Abstract: Distributed renewable energy (DRE) dispatchable region is used to quantitatively describe the ability of the power system to adapt to the uncertainty of DRE generation. Currently, research on the dispatchable region focuses on using single-phase models to describe the transmission system, with limited discussion on distribution networks with high impedance ratios and three-phase imbalance characteristics. Moreover, the impact of widespread energy storage system integration has yet to be considered, making it difficult to analyze new distribution network types accurately. To address these issues, this paper establishes a mathematical model for the dispatchable region of a distribution system with energy storage integration, fully considering the interphase coupling and three-phase imbalance characteristics of the distribution network and the energy storage system's complementary charging and discharging characteristics. A polyhedron outer approximation of the distribution network AC power flow model is constructed using convex hull relaxation and polytope outer approximation, and a convex envelope approximates the complementary relaxation constraint of the energy storage. The linear boundary of the dispatchable region of the distribution network is then constructed using the adaptive constraint generation algorithm. The simulation results demonstrate that the proposed model can effectively analyze the dispatchable region of three-phase distribution networks with energy storage integration and verify the accuracy and computational efficiency of the proposed method.