Transient analysis of three-phase transmission lines with initial voltage and current distributions

An efficient numerical inverse Laplace transformation algorithm is proposed for the transient analysis of a three-phase transmission line with arbitrary initial voltage and current distributions (known as the initial conditions) on the line. We apply the Laplace transformation to the transmission line terminals which account for the initial conditions. The distributed nature of the transmission line makes the two-port admittance matrix and the current generators irrational functions of the complex frequency, which can be approximated by the Taylor series expansions. The phase voltages and phase currents on the transmission line can then be obtained as rational functions of the complex frequency. The numerical inverse Laplace transformation can be applied to obtain the time domain waveforms.