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

Abstract

We develop an optimization method to approximate the region of feasible power injections in distribution networks. Based on the nonlinear Dist-Flow model of an alternatingcurrent (AC) network with a radial structure, we first formulate a power-injection feasibility problem considering voltage and current limits. The feasibility problem is then relaxed to a convex second-order cone program (SOCP). We utilize the strong dual problem of the SOCP to construct a convex polytopic approximation of the SOCP-relaxed feasible power injection region. We further develop a heuristic method to approximately remove the power injections that make the SOCP relaxation inexact, thus establishing an approximate polytope of solvable and safe power injections. Numerical results demonstrate a satisfactory balance reached by the proposed method between the accuracy of approximation and the simplicity of computation.