Consensus reaching with heterogeneous user preferences, private input and privacy-preservation output

This paper deals with a generic problem of matching agents with underlying preferences while guaranteeing a certain level of privacy is met. As a general framework, we consider consumers and prosumers who trade energy on a platform. Consumers buy energy to the platform to maximize their usage benefit while minimizing the cost paid to the platform. Prosumers, who have the possibility to generate energy, self-consume part of it to maximize their usage benefit and sell the rest to the platform to maximize their revenue. Inspired by a variant of the Hotelling model, product differentiation is introduced and consumers can specify preferences regarding locality and green origin of their supply. The consumers and prosumers problems being coupled through a matching probability, we provide analytical characterization of the resulting Nash equilibrium, and conditions for existence and uniqueness. Assuming supply shortages occur on the platform, we reformulate the local market clearing problem as a consensus problem that we solve using Consensus Alternating Direction Method of Multipliers (C-ADMM), enabling minimal information exchanges between prosumers and consumers. C-ADMM complexity is recalled and strategy proofness is analysed. The algorithm is then run on a case study made of 300 prosumers from New South Wales in Australia, equipped with solar panels. We consider privacy-preservation output against a centralized benchmark approach, and evaluate C-ADMM computational time under three scenarios with an increasing number of agents. Regarding economic analysis, we observe that it is more profitable for prosumers than for consumers to be flexible within a local energy community, and that belonging to a local energy community incentivizes them to reduce their demands by comparison with their initial targets. Furthermore, the expectation to make a substantial profit is a main driver for prosumers' engagement within a community; whereas for consumers, the green origin of the supply is determinant.