The combination of an alkaline water electrolyzer (AWE) with a battery system powered by photovoltaics (PV) for the production of green hydrogen is investigated. A model describes the power distribution between these three subsystems (AWE, battery and PV). Variation of AWE and battery power and capacity is carried out for two locations, to identify the most appropriate setup, where the highest energy usage and operating time can be reached. The battery helps to reduce the power level of the AWE. However, an estimation of the costs indicates that further optimization is necessary.