An exponential cone programming approach for managing electric vehicle charging

We study the electric vehicle charging management of a service provider, which faces stochastic arrival of customers as well as a total electricity cost including demand charges (costs related to the highest per-period electricity used in a finite horizon). 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 the idea from distributionally robust optimization (DRO) of employing an entropic dominance ambiguity set. We benchmark our ECP approach with sample average approximation (SAA) and a DRO approach using a semi-definite program (SDP) on numerical instances calibrated to real data. As our numerical instances are large-scale, we find that while SDP cannot be solved, ECP scales well and runs efficiently (about 50 times faster than SAA) and consequently results in a lower mean total cost than SAA. We finally extend our ECP to include the pricing decision and propose an alternating optimization algorithm, which performs better than SAA on our numerical instances. We also use ECP to generate managerial insights for both charging service providers and policy makers.