Robust Hybrid Linear State Estimator Utilizing SCADA and PMU Measurements

Ahmad Salehi Dobakhshari, Mohammad Abdolmaleki, Vladimir Terzija, Sadegh Azizi

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


This paper intends to improve the accuracy of power system State Estimation (SE) by introducing a hybrid linear robust state estimator. To this end, automatic bad data rejection is accomplished through an M-estimator, i.e. a Schweppe-type estimator with Huber loss function. The method of Iteratively Reweighted Least Squares (IRLS) is used to maximize the likelihood function in the M-estimator. Leverage measurements are also treated by a simple yet effective formulation. To run the algorithm for real-world large-scale grids, cumbersome construction of the Jacobian matrix at each iteration is avoided. In addition, convergence to the local minima faced in the large-scale Gauss-Newton algorithm is not a concern as the proposed formulation is linear with no approximation. As observability and redundancy considerations mandate SE to take advantage of traditional SCADA measurements along with available PMU measurements, the linearity of the proposed SE formulation is guaranteed regardless of whether PMU-only, SCADA-only or hybrid SCADA/PMU measurements are utilized. In this regard, covariance matrix for measurements weights is derived for both types of measurements. Thanks to the linear formulation and therefore swiftness of the proposed algorithm, SE could be run for different power systems with a few up to thousands of buses.

Original languageEnglish
Article number9154575
Pages (from-to)1264-1273
Number of pages10
JournalIEEE Transactions on Power Systems
Issue number2
Publication statusPublished - Mar 2021
Externally publishedYes


  • Huber loss function
  • pmu
  • power system operation
  • rtu
  • scada
  • schweppe-type estimator
  • state estimation


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