Analysis of the Fractal Dimension of Lightning Discharges based on a Stochastic Lightning Attachment Simulation Model

An analysis of the fractal dimension of lightning discharges simulated using a stochastic lightning attachment model is made. Two fractal dimension estimation methods are employed, incorporating developed algorithms in MATLAB software environment, namely the box-counting and sandbox methods. The statistical variation of fractal dimension results is discussed with respect to fractal dimension values reported in the literature and derived from 2D photographs of natural lightning observations. Fractal dimension results regarding lightning incidence to a 66 kV single-circuit overhead transmission line are analyzed. The effect of lightning discharge termination point to the overhead line in the estimated fractal dimension is discussed as well as the dynamic variation of the fractal dimension throughout the lightning discharge path.