Empirical Study of Stability and Fairness of Schemes for Benefit Distribution in Local Energy Communities

Abstract

The concept of local energy communities is receiving increasing attention. However, the question of how to distribute the benefit of a community among its members is still open. It is commonly desired that the benefit distribution is fair and stable. While benefit distribution schemes such as the nucleolus, Shapley value and Shapley-core are known to perform well in terms of fairness and stability, studies have shown that none of them can guarantee full fairness and stability at the same time. However, the existing studies neglect the temporal component. Hence, in order to gain more insights into the stability and fairness of the three aforementioned distributions in practice, we investigate their performance over time in simulation experiments on real-world data from Australian households. In about 90% of the cases, the Shapley value yielded a reasonably stable distribution, while the nucleolus yielded a reasonably fair distribution in about 75% of the cases. Furthermore, the experiments show an impact of the community size on the stability and fairness of the investigated distributions. One can conclude that for small communities, the Shapley value is the best choice, but that the nucleolus and Shapley–core become more and more attractive with increasing size of the community.

Keywords

• local energy community
• fairness
• stability
• Shapley value
• nucleolus
• Shapley–core