Time-Domain Analysis of Frequency-Dependent Electrical Parameters of Soil

The analysis of the impact of the frequency dependence of electrical parameters of soil on the lightning response of electrical systems has often been based on frequency-domain approaches. In this paper, a causal time-domain field formulation including the frequency dependence of soil parameters is proposed. The consistency of the developed formulation is proved considering a canonical electromagnetic problem and also comparisons with experimental results. The proposed formulation is useful for application of techniques such as the finite-difference time-domain method in problems involving dispersive soils.

I. Introduction

In the last years, relevant advances have been achieved on the frequency dependence of soil resistivity and permittivity in the typical frequency range of lightning currents. Although this effect had already been proved a long ago by Smith-Rose [1] and Scott [2], based on laboratorial measurement, until recently no reliable general expressions or models used to be available for taking this effect into account in the lightning response of grounding electrodes.