This paper investigates the potential capability of recently proposed flexible power transmisssion device, namely, variable frequency transformer (VFT), to effectively mitigate low‐frequency oscillations (LFOs). VFT with a high rotational inertia has an inherent natural damping capacity that may be utilized to attenuate power system oscillations. To provide additional system damping, a comprehensive approach is presented, which integrates the coordination of VFT with superconducting magnetic energy storage (SMES). An intelligently designed novel cascaded lead‐lag fuzzy logic controller (CLLFLC) utilizing a global stabilizing control signal constitutes the supervisory controller for VFT and SMES. The stabilizing feedback signal that contains information about overall system dynamics can be easily obtained through wide area measurement systems (WAMS) and is determined using participation factor (PF) analysis. In addition, a newly developed optimization technique known as K‐means optimizer (KO) is used for optimizing CLLFLC parameters utilized for the carefully orchestrated operation of VFT and SMES. Numerous simulation studies are conducted on two‐area multigenerator interconnected network to validate the resilience of the suggested approach. The findings demonstrate that the proposed control strategy with optimized gain parameters efficaciously damped the LFOs. To show the superior damping effectiveness of the suggested KO‐CLLFLC controller, a comparative performance evaluation with a damping controller designed on residue approach was also undertaken.