Multiarea Distribution System State Estimation via Distributed Tensor Completion

Yajing Liu, Ahmed Zamzam, Andrey Bernstein

Research output: Contribution to journalArticlepeer-review

3 Scopus Citations


This paper proposes a model-free distribution system state estimation method based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.

Original languageAmerican English
Pages (from-to)4887-4898
Number of pages12
JournalIEEE Transactions on Smart Grid
Issue number6
StatePublished - 1 Nov 2022

Bibliographical note

Publisher Copyright:
© 2010-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-84133


  • alternating direction method of multipliers
  • canonical polyadic decomposition
  • distribution system state estimation
  • Tensor completion


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