An Exponential Cone Programming Approach for Managing Electric Vehicle Charging

This project was motivated by the operational challenges of public charging stations, such as EVgo, Tesla, and Chargepoint. Other than stochastic arrivals of customers with different arrival/departure times and charging requirements, charging stations routinely incur high demand charges, costs related to the highest per-period total electricity used in a billing cycle, which can be as high as 70% of the total electricity bill. We formulate the problem of scheduling vehicle charging to minimize the expected total cost as a stochastic program and solve it using exponential cone program (ECP) approximations. We first derive an ECP for the case with unlimited chargers and provide a theoretic performance guarantee; we then extend it to the case with limited capacity using an idea from distributionally robust optimization (DRO). We finally extend our ECP approaches to include the pricing decision and propose an alternating optimization algorithm, which alternates between two optimizations iteratively. Based on a data-calibrated numerical study, we show our ECP approaches perform better than common approaches both in terms of mean and standard deviation of the total cost and the computation time. We also use ECP to generate managerial insights for both charging service providers in terms of the value of incorporating customer departure information and policy makers in terms of the composition of demand charge.