This article presents a power to SNG (synthetic natural gas) system that converts hydrogen into SNG via a methanation process. In our analysis, detailed models for all the elements of the system are built. We assume a direct connection between a wind farm and a hydrogen generator. For the purposes of our calculations, we also assume that the hydrogen generator is powered by the renewable source over a nine-hour period per day (between 21:00 and 06:00), and this corresponds to the off-peak period in energy demand. In addition, a hydrogen tank was introduced to maximize the operating time of the methanation reactor. The cooperation between the main components of the system were simulated using Matlab software. The primary aim of this paper is to assess the influence of various parameters on the operation of the proposed system, and to optimize its yearly operation via a consideration of the most important constraints. The analyses also examine different nominal power values of renewables from 8 to 12 MW and hydrogen generators from 3 to 6 MW. Implementing the proposed configuration, taking into account the direct connection of the hydrogen generator and the methanation reactor, showed that it had a positive effect on the dynamics and the operating times of the individual subsystems within the tested configuration.