# Explainable Graph Theory-Based Identification of Meter-Transformer Mapping

arXiv: https://arxiv.org/abs/2205.09874 · HTML: https://mlsanity.com/paper/2205.09874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 8 of 8)

- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Urban MV and LV Distribution Grid Topology Estimation via Group Lasso](https://mlsanity.com/paper/1611.01845/) (2016)
- [Graph Algorithms for Topology Identification using Power Grid Probing](https://mlsanity.com/paper/1803.04506/) (2018)
- [Estimating Distribution Grid Topologies: A Graphical Learning based Approach](https://mlsanity.com/paper/1602.08509/) (2016)
- [PaToPa: A Data-Driven Parameter and Topology Joint Estimation Framework in Distribution Grids](https://mlsanity.com/paper/1705.08870/) (2017)
- [Unbalanced Multi-Phase Distribution Grid Topology Estimation and Bus Phase Identification](https://mlsanity.com/paper/1809.07192/) (2018)
- [PaToPaEM: A Data-Driven Parameter and Topology Joint Estimation Framework for Time Varying System in Distribution Grids](https://mlsanity.com/paper/1812.06619/) (2018)
- [Data-Driven Approach for Distribution Network Topology Detection](https://mlsanity.com/paper/1504.00724/) (2015)

## Abstract (arXiv)

Distributed energy resources are better for the environment but may cause transformer overload in distribution grids, calling for recovering meter-transformer mapping to provide situational awareness, i.e., the transformer loading. The challenge lies in recovering meter-transformer (M.T.) mapping for two common scenarios, e.g., large distances between a meter and its parent transformer or high similarity of a meter's consumption pattern to a non-parent transformer's meters. Past methods either assume a variety of data as in the transmission grid or ignore the two common scenarios mentioned above. Therefore, we propose to utilize the above observation via spectral embedding by using the property that inter-transformer meter consumptions are not the same and that the noise in data is limited so that all the k smallest eigenvalues of the voltage-based Laplacian matrix are smaller than the next smallest eigenvalue of the ideal Laplacian matrix. We also provide a guarantee based on this understanding. Furthermore, we partially relax the assumption by utilizing location information to aid voltage information for areas geographically far away but with similar voltages. Numerical simulations on the IEEE test systems and real feeders from our partner utility show that the proposed method correctly identifies M.T. mapping.