Transient Analysis of Power Systems

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.

Autorentext

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.

Inhalt

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.GutiérrezRobles 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</p...