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Abstract-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.

Abstract-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.