  Nyquist criterion-based impedance ratio criteria (IRCs) have been widely
applied for inspecting the risk of small-signal instability among
converter-based AC power systems. Aided by a comparative study on voltage
source converter, including the single-input single-output (SISO) and multiple
input multiple output (MIMO) analyses in both the dq and the sequence domain,
two aspects are emphasized in this paper: 1) the sufficiency of SISO analysis
when the mapping function (MF) is observable to potentially unstable modes, and
2) the inconvenience of IRCs with an unintended right-half plane pole emergence
of MF due to the source-load partition. The strictness of analyses is proved by
a systematical deduction of explicit analytical impedance models using the
state space. Moreover, a novel criterion that relies on the logarithmic
derivative of MFs is proposed, which can identify the system modes directly,
serve as an alternative to IRCs, and be extended to other transfer
function-based stability analyses.
