Rigorous Green’s Function Derivation for Grounding Calculations Using the Method of Moments

The Method of Moments (MoM) is notoriously an efficient approach to simulating electrical grounding systems. Using this method, with the construction of a moment matrix, it is possible to calculate the potential at any point in space for a given excitation of the grounding mesh. By determining the potentials in the surface, the analysis of critical parameters in the design of grounding systems is enabled, such as touch voltage, step voltage and grounding resistance. This paper describes the mathematical development required to find a general solution for modeling grounding systems via MoM, using the Green’s function concept. As a final result, the use of the function in calculating the moment matrix is demonstrated in a simple simulation case: two parallel conductors buried in a uniform soil. Additionally, the advantages of the implemented solution over those presented in previous articles [1], [2] are highlighted. In this new solution, numerical integration is no longer required, making the code faster and numerically robust.