In this study, a power supply planning and operation model that considers demand and supply, as well as the geographic characteristics of electricity and gas supply infrastructure, incorporates decarbonization technologies such as synthetic methane, hydrogen facilities, and carbon capture and storage, builds a model that considers hydrogen supply infrastructure as well as electricity and city gas, and evaluates the power generation mix when achieving carbon neutrality in 2050 by comparing synthetic methane and hydrogen. The utilization of synthetic methane allows for the use of existing facilities, and it has been shown that carbon neutrality can be achieved at a low cost. From these results, it can be concluded that to achieve carbon neutrality in an economic rationality, it is important to utilize existing facilities that can be used, although the shift to electrification should be promoted. The results also suggest that the increased deployment of distributed energy resources such as cogeneration system will contribute to reducing the shadow price difference in the shadow price of electricity demand for each node in the area, and that the widespread use of cogeneration system, which can make use of existing city gas transportation infrastructure, is also significant. To achieve this, it will be necessary to reduce the cogeneration system installation cost.