The increasing share of renewable energy in the electricity generation leads to continuous rising fluctuations in the grid. Together with the political objective of reducing the CO2 emissions, this leads to the necessity of new, innovative concepts of energy storage, especially for the long term storage of electrical energy. A possible option for this purpose is the power-to-gas concept, which stores energy chemically. In this thesis a power-to-gas concept is developed, which avoids mass exchange with its surrounding and interacts with its environment only via the grid. This is achieved by the storage of all produced and required media (H2, O2, CH4, CO2 and H2O). Thus, large amounts of (surplus) electrical energy can be stored over long periods and supplied back to the grid when demanded. Therefore this work consists of two main tasks: Modeling and optimizing of such a facility. The modeling part includes the conceptual design, the layout and the implementation of the facility together with all required components in the simulation software EBSILON Professional. Optimizing involves the development of a scheme for the ideal dimensioning under given constraints as well as for the determination of ideal operation schedules. Finally the optimization results are validated and the impact of the modeled power-to-gas plant on the Austrian grid is investigated.