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When multiple uncertain resources (e.g., renewable energy and EV charging stations) are integrated into distribution systems, the uncertainties of correlated power supplies and demands pose a challenge for reliable grid operation. This challenge is compounded by the fact that this correlation cannot be modeled by standard pair copulas, e.g., Gaussian, Clayton, and Frank, as observed from the actual measurement data. To address these issues, this paper proposes a data-driven approach based on Gaussian Mixture Model (GMM) and Polynomial Chaos Expansion (PCE) for efficient grid impact studies with multiple correlated uncertain resources. The GMM is applied to segment these uncertain resources into multiple clusters, and the joint probability density within each cluster is approximated by multivariate Gaussian functions. The result is a feasibility for applying Gaussian Copula iteratively to handle the nonlinear correlation and the avoided construction of polynomial bases from arbitrary probability distributions for improved performance. Subsequently, the k-medoids clustering is utilized to strategically select experimental samples of PCE for the fast uncertainty quantification. The high efficiency and accuracy of the proposed approach has been demonstrated with real-world distribution feeder circuits together with actual measurement data from EV charging stations and solar farms.
Jiang et al. (Thu,) studied this question.