Abstract This paper proposes a novel distributed control strategy for the optimal charging of a fleet of Electric Vehicles (EVs) in case of limited overall capacity of the electrical distribution network. The optimal charging is obtained as the solution of a scheduling problem aiming at a cost-optimal profile of the aggregated energy demand. The resulting optimization problem is formulated as a quadratic programming problem with a coupling of decision variables both in the objective function and in the constraint. We assume a minimal information structure, where users locally communicate only with their neighbors, without relying on a central decision maker. The solution approach relies on an iterative distributed algorithm based on duality, proximity, and consensus theory. A simulated case study demonstrates that the approach allows achieving the global optimum.