Revisiting Impedance-based Criteria for Converter-Based AC System

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 eigenvalue-based criterion can identify a critical loop apart from the overall attribute given by the determinant-based criterion. 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. On the other hand, ambiguities exist for the eigenvalue-based criterion due to the square root of the transfer function, which takes away the intuitiveness of Nyquist plots where the open-loop right-half plane pole checks or the encirclement direction around the origin can be ignored. 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 grid-connected example of a two-level voltage source converter is focused on, and simulation results in PSCAD match the theoretical analyses.