We address the problem of characterizing the aggregate flexibility in populations of electric vehicles (EVs) with uncertain charging requirements. Extending upon prior results that provide exact characterizations of aggregate flexibility in populations of electric vehicle (EVs), we adapt the framework to encompass more general charging requirements. In doing so we give a characterization of the exact aggregate flexibility as a generalized polymatroid. Furthermore, this paper advances these aggregation methodologies to address the case in which charging requirements are uncertain. In this extended framework, requirements are instead sampled from a specified distribution. In particular, we construct robust aggregate flexibility sets, sets of aggregate charging profiles over which we can provide probabilistic guarantees that actual realized 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. Finally, we provide numerical results that validate our results and case studies that demonstrate the applicability of the theory developed herein.

翻译：本文研究了具有不确定充电需求的电动汽车（EV）群体的聚合灵活性表征问题。在先前为电动汽车群体提供精确聚合灵活性表征结果的基础上，我们扩展了该框架以涵盖更一般的充电需求。通过这一扩展，我们将精确聚合灵活性表征为广义多拟阵。此外，本文进一步推进了这些聚合方法，以处理充电需求不确定的情况。在此扩展框架中，需求是从特定分布中采样的。特别地，我们构建了鲁棒聚合灵活性集合——即一组聚合充电曲线，对于该集合我们能提供概率保证，确保实际实现的电动汽车群体能够跟踪这些曲线。通过利用建立强大有限样本保证的测度集中性结果，我们能够对这些鲁棒灵活性集合给出紧致边界，即使在低样本量情况下也适用，这非常适合于小型电动汽车群体的聚合。我们详细阐述了计算这些集合的具体方法。最后，我们提供了验证结果的数值模拟以及展示所发展理论适用性的案例研究。