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Applied Energy
Article . 2023 . Peer-reviewed
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Efficient methods for approximating the Shapley value for asset sharing in energy communities

Authors: Cremers, Sho; Robu, Valentin; Zhang, Peter; Andoni, Merlinda; Norbu, Sonam; Flynn, David;

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

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.

34 pages, 10 figures, Published in Elsevier Applied Energy

Keywords

FOS: Computer and information sciences, Computer Science - Computer Science and Game Theory, FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Computer Science and Game Theory (cs.GT)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Top 10%
Top 10%
Top 10%
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