A Novel Uncertainty Quantification Framework for PF and OPF Considering Nonlinear Correlated Power Injections With Limited Information

This paper proposes a new uncertainty quantification framework for power flow (PF) and optimal power flow (OPF) considering the nonlinear correlations of uncertain power injections with limited information. The D-Vine copula is leveraged to capture the nonlinear correlations among uncertain power injections from historical data. This is further integrated with the evidence theory and the reformulated quadratic affine form to obtain PF and OPF results. The D-Vine copula and evidence theory allow one to effectively eliminate the explosive-growth joint focal elements of large-scale power system with large numbers of partial known uncertain power injections, leading to significant reduction of computing time. The reformulated quadratic affine form aims at characterizing the PF and OPF outputs with partially known uncertain power injections in a simple form based on Dempster-Shafer structure, yielding further computational efficiency improvement without the loss of accuracy. Comparison results with other alternatives show that the proposed framework leads to more accurate PF and OPF outcomes while achieving high computational efficiency for large-scale power systems with large numbers of nonlinear correlated power injections in presence of limited information.