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

12 Scopus citations

Abstract

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
Volume11
Issue number5
DOIs
StatePublished - Sep 2020

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)

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