Optimal Energy Storage Operation under Demand Uncertainty: A Prospect Theory Analysis

In this paper, we study the consumer’s optimal energy storage operation problem under demand uncertainty. Each consumer can purchase energy storage service from an independent energy storage aggregator to shift demand from peak periods to off-peak periods under time-of-use (ToU) pricing. Previous studies on energy storage operation and investment mainly focused on the expected cost-minimization problem of a risk-neutral consumer based on the expected utility theory (EUT). We propose a prospect theory (PT) model from behavioral economics to understand the consumer’s realistic energy storage operation behaviors considering their risk preferences. Although it is challenging to solve the PT-based non-convex optimization problem, we are able to characterize the optimal solution by exploiting the unimodal structure of the objective function. Theoretical and numerical results show that the consumer’s risk preferences have a significant impact on his decisions: 1) a PT-consumer with a low reference point is more willing to use energy storage to reduce risk compared with the EUT benchmark; and 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.