This work aims to contribute to the efforts made from various disciplines to optimize the hydrogen production from renewable energy sources. The problem is posed from the perspective of the design of an alkaline water electrolyzer powered by wind energy with the assistance of the electric grid. The novelty lies in considering the resource variability in the electrolyzer sizing according to the turbine location and the operating conditions ensured by the grid. Three variable operation modes for grid assistance depending on the available wind are proposed. For each one, the nominal electrolyzer power that minimizes the annual power exchanged with the grid – and therefore the related carbon dioxide emissions – is found. The optimization results are presented in several curves that have the advantage of helping to compare the operation modes for different resource conditions characterized by the Weibull distribution. They helped to conclude that the variable operation modes are optimized with higher nominal electrolyzer powers than with the fixed mode for the same nominal turbine power.