Numerical Infinite Series Solution of the Ground-Return Pollaczek Integral

Abstract

In this paper, the Wedepohl-Wilcox series, proposed for calculating ground-return impedances of buried cables and electromagnetic transients, are analyzed in detail. The origin of this series goes back to the original integral derived by Pollaczek. To enhance the analysis developed here, a numerical comparison between the series, the direct numerical integration of Pollaczek integral, and a proposed hybrid numerical algorithm is presented in this paper. The later consists on: a) the use of a vector-type efficient algorithm for the converging series for low frequencies, and b) trapezoidal numerical integration for the high frequency range. In addition, and based on the analysis, a criterion for switching between series and direct numerical integration is proposed here.