Critical behaviour in charging of electric vehicles

TL;DR

This paper models congestion control protocols for electric vehicle charging on real distribution networks, revealing a phase transition to congestion, protocol-dependent critical points, and differences in charging time equity.

Contribution

It introduces a modeling framework for EV charging congestion, analyzes phase transitions, and compares protocol impacts on system behavior and fairness.

Findings

System undergoes a continuous phase transition to congestion.

Critical point depends on the congestion control protocol.

Proportional fairness yields more equitable charging times.

Abstract

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.