Time-Domain Implementation of Cooray–Rubinstein Formula via Convolution Integral and Rational Approximation

One of the most popular techniques to take into account the finite ground conductivity in the evaluation of the radial component of the electric field generated by a lightning return stroke is the Cooray-Rubinstein (CR) formula. As this formula is derived in the frequency domain, its application in time-domain simulation codes for the analysis of lightning-induced overvoltages on overhead lines might be challenging. In this paper, two methods allowing a simple time-domain implementation of the formula are discussed. The first one is an enhanced version of an algorithm recently proposed by two of the authors, while the second consists of a new technique, based on a suitable rational approximation of the impedance term appearing in the CR formula. This second approach is characterized by an intrinsic easiness in time-domain implementation and a considerable computational efficiency compared with conventional methods.