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Motivated by the problems of charging a number of electric vehicles via limited capacity infrastructure, this article considers the problem of individual load adjustment under a total capacity constraint. For reasons of scalability and simplified communications, distributed solutions to this problem are sought. Borrowing from communication networks (AIMD algorithms) and distributed convex optimisation, we describe a number of distributed algorithms for achieving relative average fairness whilst maximising utilisation. We present analysis and simulation results to show the performance of these algorithms. In the scenarios examined, the algorithm's performance is typically within 5% of that achievable in the ideal centralised case, but with greatly enhanced scalability and reduced communication requirements. [ABSTRACT FROM PUBLISHER]