A mean field control approach for smart charging with aggregate power demand constraints

Séguret, Adrien; Wan, Cheng; Alasseur, Clémence

doi:10.1109/isgteurope52324.2021.9639978

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…Finally, the multiplication of L(•) by ∆t Q k,p i (i,s) normalizes the transition cost and avoids its explosion when n tends to infinity. The switching costs in (2.7) showed good numerical results in [49].…”

Section: The N Pevs Control Problemmentioning

confidence: 97%

“…To overcome these difficulties, one can approximate the problem of n PEVs by considering a continuum of PEVs, leading to the techniques of optimal control of PDEs and those of convex optimization. The resulting limit mean field control problem was studied in [48] and numerically solved in [49]. Note that several articles have already dealt with smart charging problems within a mean field limit framework [16,44,46].…”

Section: Introductionmentioning

confidence: 99%

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Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging

Séguret

2023

Appl Math Optim

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We consider the optimal control of a finite population of hybrid processes (namely agents state is composed of a discrete and a continuous variable), modeling the optimal charging of a large population of identical plug-in electric vehicles (PEVs). We prove the convergence of the solution and that of the value of a sequence of finite population problems respectively to a solution and the value of a mean field optimal control problem.

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Section: The N Pevs Control Problemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging

Séguret

2023

Appl Math Optim

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“…In both [27,28], a rigorous justification was not given to guarantee that a solution will exist in the Nash equilibrium problem. More recently, the authors, in 2021 and 2023 [53,54], added constraints for battery charging and discharging in their mathematical formalism, and the authors in 2023 [55] they added behavioral considerations of the owners of electric vehicles (availability, planning, etc.) in their analysis.…”

Section: Introductionmentioning

confidence: 99%

Mean Field Game-Based Algorithms for Charging in Solar-Powered Parking Lots and Discharging into Homes a Large Population of Heterogeneous Electric Vehicles

Muhindo

2024

Energies

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An optimal daily scheme is presented to coordinate a large population of heterogeneous battery electric vehicles when charging in daytime work solar-powered parking lots and discharging into homes during evening peak-demand hours. First, we develop a grid-to-vehicle strategy to share the solar energy available in a parking lot between vehicles where the statistics of their arrival states of charge are dictated by an aggregator. Then, we develop a vehicle-to-grid strategy so that vehicle owners with a satisfactory level of energy in their batteries could help to decongest the grid when they return by providing backup power to their homes at an aggregate level per vehicle based on a duration proposed by an aggregator. Both strategies, with concepts from Mean Field Games, would be implemented to reduce the standard deviation in the states of charge of batteries at the end of charging/discharging vehicles while maintaining some fairness and decentralization criteria. Realistic numerical results, based on deterministic data while considering the physical constraints of vehicle batteries, show, first, in the case of charging in a parking lot, a strong to slight decrease in the standard deviation in the states of charge at the end, respectively, for the sunniest day, an average day, and the cloudiest day; then, in the case of discharging into the grid, over three days, we observe at the end the same strong decrease in the standard deviation in the states of charge.

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“…Controlling the sum of the consumption of each flexible consumer in order to balance the electrical system has already been investigated successfully in the specific framework of Quadratic Kullback-Leibler control problems [4]. In [29] and [20], a mean field assumption is also considered to control the charging of a large fleet of electrical vehicles (EVs for short), leading to the optimal control of partial differential equation problems.…”

Section: Introductionmentioning

confidence: 99%

A decentralized algorithm for a mean field control problem of piecewise deterministic Markov processes

Séguret,

Le Corre,

Oudjane

2024

ESAIM: PS

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This paper provides a decentralized approach for the control of a population of N agents to minimize an aggregate cost. Each agent evolves independently according to a Piecewise Deterministic Markov dynamics controlled via unbounded jumps intensities. The N-agent high dimensional stochastic control problem is approximated by the limiting mean field control problem. A Lagrangian approach is proposed. Although the mean field control problem is not convex, it is proved to achieve zero duality gap. A stochastic version of the Uzawa algorithm is shown to converge to the primal solution. At each dual iteration of the algorithm, each agent solves its own small dimensional sub problem by means of the Dynamic Programming Principal, while the dual multiplier is updated according to the aggregate response of the agents. Finally, this algorithm is used in a numerical simulation to coordinate the charging of a large fleet of electric vehicles (EVs for short) in order to track a target consumption profil

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A mean field control approach for smart charging with aggregate power demand constraints

Cited by 6 publications

References 21 publications

Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging

Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging

Mean Field Game-Based Algorithms for Charging in Solar-Powered Parking Lots and Discharging into Homes a Large Population of Heterogeneous Electric Vehicles

A decentralized algorithm for a mean field control problem of piecewise deterministic Markov processes

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