Data-driven variable-order fractional control for grid resilience: A hybrid Caputo-Hadamard framework validated with US power system data

The rapid integration of inverter-based renewable resources poses significant challenges to power systems' stability and resilience. This paper presents a data-driven variable-order fractional control framework that enhances grids' resilience through adaptive memory management. The proposed controller employs a hybrid Caputo-Hadamard structure, in which the fractional order $\alpha(t)$ adapts in real time occording to wide-area frequency measurements. The Caputo component captures short-memory transient dynamics associated with power electronic responses, while the Hadamard component represents long-memory logarithmic effects arising from variability in the load and renewable generation. Rigorous stability analysis establishes Mittag-Leffler stability under bounded order variation and Ulam-Hyers practical stability, ensuring robustness against modeling uncertainties and numerical discretization errors. Numerical validation using realistic US power system data from Pennsylvania-New Jersey-Maryland (PJM) Interconnection, California Independent System Operator (CAISO), National Renewable Energy Laboratory (NREL), and Frequency Monitoring Network (FNET/GridEye) demonstrates consistently improved performance compared with integer-order and fixed-order fractional controllers, including up to $67\%$ reduction in voltage overshoot and $72\%$ reduction in the duration of rate of change of frequency violations under compound disturbance scenarios. The proposed framework provides a mathematically rigorous and practically viable approach for adaptive control in renewable-rich power systems, aligning with ongoing grid modernization efforts that seek to balance fast transient response with long-term stability in the system.