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.