A rolling penalty function algorithm of real-time pricing for smart microgrids based on bilevel programming

Abstract

A real-time pricing scheme is formulated based on bilevel programming to tackle the uncertainties for smart microgrids equipped with renewable energy sources, dispatchable resources and storage devices. The main grid is taken as the leader, who sets electricity prices to maximize its revenue. At the lower level, the price-anticipating microgrids determine the amount of dispatchable resources generated, the load and the storage serving while maximizing their payoffs. When setting price, the main grid needs to consider the microgrids’ response. By Karush–Kuhn–Tucker conditions and a smoothing method, the primal bilevel programming is transformed into an equivalent single-level optimization problem with only smooth equality constraints, and then a rolling penalty function algorithm is designed to obtain the optimal solution. The convergence of the smoothing method is demonstrated. Simulations show that the proposed approach has good performance in cutting peak, balancing system energy distribution and improving benefits for both supply and demand.