  Uncertainty in distributed renewable generation threatens the security of
power distribution systems. The concept of the dispatchable region was
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
the 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.
