Solar PV focused LFC studies utilizing an SFS-optimized PID with fractional derivative (PIDDμ), and incorporating BESS and FESS applications

• To present the mathematical model of solar PV to improve load frequency control (LFC) within power systems. • In addition, a newly designed PID with fractional derivative is utilised first time in LFC as secondary controller. • The gains of PIDs are optimized through stochastic fractional search (SFS) algorithm considering IAE, ITAE and ITSE error definitions. • To investigate the application of BESS and FESS to improve LFC problem of power system. • The investigated results are matched with state-of-art for wider operating conditions of LFC. This study investigates the application of a PID controller with a fractional derivative component (PIDD μ ), optimized using the stochastic fractional search (SFS) technique, for load frequency control (LFC) in power systems. Additionally, solar PV and battery energy storage systems (BESS) and flywheel energy storage systems (FESS) are integrated as backup sources to enhance the LFC performance. To assess the effectiveness of the proposed approach, three error metrics—Integral Time Absolute Error (ITAE), Integral Time Multiplied Square Error (ITSE), and Integral of Absolute Error (IAE)—are evaluated. The results are compared with recent optimization-based LFC techniques across various scenarios. It is found that the SFS-PIDD μ achieves IAE=0.006786, ITSE=1.07e-05, and ITAE=0.01853, which are significantly lower than the error values produced by other LFC techniques. Furthermore, integrating solar PV, along with BESS and FESS, further reduces these error values. The graphical LFC responses of the SFS-PIDD μ outperform other optimization-based LFC techniques. The robustness of the approach is also validated against random load changes of varying magnitudes and for broader parametric variations.