Algorithms for two-time scales stochastic optimization with applications to long term management of energy storage

We design algorithms for two time scales stochastic optimization problems arising from long term storage management. Energy storage devices are of major importance to integrate more renewable energies and demand-side management in a new energy mix. However batteries remain costly even if recent market developments in the field of electrical vehicles and stationary storage tend to decrease their cost. We present a stochastic optimization model aiming at minimizing the investment and maintenance costs of batteries for a house with solar panels. For any given capacity of battery it is necessary to compute a charge/discharge strategy as well as maintenance to maximize revenues provided by intraday energy arbitrage while ensuring a long term aging of the storage devices. Long term aging is a slow process while charge/discharge control of a storage handles fast dynamics. For this purpose, we have designed algorithms that take into account this two time scales aspect in the decision making process. These algorithms are applied to three numerical experiments. First, one of them is used to control charge/discharge, aging and renewal of batteries for a house. Results show that it is economically significant to control aging. Second, we apply and compare our algorithms one a simple charge/discharge and aging problem, that is a multistage stochastic optimization problem with many time steps. We compare our algorithms to Stochastic Dynamic Programming and Stochastic Dual Dynamic Programming and we observe that they are less computationally costly while displaying similar performances on the control of a storage. Finally we show that how one of our algorithm can be used for the optimal sizing of a storage taking into account charge/discharge strategy as well as aging.