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As the global energy landscape transitions towards a more sustainable future, hydrogen has emerged as a promising energy carrier due to its potential to decarbonize various sectors. However, the economic competitiveness of hydrogen production by water electrolysis strongly depends on renewable energy source (RES) availability. Thus, it is necessary to overcome the challenges related to the intermittent nature of RESs. This paper presents a comprehensive techno-economic analysis of complementing green hydrogen production with grid electricity. An evaluation model for the levelized cost of hydrogen (LCOH) is proposed, considering both CO2 emissions and the influence of RES fluctuations on electrolyzers. A minimum load restriction is required to avoid crossover gas. Moreover, a new operation strategy is developed for hydrogen production plants to determine optimal bidding in the grid electricity market to minimize the LCOH. We evaluate the feasibility of the proposed approach with a case study based on data from the Kyushu area in Japan. The results show that the proposed method can reduce the LCOH by 11% to 33%, and increase hydrogen productivity by 86% to 140%, without significantly increasing CO2 emission levels. [ABSTRACT FROM AUTHOR]