Sample Complexity of Power System State Estimation Using Matrix Completion

Andrey Bernstein, Joshua Comden, Marcello Colombino, Zhenhua Liu

Research output: Contribution to conferencePaperpeer-review

4 Scopus Citations


In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system - a problem known as sample complexity analysis in computer science. Motivated by the increasing adoption of distributed energy resources into the distribution-level grids, it becomes imperative to estimate the state of distribution grids in order to ensure stable operation. Traditional power system state estimation techniques mainly focus on the transmission network which involve solving an overdetermined system and eliminating bad data. However, distribution networks are typically underdetermined due to the large number of connection points and high cost of pervasive installation of measurement devices. In this paper, we consider the recently proposed state-estimation method for underdetermined systems that is based on matrix completion. In particular, a constrained matrix completion algorithm was proposed, wherein the standard matrix completion problem is augmented with additional equality constraints representing the physics (namely power-flow constraints). We analyze the sample complexity of this general method by proving an upper bound on the sample complexity that depends directly on the properties of these constraints that can lower number of needed samples as compared to the unconstrained problem. To demonstrate the improvement that the constraints add to state estimation, we test the method on a 141-bus distribution network case study and compare it to the traditional least squares minimization state estimation method.


Conference2019 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids, SmartGridComm 2019

Bibliographical note

See NREL/CP-5D00-74580 for preprint

NREL Publication Number

  • NREL/CP-5D00-75822


  • matrix completion
  • power system
  • sample complexity analysis
  • state estimation


Dive into the research topics of 'Sample Complexity of Power System State Estimation Using Matrix Completion'. Together they form a unique fingerprint.

Cite this