Computation of Lightning Current from Electric Field Based on Laplace Transform and Deconvolution Method

Grzegorz Karnas

doi:10.3390/en14144201

Abstract

A method for computation of the lightning channel base current from the corresponding vertical component of lightning electric field was presented. The algorithm was developed by applying Laplace transform. The lightning current was estimated from its deconvolution with a special transfer function. The transfer function includes information about geometry and physical properties of entire lightning impulse generation system. The method was verified for a Heidler-type base current and a MTLL model of its propagation within the lightning channel. Research was done for close, middle, and far distance to the lightning strike point. Optimum performance was obtained for the middle distance of several kilometers where the electrostatic, induction, and radiation components of the transfer function were of the same range. An analysis was done for input electric field with and without noise superimposed on its time domain waveform. Relative uncertainties for the electric field and calculated lightning channel base current were similar each other. The presented approach can substantially increase a number of lightning current parameters which can be identified on the basis of its electric field signature. This method can be applied by the lightning location systems using preprocessing which increases the timing efficiency of the transfer function estimation.

Highlights

The estimation of the lightning current is one of the fundamental tasks of overvoltage protection [1]
The shape of the lightning channel base current waveform in time domain allows for the detection of a continuous and continuing current [5] being responsible for thermal destruction and fires [6]
The computation of the lightning current from its electric field signatures recorded for natural lighting can be applied for investigation of physical processes within the lightning channel [7]

Summary

Introduction

The estimation of the lightning current is one of the fundamental tasks of overvoltage protection [1]. Rakov derived a similar empirical formula from triggered experiments [20] Another approach to the estimation of the triggered lightning current peak value and the current steepness was done in 1998 by Willet et al [21] using a semiempirical equation applied to the electric field data. In 2004, Shao et al [26] presented a derivation of the theoretical formula relating radiated components of lightning electric and magnetic fields to the corresponding current in the lightning channel taking into account the nonconstant retarded time along the channel segment. Lightning current waveforms were derived from close, middle, and far electric fields The performance of this method was tested for different numerical parameters of simulation

Lightning Channel Base Current Computation Algorithm

Results and Discussion

Lightning Channel Distance Influence

Restrictions and Limitations of Algorithm