A game theoretic approach for load-shifting in the smart grid

In this paper, load-shifting within the context of smart grid demand response is investigated for an electricity market composed of a single energy provider and multiple consumers. The problem is formulated as a Stackelberg game in which the provider, acting as leader, moves first and offers price discounts across a finite time horizon to motivate consumers to shift their energy consumptions from peak periods. The consumers, acting as followers, respond by deciding if and how they shift their consumption from their nominal demand. In this model, the aim of the energy provider is to maximize its profits, while the consumers aim to minimize their total costs related to both the energy consumption and inconvenience of deviating from the nominal demand. Within this setting, a procedure is proposed to obtain equilibrium outcomes and managerial insights are derived by investigating the impact of various factors, including consumer types and market diversity, on the interactions between the energy provider and its customers. Our results show that price discounts may provide significant leverage for achieving lower peak-to-average ratios while improving the service provider´s profits. Our results demonstrate that when load-shifting is sacrificial for the consumers, equilibrium discounts and server provider profits not only depend on the size of the demand (market depth) but also the composition and the number of consumers (market breadth).