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This paper develops a general computationally efficient copula-polynomial chaos expansion (copula-PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven copula statistical model is used to capture both nonlinear and linear correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. It paves the way for leveraging PCE for surrogate modeling and uncertainty quantification of power flow results. To further improve the computational efficiency of the proposed method without sacrificing accuracy, two strategies are developed and unified together. Specifically, the branch flow sensitivity analysis (BFSA) is used to select an appropriate number of outputs that need PCE surrogate modeling while the analysis of variance (ANOVA) scheme enables us to reduce the number of basis functions and coefficients evaluations for each PCE surrogate. Simulations carried out on the IEEE 57-bus and 118-bus and PEGASE 1354-bus systems show that the proposed framework can obtain better accuracy and computational efficiency than the existing PCE-based methods with linear correlation assumption and other Monte Carlo-based methods. The sensitivities to different copula types and parameters are also investigated. • A generalized copula-PCE framework is proposed to handle both nonlinear and linear correlations among uncertain inputs. • To improve the computational efficiency of the proposed framework without loss of accuracy, the branch flow sensitivity analysis (BFSA) and ANOVA method are integrated into a unified manner. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution system. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of load and PV power injections. The sampling-based method estimates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-bus distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework. [ABSTRACT FROM AUTHOR]