Distributed Load Balancing with Nonconvex Constraints: A Randomized Algorithm with Application to Electric Vehicle Charging Scheduling

TL;DR

This paper introduces a distributed, randomized algorithm for electric vehicle charging scheduling with nonconvex constraints, ensuring convergence to a Nash equilibrium and providing suboptimality bounds as the number of EVs increases.

Contribution

It proposes a novel distributed randomized algorithm that handles nonconvex constraints in EV charging and characterizes its convergence and optimality properties.

Findings

Algorithm converges almost surely in finite iterations.

Final charging profiles are Nash equilibria of a specific game.

Suboptimality bound scales as O(1/n) with the number of EVs.

Abstract

To schedule a large number of EVs with the presence of practical nonconvex charging constraints, a distributed and randomized algorithm is proposed in this paper. The algorithm assumes the availability of a coordinator which can communicate with all EVs. In each iteration of the algorithm, the coordinator receives tentative charging profiles from the EVs and computes a broadcast control signal. After receiving this broadcast control signal, each EV generates a probability distribution over its admissible charging profiles, and samples from the distribution to update its tentative charging profile. We prove that the algorithm converges almost surely to a charging profile in finite iterations. The final charging profile (that the algorithm converges to) is random, i.e., it depends on the realization. We characterize the final charging profile---a charging profile can be a realization of the final charging profile if and only if it is a Nash equilibrium of the game in which each EV seeks to minimize the inner product of its own charging profile and the aggregate electricity demand. Furthermore, we provide a uniform suboptimality upper bound, that scales O(1/n) in the number n of EVs, for all realizations of the final charging profile.