Double-Exponential Expression of Lightning Current Waveforms

Abstract

A lightning waveform is usually defined by the rise time t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f </sub> , pulse length t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> and peak value I. In order to represent lightning current waveforms in an analytic manner, the double-exponential formula is employed to fit with the lightning current waveforms. This paper describes the relationship between the waveform parameters t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> , t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , I and the formula constants alpha, beta and A. An effective algorithm is proposed to calculate alpha, beta and A. The algorithm gives a reasonable expression for alpha, beta and A from the data points of lightning current waveforms. Numerical examples are derived from the algorithm for a few types of lightning current waveforms that are commonly used in lightning protection design. A better agreement appears between calculated and standard waveforms