POWER SYSTEMS ELECTROMAGNETIC TRANSIENTS SIMULATION : power quality with renewable energy ... and electric vehicle integration

Accurate knowledge of electromagnetic power system transients is crucial to the operation of an economic, efficient and environmentally friendly power systems network without compromising on the reliability and quality of electrical power supply. Electromagnetic transient (EMT) simulation has therefore become a universal tool for the analysis of power system electromagnetic transients in the range of nanoseconds to seconds, and is the backbone for the design and planning of power systems, as well as for the investigation of problems. In this fully revised and updated new edition of this classic book, a thorough review of EMT simulation is provided, with many simple examples included to clarify difficult concepts. Topics covered include analysis of continuous and discrete systems; state variable analysis; numerical integrator substitution; the root-matching method; transmission lines and cables; transformers and rotating plant; control and protection; power electronic systems; frequency-dependent network equivalents; steady-state assessment; mixed time-frame simulation; transient simulation in real-time; and applications. Cover Contents List of figures List of tables Preface Acronyms 1 Definitions objectives and background 1.1 Introduction 1.2 Classification of electromagnetic transients 1.3 Transient simulators 1.4 Digital simulation 1.4.1 State variable analysis 1.4.2 Method of difference equations 1.5 Historical perspective 1.6 Range of applications References 2 Analysis of continuous and discrete systems 2.1 Introduction 2.2 Continuous systems 2.2.1 State variable formulations 2.2.1.1 Successive differentiation 2.2.1.2 Controller canonical form 2.2.1.3 Observer canonical form 2.2.1.4 Diagonal canonical form 2.2.1.5 Uniqueness of formulation 2.2.1.6 Example 2.2.2 Time-domain solution of state equations 2.2.3 Digital simulation of continuous systems 2.2.3.1 Example 2.3 Discrete systems 2.4 Relationship of continuous and discrete domains 2.5 Summary References 3 State variable analysis 3.1 Introduction 3.2 Choice of state variables 3.3 Formation of the state equations 3.3.1 The transform method 3.3.2 The graph method 3.4 Solution procedure 3.5 Transient converter simulation 3.5.1 Per unit system 3.5.2 Network equations 3.5.3 Structure of TCS 3.5.4 Valve switchings 3.5.5 Effect of automatic time-step adjustments 3.5.6 TCS converter control 3.6 Example 3.7 Summary References 4 Numerical integrator substitution 4.1 Introduction 4.2 Discretisation of R,L,C elements 4.2.1 Resistance 4.2.2 Inductance 4.2.3 Capacitance 4.2.4 Components reduction 4.3 Dual Norton model of the transmission line 4.4 Network solution 4.4.1 Example: conversion of voltage sources to current sources 4.4.2 Network solution with switches 4.4.3 Example: voltage step applied to RL load 4.5 Non-linear or time varying parameters 4.5.1 Current-source representation 4.5.2 Compensation method 4.5.3 Piecewise linear method 4.6 Subsystems 4.7 Sparsity and optimal ordering 4.8 Numerical errors and instabilities 4.9 Summary References 5 The root-matching method 5.1 Introduction 5.2 Exponential form of the difference equation 5.3 z-Domain representation of difference equations 5.4 Implementation in EMTP algorithm 5.5 Family of exponential forms of the difference equation 5.5.1 Step response 5.5.2 Steady-state response 5.5.3 Frequency response 5.6 Example 5.7 Summary References 6 Transmission lines and cables 6.1 Introduction 6.2 Bergeron's model 6.2.1 Multi-conductor transmission lines 6.3 Frequency-dependent transmission lines 6.3.1 Frequency to time-domain transformation 6.3.2 Phase domain model 6.4 Overhead transmission line parameters 6.4.1 Bundled sub-conductors 6.4.2 Earth wires 6.5 Underground cable parameters 6.6 Example 6.7 Summary References 7 Transformers and rotating plant 7.1 Introduction 7.2 Basic transformer model 7.2.1 Numerical implementation 7.2.2 Parameters derivation 7.2.3 Modelling of non-linearities 7.3 Advanced transformer models 7.3.1 Single-phase UMEC model 7.3.1.1 UMEC Norton equivalent 7.3.2 UMEC implementation in PSCAD/EMTDC 7.3.3 Three-limb three-phase UMEC 7.3.4 Fast transient models 7.4 The synchronous machine 7.4.1 Electromagnetic model 7.4.2 Electro-mechanical model 7.4.2.1 Per unit system 7.4.2.2 Multi-mass representation 7.4.3 Interfacing machine to network 7.4.4 Types of rotating machine available 7.5 Summary References 8 Control and protection 8.1 Introduction 8.2 Transient analysis of control systems 8.3 Control modelling in PSCAD/EMTDC 8.3.1 Example 8.3.1.1 Time-step delay in data path 8.3.1.2 No time-step delay in data path 8.3.1.3 Root-matching technique 8.3.1.4 Numerical illustration 8.4 Modelling of protective systems 8.4.1 Transducers 8.4.1.1 CT modelling 8.4.1.2 CVT modelling 8.4.1.3 VT modelling 8.4.2 Electromechanical relays 8.4.3 Electronic relays 8.4.4 Microprocessor-based relays 8.4.5 Circuit breakers 8.4.6 Surge arresters 8.5 Summary References 9 Power electronic systems 9.1 Introduction 9.2 Valve representation in EMTDC 9.3 Placement and location of switching instants 9.4 Spikes and numerical oscillations (chatter) 9.4.1 Interpolation and chatter removal 9.5 HVDC converters 9.6 Example of HVDC simulation 9.7 FACTS devices 9.7.1 The static VAr compensator 9.7.2 The static compensator (STATCOM) 9.8 State variable models 9.8.1 EMTDC/TCS interface implementation 9.8.2 Control system representation 9.9 Summary References 10 Frequency-dependent network equivalents 10.1 Introduction 10.2 Position of FDNE 10.3 Extent of system to be reduced 10.4 Frequency range 10.5 System frequency response 10.5.1 Frequency-domain identification 10.5.1.1 Time-domain analysis 10.5.1.2 Frequency-domain analysis 10.5.2 Time-domain identification 10.6 Fitting of model parameters 10.6.1 RLC networks 10.6.2 Rational function 10.6.2.1 Error and figure of merit 10.7 Vector fitting 10.8 Model implementation 10.9 Examples 10.10 Summary References 11 Steady-state assessment 11.1 Introduction 11.2 Phase-dependent impedance of non-linear device 11.3 The time-domain in an ancillary capacity 11.3.1 Iterative solution for time invariant non- linear components 11.3.2 Iterative solution for general non-linear components 11.3.3 Acceleration techniques 11.4 The time-domain in the primary role 11.4.1 Harmonic assessment historically 11.4.2 Basic time-domain algorithm 11.4.3 Time-step 11.4.4 dc System representation 11.4.5 ac System representation 11.5 Discussion References 12 Mixed time-frame simulation 12.1 Introduction 12.2 Description of the hybrid algorithm 12.2.1 Individual program modifications 12.2.2 Data flow 12.3 TS/EMTDC interface 12.3.1 Equivalent impedances 12.3.2 Equivalent sources 12.3.3 Phase and sequence data conversions 12.3.4 Interface variables derivation 12.4 EMTDC to TS data transfer 12.4.1 Data extraction from converter waveforms 12.5 Interaction protocol 12.6 Interface location 12.7 Test system and results 12.8 Discussion References 13 Transient simulation in real-time 13.1 Introduction 13.2 Simulation with dedicated architectures 13.2.1 Hardware 13.2.1.1 Inter-rack communication (IRC) 13.2.1.2 Workstation interface (WIF) communication 13.2.1.3 Global Bus Hub (GBH) 13.2.1.4 GT ports 13.2.2 RTDS applications 13.2.2.1 Protective relay testing 13.2.2.2 Control system testing 13.3 Real-time and near real-time on standard computers 13.3.1 Example of real-time test 13.4 Summary References 14 Applications 14.1 Introduction 14.1.1 Modelling considerations 14.1.2 Time-step and plot-step 14.1.3 Avoiding singularities 14.1.4 Initialisation 14.2 Lightning studies 14.2.1 EMT modelling 14.2.2 Back-flashover modelling 14.2.3 Surge arrester modelling 14.2.4 Direct lightning strike to phase conductor 14.2.5 Lightning strike to ground wire or tower 14.3 Capacitor switching studies 14.3.1 Inrush 14.3.2 Back-to-back switching 14.3.3 Voltage magnification 14.4 Transformer energisation 14.4.1 Parallel sympathetic interaction 14.4.2 Other issues 14.4.3 Mitigation 14.4.4 Modelling 14.5 Transient recovery voltage studies 14.6 Voltage dips/sags 14.6.1 Examples 14.7 Voltage fluctuations 14.7.1 Modelling of flicker penetration 14.8 Voltage notching 14.9 Wind power 14.9.1 Type 3 WTG 14.9.2 Type 4 WTG 14.10 Solar photovoltaic farm 14.11 HVDC 14.11.1 HVDC using LCC 14.11.2 HVDC using VSC 14.12 Ferroresonance 14.13 Electric vehicle charging 14.14 Heat-pumps/air-conditioners 14.15 Battery storage 14.16 Summary References Appendix A: System identification techniques A.1 s-Domain identification (frequency-domain) A.2 z-Domain identification (frequency-domain) A.3 z-Domain identification (time-domain) A.4 Prony analysis A.5 Recursive least-squares curve-fitting algorithm References Appendix B: Numerical integration B.1 Review of classical methods B.2 Truncation error of integration formulae B.3 Stability of integration methods References Appendix C: Test systems data C.1 CIGRE HVDC benchmark model C.2 Lower South Island (New Zealand) system Appendix D: Developing difference equations D.1 Root-matching technique applied to a first-order lag function D.2 Root-matching technique applied to a first-order differential pole function D.3 Difference equation by bilinear transformation for RL series branch D.4 Difference equation by numerical integrator substitution for RL series branch D.5 Equivalence of trapezoidal rule and bilinear transform Appendix E: MATLAB® code examples E.1 Voltage step on RL branch E.2 Diode-fed RL branch E.3 General version of example E.2 E.4 Frequency response of difference equations Index Back Cover The book studies power systems electromagnetic transients simulation by presenting cohesive technical information to help students and professional engineers to understand the topic better and minimise the effort normally required to become effective users of the EMT programs. Basic knowledge of power system theory, matrix analysis and numerical techniques is presumed, but many references are given to help the readers to fill the gaps in their understanding of the relevant material This new edition of the classic on electromagnetic transient (EMT) simulation gives an up-to-date overview of the area. Thoroughly revised, it covers new topics including: simulation of very large networks; modelling of power electronic devices; integration of renewable energy sources; and real-time simulation of complex systems.