Graphical Models in Meshed Distribution Grids: Topology Estimation, Change Detection Limitations

Deepjyoti Deka, Saurav Talukdar, Michael Chertkov, Murti V. Salapaka

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Graphical models is a succinct way to represent the structure of a probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and detecting line changes for distribution grids are presented along with their theoretical limitations. We show that if distribution grids have cycles/loops of size greater than three, then nodal voltages are sufficient for efficient topology estimation without additional assumptions on system parameters. In contrast, line failure or change detection using nodal voltages does not require any structural assumption. Under noisy measurements, we provide the first non-trivial bounds on the maximum noise that the system can tolerate for asymptotically correct topology recovery. The performance of the designed algorithms is validated with non-linear AC power flow samples generated by Matpower on test grids, including scenarios with injection correlations and system noise.

Original languageEnglish (US)
Article number9025204
Pages (from-to)4299-4310
Number of pages12
JournalIEEE Transactions on Smart Grid
Issue number5
StatePublished - Sep 2020

Bibliographical note

Funding Information:
Manuscript received May 15, 2019; revised October 23, 2019 and January 29, 2020; accepted February 26, 2020. Date of publication March 5, 2020; date of current version August 21, 2020. The work of Deepjyoti Deka and Michael Chertkov was supported in part by the Department of Energy through the Grid Modernization Lab Consortium, and in part by the Center for Non Linear Studies, Los Alamos National Laboratory. The work of Saurav Talukdar and Murti V. Salapaka was supported by ARPA-E under projects titled “A Robust Distributed Framework for Flexible Power Grids” under Grant DE-AR000071, and “Rapidly Viable Sustained Grid” under Grant DE-AR0001016. Paper no. TSG-00681-2019. (Corresponding author: Deepjyoti Deka.) Deepjyoti Deka is with Los Alamos National Laboratory, Los Alamos, NM 87545 USA (e-mail:

Publisher Copyright:
© 2010-2012 IEEE.


  • Concentration matrix
  • conditional independence
  • distribution grids
  • graphical lasso
  • graphical models
  • line outage
  • measurement noise
  • power flows


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