Calculation of the inductance of conductive nonmagnetic conductors by means of finite element method simulations

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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“…Let us consider an even reaction of current density in wire 1, i.e., m = 2l. By recursive applying Equation (19), it follows that…”

Section: Analysis Of the Successive Reactionsmentioning

confidence: 99%

“…Using numerical methods, like finite elements (e.g., [5,18,19]), boundary elements (e.g., [20]), FDTD [21], solving the Fredholm equation with various basis functions (e.g., [22,23]), and others.…”

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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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“…C. Maxwell proposed a method for the calculation of current density in a solitary conductor [15]. Hundreds of works have since been published (more recently, e.g., [1,[16][17][18][19][20][21][22][23][24]) that deal with the calculation of current density in one or two conductors, and exceptionally in more conductors. The calculation of current density in one conductor is accurate, but it can only be applied to the solitary conductor connected to the ideal current source, which, however, cannot be implemented [1].…”

Section: Discussionmentioning

confidence: 99%

Transient Current Density in a Pair of Long Parallel Conductors

Coufal¹

2021

Applied Sciences

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Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

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“…A similar method was proposed by Coufal [15] or Freitas et al [16]. Besides, the finite elements were often involved [17][18][19]. Pagnetti et al [20], and independently Jabłoński et al [21], proposed a numerical-analytical method, generalizing the approach with substitutive current filaments.…”

Section: Introductionmentioning

confidence: 98%

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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Calculation of the inductance of conductive nonmagnetic conductors by means of finite element method simulations

Cited by 12 publications

References 28 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

Transient Current Density in a Pair of Long Parallel Conductors

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

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