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Analytical–Numerical Solution for the Skin and Proximity Effects in Two Parallel Round Conductors

Author

Listed:
  • Paweł Jabłoński

    (Institute of Optoelectronics and Measurement Systems, Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, Poland)

  • Tomasz Szczegielniak

    (Institute of Environmental Engineering, Faculty of Infrastructure and Environment, Czestochowa University of Technology, Brzeźnicka St. 60a, 42-200 Częstochowa, Poland)

  • Dariusz Kusiak

    (Institute of Optoelectronics and Measurement Systems, Faculty of Electrical Engineering, Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, Poland)

  • Zygmunt Piątek

    (Institute of Environmental Engineering, Faculty of Infrastructure and Environment, Czestochowa University of Technology, Brzeźnicka St. 60a, 42-200 Częstochowa, Poland)

Abstract

This paper describes an analytical-numerical method for the skin and proximity effects in a system of two parallel conductors of circular cross section—a system very frequently encountered in various applications. The magnetic field generated by the current applied on each conductor is expressed by means of vector magnetic potential and expanded into Fourier series. Using the Laplace and Helmholtz equations, as well as the classical boundary conditions, the current density induced due to the proximity and skin effect is determined in each conductor. The resulting current density is expressed as a series of successive reactions. The results obtained are compared with those obtained via finite elements. Although the paper is theoretical, the considered problem has a practical significance, because transmission lines with round conductors are universally used. Besides, the results can be used to estimate errors when only the first reaction is taken into account, which gives relatively simple formulas.

Suggested Citation

  • Paweł Jabłoński & Tomasz Szczegielniak & Dariusz Kusiak & Zygmunt Piątek, 2019. "Analytical–Numerical Solution for the Skin and Proximity Effects in Two Parallel Round Conductors," Energies, MDPI, vol. 12(18), pages 1-19, September.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:18:p:3584-:d:268810
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    Citations

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    Cited by:

    1. Artur Cywiński & Krzysztof Chwastek, 2021. "A Multiphysics Analysis of Coupled Electromagnetic-Thermal Phenomena in Cable Lines," Energies, MDPI, vol. 14(7), pages 1-20, April.
    2. Paweł Jabłoński & Dariusz Kusiak & Tomasz Szczegielniak & Zygmunt Piątek, 2020. "The Proximity Effect in Twin Line with Round Conductors Placed in Conductive Medium," Energies, MDPI, vol. 13(22), pages 1-23, November.
    3. Marek Zaręba & Tomasz Szczegielniak & Paweł Jabłoński, 2023. "Influence of the Skin and Proximity Effects on the Thermal Field in a System of Two Parallel Round Conductors," Energies, MDPI, vol. 16(17), pages 1-20, September.
    4. Paweł Jabłoński & Dariusz Kusiak & Tomasz Szczegielniak, 2020. "Analytical-Numerical Approach to the Skin and Proximity Effect in Lines with Round Parallel Wires," Energies, MDPI, vol. 13(24), pages 1-21, December.
    5. Artur Cywiński & Krzysztof Chwastek & Dariusz Kusiak & Paweł Jabłoński, 2020. "Optimization of Spatial Configuration of Multistrand Cable Lines," Energies, MDPI, vol. 13(22), pages 1-22, November.
    6. Bartosz Rozegnał & Paweł Albrechtowicz & Dominik Mamcarz & Monika Rerak & Maciej Skaza, 2021. "The Power Losses in Cable Lines Supplying Nonlinear Loads," Energies, MDPI, vol. 14(5), pages 1-15, March.

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