Bifurcation, Chaos and its Control in A Fractional Order Power System Model with Uncertainties

Abstract

The paper investigates the complex nonlinear behavior of a fractional order four dimension power system (FOFDPS). The discrete mathematical model of the FOFDPS is derived and presented. The equilibrium points along with the Eigen values of commensurate and incommensurate FOFDPS are presented. The existence of chaotic oscillations are supported by a positive Lyapunov exponent. Bifurcation plots are derived for both parameters and fractional orders to show the impact of the same on the dynamic behavior of FOFDPS. Having shown the existence of such complex behaviors in the FOFDPS, we present an adaptive fractional order sliding mode control (FOASMC) to suppress the chaotic oscillations. Numerical results are presented to support the theoretical results.