Time-Window-Based Discrete-Time Fourier Series for Electromagnetic Transients in Power Systems

Abstract

This paper approaches the solution of electromagnetic transients in the frequency domain from the point of view of choosing a time window with sufficient width to allow the time constants of the transients to decay to a small value. This criterion, and the required maximum frequency content of the simulation, fully determine the simulation parameters. Satisfying this criterion, a very simple methodology, like the discrete time Fourier series (DTFS), can provide very accurate results without the inherent difficulties of time-warping solutions based on the numerical Laplace transform (NLT). Even though the NLT can give very accurate results, it requires expert knowledge to correctly specify the damping factors, sampling schemes, and windowing functions. The DTFS solution is compared with the NLT and with analytical solution for a circuit with lumped elements, and with the most-accepted frequency-dependent transmission line models in the Electromagnetic Transients Program: the JMARTI (fdLINE) model and the Universal Line Model for a double-circuit transmission line.