Farsighted stability of distributed energy resource sharing

In a storage sharing system consisting of prosumers, the advantages of peer-to-peer energy storage sharing rely on the stability of the system. However, previous studies only considered the impact of prosumers’ myopic behaviors but overlooked their farsighted behaviors on the stability. In a farsighted view, prosumers not only consider their operating cost generated by one-step (joint) defections but also concern with the subsequent reactions of others to their actions. Directly applying the core, a myopic stability criterion, would increase the risk of misjudgment on the stability. To fill this gap, this paper proposes a method based on the largest consistent set (LCS) to capture the impact of prosumers’ farsighted behaviors on the stability under the optimal operation policy. The optimal operation policy includes an optimal storage decision and a stable cost allocation rule. This paper first derives the analytical solutions of the optimal storage that minimizes the expected daily operating cost of the system for tackling the technical complexity of generalizing from the conventional time-of-use pricing to multi-tier time-of-use pricing. Then, to identify the farsighted stability under Shapley value cost allocations, we investigate the conditions that the grand coalition is in the LCS, namely the conditions of the stable system. Combining real data on residential energy consumption, case studies show that the core will significantly underestimate the probability of the system stability. Such an underestimation increases with the growth of the system scale. This paper may stimulate future relevant studies on farsighted energy sharing.