Power to gas (PtG) is an emerging technology that allows to overcome the issues due to the increasingly widespread use of intermittent renewable energy sources (IRES). Via water electrolysis, power surplus on the electric grid is converted into hydrogen or into synthetic natural gas (SNG) that can be directly injected in the natural gas network for long-term energy storage. The core units of the Power to synthetic natural gas (PtSNG) plant are the electrolyzer and the methanation reactors where the renewable electrolytic hydrogen is converted to synthetic natural gas by adding carbon dioxide. A technical issue of the PtSNG plant is the different dynamics of the electrolysis unit and the methanation unit. The use of a hydrogen storage system can help to decouple these two subsystems and to manage the methanation unit for assuring long operation time and reducing the number of shutdowns. The purpose of this paper is to evaluate the energy storage potential and the technical feasibility of the PtSNG concept to store intermittent renewable sources. Therefore, different plant sizes (1, 3, and 6 MW) have been defined and investigated by varying the ratio between the renewable electric energy sent to the plant and the total electric energy generated by the renewable energy source (RES) facility based on a 12 MW wind farm. The analysis has been carried out by developing a thermochemical and electrochemical model and a dynamic model. The first allows to predict the plant performance in steady state. The second allows to forecast the annual performance and the operation time of the plant by implementing the control strategy of the storage unit. The annual overall efficiencies are in the range of 42–44% low heating value (LHV basis). The plant load factor, i.e., the ratio between the annual chemical energy of the produced SNG and the plant capacity, results equal to 60.0%, 46.5%, and 35.4% for 1, 3, and 6 MW PtSNG sizes, respectively.