Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires
Power and communication lines with round wires are often used in electrical engineering. The skin and proximity effects affect the current density distribution and increase resistances and energy losses. Many approaches were proposed to calculate the effects and related quantities. One of the simple...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/13/24/6716 |
| _version_ | 1827699698894372864 |
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| author | Paweł Jabłoński Dariusz Kusiak Tomasz Szczegielniak |
| author_facet | Paweł Jabłoński Dariusz Kusiak Tomasz Szczegielniak |
| author_sort | Paweł Jabłoński |
| collection | DOAJ |
| description | Power and communication lines with round wires are often used in electrical engineering. The skin and proximity effects affect the current density distribution and increase resistances and energy losses. Many approaches were proposed to calculate the effects and related quantities. One of the simplest approximate closed solutions neglects the dimensions of neighboring wires. In this paper, a solution to this problem is proposed based on the method of successive reactions. In this context, the solution with substitutive filaments is considered as the first approximation of the true solution. Several typical arrangements of wires in single-phase communication lines or three-phase bus ducts are considered to detect the limits of applicability of the first approximation. The error of the first approximation grows with wire radius to skin depth ratio and wire radius to wire spacing ratio. When the wire radius to skin depth ratio is up to 1, and the gap between the wires is above the wire radius, the error is at a level of 1%. However, lowering the distance and/or skin depth leads to a much larger error in the first approximation. |
| first_indexed | 2024-03-10T13:55:14Z |
| format | Article |
| id | doaj.art-78146c2b1025480b90e6ea803b62d0bb |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T13:55:14Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-78146c2b1025480b90e6ea803b62d0bb2023-11-21T01:41:39ZengMDPI AGEnergies1996-10732020-12-011324671610.3390/en13246716Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel WiresPaweł Jabłoński0Dariusz Kusiak1Tomasz Szczegielniak2Department of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, PolandDepartment of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, PolandDepartment of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, PolandPower and communication lines with round wires are often used in electrical engineering. The skin and proximity effects affect the current density distribution and increase resistances and energy losses. Many approaches were proposed to calculate the effects and related quantities. One of the simplest approximate closed solutions neglects the dimensions of neighboring wires. In this paper, a solution to this problem is proposed based on the method of successive reactions. In this context, the solution with substitutive filaments is considered as the first approximation of the true solution. Several typical arrangements of wires in single-phase communication lines or three-phase bus ducts are considered to detect the limits of applicability of the first approximation. The error of the first approximation grows with wire radius to skin depth ratio and wire radius to wire spacing ratio. When the wire radius to skin depth ratio is up to 1, and the gap between the wires is above the wire radius, the error is at a level of 1%. However, lowering the distance and/or skin depth leads to a much larger error in the first approximation.https://www.mdpi.com/1996-1073/13/24/6716multi-wire bus ductskin effectproximity effectcylindrical conductorscurrent filamentcurrent density |
| spellingShingle | Paweł Jabłoński Dariusz Kusiak Tomasz Szczegielniak Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires Energies multi-wire bus duct skin effect proximity effect cylindrical conductors current filament current density |
| title | Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires |
| title_full | Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires |
| title_fullStr | Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires |
| title_full_unstemmed | Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires |
| title_short | Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires |
| title_sort | analytical numerical approach to the skin and proximity effect in lines with round parallel wires |
| topic | multi-wire bus duct skin effect proximity effect cylindrical conductors current filament current density |
| url | https://www.mdpi.com/1996-1073/13/24/6716 |
| work_keys_str_mv | AT pawełjabłonski analyticalnumericalapproachtotheskinandproximityeffectinlineswithroundparallelwires AT dariuszkusiak analyticalnumericalapproachtotheskinandproximityeffectinlineswithroundparallelwires AT tomaszszczegielniak analyticalnumericalapproachtotheskinandproximityeffectinlineswithroundparallelwires |