Modified finite difference time domain modelling of lightning propagation considering non-uniform and frequency dependent soil

Abstract

When cloud-ground lightning occurs, electromagnetic waves, known as electromagnetic pulses (EMPs) propagate within the earth’s atmosphere. Consequently, they may interfere with many man-made systems such as electric power lines and telecommunication networks. Several theoretical lightning return stroke models had been previously proposed. However, these models can still be improved in terms of the accuracy of the electromagnetic field (EMF) generated, the applicability for nonlinear conditions for EMP propagation, such as frequency dependence of soil parameters, the applicability for complex geometries for EMP interference with surrounding objects, and the efficiency of computation. In this research, an improvement to the finite-difference timedomain (FDTD) method was made to solve Maxwell equations in dispersive media. This includes the utilization of the recursive convolution for the solution of Ampere's law-Maxwell equations for the nonlinear conditions faced when considering the frequency dependency of soil permittivity and conductivity. Due to the relationship between the total current density and the total admittance of the soil, the convolution operator will be only used between the electric field and a time-dependent admittance. A C++ programming language was utilised to build a 3D constant recursive convolution finite-difference time-domain (CRC-FDTD) model. The proposed CRC-FDTD method had made it possible to study the effects of various factors, such as soil structures, water content, distance, and return strokes parameters, on the behaviour of lightning EMF propagation. The main EMFs considered are the vertical and horizontal electric fields, and the azimuthal magnetic field, the magnitudes of which were measured both above and underground. The results obtained from the proposed method were compared to those using the finite element analysis (FEA) based on COMSOL and the previous results adopted Delfino’s expressions. This study has successfully developed a time-domain analysis of frequency dependency by combining the CRC and FDTD techniques. The CRC-FDTD method could determine electromagnetic radiation over frequency-dependent soil in the time domain with less simulation duration, lower computational requirements, a simpler procedure, and better applicability compared to its predecessors. This has enabled us to improve the accuracy and efficiency of lightning EMF modelling and computation and investigate the effects of the soil model on electromagnetic propagation through a comparison between frequency dependent soil (FDS) model and frequency independent soil (FIS) model. The CRC-FDTD has enabled these effects such as observation distance, soil moisture, soil structure, and parameters of lightning current, to be accurately studied and analysed. CRC-FDTD is comparable to Delfino’s expressions with a slight difference in tail time, and to FEA with mean differences of 3.2% for the peak magnitude, 3.3 % for the front time, and 7.6 % for the tail time. These mean differences are considered acceptable and the validation of the CRC-FDTD can be said to be accomplished.