A fractal-based stepped downward leader model including branched channel charge distribution and branch fading

Abstract

In this paper, a fractal-based model is proposed for lightning downward leader propagation through the air. The model simulates the zigzag movement and the branching nature of lightning close to reality in comparison to previous existing models. The probabilistic behavior of lightning is well modeled using the fractal approach. A new model is also introduced for charge distribution along different branches of the lightning downward leader. The model calculates the charge density of each branch based on the concept of electric field through the branches. Moreover, the probability of branch fading is considered in the simulations. The proposed model is evaluated for striking distance calculation of a transmission line structure and the results are compared to those of Leader Progression Model (LPM), and different models of Electrogeometric Model (EGM). Moreover, Shielding Failure Rate (SFR) of some structures is obtained by the proposed method and the results are compared to those of field observations. In addition, the electrical field on the ground near the striking point of lightning is calculated and compared to the measurements. The branch fading and the fractal dimension of simulated lightning are also discussed. The simulations show how the proposed model simulates the lightning in an acceptable manner.