Green hydrogen is likely to play an important role in meeting the net-zero targets of countries around the globe. One potential option for green hydrogen production is to run electrolysers directly from offshore wind turbines, with no grid connection and hence no expensive cabling to shore. In this work, an innovative proof of concept of a wind farm control methodology designed to reduce variability in wind farm active power output is presented. Smoothing the power supplied by the wind farm to the battery reduces the size and number of battery charge cycles and helps to increase battery lifetime. This work quantifies the impact of the wind farm control method on battery lifetime for wind farms of 1, 4, 9 and 16 wind turbines using suitable wind farm, battery and electrolyser models. The work presented shows that wind farm control for smoothing wind farm power output could play a critical role in reducing the levelised cost of green hydrogen produced from wind farms with no grid connection by reducing the damaging load cycles on batteries in the system. Hence, this work paves the way for the design and testing of a full implementation of the wind farm controller.