Charging stations have become indispensable infrastructure to support the rapid proliferation of electric vehicles (EVs). The operational scheme of charging stations is crucial to satisfy the stability of the power grid and the quality of service (QoS) to EV users. Most existing schemes target either of the two major operations: charging rate control and demand balancing. This partial focus overlooks the coupling relation between the two operations and thus causes the degradation on the grid stability or customer QoS. A thoughtful scheme should manage both operations together. A big challenge to design such a scheme is the aggregated uncertainty caused by their coupling relation. This uncertainty accumulates from three aspects: the renewable generators co-located with charging stations, the power load of other (or non-EV) consumers, and the charging demand arriving in the future. To handle this aggregated uncertainty, we propose a stochastic optimization based operational scheme. The scheme jointly manages charging rate control and demand balancing to satisfy both the grid stability and user QoS. Further, our scheme consists of two algorithms that we design for managing the two operations respectively. An appealing feature of our algorithms is that they have robust performance guarantees in terms of the prediction errors on these three aspects. Simulation results demonstrate the efficacy of the proposed operational scheme and also validate our theoretical results.