Efficient Methods for Approximating the Shapley Value for Asset Sharing in Energy Communities

TL;DR

This paper introduces a new stratified expected value method for approximating the Shapley value in energy communities, demonstrating high accuracy and significantly reduced computational costs compared to existing methods for large groups of prosumers.

Contribution

It formalizes and compares approximation methods for the Shapley value in energy communities and proposes a novel, efficient stratified expected value approach.

Findings

Approximation methods achieve under 1% error for large communities.

The new stratified method has similar accuracy to state-of-the-art but is computationally more efficient.

Exact Shapley value computation is feasible for communities of up to several hundred prosumers.

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.