Optimal Electric Vehicle Charging Strategies for Long-Distance Driving

Electric vehicles (EVs) provide sustainable and eco-friendly transportation. However, long-range driving is challenging due to limited battery capacity. While charging stations can replenish the battery, they are not as widely deployed as gas stations, causing the battery depletion of EVs. This paper presents a novel optimal charging strategy for EV long-range driving. The strategy offers EV drivers the optimal charging instructions for a given trip. A new finite-horizon Markov decision process (FH-MDP) problem is formulated to minimize the travel time of an EV while preventing its battery depletion, by optimally selecting the charging stations and charging times along the trip. By confirming the monotonicity and subadditivity of the FH-MDP, we prove the existence of a monotone deterministic Markovian policy for the optimal charging decision and reveal the optimal charging time is monotone regarding the remaining battery level and driven distance. We also reveal that the optimal charging time only changes when either of two thresholds regarding the remaining battery level or driving distance is met. By comparing its state with the thresholds, the EV can make optimal decisions with linear complexity. Simulations corroborate that our algorithm can save travel time by at least 12.6% under our simulation settings, compared to alternative methods.