Detection and analysis of hidden and isolated subharmonic ferroresonant solutions in power systems

Abstract

This thesis is concerned with the existence and evolution of subharmonics when ferroresonance occurs in a power system The existence problem is addressed using two basic approaches i unearthing the hidden solutions in the unstable segments in the fundamental solution continuation path and ii detection of isolated solutions by continuation of steady states obtained newlinefrom temporal bifurcation diagram To the author s knowledge these approaches have not been applied by the early investigators Further analysis of subharmonic solutions and stability are carried out using a hybrid approach and tools of nonlinear dynamics The hybrid approach is the unification of conventional time domain and continuation approaches In the course of investigation of hidden solutions abnormal solutions such as subharmonic quasi periodic and banded chaotic are encountered The bifurcations that occur include period doubling period halving cyclic fold pitchfork and Neimark Sacker Practically analysis of hidden subharmonic is relevant when a normally operating system drifts to an unstable region due to varying system conditions Once in the unstable region it can lock into a subharmonic or quasi periodic or chaotic ferroresonant state newline