A method for computing electrical transients of transmission lines by numerical laplace transform

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Abstract
This paper proposes a numerical method of solution for the transient phenomena on transmission line terminated by simple load, including a nonlinear element. The method is based on the discrete numerical Laplace transform and its inverse, utilizing the discrete Fourier transform. Problems and the solutions in the method are discussed. The feature of the method is that the voltage, current and surge impedance matrix of the transmission line are specified on the complex frequency (s) plane, while the boundary condition is given on the time (t) domain. Numerical solutions in the two regions are combined by Laplace transform and its inverse. The Laplace transform and its inverse by discrete Fourier transform have a drawback in that the accuracy of the computation deteriorates at t = 0 for stepwise change of the waveform. A method to solve this problem is described. For the latter half of the sampling point sequence in the Laplace and inverse transforms, the computation error is increased, which effectively halves the sampling points in the computation of the reflected wave. For this problem, a method is presented by which the accuracy of the computation is retained for each calculation of the reflected wave, keeping constant the number of sampling points. The convolution required in the calculation of the boundary condition is time‐consuming, and a solution for this is proposed. As an example of the solution, the transient phenomenon in the multiconductor transmission‐line terminated by the surge arrester is calculated, taking the skin effect into consideration.

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