Critical behaviour in charging of electric vehicles
For grid operators and policymakers, this work provides a theoretical framework to understand and manage congestion in EV charging, though it is incremental as it applies known protocols to a new domain.
This paper models congestion in low-voltage distribution networks due to electric vehicle charging, finding a continuous phase transition to a congested state. It shows that proportional fairness yields more equitable charging times than max-flow.
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.