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Mathematical Problems in Engineering
Volume 2018, Article ID 8760575, 10 pages
Research Article

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

Hongbo Zhu,1,2 Yan Gao,1 and Yong Hou3,4

1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
2Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223003, China
3Institute for Energy Studies, University of North Dakota, Grand Forks, ND 58202, USA
4Clean Republic LLC, Grand Forks, ND 58302, USA

Correspondence should be addressed to Yan Gao; nc.ude.tssu@nayoag

Received 10 May 2017; Revised 13 December 2017; Accepted 31 December 2017; Published 29 January 2018

Academic Editor: Bogdan Dumitrescu

Copyright © 2018 Hongbo Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.