  Multiple types of Nyquist-like impedance-based criteria are utilized for the
small-signal stability analysis of converter-based AC systems. It is usually
considered that the determinant-based criterion can determine the overall
stability of a system while the eigenvalue-based criterion can give more
insights into the mechanism of the instability. This paper specifies such
understandings starting with the zero-pole calculation of impedance matrices
obtained by state-spaces with the Smith-McMillan form, then clarifying the
absolute reliability of determinant-based criterion with the common assumption
for impedance-based analysis that each subsystem can stably operate before the
interconnection. However, ambiguities do exist for the eigenvalue-based
criterion when an anticlockwise encirclement around the origin is observed in
the Nyquist plot. To this end, a logarithmic derivative-based criterion to
directly identify the system modes using the frequency responses of loop
impedances is proposed, which owns a solid theoretical basis of the Schur
complement of transfer function matrices. The theoretical analysis is validated
using a PSCAD simulation of a grid-connected two-level voltage source
converter.
