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

Abstract

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

An efficient time-domain method for lightning induced voltage calculation on a finite-length horizontal overhead conductor above lossy ground

“…Andreotti et al . also presented a formula for the calculation of the induced voltage on an overhead line considering an ideal soil, and an improvement in the formula to consider a finitely conducting earth was recently presented in . The method proposed in the present paper, due to its computational efficiency, may be a powerful tool for lightning performance studies.…”

Effect of combined AC and lightning-induced overvoltages on the risk of MV insulator flashovers above lossy ground

“…Later, it was realized that soil resistivity is one of the important parameters that can significantly enhance the lightninginduced overvoltages when compared to perfectly conducting soil. Consequently, the influence of lossy ground on lightninginduced overvoltages has been explored using both coupling and electromagnetic models [6][7][8][9][10][11][12][13][14][15][16]. Accordingly, Darveniza empirically extended Rusck's model to incorporate the effect of finite ground resistivity on lightning-induced overvoltages [17].…”

On the Lightning Induced Voltage Along Overhead Power Distribution Line

“…In order to study the current wave shapes at the channel base and at different heights along the lightning channel, different current functions and models are proposed respectively. In previous studies, non-realistic current functions and models have been applied in the analytical voltage expressions [11,[18][19].…”