Analytical Representation of Single- and Double-Peaked Lightning Current Waveforms

An analytical representation for first and subsequent stroke currents is proposed, and simple application examples are given. The waveforms are able to reproduce the characteristic concave profile at the front of first stroke currents, including or not a second peak that is usually observed in the data available from direct measurements on actual lightning. They also reproduce, with good accuracy, median parameters describing lightning currents measured at short instrumented towers. The proposed waveforms have the advantage of using a sum of Heidler functions that last over the entire time of analysis. This avoids the use of separate functions to characterize the front and the tail of the synthesized currents and makes the proposed waveforms suitable for lightning computational analysis.

I. Introduction

An accurate assessment of lightning effects on power systems depends, among other factors, on an appropriate representation of the lightning current. For several decades, an expression composed of the sum of two exponential functions was applied with this purpose [1]. In addition to being unable to determine a maximum steepness near the current peak, a feature that is dominant especially in first stroke currents, this expression was later shown to be inconvenient mostly because of a discontinuity at 0 of its first time derivative.