  The distribution optimal power flow (D-OPF) models have gained attention in
recent years to optimally operate acentrally-managed distribution grid. On
account of nonconvex formulation that is difficult to solve, several relaxation
methods have been proposed; the exactness of the solutions obtained from the
relaxed models, however, remain a concern. In this paper, we identify one such
problem related to radial distribution feeder where second-order cone program
(SOCP) relaxation does not yield a solution that is feasible with respect to
the original nonlinear OPF model. Specifically, we formulate an OPF model for
PV hosting capacity problem to obtain maximum PV capacity that a feeder can
integrate without violating the operating constraints. The SOCP relaxation for
this problem yields infeasible solutions. To address this concern, we propose a
convex iteration technique to simultaneously achieve optimal and feasible OPF
solution for the PV hosting (maximization) problem. The proposed approach
minimizes the feasibility gap with respect to original nonlinear constraints at
each SOCP iteration. The effectiveness of the proposed approach is validated
using IEEE-13 node and IEEE-123 node test systems.
