With the steady advancement of the Dual-carbon goal in China, more and more user-side microgrids which mainly include renewable energy sources are being connected to the distribution system, which makes the operating modes and methods of distribution system change greatly. In particular, when a distribution system failure occurs, how to efficiently use these microgrids to provide active power support for the distribution system will be one of the key factors that promote the regional autonomy capability and the safe and reliable operation level of a novel distribution system. However, the existing distribution automation level cannot meet the demand of massive user-side grid-connected microgrids which participate in the active power support in real time. In addition, the uncertainties in renewable energy sources and loads in microgrids pose a challenge to the power supply restoration in the distribution system. Based on the emergence of cloud-edge collaboration architecture and taking into account the advantage of edge computing, a limited risk power supply restoration method considering uncertainties in renewable energy sources and loads in microgrid group is proposed in this paper, in which the risk is modeled and characterized by conditional value-at-risk. First, the power supply restoration architecture of distribution system with microgrid group based on the cloud-edge collaboration technology is put forward, and a support power model of microgrid is established. Second, with the goal of minimizing the cost of central cloud power supply restoration and maximizing the profit of edge cloud microgrid operator, an optimization model of power supply restoration is established, in which each edge cloud microgrid operator can make power supply restoration decisions independently, and the central cloud makes overall arrangements to ensure that the risk constraints on the whole system are satisfied. Finally, through simulation analysis, results show that the proposed method can effectively restore power at a smaller risk index while maximally reducing the power supply restoration cost, and it can well improve the profit of microgrid operators. Moreover, it is also proved that the cloud-edge collaboration technology can improve the flexibility of power supply restoration and effectively reduce the computational burden.