Maximum Marginal Likelihood Estimation of Phase Connections in Power Distribution Systems

Abstract

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.

Denoising with Singular Value Decomposition for Phase Identification in Power Distribution Systems

“…The choice of 3σ = νx mn ensures that there is a 99.7% probability that a noisy sample will be within ν percent of the original x mn . A similar noise model has been used before [17] and allows us to model the noise as Gaussian.…”

Estimate Three-Phase Distribution Line Parameters With Physics-Informed Graphical Learning Method

“…The transition function is constructed based on the nonlinear power flow model of the distribution system. Let s n [s a n , s b n , s c n ] T be a 3×1 vector of nodal three-phase complex power injection of node n. s i n p i n +jq i n , i = a, b, c, where p i n and q i n are node n's real and reactive power injection of phase i. s n can be derived from smart meters' power consumption data and phase connections as described in Section III-A of [4]. Similarly, we define three-phase complex nodal voltage as…”

“…Although topology estimation for distribution networks has been studied extensively [3], [4], the estimation of distribution network parameters such as line impedances still needs further development. It is more challenging to estimate parameters of power distribution networks than that of transmission networks.…”

Phase identification using co‐association matrix ensemble clustering

“…The demonstrated results are excellent, although they do rely on the accuracy of the included topology constraints, otherwise the errors there are propagated through into the phase identification results. Wang and Yu [40] formulate the phase identification problem as a maximum marginal likelihood estimation problem that utilises both smart meter data (voltage and real and reactive power) as well as topology information from the feeder. This method relies on accurate knowledge of the feeder topology and three smart meter data streams.…”