Decentralized optimization for energy efficiency under stochasticity.

Summary Electricity grids have to absorb an increasing production of renewable energy in a decentralized way. Their optimal management leads to specific problems. We study in this thesis the mathematical formulation of such problems as multi-step stochastic optimization problems. We analyze more specifically the time and space decomposition of such problems. In the first part of this manuscript, Time Decomposition for the Optimization of Domestic Microgrid Management, we apply stochastic optimization methods to small microgrid management. We compare different optimization algorithms on two examples: the first one considers a domestic microgrid equipped with a battery and a micro-cogeneration plant. The second one considers another domestic microgrid, this time equipped with a battery and solar panels. In the second part, Temporal and spatial decomposition of large optimization problems, we extend the previous studies to larger microgrids, with different units and storages connected together. The frontal solution of such large problems by Dynamic Programming proves impractical. We propose two original algorithms to overcome this problem by mixing a temporal decomposition with a spatial decomposition --- by prices or by resources. In the last part, Contributions to the Stochastic Dual Dynamic Programming algorithm, we focus on the emph{Stochastic DualDynamic Programming} (SDDP) algorithm which is currently a reference method for solving multi-time step stochastic optimization problems. We study a new stopping criterion for this algorithm based on a dual version of SDDP, which allows to obtain a deterministic upper bound for the primal problem.