A Mathematical Model for the Transient Lightning Response from Grounding Systems

With the Fast Fourier Transform (FFT), a mathematical model for accurately computing distribution of a lightning currents flowing along a high voltage a.c. substation’s grounding system buried in half infinite homogenous earth has been developed in this paper. It is a hybrid of Galerkin’s method of moment (MoM) and a conventional nodal analysis method. The model can directly calculate the distribution of both branch and leakage currents along the grounding system. A dynamic state complex image method and a closed form of Green’s function of a dipole or monopole in the half infinite homogenous earth model are introduced into this model to accelerate calculations of mutual impedance and induction coefficients. Analytical formulae for the mutual induction and impedance coefficients have been developed to accelerate the calculation for near field case by using Maclaurin expansion. With the inverse FFT, the model can be used to study the transient lightning response of a grounding system.