Efficient methods for approximating the Shapley value for asset sharing in energy communities

Sho Cremers*, Valentin Robu, Peter Zhang, Merlinda Andoni, Sonam Norbu, David Flynn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

With the emergence of energy communities, where a number of prosumers invest in shared generation and storage, the issue of fair allocation of benefits is increasingly important. The Shapley value has attracted increasing interest for redistribution in energy settings — however, computing it exactly is intractable beyond a few dozen prosumers. In this paper, we first conduct a systematic review of the literature on the use of Shapley value in energy-related applications, as well as efforts to compute or approximate it. Next, we formalise the main methods for approximating the Shapley value in community energy settings, and propose a new one, which we call the stratified expected value approximation. To compare the performance of these methods, we design a novel method for exact Shapley value computation, which can be applied to communities of up to several hundred agents by clustering the prosumers into a smaller number of demand profiles. We perform a large-scale experimental comparison of the proposed methods, for communities of up to 200 prosumers, using large-scale, publicly available data from two large-scale energy trials in the UK (UKERC Energy Data Centre, 2017, UK Power Networks Innovation, 2021). Our analysis shows that, as the number of agents in the community increases, the relative difference to the exact Shapley value converges to under 1% for all the approximation methods considered. In particular, for most experimental scenarios, we show that there is no statistical difference between the newly proposed stratified expected value method and the existing state-of-the-art method that uses adaptive sampling (O'Brien et al., 2015), although the cost of computation for large communities is an order of magnitude lower.

Original languageEnglish
Article number120328
JournalApplied Energy
Volume331
Early online date30 Nov 2022
DOIs
Publication statusPublished - 1 Feb 2023

Keywords

  • Energy community
  • Fair allocation
  • Prosumer
  • Shapley value

ASJC Scopus subject areas

  • Building and Construction
  • Mechanical Engineering
  • Energy(all)
  • Management, Monitoring, Policy and Law

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