Efficient modeling of parallel counterpoise wires using an FDTD-based transmission line approach

Abstract

This paper presents an efficient modeling approach for parallel counterpoise wires used in the tower-footing grounding systems of high-voltage transmission lines. The proposed method is based on transmission line theory, with the governing equations solved using the Finite Difference Time Domain (FDTD) technique. The formulation incorporates frequency-dependent effects in both longitudinal impedance and shunt admittance, and its accuracy is validated through comparison with a rigorous electromagnetic model. The results show excellent agreement between the models, with deviations below 5 % across all analyzed cases, becoming negligible as soil resistivity increases. It was also observed that increasing the separation distance between the counterpoise wires leads to a reduction in both the Ground Potential Rise (GPR) and impulse impedance, although this reduction is not particularly significant, ranging from approximately 10 % to 13 % for the analyzed soil resistivities when the separation distance is increased fourfold. A novel finding of this study is that the effective length of counterpoise wires is independent of the separation distance between them, which simplifies the design process for transmission lines with varying right-of-way widths. Additionally, the developed formulation allows for the future incorporation of nonlinear effects, such as soil ionization, providing an accurate and computationally efficient tool for analyzing and designing the lightning response of grounding systems in high-voltage transmission lines.