Improved Approximation of Dispatchable Region in Radial Distribution Networks via Dual SOCP

The concept of dispatchable region is useful in quantifying how much renewable generation the power system can handle. In this paper, we aim to provide an improved approximation of the dispatchable region in distribution networks. First, based on the nonlinear Dist-Flow model, an optimization problem is formulated to characterize the dispatchable region. The problem is then relaxed to a solvable second-order cone program (SOCP) whose strong dual problem (also an SOCP) is derived. An SOCP-based projection algorithm (Algorithm 1) is developed to construct a convex polytopic approximation. We prove that Algorithm 1 can generate the accurate SOCP-relaxed dispatchable region under certain conditions, which is an improvement over earlier studies that could only generate approximations. Furthermore, a heuristic method (Algorithm 2) 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 algorithms may provide a better approximation of the actually nonconvex dispatchable region than previous work that could construct convex sets only. Numerical comparisons demonstrate that the proposed method can achieve a better balance between ensuring security and reducing conservatism.