Frequency domain analysis of a power transformer experiencing sustained ferroresonance

Most transformer finite-element electromagnetic analysis is performed in the frequency domain (with an implicit sinusoidal variation of flux, current and voltage), since the calculation of the transient time-domain solution, particularly of multiple cases or conditions, is currently restricted by the conventional computational power (especially in three dimensions). At high levels of saturation, though, core flux can be very non-sinusoidal. Where sinusoidal conditions do not hold, for example ferroresonant currents, a time-domain solution is normally indicated; however, this article discusses an alternative methodology for periodic modes of sustained ferroresonance, which can be facilitated in the frequency domain. Specifically, the problem is approached by considering the ferroresonance excitation waveforms as a harmonic series. It is demonstrated that the basic frequency of a sustained resonance condition not only contributes to the overall saturation but also controls the way the core moves into and out of saturation. All the other frequencies contribute to the extreme of core saturation. The proposed method is validated through ferroresonance field test recordings.