To completely describe the maximum permissible operation range of flexible DC distribution network under the premise of meeting N-1 security criterion

this paper proposes the N-1 security region model and its analytical solving method for flexible DC distribution network. First

the typical connection modes and the steady-state characteristics before and after N-1 contingencies of flexible DC distribution network are discussed. On this basis

the N-1 security region model for flexible DC distribution network is established

and the differences between this model and that for AC distribution network

as well as the reasons why this model is suitable for flexible DC distribution network

are analyzed. Then

the model is analytically solved by linearization of DistFlow branch power flow and processing of droop nodes. Finally

the effectiveness of the model and its solving method is verified by case study. The results show that the proposed model and solving method can be utilized to obtain the analytical expressions of the security region of flexible DC distribution network under master-slave control

voltage margin control

and droop control. The rules of the security region size under different control strategies are that the size under voltage margin control is smaller than that under master-slave control

and the size under droop control is smaller than or equal to that under master-slave control.