Proposal of a price-based demand-response model to balance supply and demand.
Formulation of the electricity trading process into a Stackelberg game.
Introduction of a pricing function as the coordinator during the trading process.
Proposal of an iterative algorithm to determine optimal generation and demands.
Performances of flattening peak demands and reducing supply–demand mismatch.
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.
Traditional power grids are confronting the challenges of increased demand, and grid stability and environmental pollution [1,2]. Smart grids are envisioned as novel power-grid systems incorporating a smart metering infrastructure capable of sensing and measuring the power consumption of users [3–5], along with demand-response (DR) programs that promise solutions for enhancing the efficiency of future power girds [6–8]. DR considers energy usage changes of users in response to varying electricity prices or to incentive payments with the aim of balancing supply and demand and reducing power generation costs through alleviation of the peak load and shifting demand from on-peak to off-peak times [9–11]. Hence, it hopes to achieve better utilization of generated power and to bring economic benefits for both the utility supplier and users. Using a DR program, it becomes possible for the utility supplier to motivate users to jointly flatten the demand curve and match supply to demand [12,13], ensuring the stability of the grid [14–17].
Given the interoperation parameters among different entities in the DR program, game theory provides a naturally suitable framework for modeling interactions among different participators with various objectives [18–20]. Recently, Stackelberg games, which are used to study hierarchical decision-making processes of multiple decision makers, have attracted attention in the design of energy management schemes . The Stackelberg game has been used to model electricity trading between the retailer and customers , with the aim of minimizing the customer’s daily payments while maximizing the retailer’s profit by optimizing electricity prices. Chen et al.  proposed a Stackelberg game-based power scheduling scheme between a service provider and residential consumers with similar objectives; the inconvenience cost incurred by delaying loads to a cheaper price period is also considered, alongside minimization of electricity bills. A bi-level programming technique has been used  to design a Stackelberg game for modeling the demand response in electricity retail markets with the aim of reducing the comfort losses of consumers as well as the costs of purchasing electricity in the lower subproblems, which is subject to the retailer’s upper sub-problem of reducing imbalances caused by deviations in wind power production from day-ahead forecasts. Kilkki et al.  proposed a Stackelberg game scenario for electricity markets, wherein the retailer is taken as the main perspective, with the goal of profit maximization. A simulation framework was designed involving customers’ uncertainties of electricity storage space heating loads, upon which partial imbalance could be eliminated by offering additional discounts to customers. Maharjan et al.  presented a Stackelberg game framework involving multiple utilities and consumers aimed at maximizing each game player’s revenue.
In general, the players in a game, together with their strategies and utility functions, differ from each other according to the specific system model . Most DR models presented so far aim to maximize the profit of a utility/retailer/service provider without considering load fluctuations in the power system [22–24,26]. However, in practice, it is also important to flatten loads in the system in order to avoid building expensive backup generators to compensate for the peak load [15,28], and a reduced peak load is advantageous for maintaining the stability of the power grid .
In this paper, we present a novel demand-response model between one utility company and multiple users. Unlike previous studies, which dealt solely with profit maximization for the utility company and cost minimization for the user, this study aimed to balance supply and demand as well as flatten the aggregated loads in the system while guaranteeing the profit of the utility company and cost minimization for the user through carefully defining the objective function at each side. The main contributions from this paper are as follows:
(1) A price-based DR model is proposed for modeling the electricity trading process between the utility company and users, with the aim of balancing supply and demand, as well as smoothing the aggregated load in the system.
(2) The interactions between the utility company and users is formulated into a 1-leader, N-follower Stackelberg game, where a pricing function is adopted for regulating realtime prices (RTP) and acts as a coordinator to induce users to join the proposed game.
(3) An iterative algorithm is proposed between the utility company and users to derive the Stackelberg equilibrium, through which the optimal power generation and demands are determined for the utility company and users respectively.
The rest of the paper is organized as follows: In Section 2, the system model is presented in detail including the formulation of the Stackelberg game and description of an iterative algorithm for reaching the outcome of the game. Section 3 provides the numerical analyses of the proposed method. Conclusions and future works are presented in Section 4.