Learning with End-Users in Distribution Grids: Topology and Parameter Estimation

Sejun Park, Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This article studies the problems of topology and parameter estimation in radial balanced distribution grids where measurements are restricted to only the leaf nodes and all intermediate nodes are unobserved/hidden. To this end, we propose two exact learning algorithms that use balanced voltage and injection measured only at the end users. The first algorithm requires time-stamped voltage samples, statistics of nodal power injections, and permissible line impedances to recover the true topology. The second and improved algorithm requires only time-stamped voltage and complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, and permissible line impedances). We prove the correctness of both learning algorithms for grids where unobserved buses/nodes have a degree greater than three and discuss extensions to regimes where that assumption doesn't hold. Further, we present computational and, more important, the sample complexity of our proposed algorithm for joint topology and impedance estimation. We illustrate the performance of the designed algorithms through numerical experiments on the IEEE and custom power distribution models.

Original languageEnglish (US)
Article number9031561
Pages (from-to)1428-1440
Number of pages13
JournalIEEE Transactions on Control of Network Systems
Issue number3
StatePublished - Sep 2020


  • Distribution networks
  • missing data
  • power flows
  • sample complexity
  • topology and impedance estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization


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