Evaluation of the longitudinal parameters of an overhead transmission line with non-homogeneous cross section

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.

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“…Representing the conductors as multiple wires of "small" cross sections and connected in parallel-e.g., [2,4,25,26].…”

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confidence: 99%

“…This paper can be regarded as an extension the mentioned works. The idea is to represent the neighboring wire not with a single filament, but with a set of filaments rather, similarly as in [26]. This makes it possible to take into account the reverse reaction of the induced eddy currents, keeping analytical form of the solution.…”

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confidence: 99%

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

et al. 2019

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“…Piątek et al used a numerical approach based on the integral equation [14]. A similar method was proposed by Coufal [15] or Freitas et al [16]. Besides, the finite elements were often involved [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…Figure16. The effect of frequency and conductivity of the medium: the values of the magnitude of the relative current density in conductor 2 across its diameter (see the leftmost inset) for various R 2 /δ 2 ratios (proportional to f ); traces 1-3 are for same currents, traces 4-6 are for opposing currents; dashed lines are for non-conductive medium, whereas solid lines are for σ m = 1 MS/m; the remaining parameters are given in the middle inset.…”

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confidence: 99%

The Proximity Effect in Twin Line with Round Conductors Placed in Conductive Medium

et al. 2020

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Power lines are often placed in ground or sea water, which are weakly conductive media. In the paper, a new analytical formula, taking into account the proximity effect in a twin line placed in a weakly conductive medium, is derived, and the effect of the conductive medium is considered. In the first step, one of the wires is replaced by a current filament, and the solution is sought for magnetic vector potential around the filament. In the next step, an analytical formula for eddy currents induced in a long straight conductor of circular cross-section placed near to the current filament in the extensive conductive medium is found by using the method of separation of variables. The correctness of the formula is checked by comparison with the results obtained via other methods like finite and boundary element methods. Then, the effect of various parameters on the eddy current distribution is tested. Next, the proximity effect in a twin symmetrical line is considered, and the effect of the conductivity of the surrounding medium is investigated. The results indicate that the conductive medium weakens the proximity effect, but in typical cases (ground and sea water), the effect is very small.

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“…Analytical solutions of the magnetic field and inductance of conductors are only available for the simplest shapes of cross-sections, circular conductors (Morgan, 2013;Smith, 2014) and infinitely wide flat sheets (Berleze and Robert, 2003). For other shapes, such as the rectangular, triangular, or elliptical, only approximate expressions are available (Antonini et al, 1999;De Smedt, 2014;Freitas et al, 2015;Holloway and Kuester, 2009;Holloway et al, 2013;Matsuki and Matsushima, 2012;Morgan, 2013;Tsiboukis and Kriezis, 1983). In this case, different techniques have been proposed in the technical literature for computing the inductance of the conductor, such as direct methods of the functional analysis in Tsiboukis and Kriezis (1983), analytic solutions (Martinez et al, 2014;Högas et al, 2015;Brandao Faria and Raven, 2013), or semi analytical approximations (De Smedt, 2014;Chassart et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Internal inductance of a conductor of rectangular cross-section using the proper generalized decomposition

Pineda-Sánchez

Sapena-Bañó

Pérez-Cruz

et al. 2016

COMPEL

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Purpose-Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for its design and optimization, but no explicit solution for the ac resistance and internal inductances per-unit length of a linear conductor with a rectangular cross section has been found, so numerical methods must be used. This paper introduces the use of a novel numerical technique, the Proper Generalized Decomposition (PGD), for the calculation of dc and ac internal inductances of rectangular conductors. rectangular cross section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the ac inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

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Evaluation of the longitudinal parameters of an overhead transmission line with non-homogeneous cross section

Cited by 12 publications

References 11 publications

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

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

The Proximity Effect in Twin Line with Round Conductors Placed in Conductive Medium

Internal inductance of a conductor of rectangular cross-section using the proper generalized decomposition

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