One option to utilize excess electric energy is its conversion to hydrogen and the subsequent methanation. An alternative to the classical chemical Sabatier process is the biological methanation (methanogenesis) within biogas plants. In conventional biogas plants methane and carbon dioxide is produced. The latter can be directly converted to methane by feeding hydrogen into the reactor, since hydrogenotrophic bacteria are present. In the present contribution, a comprehensive simulation study with respect to stationary operating conditions and disturbances is presented. It reveals two qualitative different limitations, namely a biological limit (appr. at 4m<SUB>H2</SUB><SUP>3</SUP>/m<SUB>CO2</SUB><SUP>3</SUP> corresponds to 4.2m<SUB>H2,STP</SUB><SUP>3</SUP>/m<SUB>liq</SUB><SUP>3</SUP>/d) as well as a transfer limit. A parameter region for a safe operation was defined. The temporary operation with stationary unfeasible conditions was analysed and thereby three qualitatively different disturbances can be distinguished. In one of these the operation for several days is possible. On the basis of these results, a controller was proposed and tested that meets the demands on the conversion of hydrogen and also prevents the washout of the microbial community due to hydrogen overload.