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Renewable energy sources (RESs) and flexible loads have introduced significant uncertainties in the operation and control of power systems especially voltage regulation at the distribution system level. Assessing the impacts of uncertainties on power system behavior and response has become a key factor for modern power system operation and planning. Although several probabilistic methods have been used for quantifying uncertainties such as Monte Carlo simulation and perturbation techniques, they are computationally expensive and cannot be directly embedded in power system models. Also, the existence of more than one source of randomization requires complicated correlation models via intensive statistical approaches. To overcome the aforementioned challenges, this article proposes a generalized polynomial chaos (gPC) based approach to quantify the impacts of uncertainties resulting from RESs and load variations on voltage magnitudes of distribution systems through propagating uncertainties in the system under study. 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 several systems including the IEEE 13-node, the IEEE 123-node, the 240-node, and the 8500-node distribution systems integrated with solar and wind energy sources 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.
Abdelmalak et al. (Sat,) studied this question.