Bifurcation analysis of three-phase ferroresonant oscillations in ungrounded power systems

The study of power networks prone to ferroresonant oscillations by means of simulation turns out to be a tedious task. Therefore, a direct calculation of the stability domains of the various oscillation modes is preferable. In this paper, the software package AUTO is used to determine the periodic solutions of the differential equations describing a typical three-phase network in which ferroresonance has occurred. A small modification of the system equations is introduced to approximate the quasi-periodic oscillations by periodic ones, without major impact on the position of the stability domains. Finally, an example of the automated dimensioning of a damping circuit using a continuation scheme is presented.