On the estimation of Heidler function parameters for reproduction of various standardized and recorded lightning current waveshapes Dino Lovrić * ,† , Slavko Vujević and Tonći Modrić Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia SUMMARY A highly accurate and robust Marquardt least squares method, which simultaneously solves a set of nonlinear equations, is employed to analyse the accuracy of the Heidler function parameters recommended by IEC 62350–1 Ed. 2. In addition, Heidler function parameters for reproduction of various frequently used standardized waveshapes are provided. The possibility of using the Marquardt least squares method for fitting Heidler function to actual measured data is explored. Copyright © 2011 John Wiley & Sons, Ltd. key words: lightning current; lightning function parameters; least squares method; Marquardt method; IEC 62305–1 Ed. 2 1. INTRODUCTION The international standard IEC 62305–1 Ed. 2 [1] defines three types of lightning impulses relevant to lightning research and engineering applications. These are the first positive impulse, the first negative impulse and the subsequent impulse. All these current waveshapes are mathematically described by using a special case of the Heidler function with the current steepness factor n = 10 [2,3]. The advantage of the Heidler function in relation to some of the previously used functions such as the double-exponential function is that it much more realistically approximates the lightning return stroke. For example, the double-exponential function’s first-time derivation for t = 0 does not equal zero, which is not physically valid because in such a way the function has a discontinuity at the start. In addition, the double-exponential function deviated from the measured lightning current waveshapes [4]. Unlike the double-exponential function, the Heidler function does not have a discontinuity at the start. In addition, it permits a good separation of the characteristic lightning current quantities. The main drawback of the Heidler function was the absence of an analytical solution in the frequency domain [2]. In Reference [5], a highly accurate analytical expression for the Heidler function in the frequency domain is proposed, which employs numerical integration techniques to solve the well-known exponential integral function [6]. Another procedure for obtaining the Heidler function in the frequency domain is proposed in Reference [7] by approximating the Heidler function in the time domain with a linear combination of exponential functions. Other mathematical functions other than the Heidler function, which model the first and subsequent lightning return strokes, were also developed by a number of authors [8–12]. The aim of this paper is to employ a highly accurate and robust Marquardt least squares method [13] to analyse the accuracy of the lightning function parameters recommended by IEC 62350–1 Ed. 2 [1]. This Marquardt least squares method simultaneously solves a set of two, three or four nonlinear equations pertinent to the lightning strike. The number of nonlinear equations depends on the input *Correspondence to: Dino Lovrić, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia. † E-mail: dlovric@fesb.hr Copyright © 2011 John Wiley & Sons, Ltd. EUROPEAN TRANSACTIONS ON ELECTRICAL POWER Euro. Trans. Electr. Power (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.669