含电磁功率扰动的分数阶电力系统混沌分析与同步控制

混沌振荡是电力系统的固有现象,当系统运行情况变得复杂时,整数阶互联系统模型已无法满足研究要求. 本文提出了一个简单的含电磁功率扰动的分数阶互联电力系统模型,利用分岔图、李雅普诺夫指数谱、庞加莱截面等分析系统产生混沌振荡的最低阶次. 通过改变电磁功率扰动幅值和频率因子,观察到系统由倍周期分岔通往混沌直至功角失稳,并导致系统崩溃. 同时,采用双参数分析法对系统的周期运动、混沌和功角失稳详细划分与分析,由于功角稳定性被破坏前并没有明显的迹象,但会出现分岔和混沌行为,若能对混沌运动进行控制,就可以避免功角失稳对系统造成的巨大危害. 最后,设计一种符合该系统稳定性要求的非线性控制器,实现分数阶互联电力系统的同步控制,仿真结果证明了控制方法的有效性,为电力系统的安全稳定运行提供了依据.

Chaotic Analysis and Synchronization Control of Fractional OrderPower System with the Disturbance of Electromagnetic Power

Chaotic oscillation is an inherent phenomenon of nonlinear power system. However,when the operation conditions in power system become complicated,the integer-order system models have not fully met the demands of research needs. In this paper,the basic dynamic properties of the fractional-order power system are investigated with the disturbance of electromagnetic power through the bifurcation diagram,Lyapunov exponent spectrum and Poincaré section. In the case of fractional-order power system,the lowest order at which chaos exists is observed. With the disturbance amplitude of electromagnetic power and the frequency factor varying,this power system shows rich dynamic behaviors characterized as period-doubling bifurcation transferring to chaos and angle instability. Based on the double parameters mapping,the regions are divided into the domains of periodic motion,chaos and angle instability. Due to the route to chaos appearing before the angle instability,the control method which can eliminate the chaos should be designed to avoid the harm of angle instability in power system. Therefore,a nonlinear controller which meets the stability requirement is designed to realize the synchronization of the fractional-order chaotic power system. Simulation results verify the effectiveness of the proposed methods,and provide theoretical references for the secure and stable operation of power system.