A new formalism for the analysis of electromagnetic coupling between the lightning and a complex network of lines or cables

In this paper we propose a new formalism for the analysis of electromagnetic coupling between the lightning wave and a complex network of lines or cables. This approach allows obtaining induced currents and voltages directly on the all network nodes (junctions and extremities). For this objective we represent the lightning wave by current generators. Then by using a mathematical formulation based on the topological analysis of a network, we deduce a linear matrix equation which resolution leads directly to the induced currents and voltages. In order to confirm our theoretical work, we present some applications that allow validating this formalism.