I. Introduction
The microgrid control is typically deployed in three layers [24]. In particular, the design of the higher layer (or tertiary level) is made difficult by uncertainties in power generation and demand. Moreover, in order to manage the energy optimally, the future power trajectories of loads and generators have often to be shared with a central unit or the other grid players and this can cause privacy issues. Finally, if the number of agents of the network is high, a large computational power may be required. In this paper, we consider these challenges by proposing a distributed method for Energy Management System (EMS) that is privacy-preserving, reduces the computational cost with respect to the centralised case and allows to deal with uncertainties.