In this paper, the application of flux-coupling-type superconducting fault current limiters (FC-SFCLs) in a renewable power system (RPS) with paralleled synchronous and virtual synchronous generators is studied. First, the configuration of the RPS and the working principles of the FC-SFCLs are elaborated, and the potential influences of the FC-SFCLs on the RPS are theoretically investigated from the perspectives of system stability enhancement and fault current limitation. Then, the conceptual design of the FC-SFCLs based on YBCO tapes is carried out and the superconducting coil's quench resistance is determined. Digital simulations confirm the adequacy of the electrical properties and dissipated energy of the FC-SFCLs, while the relatively short current-limiting duration ensures the generated heat in the FC-SFCLs is within acceptable limits. Moreover, using the FC-SFCLs can suppress the fault currents, mitigate the rotor speed deviation, and alleviate the imbalanced power for the RPS. Hence, the stability improvement of the RPS is fulfilled, and the effectiveness of the FC-SFCLs in the RPS is validated.