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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