Submodular optimization for control of prosumer networks

We propose here a control based method for improving the storage placement in a prosumer network where generators and loads are stochastic. The particularity of our approach is to use the energy required for stabilizing the system as a criterion for the optimization of the storage placement. We use a linearized AC model for the dynamic of the system and we consider the control inputs as being the amount of power injected in the grid by the batteries. Because a prosumer may both consume and produce electricity using renewable generators (DER), power imbalances are very likely, such that the system might lose synchrony and require the controlled actions of batteries. We show that the amount of energy that has to be used is this kind of situation depends on the storage locations. We chose the placement that minimizes, over the perturbations that may occur, the average energy required for driving the system back to equilibrium. For this purpose, we propose and validate an algorithm based on a submodular optimization that includes the physical constraints of the system and has a worst case guarantee.