  Accurate phase connectivity information is essential for advanced monitoring
and control applications in power distribution systems. The existing
data-driven approaches for phase identification lack precise physical
interpretation and theoretical performance guarantee. Their performance
generally deteriorates as the complexity of the network, the number of phase
connections, and the level of load balance increase. In this paper, by
linearizing the three-phase power flow manifold, we develop a physical model,
which links the phase connections to the smart meter measurements. The phase
identification problem is first formulated as a maximum likelihood estimation
problem and then reformulated as a maximum marginal likelihood estimation
problem. We prove that the correct phase connection achieves the highest log
likelihood values for both problems. An efficient solution method is proposed
by decomposing the original problem into subproblems with a binary
least-squares formulation. The numerical tests on a comprehensive set of
distribution circuits show that our proposed method yields very high accuracy
on both radial and meshed distribution circuits with a combination of
single-phase, two-phase, and three-phase loads. The proposed algorithm is
robust with respect to inaccurate feeder models and incomplete measurements. It
also outperforms the existing methods on complex circuits.
