Potential distribution for a harmonic current point source in horizontally stratified multilayer medium

Abstract

Purpose

This paper aims to describe a numerical procedure for approximating the potential distribution for a harmonic current point source, which is either buried in horizontally stratified multilayer earth, or positioned in the air. The procedure is very efficient and general. The total number of layers and the source position in relation to the medium model layers are completely arbitrary.

Design/methodology/approach

The efficiency of the computation procedure is based on the successful application of the numerical approximation of two kernel functions of the integral expression for the potential distribution within an arbitrarily chosen layer of the medium model. Each kernel function of the observed layer is approximated using a linear combination of 15 real exponential functions. Using these approximations and the analytical integration based on the Weber integral, a simple expression for numerical approximation of potential distribution within boundaries of the observed medium layer is given. Potential retardation is taken into account approximately.

Findings

The numerical procedure developed for the approximation of potential distribution for a harmonic current point source, which is positioned arbitrarily in air or in horizontally stratified multilayer earth, is efficient, numerically stable and generally applicable.

Research limitations/implications

Numerical model developed for the harmonic current point source is the basis of a wider numerical models for computation of the harmonic and transient fields of earthing system, which consists of earthing grids buried in horizontally stratified multilayer earth and metallic structures in the air.

Originality/value

This is efficient and numerically stable frequency dependent harmonic current point source model. Potential retardation, which has been neglected at the first step of the approximation, is subsequently added to the potential expression in such a way that the Helmholtz differential equation has been approximately solved without introducing the Sommerfeld integrals.

Citation

Vujević, S. and Sarajčev, P. (2008), "Potential distribution for a harmonic current point source in horizontally stratified multilayer medium", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 3, pp. 624-637. https://doi.org/10.1108/03321640810861070