Probabilistic small-signal stability analysis of power systems based on Hermite polynomial approximation

Abstract

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

Keywords

• Probabilistic small-signal stability
• Polynomial approximation
• Hermite polynomial
• Chebyshev polynomial
• Eigenvalue analysis
• Monte Carlo simulation