Lightning Return-Stroke Transmission Line Modelling Based on the Derivative of Heidler Function and CN Tower Data

One of the most important parameters in a lightning flash that is of interest to researchers is the lightning return-stroke current as it causes most of the destructions and disturbances in electrical and telecommunication networks. In most cases, the lightning return-stroke current can not be directly measured and current characteristics are determined from measured electric and magnetic fields through the use of lightning return-stroke models. The main objective of this work is the development of a lightning return-stroke model for an elevated object. Also, an important objective is the correlation of the wavefront parameters (peak, maximum rate of rise and risetime) of the return-stroke current with the wavefront parameters of its associated lightning electromagnetic pulse (LEMP), measured 2 km north of the tower. The developed field-current parameter relationships for CN Tower lightning return strokes are compared with those obtained from measurements conducted at the Peissenberg Tower in Germany. A 3-section transmission line (TL) model of the CN Tower, along with the derivative of the modified Heidler function, is used to simulate the measured current derivative signal. Then, the spatial-temporal distribution of the lightning current along the CN Tower and the lightning channel, during the lightning return-stroke phase, is determined. The presented model simulates the measured current derivative signal instead of the current as has been used by other researchers. The use of the derivative of the modified Heidler function to simulate the lightning current derivative proved to be superior than simulating the lightning current. For the quantitative assessment of the proposed model, a comparison between the simulated field, obtained through the usage of Maxwell’s equations and the simulated current, and the measured field is performed. The developed 3-section TL model based on the measured current derivative and the derivative of the modified Heidler function produced a simulated magnetic field that is much closer to the measured field in comparison with previous models. The developed field-current parameter relationships as well as the experimentally verified lightning return-stroke model can contribute to solving the inverse-source problem, one of the most challenging problems in lightning research, where the lightning current characteristics are estimated based on the characteristics of the measured LEMP.