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

Andriy Chaban, Marek Lis, Andrzej Szafraniec and Vitaliy Levoniuk
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Andriy Chaban: Faculty of Transport, Electrical Engineering, and Computer Science, University of Technology and Humanities, 26-600 Radom, Poland
Marek Lis: Faculty of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland
Andrzej Szafraniec: Faculty of Transport, Electrical Engineering, and Computer Science, University of Technology and Humanities, 26-600 Radom, Poland
Vitaliy Levoniuk: Department of Electrical Systems, Lviv National Agrarian University, 80381 Dubliany, Ukraine

Energies, 2022, vol. 15, issue 3, 1-16

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%.

Keywords: mathematical modelling; long line equation; three-phase power grid; electric network; distributed parameters; transient electromagnetic processes (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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