Laplace-based computation of transient profiles along transmission lines including time-varying and non-linear elements

In this paper, a combination of a transmission line model defined in the q-s domain (spatial frequency-temporal frequency), the two-dimensional Laplace transform and the principle of superposition is applied to compute transient voltage and current profiles along transmission systems including time-dependent and non-linear elements. The detailed internal information provided by these profiles can be very useful in applications such as insulation coordination design, fault detection and location. The method presented in this paper has significant advantages over the computation of transient profiles using EMTP-type software, given that the latter requires the subdivision of the line, which is time consuming and prone to numerical error accumulation. Additionally, since the line model is defined in the frequency domain, it is possible to include the frequency dependence of the electrical parameters in a very straightforward manner. In order to evidence the accuracy and versatility of the proposed method, several applications examples are presented, and the computed results are compared with those obtained using ATP.