Renewable energy curtailment often occurs to accommodate large amounts of renewable energy sources in power systems while maintaining system stability and reliability. Widely known methods, such as new transmission line construction, the introduction of demand-side resources, and the reduction of conventional generator output, can minimize the occurrence of curtailment; however, there are difficulties in introducing them because of social and economic problems. For these problems, the Jeju power system adopted a battery energy storage system (BESS) resource to mitigate the curtailment and secure frequency stability with the high penetration of renewable energy. The small-size Jeju island power system is operated with reliability must-run (RMR) units and high-voltage direct current (HVDC) lines connected to the mainland. Since the number of RMR units contributes to frequency stability by providing inertia, reducing the number of operating units for curtailment mitigation is difficult. Therefore, in this paper, based on the current “Carbon-Free island” policy and operation plan of the Jeju power system, we proposed a BESS for reducing the number of RMR units, observe the effect of reducing curtailment using the BESS, and suggest a practical operation plan to reduce the number of RMR units under conditions that secure frequency stability.