A systematic methodology for the synthesis of power systems has been developed, which explores the interactions among the equipment as well as the processes in power and utility systems. Also, the optimization is able to study the integration of CO2 capture processes with power systems for minimizing site-wide fuel consumption. Typical operating conditions for I precombustion as well as postcombustion CO2 capture have been applied to estimate energy demand within the CO2 capture; process. The power system is designed not only to meet the electricity and shaft power demand from the background process but also to satisfy the additional energy requirement incurred by CO2 removal. With the energy integration for the overall systems, the fuel consumption could be reduced, and operating cost, minimized. A case study is presented to demonstrate the usefulness and effectiveness of the proposed methodology for the design of energy and power systems in liquid natural gas (LNG) plants, under a carbon-constrained business environment.