Two-Stage Robust Unit Commitment with Uncertain Demand Response

A day-ahead unit commitment model is proposed considering uncertainty in demand response. While a demand response program can be integrated into any day-ahead unit commitment model by allowing customers to bid for flexible demand, the bid price, which represents the utility of real-time power consumption, is often uncertain. To hedge against this uncertainty, the proposed model uses a two-stage optimization framework assuming the day-ahead and the real-time stages, where customers bid at the real-time stage. The objective of the proposed model is to maximize social welfare under worst-case scenarios of the real-time utility. Compared with existing models with the same objective, the proposed model is novel in that it explicitly considers the winning status of each customer, i.e., whether his/her bidding is accepted, as a decision variable optimized for the actual real-time utility. This enables modeling more generalized constraints in demand response. The proposed model is formulated as a two-stage robust optimization problem whose second-stage problem is a mixed-integer linear programming problem with an uncertain objective function. To solve the proposed model, a nested column-and-constraint generation algorithm is suggested. Simulation results show the effectiveness of the proposed model.