Along with expanding power systems, stochastic factors affecting the performance of these systems have increased. Uncertainties due to successive changes in the load power are one of the mentioned factors. These random changes have made the methods of uncertainty analysis particularly important in the analysis of power systems stability. This paper propose a probabilistic small-signal stability analysis method based on polynomial approximation of eigenvalues. Since the correct determination of unknown coefficients has a direct effect on the accuracy of the polynomial approximation method, this paper presents a method that can determine the mentioned coefficients, with more coverage on the probabilistic input domain of the problem. With increasing the number of random input variables, the proposed method can continue to maintain its efficiency. After determining the unknown coefficients, the load flow results and the system state matrix are determined for random changes of all loads based on the Hermite polynomial approximation. Then, the small-signal stability of the system is probabilistically evaluated based on a stochastic analysis of eigenvalues in the system. The consistency and validity of the proposed method are demonstrated based on the simulation studies in the MATLAB® software environment. In the simulation studies, the performance of the proposed method is examined by comparison with the Monte Carlo and Point Estimation methods, for the 14-bus IEEE test system.

随着电力系统的扩大，影响这些系统性能的随机因素也增加了。由于负载功率的连续变化引起的不确定性是上述因素之一。这些随机变化使得不确定性分析方法在电力系统稳定性分析中显得尤为重要。本文提出了一种基于特征值多项式逼近的概率小信号稳定性分析方法。由于未知系数的正确确定对多项式逼近方法的精度有直接影响，本文提出了一种可以确定上述系数的方法，对问题的概率输入域有更多的覆盖。随着随机输入变量数量的增加，所提出的方法可以继续保持其效率。在确定未知系数后，基于 Hermite 多项式近似确定所有负载的随机变化的潮流结果和系统状态矩阵。然后，基于系统中特征值的随机分析，对系统的小信号稳定性进行概率评估。基于 MATLAB® 软件环境中的仿真研究证明了所提出方法的一致性和有效性。在仿真研究中，针对 14 总线 IEEE 测试系统，通过与蒙特卡罗和点估计方法进行比较来检查所提出方法的性能。系统的小信号稳定性基于系统中特征值的随机分析进行概率评估。基于 MATLAB® 软件环境中的仿真研究证明了所提出方法的一致性和有效性。在仿真研究中，针对 14 总线 IEEE 测试系统，通过与蒙特卡罗和点估计方法进行比较来检查所提出方法的性能。系统的小信号稳定性基于系统中特征值的随机分析进行概率评估。基于 MATLAB® 软件环境中的仿真研究证明了所提出方法的一致性和有效性。在仿真研究中，针对 14 总线 IEEE 测试系统，通过与蒙特卡罗和点估计方法进行比较来检查所提出方法的性能。