Lightning-Induced Voltages on Transmission Lines Over a Lossy Ground—An Analytical Coupling Model Based on the Cooray–Rubinstein Formula

Space-time closed-form expressions for the vertical-electric-dipole-induced Thévenin-voltage responses on a transmission line above a lossy ground are derived analytically. The problem is formulated via the electromagnetic reciprocity theorem of the time-convolution type and subsequently solved with the aid of the Cooray-Rubinstein formula and the Cagniard-de Hoop method. It is demonstrated that the obtained results are readily applicable to calculating lightning-induced voltages on overhead transmission lines over a finitely conducting ground.