Hydrogen produced by electrolysis is expected to be massively produced accross the world providing hydrogen to mobility systems and industry in an attempt to decarbonize them. The economical acceptability of such a transition can be insured by the selling price of hydrogen and the avoided CO2 emission cost. Even, if the investment cost are important, the levelized cost of hydrogen is dominated by the electricity cost when the electrolyzer is supplied from the grid. However, with the increase of the renewable electricity generation in the mix, hydrogen production may play a role as grid stabilizer consuming excess electricity. This situation leads to lower to almost zero electricity cost but with a lower hydrogen production by the electrolyzer leading to a higher weight of the investment cost. In this paper, a model is proposed to assess the levelized cost of hydrogen and its carbon content based on several strategies.