An Effective Method for Fast Evaluation of Lightning-Induced Voltages on the Overhead Transmission Lines Combining Electromagnetic Topology and Matrix Pencil Method

In this article, an effective method combining electromagnetic topology (EMT) and matrix pencil method (MPM) for the fast evaluation of the lightning-induced voltages on the overhead transmission line (TL) is proposed. First, the EMT of the TL network is established based on the structure characteristic of the TL network and the scattering hypermatrix is constructed according the information of the junctions and terminal loads. Then, the piecewise sampling is performed for the spectrum of lightning signal, and the calculation of the lightning electromagnetic fields (LEMFs) of all observation points along the TL at the sampling frequency point is accomplished. Next, the supervector of the excitation source is constructed to realize the generation of the Baum-Liu-Tesche matrix equation, and the results of the lightning-induced voltages of all junctions on the TL network at the sampling frequencies are obtained. Finally, the lightning-induced voltages at all frequencies are obtained by using MPM to fit the sampled results, and the time-domain results can be generated by inverse fast Fourier transform (IFFT). In the proposed method, the LEMFs above the lossy ground are solved by the C-R formula and those below the lossy ground are calculated by the Cooray formula. Moreover, the feasibility of using EMT to analyze the lightning-induced voltages of the junctions on the TL network and adopting MPM to fit the sampled values of the lightning-induced voltages is verified. The correctness and efficiency of the proposed method are validated and proved by several numerical examples.