A robust data-driven koopman kalman filter for power systems dynamic state estimation

Marcos Netto, Lamine Mili

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


This paper develops a robust generalized maximum-likelihood Koopman operator-based Kalman filter (GM-KKF) to estimate the rotor angle and speed of synchronous generators. The approach is data driven and model independent. Its design phase is carried out offline and requires estimates of the synchronous generators' rotor angle and speed, along with active and reactive power at the generators' terminal; in real-time operation, only measurements of the rotor speed, active, and reactive power are used. We first investigate the probability distribution of the transformed dynamic states by means of Q-Q plots and verify that the states of the GM-KKF approximately follow a Student's t-distribution with 20 degrees of freedom when the initial state vector is normally distributed. Under this assumption, our filter presents high statistical efficiency. Numerical simulations carried out on the IEEE 39-bus test system reveal that the GM-KKF has a faster convergence rate than the non-robust Koopman operator-based Kalman filter thanks to the adoption of a batch-mode regression formulation. They also show that the computing time of the GM-KKF is roughly reduced by one-third as compared to the one taken by our previously developed robust GM-extended Kalman filter.

Original languageEnglish (US)
Article number8384030
Pages (from-to)7228-7237
Number of pages10
JournalIEEE Transactions on Power Systems
Issue number6
StatePublished - Nov 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


  • Dynamic state estimation (DSE)
  • Kalman filter
  • Koopman mode decomposition
  • Koopman operator
  • modal analysis
  • power system state estimation
  • robust estimation
  • robust statistics
  • spectral analysis


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