Dynamics and Optimization in Spatially Distributed Electrical Vehicle Charging

We consider a spatially distributed demand for electrical vehicle recharging, which must be covered by a fixed set of charging stations. Arriving electrical vehicles receive feedback on transport times to each station, and waiting times at congested ones, based on which they make a selfish selection...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 12; no. 1; pp. 403 - 415
Main Authors: Paganini, Fernando, Ferragut, Andres
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Control systems
Costs
Delays
Differential equations
Distributed algorithms/control
Electric vehicle charging
electrical vehicle (EV) charging
Mathematical models
Network systems
Optimization
Resource management
Road traffic
Routing
transportation networks
Vehicle dynamics
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:We consider a spatially distributed demand for electrical vehicle recharging, which must be covered by a fixed set of charging stations. Arriving electrical vehicles receive feedback on transport times to each station, and waiting times at congested ones, based on which they make a selfish selection. This selection determines total arrival rates in station queues, which are represented by a fluid state; departure rates are modeled under the assumption that clients have a given sojourn time in the system. The resulting differential equation system is analyzed with tools of optimization. We characterize the equilibrium as the solution to a specific convex program, which has connections to optimal transport problems, and also with road traffic theory. In particular, a price of anarchy appears with respect to a social planner's allocation. From a dynamical perspective, global convergence to equilibrium is established, with tools of Lagrange duality and Lyapunov theory. An extension of the model that makes customer demand elastic to observed delays is also presented, and analyzed with extensions of the optimization machinery. Simulations to illustrate the global behavior are presented, which also help validate the model beyond the fluid approximation.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2024.3487650