Segmented Distributionally Robust Optimization for Real-Time Power Dispatch With Wind Uncertainty

This paper proposes a novel segmented distributionally robust optimization method for real-time power dispatch with correlated wind forecast errors. In the proposed dispatch model, a segmented linear decision rule incorporating an allowed threshold for wind forecast error is developed. The excess wind fluctuation beyond the optimized threshold will be first discarded, and then units adopts the segmented linear decision for the remaining wind forecast error. The segmented linear decision rule upgrades the traditional parameterized ambiguous set into a variable-involved segmented ambiguous set, which makes the dispatch more flexible but meanwhile harder to solve. Through the equivalent conversion of uncertain variables and dual theory of semi-infinite problems, the proposed dispatch model is recast as a semidefinite programming with nonconvex bilinear constraints. To solve the complex problem, a difference-of-convex optimization (DCO) addressing bilinear constraints with alternating optimization (AO)-based initialization is developed. AO with fast computing speed accelerates the convergence by producing a good enough initial feasible solution, while DCO with stronger search ability enhances the solution quality in the subsequent optimization. Finally, numerical simulations in three cases validate the economic efficiency of the proposed model and the superiority of the convexified solving method.