arXiv:2610.22227v1 Announce Type: new Abstract: Stability issues in converter-dominated grids have a multifold nature, where static, small-signal and large-signal phenomena can influence each other. Capturing the interplay among these different stability aspects requires a rethinking of conventional modeling and analysis tools for power systems. As a further complication, Intellectual Property protection among manufacturers and system operators makes detailed converters and grid models unattainable. This motivates the use of data-driven approaches for stability analysis and control, nevertheless achieving an insightful representation of static, small-signal and large-signal phenomena from data still leaves many open questions. This paper discusses model-based and data-driven methodologies for stability analysis of converter-dominated grids. The instability mechanisms of static, small-signal and large-signal phenomena are conceptually explained, and the capability of different modeling and analysis tools to investigate them is examined. The effectiveness of data-driven methodologies to analyze instability phenomena in their multifold nature is debated, and the challenges on data completeness, model generalization under untrained conditions, physical interpretability, and uncertainty awareness are discussed.