There is a great challenge to the safe and reliable operation of distribution networks based on a large number of highly uncertain distributed generators(DGs)connected to the grid. The dispatchable region of DG can provide a reference for the access location of the DG and be used for real-time monitoring of safety of distribution networks to achieve early warning and preventive control. An affine algorithm for solving the dispatchable region of DGs with uncertain in three-phase unbalanced distribution networks is proposed. Firstly

the approximate linear expression of the node voltage on the DG output uncertain variable is obtained by the power flow based on affine arithmetic. Then

considering the constraints

such as feeder capacity

reverse current flow and safety range of voltage expression

the optimal solution model of dispatchable region is constructed. Finally

the dispatchable region boundary of each DG in the distribution network is obtained by solving the model. By the simulation of modified IEEE 123 three-phase unbalanced system and comparison with the approximate exact simulation approximation method

the accuracy and efficiency of the proposed methodology are proved.