An adjustable pricing scheme for public charging stations: Balancing drivers' range anxiety and operational efficiency

With the increasing penetration of electric vehicles, the shortage of public charging piles impacts the charging experience of electric vehicle drivers, exacerbating their range anxiety. In particular, low charging power at a high state of charge (SOC) reduces the service efficiency of public charging facilities, leads to long access time for drivers waiting for charging, and restrains the profit of a public charging operator. To address this challenge, we develop a market equilibrium model and introduce an adjustable pricing scheme in which the price per unit amount of charging (i.e., unit price) changes linearly with the SOC to affect drivers' charging decisions (i.e., whether to charge and when to stop charging) and improve social welfare, which includes drivers' utility from charging and the operator’s profit. We further formulate three optimization scenarios (i.e., social welfare maximization, profit maximization, and second best), and deduce the properties of the optimal solutions. We theoretically prove that the welfare-oriented operator should adopt a zero unit price at the minimum SOC and gradually raise the unit price as the current SOC increases. Moreover, whether in pursuit of maximum profit or maximum social welfare, the operator should avoid the 'inefficient charging' behavior of drivers (i.e., persisting in charging at a high SOC), even with low potential demand or sufficient charging piles. We also compare the proposed adjustable pricing scheme with traditional static pricing strategies, proving that the adjustable pricing scheme is superior in improving social welfare. We further conduct numerical experiments to verify the above analytical findings. The proposed adjustable pricing scheme is demonstrated to be able to allow the public charging operator to achieve a higher welfare or profit. Its practical feasibility and policy implications are discussed. The proposed model is also extended to account for heterogeneous VOT and EV charging specifications, quadratic pricing, and pricing linearly dependent on charging power. The numerical results of the extended models show that the welfare-oriented operator still sets a high unit price at high SOC levels to deter drivers from inefficient charging.