Differentially private distributed protocol for electric vehicle charging

In distributed electric vehicle (EV) charging, an optimization problem is solved iteratively between a central server and the charging stations by exchanging coordination signals that are publicly available to all stations. The coordination signals depend on user demand reported by charging stations and may reveal private information of the users at the stations. From the public signals, an adversary can potentially decode private user information and put user privacy at risk. This paper develops a distributed EV charging algorithm that preserves differential privacy, which is a notion of privacy recently introduced and studied in theoretical computer science. The algorithm is based on the so-called Laplace mechanism, which perturbs the public signal with Laplace noise whose magnitude is determined by the sensitivity of the public signal with respect to changes in user information. The paper derives the sensitivity and analyzes the suboptimality of the differentially private charging algorithm. In particular, we obtain a bound on suboptimality by viewing the algorithm as an implementation of stochastic gradient descent. In the end, numerical experiments are performed to investigate various aspects of the algorithm when being used in practice, including the number of iterations and tradeoffs between privacy level and suboptimality.