Maximum Marginal Likelihood Estimation of Phase Connections in Power Distribution Systems.

The successful implementation of advanced distribution monitoring and control applications heavily depends on accurate distribution phase connectivity information. Most of the existing data-driven approaches for phase identification lack physical interpretation and theoretical guarantee. Their performance generally deteriorates as the complexity of the network, the number of phase connections, and the level of load balanceness increase. In this paper, we develop a physical model, which links the phase connections to the voltage magnitudes and power injections via the three-phase power flow manifold. The phase identification problem is formulated and then reformulated as a maximum likelihood estimation problem and a maximum marginal likelihood estimation problem. We prove that the correct phase connection solution achieves the highest log likelihood values for both problems. 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 also outperforms the existing methods on complex circuits.