Compact Matrix Formulation for Calculating Lightning-Induced Voltages on Electromagnetic Transient Simulators

In this paper, a compact matrix formulation that simplifies the calculation of the lumped sources necessary to estimate lightning-induced effects using transmission line models available in electromagnetic transient programs is proposed. As opposed to an existing solution strategy that requires the sequential calculation of the convolution integrals involving the horizontal component of the incident electric field along multiple segments along the line, the proposed matrix solution allows such convolutions to be performed at once. This not only increases the model efficiency, but also simplifies the assembly of the solution in matrix-oriented simulation tools. The equations are described in both phase and modal domains, with formulations that are compatible with the universal line model and the frequency-dependent transmission line model proposed by Marti. It is shown that both formulations can be accurately used for calculating lightning-induced voltages on overhead lines.