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Optimal control of energy flexibilities in a stochastic environment

Abstract : In this PhD dissertation, we use tools from stochastic optimal control, stochastic optimization and convex optimization to design mechanisms to control energy storage systems, to deal with the challenges created by the uncertain production of intermittent energy sources. First, we introduce a commitment mechanism where an individual consumer chooses a consumption profile, then controls its storage devices to track in real-time this profile. We formulate a Mean-Field Control problem to model this situation, for which we establish theoretic and numerical results. Second, we introduce a control problem for a large population of Thermostatically Controlled Loads (TCLs) subject to a common noise and providing ancillary services to the grid. We show that the centralized control problem can be replaced by a stochastic Stackelberg differential game with minimal information-sharing. This allows for a decentralized control scheme with performance guarantees, while preserving privacy of consumers and limiting telecommunication requirements. We then develop a Newton method for stochastic control problems. We show that the computation of the Newton step reduces to solving Backward Stochastic Differential Equations, then we design an appropriate line-search procedure and prove global convergence of the Newton method with line-search in an appropriate space. Its performance is illustrated on a problem of control of a large number of batteries providing services to the grid. Last, a multi-stage stochastic Alternating Current Optimal Power Flow problem is formulated in order to control a power network equipped with energy storage systems. A priori conditions ensuring a vanishing relaxation gap are derived and an easily computable a posteriori bound on the relaxation gap of the problem is given. Using Shapley-Folkman-type results, a priori bounds on the duality gap of non-convex multi-stage stochastic problems with a generic structure are derived.
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https://tel.archives-ouvertes.fr/tel-03221066
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Submitted on : Friday, May 7, 2021 - 4:42:08 PM
Last modification on : Saturday, May 8, 2021 - 3:38:23 AM

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Maxime Grangereau. Optimal control of energy flexibilities in a stochastic environment. Optimization and Control [math.OC]. Institut Polytechnique de Paris, 2021. English. ⟨NNT : 2021IPPAX010⟩. ⟨tel-03221066⟩

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