  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.
