Adaptive Robust Expansion Planning for a Distribution Network With DERs

Distribution expansion planning (DEP) is used to determine the best expansion plan of a distribution system. Considering the uncertainties of loads and of power productions of wind distributed energy resources (DERs) and incorporating AC power flow equations make the DEP problem increasingly challenging. In this context, this paper presents a new adaptive robust distribution expansion planning model to identify the timing of feeder reinforcements in addition to the location, capacity, and installation time of dispatchable and wind DERs. The proposed approach characterizes the uncertain nature of loads and power productions of wind DERs through polyhedral uncertainty sets and the robustness of the solution can be controlled by means of a budget of uncertainty. Since AC power flow equations rather than DC ones are considered, the proposed model is a nonlinear and non-convex min-max-min optimization problem, which cannot be solved directly by commercial optimization packages. Hence, a trilevel decomposition algorithm using both primal and dual cutting planes is introduced to solve the problem. Additionally, to attain a smoother optimization problem, the non-convex AC power flow equations are convexified. The working of the proposed model is illustrated using 33-bus and 123-bus distribution networks.