Exponential approximation of the Heidler function for the reproduction of lightning current waveshapes

Abstract

In this paper the lightning current function proposed by Heidler is approximated by a linear combination of exponential functions in the time domain, which is afterward analytically transformed into the frequency domain. The unknown coefficients of the exponential approximation for the most frequently used values of the current steepness factor are computed using the least squares method. The developed exponential approximation is general with respect to the current steepness factor in the Heidler function. Approximation of the Heidler function with a linear combination of exponential functions enables the approximation of various Heidler function based lightning current functions. Heidler function in the frequency domain can be used for transient analysis of electromagnetic phenomena that include lightning protection, grounding grid analysis and electromagnetic compatibility problems.