With the rapid development of distributed power, energy storage and automation control technologies in the distribution network, the active and intelligent distribution network provides strong support for its island operation. Facing the problem of islanding of active distribution network (ADN) after a fault in the upper-level power grid, a robust optimal partition model with the least comprehensive loss of load outage is established. Among them, the comprehensive loss of power outage takes into account the compensation cost of cutting off the interruptible load and the load loss cost caused by non-agreement blackout. The loss cost is modeled by piecewise linearization, and a unified linear constraint is constructed by adding logical variables. In order to avoid the frequent switching on and off of any load in the island operation scheme, the continuous state constraint of load power failure and its linearization method are proposed. Further, considering the uncertainty of the output characteristics of distributed energy in ADN, the deterministic model is transformed into a two-stage robust optimization model, and the conservativeness of the flexible adjustment scheme of robust adjustment coefficients is introduced. At the same time, the model is solved based on duality theory and column generation algorithm. Cases studies verify the effectiveness of the proposed model and method.