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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. [ABSTRACT FROM AUTHOR]

Summary: As the key component of demand response management in smart grid, real‐time pricing has been an open issue to address. In this paper, a Stackelberg game with multiple power retailers and multiple users is proposed to maximize the revenue of each retailer and the payoff of each user in power retail market. The existence of Stackelberg equilibrium is analyzed and proved. A distributed algorithm is developed to ensure the convergence of Stackelberg equilibrium for retailers and users with only local information. Additionally, we design an incentive factor that adjusts the price information from retailers to guarantee the grid operation and assure supply‐demand balance since the smart grid still can be susceptible to the issues about privacy and security. The simulation results show the effectiveness of algorithm and the impact of incentive factor. [ABSTRACT FROM AUTHOR]

As an essential characteristic of smart grid, demand response may reduce the power consumption of users and the operating expense of power suppliers. Real-time pricing is the key component of demand response that encourages power utilization in an efficient and economical way. In this paper, we study the real-time pricing scheme in smart grid with multiple retailers and multiple residential users using Stackelberg game. Additionally, the price competition among power retailers is formulated as a non-cooperative game, while the coordination among the residential users is formulated as an evolutionary game considering the private information of power retailers and residential users. The existence of Stackelberg equilibrium is proved. Moreover, two special algorithms are developed to solve the equilibrium. Numerical results show the convergence of algorithms, and also confirm the efficiency and effectiveness of proposed real-time pricing scheme. [ABSTRACT FROM AUTHOR]

Summary: The advertising differential game is introduced to depict the competition among electricity retailers in continuous time. A Stackelberg game model with one leader and multiple followers is established to study the real‐time pricing scheme in a smart community. By solving the optimization problem on users' side with budget constraint and the noncooperative differential game among retailers, the Stackelberg equilibrium between the retailers and the users is obtained. Finally, numerical simulation is carried out to discuss the influence of different factors on the payoff of electricity retailers and users and verify the rationality of the pricing scheme. [ABSTRACT FROM AUTHOR]