An Exact Closed-Form Solution for Lightning-Induced Overvoltages Calculations

We present the evaluation of the induced voltages in a lossless single transmission line, located at a given height over an infinite conductivity ground plane, and exited by an external field due to a step current moving along a vertical channel. This is a classic topic of the theory of lightning-induced voltages on power lines. The technical literature related to this topic has performed a significant effort; however, only approximated formulas have been obtained so far. In this paper, we derive the exact closed-form solution. We also will discuss, evaluate, and compare the approximated formulas with reference to the proposed exact one, thus contributing to clarifying a matter that still is debated and sometimes misleading, as we will show in the paper. We furthermore recall that the examined lightning-induced voltages model is fundamental for the IEEE standard 1410, a guide for improving the lightning performance of power distribution line.