Large scale charging of electric vehicles: A multi-armed bandit approach

The problem of centralized scheduling of large scale charging of electric vehicles (EVs) by a service provider is considered. A Markov decision process model is introduced in which EVs arrive randomly to the charging facility with random demand and completion deadlines. The service provider faces random charging costs, convex non-completion penalties, and a peak power constraint that limits the maximum number of simultaneous activation of EV chargers. Formulated as a restless multi-armed bandit problem, the EV charging problem is shown to be indexable, thus low complexity index policies exist. A closed-form expression of the Whittle´s index is obtained for the case when the charging costs are constant. The Whittle´s index policy, however, is not optimal in general. An enhancement of the Whittle´s index policy based on spatial interchange according to the less laxity and longer processing time (LLLP) principle is presented. The proposed policy outperforms existing charging algorithms, especially when the charging costs are dynamic.