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Accurate phase connectivity information is essential for advanced monitoringand control applications in power distribution systems. The existingdata-driven approaches for phase identification lack precise physicalinterpretation and theoretical performance guarantee. Their performancegenerally deteriorates as the complexity of the network, the number of phaseconnections, and the level of load balance increase. In this paper, bylinearizing the three-phase power flow manifold, we develop a physical model,which links the phase connections to the smart meter measurements. The phaseidentification problem is first formulated as a maximum likelihood estimationproblem and then reformulated as a maximum marginal likelihood estimationproblem. We prove that the correct phase connection achieves the highest loglikelihood values for both problems. An efficient solution method is proposedby decomposing the original problem into subproblems with a binaryleast-squares formulation. The numerical tests on a comprehensive set ofdistribution circuits show that our proposed method yields very high accuracyon both radial and meshed distribution circuits with a combination ofsingle-phase, two-phase, and three-phase loads. The proposed algorithm isrobust with respect to inaccurate feeder models and incomplete measurements. Italso outperforms the existing methods on complex circuits.

Maximum Marginal Likelihood Estimation of Phase Connections in Power Distribution Systems