Managing Electric Vehicle Charging: An Exponential Cone Programming Approach

Abstract

A key to the mass adoption of electric vehicles (EVs) is ease of charging, in which public charging will play an increasingly important role. We study the EV charging management of a charging service provider, which faces uncertainty in customer arrivals (e.g., arrival/departure time and charging requirements) and a tariff structure including demand charges (costs related to the highest per-period charging quantity in a finite horizon). We formulate this problem to minimize the total expected costs as a two-stage stochastic program. A common approach to solve this program, sample average approximation, suffers from its large-scale nature. Therefore, we develop an approach based on exponential cone programs, ECP-U and ECP-C for the uncapacitated and capacitated cases, respectively, which can be solved efficiently. We obtain ECP-U by leveraging the problem structure and also provide a theoretical performance guarantee. We obtain ECP-C by also using the idea from distributionally robust optimization to employ an entropic dominance ambiguity set. Based on numerical experiments with a model calibrated to EV charging data from the U.K., we demonstrate that ECP-C not only runs faster than sample average approximation (about sixty times faster for a representative capacity level) but also leads to a lower out-of-sample expected cost and the standard deviation of this cost. Our numerical results also shed light on the effect of the composition of demand charges in smoothing electricity load over time. Our methods to construct both ECP approximations could potentially be used to solve other two-stage stochastic linear programs.