Optimal battery purchasing and charging strategy at electric vehicle battery swap stations

A battery swap station (BSS) is a facility where electric vehicle owners can quickly exchange their depleted battery for a fully-charged one. In order for battery swap to be economically sound, the BSS operator must make a long-term decision on the number of charging bays in the facility, a medium-term decision on the number of batteries in the system, and short-term decisions on when and how many batteries to recharge. In this paper, we introduce a periodic fluid model to describe charging operations at a BSS facing time-varying demand for battery swap and time-varying prices for charging empty batteries, with the objective of finding an optimal battery purchasing and charging policy that best trades off battery investment cost and operating cost including charging cost and cost of customer waiting. We consider a two-stage optimization problem: An optimal amount of battery fluid is identified in the first stage. In the second stage, an optimal charging rule is determined by solving a continuous-time optimal control problem. We characterize the optimal charging policy via Pontryagin's maximum principle and derive an explicit upper bound for the optimal amount of battery fluid which allows us to quantify the joint effect of demand patterns and electricity prices on battery investment decisions. In particular, fewer batteries are needed when the peaks and the troughs of these periodic functions occur at different times. (C) 2019 Elsevier B.V. All rights reserved.