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Impedance models of power systems are useful when state-space models ofapparatus such as inverter-based resources (IBRs) have not been made availableand instead only black-box impedance models are available. For tracing the rootcauses of poor damping and tuning modes of the system, the sensitivity of themodes to components and parameters are needed. The so-called criticaladmittance-eigenvalue sensitivity based on nodal admittance model has provideda partial solution but omits meaningful directional information. Thealternative whole-system impedance model yields participation factors ofshunt-connected apparatus with directional information that allows separatetuning for damping and frequency, yet do not cover series-connected components.This paper formalises the relationships between the two forms of impedancemodels and between the two forms of root-cause analysis. The calculation ofsystem eigenvalue sensitivity in impedance models is further developed, whichfills the gaps of previous research and establishes a complete theory ofimpedance-based root-cause analysis. The theoretical relationships and thetuning of parameters have been illustrated with a three-node passive network, amodified IEEE 14-bus network and a modified NETS-NYPS 68-bus network, showingthat tools can be developed for tuning of IBR-rich power systems where onlyblack-box impedance models are available.

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