Abstract
This paper has numerically studied the dynamical behaviors of a fractional-order single-machine infinite-bus (FOSMIB) power system. Periodic motions, period- doubling bifurcations and chaotic attractors are observed in the FOSMIB power system. The existence of chaotic behavior is affirmed by the positive largest Lyapunov exponent (LLE). Based on the fractional-order backstepping method, an adaptive controller is proposed to suppress chaos in the FOSMIB power system. Numerical simulation results demonstrate the validity of the proposed controller.
Highlights
Open AccessAs a mathematical branch with a history of over 300 years, fractional calculus and its applications to physics and engineering have attracted increasing attentions in recent years [1] [2]
We numerically investigate the chaotic dynamics of a fractional-order single-machine infinite-bus (FOSMIB) power system
With the proposed controller and adaptive law, the FOSMIB power system is asymptotically stable at the equilibrium point E2 ( π, 0)
Summary
As a mathematical branch with a history of over 300 years, fractional calculus and its applications to physics and engineering have attracted increasing attentions in recent years [1] [2]. Fractional calculus provides a good instrument to describe the memory, hereditary, non-locality and self-similarity properties of various materials and processes Many chaotic systems, such as Lorenz system [3], Chua’s system [4], Duffing system [5], Rössler system [6], Chen system [7] and so on, still remain chaotic when their equations become fractional. Sun and Li investigated the chaotic and bifurcation phenomena in a fractional-order three-bus power system and the existence of chaos was demonstrated for different orders [16]. We numerically investigate the chaotic dynamics of a fractional-order single-machine infinite-bus (FOSMIB) power system.
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