Mathematical Modelling of Transient Processes in a Section of an Electricity Network with Varying Configurations of its Components

Abstract

This article presents mathematical models of power grid segments. Three load configurations representing real power systems were analysed. The mathematical models were developed using a field-circuit approach. A long line element was considered as a system with distributed parameters. A second-order partial differential equation was used to describe the line. The spatial derivative was discretised using the method of lines. Boundary conditions for the line equation were sought on the basis of circuit approaches. First-order boundary conditions were used. The resulting systems of differential equations were integrated using the implicit Euler method. Using the developed mathematical models, simulations of the behaviour of the systems were carried out. Transient processes during voltage switching were analysed. The results are presented in the form of waveforms of current and voltage at various points on the line. Spatial waveforms of the voltage and current in the line were also prepared.