  Simulations have shown that while semi-definite relaxations of AC optimal
power flow (AC-OPF) on three-phase radial networks with only wye connections
tend to be exact, the presence of delta connections seem to render them
inexact. This paper shows that such inexactness originates from the
non-uniqueness of relaxation solutions and numerical errors amplified by the
non-uniqueness. This finding motivates two algorithms to recover the exact
solution of AC-OPF in the presence of delta connections. In simulations using
IEEE 13, 37 and 123-bus systems, the proposed algorithms provide exact optimal
solutions up to numerical precision.
