一个电力系统三阶模型的混沌与控制
Chaos and Control of a Third-Order Power System Model
摘要: 研究了电力系统三阶模型的动力学行为和控制问题。利用现有的电力系统三阶数学模型进行了数值仿真，得到了对应的微分方程组的分岔图、Lyapunov指数图、相图等，进而分析了系统参数的变化对系统动力学行为产生的影响，得到了系统在一定条件下会随着系统参数的变化出现Hopf分岔现象和混沌现象，通过计算系统的向量场散度，验证了系统是耗散的，并计算了系统的分维数。在出现混沌时，利用李雅普诺夫稳定性理论，分别给出了自适应控制和非线性反馈控制两种控制方案，此外讨论了某些参数未知时控制器设计方案。通过构造Lyapunov函数在理论上证明了三种方案可以使系统达到渐近稳定。最后对三种控制方案进行了数值仿真。
Abstract: The dynamical behaviors and control problems are investigated in the third-order model of power system. The bifurcation diagram, Lyapunov exponential diagram and phase diagram of the corre-sponding differential equations are obtained by numerical simulation using the existing third-order mathematical model of power system. Furthermore, the influences of system parameters change on the dynamic behavior of the system are analyzed, and the Hopf bifurcation and chaos phenomena occur with the change of system parameters under certain conditions. By calculating the divergence of a vector field of the system, the dissipation of the system is obtained, and the fractal dimension of the system is calculated. When chaos appears, two control schemes of adaptive control and nonlinear feedback control are presented, respectively, to verify the proposed control schemes by using Lyapunov stability theory. In addition, the controller design scheme is discussed when some parameters are unknown. By constructing Lyapunov function, it is proved theoretically that three schemes can make the system asymptotically stable. Finally, three control schemes are simulated numerically.
文章引用：华存, 刘辉昭. 一个电力系统三阶模型的混沌与控制[J]. 动力系统与控制, 2019, 8(3): 191-204. https://doi.org/10.12677/DSC.2019.83021

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