A Concise Approach of Soil Models for Time-Domain Analysis

This paper proposes to represent the frequency dependence of soil parameters via a rational approximation in the frequency domain. Two types of causal soil models were considered, namely, Smith-Longmire and Alipio-Visacro (AV). Results indicated that for both soil models, the analyzed parameters maintain a fixed ratio between the poles and residues, and for the AV soil model, there is a unique set of poles, representing a “universal” set of relaxation frequencies. Thus, without resorting to an additional fitting process, one can find a suitable rational approximation of a frequency-dependent soil for an arbitrary conductivity, which is very useful for its inclusion in computational codes in time or frequency domains.

I. Introduction

A key parameter in the transient performance of grounding systems and transmission lines is the behavior of soil parameters. Typically, when low-frequency phenomena are involved, the soil is assumed to be represented by a constant resistivity (conductivity), while for wideband electromagnetic transients and fields, one has to resort to a more detailed soil representation, including the frequency dependence of the soil conductivity, , and permittivity, . The early works to deal with the latter date from the early 1930s [1]. In the 1970s, several improvements in the matter were carried out, considering both theoretical and experimental approaches (see, for instance, [2]–[5]). In recent years, a renewed interest has been drawn toward the inclusion of frequency-dependent ground parameters in electromagnetic transients [6]–[8] and in the lightning performance of grounding electrodes [9]–[11].