One of the main objectives of a peer-to-peer energy market is to efficiently manage distributed energy resources while creating additional financial benefits for the participants. Cooperative game theory offers such a framework, and the Shapley value, a cooperative game payoff allocation based on the participants’ marginal contributions made to the local energy coalition, is shown to be fair and efficient. However, its high computational complexity limits the size of the game. In order to improve this peer-to-peer cooperative scheme’s scalability, this paper investigates and adapts a stratified sampling method for the Shapley value estimation. It then proposes a multi-step sampling strategy to further reduce the computation time by dividing the samples into incremental parts and terminating the sampling process once a certain level of estimation performance is achieved. Finally, selected case studies demonstrate the effectiveness of the proposed method, which is able to scale up the game from 20 players to 100 players.

点对点能源市场的主要目标之一是有效管理分布式能源，同时为参与者创造额外的财务利益。合作博弈理论提供了这样的框架，Shapley值（基于参与者对当地能源联盟的边际贡献的合作博弈收益分配）被证明是公平有效的。但是，其高计算复杂度限制了游戏的大小。为了提高这种对等协作方案的可扩展性，本文研究并采用了分层抽样方法进行Shapley值估计。然后，提出了一种多步骤采样策略，通过将采样分为增量部分并在达到一定级别的估计性能时终止采样过程来进一步减少计算时间。最后，选定的案例研究证明了所提出方法的有效性，该方法能够将游戏人数从20名增加到100名。