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Critical behaviour in charging of electric vehicles

Carvalho, Rui; Buzna, Lubos; Gibbens, Richard; Kelly, Frank

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Lubos Buzna

Richard Gibbens

Frank Kelly


The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on low voltage networks will be a crucial component of the electric vehicle revolution and the move away from fossil fuels in transportation. Here, we model the max-flow and proportional fairness protocols for the control of congestion caused by a fleet of vehicles charging on two real-world distribution networks. We show that the system undergoes a continuous phase transition to a congested state as a function of the rate of vehicles plugging to the network to charge. We focus on the order parameter and its fluctuations close to the phase transition, and show that the critical point depends on the choice of congestion protocol. Finally, we analyse the inequality in the charging times as the vehicle arrival rate increases, and show that charging times are considerably more equitable in proportional fairness than in max-flow.


Carvalho, R., Buzna, L., Gibbens, R., & Kelly, F. (2015). Critical behaviour in charging of electric vehicles. New Journal of Physics, 17(9), Article 095001.

Journal Article Type Article
Acceptance Date Mar 23, 2016
Online Publication Date Sep 2, 2015
Publication Date 2015-09
Deposit Date Mar 23, 2016
Publicly Available Date Mar 23, 2016
Journal New Journal of Physics
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 17
Issue 9
Article Number 095001
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Published Journal Article (1.6 Mb)

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Copyright Statement
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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