Chaotic oscillations control in the voltage transformer including nonlinear core loss model by a nonlinear robust adaptive controller

In this paper, control of chaos is done in presence of ferroresonant oscillations in a voltage transformer with nonlinear model of core losses. In order to control the chaotic oscillations, nonlinear adaptive approach is employed. Moreover, a Time Delay Feedback Controller (TDFC) is implemented to stabilize Unstable Periodic Orbits (UPOs). Also multiple scales method to analyze chaotic behavior and types of fixed points in ferroresonance occurrence at voltage transformers considering different types of core loss models is applied. In the literature ferroresonance phenomenon in voltage transformers is proved to be classified in chaotic dynamics systems. In this contribution, chaos occurs in the system from a sequence of Period Doubling Bifurcation (PDB). This phenomenon consists of different types of bifurcations such as Period Doubling Bifurcation (PDB), Saddle Node Bifurcation (SNB), Hopf Bifurcation (HB) and chaos. Dynamic analysis of ferroresonant circuit is performed using bifurcation theory. bifurcation diagrams and phase plane diagrams are illustrated using a continuation method for linear and nonlinear core loss models. For analyzing ferroresonance phenomenon, Lyapunov exponents are calculated using multiple scales method and feigenbaum numbers are obtained. Bifurcation diagrams illustrate variation of parameter control and as a result chaos is created and increased in the system.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► To control the chaotic oscillations, the nonlinear adaptive approach is employed. ► This control method does not depend on the states and model of system. ► Because of model uncertainties the robust stabilization is considered. ► Using Adaptive control method, chaotic behavior of voltage transformer is removed. ► Multiple scales method to analyze chaos in ferroresonance occurrence is applied.