We address the problem of characterising the aggregate flexibility in populations of electric vehicles (EVs) with uncertain charging requirements. Building on previous results that provide exact characterisations of the aggregate flexibility in populations with known charging requirements, in this paper we extend the aggregation methods so that charging requirements are uncertain, but sampled from a given distribution. In particular, we construct \textit{distributionally robust aggregate flexibility sets}, sets of aggregate charging profiles over which we can provide probabilistic guarantees that actual realised populations will be able to track. By leveraging measure concentration results that establish powerful finite sample guarantees, we are able to give tight bounds on these robust flexibility sets, even in low sample regimes that are well suited for aggregating small populations of EVs. We detail explicit methods of calculating these sets and provide numerical results that validate the theory developed here.

翻译：我们研究在以不确定充电需求为特征的电动汽车群体中表征聚合灵活性问题。基于先前为具有已知充电需求的群体提供精确聚合灵活性表征的成果，本文扩展了聚合方法，使充电需求变为不确定，但服从给定分布采样。具体而言，我们构建了**分布鲁棒聚合灵活性集合**——能够提供概率保证的聚合充电曲线集合，确保实际实现的群体能够跟踪这些曲线。通过利用建立强有限样本保证的测度集中性结果，我们能够给出这些鲁棒灵活性集合的紧致界，即使在适用于小规模电动汽车群体聚合的低样本情况下也是如此。我们详细阐述了这些集合的显式计算数值方法，并提供了验证本文所发展理论的数值结果。