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.%该文以含励磁环节的分数阶四阶电力系统模型为对象,研究其动力学行为并加以同步控制.首先,固定系统参数,利用分岔图和最大Lyapunov指数谱计算系统产生混沌振荡的最低阶次.其次,以单变量法分别研究机械功率、阻尼系数和励磁增益的改变对系统动力学行为的影响,通过数值仿真绘制系统随参数变化下的分岔图、Lyapunov指数谱等,选取不同的系统初值,研究同一系统在不同初值的情况下存在的多吸引子共存现象.最后,基于分数阶系统稳定性理论和非线性反馈控制理论,设计同步控制器实现系统混沌控制,数值仿真验证了所设计控制器的有效性.
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