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To sustain a system frequency within acceptable limits, it is widely conceded that retaining a power balance between generation and demand is necessary. In order to regulate the frequency of power systems (PSs) this article proposes a novel cascaded based fractional-order controller termed as fractional-order integer- (FOI-) fractional-order proportional integral with double derivative (FOPIDD2). In addition to redox flow batteries and capacitive energy storage, the recommended control strategy has been validated with gas, thermal reheat, hydro, and nuclear power systems. Additionally, a newly designed algorithm known as squid game optimizer (SGO) optimizes the gains of the new FOI-FOPIDD2 controller. The squid game optimizer technique is inspired by the fundamental principles of a conventional Korean sport. It employs a population of candidate solutions and iteratively adjusts the control parameters to discover the optimal set that reduces frequency abnormalities and improves system stability. A comparison is also made between the controller's performance and benchmarks, including the jellyfish search algorithm, the firefly algorithm, the grey wolf optimizer, and the particle swarm algorithm. The proposed algorithms reduced peak overshoot as compared to grey wolf optimizer algorithm by 35.34%, 46.78%, and 76.89%; jellyfish search optimization algorithm by 34.76%, 77.22%, and 82.56%; and firefly algorithm by 82.67%, 89.23%, and 29.67% for frequency variations in area 1, area 2 and tie line power, respectively. Furthermore, SGO-FOI-FOPIDD2 controllers under different loading circumstances and conditions were evaluated and endorsed for their ability to withstand uncertainties in power system parameters. [ABSTRACT FROM AUTHOR]