A Bilevel Approach for Energy Pricing Problems

Pricing models for demand side management methods are traditionally used to control electricity demand which became quite irregular recently and resulted in inefficiency in supply. In this work,we propose bilevel pricing models to explore the relationship  between energy suppliers and customers who are connected to a smart grid. The smart grid technology allows customers to keep track of hourly prices and shift their demand accordingly, and allows the provider to observe the actual demand response to its pricing strategy.

Due to their definition, bilevel models  enable to integrate customer response into the optimization process of supplier who aims to maximize revenue or minimize capacity requirements. In our setting, the energy provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. The pricing problems, we model, belong to the category of single leader single follower problems.

Considering both the monopolistic and competitive environment we present 2 bilevel bilinear problems with continuous variables. Heuristics solutions methods are defined to solve large size instances of the models. They are based on the interactions between prices, schedules and peaks. 

Numerical results on randomly generated instances illustrate numerically the validity of the approach, which achieves an `optimal' trade-off between three objectives: revenue, user cost, and peak demand.  Moreover, they put into highlight the ability of the heuristics to produce high quality results compared to the solution of MIP reformulations of the models.