Spurious local minima in power system state estimation

Richard Y. Zhang, Javad Lavaei, Ross Baldick

Research output: Contribution to journalArticlepeer-review


The power system state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares. This is a nonconvex optimization problem, so even in the absence of measurement errors, local search algorithms like Newton/Gauss-Newton can become 'stuck' at local minima, which correspond to nonsensical estimations. In this paper, we observe that local minima cease to be an issue as redundant measurements are added. Posing state estimation as an instance of the low-rank matrix recovery problem, we derive a bound for the distance between the true solution and the nearest spurious local minimum. We use the bound to show that spurious local minima of the nonconvex least-squares objective become far-away from the true solution with the addition of redundant information.

Original languageEnglish (US)
Article number8728030
Pages (from-to)1086-1096
Number of pages11
JournalIEEE Transactions on Control of Network Systems
Issue number3
StatePublished - Sep 2019
Externally publishedYes


  • Critical points
  • local minima
  • nonconvex optimization
  • power systems
  • state estimation

ASJC Scopus subject areas

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


Dive into the research topics of 'Spurious local minima in power system state estimation'. Together they form a unique fingerprint.

Cite this