Development of a Mathematical Model of Transitional Processes in the Electrical Network in Phase Coordinates

Abstract

Distribution electrical networks of great length are characterized by a high order of the system of equations of electromagnetic transients. To improve the efficiency of modelling such networks, it is necessary to develop formalized procedures that provide automation of both the solution and the formation of systems of equations using modern computer technology. To simplify the development of mathematical models, transformations are used to move from a real three-phase network to other coordinate systems, but this is achieved at the expense of additional restrictions. To solve the problems of choosing and increasing the efficiency of means for limiting currents and overvoltages during transient processes in electrical networks, it is necessary to have a model reflecting a number of features, both of the networks themselves, and of the transient processes occurring in them. This is implemented in a model based on the representation of network elements not by single-phase equivalents, but by equations in phase coordinates. These equations contain the parameters of the network elements (active resistances, own and mutual inductances and capacitances) and the parameters of its mode (currents, voltages, phase powers), corresponding to the real physical parameters of electrical systems. A mathematical model of electromagnetic transient processes in an electrical network in phase coordinates has been developed. Calculation of the transient process when using the implicit method and representing the three-phase elements at the integration step by discrete models makes it possible to reduce the solution of a system of differential equations to multiple formation and solution of a system of equations. The diakoptic method for studying complex systems was developed, which was used to develop a mathematical model of electromagnetic transient processes in a three-phase electrical network. The proposed form of representation of discrete models of three-phase multipoles allows one to formalize both the solution procedure and the procedure for drawing up equations of transient processes for three-phase circuits of electrical networks of arbitrary configuration. Prospects for further research are computational experiments to study electromagnetic transient processes during ground faults in electrical networks of arbitrary configuration with various neutral modes and means of limiting currents and overvoltages.