Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit

Andriy Chaban,Marek Lis,Vitaliy Levoniuk,Andrzej Szafraniec

doi:10.3390/en15031126

Abstract

Field approaches are employed to develop a mathematical model of a power network section. The facility consists of two electric power subsystems described with ordinary differential equations and presented as concentrated parameter systems connected with a three-phase power supply line, presented as a distributed parameter system. The model of the electric power line is described with partial differential equations. Mathematically, the supply line model is described utilizing a mixed problem with explicitly indefinite boundary conditions. All electromagnetic state equations of the integrated system are introduced in their matrix-vector forms. The equation of the three-phase long supply line is expressed untraditionally as a system of two first-order differential equations as a function of long line voltage. Since the power supply line is part of the integrated system that includes two subsystems, the boundary conditions at the line’s start and end are implicitly defined, avoiding the traditional application of the Dirichlet first-type boundary condition. An expanded system of ordinary differential equations that describe physical processes in both the supply and loading subsystems is used to calculate the boundary conditions. To this end, third-type boundary conditions, or Poincaré’s conditions, serve to describe the wave equation of the electric power line. Such an integrated model of an electric power system helps analyse transient processes across the supply line when the electric power system is switched on and is single-phase short-circuited at the final point of the electric power line. A comparison of computer simulation results with well-known software packages shows a convergence of approx. 96%.

Highlights

IntroductionAn expanded system of ordinary differential equations that describe physical processes in both the supply and loading subsystems is used to calculate the boundary conditions
Faculty of Transport, Electrical Engineering, and Computer Science, University of Technology and Faculty of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland; Department of Electrical Systems, Lviv National Agrarian University, 80381 Dubliany, Ukraine; Abstract: Field approaches are employed to develop a mathematical model of a power network section
An integrated system of equations of an electric network section was solved by discretising spatial derivatives in the line equation using the straight-line method, including successive integration of equations of the electric power line, supply, and loading subsystems using the 2nd order implicit

Summary

Introduction

An expanded system of ordinary differential equations that describe physical processes in both the supply and loading subsystems is used to calculate the boundary conditions To this end, third-type boundary conditions, or Poincaré’s conditions, serve to describe the wave equation of the electric power line. We propose here a method of finding third-type boundary conditions for the long-line equation in its matrix-vector form This approach helps calculate complex physical processes in an electric power system to a high degree of adequacy, on the one hand, and provides for the use of the line model as an autonomous physical object in complicated electric power systems on the other. An integrated system of equations of an electric network section was solved by discretising spatial derivatives in the line equation using the straight-line method, including successive integration of equations of the electric power line, supply, and loading subsystems using the 2nd order implicit

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Results

Conclusion