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

Abstract

Abstract-In this paper, a frequency-domain-based transient electromagnetic model of grounding system in horizontally stratified multilayer medium is presented. The basis of the model is an improved version of the time-harmonic electromagnetic model of grounding system. Using the originally developed continuous numerical Fourier transform algorithm, the results obtained by the time-harmonic model are synthesized into a complete time domain solution. The presented model features very high accuracy and fast execution speed and is validated through several numerical examples.

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“…Current of the conductor segments is divided into two dependent parts -the longitudinal current which flows along the conductor segment axis and the leakage current which leaks from the conductor segment surface into the surrounding medium. In the presented electromagnetic model, the longitudinal current of the segment is approximated linearly while the leakage current is, consequently, a constant along the segment length [12]. The effect of medium heterogeneity is taken into account using the robust and accurate fixed image method originally developed in [16].…”

“…Initially, all conductor segments are disconnected in order to create a complete local system of equations which is formed using the Galerkin-Bubnov method. This is a linear system of equations for longitudinal and leakage segment currents which is transformed into an equivalent complete local system of linear equations for nodal currents [12]:…”

“…where Z t is a symmetrical transversal segment impedance matrix [17,18]; Z b is a nonsymmetrical matrix of longitudinal impedances between segments and beginning nodes of segments [12]; Z e is a nonsymmetrical matrix of longitudinal impedances between segments and ending nodes of segments [12];…”

“…[E] is the unit matrix; nĪ is a vector representing local nodal currents; nΦ is a vector representing local nodal potentials. Elements of the symmetrical transversal segment impedance matrix Z t are computed analytically and have been derived in detail in [17,18] whereas the nonsymmetric matrices Z e and Z e are computed numerically using an improved Gaussian quadrature [12]. The complete local system of equations for nodal currents can then be obtained from Eq.…”