Promoting electric vehicles (EVs) is regarded as an effective solution for reducing carbon emissions and addressing growing environmental concerns. However, the increasing number of EVs has significantly heightened the demand for electric power charging, posing challenges to distribution systems. Studies have shown that a coordination strategy combining various compensation devices, such as energy storage systems and reactive power compensation devices, can enhance the integration capability of EVs. Furthermore, EVs can be managed as controllable loads that can be shed at low costs, contributing to the flexibility of the distribution network. This paper explores the uncertainties of EV load sizes and the coordination of active and reactive power. A multi-objective optimization model was developed to augment the flexibility of the distribution network and mitigate the risk of load shedding. The Monte Carlo method is utilized to simulate scenarios with EV load uncertainties. To simplify the power flow calculations in the proposed convex optimization model, the Distflow equation was adopted. Case study results demonstrate that managing EV loads in the distribution network can significantly reduce load shedding costs by 80 %, and the proposed EV charging strategy can effectively eliminate load shedding costs in most scenarios.