Green hydrogen production from low or zero-emission electricity systems using water electrolysis has recently emerged to replace fossil fuel in different sectors such as transportation. However, the cost of electrolysis-based hydrogen production is still relatively high. In this regard, this paper proposes a new model to optimize the design of a centralized Electrolysis Hydrogen Plant (EHP). The EHP consists of electrolysis, compressor, and hydrogen storage tank and it is connected to the power transmission system. The proposed model aims at determining the optimal sizing of the plant components combined with the electrolysis internal parameters i.e., membrane thickness, cell area, and cathodic pressure. Simulation results show that the proposed design model has improved the overall efficiency of the EHP plant and, thus, reduced the cost of hydrogen production by 8.7% compared to using non-optimized internal parameters from the commercially available units in the market.