Design of Dynamic Prices for Retailers Based on User Equilibrium

Dynamic prices are effective demand-side management (DSM) methods. However, the complex interactive behavior among many loads poses challenges for dynamic price design. To address this, a user equilibrium (UE)-based bilevel dynamic price design model is proposed. In the upper-level model, the retailer designs dynamic prices to maximize profits considering the interaction response of loads. In the lower-level model, the interactive load behavior is represented by the convex UE model, which offers significant advantages over the conventional Nash Equilibrium (NE) in handling large-scale load flexibility. The bi-level model is reformulated as a mixed integer quadratic programming (MIQP) problem by using Karush-Kuhn-Tucker (KKT) conditions, Big-M methods, duality theory, and binary expansion methods. A branch-and-price algorithm is then used to efficiently solve the problem. Simulation results demonstrate that the proposed method supports large-scale dynamic pricing, maximizing retailer's profits while minimizing electricity bills for loads.