Flexible district which interconnects several AC districts through the flexible devices is able to make full use of capacity of transformers and cope with large-scale EV charging loads. The coupled districts could be co-operated. Hence,it enhances both the security and economy. The security-economy operational boundary model,as well as the concept of security margin percentage,is proposed for the operaiton of flexible district. Furthermore,a convex-hull based two-dimensional security-economy region is constructed to promote the co-operation among numerous charging stations. Numerical results demonstrate both the extensibility and the practicality of the proposed security-economy operational boundary. Besides,numerical results reveal that economic index has dramatic influence on the shape of security-economy operational boundary,and the boundary shapes for AC charging station and DC charging station are different.