Renewable electric energy can be transformed into storable methane via electrolysis and subsequent methanation. Power to Gas systems appear as a promising technology to exploit the surplus energy from renewable power plants; different gases can be produced (e.g. methane or hydrogen). In this Master Thesis work, two different Power to Gas systems are modelled using Matlab Simulink: a Solid Oxide Electrolyser with a CO2-methanator and a Solid Oxide Co-Electrolyser with a CO-methanator. This latter component can operate with an inlet H2/CO-ratio equal to 3 or larger. A ratio of 5 is also considered. The CO2, coming from biogas produced in the Waste Water Treatment Plant of EDAR Riu Sec situated in Sabadell (Barcelona), is captured and processed in order to obtain methane.