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Demand side management (DSM) has become a popular approach to control the increase in electricity demand, as well as the fluctuation in electricity consumption. Two popular DSM approaches include energy efficiency and demand response (DR). Energy efficiency approach focuses on lifelong effects in the electricity demand by using devices that consume less energy without modifying the consumers’ actions (Lee et al., 2014) or by allocating and scheduling energy sources effectively (Khaitan et al., 2015). The DR approach focuses on altering the consumers’ short-term actions by encouraging them to reduce or shift the demand during peak time periods (Lee et al., 2014; Siano, 2014).
In order to influence the consumers’ electricity consumption behavior, electricity producers have relied on smart grid innovations. The development of smart grids has given electricity producers leverage for better control and communication so that they can respond effectively to the levels of electricity consumption. With these tools, they have gained the capability to apply DR techniques to decrease the peak to average (PAR) consumption ratio. The effective deployment of DR will benefit all of the stake holders in the smart grid. Consumers benefit from reduced electricity bills while electricity suppliers benefit from better grid efficiency and reliability. Furthermore, the operation with a high PAR is more costly for the electricity provider as it compels the provider use fuel that is more costly and has high carbon emissions so as to meet the high peak demand (Sims et al., 2003; Soliman & Leon-Garcia, 2014).
Typically, electricity consumption varies throughout the day and reaches a consumption peak during the afternoon and early evening hours. These hours are considered peak periods, while the rest of the day can be considered as off-peak (DOE, 2006). The use of dynamic pricing, where an extra tariff is charged during peak consumption hours or an incentive provided during off-peak hours, is one DR approach that encourages customers to reduce or shift their consumption from peak to off-peak periods. Typically, the main goal is to dampen the swings in electricity consumption and reduce PAR, which lead to high production costs for the electricity providers and possibly power shortages. Various mathematical techniques have been used to analyze DR in order to provide effective strategies for the reduction of PAR. One technique for this analysis involves the use of game theory, where electricity producers’ and consumers’ strategies and incentives are analyzed under leader-follower Stackelberg games (Saad et al., 2012). In such games, the leader moves first and makes its decision followed by the second decision stage, where the follower(s) responds with their decision(s).
In this paper, we develop a Stackelberg game model to study the interaction between a single electricity provider and multiple consumers in an electricity market. Typically, the electricity provider’s production cost increases in the production amount with an increasing rate. As such, she is motivated to dampen the peak load, which can be achieved by shifting the peak load to other periods. To achieve that, the electricity provider acts as the leader and sets a price discount for each time slot depending on the expected aggregate demand. Consumers react by deciding how to shift their electricity consumptions across the planning horizon. Our analysis focuses on load-shifting behavior and as such, in order to single out load-shifting, we do not consider load-shaving. In other words, we consider the case where the total consumption of consumers does not change across the planning horizon; however, they can shift their consumption from one period to another. Consumers determine their consumption in each period based on the electricity prices, their nominal demand, and their inconvenience cost incurred by changing their intended behavior. It is important to highlight that each consumer has their own inconvenience function such that not only does it vary between consumers but also varies across time periods for the same consumer. With the proposed model, we investigate the impact of consumers’ inconvenience types on the electricity provider’s ability to control the fluctuations in electricity demand and the PAR via the use of price discounts.