Formulation of the Field-to-Transmission Line Coupling Equations in Terms of Scalar and Vector Potentials

More than 60 years ago, Prof. S. Rusck introduced a coupling model to take into account the interaction of lightning-generated electromagnetic fields with overhead power transmission and distribution lines. The model which assumes that the ground is perfectly conducting has served the power system research community for many decades. Recently, it was found that this model is not complete because some of the forcing terms in the relevant transmission line equations, which are based purely on the scalar and vector potentials, were missing. In the present paper, the correct transmission line equations pertinent to the interaction of external electromagnetic fields with overhead lines, described in terms of scalar and vector potentials, are derived by incorporating the effects of a finitely conducting ground. The model presented in this paper can be considered as a correction and an extension of the Rusck model to account for a finitely conducting ground.