Development of a Discrete Mathematical Model for Medium-Length Transmission Lines

This paper presents a discrete mathematical model of a three-phase medium-length transmission line. Initially, the model is composed of a system of differential equations for current, sending- and receiving-end voltage calculations. These equations have been written in Cartesian coordinate system, the use of which decreases their total number by one third, however, this also limits the implementation of the model for symmetrical conditions only. The model has been developed for the analysis of both transient and steady-state conditions. Based on this model, the discreet mathematical model has been proposed, in which the system of the differential equations have been replaced by a system of algebraic equations. Both algorithms have been developed using MATLAB. The accuracy of the results and computational time have been compared and evaluated. A numerical example with graphical results has been presented.