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In this paper, we thoroughly review all analytical solutions (both exact and approximate) presented to date in the literature for evaluation of voltages induced on a lossless horizontal conductor, placed over an infinite-conductivity ground, and excited by an external field produced by either a step function or a linearly rising current, moving unattenuated and undistorted along a vertical lightning channel. We also obtain the exact analytical solution for the step-function current case in the time domain via development in the s -domain. To date, there had been three attempts to obtain such solution, all of which yielding incorrect results.

In this paper, we present a new solution for the evaluation of the horizontal electric field in the presence of finitely conducting ground in the time domain. The solution is general, numerically robust, and overcomes the problems related to previously proposed approaches.

In this paper, we propose a new channel-base current function for lightning studies. Main features of the new function are presented, also by comparison with existing expressions; relevant advantages are highlighted. For this new function, closed-form solutions of the time integral (representing the transferred charge), of the Fourier transform, and of the specific energy are given.

A rigorous formula representing the counterpart of the Cooray–Rubinstein expression in the time domain has recently been derived by the authors. In this paper, the formula is particularized for the cases of a unit step and a linearly rising channel-base current, waveforms frequently used in lightning performance studies. Furthermore, an approximate kernel of the formula is also presented, allowing a very compact and straightforward solution for the case of linearly rising currents.

We present a study on lightning-induced voltages on overhead lines produced by tortuous lightning channels, by using a recently developed tool called CiLIV (Andreotti et al . 2015). CiLIV, initially developed for straight and vertical channels, is here extended to account for tortuosity. High-resolution stereoscopic images of six triggered lightning channels have been 3-D digitized and used as input data for CiLIV. The result is that tortuosity, usually ignored in lightning-induced voltage assessment, can instead play a significant role: an attempt is made in characterizing and quantifying these effects. It is shown that, in contrast to other lightning parameters, like channel-base peak current, which are log-normally distributed and generate log-normally distributed induced voltages too, tortuosity generates normally distributed induced voltages. It is also shown that these voltages can deviate up to 23% (relative standard deviation) from the mean value.

In this paper, a new formulation in the time domain of the Cooray-Rubinstein expression is presented. This new formulation overcomes the problems related to the previous formulation: The Dirac pulse contained in the kernel of the previous formulation is extracted, making the numerical treatment easier and more accurate.

Effects of lightning channel tortuosity and tilt on lightning electric fields and voltages induced on overhead conductors are examined. Overall inclination of the bottom few hundred meters of the lightning channel can appreciably change both the ground-level vertical electric field at distances less than 1 km or so and induced voltage peak relative to the vertical-channel assumption. Smaller-scale tortuosity is responsible for the fine structure of field and induced voltage waveforms. This fine structure can be pronounced at some hundreds of meters and beyond, but is insignificant at shorter ranges

A correspondence has been published to comment on the recently published paper “A new channel–base current function for lightning studies” by the authors. The correspondence contains a number of criticisms to the solutions presented in that paper. In this paper, we provide our replies to the raised criticisms.

We propose a procedure to identify the lightning return stroke current characteristics, in the context of return stroke engineering models. The main effort of the up-to-date literature is to find approximate current shapes, which best fit the experimental data. The method hereafter proposed does not follow these approaches, but proposes an inverse algorithm, which allows us to accurately identify the return stroke current for simulated data.