Influence of a lossy ground on lightning-induced voltages on overhead lines

A comprehensive study on the effect of a lossy ground on the induced voltages on overhead lines by a nearby lightning is presented. The ground conductivity plays a role in both the evaluation of the lightning radiated fields and of the line parameters. To be calculated by means of a rigorous theory, both fields and line constants need important computation time, which, for the problem of interest, is still prohibitive. The aim of this paper is to discuss and analyze the various simplified approaches and techniques that have been proposed for the calculation of the fields and the line constants when the ground cannot be assumed as a perfectly conducting plane. Regarding the radiated electromagnetic field, it is shown that the horizontal electric field, the component which is most affected by the ground finite conductivity, can be calculated in an accurate way using the Cooray-Rubinstein simplified formula, The presence of an imperfectly conducting ground is included in the coupling equations by means of two additional terms: the longitudinal ground impedance-and the transverse ground admittance, which are both frequency-dependent The latter can generally be neglected for typical overhead lines, due to its small contribution to the overall transverse admittance of the line. Regarding the ground impedance, a comparison between several simplified expressions used in the literature is presented and the validity limits of these expressions are established. It is also shown that for typical overhead lines the wire impedance can be neglected as regard to the ground impedance. We also investigate the time-domain representation of held-to-transmission line coupling equations where the frequency-dependence of the ground is taken into account by the convolution integral. Finally, examples of voltages induced by a typical subsequent return stroke on an overhead line are presented, emphasizing the effect of the finitely conducting ground. It is shown that for lines whose length does not exceed a certain 'critical' value (typically 2 km), the surge propagation along the line is not appreciably affected by the ground finite conductivity which, therefore, can be neglected in the computation process.