An Optimal Pricing Formula for Smart Grid based on Stackelberg Game

TL;DR

This paper develops an analytical Stackelberg game model for optimal electricity pricing in smart grids, providing explicit formulas for pricing and demand equilibrium, and offers solutions for scenarios with prediction errors and renewable energy supply.

Contribution

It introduces the first analytical optimal pricing formula for demand response in smart grids based on Stackelberg game theory, including solutions under uncertainties.

Findings

Derived the optimal pricing formula for utility companies.

Established the unique Nash equilibrium for user demand.

Provided a numerical algorithm for non-analytical cases.

Abstract

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.