This paper investigates interaction among residential electricity users and utility company in a distribution network with the capability of two-way communication provided by smart grid. The energy consumption scheduling of electricity users is formulated as a game-theoretic problem within a group where all players are not totally selfish. Considering altruistic behavior of human decision-making, altruistic player action to other players actions can be influenced by recognizing the well being of others. The proposed model captures the empathy of electricity users in energy consumption scheduling and how this behavior affect peak demand and electricity prices. Numerical results demonstrate that both residential users and utility company can benefit through the channel of empathy.
The Stackelberg or leader-follower game models the hierarchical interactions between players where the leader moves first and the follower chooses his strategy in response to that. Here, the leader would be the utility company or aggregator which sets prices and the follower is the end-user which determines load profile based on electricity prices. In @cite_27 @cite_7 @cite_16 @cite_22 @cite_17 @cite_20 , Stackelberg game with one leader and N-followers was employed to model DR problem. More generalized form of this problem is to have multiple utilities which compete each other to maximize their payoff by setting electricity prices and each user manages electricity portfolio by choosing among them @cite_25 @cite_8 . In this paper, we model empathy in non-cooperative DR within a group of residential users and single utility company with limited generation resources and explore how it affects electricity prices and total demand. By employing dual decomposition method, we show that the social maximization problem can be solved in a distributed manner without need for access to the generation cost of utility company and payoff functions of users.
@cite_22 @cite_7 @cite_8 @cite_27 @cite_16 @cite_25 @cite_20 @cite_17
1764576420 2204963357 1987785569 2059049926
We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of m priceable edges in a graph. The other edges have a fixed cost. Based on the leader’s decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader’s prices. The leader receives as revenue the total amount of prices paid by the followers for priceable edges in their solutions. Our model extends several known pricing problems, including single-minded and unit-demand pricing, as well as Stackelberg pricing for certain follower problems like shortest path or minimum spanning tree. Our first main result is a tight analysis of a single-price algorithm for the single follower game, which provides a (1+e)log m-approximation. This can be extended to provide a (1+e)(log k+log m)-approximation for the general problem and k followers. The problem is also shown to be hard to approximate within @math for some e>0. If followers have demands, the single-price algorithm provides an @math -approximation, and the problem is hard to approximate within @math for some e>0. Our second main result is a polynomial time algorithm for revenue maximization in the special case of Stackelberg bipartite vertex-cover, which is based on non-trivial max-flow and LP-duality techniques. This approach can be extended to provide constant-factor approximations for any constant number of followers. Demand-response (DR) is regarded as a promising solution for future power grids. Here we use a Stackelberg game approach, and describe a novel DR model for electricity trading between one utility company and multiple users, which is aimed at balancing supply and demand, as well as smoothing the aggregated load in the system. The interactions between the utility company (leader) and users (followers) are formulated into a 1-leader, N-follower Stackelberg game, where optimization problems are formed for each player to help select the optimal strategy. A pricing function is adopted for regulating real-time prices (RTP), which then act as a coordinator, inducing users to join the game. An iterative algorithm is proposed to derive the Stackelberg equilibrium, through which optimal power generation and power demands are determined for the utility company and users respectively. Numerical results indicate that the proposed method can efficiently reshape users’ demands, including flattening peak demands and filling the vacancy of valley demands, and significantly reduce the mismatch between supply and demand. This paper proposes a Stackelberg game approach to deal with demand response (DR) scheduling under load uncertainty based on real-time pricing (RTP) in a residential setup. We formulate the optimization problems for the service provider that acts as the leader and for the users who are the multiple followers, respectively. We derive the Stackelberg Equilibrium (SE) consisting of the optimal real-time electricity price and each user's optimal power consumption. Simulation results show the proposed DR scheduling not only can control the total power consumption, but also is beneficial to the service provider's revenue. Moreover, the load uncertainty increases the service provider's revenue and decreases each user's payoff. This paper proposes a real-time price (RTP)-based demand-response (DR) algorithm for achieving optimal load control of devices in a facility by forming a virtual electricity-trading process, where the energy management center of the facility is the virtual retailer (leader) offering virtual retail prices, from which devices (followers) are supposed to purchase energy. A one-leader, @math -follower Stackelberg game is formulated to capture the interactions between them, and optimization problems are formed for each player to help in selecting the optimal strategy. The existence of a unique Stackelberg equilibrium that provides optimal energy demands for each device was demonstrated. The simulation analysis showed that the Stackelberg game-based DR algorithm is effective for achieving the optimal load control of devices in response to RTP changes with a trivial computation burden.