Application of the numerical inverse laplace transform to transition process-related problems in electrical circuits

When dealing with transition processes, electrical circuits are described by means of a set of integro-differential equations. The Laplace transform can be favourably applied to those equations. When looking for the inverse Laplace transform, two approaches are used: analytical and numerical. The numerical approach can offer more advantages when solving more complex cases in which the application of the analytical approach is much more complicated. Consequently, this paper will focus on the numerical solution of the inverse Laplace transform, while also looking with interest at the Gaver-Stehfest algorithm and the Dubner and Abate method. Application of the two methods will be illustrated at the example of simulated behaviour of a current transformer for protection against fault (short-circuit) in a distribution system. The obtained results will subsequently be compared with the analytical solution of the aforesaid example. The solution will be implemented in C++ language.