The simulation of electromagnetic transients is a mature field that plays an important role in the design of modern power systems. Since the first steps in this field to date, a significant effort has been dedicated to the development of new techniques and more powerful software tools. Sophisticated models, complex solution techniques and powerful simulation tools have been developed to perform studies that are of supreme importance in the design of modern power systems. The first developments of transients tools were mostly aimed at calculating over-voltages. Presently, these tools are applied to a myriad of studies (e.g. FACTS and Custom Power applications, protective relay performance, simulation of smart grids) for which detailed models and fast solution methods can be of paramount importance. This book provides a basic understanding of the main aspects to be considered when performing electromagnetic transients studies, detailing the main applications of present electromagnetic transients (EMT) tools, and discusses new developments for enhanced simulation capability. Key features: Provides up-to-date information on solution techniques and software capabilities for simulation of electromagnetic transients. Covers key aspects that can expand the capabilities of a transient software tool (e.g. interfacing techniques) or speed up transients simulation (e.g. dynamic model averaging). Applies EMT-type tools to a wide spectrum of studies that range from fast electromagnetic transients to slow electromechanical transients, including power electronic applications, distributed energy resources and protection systems. Illustrates the application of EMT tools to the analysis and simulation of smart grids.

Table of Contents:
Preface xv About the Editor xvii List of Contributors xix 1 Introduction to Electromagnetic Transient Analysis of Power Systems 1 Juan A. Martinez-Velasco 1.1 Overview 1 1.2 Scope of the Book 4 References 6 2 Solution Techniques for Electromagnetic Transients in Power Systems 9 Jean Mahseredjian, Ilhan Kocar and Ulas Karaagac 2.1 Introduction 9 2.2 Application Field for the Computation of Electromagnetic Transients 10 2.3 The Main Modules 11 2.4 Graphical User Interface 11 2.5 Formulation of Network Equations for Steady-State and Time-Domain Solutions 12 2.5.1 Nodal Analysis and Modified-Augmented-Nodal-Analysis 13 2.5.2 State-Space Analysis 20 2.5.3 Hybrid Analysis 21 2.5.4 State-Space Groups and MANA 25 2.5.5 Integration Time-Step 27 2.6 Control Systems 28 2.7 Multiphase Load-Flow Solution and Initialization 29 2.7.1 Load-Flow Constraints 31 2.7.2 Initialization of Load-Flow Equations 33 2.7.3 Initialization from Steady-State Solution 33 2.8 Implementation 34 2.9 Conclusions 36 References 36 3 Frequency Domain Aspects of Electromagnetic Transient Analysis of Power Systems 39 José L. Naredo, Jean Mahseredjian, Ilhan Kocar, JoséA.Gutiérrez–Robles and Juan A. Martinez-Velasco 3.1 Introduction 39 3.2 Frequency Domain Basics 40 3.2.1 Phasors and FD Representation of Signals 40 3.2.2 Fourier Series 43 3.2.3 Fourier Transform 46 3.3 Discrete-Time Frequency Analysis 48 3.3.1 Aliasing Effect 50 3.3.2 Sampling Theorem 51 3.3.3 Conservation of Information and the DFT 53 3.3.4 Fast Fourier Transform 54 3.4 Frequency-Domain Transient Analysis 56 3.4.1 Fourier Transforms and Transients 56 3.4.2 Fourier and Laplace Transforms 62 3.4.3 The Numerical Laplace Transform 63 3.4.4 Application Examples with the NLT 65 3.4.5 Brief History of NLT Development 65 3.5 Multirate Transient Analysis 66 3.6 Conclusions 69 Acknowledgement 70 References 70 4 Real-Time Simulation Technologies in Engineering 72 Christian Dufour and Jean Bélanger 4.1 Introduction 72 4.2 Model-Based Design and Real-Time Simulation 73 4.3 General Considerations about Real-Time Simulation 74 4.3.1 The Constraint of Real-Time 74 4.3.2 Stiffness Issues 75 4.3.3 Simulator Bandwidth Considerations 75 4.3.4 Simulation Bandwidth vs. Applications 75 4.3.5 Achieving Very Low Latency for HIL Application 76 4.3.6 Effective Parallel Processing for Fast EMT Simulation 77 4.3.7 FPGA-Based Multirate Simulators 79 4.3.8 Advanced Parallel Solvers without Artificial Delays or Stublines: Application to Active Distribution Networks 79 4.3.9 The Need for Iterations in Real-Time 80 4.4 Phasor-Mode Real-Time Simulation 82 4.5 Modern Real-Time Simulator Requirements 82 4.5.1 Simulator I/O Requirements 83 4.6 Rapid Control Prototyping and Hardware-in-the-Loop Testing 85 4.7 Power Grid Real-Time Simulation Applications 85 4.7.1 Statistical Protection System Study 85 4.7.2 Monte Carlo Tests for Power Grid Switching Surge System Studies 87 4.7.3 Modular Multilevel Converter in HVDC Applications 88 4.7.4 High-End Super-Large Power Grid Simulations 89 4.8 Motor Drive and FPGA-Based Real-Time Simulation Applications 90 4.8.1 Industrial Motor Drive Design and Testing Using CPU Models 90 4.8.2 FPGA Modelling of SRM and PMSM Motor Drives 91 4.9 Educational System: RPC-Based Study of DFIM Wind Turbine 94 4.10 Mechatronic Real-Time Simulation Applications 95 4.10.1 Aircraft Flight Training Simulator 95 4.10.2 Aircraft Flight Parameter Identification 95 4.10.3 International Space Station Robotic Arm Testing 95 4.11 Conclusion 97 References 97 5 Calculation of Power System Overvoltages 100 Juan A. Martinez-Velasco and Francisco González-Molina 5.1 Introduction 100 5.2 Power System Overvoltages 101 5.2.1 Temporary Overvoltages 101 5.2.2 Slow-Front Overvoltages 102 5.2.3 Fast-Front Overvoltages 102 5.2.4 Very-Fast-Front Overvoltages 103 5.3 Temporary Overvoltages 103 5.3.1 Introduction 103 5.3.2 Modelling Guidelines for Temporary Overvoltages 103 5.3.3 Faults to Grounds 104 5.3.4 Load Rejection 110 5.3.5 Harmonic Resonance 115 5.3.6 Energization of Unloaded Transformers 120 5.3.7 Ferroresonance 125 5.3.8 Conclusions 133 5.4 Switching Overvoltages 135 5.4.1 Introduction 135 5.4.2 Modelling Guidelines 135 5.4.3 Switching Overvoltages 139 5.4.4 Case Studies 149 5.4.5 Validation 154 5.5 Lightning Overvoltages 154 5.5.1 Introduction 154 5.5.2 Modelling Guidelines 155 5.5.3 Case Studies 163 5.5.4 Validation 172 5.6 Very Fast Transient Overvoltages in Gas Insulated Substations 174 5.6.1 Introduction 174 5.6.2 Origin of VFTO in GIS 174 5.6.3 Propagation of VFTs in GISs 176 5.6.4 Modelling Guidelines 180 5.6.5 Case Study 9: VFT in a 765 kV GIS 182 5.6.6 Statistical Calculation 183 5.6.7 Validation 185 5.7 Conclusions 187 Acknowledgement 187 References 187 6 Analysis of FACTS Controllers and their Transient Modelling Techniques 195 Kalyan K. Sen 6.1 Introduction 195 6.2 Theory of Power Flow Control 199 6.3 Modelling Guidelines 206 6.3.1 Representation of a Power System 206 6.3.2 Representation of System Control 206 6.3.3 Representation of a Controlled Switch 209 6.3.4 Simulation Errors and Control 210 6.4 Modelling of FACTS Controllers 210 6.4.1 Simulation of an Independent PFC in a Single Line Application 212 6.4.2 Simulation of a Voltage Regulating Transformer 212 6.4.3 Simulation of a Phase Angle Regulator 214 6.4.4 Simulation of a Unified Power Flow Controller 215 6.5 Simulation Results of a UPFC 230 6.6 Simulation Results of an ST 238 6.7 Conclusion 245 Acknowledgement 245 References 245 7 Applications of Power Electronic Devices in Distribution Systems 248 Arindam Ghosh and Farhad Shahnia 7.1 Introduction 248 7.2 Modelling of Converter and Filter Structures for CPDs 250 7.2.1 Three-Phase Converter Structures 250 7.2.2 Filter Structures 251 7.2.3 Dynamic Simulation of CPDs 252 7.3 Distribution Static Compensator (DSTATCOM) 253 7.3.1 Current Control Using DSTATCOM 253 7.3.2 Voltage Control Using DSTATCOM 256 7.4 Dynamic Voltage Restorer (DVR) 258 7.5 Unified Power Quality Conditioner (UPQC) 263 7.6 Voltage Balancing Using DSTATCOM and DVR 267 7.7 Excess Power Circulation Using CPDs 271 7.7.1 Current-Controlled DSTATCOM Application 271 7.7.2 Voltage-Controlled DSTATCOM Application 272 7.7.3 UPQC Application 276 7.8 Conclusions 278 References 278 8 Modelling of Electronically Interfaced DER Systems for Transient Analysis 280 Amirnaser Yazdani and Omid Alizadeh 8.1 Introduction 280 8.2 Generic Electronically Interfaced DER System 281 8.3 Realization of Different DER Systems 283 8.3.1 PV Energy Systems 283 8.3.2 Fuel-Cell Systems 284 8.3.3 Battery Energy Storage Systems 284 8.3.4 Supercapacitor Energy Storage System 285 8.3.5 Superconducting Magnetic Energy Storage System 285 8.3.6 Wind Energy Systems 286 8.3.7 Flywheel Energy Storage Systems 287 8.4 Transient Analysis of Electronically Interfaced DER Systems 287 8.5 Examples 288 8.5.1 Example 1: Single-Stage PV Energy System 288 8.5.2 Example 2: Direct-Drive Variable-Speed Wind Energy System 298 8.6 Conclusion 315 References 315 9 Simulation of Transients for VSC-HVDC Transmission Systems Based on Modular Multilevel Converters 317 Hani Saad, Sébastien Dennetière, Jean Mahseredjian, Tarek Ould-Bachir and Jean-Pierre David 9.1 Introduction 317 9.2 mmc Topology 318 9.3 mmc Models 320 9.3.1 Model 1 – Full Detailed 320 9.3.2 Model 2 – Detailed Equivalent 321 9.3.3 Model 3 – Switching Function of MMC Arm 322 9.3.4 Model 4 – AVM Based on Power Frequency 325 9.4 Control System 327 9.4.1 Operation Principle 327 9.4.2 Upper-Level Control 328 9.4.3 Lower-Level Control 333 9.4.4 Control Structure Requirement Depending on MMC Model Type 336 9.5 Model Comparisons 336 9.5.1 Step Change on Active Power Reference 337 9.5.2 Three-Phase AC Fault 337 9.5.3 Influence of MMC Levels 338 9.5.4 Pole-to-Pole DC Fault 338 9.5.5 Startup Sequence 340 9.5.6 Computational Performance 340 9.6 Real-Time Simulation of MMC Using CPU and FPGA 342 9.6.1 Relation between Sampling Time and N 344 9.6.2 Optimization of Model 2 for Real-Time Simulation 345 9.6.3 Real-Time Simulation Setup 346 9.6.4 CPU-Based Model 347 9.6.5 FPGA-Based Model 350 9.7 Conclusions 356 References 357 10 Dynamic Average Modelling of Rectifier Loads and AC-DC Converters for Power System Applications 360 Sina Chiniforoosh, Juri Jatskevich, Hamid Atighechi and Juan A. Martinez-Velasco 10.1 Introduction 360 10.2 Front-End Diode Rectifier System Configurations 361 10.3 Detailed Analysis and Modes of Operation 365 10.4 Dynamic Average Modelling 368 10.4.1 Selected Dynamic AVMs 370 10.4.2 Computer Implementation 372 10.5 Verification and Comparison of the AVMs 372 10.5.1 Steady-State Characteristics 372 10.5.2 Model Dynamic Order and Eigenvalue Analysis 376 10.5.3 Dynamic Performance Under Balanced and Unbalanced Conditions 377 10.5.4 Input Sequence Impedances under Unbalanced Conditions 382 10.5.5 Small-Signal Input/Output Impedances 383 10.6 Generalization to High-Pulse-Count Converters 386 10.6.1 Detailed Analysis 387 10.6.2 Dynamic Average Modelling 388 10.7 Generalization to PWM AC-DC Converters 391 10.7.1 PWM Voltage-Source Converters 391 10.7.2 Dynamic Average-Value Modelling of PWM Voltage-Source Converters 392 10.8 Conclusions 394 Appendix 394 References 395 11 Protection Systems 398 Juan A. Martinez-Velasco 11.1 Introduction 398 11.2 Modelling Guidelines for Power System Components 400 11.2.1 Line Models 400 11.2.2 Insulated Cables 401 11.2.3 Source Models 401 11.2.4 Transformer Models 401 11.2.5 Circuit Breaker Models 403 11.3 Models of Instrument Transformers 403 11.3.1 Introduction 403 11.3.2 Current Transformers 404 11.3.3 Rogowski Coils 408 11.3.4 Coupling Capacitor Voltage Transformers 410 11.3.5 Voltage Transformers 412 11.4 Relay Modelling 412 11.4.1 Introduction 412 11.4.2 Classification of Relay Models 412 11.4.3 Relay Models 413 11.5 Implementation of Relay Models 418 11.5.1 Introduction 418 11.5.2 Sources of Information for Building Relay Models 419 11.5.3 Software Tools 420 11.5.4 Implementation of Relay Models 421 11.5.5 Interfacing Relay Models to Recorded Data 422 11.5.6 Applications of Relay Models 423 11.5.7 Limitations of Relay Models 424 11.6 Validation of Relay Models 424 11.6.1 Validation Procedures 424 11.6.2 Relay Model Testing Procedures 425 11.6.3 Accuracy Assessment 426 11.6.4 Relay Testing Facilities 426 11.7 Case Studies 427 11.7.1 Introduction 427 11.7.2 Case Study 1: Simulation of an Electromechanical Distance Relay 428 11.7.3 Case Study 2: Simulation of a Numerical Distance Relay 430 11.8 Protection of Distribution Systems 450 11.8.1 Introduction 450 11.8.2 Protection of Distribution Systems with Distributed Generation 451 11.8.3 Modelling of Distribution Feeder Protective Devices 451 11.8.4 Protection of the Interconnection of Distributed Generators 460 11.8.5 Case Study 3 460 11.8.6 Case Study 4 465 11.9 Conclusions 471 Acknowledgement 475 References 476 12 Time-Domain Analysis of the Smart Grid Technologies: Possibilities and Challenges 481 Francisco de León, Reynaldo Salcedo, Xuanchang Ran and Juan A. Martinez-Velasco 12.1 Introduction 481 12.2 Distribution Systems 482 12.2.1 Radial Distribution Systems 483 12.2.2 Networked Distribution Systems 484 12.3 Restoration and Reconfiguration of the Smart Grid 487 12.3.1 Introduction 487 12.3.2 Heavily Meshed Networked Distribution Systems 487 12.4 Integration of Distributed Generation 498 12.4.1 Scope 498 12.4.2 Radial Distribution Systems 499 12.4.3 Heavily Meshed Networked Distribution Systems 503 12.5 Overvoltages in Distribution Networks 515 12.5.1 Introduction 515 12.5.2 Ferroresonant Overvoltages 516 12.5.3 Long-Duration Overvoltages due to Backfeeding 519 12.6 Development of Data Translators for Interfacing Power-Flow Programs with EMTP-Type Programs 529 12.6.1 Introduction 529 12.6.2 Power-Flow to EMTP-RV Translator 530 12.6.3 Example of the Translation of a Transmission Line 533 12.6.4 Challenges of Development 533 12.6.5 Model Validation 535 12.6.6 Recommendations 542 Acknowledgement 546 References 546 13 Interfacing Methods for Electromagnetic Transient Simulation: New Possibilities for Analysis and Design 552 Shaahin Filizadeh 13.1 Introduction 552 13.2 Need for Interfacing 553 13.3 Interfacing Templates 554 13.3.1 Static Interfacing 554 13.3.2 Dynamic Interfacing and Memory Management 555 13.3.3 Wrapper Interfaces 555 13.4 Interfacing Implementation Options: External vs Internal Interfaces 555 13.4.1 External Interfaces 556 13.4.2 Internal Interfaces 556 13.5 Multiple Interfacing 556 13.5.1 Core-Type Interfacing 557 13.5.2 Chain-Type Interfacing 557 13.5.3 Loop Interfacing 558 13.6 Examples of Interfacing 558 13.6.1 Interfacing to Matlab/Simulink 558 13.6.2 Wrapper Interfacing: Run-Controllers and Multiple-Runs 560 13.7 Design Process Using EMT Simulation Tools 560 13.7.1 Parameter Selection Techniques 561 13.7.2 Uncertainty Analysis 563 13.8 Conclusions 566 References 566 Annex A: Techniques and Computer Codes for Rational Modelling of Frequency-Dependent Components and Subnetworks 568 Bjørn Gustavsen A. 1 Introduction 568 A. 2 Rational Functions 569 A. 3 Time-Domain Simulation 569 A. 4 Fitting Techniques 569 A.4. 1 Polynomial Fitting 569 A.4. 2 Bode’s Asymptotic Fitting 570 A.4. 3 Vector Fitting 570 A. 5 Passivity 571 A. 6 Matrix Fitting Toolbox 572 A.6. 1 General 572 A.6. 2 Overview 572 A. 7 Example A.1: Electrical Circuit 573 A. 8 Example 6.2: High-Frequency Transformer Modelling 575 A.8. 1 Measurement 575 A.8. 2 Rational Approximation 575 A.8. 3 Passivity Enforcement 575 A.8. 4 Time-Domain Simulation 576 A.8. 5 Comparison with Time-Domain Measurement 577 References 579 Annex B: Dynamic System Equivalents 581 Udaya D. Annakkage B. 1 Introduction 581 B. 2 High-Frequency Equivalents 582 B.2. 1 Introduction 582 B. 2 Frequency-Dependent Network Equivalent (FDNE) 582 B.2. 3 Examples of High-Frequency FDNE 583 B.2. 4 Two-Layer Network Equivalent (TLNE) 586 B.2. 5 Modified Two-Layer Network Equivalent 592 B.2. 6 Other Methods 594 B.2. 7 Numerical Issues 594 B. 3 Low-Frequency Equivalents 595 B.3. 1 Introduction 595 B.3. 2 Modal Methods 596 B. 3 Coherency Methods 596 B.3. 4 Measurement or Simulation-Based Methods 597 B. 4 Wideband Equivalents 597 B. 5 Conclusions 597 References 598 Index 601