[en] In liberalized power markets, there are significant power price fluctuations due to independently varying changes in demand and supply, the latter being substantial in systems with high wind power penetration. In such systems, hydrogen production by grid connected electrolysis can be cost optimized by operating an electrolyzer part time. This paper presents a study on the minimization of the hydrogen production price and its dependence on estimated power price fluctuations. The calculation of power price fluctuations is based on a parameterization of existing data on wind power production, power consumption and power price evolution in the West Danish power market area. The price for hydrogen is derived as a function of the optimal electrolyzer operation hours per year for four different wind penetration scenarios. It is found to amount to 0.41-0.45 EUR/Nm³. The study further discusses the hydrogen price sensitivity towards investment costs and the contribution from non-wind power sources. (author)