Maximum Marginal Likelihood Estimation of Phase Connections in Power Distribution Systems

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.Comment: Several updates in this version. First, more comprehensive and difficult numerical tests are added, in which we compare our method with existing methods on different test feeders, with missing measurements and erroneous models. Second, we clarify and re-write theoretical derivations and assumptions so that it is easier to understan