Analytical Formulations for Lightning-Induced Voltage Calculations

Recently, Andreotti (2009) have presented an analytical solution for the evaluation of voltages induced on an infinitely long, lossless, single-conductor located at a given height above an infinite-conductivity ground plane, and excited by an external field due to a step current wave moving without attenuation and at a constant speed along a vertical lightning channel. The solution presented, in contrast to previously published solutions, was derived in an exact way, i.e., no approximations were introduced in its derivation. In this paper, this exact approach is extended to more practical line configurations. Specifically, still for the case of an external field due to a step current and perfectly conducting ground, the cases of terminated single-conductor line and multiconductor line (including grounded conductors) will be studied. Further, single- and multiconductor lines (including grounded conductors) excited by an external field due to a linearly rising current will be examined.