A computer model for transient analysis of a network of buried and above ground conductors is presented The model is based on the electromagnetic field theory approach and the modified image theory Validation of the model is achieved by comparison with field measurements The model is applied for computation of transient voltages to remote ground of large grounding grid conductors Also computation of longitudinal and leakage currents, transient impedance, electromagnetic fields, and transient induced voltages is possible This model is aimed to help in EMC and lightning protection studies that involve electrical and electronic systems connected to grounding systems

Computer analysis of transient voltages in large grounding systems

The behaviour of grounding systems excited by high impulse currents (such as lightning strokes or phase to ground faults) considerably differs from that at low-frequency and at low-current: inductive behaviour can become more and more important with respect to resistive behaviour and, in addition, these currents can generate soil breakdown (which makes the impulse response typically nonlinear). Many experimental tests confirm these aspects. In order to obtain a correct design of electrical systems, with respect to the protection of installations against anomalous events, it is fundamental to predict the impulse characteristics of grounding systems. An efficient solution to this problem may be obtained by a mathematical model based on a circuit approach. The development of this model (which is able to simulate complex grounding systems when nonlinear ionization phenomena take place) is described in this paper. The model has been validated by comparing the numerical results both with experimental tests and with the simulations executed by various approaches.

Behaviour of grounding systems excited by high impulse currents: the model and its validation

This review paper, prepared for this second special issue on lightning of the IEEE Transactions on Electromagnetic Compatibility, summarizes major publications on lightning and lightning protection since the first special issue published in November 1998, i.e., during the last decade. The review is organized in the following five sections: lightning discharge-observations, lightning discharge-modeling, lightning occurrence characteristics/lightning locating systems, lightning electromagnetic pulse and lightning-induced effects, and protection against lightning-induced effects.

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Overview of Recent Progress in Lightning Research and Lightning Protection

An experimental methodology was applied to determine the frequency dependence of the soil resistivity and permittivity under field conditions. A large number of soils of low-frequency resistivity ranging from 50 to 9100 .m were tested and showed strong variation of both parameters in the Hz frequency interval. Simplified expressions were proposed to predict this frequency dependence. The response of grounding electrodes subjected to lightning currents was simulated using an electromagnetic model under the assumption of variation of soil parameters given by such expressions and obtained from measurements. The results were very similar, though quite different from those obtained under the assumption of constant values for soil resistivity and permittivity.

Frequency Dependence of Soil Parameters: Experimental Results, Predicting Formula and Influence on the Lightning Response of Grounding Electrodes

Vertical ground rods have been used extensively from the early days of electrical engineering for earth termination of electrical and lightning protection systems. They are usually represented with equivalent circuits with lumped and distributed parameters based on quasistatic approximation, which limits the upper frequency of their validity domain. However, lightning-related studies often require modeling in the megahertz frequency range. Also, emerging technologies, such as power-line communications, require analysis in frequency ranges even up to a few tens of megahertz. The rigorous electromagnetic (EM) field theory approach may be used for such frequency ranges, but equivalent circuits are needed for the usual network analysis methods. In this paper, we look at possibilities to construct simple equivalent circuits that can approximate or match results from the EM model. In particular, we compare a usual homogenous distributed parameter circuit with a nonhomogenous one determined by curve matching with results from the EM model. The analysis is illustrated using numerical simulations.

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On high-frequency circuit equivalents of a vertical ground rod

The development and application of a computer model for analyzing the transient performance of grounding systems based on electromagnetic field theory is described. The use of a combination of numerical integration techniques, method of moments, adaptive interpolation, and fast Fourier transform constitutes the basis for the computation of various physical quantities such as the electric fields in the ground, longitudinal and leakage currents in the ground conductors, and ground impedances. It is shown that the analysis of conductors energized by current waves can require computations at frequencies higher than the significant frequencies in the spectrum of the excitation signal, while simpler models may fail to predict accurately the transient performance. The main limitation of the computer model is the time required for the analysis of large or complex grounding systems. >

An electromagnetic model for transients in grounding systems

The lightning current waveform has a major influence on the dynamic performance of ground electrodes. While high lightning current intensity improves the dynamic grounding performance due to ionization of the soil, very fast fronted pulses might worsen the performance in case of inductive behavior. The previous analysis has often been based on quasistatic approximation that is not applicable to very fast fronted pulses. To extend the analysis to fast fronted pulses in this paper, the full-wave analysis method based on the rigorous electromagnetic-field theory approach is used. In addition, realistic lightning current waveforms are applied, which reproduce the observed concave rising portion of typical recorded lightning current pulses. Based on the simulation results, new empirical formulas applicable for slow and very fast fronted lightning current pulses are proposed. The effects of the ionization of the soil are disregarded; therefore, the new formulas are applicable for a conservative estimate of the upper bound of the impulse impedance of ground electrodes.

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Impulse Efficiency of Ground Electrodes

In spite of the existence of a number of analytical models aimed for transient analysis of large grounding systems, more detailed analysis of the influence of different parameters on the transient performance of large ground grids subjected to lightning current impulse is not available. This paper presents analysis of the influence of soil conductivity, location of feed point, grid size, depth, conductor separation, ground rods, and shape of the lightning current impulse, on the transient performance of ground grids with sizes ranging from 10/spl times/10 m/sup 2/ to 120/spl times/120 m/sup 2/ and with 4 to 124 meshes. Maximal transient ground potential rise and frequency dependent impedance are analyzed in time and frequency domain, respectively. Computations are made with computer model based on the electromagnetic field theory approach, taking accurately into account frequency dependent characteristics of large ground grids. Instead of usual simple approximations of the lightning current impulse, recorded channel base currents from triggered lightning are used for the time domain analysis.

Leonid Grcev

Papers

An electromagnetic model for transients in grounding systems

Computer analysis of transient voltages in large grounding systems

On high-frequency circuit equivalents of a vertical ground rod

Impulse Efficiency of Ground Electrodes

Frequency Dependent and Transient Characteristics of Substation Grounding Systems