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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:
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
Juan A. Martinez-Velasco received his Ingeniero Industrial and Doctor Ingeniero Industrial degrees from the Universitat Politècnica de Catalunya (UPC), Spain. He is currently with the Departament d'Enginyeria Elèctrica of the UPC where his teaching and research areas cover Power Systems Analysis, Transmission and Distribution, Power Quality and Electromagnetic Transients. He has authored and co-authored more than 200 journal and conference papers. He is also an active member of several IEEE and CIGRE Working Groups.
