Improved determination of Floquet's reference frame for the phase to ground short circuit of damped alternator

Abstract

The unsymmetrical short-circuit operation of a nonsalientpole alternator with dampers is described by four linear periodic coefficient equations. All periodic terms are at fundamental frequency. The equations are solved by indirect use of Floquet's theorem, allowing the time constants to be determined first. This determination is based on the fact that there exist recurrent relations for the current's harmonics, and it is shown in the paper that convergence of these recurrent relations for{pm}{infty}can be ensured only if the time constants fulfill a relationship which is one of the findings of the paper. Then, it is shown that a knowledge of the time constants and of the above-mentioned recurrent relations yields a convenient Floquet reference frame. Eventually there is no more difficulty to completely determine the currents from the initial conditions. A complete numerical example has been treated and the results of the present method tally with those yielded by a classical Runge-Kutta method.