The power system on Jeju Island currently faces challenges due to an imbalance between power supply and demand owing to increasing renewable energy (RE) generation. Consequently, the multi-infeed high-voltage direct-current (MIDC) systems are expected to play an important role in reducing RE curtailment and increasing RE penetration. However, despite the balance between power supply and demand, transmission line (TL) overloads on Jeju Island, which has a low permissible rating, may lead to RE curtailment. We propose an operational strategy for the MIDC systems to mitigate TL overloading and RE curtailment. This strategy was aimed at managing the possible congestion of TLs, maintaining a power supply–demand balance, and increasing the penetration level of RE. In this paper, we present a scheme for calculating the operating points of the MIDC systems and allocating RE curtailment using optimization with security constraints to mitigate TL overloading. The proposed optimization model simplifies solving the mathematical equations involved by employing a sensitivity factor called the power transfer distribution factor (PTDF), using which linear programming (LP) optimization can be performed. To verify the feasibility of the operational strategy, case studies are conducted using an actual Jeju Island power system with a power system analysis tool—Power System Simulator for Engineering (PSS/E). The optimization problem was solved using MATLAB.