Finite-difference time-domain modeling of multi-stage soil ionization with residual resistivities—Part I: Theoretical background and the proposed FDTD formulation

Abstract

In this first part of the paper, a Finite-Difference Time-Domain (FDTD) model for multi-stage soil ionization with residual resistivities is proposed to obtain realistic transient responses of grounding systems subjected to high intensity currents. Four phases of soil ionization process are modeled: non-ionization (linear soil representation), presparking (first stage of ionization), sparking (second stage of ionization) and deionization. Mechanisms identified experimentally in literature for water ionization explain presparking and sparking phases of soil ionization. Weak ionization in clusters of gas bubbles produced due to high current flows explains the presparking phase. The sparking phase is governed by ionization of aqueous solutions in soil. A mathematical function is defined to represent the rise of electrical conductivity over time for each point in the soil FDTD lattice during sparking phase. Additionally, effects associated with limited production of free charges over time and their increasing reduction of mobility are considered by means of residual resistivities in presparking and sparking phases. Due to the complex nature of the phenomenon, which involves various physical processes, comprehensive theoretical background is also provided in part I. The second part of the paper presents numerical validation cases for the proposed FDTD soil ionization model.