A monotonic optimization based optimal discrete charging protocol for electric vehicles with multilevel charging rates

In this paper, we propose ODCP, a novel optimal discrete charging protocol, to investigate the optimal charging strategy for Electric Vehicles (EVs) with multilevel charging rates. Unlike the assumptions in most previous works that the charging rate is continuously adjustable below the power rating and the charging process can be intermittent, the proposed ODCP model explicitly takes into account the facts that the charging rate is discrete and the charging process should not be interrupted, which is a favorable yet conventional practice to prolong the battery lifetime. Specifically, the ODCP is first formulated as a semi-infinite programming problem, which is proved to be reducible by presenting an equivalent discretized model. The discretized model is combinatorial in the charging rate and is a nonconvex optimization problem which is generally difficult to sovle. Nevertheless, by exploiting the hidden monotonicity in this model, we transform the problem into a canonical monotonic optimization problem. Based on the Polyblock outer approximation algorithm, we propose the GorPa algorithm, which efficiently solves the problem to global (η,ε)-optimal under the case when EVs' operational intervals do not overlap. We demonstrate the applicability of the proposed algorithm and show its convergence by real data simulation.