Peer-to-peer (P2P) energy trading and energy communities have garnered much attention over in recent years due to increasing investments in local energy generation and storage assets. However, the efficiency to be gained from P2P trading, and the structure of local energy markets raise many important challenges. To analyse the efficiency of P2P energy markets, in this work, we consider two different popular approaches to peer-to-peer trading: centralised (through a central market maker/clearing entity) vs. fully decentralised (P2P), and explore the comparative economic benefits of these models. We focus on the metric of Gains from Trade (GT), given optimal P2P trading schedule computed by a schedule optimiser. In both local market models, benefits from trading are realised mainly due to the diversity in consumption behaviour and renewable energy generation between prosumers in an energy community. Both market models will lead to the most promising P2P contracts (the ones with the highest Gains from Trade) to be established first. Yet, we find diversity decreases quickly as more peer-to-peer energy contracts are established and more prosumers join the market, leading to significantly diminishing returns. In this work, we aim to quantify this effect using real-world data from two large-scale smart energy trials in the UK, i.e. the Low Carbon London project and the Thames Valley Vision project. Our experimental study shows that, for both market models, only a small number of P2P contracts, and only a fraction of total prosumers in the community are required to achieve the majority of the maximal potential Gains from Trade. We also study the effect that diversity in consumption profiles has on overall trading potential and dynamics in an energy community.

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