A Bi-Level Optimization Formulation of Priority Service Pricing

Priority service pricing is a promising approach for mobilizing residential demand response, by offering electricity as a service with various levels of reliability. Higher levels of reliability correspond to higher prices. Proper pricing guarantees that consumers self-select a level of reliability that corresponds to the reliability that the system can offer. However, the traditional theory for menu design is based on numerous stringent assumptions, which may not be respected in practice, such as well-behaved convex cost functions for generators. In this article, we design a priority service menu as the equilibrium solution to a Stackelberg game, which is modeled as a bi-level optimization problem involving a vertically integrated utility and consumers. We reformulate the equilibrium as a mixed-integer problem. As a consequence of this approach, we can integrate the menu design problem within a day-ahead unit commitment model. This allows us to design a menu which exactly meets the profit requirements of a firm. The approach is illustrated on a toy numerical example as well as a large-scale model of the Belgian power market.