Why do computer methods for grounding analysis produce anomalous results?

Grounding systems are designed to guarantee personal security, protection of equipment, and continuity of power supply. Hence, engineers must compute the equivalent resistance of the system and the potential distribution on the earth surface when a fault condition occurs. While very crude approximations were available until the 1970s, several computer methods have been more recently proposed on the basis of practice, semiempirical works and intuitive ideas such as superposition of punctual current sources and error averaging. Although these techniques are widely used, several problems have been reported. Namely, large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error. A boundary element formulation for grounding analysis is presented in this paper. Existing computer methods such as APM are identified as particular cases within this theoretical framework. While linear and quadratic leakage current elements allow to increase accuracy, computing time is reduced by means of new analytical integration techniques. Former intuitive ideas can now be explained as suitable assumptions introduced in the BEM formulation to reduce computational cost. Thus, the anomalous asymptotic behavior of this kind of method is mathematically explained, and sources of error are rigorously identified.