Impedance-based Root-cause Analysis: Comparative Study of Impedance Models and Calculation of Eigenvalue Sensitivity

Yue Zhu, Yunjie Gu, Yitong Li, Timothy C. Green

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)
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Impedance models of power systems are useful when state-space models of apparatus such as inverter-based resources (IBRs) have not been made available and instead only black-box impedance models are available. For tracing the root causes of poor damping and tuning modes of the system, the sensitivity of the modes to components and parameters are needed. The so-called critical admittance-eigenvalue sensitivity based on nodal admittance model has provided a partial solution but omits meaningful directional information. The alternative whole-system impedance model yields participation factors of shunt-connected apparatus with directional information that allows separate tuning for damping and frequency, yet do not cover series-connected components. This paper formalises the relationships between the two forms of impedance models and between the two forms of root-cause analysis. The calculation of system eigenvalue sensitivity in impedance models is further developed, which fills the gaps of previous research and establishes a complete theory of impedance-based root-cause analysis. The theoretical relationships and the tuning of parameters have been illustrated with a three-node passive network, a modified IEEE 14-bus network and a modified NETS-NYPS 68-bus network, showing that tools can be developed for tuning of IBR-rich power systems where only black-box impedance models are available.
Original languageEnglish
Pages (from-to)1642 - 1654
Number of pages13
JournalIEEE Transactions on Power Systems
Issue number2
Early online date30 May 2022
Publication statusPublished - 1 Mar 2023


  • Admittance
  • Analytical models
  • Eigenvalues and eigenfunctions
  • Impedance
  • Integrated circuit modeling
  • Mathematical models
  • Root-cause analysis
  • Sensitivity
  • eigenvalue sensitivity
  • grey-box approach
  • impedance model

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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