Based on the four-order power system model, a fractional-order power system model with excitation model is presented in this paper and the dynamic properties of the fractional-order system are investigated and controlled. Firstly, the fractional-order power system of 4D is given and then the minimum order for existence of chaotic oscillation in power system with fixed parameters is achieved through bifurcation diagram and maximum Lyapunov exponent. Secondly, the influence of mechanical power, damping coefficient and excitation gain on system dynamics behavior is studied respectively. The bifurcation diagrams and Lyapunov exponent spectrum of the system are plotted through numerical simulations, respectively. In addition, the coexistence of attractors with different initial conditions in the same system is investigated. Finally, from the stability theory of fractional-order system and nonlinear feedback control theory, a synchronous controller of two power systems with different initials is designed, and numerical simulations show the effectiveness of the controller.
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