Uncertainty and Autarky: Cooperative Game Theory for Stable Local Energy Market Partitioning

Abstract

Local energy markets empower prosumers in distribution grids to form coalitions for collective self-consumption. An open question is to analyze the scale and composition of local energy market coalitions formed by strategic prosumers in distribution grids. This analysis must account for grid constraints, stochasticity of load and generation, as well as the interaction between possibly multiple local energy markets in the distribution grid. In this work, we present a cooperative game theoretic framework to study distribution grid partitioning into local energy markets under uncertain prosumption, grid constraints, and coalitional externalities. We formulate the optimal stable partitioning problem to balance the interests of the grid operator with that of strategic prosumers. Under deterministic load and generation, we show that the largest market coalition is the optimal stable partition. Under high levels of grid congestion, we show that individual self-consumption corresponds to the optimal stable partition. For the general case of stochastic prosumption and moderate grid congestion levels, we provide an algorithm to evaluate the optimal stable partition. We validate our algorithm and theory using numerical experiments on benchmark and real world distribution grids. Our results help in understanding the impact of prosumption uncertainty and grid constraints on coalition formation.