Investigation of Impedance-Based Stability Criteria via Irreducible General Port Model: Applications to Ring and Multiterminal Scenarios

Impedance-based stability criterion is widely used in small-signal stability analysis of converter-interfaced power systems. However, this criterion faces challenges in some multiterminal scenarios. For example, when a new connection is added to form a ring network, the criterion may yield erroneous results because the two ports are not independent. Moreover, its application becomes very complex in multi-terminal system with both impedance-stable (IS) and admittance-stable (AS) devices. To address these challenges, this paper develops an irreducible general port model based on transfer function matrix theory. This model offers a rigorous theoretical framework to revisit the fundamental principles of impedance-based criteria, clarifying their equivalence and sufficiency in high-dimensional cases. We further classify subsystems and analyze their relationships from both mathematical and physical perspectives, summarizing the rules for applying these criteria. Building on this theoretical foundation, a method based on constructing virtual subsystems is proposed for ring network formation scenarios, which accurately predicts stability. For systems with both IS and AS devices, the impedance-based criterion is extended via a rearranged port model, significantly simplifying modeling and analysis. Case studies on diverse multi-terminal systems demonstrate the effectiveness and applicability of the proposed methods.