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.
Highlights
A system of two or more wires of circular cross section is very often used in power and signal transmission lines
In a three phase cable line, there are three round wires arranged into a three-core cable or three single-core cables in the trefoil or flat formation [1]
Eddy currents are induced by a magnetic field generated by the current in the wire itself, as well as by the neighboring alternating phase currents
Summary
A system of two or more wires of circular cross section (cylindrical wires, briefly called round wires) is very often used in power and signal transmission lines. In a three phase cable line, there are three round wires arranged into a three-core cable or three single-core cables in the trefoil or flat formation [1]. Eddy currents are induced by a magnetic field generated by the current in the wire itself (skin effect), as well as by the neighboring alternating phase currents (proximity effect). These currents add to the applied currents. The total current densities in conductors become non-uniform and non-symmetrical, and significantly affect the electromagnetic field, power losses in the wires, and the impedance matrix of such a system of conductors [2,3,4,5]. The knowledge on the current density distribution is essential in determining the network properties of such lines
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