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The initiative of users to participate in power grid operation is a key factor in realizing the optimal allocation of power. Demand response (DR) management mechanisms based on real-time pricing (RTP) can effectively promote the enthusiasm of users, stimulate the efficiency of microgrids for power dispatch, and achieve the goasl of power peak shifting and valley filling. In this paper, we consider a microgrid composed of several energy providers (EPs) and multiple users, and each user is equipped with several electric vehicles (EVs). It should be noted that EVs may be attacked by networks in the process of data exchange when EVs connect to the MG. In this environment, we establish a multi-time slots social welfare maximization model that reflects the common interests of EPs and users. To simplify the problem, we decompose this multi-time slots model into a set of single-time slot optimization problems by the relaxation method. Furthermore, the mechanisms of identification and processing (MIP) for EVs under cyber-attack are proposed. The problem is decoupled to EPs and users by duality decomposition. Then, through integration with MIP, a distributed RTP algorithm based on the dual subgradient algorithm is designed to obtain the optimal electricity price. Finally, the simulation results verify the feasibility of the model and the effectiveness of the proposed algorithm. Through comparative analysis, the necessity of identifying EVs under cyber-attack is fully embodied. [ABSTRACT FROM AUTHOR]

A real-time pricing scheme is formulated based on bilevel programming to tackle the uncertainties for smart microgrids equipped with renewable energy sources, dispatchable resources and storage devices. The main grid is taken as the leader, who sets electricity prices to maximize its revenue. At the lower level, the price-anticipating microgrids determine the amount of dispatchable resources generated, the load and the storage serving while maximizing their payoffs. When setting price, the main grid needs to consider the microgrids' response. By Karush–Kuhn–Tucker conditions and a smoothing method, the primal bilevel programming is transformed into an equivalent single-level optimization problem with only smooth equality constraints, and then a rolling penalty function algorithm is designed to obtain the optimal solution. The convergence of the smoothing method is demonstrated. Simulations show that the proposed approach has good performance in cutting peak, balancing system energy distribution and improving benefits for both supply and demand. [ABSTRACT FROM AUTHOR]

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]

Highlights • Formulating a maximization model of expected social welfare by given a classification of smart home applications. • Representing operating process of household appliances by Markov decision process. • Dividing the optimization problem into two sub-problems in terms of users and energy supplier. • Solving the maximization model with distributed algorithms. • Simulation studies are given to show performance of the proposed algorithm. Abstract Demand side management (DSM) aims to match power demand to supply through cutting the peak and filling the valley. It is one of the most important factors in smart grid. The real-time pricing (RTP) scheme is an ideal method to adjust power balance between supply and demand. Considering the classification of smart home appliance (SHA) and the correlation of power consumption among users, a social welfare maximization model is proposed based on Markov decision process (MDP) in the research. A probabilistic transfer matrix has been introduced to characterize the elastic appliance in smart home. Several state transfer functions have been utilized to reflect the operating process of the semi-elastic appliance also. In this way, the specific characteristics of SHA can be fully embodied. In order to improve computing efficiency and protect the user's privacy, this project divides the optimization into two subproblems in terms of users and energy supplier (ES). At user side, a modified simulated annealing RTP algorithm is developed to solve the optimization problem. Also, at ES side, the dual sub-gradient method is used to solve the convex optimization problem in the paper. Finally, the simulation results validate the rationality and feasibility of the optimization model by the decentralized RTP algorithm. [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]

Demand side management aims to match power demand to supply through cutting the peak and filling the valley, is one of the most important factors in smart grid. The real-time pricing (RTP) mechanism is an ideal method to adjust power balance between supply and demand. Its implementation has a profound impact on users’ behavior, and on operation and management of the power grid. In this research, we propose an expectation social welfare maximization model, considering the classification of the smart home appliances (SHA) and the correlation of power consumption of multi-time slots. Users can arrange their appliances more profitable and more closely to reality with the advantage of multi-time slots RTP strategy. The constraint in the model reflects the fluctuation (uncertainty) of power consumption caused by operating continuity of the SHA. By introducing probabilistic constraints, the uncertainty optimization model is transformed into a convex optimization problem. The existence and uniqueness of the optimal solution are shown, and its properties are further analyzed. Considering the convex optimization problem is separable in dual domain, this study proposes a decentralized online RTP algorithm to determine each user’s demand and energy supplier’s supply simultaneously. By utilizing Armijo line search to instead of fixed step size of the dual subgradient method, the decentralized online RTP algorithm proposed in this research can overcome the defects of slow convergence and even no convergence from the original dual subgradient method. Finally, the simulation validates the rationality and feasibility of optimization model by the decentralized online RTP algorithm. [ABSTRACT FROM AUTHOR]

The real-time pricing mechanism based on demand response is an ideal method balancing supply and demand in the smart grid system. Its implementation will have a profound impact not only on behavior of the users, but on operation and management style of the electric power suppliers. Considering the relationship between two stages of users' power demand, a periodic social welfare maximization model based on Markov chain is presented in the research. As the result of solving the maximization model, the user may get an optimal real-time pricing strategy that helps its schedule of power consumption more reasonable and practical. The presented model has considered the known and unknown cases of parameters in the state transition probability matrix. Users with type alike have been given the realtime pricing strategy, in accordance with its correlation of influence and restrict condition of consuming electricity. Users with type not alike have been distinguished by offering different electric prices. A modified simulated annealing algorithm with centralized and distributed pricing strategy has been designed according to parameters known and unknown, respectively. Finally, a simulation process has validated rationality and feasibility of the optimization model developed in the research. [ABSTRACT FROM AUTHOR]

• A win-win real-time pricing strategy for smart grid is studied. • A holistic Markov decision process model is proposed. • Reinforcement learning methodology is adopted to solve the model. • A distributed online algorithm is designed to decide the electricity price adaptively. The real-time pricing (RTP) plays an important role in demand side management of smart grid. In this paper, a distributed RTP strategy which takes the interests of both supply and demand sides into consideration is studied. A holistic model focusing on the interactions between users and the power supplier is proposed in the framework of Markov decision process (MDP). The MDP presentation of smart appliances' operational processes well embodies their characteristics and the energy correlation of adjacent time slots. Different from existing ones, a novel distributed online algorithm based on a reinforcement learning approach is proposed to solve the MDP model without acquisition of the transition probabilities. Through information exchange between users and the power supplier, the real-time electricity price is decided adaptively, meanwhile, the optimal strategy of power supply and consumption is obtained. The specific information of the utility function for each user does not need to be disclosed to the supplier and other users. Simulation results show that the proposed model and algorithm balance energy supply and demand well, and have a good performance in peak shaving and valley filling. [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]