Harmonic balance based bifurcation analysis of three-phase ferroresonance with full scale experimental validation

The determination of ferroresonant oscillations in circuits with voltage transformers is a highly nonlinear problem due to the possible core saturation. It is achieved with an algorithm based upon the harmonic balance method in the frequency domain. Advantages over a time domain description are discussed. Branches of solutions in relevant parameter planes can be continued beyond bifurcation points and lead to a better understanding of the stability domains of the periodic ferroresonant oscillations. The method has been extended to the study of quasi-periodic oscillations by approximation models. The theoretical principles are validated on a full scale three-phase 15 kV configuration with ungrounded neutral, in which fundamental, subharmonic and quasi-periodic oscillations are initiated by controlled current pulse injections. Experimental stability limits have been determined and yielded good agreement with the theoretical ones. The limit value of the damping resistor in the delta-connected tertiary windings of the transformers is determined by the presented method.