###### Abstract
The FOPI-FOPD controller parameters are set using the ITAE cost function, and the simulation time is set to 10 s. In [44], a PI-TID cascaded controller is introduced, and its parameters are adjusted using the CBO algorithm to enhance frequency stability in the power system. The PI-TID cascaded controller parameters are determined using the _ISE_ cost function, and the simulation time is set to 120 s. Furthermore, in [45], a PI-FOPID cascaded controller is investigated for improving frequency stability in the power system. The parameters of the PI-FOPID cascaded controller are adjusted using the GTO technique. The ITAE cost function is employed to set the PI-FOPID cascaded controller parameters, and the simulation time is set to 30 s. In [46], the cascaded FOPDN-FOPIDN controller, whose coefficients are optimized using the CSA, is utilized for automatic generation control of production in the power system. The _ISE_ cost function is considered in optimizing the controller coefficients, and the simulation time is set to 100 s.  
The main difference between the _ISE_ and ITAE cost functions lies in the method of error calculation. Both cost functions are used to evaluate the quality of control, but they differ in how they quantify and integrate the errors over time. In the _ISE_ cost function, the squared errors at each time point are integrated over the entire time period. This means that the errors are squared and then summed up. The _ISE_ cost function is commonly used for stable control of control systems. On the other hand, the ITAE cost function calculates the absolute errors at each time point, multiplies them by time, and then sums them up. The ITAE cost function captures the process dynamics in the time domain. It emphasizes the errors that occur during the initial response of the system and can be more sensitive to transient behavior. In the context of the paper mentioned, the _ISE_ cost function is used to evaluate the frequency stability of the power system in the presence of a wind turbine. The goal is to control the power system effectively. Reference [41] also utilizes the _ISE_ cost function to control the frequency of the power system with a wind turbine and to adjust the coefficients of the PID controller. The choice of the _ISE_ cost function in this paper allows for comparison with the results obtained using the PID controller in [41]. In this paper, a novel method called the FOPD-FOPID cascaded controller is proposed for the coordinated control of the LFC system and SMES in a power system that includes a wind turbine. The parameters of the FOPD-FOPID cascaded controller are optimized using the developed Owl Search Algorithm (DOSA). The reason for selecting the FOPD-FOPID cascaded controller over other cascaded controllers, such as PI-FOPID, in the power system structure is that the FOPD-FOPID controller, incorporating the FOPD component, provides more accurate and rapid response to frequency changes in the presence of a wind turbine. This characteristic enhances the frequency stability of the power system and ensures robustness against load disturbances, wind turbine disturbances, and uncertainties associated with power system parameters. The DOSA algorithm is employed to optimize the parameters of the cascaded controller within the power system structure. The DOSA algorithm offers several advantages over other meta-heuristic algorithms such as ABC, PSO, MSA, and GTO. These advantages include: (1) robustness in the face of uncertainty related to the objective function, (2) a reduced number of control parameters, and (3) global optimization capability. The paper presents several key innovations, including:  
1. Enhancing the responsiveness of the power system in the presence of a wind turbine using the cascaded FOPD-FOPID controller. 2. Refining the parameters of the FOPD-FOPID controller through the application of the novel DOSA approach, which has not been previously explored in power system research. 3.