A Technique of Calculation of the Dynamic Mode in Computer Simulations of Electric Power Systems with an Arbitrary Configuration

Abstract

The algorithmic implementation of calculations of the dynamic mode during computer simulation of electric power systems with arbitrary topology has been considered. This is more easily done when the electric circuit graph is used in full form (when just one circuit element can be placed at one branch) despite its redundancy. In this case, the graph branches can be connected with the elements of an electric circuit. Mathematical models of elements, which are based on the differential equations in the Park–Gorev axes rotating along with the rotor of a synchronous generator, allow one to eliminate variable coefficients in most differential equations of elements. In the computer simulations, the method of calculations based on the equations for nodal voltages is used. An algorithm to create conductivity and current matrices according to the technique of element-to-element contribution is given. The algorithm to determine an inverse matrix in the equation for nodal voltages is based on the Jordan–Gauss method. To calculate the dynamic mode, it is suggested to use the fourth-order Runge–Kutta method, which allows one to obtain a relatively accurate solution using information at just one previous point. In the view of the development of information technologies, the considered approach allows one both to automated separate stages of design, calculations, and analysis of operation of the electric power system and to take into account the correlation between all the stages of life cycle of the electrotechnical equipment starting with the design stage and ending with equipment decommissioning.