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Hyperscale data centers operate under ultra-stringent electrical reliability requirements, where even sub-cycle voltage disturbances may trigger cascading server shutdowns, UPS transfers, and digital service interruption. Voltage sags defined under IEEE Std 1159-2019 [1] interact nonlinearly with tightly regulated constant-power electronic loads, introducing negative incremental impedance behavior and reducing effective damping at the low-voltage distribution bus. While IEEE Std 519-2014 [2] governs harmonic distortion limits for steady-state waveform quality, it does not address transient dynamic stability during short-duration disturbances. Conventional mitigation strategies based on double-conversion UPS systems and battery energy storage systems (BESS) are constrained by inverter bandwidth limitations and electrochemical degradation under frequent short-duration cycling. Superconducting Magnetic Energy Storage (SMES), which stores energy magnetically according to E = 1/2 L I^2, provides near-instantaneous bidirectional active power exchange with negligible cycle degradation [3]. This work develops a deterministic engineering framework for integrating High-Temperature Superconducting (HTS) SMES into hyperscale data center infrastructure. The framework integrates architectural design, dq-frame state-space modeling, small-signal eigenvalue analysis, electromagnetic transient validation, statistical disturbance modeling, cryogenic thermodynamic assessment, and lifecycle techno-economic evaluation. The study positions SMES not merely as a fast storage device, but as an embedded dynamic stability augmentation layer for mission-critical digital infrastructure.