A hierarchical algorithm for optimal plug-in electric vehicle charging with usage constraints

We present a hierarchical offline coordination algorithm for charging of Plug-in Electric Vehicles (PEVs), in which PEVs aim to optimally charge their batteries, subject to usage constraints along the day. With this algorithm, each PEV adjusts its charging strategy according to the price information, which is provided by an aggregator, while usage schedule constraints are respected at every iteration. A non-anonymous version of the algorithm is able to operate under communication failures. Both versions of the algorithm are proven to converge to the set of optimal solutions of the charging problem. This solution is optimal in the sense that it minimizes the cost of the consumed energy by both PEV and non-PEV loads. The solution has a valley-filling profile, since it leads to a configuration where PEVs aim to charge at low demand hours, minimizing, if possible, load peaks that are known to degrade the performance of power systems. In order to show convergence, we present an invariance result for difference inclusions, which works under a set of assumptions where LaSalle invariance principle does not apply. The algorithm performance is demonstrated throughout simulations.