Adaptive State Estimation for Power Systems Measured by PMUs with Unknown and Time-Varying Error Statistics

Gang Cheng, Yuzhang Lin, Yanbo Chen, Tianshu Bi

Research output: Contribution to journalArticlepeer-review


Measurement error is a crucial factor that determines the accuracy of state estimation (SE). Conventional estimators have fixed models, and can yield optimal performance only when the measurement error statistics exactly meet the assumptions. In reality, however, the error distribution is usually unknown and time-varying, resulting in suboptimal state estimates in most cases. This paper develops the concept of adaptive SE for power systems measured by phasor measurement units (PMUs). First, the Gaussian-Laplacian Mixture (GLM) model is developed to fit the body and tail of unknown measurement error distributions. Then, an adaptive estimation framework is proposed based on the Expectation-Maximization (EM) algorithm. It is capable of tracking the actual error statistics online, and adjusting the parameters of SE to maintain near-optimality of state estimates under complex measurement error conditions. Simulation results demonstrate that the proposed adaptive estimator yields more accurate state estimates than the well-known Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) estimators by adapting itself to the variations of measurement error statistics.

Original languageEnglish (US)
Article number9337223
Pages (from-to)4482-4491
Number of pages10
JournalIEEE Transactions on Power Systems
Issue number5
StatePublished - Sep 2021


  • Expectation maximization
  • non-gaussian
  • phasor measurement unit
  • power system monitoring
  • situational awareness
  • state estimation
  • unknown measurement errors

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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