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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| Veröffentlicht in: | IEEE transactions on control of network systems Jg. 12; H. 1; S. 403 - 415 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Piscataway
IEEE
01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 2325-5870, 2372-2533 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Paganini, Fernando Ferragut, Andres |
| Author_xml | – sequence: 1 givenname: Fernando orcidid: 0000-0002-1258-9049 surname: Paganini fullname: Paganini, Fernando email: paganini@ort.edu.uy organization: Mathematics Applied to Telecommunications and Energy Research Group, Universidad ORT Uruguay, Montevideo, Uruguay – sequence: 2 givenname: Andres orcidid: 0000-0003-0134-5548 surname: Ferragut fullname: Ferragut, Andres organization: Mathematics Applied to Telecommunications and Energy Research Group, Universidad ORT Uruguay, Montevideo, Uruguay |
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| SubjectTerms | 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 |
| Title | Dynamics and Optimization in Spatially Distributed Electrical Vehicle Charging |
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