Water electrolysis is the most established and effective method for generating green hydrogen. This research aim is to investigate the electrolyzer system model, by integrating several electrolytes (i.e., NaOH, KOH and H2SO4) and, the mathematical framework which depends on the foundation of thermal, electrochemical and system analysis. The system in Aspen Plus, with a maximum electrolyzer power of 15 kW, has been modelled by using the experimental reference system. This model relies on empirical expressions that explain how the cell potential, Faraday efficiency, excess heat, net power, and gas purity alters, at an operational conditions like temperature and pressure as well as the current density. The outcome demonstrates that at 10 bar pressure, electrolyte produces hydrogen with 99.84 % purity level. The maximum system efficiency of 84.13 % is recorded, whereas the maximum hydrogen production of 7.994 Nm(3)/h by using NaOH which is 4.57 % and 12.23 % higher than KOH and H2SO4 electrolytes when current density is 0.55 A/cm(2). The economic analysis is done by evaluating maximum capital cost of 3042.78 k$/year. Also, sensitivity analysis has been done to evaluate the performance of electrolyzer ability for splitting of water into hydrogen and oxygen.