A cooperative game-theory approach for incentive systems in local energy communities

Prosumers have a central role in the context of smart grids, and in particular within local energy communities (LECs), as they are capable of being both energy producers and consumers. In a scenario where peer-to-peer (P2P) energy trading is allowed, prosumers can exchange the energy they produce with other prosumers: the primary outcome of this is the improvement of energy self-consumption across the grid, which leads to decreased transmission losses, as well as lower energy costs and diminished long-term damage to the grid itself. Previous work proposed a mechanism to achieve multiple objectives for a cooperative game theory perspective for small coalitions, but its behavior for coalitions of arbitrary size remains unexplored, and it does not consider the objective of peak shaving. This paper aims to (i) design an algorithm for calculating schedules for coalitions of arbitrary size, (ii) analyze the behavior of this mechanism for large coalitions, (iii) create a new incentive mechanism by proposing new selling functions that ensure that the resulting mechanism would optimize for the objective of peak shaving when all the prosumers work together in one large coalition, and (iv) demonstrate the performance of the existing mechanism in terms of peak shaving, by comparing against the mechanism specifically optimized for this objective. Simulations conducted on data from a grid in Cardiff, UK, reveal that the existing mechanism works particularly well for the non-cooperative game, achieving results for cost reduction and self-consumption almost identical to the cooperative game, no matter the size of the coalitions. More precisely, although all mechanisms achieve optimal peak shaving for the grand coalition, the existing mechanism achieves this objective even within the framework of the selfish game, resulting in a reduction of the peak by approximately 29% compared to alternative methods. Furthermore, the mechanism is proven to optimally achieve peak shaving in both cooperative and non-cooperative cases.