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We develop a bilevel model, which captures strategic decision making by plug-in electric vehicle (PEV) owners, to optimize the design of a PEV charging station with distributed energy resources. The upper level of the model determines the optimal configuration of the station and pricing schemes, whereas the lower level captures charging decisions by PEV owners. A robust formulation is employed to capture uncertain wholesale energy prices, renewable resource availability, and PEV flows. The resulting bilevel robust optimization model is transformed into an equivalent single-level optimization problem by replacing the lower level problem with Karush–Kuhn–Tucker optimality conditions. A column-and-constraint-generation algorithm is used to solve the resultant single-level problem. Results from a realistic case study and a parameter analysis demonstrate the effectiveness of the proposed model in capturing the impacts of uncertainty and self-interested behavior by PEV owners.
Zeng et al. (Thu,) studied this question.