Leonid Grcev

An electromagnetic model for transients in grounding systems

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. >

Computer analysis of transient voltages in large grounding systems

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.

Frequency Dependent and Transient Characteristics of Substation Grounding Systems

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.

EMTP-based model for grounding system analysis

EMC and lightning protection analyses of large power systems require the knowledge of the dynamic behavior of extended grounding systems. They cannot be regarded as equipotential planes, but must be treated as coupling paths for transient overvoltages. This contribution presents a model for linear earth conductors based on the transmission line approach and outlines its integration in the transients program EMTP. Validation of the presented model is achieved by comparison with field measurements and with a rigorous electromagnetic model. Overvoltages and electrical fields throughout electrical power systems can thus be computed. >

On high-frequency circuit equivalents of a vertical ground rod

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.

Impulse Efficiency of Ground Electrodes

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.

Transient electromagnetic fields near large earthing systems

Electromagnetic compatibility studies require knowledge of transient voltages that may be developed near earthing systems during lightning discharge, since such voltages may be coupled to sensitive electronic circuits. For such purpose, accurate evaluation of the transient electric field near to and/or at the surface of the grounding conductors is necessary. In this paper, a procedure for computation of transient fields near large earthing systems, as a response to a typical lightning current impulse, based on computational methodology developed in the field of antennas, is presented. Computed results are favorably compared with published measurement results. The model is applied to check the common assumption that the soil ionization can be neglected in case of large earthing systems. Presented results show that the soil ionization threshold is met and exceeded during typical lightning discharge in a large earthing system.

Modeling of Grounding Electrodes Under Lightning Currents

More precise modeling of the dynamic performance of grounding electrodes under lightning currents must include both the time-dependent nonlinear soil ionization and the frequency-dependent phenomena. These phenomena might have mutually opposing effects since the soil ionization effectively improves, while frequency-dependent inductive behavior impairs, the grounding performance. Modern approaches that take into account both phenomena are based on circuit theory that does not allow for accurate analysis of high-frequency behavior. This paper aims to further improve the understanding of the dynamic behavior of grounding electrodes under lightning currents by focusing on the following aspects: analyzing the validity domains of popular modeling approaches, based on circuit, transmission line, and electromagnetic theory; providing parametric analysis that takes into account both the propagation and soil ionization effects; analyzing simple formulas for surge characteristics; and comparing the modeling with experimental data. A model and a simple formula that combine the electromagnetic approach, suitable for high-frequency analysis, with the method that accounts for the soil ionization effects, recommended by the International Council on Large Electric Systems (CIGRE) and the IEEE Working Groups, are used for the parametric analysis. Both the model and the simple formula are verified by comparison with experimental results available in the literature.

Time- and Frequency-Dependent Lightning Surge Characteristics of Grounding Electrodes

Two phenomena dominantly influence the dynamic performance of grounding electrodes during lightning discharge: 1) the time-dependent nonlinear behavior related to soil ionization during high-current pulses and 2) the frequency-dependent electromagnetic (EM) effects related to fast rise-time current pulses. The first phenomenon improves the grounding performance, while the second might have the opposite effect of impairing the grounding characteristics. It is important to simultaneously analyze these opposing effects; however, modern approaches that take into account both phenomena are mostly based on circuit theory, which does not allow for accurate analysis of fast rise-time pulses. This paper proposes a procedure that combines a rigorous EM approach based on the method of moments with an approximation method for assessing soil ionization effects as recently recommended by the CIGRE and IEEE Working Groups. Based on this procedure, we derive a simple new formula for approximating the surge characteristics that include time-dependent ionization and frequency-dependent inductive effects. We verify the model and formula by comparing our data with published experimental results. We also describe a parametric analysis of the opposing ionization and inductive effects.

On tower impedances for transient analysis

The analysis of the dynamic behavior of power transmission line and telecommunication towers is of interest in protection and EMC studies related to lightning. Usually, time-domain surge impedance is used to characterize tower dynamic behavior. The main drawback in the definition of such surge impedance is that it is dependent on the excitation waveshape and there is no consensus on the current waveshape to be used. Also, there is no consensus on the unique definition of the involved voltage. This paper explores possibilities for a systematized approach to the analysis and uniquely defined quantities that characterize transient response of towers. Further, limitations associated with simplified approaches are emphasized by examining examples of direct comparison between computations based on transmission-line approach and antenna theory for a 100-m tall tower. It is pointed out that problems in the definition of voltages might occur above 100 kHz, especially near resonant frequencies, while differences in current distribution exist already at the lowest frequencies.