Power Systems Electromagnetic Transients Simulation

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
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