Computation of ground potential rise and grounding impedance of simple arrangement of electrodes buried in frequency-dependent stratified soil

Grounding electrodes are used to provide a low-impedance dissipation path for the excess lightning or fault currents. Several studies have been dedicated to the computation of the grounding impedance of different electrode arrangements considering either the frequency dependence of soil parameters (resistivity rho and relative permittivity epsilon(r)) or the multi-layer nature of soil. This paper aims at the calculation of the grounding impedance and the ground potential rise (GPR) of simple electrode arrangements (vertical and cross electrodes) due to the injection of first and subsequent lightning currents in various configurations of soil, considering a frequency-dependent stratified soil. A frequency-domain full-wave electromagnetic solver based on the Method of Moment (MoM) that employs a stratified medium Green's function is used to compute the grounding impedance in a frequency range of 100 Hz to 10 MHz. The transient GPRs are computed using the equivalent circuit of the grounding system, obtained through the application of the Vector Fitting (VF) technique and recursive convolution method. The simulation results show that considering the frequency dependence of the soil parameters has no effect on the low-frequency grounding impedance up to approximate to 10 kHz. However, the frequency dependence of soil parameters leads to a considerable variation of the grounding impedance at higher frequencies especially for soils of higher resistivity. Furthermore, it is shown that considering the layers of soil has a more significant impact on the GPR of the vertical electrode than that of the cross electrode.