Laxity Differentiated Pricing and Deadline Differentiated Threshold Scheduling for a Public Electric Vehicle Charging Station

In this article, we study the online pricing and charging scheduling problem for a public electric vehicle (EV) charging station under stochastic electricity prices and renewable generation. We formulate the sequential decision making problem as a partially observable Markov decision process with continuous state and action spaces, with an objective of profit or social welfare maximization. The joint pricing and charging problem is challenging due to the curse of dimensionality (in both the system state and action spaces) and the unknown dynamics of system uncertainties. We propose a novel laxity differentiated pricing (LDP) scheme to tradeoff between electricity cost (associated with EV charging) and opportunity cost (associated with parking infrastructure occupancy). Shown to be optimal under arbitrary system dynamics, the characterized deadline-differentiated threshold charging (DTC) policy is integrated into a model-free soft actor critic (SAC) algorithm to reduce the action dimensionality. Numerical results demonstrate that the proposed SAC + LDP + DTC approach significantly outperforms alternative methods with various pricing and charging schemes.