A Polynomial Chaos-based Approach to Quantify Uncertainties of Correlated Renewable Energy Sources on Voltage Regulation

Abstract

Assessing the impacts of uncertainties on various power system operations has become a key factor for modern power grids. Renewable energy sources (RESs) have introduced significant uncertainties especially in electric power distribution systems. Although several probabilistic methods have been used for quantifying uncertainties such as Monte Carlo simulation and perturbation techniques, they usually have high computational time. In addition, the existence of more than one source of randomization requires deep understanding of the correlation between them via intensive statistical approaches. This paper proposes a Generalized Polynomial Chaos (gPC)-based approach to quantify the impacts of uncertainties resulting from RESs on voltage magnitudes of distribution systems. The gPC has been used to propagate uncertainties in the transmission system. In the gPC, the behavior of each random variable is transformed into a series of orthogonal polynomials that can be easily evaluated. A correlation matrix is calculated and used to estimate the proper values of each RES. The proposed method is implemented on the IEEE-13 and IEEE-123 distribution systems integrated with solar energy and wind energy at various locations. The results show that the proposed algorithm provides high efficiency and significant reduction in computation time in comparison with Monte Carlo simulation.