考虑高斯激励的多机电力系统的p阶随机稳定性分析

P-Moment Stochastic Stability Analysis of Multi-machine Power Systems Under Gaussian Excitation

随着大规模、高比例新能源并网发电,电力系统的稳定运行受到了显著的影响。在传统随机稳定性研究的基础上,考虑随机激励下的多机电力系统的p阶稳定性。首先利用随机微分方程理论和扩展等面积法将随机激励下的多机电力系统等效为双机系统,同时对等效模型以及原多机模型进行线性化处理,将单机无穷大系统的p阶稳定性判据推广到多机系统的p阶稳定性。然后以四机两区系统为例,通过Euler-Maruyama数值方法对系统的功角、转速等随时间变化的趋势进行仿真分析。最后利用蒙特卡罗方法,对等效转换前后系统的功角的概率密度函数曲线进行模拟,由于概率密度曲线没有发生显著变化,因此等效转换前后系统的p阶稳定性没有发生改变,从而可以将单机无穷大系统的p阶稳定性推广到多机系统的p阶稳定性。

With growing new energy connected to the grid in large scale,the stability of power system has been challenged.Based on the traditional studies on stochastic stability,this paper studied the p-moment stability of multi-machine power systems under random excitation.Firstly,the stochastic differential equation theory and the extended equal-area method were applied to equilibrate the multi-machine power system under random excitation to a two-machine system.Meanwhile,the equivalent model and the original multi-machine model were linearized and homogenized,thereof extending the p-moment stability from single-machine infinite system to multi-machine systems.Secondly,based on a four-machine two-area system,this paper made use of the Euler-Maruyama numerical method to simulate the trend of the power angle and the diachronic rotation speed of the system.Finally,this paper took Monte Carlo method to simulate the probability density function curve of the power angle of the system before and after the equivalent conversion.This paper finds that the p-moment stability of a single-machine infinite system can be extended to the p-moment stability of a multi-machine system for the fact that since the probability density curve does not change significantly,the p-moment stability of the system before and after the equivalent conversion does not change.