An Approximation to the Heidler Function With an Analytical Integral

Abstract

An analytical integral of a lightning current model is required in the analysis of lightning events including the induced effects and frequency analysis of lightning strikes. Previous work in this area has produced very specific forms of the Heidler function that are used to represent lightning current waveshapes. This work, however, focuses on a generic approximation, with parameters that can be modified to produce any required lightning current waveshape. The approximation function proposed has an analytical solution to the integral allowing for a true representation of Maxwell's equations for electromagnetic fields. Moreover, the approximation is designed in the Laplace domain allowing for a complete analytical frequency domain analysis. The function has parameters that can be changed to obtain different waveshapes (such as 10/350 and 0.25/100). The characteristics of the approximation are compared with those of the Heidler function to confirm that it is applicable for use with in IEC 62305-1 lightning protection standard applications. The maximum error in amplitude for the first and subsequent lightning stroke currents is less than 1.5%. The maximum error in the derivative is greater but still less than 8%. This is within the parameters defined in the standard.