With the emergence of energy communities, where a number of prosumers (consumers with their own energy generation) invest in shared renewable generation capacity and battery storage, the issue of fair allocation of benefits and costs has become increasingly important. The Shapley value, a solution concept in cooperative game theory initially proposed by Nobel prize-winning economist Lloyd Shapley, has attracted increasing interest for redistribution in energy settings. However, due to its high time complexity, it is intractable beyond communities of a few dozen prosumers. This study proposes a new deterministic method for approximating the Shapley value in realistic community energy settings and compares its performance with existing methods. To provide a benchmark for the comparisons of these methods, we also design a novel method to compute the exact Shapley value for communities of up to several hundred agents by clustering consumers into a smaller number of demand profiles. Experimental analyses with large-scale case studies of a community of up to 200 household consumers in the UK show that the newly proposed method can achieve very close redistribution to the exact Shapley values but at a much lower (and practically feasible) computation cost. Furthermore, it performed similarly to the probabilistic, state-of-the-art approximation method while having smaller time complexity as well as other desirable characteristics for cost redistribution in energy communities.

With the emergence of energy communities, where a number of prosumers invest in shared renewable generation capacity and battery storage, the issue of fair allocation of benefits and costs has become 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 examine a number of methods for approximating the Shapley value in realistic community energy settings, and propose a new one. To compare the performances of these methods, we also design a novel method to compute the Shapley value exactly, for communities of up to several hundred agents by clustering consumers into a smaller number of demand profiles. We compare the methods in a large-scale case study of a community of up to 200 household consumers in the UK, and show that our method can achieve very close redistribution to the exact Shapley values but at a much lower (and practically feasible) computation cost.

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