Abstract
We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.
Highlights
Smart grid holds the promise that the power sector can go “green” by taking more aggressive measures to lower the carbon dioxide (CO2) emissions through efficient integration of renewable energy sources [1, 2]
Chaos suppression in fractional order brushless DC motor using sliding mode controllers [19] and fractional order permanent magnet synchronous motor, pi controlled induction motor by extended back stepping control [20], and fractional order PMSM motors with adaptive nonlinear controllers [21] is earlier investigated in the literatures
Motivated by the above discussions, in this paper we propose a chaos control scheme for a fractional order smart grid model with fractional order adaptive sliding mode controllers (FOASMC) and genetically optimized fractional order PID controllers (FOGAPID)
Summary
Smart grid holds the promise that the power sector can go “green” by taking more aggressive measures to lower the carbon dioxide (CO2) emissions through efficient integration of renewable energy sources [1, 2]. In chaos control of electrical systems fractional order controllers play an important role as larger Lyapunov exponents occur when fractional orders are close to “1” [19,20,21]. Chaos suppression in fractional order brushless DC motor using sliding mode controllers [19] and fractional order permanent magnet synchronous motor, pi controlled induction motor by extended back stepping control [20], and fractional order PMSM motors with adaptive nonlinear controllers [21] is earlier investigated in the literatures. Motivated by the above discussions, in this paper we propose a chaos control scheme for a fractional order smart grid model with fractional order adaptive sliding mode controllers (FOASMC) and genetically optimized fractional order PID controllers (FOGAPID). Fractional order adaptive sliding mode (FOASM) controllers and genetically optimized fractional order PID controllers are proposed to suppress the chaotic oscillations. The proposed GAFOPID controllers are implemented in FPGA to show that the proposed control scheme is hardware realizable
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