Analytical integration techniques for earthing grid computation by boundary element methods

Abstract

[Abstract] Analysis and design of substation earthing involves computing the equivalent resistance of grounding systems, but also distribution of potentials on the earth surface due to fault currents [1]. While very crude approximations were available in the sixties, several methods have been proposed in the last two decades, must of them on the basis of intuitive ideas such as superposition of punctual current sources and error averaging [2,3]. Although these techniques represented a significant improvement in the area of earthing analysis, a number of problems have been reported. Namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [3]. In this paper, a 1D Boundary Element formulation is presented. Several widespread intuitive methods (such as APM) are identified as particular cases of this general approach. Thus, former intuitive ideas can now be explained as suitable assumptions introduced in the BEM formulation to reduce computational cost. The anomalous asymptotic behaviour of this kind of methods is mathematically explained, and sources of error are pointed out. While linear and parabolic leakage current elements allow to increase accuracy, computing time is drastically reduced by means of new analytical integration techniques. Finally, an application example to a real problem is presented.