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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2022

Extended McKean-Vlasov optimal stochastic control applied to smart grid management

Abstract

We study the mathematical modeling of the energy management system of a smart grid, related to a aggregated consumer equipped with renewable energy production (PV panels e.g.), storage facilities (batteries), and connected to the electrical public grid. He controls the use of the storage facilities in order to diminish the random fluctuations of his residual load on the public grid, so that intermittent renewable energy is better used leading globally to a much greener carbon footprint. The optimization problem is described in terms of an extended McKean-Vlasov stochastic control problem. Using the Pontryagin principle, we characterize the optimal storage control as solution of a certain McKean-Vlasov Forward Backward Stochastic Differential Equation (possibly with jumps), for which we prove existence and uniqueness. Quasi-explicit solutions are derived when the cost functions may not be linear- quadratic, using a perturbation approach. Numerical experiments support the study.
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Dates and versions

hal-02181227 , version 1 (12-07-2019)
hal-02181227 , version 2 (12-01-2021)

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Emmanuel Gobet, Maxime Grangereau. Extended McKean-Vlasov optimal stochastic control applied to smart grid management. ESAIM: Control, Optimisation and Calculus of Variations, 2022, 28, pp.40. ⟨10.1051/cocv/2022034⟩. ⟨hal-02181227v2⟩
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