Real-Time Pricing for Demand Response in Smart Grid Based on Alternating Direction Method of Multipliers

The real-time pricing (RTP) scheme is an ideal method to adjust the power balance between supply and demand in smart grid systems. This scheme has a profound impact on users' behavior, system operation, and overall grid management in the electricity industry. In this research, we conduct an extended discussion of a RTP optimization model and give a theoretical analysis of the existence and uniqueness of the Lagrangian multiplier. A distributed optimization method based on the alternating direction method of multipliers (ADMM) algorithm with Gaussian back substitution (GBS) is proposed in this study. On the one hand, the proposed algorithm takes abundant advantage of the separability among variables in the model. On the other hand, the proposed algorithm can not only speed up the convergence rate to enhance the efficiency of computing, but also overcome the deficiency of the distributed dual subgradient algorithm, the possibility of nonconvergence in the iteration process. In addition, we give the theoretical proof of the convergence of the proposed algorithm. Furthermore, the interdependent relationship between variables has been discussed in depth during numerical simulations in the study. Compared with the dual subgradient method, the simulation results validate that the proposed algorithm has a higher convergence speed and better implementation effect.