An Optimal Pricing Formula for Smart Grid based on Stackelberg Game

The dynamic pricing of electricity is one of the most crucial demand response (DR) strategies in smart grid, where the utility company typically adjust electricity prices to influence user electricity demand. This paper models the relationship between the utility company and flexible electricity users as a Stackelberg game. Based on this model, we present a series of analytical results under certain conditions. First, we give an analytical Stackelberg equilibrium, namely the optimal pricing formula for utility company, as well as the unique and strict Nash equilibrium for users' electricity demand under this pricing scheme. To our best knowledge, it is the first optimal pricing formula in the research of price-based DR strategies. Also, if there exist prediction errors for the supply and demand of electricity, we provide an analytical expression for the energy supply cost of utility company. Moreover, a sufficient condition has been proposed that all electricity demands can be supplied by renewable energy. When the conditions for analytical results are not met, we provide a numerical solution algorithm for the Stackelberg equilibrium and verify its efficiency by simulation.