Mathematical tools to manage distributed flexibilities in power systems

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.