Before looking further in the control challenges, it is better to try to formalize a simplifiedmodel of the prosumer community dynamics to use in the design of a decentralized controlscheme. We consider a low-voltage distribution network composed by N ∈ N buses,where one bus is the root connection, the point of connection between the communityand the power system, while the remaining N − 1 buses are the Npro ∈ N prosumers’dwellings inside the EPC. The number of branches in the network is L ∈ N, with Rl andXl as, respectively, the resistance and the reactance of the l − th branch (l ∈ { 1 . . . L }).For simplicity we will consider a linear network like the one in Fig.3.1, with batteries andsolar photovoltaic panels installed at each prosumer bus.