Abstract
Discussing the dynamical properties of various power system models is of significant importance in order to understand its complete behavior. Even though there are many literatures discussing about the chaotic behavior shown by phase converter circuits, none of them have reported the hazardous phenomenon of multistability. In this paper, we derive the fractional-order model of a phase converter circuit and investigate its dynamics. Bifurcation of the system with the parameters and fractional order are investigated. A forward and backward continuation scheme is adopted to display various coexisting attractors; the property of multistability is also discussed. Using forward and backward continuation, various coexisting attractors and the property of multistability are discussed. Two different sliding mode controllers for controlling chaotic oscillations with model disturbances and parameter uncertainties are derived, and the effectiveness of the controllers is discussed with numerical simulations.
Highlights
The nonlinear dynamical systems are described using nonlinear differential equations and represented in state space
The system state in steady state can be defined by equilibrium point and by limit cycles in state space; when the system is subjected to aperiodic oscillations, the system can be in quasiperiodic or in chaotic state
A fractional-order phase converter circuit is derived from its integer-order mathematical model, and various
Summary
The nonlinear dynamical systems are described using nonlinear differential equations and represented in state (phase) space. Most of the power systems are composed of ordinary differential equations; the system state changes (drastic changes in current or voltage decreasing or increasing rate) lead to the nonlinear dynamical behavior and makes the circuit modeling complex [1]. This paper is aimed at analyzing the PCC system in its fractional-order form and proposing sliding mode controllers to suppress chaotic oscillations with external disturbances and parameter uncertainties.
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