Alternative method to include the frequency-effect on transmission line parameters via state-space representation

Abstract

This article describes an alternative method and investigates its performance on the transient responses considering a frequency-dependent lumped parameter model (FDLPM) to represent the transmission line (TL) in the literature. This model includes the fundamental behavior of the frequency dependency on longitudinal parameters, and it is developed directly in the time domain (without the use of frequency-to-time conversion tools). The alternative method individually solves a system of state-space equations for each π circuit of the LPM. Consequently, this method reduces the order of the state-space matrices, providing excellent performance associated with lower computational efforts (faster speed) compared to that obtained with the classical method. The alternative method was used to calculate the electromagnetic transients (current and voltages) in the single- and three-phase transmission lines subjected to energization maneuver and lightning strike for several scenarios at the receiving end. All responses are calculated using a programming code in MATLAB®. Results demonstrated that the alternative method closely follows the responses calculated with the classical, indicating its excellent accuracy. Besides, the smaller dimension of state-space matrices lead to low computational times, varying from 230 to 300 times smaller, depending on the line configuration compared to the other method, assuming the same fixed time step.