Time-Harmonic Current Distribution on Conductor Grid in Horizontally Stratified Multilayer Medium

Abstract

Abstract-This paper presents a novel time-harmonic electromagnetic model for determining the current distribution on conductor grids in horizontally stratified multilayer medium. This model could be seen as a basis of the wider electromagnetic model for the frequency-domain transient analysis of conductor grids in multilayer medium. The total number of layers and the total number of conductors are completely arbitrary. The model is based on applying the finite element technique to an integral equation formulation. Each conductor is subdivided into segments with satisfying the thin-wire approximation. Complete electromagnetic coupling between segments is taken into account. The computation of Sommerfeld integrals is avoided through an effective approximation of the attenuation and phase shift effects. Computation procedure for the horizontally stratified multilayer medium is based on the successful application of numerical approximations of two kernel functions of the integral expression for the potential distribution within a single layer, which is caused by a point source of time-harmonic current. Extension from the point source to a segment of the earthing grid conductors is accomplished through integrating the potential contribution due to the line of time-harmonic current source along the segments axis.

Fixed-Image-Method-Based Transient Electromagnetic Model of Grounding System in Horizontally Stratified Multilayer Medium

“…Furthermore, the ground in which these conductors are situated is highly heterogeneous in most cases. In most cases the ground is approximated by several horizontal layers [1][2][3] and, in some cases, even vertical [4] or spherical layers [5] all characterized by highly diverse soil parameters. Naturally since the grounding system conductors are buried in a lossy heterogeneous medium both longitudinal current which flows through the conductor and leakage current which flows into the surrounding medium must be taken into account.…”

“…This transient model introduces improvements to previously published time-harmonic model of the grounding system [3,13,14] and features a novel algorithm for transformation purposes between the time and frequency domain and vice versa. These algorithms for continuous numerical Fourier transform (CNFT) [15] and inverse continuous numerical Fourier transform (ICNFT) [16] are robust, accurate and versatile which is clearly demonstrated in the aforementioned papers.…”

“…In the time-harmonic electromagnetic model published in [3,13,14] and improved in this paper, conductors of the grounding system are subdivided into straight segments which satisfy the thin-wire approximation. Longitudinal current of the conductor segment is in the improved model approximated using a linear approximation instead of a constant as used in [3,13,14].…”

“…Longitudinal current of the conductor segment is in the improved model approximated using a linear approximation instead of a constant as used in [3,13,14]. Complete electromagnetic coupling between segments is taken into account.…”

“…Complete electromagnetic coupling between segments is taken into account. Computation of Sommerfeld integrals is circumvented using an effective approximation of the attenuation and phase shift effects which significantly contributes to the execution speed of the model [3,13,14]. Segments of the grounding system can be situated in any layer of the horizontally stratified multilayer medium which includes the air layer and an arbitrary number of ground layers.…”