With the rapid development of renewable energy, microgrids are becoming more and more essential in distribution networks. However, uncertainties brought by new energy sources have posed great challenges to the energy safety and stability of distribution networks, especially in the process of fault restoration. To address these issues, this paper investigates an emergency power supply recovery strategy for distribution networks by considering the support capability of microgrids and the high-dimensional dynamic correlations of uncertainty. Firstly, the structure of distribution networks including microgrids is analyzed. Then, the high-dimensional dynamic vine copula model is proposed to model the joint output uncertainty process. Next, island partition and operation models are established, including the objective function and constraint conditions, and the model solving methods are also presented. Finally, an example analysis is conducted to verify the effectiveness of the proposed strategy. The results show that the proposed strategy is able to deal with the uncertainties brought by renewable energy sources in distribution networks with microgrid support, improving energy safety and stability. This research provides valuable insights for the development of emergency power supply strategies in distribution networks.