  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.
