###### Abstract
Due to these advantages, FOPID controllers have been widely used in LFC systems related to the power system in order to improve the frequency stability; among these FOPID controllers [28; 29] are: FOPID controllers whose parameters are optimized using the ICA [30], FOPID controllers whose parameters are optimized using the GBMO [31], FOPID controllers whose parameters are optimized using the SCA [32], FOPID controllers whose parameters are optimized using the PSO [33], and FOPID controllers whose parameters are optimized using the JSO algorithm [34]. The performance of FOPID controllers is favorable against disturbances and uncertainty related to system parameters, but their performance is affected by severe disturbances. Superconducting magnetic energy storage (SMES) systems store electric energy in their magnetic field and release it as needed, making them a significant contributor to improving frequency stability alongside the LFC system in power systems [35], due to their extended lifespan and high storage capacity. In [36], coordinated control of the LFC system and SMES is discussed using an H2/Hoo robust controller. However, designing such a robust controller necessitates an accurate model of the power system, and since some components may be ignored in the model, the controller's optimal performance may be compromised in real-world systems. Another approach to coordinated control is presented in [37], where a neuro-fuzzy controller is employed. Although the neuro-fuzzy controller demonstrates good results in addressing uncertainties related to the power system parameters, it is not robust against disturbances caused by the power system load. In [38], the coordinated control of the LFC system and SMES using a type-2 fuzzy controller is discussed. However, this controller is also not resistant to severe disturbances in the power system. Similarly, [39] explores the coordinated control of the LFC system and SMES using a PID controller with parameters optimized by the DE algorithm. Unfortunately, this method is also not resistant to disturbances and uncertainties in power system parameters. Reference [40] presents the coordinated control of the LFC system and SMES using a PI controller with parameters optimized using the PSO, taking into account the presence of wind turbines in the power system. However, the performance of this control method is challenging due to the severe disturbances caused by the wind turbine, making the PI controller optimized with the PSO non-resistant to such disturbances. Reference [41] discusses the coordinated control of the LFC system and SMES using a PID controller with parameters optimized by the MSA, considering the presence of wind turbines in the power system. Nevertheless, the performance of this control method is not resistant to load disturbances and disturbances from the wind turbine. In [42], the coordinated control of the LFC system and SMES using a dynamic resistance controller in the presence of wind turbines is discussed. This method exhibits resistance to load disturbances, wind turbine disturbances, and uncertainties related to power system parameters. However, it has certain drawbacks, including: (1) the complexity of the control method, which requires setting numerous parameters and involves heavy calculations, and (2) the necessity for an accurate power system model, as some parameters cannot be accurately modeled, impacting the performance of this control method. Currently, cascaded controllers are recognized for their superior system control performance compared to single controllers such as PID and FOPID. These cascaded controllers have been employed to enhance frequency stability in power systems [43; 44; 45; 46]. In [43], a cascaded FOPI-FOPD controller with optimized parameters using the DSA method is utilized to improve frequency stability in the power system.