A production of electrical energy via direct conversion of Solar energy with zero carbon dioxide (CO2) emission is essential from the aspect of energy supply security as well as from the aspect of environmental protection. That task can be solved by basic technological components of the system such as the photovoltaic (PV) cell, an elektrolyser, a hydrogen storage, a hydrogen fuel cell and water as the main operating fluid. For all that, the focus of this doctoral disertation is a design of the experimental electrolytic cell with potassium hydroxide (KOH) solution (alkaline solution, alkali) as the electrolyte. Within electrolyser testing it was recorded its operating (UI) characteristic with calculated efficiency which is in the known literature ranges. It was observed that intensity of the production and utilization of hydrogen can be affected by changing the electrolyte velocity through the porous electrodes of the electrolytic cell. Apart of the original section of this doctoral disertation it is also given a review of the historical development of alkaline electrolysers and descriptions of the known technical concepts of designs. The investigations of the system for hydrogen production via water electrolysis using Solar energy and photovoltaic cell (PVH2 system) are related to the experimental measurements and modeling of the PV cell and an electrolyser each separately then as the coupled system. The goal lies in the increasing of the system efficiency and its simplification. Performed experiments of the PV cell define the parameters effect on its UI characteristic and on a maximum power point trajectory (MPP trajectory). MPP trajectory is the trajectory of the maximum power point in the real conditions of the intermittent global insolation. Furthermore, an alkaline electrolyser is characterized experimentally and mathematically with the same goal. The basic parameters needed for the system design, particularly for an electrolyser, are obtained from the final mathematical model of the system. From the broader point, the result of the research is a method development for the adjusting of these two systems (an electrolyser and PV module) in one system which is much simple, more reliable, cheaper and more effective in comparison to the similar existing systems for hydrogen production without CO2 emission.