Approximation of Lightning Current Waveforms Using Complex Exponential Functions

A key aspect to evaluate the lightning performance of transmission lines is the correct representation of the lightning current waveform considered. Traditionally, the analytical modeling of such data might involve the use of double-exponential functions or even Heidler functions series, i.e., partial fractions with polynomial functions of variable degree. Herein, we propose the fitting of lightning current waveforms to obtain a pole-residue model as an alternative procedure. Purposely, we investigate the performance of the vector fitting (VF) and time-domain vector fitting (TD-VF) methods to represent continuous lightning current waveshapes originally modeled using Heidler function series. Four nontrivial test cases of single-crest and double-crest peaked lightning waveforms are analyzed. Albeit comparatively accurate results are achieved, the TD-VF provides models with lower pole orders than the VF approach for equivalent window observation times and time steps. Incorporation of pole-residue models in transient simulation programs can be straightforward as compared to a Heidler function series heuristic approach.