Generalized Nyquist Criterion Limitations and Misconceptions for Frequency Domain Stability Analysis of Inverter-based Resources Integrated Power Grids

Abstract

This paper presents theoretical and numerical studies demonstrating the limitations of the Generalized Nyquist Criterion (GNC) in assessing the small-signal stability of inverter-based resources (IBRs) modeled as multi-input, multi-output (MIMO) systems. GNC leads to unnecessary computational burden and increased analytical complexity for nominal stability analysis. The paper demonstrates that the GNC framework is not reliable for robust-stability analysis and may lead to misleading results when applied to MIMO IBR systems. To demonstrate these limitations and enable a proper MIMO robust stability assessment of IBRs using mu-analysis, the paper develops a model-uncertainty-augmented representation of an IBR-integrated power grid. The proposed model explicitly captures the structural characteristics and spatial distribution of various uncertainty sources, such as parametric variations, unmodeled dynamics, and measurement errors. Since these uncertainties naturally occur in the physical three-phase (abc) systems, they are systematically transformed into the dq0 frame within the developed model.