A meshless numerical approach for the analysis of earthing systems in electrical installations

Abstract

[Abstract] In the last three decades some numerical formulations have been developed for solving potential problems in electrical engineering applications. In the particular case of the grounding analysis area, in recent years we have developed a general numerical approach based on the Boundary Element Method for homogeneous and isotropic soil models, which has been succesfully applied to the analysis of large grounding systems. This numerical approach has been recently extended for the study of earthing grids embedded in stratified soils, which enables to solve some frequent practical cases, such as the two-layered soil models. Nevertheless, boundary element approaches imply a considerable computational effort when applied to the grounding analysis buried in more stratified soils or completely heterogeneous. This difficulty of the extremely high cost also arises which the use of standard numerical techniques (Finite Differences or Finite Elements) which require the discretization of the whole domain: the ground. Since early nineties, several numerical methods where meshes are unnecessary ("meshless methods") have been proposed in several engineering applications. In this paper, we briefly review some of these meshless techniques, and propose the use of a Moving Least Square methodology with a point collocation scheme for solving problems in electrical engineering. Furthermore, the use of enrichment procedure in these meshless formulations is explored to improve results and decrease the computational cost required.