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PurposeThis 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/approachThe 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.FindingsThe 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/implicationsNumerical 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/valueThis 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.

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.

This paper describes the algorithm for optimal distribution network reconfiguration using the combination of a heuristic approach and genetic algorithms. Although similar approaches have been developed so far, they usually had issues with poor convergence rate and long computational time, and were often applicable only to the small scale distribution networks. Unlike these approaches, the algorithm described in this paper brings a number of uniqueness and improvements that allow its application to the distribution networks of real size with a high degree of topology complexity. The optimal distribution network reconfiguration is formulated for the two different objective functions: minimization of total power/energy losses and minimization of network loading index. In doing so, the algorithm maintains the radial structure of the distribution network through the entire process and assures the fulfilment of various physical and operational network constraints. With a few minor modifications in the heuristic part of the algorithm, it can be adapted to the problem of determining the distribution network optimal structure in order to equalize the network voltage profile. The proposed algorithm was applied to a variety of standard distribution network test cases, and the results show the high quality and accuracy of the proposed approach, together with a remarkably short execution time.