On the complexity of optimal electric vehicles recharge scheduling

The massive introduction of Electric Vehicles (EVs) is expected to significantly increase the power load experienced by the electrical grid, but also to foster the exploitation of renewable energy sources: if the charge process of a fleet of EVs is scheduled by an intelligent entity such as a load aggregator, the EVs' batteries can contribute in flattening energy production peaks due to the intermittent production patterns of renewables by being recharged when energy production surpluses occur. To this aim, time varying energy prices are used, which can be diminished in case of excessive energy production to incentivize energy consumption (or increased in case of shortage to discourage energy utilization). In this paper we evaluate the complexity of the optimal scheduling problem for a fleet of EVs aimed at minimizing the overall cost of the battery recharge in presence of timevariable energy tariffs. The scenario under consideration is a fleet owner having full knowledge of the customers' traveling needs at the beginning of the scheduling horizon. We prove that the problem has polynomial complexity, provide complexity lower and upper bounds, and compare its performance to a benchmark approach which does not rely on prior knowledge of the customers' requests, in order to evaluate whether the additional complexity required by the optimal scheduling strategy w.r.t. the benchmark is worthy the achieved economic advantages. Numerical results show considerable cost savings obtained by the optimal scheduling strategy.