The dynamic operation of a power-to-gas plant powered by wind energy is theoretically studied by coupling an empirical model of an alkaline water electrolyzer with a 1D heterogeneous model of a methanation reactor. H(2)produced by the electrolyzer follows the wind power profile, but operation in the part-load range can raise safety concerns. The dynamically generated methane quality comes close to the required value for injection into the gas grid, if the stoichiometric ratio is controlled. To satisfy the gas quality at all times, it is necessary to design a more tolerant reactor.