Evaluation of an Approximate Channel-Base Current and Its Analytical Function Parameters Based on the Measured Lightning Magnetic Field

Abstract

In this paper, a new method is proposed for directly evaluating approximate lightning channel-base-current (CBC) parameters ( $I_{m}$ , ( di / dt )max, t FD, and t SD) and analytical function parameters (AFPs) of the CBC based on the measured lightning magnetic fields using a deconvolution and differential evolution (DE) method. This proposed method comprises two sequential steps. The first step is for determining the lightning CBC based on the measured magnetic field using modified transmission line model with exponential current decaying with height (MTLE) through deconvolution, while the second step is for evaluating the AFPs (Heidler's function) corresponding to the lightning CBC obtained from the first step. Data from the measured magnetic field above ground level ( z = 10 m) at different horizontal distances ( r = 9 km, 4.6 km, 2 km, and 50 m) from the lightning channel are considered for testing the proposed method. The sum of two Heidler's functions is used to represent the lightning CBC; and its parameters, namely I 01, I 02, τ 11, τ 12, τ 21, τ 22, n 1 , and n 2 are identified using DE as a tool. Further, this methodology is helpful in the evaluation of the CBC parameters and mathematical modeling of the lightning CBC and the estimation of the lightning current through the channel using data from the measured magnetic field for different engineering return stroke models.