Stochastic Distributed Protocol for Electric Vehicle Charging with Discrete Charging Rate

To address the grid-side challenges associated with the anticipated high electric vehicle (EV) penetration level, various charging protocols have been proposed in the literature. Most if not all of these protocols assume continuous charging rates and allow intermittent charging. However, due to charging technology limitations, EVs can only be charged at a fixed rate, and the intermittency in charging shortens the battery lifespan. We consider these charging requirements, and formulate EV charging scheduling as a discrete optimization problem. We propose a stochastic distributed algorithm to approximately solve the optimal EV charging scheduling problem in an iterative procedure. In each iteration, the transformer receives charging profiles computed by the EVs in the previous iteration, and broadcasts the corresponding normalized total demand to the EVs; each EV generates a probability distribution over its potential charging profiles accordingly, and samples from the distribution to obtain a new charging profile. We prove that this stochastic algorithm almost surely converges to one of its equilibrium charging profiles, and each of its equilibrium charging profiles has a negligible sub-optimality ratio. Case studies corroborate our theoretical results.