Time decomposition methods for optimal management of energy storage under stochasticity.

Summary The evolution of energy storage allows the development of innovative methods of energy management at a local scale. Microgrids are an emerging form of small-scale power systems with local generation, energy storage and in particular an Energy Management System (EMS). Numerous studies and scientific researches have been conducted to propose various strategies for the implementation of these EMS. Nevertheless, there is no clear and formal articulation of these methods that would allow their comparison. One of the main difficulties for EMS is the management of the dynamics of the different energy systems. The current variations go at the speed of the electron, the solar photovoltaic energy production varies according to the clouds and different storage technologies can react more or less quickly to these unpredictable phenomena. In this manuscript, we study a mathematical formalism and algorithms based on the theory of multi-step stochastic optimization and Dynamic Programming. This formalism allows to model and solve inter-temporal decision problems in the presence of uncertainties, using temporal decomposition methods that we apply to energy management problems. In the first part of this thesis, "Contributions to time decomposition in multi-step stochastic optimization", we present the general formalism we use to time decompose stochastic optimization problems with a large number of time steps. We then classify different optimal control methods within this formalism. In the second part, "Stochastic optimization of energy storage for microgrid management", we compare different methods, introduced in the first part, on real cases. In a first step, we control a battery as well as ventilations in a subway station recovering energy from train braking, by comparing four different algorithms. In a second step, we show how these algorithms could be implemented on a real system using a hierarchical control architecture of DC microgrids. The studied microgrid connects this time photovoltaic energy to a battery, a super-capacitor and an electrical load. Finally, we apply the temporal block decomposition formalism presented in the first part to address a battery charge management problem but also its long term aging. This last chapter introduces two algorithms based on temporal block decomposition that could be used for hierarchical control of micro networks or stochastic optimization problems with a large number of time steps. In the third and last part, "Software and Experiments", we present DynOpt.jl a package developed in the Julia language which has allowed the development of all the applications of this thesis and many others. We finally study the use of this package in a real case of energy system control: the intelligent management of the temperature in a house with the Sense City equipment.