A One-Step Finite Element Method for Multiconductor Skin Effect Problems

In this paper, an efficient method for the three-dimensional (3-D) computation of steady-state skin effect problems in current-carrying conductors is presented. It is assumed that the total current is composed of the source current and eddy current, and source current density is proportional to the precalculated electric field intensity. The additional variable is the proportional coefficient which is constant for one conductor. To calculate the magnetic vector potential and the proportional coefficient, the iterative procedure is employed. The proposed method requires much less computational resource and can be easily implemented in the existing 3-D finite element code with slight modification. The method is validated by comparison to known solutions of slot-embedded model and applied to the analysis of current distribution in the GIS conductors.Index Terms-Current-carrying conductor, eddy current, iterative method, skin effect.

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“…For 3-D quasistationary harmonic eddy current problems, the governing equation and current composition equation can be expressed as follows [1]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…The source current density could be calculated if the potential difference between the two end sides of a conductor is known [1]. However, the only measurable known quantity is the total current which is the surface integral of the total current density on the cross section of the conductor.…”

Section: Governing Equationsmentioning

confidence: 99%

Efficient Technique for 3-D Finite Element Analysis of Skin Effect in Current-Carrying Conductors

et al. 2004

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“…The 2D finite element formulation to model eddy currents in this work is similar to [4]. The eddy-current effect in the windings is considered by adding an extra equation for each conductor.…”

Section: The Eddy-current Problem Formulationmentioning

confidence: 99%

Macro elements in the finite element analysis of multi-conductor eddy-current problems

Szucs¹

2000

IEEE Trans. Magn.

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The use of macro elements which replace the multiconductor winding in the time-stepping finite element analysis of electrical machines is presented in the paper. The effect of eddycurrents in the windings is considered by a traditional finite element formulation combined with the so called elimination of inner nodes to achieve fast solution. The elimination method is incorporated into time stepping analysis in such a way that the creation of the numerical macro element is performed only once in a whole time stepping analysis.Index Terms-Eddy currents, finite element methods, machine windings, macro elements, skin effect.

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“…This system consists of a long corridor shared between one respectively. 1 a lies on the x-y plane, the linear twodimensional electromagnetic diffusion problem for the zdirection components of the Magnetic Vector Potential (MVP) Az and of the total current density vector ]z is described by the system of equations [11][12] Si where a is the conductivity, co is the angular frequency, #0 and/4-are the vacuum and relative permeabilities respectively, ]= is the source current density [13] in the z-direction and Ii is the rms value of the current flowing through conductor i of cross section Si. Aluminium mitigation wires shown in Fig.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…The matrix equation obtained [13] from the finite element formulation of equations (la-c) is solved using the Crout variation of Gauss elimination. MVP values in every node of the discretization domain as well as the unknown source current densities are calculated using the matrix equation solution.…”

Section: Finite Element Formulationmentioning

confidence: 99%

The influence of multi-layer ground on the electromagnetic field of an overhead power transmission line in the presence of buried conductors

Satsios

Labridis

Dokopoulos

1997

Electrical Engineering

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ContentsThe present work investigates the two dimensional, quasi stationary, electromagnetic field of a faulted power transmission line in the presence of a buried pipeline, of mitigation wires and of a multi-layer ground. The related diffusion equation has been numerically solved by using the Finite Element Method (FEM). Using FEM results and Faraday's law, magnetic vector potential, as well as the voltages induced across the buried pipeline and remote earth, are calculated. Parametric analysis has shown that there is a significant influence of the depth and resistivity of the first ground layer, of the resistivities of the different ground layers and of the configuration of mitigation wires on the electromagnetic field and on the voltages induced across the buried pipeline and remote earth. Der EinflulJ der mehrschichtigen Erde auf das elektromagnetische Feld einer Ubertragungsleitung in der Anwesenheit yon unterirdischen LeiternObersicht In der vorliegenden Arbeit wird das zweidimensionale, quasi stationfire, elektromagnetische Feld einer mit einem Fehler behafteten Ubertragungsleitung in der Anwesenheit einer unterirdischen Rohrleitung, mehreren Schutzleitungen und einer mehrschichtigen Erde untersucht. Die entsprechende Diffusionsgleichung wird numerisch mit Hilfe der Finiten Elementen Methode (FEM) berechnet. Anschlieflend werden mit Hilfe der Ergebnisse der FEM und der Faraday schen Gleichung das magnetische Vektorpotential und die zwischen der Rohrleitung und der fernen Erde induzierten Spannungen berechnet. Untersuchungen zeigten, daft ftir das Feld und die zwischen Rohrleitung und der fernen Erde induzierten Spannungen folgende Parameter yon grofler Bedeutung sind: Die Dichte der ersten Erdschicht, die spezifischen Widerstgnde der Erdschichten und die Anordung der Schutzleitungen. 1

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A One-Step Finite Element Method for Multiconductor Skin Effect Problems

Cited by 93 publications

References 14 publications

Efficient Technique for 3-D Finite Element Analysis of Skin Effect in Current-Carrying Conductors

Efficient Technique for 3-D Finite Element Analysis of Skin Effect in Current-Carrying Conductors

Macro elements in the finite element analysis of multi-conductor eddy-current problems

The influence of multi-layer ground on the electromagnetic field of an overhead power transmission line in the presence of buried conductors

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