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 frequency domain. However, following switching events and system disturbances the energy exchanges subject the circuit components to higher stresses, resulting from exces sive currents or voltage variations, the prediction of which is the main objective of power system transient simulation.

In the state variable solution it is the set of first order differential equations, rather than the system of individual elements, that is solved by numerical integration. The most popular numerical technique in current use is implicit trapezoidal integration, due to its simplicity, accuracy and stability. Solution accuracy is enhanced by the use of iterative methods to calculate the state variables. State variable is an ideal method for the solution of system components with time-varying non-linearities, and particularly for power electronic devices involv ing frequent switching. This has been demonstrated with reference to the static a.c.-d.c. converter by an algorithm referred to as TCS (Transient Converter Simu lation). Frequent switching, in the state variable approach, imposes no overhead on the solution. Moreover, the use of automatic step length adjustment permits optimising the integration step throughout the solution.

An alternative to the difference equation using the trapezoidal integration developed in Chapter 4 for the solution of the differential equations has been described in this chapter. It involves the exponential form of the difference equation and has been developed using the root-matching technique. The exponential form offers the following advantages: 1) Eliminates truncation errors, and hence numerical oscillations, regardless of the step length used. 2) Can be applied to both electrical networks and control blocks. 3) Can be viewed as a Norton equivalent in exactly the same way as the difference equation developed by the numerical integration substitution (NIS) method. 4) It is perfectly compatible with NIS and the matrix solution technique remains unchanged. 5) Provides highly efficient and accurate time domain simulation. The exponential form can be implemented for all series and parallel RL, RC, LC and RLC combinations, but not arbitrary components and hence is not a replacement for NIS but a supplement.

The basic theory of the single-phase transformer has been described, including the derivation of parameters, the modelling of magnetisation non-linearities 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. Rotating machine modelling based on Park's transformation is reasonably stan dard, 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 computer implementation of power electronic devices in electromagnetic transient programs has taken much of the development effort in recent years, aiming at preserving the elegance and efficiency of the EMTP algorithm. The main feature that characterises power electronic devices is the use of frequent periodic switching of the power components under their control. The incorporation of power electronics in EMT simulation is discussed in this 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. A concise description of the PSCAD/EMTDC program structure is given in Appendix A. This chapter also describes the state variable implementation of a.c.-d.c. 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.

Modelling of voltage sags and voltage interruptions requires accurate representation of the dynamic characteristics of the main system components, particularly the synchronous generators and induction motors, power electronic equipment and their protection and control. The EMT programs meet all these requirements adequately and can thus be used with confidence in the simulation of sag characteristics, their effects and the role of sag compensation devices. Subject to the unpredictability of the arc furnace characteristics, EMT simulation with either deterministic or stochastic models of the arc behaviour can be used to investigate possible mitigation techniques. Flicker penetration can also be predicted with these programs, although the derivation of the IEC short and long-term flicker indices is currently computationally prohibitive. However, real-time digital simulators should make this task easier.

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

System identification techniques used in Power Systems Electromagnetic Transients Simulation.

The CIGRE benchmark model consists of weak rectifier and inverter a.c. systems resonant at the second harmonic and a d.c. system resonant at the fundamental frequency. Both a.c. systems are balanced and connected in star-ground. The HVDC link is a 12-pulse monopolar configuration with the converter transformers connected star-ground/star and star-ground/delta. Impedance scans of the a.c. and d.c. systems. A phase imbalance is created in the inverter a.c. system by inserting typically a 5.0 per cent resistance into one phase in series with the a.c. system.

The section shows MATLAB code examples for Power Systems Electromagnetic Transients Simulation.

This sections shows the use of FORTRAN code for EMT simulation.