Design of Dynamic Prices for Retailers Based on User Equilibrium

Dynamic prices vary with the grid load, reflecting the generation cost. In this paper, a bi-level model for the design of dynamic prices for a retailer is proposed. In the upper level, the retailer designs the price to maximize profits considering the response of loads. In the lower level, the interactive load behavior is characterized by the user equilibrium (UE) model. Compared with the common Nash Equilibrium (NE), UE gains an obvious advantage in managing a large number of flexible loads. The bi-level model is transformed into a mixed integer program using the Karush-Kuhn-Tucker (KKT) conditions. Then an efficient algorithm is proposed based on the branch-and-price method. The designed dynamic price can reflect the actual response of loads and maximize the retailer’s profits, which is validated in numerical examples.