Harmonic grounding impedance of rods in horizontally stratified soils using ABCD-matrix approach

Grounding electrodes play a fundamental role in the operation of power systems. In this context, precise computation of grounding impedance must consider the frequency-dependence of the soil parameters and the ground organized in stratified layers of soil. This paper proposes an ABCD matrix approach to compute the harmonic grounding impedance of rods buried in frequency-dependent stratified soils directly in the frequency domain. This technique is based on the traditional ABCD matrix used for overhead multi-phase transmission lines extended to grounding systems. In this approach, each rod segment is modeled as a short transmission line where the equivalent harmonic grounding impedance is calculated. Then, the Ground Potential Rise (GPR) waveforms are computed by lightning currents injected into the rods buried in different scenarios. Results indicated that the ABCD matrix approach has shown a good agreement with those obtained using a full-wave electromagnetic software FEKO. The frequency-dependence of the soil electrical parameters causes a significant modification in the harmonic impedance of grounding rods which reduces the GPR peaks considerably, being this reduction more pronounced in homogeneous and 2-layer soils. The proposed technique is an attractive tool since that considers the frequency dependence on each layer of soil, with a low computational cost and good accuracy from 100 Hz up to 1 MHz

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 and relative permittivity) 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 =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