Lightning electromagnetic field coupling to overhead power distribution lines

In this work we study the coupling of a lightning wave with an overhead power distribution lines. The study is led directly in the time domain with hold in account of the effect of a finite conductivity of the soil. By the classic method poses a problem of digital heaviness linked to the spatial discretization and taking into account the electrical conditions at the ends of nodes and connections. The formalism that we propose overcomes the spatial discretization taking into account the electromagnetic aggression along each conductor and the electrical conditions at the ends allowing us to deduce the currents and voltages induced in every node of the line directly. After discretization by the method so-called FDTD (Finite Difference Time Domain) of the lines equations excited by a lightning wave and the application in every node of the network of the Kirchhoff's laws in current and voltage, we deduct a equations system linear or no, of which the resolution permits us to deduct the induced electric quantities in every node of the network. In this study we propose a concept for the coupling analysis of a lightning wave with an overhead line without use of the least FFT. In order to confirm our theoretical work, we present a set of applications that allows validating this study.