In this paper a dynamic model for the simulation of pressurized alkaline water electrolyzers is presented. The model has been developed following a multiphysics approach, integrating electrochemical, thermodynamic, heat transfer and gas evolution processes in order to faithfully reproduce the complete dynamical behavior of these systems. The model has been implemented on MATLAB/Simulink and validated through experimental data from a 1 Nm3/h commercial alkaline water electrolyzer. Validations have been performed under real scenarios where the electrolyzer is working with power profiles characteristic from renewable sources, wind and photovoltaic. The simulated results have been found to be consistent with the real measured values. This model has a great potential to predict the behavior of alkaline water electrolyzers coupled with renewable energy sources, making it a very useful tool for designing efficient green hydrogen production systems. This work has been supported by the Spanish State Research Agency (MCIN/AEI/10.13039/501100011033) under grants PID2019-111262RBI00, PID2019-110956RB-I00 and TED2021-132457B-I00 (also funded by the European Union NextGenerationEU/PRTR), by Ingeteam R&D Europe and by Ingeteam Power Technology.