The work presents the results of a study regarding the impact of some Demand Response control logics on an isolated distribution network. The proposed control is divided into precise steps in which the coordination between the general aggregator controller and the single local Energy Management Systems is developed and illustrated with details. The control is applied to the flexible loads and to the storage systems of photovoltaic plants installed at the end-users' houses and connected to the network. The study is carried out delivering a suitable network model of the island's system, with the implementation of load profiles for all the loads of the network for a total simulation time of 24 hours. Different scenarios are examined, in order to assess the impact of the DR control actions on the network.