A Comparison of Techniques for State-Space Transient Analysis of Transmission Lines

This paper reviews and compares several methods to analytically obtain the transient response of transmission lines in the time domain, in those cases where frequency independent parameters can be assumed. The distributed-parameter line is modeled by the cascaded connection of a number of lumped-parameter circuits, each one representing a fraction of the line length, leading to a linear time-invariant (LTI) circuit. The associated state-space equations are formulated, allowing explicit expressions for the state variables to be written in the time domain. The solution is then obtained by means of three different approaches, all of them requiring that the natural frequencies be previously computed, namely: eigenvector-based procedure, Vandermonde matrix method, and Lagrange interpolation formula. Numerical integration by the trapezoidal rule is also considered for comparison. Two kinds of test results are presented. First, accuracy of the results provided by the LTI lumped-parameter model are compared with those obtained using the Electromagnetic Transients Program. Second, a comparison is performed in terms of the computational cost involved in each method. Two cases of practical interest are assessed, namely solving from scratch the state equations and updating the solution for a new set of initial conditions.