Modeling subharmonic and chaotic ferroresonance with transformer core model including magnetic hysteresis effects

Ferroresonance is a highly destructive power quality phenomenon caused by complex oscillations generated by nonlinear magnetizing inductances in ferromagnetic materials and capacitive elements in power systems. In an effort to better understand ferroresonance and predict bifurcations and responses, an improved nonlinear transformer model for dynamic and steady-state operating conditions is developed which includes magnetic hysteresis nonlinearities of the transformer core. The model expands on Tellinen’s scalar hysteresis approach which includes major and minor hysteresis loop effects. This paper carries out an investigation into single-phase transformer ferroresonance initiated by switching transients using the developed model. A range of ferroresonance modes (e.g., subharmonic and chaotic) initiated by switching transients is identified with the transformer core model. The model is used to compute time-domain waveforms of transformer flux, voltage and magnetizing current for several ferroresonance modes. Furthermore, Poincaré and phase-plane portraits are used to examine the stability domain of observed ferroresonance modes. The main contribution of this work is a new analysis into ferroresonance through an improved transformer model which incorporates magnetic hysteresis effects. Key–Words: Chaos, ferroresonance, hysteresis model, nonlinear dynamics, Poincaré, power quality, transformer.