Comparison of the distribution optimal power flow relaxations for unbalanced loads and generations

Abstract

This paper presents a numerical comparison between the second order cone relaxation for single-phase distribution systems and the semidefinite relaxation for the multiphase distribution systems for the optimal power flow problem considering unbalanced load and generation. Towards this end, the IEEE 37-bus test feeder is adapted using four different distribution line models for the various feeder segments and by populating selected nodes with photovoltaic inverters. Results generated by Matlab Software for Disciplined Convex Programming (CVX) suggest that solutions found using the four line models are almost identical for the multiphase algorithm, but losses may be larger using the single-phase algorithm.