  This paper develops a grey-box approach to 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 enhances the impedance transfer function approach
popular in power electronic systems and favoured by manufacturers of wind and
solar systems for the limited disclosure required. Impedance participation
factors are proposed and defined in terms of the residues of the whole-system
admittance matrix. It is proved that, so defined, these impedance participation
factors equal the sensitivity of whole-system eigenvalues to apparatus
impedances. The classic state participation factors are related to the
impedance participation factors 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 information available. The association of
impedance participation factors with eigenvalue sensitivity points to the
re-tuning that would stabilize the system. The impedance participation factors
can be measured in the field or calculated from black-box impedance spectra
with little prior-knowledge required.
