Model-Free State Estimation Using Low-Rank Canonical Polyadic Decomposition

Ahmed Zamzam, Yajing Liu, Andrey Bernstein

Research output: Contribution to journalArticlepeer-review

3 Scopus Citations


As electric grids experience high penetration levels of renewable generation, fundamental changes are required to address real-time situational awareness. This letter utilizes unique traits of tensors to devise a model-free situational awareness and energy forecasting framework for distribution networks. This letter formulates the state of the network at multiple time instants as a three-way tensor; hence, recovering full state information of the network is tantamount to estimating all the values of the tensor. Given measurements received from μ phasor measurement units and/or smart meters, the recovery of unobserved quantities is carried out using the low-rank canonical polyadic decomposition of the state tensor - that is, the state estimation task is posed as a tensor imputation problem utilizing observed patterns in measured (sampled) quantities. Two structured sampling schemes are considered, namely, asynchronous slab and fiber sampling. For both schemes, we present sufficient conditions on the number of sampled slabs and fibers that guarantee identifiability of the factors of the state tensor. Numerical results demonstrate the ability of the proposed framework to achieve high estimation accuracy in multiple sampling scenarios.

Original languageAmerican English
Article number9123942
Pages (from-to)605-610
Number of pages6
JournalIEEE Control Systems Letters
Issue number2
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

NREL Publication Number

  • NREL/JA-5D00-76262


  • Distribution system state estimation
  • model-free estimation
  • tensor decomposition
  • tensor sampling


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