Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/3/1126 |
| _version_ | 1797488009332916224 |
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| author | Andriy Chaban Marek Lis Andrzej Szafraniec Vitaliy Levoniuk |
| author_facet | Andriy Chaban Marek Lis Andrzej Szafraniec Vitaliy Levoniuk |
| author_sort | Andriy Chaban |
| collection | DOAJ |
| description | 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%. |
| first_indexed | 2024-03-09T23:56:00Z |
| format | Article |
| id | doaj.art-ea43cc2322284ccca203a832ca5f1cf6 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T23:56:00Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-ea43cc2322284ccca203a832ca5f1cf62023-11-23T16:25:36ZengMDPI AGEnergies1996-10732022-02-01153112610.3390/en15031126Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-CircuitAndriy Chaban0Marek Lis1Andrzej Szafraniec2Vitaliy Levoniuk3Faculty of Transport, Electrical Engineering, and Computer Science, University of Technology and Humanities, 26-600 Radom, PolandFaculty of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, PolandFaculty of Transport, Electrical Engineering, and Computer Science, University of Technology and Humanities, 26-600 Radom, PolandDepartment of Electrical Systems, Lviv National Agrarian University, 80381 Dubliany, UkraineField 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%.https://www.mdpi.com/1996-1073/15/3/1126mathematical modellinglong line equationthree-phase power gridelectric networkdistributed parameterstransient electromagnetic processes |
| spellingShingle | Andriy Chaban Marek Lis Andrzej Szafraniec Vitaliy Levoniuk Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit Energies mathematical modelling long line equation three-phase power grid electric network distributed parameters transient electromagnetic processes |
| title | Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit |
| title_full | Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit |
| title_fullStr | Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit |
| title_full_unstemmed | Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit |
| title_short | Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit |
| title_sort | mathematical modelling of transient processes in a three phase electric power system for a single phase short circuit |
| topic | mathematical modelling long line equation three-phase power grid electric network distributed parameters transient electromagnetic processes |
| url | https://www.mdpi.com/1996-1073/15/3/1126 |
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