Existence and stability analysis of ferroresonance using the generalized state-space averaging technique

Abstract

Ferroresonance can induce an undesired over-voltage often accompanied with a phase reversal which can damage power distribution transformers and motors and cause injury to the system operators. Similarly, under some conditions, power distribution transformers can excite subharmonic frequencies which in turn can damage the transformer winding and loads connected to the grid lines. While present analysis tools are based on analytical or experimental investigations, no rigorous systematic way exists to analyze ferroresonance and subharmonic problems in power distribution transformers. The purpose of this thesis is to develop a systematic methodology to study ferroresonance and subharmonic problems in power distribution transformers, particularly, their existence, stability, and bifurcations. The methodology proposed for studying the ferroresonance problem is the generalized state-space averaging technique. Both single-phase and three-phase ferroresonance are considered. Appropriate models are developed for the single phase and three-phase power distribution transformers which are suitable for the study of the ferroresonance problem, i.e, low frequency models. The theory of the incremental-input describing function is revisited and a subtle flaw in the formulation of the theory is modified to address the stability of general systems, particularly at synchronous frequency. A generalized Nyquist criterion is presented to assess the stability of the periodic solutions. The modified incremental-input describing function theory is applied to single-phase ferroresonance systems.