International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Shornikov Y.V.   Dostovalov D.N.   Nasyrova M.S.  

Specification and analysis of transients in electrical power systems using the methodology of hybrid systems

Reporter: Shornikov Y.V.

This paper discusses discrete-continuous (hybrid) systems [1, 2] and corresponding simulation tools. Hybrid system (HS) is characterized by set of instantly changing continuous modes. In this case, the use of analytical methods is often impossible and computer experiment becomes the only universal way of studying the event-continuous behavior. Typically regime change caused by one-sided events when the phase trajectory of the system is discontinuous when the event occurred. Modern computer simulation tools (MATLAB/Stateflow, Rand Model Designer, AnyLogic, etc.) support HS class, but not take into account the one-sided events [2, 3]. Therefore, the development of original tools for computer research of HS is an important task.
Modern HS formalism can be effectively used by application specialists in problem-oriented environments of computer analysis. One of the many HS applications is the study of transients in electrical power systems (EPS). The electromagnetic and electromechanical processes in electrical machines are of particular importance. They are simulated to determine the synchronism of the power station units, evaluate the reliability and stability of EPS.
To solve this problem a special module was developed in ISMA simulation environment. Fig. 1 is a schematic diagram of six-machine power system [4] specified in ISMA by designed LISMA_EPS language. Park-Gorev’s ordinary differential equations are used for the research of transient processes. Discrete behavior of EPS associated with nonlinear characteristics of generator speed regulators. Also, the EPS operating mode can be changed upon the occurrence of certain events: switching, short circuit, breakage of power lines, etc. Therefore HS methodology is adequate for description and study of transient processes in EPS.
The central object of study in ISMA is a hybrid model obtained by interpretation of graphical programming model (Fig. 1). The solver of simulation environment uses the library of classical and original numerical methods intended for solving systems of differential-algebraic equations with discontinuities. The original algorithm of correct event detection was developed for processing gaps, which is an integral part of numerical analysis. The correctness of the algorithm is theoretically proved in [2]. The efficiency of the proposed methodology is in general constructively proved on a set of test problems.

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