Uncertainty in distributed renewable generation threatens the security of power distribution systems. The concept of dispatchable region is developed to assess the ability of power systems to accommodate renewable generation at a given operating point. Although DC and linearized AC power flow equations are typically used to model dispatchable regions for transmission systems

these equations are rarely suitable for distribution networks. To achieve a suitable trade-off between accuracy and efficiency

this paper proposes a dispatchable region formulation for distribution networks using tight convex relaxation. Second-order cone relaxation is adopted to reformulate AC power flow equations

which are then approximated by a polyhedron to improve tractability. Further

an efficient adaptive constraint generation algorithm is employed to construct the proposed dispatchable region. Case studies on distribution systems of various scales validate the computational efficiency and accuracy of the proposed method.