Real-time pricing based on convex hull method for smart grid with multiple generating units

With the growing demand and complex supply structure for electricity, higher requirements are proposed for generating units to regulate the peak load, resulting in significant increases in the startup cost. These issues bring urgent need to develop new pricing mechanisms. The real-time pricing (RTP) is an ideal pricing mechanism for clipping peak load and balancing supply and demand. This paper designs an RTP mechanism for the smart grid which integrates multiple generating units on the supply side and distributed renewable energy generation devices and energy storage systems on the demand side. Focusing on the interests of both supply and demand sides, a social welfare maximization model that incorporates startup costs of generating units is formulated. To tackle the discontinuity in the proposed model, the convex hull method is utilized to transform the primal model and derive the convex hull price which is widely regarded as an optimal price that can reflect the aggregate cost of generating units but has rarely extended to RTP. The related dual theory indicates that the convex hull price can be obtained by the Lagrange multiplier of the proposed social welfare maximization problem associated with the supply–demand balance constraint. Moreover, a distributed iterative algorithm based on the subgradient projection method is employed to solve the dual problem. Simulation results validate rationality and effectiveness of the proposed pricing mechanism.