Participation Analysis in Impedance Models: The Grey-Box Approach for Power System Stability

Yue Zhu, Yunjie Gu, Timothy Green

Research output: Contribution to journalArticlepeer-review

32 Citations (SciVal)
122 Downloads (Pure)


This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required.
Original languageEnglish
Pages (from-to)343-353
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number1
Early online date10 Jun 2021
Publication statusPublished - 1 Jan 2022

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council of U.K. (EPSRC) under Awards EP/S000909/1 and EP/T021780/1.


  • Admittance
  • Eigenvalue sensitivity
  • Impedance
  • Inverter-based resource
  • Participation factor

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Participation Analysis in Impedance Models: The Grey-Box Approach for Power System Stability'. Together they form a unique fingerprint.

Cite this