Alternative method using recursive convolution for electromagnetic transient analysis in balanced overhead transmission lines

Abstract

This study proposes an alternative method to calculate the transient responses of multi-conductor overhead transmission lines based on ABCD representation, recursive convolutions and numerical method for rational approximation in the frequency-dependent curves. In the classical universal line model, the characteristic admittance matrix Y c ( ω ) and propagation matrix H ( ω ) are represented by rational functions. In H ( ω ) , previous and correct identification of the modal travelling times is required. However, these modal travelling times are estimated numerically, which do not offer good accuracy in some cases. This fact has a considerable effect on the rational representation of H ( ω ) itself and consequently on the transient responses. In the alternative method, a previous estimation of the modal travel times is unnecessary because when using the ABCD representation for each propagation mode, a direct relation exists between the currents and tensions of the receiving and sending ends. These relationships are fitted by smooth rational functions, and then, using recursive convolution methods, the authors obtain the explicit equations of the currents and voltages to calculate the transient responses. The results demonstrate that the alternative method is accurate when compared with the frequency-domain solution of the transmission line transformed to the time domain using the numeric Laplace transform and with the Bergeron method.