Modelling a positive lightning downward leader to study its effects on engineering systems

A mathematical model of a positive lightning downward leader is presented and its radiated fields calculated. The approach is based on the idea that a substantial similarity exists between lightning phenomena and the discharge in large airgaps. By assuming the discharge channel to be a long conductor and by using an LCR representation for a single conductor line (L, C and R being, respectively, the inductance, the capacitance and the resistance), a predictive model of the positive lightning can be developed enabling description of the evolution of the whole discharge. Taking into account some atmospheric conditions, the model enables the determination of the leader current and the corresponding charge, its propagation velocities, the potential drop along its channel, the power and energy injected into the gap, the leader and streamer lengths through its propagation and a trajectory of the discharge plotted in 3D in real time obtained from a probabilistic distribution. Furthermore, an application concerning the evolution of the radiated electric and magnetic fields of the leader is given. The results obtained are quite satisfactory.