Small-signal Stability Analysis of Lossless Power Systems Using Convexity of Energy Functions

Abstract

In this study, we propose a theoretical framework for evaluating the small-signal stability of power systems. Specifically, we derive a new necessary and sufficient condition for the small-signal stability of power systems in an analytically tractable form. Furthermore, this condition is invariant to the state dimension of synchronous generator models with varying levels of detail, effectively unifying the stability criteria for synchronous generators and grid-forming inverters. This proposal systematizes the analysis of mixed-source systems, thereby supporting more reliable decision-making in the planning and operation of future power systems.