This work has been performed within a Research and Development contract on Hydrogen Energy granted by Acciona Biocombustibles S. A., a branch of Acciona Energía, to the Public University of Navarra and deals with the production of sustainable hydrogen from renewable primary energy sources. In this work, the results obtained in several experiments carried out with a commercial alkaline water electrolyzer of 5 kW working under the dynamic conditions typical of wind energy systems are presented. Actual wind speed data from a wind farm were considered and allowed us to establish the power profile that would give a wind turbine of a rated power equivalent to that of the electrolyzer under the considered wind conditions. This power profile was supplied to the electrolyzer by means of a power supply (wind emulator) designed and built by our group. The evolution of the stack voltage, efficiency, and temperature, as well as the purity of the produced hydrogen and oxygen, was monitored. The results showed that the electrolyzer behavior was reliable with high efficiencies, satisfactory gas purities, and fast dynamic response to the varying conditions imposed.