Power Systems Electromagnetic Transients Simulation (2nd Edition)
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 rootmatching method; transmission lines and cables; transformers and rotating plant; control and protection; power electronic systems; frequencydependent network equivalents; steadystate assessment; mixed timeframe simulation; transient simulation in realtime; and applications.
Inspec keywords: power system simulation; power system transients; electromagnetic interference
Other keywords: matrix analysis; power systems electromagnetic transients simulation; EMT programs; numerical techniques; power system theory
Subjects: Education and training; Electromagnetic compatibility and interference; Power systems; General electrical engineering topics
 Book DOI: 10.1049/PBPO123E
 Chapter DOI: 10.1049/PBPO123E
 ISBN: 9781785614996
 eISBN: 9781785615009
 Page count: 527
 Format: PDF

Front Matter
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1 Definitions objectives and background
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The operation of an electrical power system involves continuous electromechanical and electromagnetic distribution of energy among the system components. During normal operation, under constant load and topology, these energy exchanges are not modelled explicitly and the system behaviour can be represented by voltage and current phasors in the frequencydomain. However, following switching events and system disturbances the energy exchanges subject the circuit components to higher stresses, resulting from excessive currents or voltage variations, the prediction of which is the main objective of power system transient simulation.

2 Analysis of continuous and discrete systems
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Linear algebra and circuit theory concepts are used in this book chapter to describe the formulation of the state equations of linear dynamic systems. The Laplace transform, commonly used in the solution of simple circuits, is impractical in the context of a large power system. Some practical alternatives discussed here are Modal Analysis, Numerical Integration of the differential equations and the use of Difference Equations. An electrical power system is basically a continuous system, with the exceptions of a few auxiliary components, such as the digital controllers. Digital simulation, on the other hand, is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time.

3 State variable analysis
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State variables are the parameters of a system that define completely its energy storage state. State Variable analysis was the dominant technique in transient simulation prior to the appearance of the Numerical Integration Substitution method. The application of Kron's tensor techniques led to an elegant and efficient method for the solution of systems with periodically varying topology, such as an ac/dc converter. Its main advantages are more general applicability and a logical procedure for the automatic assembly and solution of the network equations. Thus, the programmer no longer needs to be aware of all the sets of equations describing each particular topology. The use of diakoptics, as proposed by Kron, reduces considerably the computational burden but is subject to some restrictions on the types of circuit topology that can be analysed. Those restrictions, the techniques used to overcome them and the computer implementation of the state variable method are considered in this book chapter.

4 Numerical integrator substitution
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Numerical Integration Substitution (NIS) constitutes the basis of Dommel's EMTP, which is now the most generally accepted method for the solution of electromagnetic transients. This book chapter describes the basic formulation and solution of the numerical integrator substitution method as implemented in the electromagnetic transient programmes.

5 The rootmatching method
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The purpose of the rootmatching method is to transfer correctly the poles and zeros from the splane to the zplane, an important requirement for reliable digital simulation, to ensure that the difference equation is suitable to simulate the continuous process correctly. This book chapter describes the use of rootmatching techniques in the Electromagnetic Transient Simulation and compares its performance with that of the conventional Numerical Integrator Substitution method described in a previous chapter.

6 Transmission lines and cables
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The book chapter considers transmission lines and cables focusing specifically on: Bergeron's model; frequencydependent transmission lines; overhead transmission line parameters and underground cable parameters. For all except very short transmission lines travelling wave transmission line models are preferable. If frequency dependence is important, then a frequency transmission line dependent model will be used. Details of transmission line geometry and conductor data are then required in order to calculate accurately the frequencydependent electrical parameters of the line. The simulation timestep must be based on the shortest response time of the line.

7 Transformers and rotating plant
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The basic theory of the single phase transformer has been described, including the derivation of parameters, the modelling of magnetisation nonlinearities and its numerical implementation in a form acceptable for electromagnetic transients programs. The need for advanced models has been justified, and a detailed description made of UMEC (the Unified Magnetic Equivalent Circuit), a general transformer model developed for the accurate representation of multiphase, multiwinding arrangements. UMEC is a standard transformer model in the latest version of PSCAD/EMTDC. The rotating machine modelling based on Park's transformation is reasonably standard, the different implementations relating to the way of interfacing the machine to the system. A state variable formulation of the equations is used but the solution, in line with EMTP philosophy, is carried out by numerical integrator substitution. The great variety of rotating machines in existence precludes the use of a common model and so the electromagnetic transient programs include models for the main types in current use, most of these based on general machine theory.

8 Control and protection
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As well as accurate modelling of the power components, effective transient simulation requires detailed representation of their control and protection processes. A variety of network signals need to be generated as inputs to the control system, such as active and reactive powers, RMS voltages and currents, phase angles, harmonic frequencies, etc. The output of the control functions are then used to control voltage and current sources as well as provide switching signals and firing pulses to the power electronic devices. These signals can also be used to dynamically control the values of resistors, inductors and capacitors. A concise description of the control functions attached to the state variable solution has been made in a previous chapter. The purpose of this book chapter is to discuss the implementation of control and protection systems in the EMT programs.

9 Power electronic systems
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The incorporation of power electronics in EMT simulation is discussed in this book chapter with reference to the EMTDC version but appropriate references are made, as required, to other EMTP based algorithms. This is partly due to the fact that the EMTDC program was specifically developed for the simulation of HVDC transmission and partly to the authors involvement in the development of some of its recent components. This chapter also describes the state variable implementation of ac/dc converters and systems, which offers some advantages over the EMTP solution, as well as a hybrid algorithm involving both the state variable and EMTP methods.

10 Frequencydependent network equivalents
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Although the emphasis of this book chapter is on frequencydependent network equivalents, the same identification techniques are applicable to the models of individual components. For example, a frequencydependent transmission line (or cable) equivalent can be obtained by fitting an appropriate model to the frequency response of its characteristic admittance and propagation constant.

11 Steadystate assessment
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An important part of power quality is steadystate (and quasisteadystate) waveform distortion. The resulting information is sometimes presented in the timedomain (e.g. notching) and more often in the frequencydomain (e.g. harmonics and interharmonics). Randomly varying nonlinear loads, such as arc furnaces, as well as substantial and varying harmonic (and interharmonic) content, cause voltage fluctuations that often produce flicker. The random nature of the load impedance variation with time prevents an accurate prediction of the phenomena. However, the EMTP method can still help in the selection of compensating techniques, with arc models based on the experience of existing installations. Another application of the EMTP method for steadystate assessment is its use in developing accurate harmonically coupled models for other modelling frameworks, such as the harmonic domain. This is desirable as frequencydomain techniques are more amendable for simulating very large power systems.

12 Mixed timeframe simulation
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This chapter discusses the principles of mixed timeframe simulation with reference to a power system with LCCbased HVDC transmission system as part of it. This approach has been extended and used for other cases, such as to multiterminal VSCbased HVDC. The smart grid initiative involves intertwining the electrical power network with sensors and communication infrastructure so as to control the system in a smarter way. The increasing interdependency of the electrical power system on signals and communication infrastructure greatly complicates the dynamic response and increases the need for cosimulation techniques. Moreover, the need to test equipment prior putting in service requires applying realtime simulation techniques to cosimulation.

13 Transient simulation in realtime
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Advances in digital parallel processing, combined with the ability of power systems to be processed by means of subsystems, provides the basis for realtime transient simulation. Simulation in realtime permits realistic testing of the behaviour of control and protection systems. This requires the addition of digitaltoanalogue and analoguetodigital converters, as well as analogue signal amplifiers. The original, and at present still the dominant product on the market for the simulation of electrical power systems, is a simulator based on dedicated architecture called RTDS (RealTime Digital Simulator). This unit practically replaced all the scaledown physical simulators and can potentially represent any size system. The development of multipurpose parallel computing is now providing the basis for realtime simulation using standard computers instead of dedicated architectures and should eventually provide a more economical solution.

14 Applications
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The advances in semiconductor technology has led to the development of power electronic based solutions for many applications. Their higher efficiency, increased controllability and smaller footprint has resulted in their rapid deployment. The behaviour of such equipment often can only be adequately modelled using detailed EMT studies. The time constants and switching frequency of such equipment limits the maximum timestep that can be used. The computational burden and complexity means that when many items of equipment (such as WTGs) must be considered they are represented by multiplying the characteristics of one modelled in detail. A few key applications have been presented to illustrate the use of EMT simulation, as well as some typical dynamic responses. Many of the building blocks for the smart grid initiative, such as ac/dc, dc/dc and dc/ac converters have been illustrated. The role of EMT simulation will only increase as the network becomes more complex. The challenge is to model a largescale power system using EMT simulation. This will mean cosimulation and hybrid (time/frequencydomain) techniques will come to the fore as DRTSs are still too expensive to be a general tool for all.

Appendix A: System identification techniques
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This appendix chapter from the book Power Systems Electromagnetic Transients Simulation covers: sDomain identification (frequencydomain); zDomain identification (frequencydomain); zDomain identification (timedomain); Prony analysis and Recursive leastsquares curvefitting algorithm.

Appendix B: Numerical integration
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This appendix chapter from the book Power Systems Electromagnetic Transients Simulation covers: Review of classical methods; Truncation error of integration formulae and Stability of integration methods.

Appendix C: Test systems data
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The book chapter appendix for Power Systems Electromagnetic Transients Simulation covers the CIGRE HVDC benchmark model and Lower South Island (New Zealand) system.

Appendix D: Developing difference equations
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The book chapter appendix presents information on difference equations. it covers: Rootmatching technique applied to a firstorder lag function; Rootmatching technique applied to a firstorder differential pole function; Difference equation by bilinear transformation for RL series branch; Difference equation by numerical integrator substitution and Equivalence of trapezoidal rule and bilinear transform.

Appendix E: MATLAB® code examples
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This appendix chapter in the book Power Systems Electromagnetic Transients Simulation covers Voltage step on RL branch; Diodefed RL branch and Frequency response of difference equations.

Back Matter
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