# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2018178

## A real-time pricing scheme considering load uncertainty and price competition in smart grid market

 1 School of Business, Qingdao University, Qingdao 266071, China 2 School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China 3 School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received  October 2017 Revised  July 2018 Published  December 2018

As a powerful tool of Demand Response (DR) techniques in smart grid market, Real-time Pricing (RTP) may optimize the electricity consumption pattern of users and improve the efficiency of electricity market. In this paper, a multi-leader-follower Stackelberg Game (SG) based on RTP is established to model the strategic interaction behavior between multiple electricity retailers and multiple users while simultaneously considering the power load uncertainty of users and the price competition among electricity retailers. In the game model, electricity retailers aim to seek their revenue maximization while the optimal power consumption competition among the users is taken into account. Lagrange multiplier method is utilized to solve the Nash Equilibriums (NE) of two non-cooperative games, and the closed-form optimal solution is obtained, then the Stackelberg Equilibrium (SE) consisting of the optimal real-time prices of electricity retailers and the power consumption of users is given. Finally, the numerical analysis results verify that the proposed scheme can reduce the real-time electricity price and increase the users' satisfaction under feasible constraint, which shows the effectiveness and better performance of proposed RTP scheme.

Citation: Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu, Lu Li. A real-time pricing scheme considering load uncertainty and price competition in smart grid market. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018178
##### References:

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##### References:
RTP data from ComEd
Optimal real-time pricing of retailers
Optimal real-time pricing of retailers when $\sigma = 0.1,0.2,0.3$
Expected revenue of electricity retailers
Aggregate power load of user 1 and user 2
Expected power payoff of user 1 and user 2
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