Iterative linear cuts strenghtening the second-order cone relaxation of the distribution system optimal power flow problem

We present a novel iterative algorithm to solve the distribution system optimal power flow problem over a radial network. Our methodology makes use of a widely studied second order cone relaxation applied to the branch flow model of a radial network. Several types of conditions have been established under which this relaxation is exact and we focus here on the situations where this is not the case. To overcome this difficulty, we propose to add increasingly tight linear cuts to the second-order cone problem until a physically meaningful solution is obtained. We apply this technique to a sample system taken from the literature and compare the results with a traditional nonlinear solver.