Modeling ferroresonance in asymmetric three-phase power transformers

Ferroresonance is a highly dynamic and nonlinear power quality phenomenon notorious for causing severe damage to power systems. The nonlinear inductances in ferromagnetic materials (e.g., transformer core structures) and power system capacitances can sometimes lead to oscillatory ferroresonance modes with large over-voltages and distortions. Largely neglected in system studies is the interaction of ferroresonance with multi-legged three-phase transformer cores, especially with respect to the asymmetric magnetic cross-coupling effects. This paper investigates such nonlinearities by employing a suitable duality-based time-domain model of an asymmetric three-phase nonlinear transformer. The impact of system capacitances and open-phase behavior (e.g., single-phase circuit breaker operation) are analyzed. The seemingly innocuous action of unbalanced switching is shown to cause a wide variety of ferroresonance modes. For a better understanding of the dynamics and stability domain of ferroresonance in asymmetric transformers, bifurcation and phase-plane analysis techniques are applied in this work.