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Abstract This paper proposes a probabilistic small-signal stability analysis method based on the polynomial approximation approach. Since the correct determination of unknown coefficients has a direct effect on the accuracy of the polynomial approximation method, this paper presents a method for determining these coefficients, with high coverage on the probabilistic input domain of the problem. In this method, by 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 stochastic analysis of the system eigenvalues. 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 Point Estimation, Cumulant, Monte Carlo, and Chebyshev polynomial-based methods, for IEEE 14-bus and IEEE 39-bus test systems. Article highlights Probabilistic small-signal stability analysis of power systems Modeling of governing equations of power system based on Hermite polynomial approximation Forming the Collocation matrix based on a robust method

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.