Strategic Storage Investment and Operation under Uncertainty: Behavioral Economics Analysis

In this paper, we propose a two-stage Stackelberg game to investigate the strategic storage investment and operation interaction between the storage aggregator and consumers under demand uncertainty. In the first stage, the storage aggregator makes the storage investment and pricing decisions to maximize its profit. After observing the storage aggregator's decisions, each consumer makes its own storage operation decisions to minimize its electricity bill. Different from previous studies that mainly assumed a risk-neutral consumer based on the expected utility theory (EUT), we propose a prospect theory (PT) model to capture consumers' risk preferences. To solve the PT-based non-convex problem, we exploit the unimodal structure of the objective function and characterize the equilibrium solutions. Theoretical and numerical results show that the consumers' risk preferences have significant impacts on the equilibrium solutions: 1) a PT-consumer with a low reference point is more willing to use energy storage to reduce risk compared with the EUT benchmark; 2) a PT consumer is more willing to use the energy storage when the probability of high demand is small, due to the probability distortion; 3) the consumers with a lower level of risk preference are easier to be affected by the increase of storage investment cost.