Cryogenic Carbon Capture (CCC) is a CO2 mitigation process that can be integrated into existing baseline and load following fossil-fueled power plants. This process consumes less energy than conventional chemical absorption and includes energy storage capability. The CCC process has a fast response time to load changes to allow higher utilization of intermittent renewable power sources to be used at a grid-scale level in the power sector. The impact of the CCC process on the performance and operating profit of a single fossil-fueled power generation unit is studied in this paper. The proposed system (power production from wind, coal, and natural gas) meets the total electricity demand with 100% utilization of the available wind energy. The operational strategy for the hybrid energy-carbon capture system and the change in the performance of the hybrid system due to the seasonal changes are also examined in this paper. A sensitivity analysis is implemented to investigate the change in operating strategy of the hybrid system based on the relative fraction of wind energy adoption. The optimal wind energy adoption factor in the proposed system is obtained.