Abstract: With the massive integration of renewable energies (photovoltaic (PV) and wind power) into the power grid, new uncertainties are impacting the power balance. At the same time, advances in « smart » technologies and batteries offer new flexibilities with the possibility of controlling the consumption of a large number of electrical appliances (electric vehicle recharging, heat pumps, etc.). In this framework, a major technical challenge is to optimize the management of this large number of heterogeneous flexibilities distributed across the network to help in balancing the system. This constitutes a large scale optimization problem under uncertainties, which can benefit from mean-field approximations.