Optimal Operation of Microgrids with Worst-Case Renewable Energy Outage: A Mixed-Integer Bi-Level Model

With the increasing penetration of renewable energy resources, such as wind and photovoltaic (PV) production, in future microgrids, challenges arise due to the potential interruption of these resources caused by changing weather conditions. In this paper, we propose a mixed-integer quadratic programming (MIQP) based bi-level model for the optimal operation of microgrids under worst-case (WC) scenarios of renewable energy resource outages. The upper-level problem formulates the minimization of energy loss and load shedding in a demand-side management (DSM) program, as well as optimal charging and discharging of electric vehicles (EVs) and energy storage systems (ESSs). The lower-level problem models the maximization of renewable energy curtailment to account for the worst-case realization of renewable resource outages. A decomposition and re-formulation method is adopted to solve the proposed bi-level optimization model, which includes binary variables in both levels. The proposed model and algorithm are implemented in the Julia programming language and solved with the Gurobi commercial solver. The model is analyzed using a 33-node microgrid under different cases to evaluate its performance, showcasing optimal microgrid operation results under worst-case renewable resource interruptions.