A comprehensive analysis of electrolytic hydrogen production systems based on solar radiation is carried in this work. In the referred analysis, directly coupled photovoltaic-electrolyzer hydrogen production systems were studied. Specifically, the studied systems were split into three subsystems, (i) photovoltaic (PV) power production, (ii) electrolyzer based hydrogen production, and (iii) hydrogen storage in tanks, each of them having its own model considerations and restrictions. Detailed mathematical models for the referred subsystems, including different photovoltaic and electrolyzer related technologies, have been developed and utilized in the analyses performed here. In particular, employing the aforementioned mathematical models, a modeling and simulation platform has been developed. Once developed, such platform has been used to parametrically study the behavior of entire hydrogen production systems, accounting for key variables such as solar irradiance, photovoltaic modules and electrolyzer cells temperature, and hydrogen production rate. Several plant designs options have been firstly determined and from the obtained results a specific one has been selected to further assessments. The particular system studied here is currently in the design phase so the outcomes from this work will be used in future for not only properly sizing it but also building and testing it. It is expected that the implementation of large-scale green hydrogen production plants will reduce the impact of energy production systems on both health and environment.