Numerical Simulation of Potential Distribution in Grounding Systems Using the Finite Difference Matrix Operators Approach with Non-Uniform Mesh

In this paper, we introduce the development of the Finite Difference Matrix Operators (FDMO) algorithm for solving the three-dimensional (3D) electromagnetic problem governed by the Laplace–Poisson equation. Specifically, we propose a novel approach by integrating the FDMO approach with non-uniform mesh of the 3D solution domain, optimizing computational efficiency and adaptability for complex grounding system geometries, to compute and analysis the earth potential distribution in grounding systems. The study considers two typical grid configurations—square and L-shaped of IEEE Std 80™—as well as a real-world grounding system of high voltage substation in Vietnam. The results of potential distribution, touch, and step voltages obtained from the proposed method demonstrate high agreement with those computed using the Finite Element Method (FEM) and IEEE Std 80™, confirming the accuracy, robustness, and practical utility of the proposed method for the grounding design of high voltage substations in power systems.