# Michel De Lara

## Large-Scale Microgrids Optimal Management by Mixing Stochastic Dynamic Programming with Spatial Decomposition

Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate issue. We add another layer of complexity by considering microgrids where different buildings stand at the nodes of a network and are connected by the arcs; some buildings host local production and storage capabilities, and can exchange with others their energy surplus. We formulate the problem as a multistage stochastic optimization problem, corresponding to the minimization of the expected temporal sum of operational costs, while satisfying the energy demand at each node, for all time. The resulting mathematical problem has a large-scale nature, exhibiting both spatial and temporal couplings. However, the problem displays a network structure that makes it amenable to a mix of spatial decomposition-coordination with temporal decomposition methods. We conduct numerical simulations on microgrids of different sizes and topologies, with up to 48 nodes and 64 state variables. Decomposition methods are faster and provide more efficient policies than a state-of-the-art Stochastic Dual Dynamic Programming algorithm. Moreover, they scale almost linearly with the state dimension, making them a promising tool to address more complex microgrid optimal management problems (joint work with Pierre Carpentier, Jean-Philippe Chancelier and François Pacaud).