An Efficacious Computational Procedure to Solve Electromagnetic Transients on Transmission Lines Represented by State Equations

Abstract

This work presents an analytic solution to evaluate electromagnetic transients on transmission lines. Several papers apply a line modeling by lumped parameters and state space representation due the relative facility implementation and accuracy over considerable frequency rage. Although the efficacy and precision of transients simulations is intrinsically attached to the methodology applied for resolution of state equations which represent these phenomena. Therefore the current work describes a procedure to solve the state equations based on matrix diagonalization and Eigensystem-Based Solution for state equations. This procedure is compared to results obtained by well known numerical solution of Trapezoidal Rule and to results obtained by EMTP. The transients are evaluated considering a variable integration step Delta t and from this procedure, the proposed solution proves to be greatly robust, numerically stable and more efficient than the widely applied Trapezoidal Rule. The transmission line modeling applied in the proposed analyses takes into account the variation of longitudinal parameters in function of frequency and then it is inserted in a cascade of pi circuits through the synthesis of a rational function F(omega), this method is entitled as Vector Fitting and also described by this paper.