arXiv:2611.13497v1 Announce Type: new Abstract: With the increasing penetration of power-electronic equipment, the transient stability of grid-forming (GFM) and grid-following (GFL) converters is increasingly characterized through the region of attraction (ROA) of the post-fault equilibrium. Sum-of-squares (SOS) programming yields certified inner approximations of the ROA, yet its computational cost grows rapidly with system order. Reduced-order models are therefore widely used to reduce computational cost and, more importantly, to enable analytical investigation. However, ROA analyses based on these models often assume that reproducing the converter's transient response, or retaining more dynamics in the correct time-frame, is sufficient to preserve the ROA of the full-order system. Using time-domain ODE simulations as a reference, the SOS-based ROA of each reduced-order GFM and GFL model is assessed against both its own simulated ROA and that of the corresponding full-order model, thereby separating SOS-induced conservativeness from model-order-induced ROA distortion. The results indicate that increasing reduced-order model complexity does not necessarily improve SOS-based ROA fidelity. In the cases examined, more complex reduced-order models yield lower SOS coverage of the full-order reference ROA, despite closer ODE-boundary agreement in some regions. Model selection should therefore consider both full-order ROA fidelity and certified coverage of the practical operating range, rather than model complexity alone.