model 1093.4.2 MTDC Grid Load flow Model 1103.4.2.1 MTDC Interface with AC System 1103.4.2.2 MTDC AC Side Load flow Model 1103.4.2.3 Interface of MTDC AC and DC Sides 1113.4.2.4 MTDC DC Side Load flow Model 1123.4.2.5 MTDC Converter Control Modes 1123.4.3 AC–MTDC Grid Load flow Solution 1143.5 AC–MTDC Grid Model for Nonlinear Dynamic Simulation 1203.5.1 Initialization of Dynamic Models 1213.5.1.1 MTDC Grid 1223.5.1.2 AC Grid 1223.6 Small-signal Stability Analysis of AC–MTDC Grid 1223.6.1 Linear Model of Converters and Controllers 1233.6.2 Linear Model of DC Network 1283.6.3 Eigenvalue, Eigenvector, and Participation Factor 1303.7 Transient Stability Analysis of AC–MTDC Grid 1303.7.1 Large Disturbance Simulation 1313.7.2 Representation of Rotor and Phase Angles 1323.8 Case Studies 1323.9 Case Study 1: The North Sea Benchmark System 1333.9.1 Study Network 1333.9.2 Nonlinear Simulation 1343.9.2.1 Small Disturbances 1343.9.2.2 Converter Outage 1353.9.3 Small-signal Stability Analysis 1373.9.3.1 Eigenvalue Analysis 1373.9.3.2 Participation Factor Analysis 1383.10 Case Study 2: MTDC Grid Connected to Equivalent AC Systems 1393.10.1 Study Network 1393.10.2 Nonlinear Simulation 1403.10.2.1 Small Disturbances 1423.10.2.2 Large Disturbances 1423.10.3 Small-signal Stability Analysis 1423.11 Case Study 3: MTDC Grid Connected to Multi-machine AC System 1433.11.1 Study Network 1433.11.2 AC–MTDC Grid Load flow Solution 1453.11.3 Small-signal Stability Analysis 1463.11.4 Nonlinear Simulation 1473.11.4.1 AC Side Fault 1473.11.4.2 DC Cable Fault 1483.11.4.3 Converter Outage 1504 Autonomous Power Sharing 1534.1 Introduction 1534.2 Steady-state Operating Characteristics 1564.3 Concept of Power Sharing 1574.3.1 Power Sharing Among Synchronous Generators 1574.3.2 Power Sharing in AC Microgrids 1584.4 Power Sharing in MTDC Grid 1594.4.1 Voltage Margin Control 1594.4.2 Droop Control 1624.4.2.1 Ratio and Priority Control 1664.4.3 Adaptive Droop Control 1674.5 AC–MTDC Grid Load flow Solution 1684.6 Post-contingency Operation 1694.6.1 Local DC Link Voltage Feedback 1704.6.2 Common DC Link Voltage Feedback 1714.6.3 Adaptive Droop Control 1724.7 Linear Model 1734.8 Case Study 1744.8.1 Study Network 1744.8.2 Small-signal Stability Analysis 1754.8.3 Nonlinear Simulation 1774.8.3.1 Validation Against Switched Model 1774.8.3.2 Problems with Local Voltage Feedback 1784.8.3.3 Fixed vs Adaptive Droop 1795 Frequency Support 1875.1 Introduction 1875.2 Fundamentals of Frequency Control 1895.3 Inertial and Primary Frequency Support from Wind Farms 1905.4 Wind Farms in Secondary Frequency Control (AGC) 1915.5 Modified Droop Control for Frequency Support 1925.6 AC–MTDC Load Flow Solution 1945.7 Post-Contingency Operation 1955.7.1 Analysis for AC System 1965.7.2 Analysis for Converter Station 1965.7.2.1 AC Side Disturbances 1975.7.2.2 Converter Outage 1975.7.3 Analysis for AC System Connected to Converter Stations 1985.7.4 Analysis of AC–MTDC Grid 1995.8 Case Study 2005.8.1 Study Network 2005.8.2 AC–MTDC Grid Load flow Solution 2025.8.3 Small-signal Stability Analysis 2035.8.4 Nonlinear Simulation 2045.8.4.1 AC Side Disturbances 2045.8.4.2 Converter Station Disturbances 2126 Protection of MTDC Grids 2196.1 Introduction 2196.2 Converter Station Protection 2206.3 DC Cable Fault Response 2206.3.1 Fault Response of Two-level VSC 2216.3.1.1 Analysis 2246.3.2 Fault Response of Half-bridge mmc 2256.3.3 Challenges 2276.4 Fault-blocking Converters 2286.4.1 Full-bridge mmc 2286.4.2 Variants of Full-bridge mmc 2306.5 DC Circuit Breakers 2316.5.1 Solid-state DC Breaker 2326.5.2 Proactive Hybrid DC Breaker 2336.5.3 DC/DC Converter 2356.6 Protection Strategies 2376.6.1 Strategy I 2386.6.2 Strategy II 2406.6.3 Strategy III 2416.6.3.1 Detection and Identification 2416.6.4 Backup Protection 245References 249Index 257