Spurious Critical Points in Power System State Estimation

Richard Yi Zhang, Javad Lavaei, Ross Baldick

Research output: Contribution to conferencePaperpeer-review


The power systems state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares (NLS). 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 quadratic 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 critical points of the nonconvex least squares objective become increasing rare and far-away from the true solution with the addition of redundant information.
Original languageEnglish (US)
Number of pages10
StatePublished - Jan 3 2018
Externally publishedYes
EventHawaii International Conference on System Sciences 2018 - Hilton Waikoloa Village, United States
Duration: Jan 3 2018Jan 6 2018
Conference number: 51


ConferenceHawaii International Conference on System Sciences 2018
Abbreviated titleHICSS 2018
Country/TerritoryUnited States
CityHilton Waikoloa Village


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


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