A Distributionally Robust Chance-Constrained MILP Model for Multistage Distribution System Planning with Uncertain Renewables and Loads

Successful transition to active distribution networks (ADNs) requires a planning methodology that includes an accurate network model and accounts for the major sources of uncertainty. Considering these two essential features, this paper proposes a novel model for the multistage distribution expansion planning (MDEP) problem, which is able to jointly expand both the network assets (feeders and substations) and renewable/conventional distributed generators. With respect to network characteristics, the proposed planning model employs a convex conic quadratic format of ac power flow equations that is linearized using a highly accurate polyhedral-based linearization method. Furthermore, a chance-constrained programming approach is utilized to deal with the uncertain renewables and loads. In this regard, as the probability distribution functions of uncertain parameters are not perfectly known, a distributionally robust (DR) reformulation is proposed for the chance constraints that guarantees the robustness of the expansion plans against all uncertainty distributions defined within a moment-based ambiguity set. Effective linearization techniques are also devised to eliminate the nonlinearities of the proposed DR reformulation, which yields a distributionally robust chance-constrained mixed-integer linear programming model for the MDEP problem of ADNs. Finally, the 24-node and 138-node test systems are used to demonstrate the effectiveness of the proposed planning methodology.