中文摘要：

电力系统是一个存在着诸多随机扰动的非线性系统。近年来电力行业的发展引起电网产生更多的随机因素,传统的确定型系统分析方法已不能满足要求。因此,在电力系统随机扰动特征分析的基础上,将随机系统的思想和方法应用于电力系统,建立电力系统更精确的数学模型,分析系统的稳定性具有重要的理论与应用价值。针对外部随机激励的非线性系统,构建了含随机扰动的非线性系统模型,证明了在随机小扰动下电力系统的均值稳定性和均方稳定性。对新英格兰10机39节点系统,利用Euler-Maruyama（EM）算法进行模拟计算,对不同随机激励强度下的响应轨迹进行分析,通过仿真结果验证电力系统稳定性理论的正确性。

英文摘要：

Power system is a nonlinear system with many random disturbances. In recent years, the development of electric power industry has caused more and more stochastic factors of the network. The traditional deterministic analysis methods can no longer meet the requirements. Therefore, it has important value of theory and application to apply the thought and method of stochastic system to power system by full analysis of the random disturbance characteristics of power system, and to establish more precise mathematics model of power system and analyze stability of power system. Aimed at external random excitation, the model of non-linear system with random disturbance was constructed and the result that the system is mean stable and mean square stable under stochastic small disturbance was proved in this paper. Euler-Maruyama （EM） algorithm was used to simulate the stability of new England 10 generator 39 bus system, the response trajectories under different random excitation intensity were analyzed, and the stability theory of 15ower system was validated by the simulation results in this paper.