In this work, the authors have studied the interaction between electromagnetic fields which are generated by lightning and overhead line in electrical power system. For this study, the authors constructed a system of equations. In which the network topology; with all its elements (linear or not) and wave exciter lightning are taken into account. This analysis is developed in time from the general equations of transmission lines with second members, with consideration of the frequency dependence of the correction terms related to the impedance of a finite conductivity of ground as well as non-linearities loads. The simulation results presented in this study demonstrate the effectiveness of this analysis for the calculation of induced voltages generated by lightning on a grid of lines.