  The concept of dispatchable region is useful in quantifying how much
renewable generation power the system can handle. In this paper, we aim to
provide an improved dispatchable region approximation method in distribution
networks. First, based on the nonlinear Dist-Flow model, an optimization
problem that minimizes the sum of slack variables is formulated to describe the
dispatchable region. The nonconvexity caused by alternating-current (AC) power
flow constraints makes it intractable. To deal with this issue, the problem is
relaxed to a second-order cone program (SOCP) whose strong dual problem is
derived. Then, an SOCP-based projection algorithm is developed to construct a
convex polytopic approximation. We prove that the proposed algorithm can
generate the accurate SOCP-relaxed dispatchable region under certain
conditions. Furthermore, a heuristic method is proposed to approximately remove
the regions that make the SOCP relaxation inexact. The final region obtained is
the difference of several convex sets and can be nonconvex. Thus, the proposed
approach may provide a better approximation of the actually nonconvex
dispatchable region than previous work that could construct convex sets only.
Numerical results demonstrate that the proposed method can achieve a high
accuracy of approximation with simple computation.
