Evaluation of High-Frequency Circuit Models for Horizontal and Vertical Grounding Electrodes

Circuit models of horizontal and vertical grounding electrodes are traditionally used in high-frequency (HF) analysis, although underlying approximations limit their accuracy in some low-frequency ranges. Recently, a number of new circuit models have been introduced, but the improvement of the accuracy at HF has not been systematically evaluated. In this paper, we show that new circuit models can be directly derived from method of moments solutions of the integral forms of Maxwell equations by introducing different assumptions. This approach helps to categorize different models into only a few categories based on underlying approximations. To determine the applicable range, we analyze the error for impedance to ground computed by different circuit models in comparison to that calculated by a rigorous full-wave model over wide ranges of parameters, such as electrode length, soil resistivity, and frequency. This paper: 1) provides a parametric analysis that enables the estimation of the applicability of the particular circuit model for application to a practical case based on its accuracy; 2) presents a unified systematic approach to derive circuit models with different capabilities; and 3) reveals that the modeling of the mutual coupling between different parts of the grounding electrode is the key factor for radically improving the accuracy of circuit models at HF.