On Time-Domain Expressions for Calculating the Horizontal Electric Field From Lightning

This paper analyzes three time-domain expressions for the surface impedance, which allows the calculation of the horizontal electric field produced by a lightning return stroke. They are the expression obtained by Barbosa and Paulino directly in the time domain, the expression obtained by Andreotti et al. as a time-domain counterpart of the Cooray-Rubinstein formula, and an approximate expression derived independently from the two former expressions. The analysis is carried out by comparing the kernels of the expressions and by comparing the lightning-induced voltages (LIVs) on an aerial line. The results show that the two former expressions provide almost identical LIVs, while the approximate one provides peak values from 5% to 7% lower than those provided by the other expressions. A detailed discussion of the results is included in the paper.