We focus on the charging process of a fleet of electric vehicles overnight for providing load-side regulation service. At the heart of this complex problem, the goal is to transfer a certain amount of energy to the fleet by a given deadline; however, when and how fast the energy is sent is flexible. We examine a unidirectional setting in the cases where regulation signals are deterministic (worst case) and stochastic. We study both a single-shot optimization scenario carried at the start of the charging period, and a dynamic optimization scenario, where the optimal control strategy is re-evaluated several times over the duration of the charging interval. We show that most of the gains from dynamic optimization can be obtained by re-evaluating the optimization problem at the midpoint of the charging interval. Moreover, the optimal value of the regulation service in the worst-case deterministic setting nearly matches the stochastic setting with dynamic optimization. We validate our results using both simulation and real-world data.