Harmonic Detection of Power Quality Based on Fractional-Order Memristive Hyperchaotic System

Fractional calculus has always been regarded as an ideal mathematical tool to describe the memory of complex systems and special materials. In this paper, firstly, a fractional-order voltage-controlled ideal memristor model is proposed. Secondly, by introducing the memristor into a five-dimensional chaotic system through state feedback, a fractional-order memristive hyperchaotic system is obtained. The phase diagrams and Lyapunov exponents are used to analyze its dynamic behaviors. It is found that the system has three positive Lyapunov exponents. Thirdly, the fractional-order terminal sliding mode controller is designed to control the chaotic system to the origin. Finally, a harmonic detection system is proposed based on a controlled fractional-order memristive hyperchaotic system. The detection system can detect the harmonic frequencies of power quality embedded in Gaussian white noise, and does not need to determine the critical chaotic state.