The objective of this paper is to present the modelling and experimental validation of the 46 kW PEM high pressure water electrolyzer installed on the MYRTE platform, which is a real-scale demonstrator that aims to study the deployment of hydrogen to store the energy associated to intermittent renewable energy source systems. An electrochemical steady-state and semi-empirical submodel coupled with a lumped thermal capacitance dynamic submodel is developed to predict the stack voltage and the stack temperature evolution from instantaneous operating conditions such as the applied current, the gas storage pressure tanks ( and ) and the ambient temperature. The Particle Swarm Optimization algorithm is used to find the electrochemical submodel parameters and a multivariable Matlab-Simulink® linked modular mathematical model is developed for validation. Results indicate that within a temperature range of 20–60 °C, and a pressure range of 15–35 bar, the stack voltage and the temperature evolution can be predicted even in transitory operating phases. The strategy used for the parameters identification is explained in detail and can be applied to any PEM water electrolyzer.