Pricing-based distributed control of fast EV charging stations operating under cold weather

As the electric vehicle (EV) adoption rates increase there is a pressing need for designing charging stations that accounts for heterogeneity (e.g. charging rates, duration) in EV demand. Battery temperature is a major factor determining the maximum charging rates as the EV charging power is limited to ensure the safety of batteries. As a consequence, each vehicle receives a different charging rate and the station can be modelled as a multi-class queuing facility. As the coverage of such networks grows the power network elements become more congested and controlling the charging demand is needed to avoid overloading. This paper models a network of fast chargers as a multi-dimensional loss system and proposes an EV load control framework that leverages pricing dynamics to keep the aggregate demand below station capacity with minimal loss of load (outage) events. The global problem is formulated to maximise the social welfare of all users, and optimal arrival rates are calculated in a distributed manner. The mathematical analysis further shows how to induce a socially optimal charging behaviour through the computation of congestion prices. The results show that class-specific prices provide fairness to EVs with colder batteries, as they receive slower service.