互联电力系统的Adomian分解法求解及其混沌特性分析

Solution of the interconnected power system based on Adomian decomposition method and its chaotic characteristic analysis

利用Adomian分解法研究了一个互联电力系统,给出了其近似解析解。根据近似解析解,通过MATLAB仿真分析了互联电力系统的混沌特性,给出了不同周期负荷扰动下的分岔图和相平面图。仿真结果表明,在受到较大的周期负荷扰动时,系统将会出现混沌振荡。最后,在不同的时间步长下,对比了Adomian分解法和四阶Runge-Kutta法的数值解。对比结果表明Adomian分解法不仅精确度更高、计算时间更少,而且收敛速度更快。

The approximate analytical solution of an interconnected power system has been studied by using the Adomian decomposition method（ ADM）. Bifurcation diagram and phase diagram under different periodic load disturbance,chaotic characteristics of the system are studied by the MATLAB simulation based on the interconnected power system. Simulation results indicate that the chaotic oscillation of system will occur under a comparatively large periodic load disturbance. Finally,comparisons between the decomposition solutions and the fourth-order Runge-Kutta（ RK4）numerical solutions are made for various time steps. Results show that compared with the RK4,Adomian decomposition method not only yields more accurate results and needs less calculation time,but also can improve the convergence speed.