Fast Evaluation of Lightning-Induced Voltages on the Transmission Lines Above a Lossy Ground

To achieve the fast evaluation of the lightning-induced voltages on the transmission lines (TLs) above a lossy ground, the matrix pencil method (MPM) is adopted in this article to perform the fast calculation of the lightning electromagnetic field (LEMF). The feasibility of using MPM to accelerate the calculation of the LEMF is discussed and verified. For the observation point above a lossy ground, the Cooray–Rubinstein formula is selected to complete the calculation of the lightning horizontal electric field. For the observation point below a lossy ground, the Cooray method is adopted. Then, on the premise of considering the influence of ground impedance and admittance, the iterative expressions of the voltages and currents on the overhead TLs are derived. Moreover, for the TLs with periodic grounding properties, the iterative expression of the voltage at the node is analyzed according to Kirchhoff's law. Finally, the correctness and efficiency of the proposed method are verified by several numerical examples.