Classification of chaotic ferroresonant oscillations in voltage transformer with applying nonlinearmodel for core loss

In this paper a new method for classification of different types of ferroresonantoscillations modes is introduced. Using this method, ferroresonant modes such as harmonic,subharmonic, quasi periodic and chaotic modes are characterized and using multiple scalesmethod chaotic behavior and types of fixed points in occurrence of ferroresonance in voltagetransformer with considering a nonlinear core loss model is analyzed and investigated. It isproved that ferroresonance phenomenon in voltage transformer can be classified in chaoticdynamics systems. In this contribution chaos occurs in system from a sequence of period doublingbifurcation (PDB). This phenomenon includes different types of bifurcations such as perioddoubling bifurcation (PDB), saddle node bifurcation (SNB), hopf bifurcation (HB) and chaos.Analysis of dynamics of ferroresonant circuit is carried out using bifurcation theory. For this workbifurcation diagrams and phase plane diagrams are drawn using a continuation method for linearand nonlinear core loss models, lyapunov exponents are gained using multiple scales method andfeigenbaum number are used. Bifurcation diagrams show with changing parameter of control andits increasing chaos occur in system. Border collision is shown in bifurcation diagrams.

Classification of chaotic ferroresonant oscillations in voltage transformer with applying nonlinearmodel for core loss Keywords:

Ferroresonant oscillations , chaos theory , Period doubling , Subharmonic mode , Poincare map , Bifurcation diagram