Display omitted •Thermal decoupling of methanation and electrolysis is an effective solution.•Power-to-Gas feasibility is strictly related on oxygen selling and local grants.•Highly efficient natural gas production with 75% conversion efficiency.•Optimization suggests reducing the capacity of the methanation reactor. This work presents a numerical analysis of a fully renewable Power-to-Gas system driven by photovoltaic and anaerobic digestion technologies, to produce synthetic renewable natural gas. The anaerobic digester is supplied by municipal wastes and it produces biogas, including about 35 % of carbon dioxide. This carbon dioxide is separated by means of an upgrading unit and it is combined in a three stage multi-tubular methanation reactor with the hydrogen produced by solid oxide electrolysis. A novel control strategy is developed to achieve a stable, safe, and efficient operation of the reactor. Suitable zero-dimensional and one-dimensional steady state models are developed in MatLab for the solid oxide electrolyzer and the methanation reactor. Such MatLab models are subsequently integrated into TRNSYS environment to perform the dynamic simulation for one year of operation of the whole system. A suitable thermoeconomic analysis is also implemented, also considering the possibility of selling the oxygen produced by the electrolyzer for industrial purposes. The results show that the proposed system achieves a primary energy saving of 30.33 GWh per year with 6,330 tCO2eq per year saved. The economic profitability of the is also very good, showing a Simple Payback of 2.63 years. The income due to the selling of oxygen plays a crucial role in this result. The overall efficiency of the system is equal to 0.75, that is extremely high when compared to similar layouts. The results from the thermoeconomic optimization show that the lowest Simple Payback value, i.e. less than 2 years, is obtained when the capacity of the methanation reactor is reduced by five times.