Learning topology of the power distribution grid with and without missing data

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

30 Scopus citations


Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original loopy grid graph by opening switches on some lines. Due to limited presence of real-time switch monitoring devices, the operating structure needs to be estimated indirectly. This paper presents a new learning algorithm that uses only nodal voltage measurements to determine the operational radial structure. The algorithm is based on the key result stating that the correct operating structure is the optimal solution of the minimum-weight spanning tree problem over the original loopy graph where weights on all permissible edges/lines (open or closed) is the variance of nodal voltage difference at the edge ends. Compared to existing work, this spanning tree based approach has significantly lower complexity as it does not require information on line parameters. Further, a modified learning algorithm is developed for cases when the input voltage measurements are limited to only a subset of the total grid nodes. Performance of the algorithms (with and without missing data) is demonstrated by experiments on test cases.

Original languageEnglish (US)
Title of host publication2016 European Control Conference, ECC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Electronic)9781509025916
StatePublished - 2016
Externally publishedYes
Event2016 European Control Conference, ECC 2016 - Aalborg, Denmark
Duration: Jun 29 2016Jul 1 2016

Publication series

Name2016 European Control Conference, ECC 2016


Conference2016 European Control Conference, ECC 2016


  • Computational Complexity
  • Graphical Models
  • Load estimation
  • Missing data
  • Power Distribution Networks
  • Power Flows
  • Spanning Tree
  • Voltage measurements

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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