Optimal scheduling of electrical vehicle charging under two types of steering signals

The increasing penetration of electrical vehicles and plug-in hybrid electrical vehicles is causing an increasing load upon our residential distribution network. However, the charging of these vehicles is often shiftable in time to off-peak hours due to long parking times at a fixed location during the night. This implies that these vehicles offer great potential for use in demand side management. For scalability reasons, demand side management methodologies often apply steering signals to control appliances. These steering signals are used locally to generate a schedule for these appliances. In this paper we consider the problem of generating an optimal schedule for electrical vehicles based upon two types of steering signals; time-varying prices and a target profile. The local objective, to be minimized at the appliance side, is a weighted sum of the consumption cost implied by the prices and the squared deviation from the target profile. We show that, using the structure of the problem, an efficient algorithm of time complexity $O(n \log n)$ can be derived to solve the minimization problem to optimality. We implemented the algorithm in Matlab and tested it against a traditional convex optimization solver to verify its validity and efficiency. The resulting algorithm outperformed the convex solver by roughly four orders of magnitude. Furthermore, the very low computational time of the algorithm implies that it is suitable for being implemented on a low-cost local controller within a household or EV charging station.