arXiv:2611.05939v1 Announce Type: new Abstract: Oscillatory power components in AI data-center demand can produce large frequency deviations when they coincide with vulnerable grid modes. Mode-aware hybrid energy storage systems (HESSs) can selectively suppress these components, but their effectiveness degrades when the grid mode changes while the control target remains fixed. This paper proposes a closed-loop grid-mode-adaptive HESS control framework that integrates measurement-based modal identification with mode-selective control. A sliding-window N4SID estimator identifies the local grid dynamics from grid-side power and frequency measurements, and the resulting natural-frequency estimate is used to retune the modal suppression branch assigned to the supercapacitor. The framework is evaluated under a grid-mode shift from 0.50 to 1.35Hz while maintaining equal physical damping and approximately equal load excitation at both frequencies. Compared with the fixed-target controller, the adaptive method reduces the post-change grid-side modal power component from 8.78 to 2.02MW, corresponding to a 76.94% reduction, and substantially lowers the resulting frequency deviation.