# Unbalanced Multi-Phase Distribution Grid Topology Estimation and Bus Phase Identification

arXiv: https://arxiv.org/abs/1809.07192 · HTML: https://mlsanity.com/paper/1809.07192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2018.

## Built on by (most cited first, 4 of 4)

- [Learning Distribution Grid Topologies: A Tutorial](https://mlsanity.com/paper/2206.10837/) (2022)
- [Estimate Three-Phase Distribution Line Parameters With Physics-Informed Graphical Learning Method](https://mlsanity.com/paper/2102.09023/) (2021)
- [Quick Line Outage Identification in Urban Distribution Grids via Smart Meters](https://mlsanity.com/paper/2104.02056/) (2021)
- [Explainable Graph Theory-Based Identification of Meter-Transformer Mapping](https://mlsanity.com/paper/2205.09874/) (2022)

## Abstract (arXiv)

There is an increasing need for monitoring and controlling uncertainties brought by distributed energy resources in distribution grids. For such goal, accurate multi-phase topology is the basis for correlating measurements in unbalanced distribution networks. Unfortunately, such topology knowledge is often unavailable due to limited investment, especially for revvlow-voltage distribution grids. Also, the bus phase labeling information is inaccurate due to human errors or outdated records. For this challenge, this paper utilizes smart meter data for an information-theoretic approach to learn the topology of distribution grids. Specifically, multi-phase unbalanced systems are converted into symmetrical components, namely positive, negative, and zero sequences. Then, this paper proves that the Chow-Liu algorithm finds the topology by utilizing power flow equations and the conditional independence relationships implied by the radial multi-phase structure of distribution grids with the presence of incorrect bus phase labels. At last, by utilizing Carson's equation, this paper proves that the bus phase connection can be correctly identified using voltage measurements. For validation, IEEE systems are simulated using three real data sets. The simulation results demonstrate that the algorithm is highly accurate for finding multi-phase topology even with strong load unbalancing condition and DERs. This ensures close monitoring and controlling DERs in distribution grids.