###### Abstract  
The penetration of intermittent wind turbines in power systems imposes challenges to frequency stability. In this light, a new control method is presented in this paper by proposing a modified fractional order proportional integral derivative (FOPID) controller. This method focuses on the coordinated control of the load-frequency control (LFC) and superconducting magnetic energy storage (SMES) using a cascaded FOPD-FOPID controller. To improve the performance of the FOPD-FOPID controller, the developed owl search algorithm (DOSA) is used to optimize its parameters. The proposed control method is compared with several other methods, including LFC and SMES based on the robust controller, LFC and SMES based on the Moth swarm algorithm (MSA)-PID controller, LFC based on the MSA-PID controller with SMES, and LFC based on the MSA-PID controller without SMES in four scenarios. The results demonstrate the superior performance of the proposed method compared to the other mentioned methods. The proposed method is robust against load disturbances, disturbances caused by wind turbines, and system parameter uncertainties. The method suggested is characterized by its resilience in addressing the challenges posed by load disturbances, disruptions arising from wind turbines, and uncertainties surrounding system parameters. I +
Footnote †: journal: _Algorithms_  
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Footnote 7: email: [EMAIL_ADDRESS]. The classic proportional integral derivative (PID) controller is still one of the most popular and widely used controllers in the power industry, which is widely used in power system LFC due to its simplicity, ease of use, fast performance, and stability [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. In LFC systems related to power systems, a number of PID controllers are used in order to improve frequency stability; among these PID controllers [11; 12] are: PID controllers whose parameters are optimized using the ICA [13] (see list of abbreviations at the end of the article), PID controllers whose parameters are optimized using the PSO [14], PID controllers whose parameters are optimized using the EHO [15], PID controllers whose parameters are optimized using the ACO [16], fuzzy PID controllers [17], fuzzy PID controllers whose parameters are optimized using the optimization algorithm based on novel HLUS-TLBO [18], fuzzy PID controllers whose parameters are optimized using the DE algorithm [19], fuzzy PID controllers whose parameters are optimized using the HDE-PS algorithm [20], fuzzy PID controllers whose parameters are optimized using the PSO [21], fuzzy PID controllers whose parameters are optimized using ACO [22], fuzzy PID controllers whose parameters are optimized using the HFA-PS algorithm [23], control fuzzy PID controllers whose parameters are optimized using MBA [24], and fuzzy PID controllers whose parameters are optimized using FA [25]. In [26], the fuzzy PID controller whose coefficients are optimized using GA is used to improve the frequency of the power system. The PID controller does not perform effectively against disturbances in the power system and the uncertainty of the parameters related to the power system. Fuzzy PID controllers are somewhat resistant to power system disturbances, but they do not perform well against the uncertainty related to the power system. The fractional order PID (FOPID) controller has two degrees of freedom compared to the PID controller, and these two degrees of freedom have advantages such as: (1) more accuracy, (2) better stability, and (3) robust performance in systems with disturbance and parameter uncertainty [27].