On the Impact of Operating Points on Small-Signal Stability: Decentralized Stability Sets via Scaled Relative Graphs

Abstract: This paper presents a decentralized frequency-domain framework to characterize the influence of the operating point on the small-signal stability of converter-dominated power systems. The approach builds on Scaled Relative Graph (SRG) analysis, extended here to address Linear Parameter-Varying (LPV) systems. By exploiting the affine dependence of converter admittances on their steady-state operating points, the centralized small-signal stability assessment of the grid is decomposed into decentralized, frequency-wise geometric tests. Each converter can independently evaluate its feasible stability region, expressed as a set of linear inequalities in its parameter space. The framework provides closed-form geometric characterizations applicable to both grid-following (GFL) and grid-forming (GFM) converters, and validation results confirm its effectiveness.