A Novel Interval Power Flow Method Based on Hybrid Box-Ellipsoid Uncertain Sets

To account for the probability distribution information of uncertain scenarios, this letter proposes a novel interval power flow (NIPF) method based on hybrid uncertain sets. Firstly, a NIPF model is established by integrating the hybrid box-ellipsoid sets characterizing uncertainties in interval power flow (IPF), which is solved by the optimizing-scenario method (OSM). Then, a multivariate statistical analysis method (MSAM) and a chance-constrained programming-based method (CCPM) are proposed for determining the optimal radii of the ellipsoid set and side length of the box set under two scenarios, respectively, namely, the normal distributions without correlations and the arbitrary distributions with correlations. Finally, case studies validate the effectiveness and advantage of the proposed method compared with traditional IPF methods based on Monte Carlo simulation, box sets, and ellipsoid sets.