Robust Frequency Regulation of Hybrid Wind–PV Thermal Power Systems via Adaptive Fractional-Order PID Control

As modern electrical grids increasingly incorporate renewable generation—specifically from wind and solar–thermal installations—they face heightened volatility and operational complexities, which severely complicate load frequency regulation. While fractional-order proportional-integral-derivative (FOPID) controllers are commonly employed for this purpose, their conventional formulations rely on fixed fractional parameters that cannot adapt to fluctuating network conditions. To address this limitation, the present study develops an adaptive FOPID (AFOPID) control architecture capable of real-time adjustment of fractional orders, thereby enhancing regulatory effectiveness. The Coot Optimization Algorithm (COA) is utilized to optimally determine the operational parameters of all controllers under investigation. The proposed strategy is validated on a simulated hybrid power system comprising wind generation, solar–thermal units, and physical nonlinearities including governor dead band and generation rate constraints. A comparative analysis is conducted across four distinct operating scenarios, benchmarking the COA-tuned AFOPID against conventional PI, PID, and standard FOPID controllers. Quantitative results demonstrate that the proposed COA-AFOPID configuration achieves superior performance, with improvements in settling time up to 46.06% and reductions in ITAE index up to 89.89% compared to traditional methods. These findings confirm the enhanced stability and robustness of the proposed approach for frequency regulation in sustainable energy networks.