Mixing Time Blocks and Price/Resource Decompositions Methods

We provide a method to decompose multistage stochastic optimization problems by time blocks. This method is based on reducing the so-called history space using a compressed ``state'' variable. It leads to a reduced dynamic programming equation. Then We apply the reduction method by time blocks to two time-scales stochastic optimization problems arising from long term storage management of batteries. 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. We show on instances with huge time steps 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. Numerical results show that it is economically significant to control aging. We also compare our algorithms to SDP and Stochastic Dual Dynamic Programming on small instances and we observe that they are less computationally costly while displaying similar performances on the control of a storage.Non UBCUnreviewedAuthor affiliation: École des Ponts ParisTechFacult