Computation of transient profiles along non-uniform transmission lines using the numerical Laplace transform

This paper describes a method in the frequency domain to compute voltage and currents at interior points of a non-uniform multiconductor transmission line during electromagnetic transients, including the effect of time-dependent elements (such as switches). The non-uniformities of the line are incorporated into the model by means of the cascaded connection of chain matrices. This technique subdivides the transmission line into several smaller line segments (chain matrices), each one with different electrical parameters, allowing to simulate the change in parameters along the line. The inclusion of time-dependent elements is done by means of the principle of superposition, where each switching maneuver (or any change in the network topology) is treated as an initial condition problem. The numerical Laplace transform is used to transform the frequency domain solutions to the time domain, where they can be easily analyzed. In order to validate the accuracy of the method presented in this paper, two test cases are presented and the results are compared with those computed with ATP simulations.