The goal of this thesis is the development of a realistic dynamic model of a Proton Exchange Membrane (PEM) electrolyser with respect to the already existing models present in the literature. Initially, a base model was constructed using standard equations to describe the typical operating behavior of an electrolyzer. Implementations have been done to enhance the model realism and to implement the common models of the literature. A differentiation between the liquid and vapor phases of water within the electrodes has been introduced through a formulation based on partial pressures. In addition, the development of the internal double layer at the anode and cathode has been modeled in order to reproduce a more realistic behavior during the transient and a time delay response with respect to a dynamic changing input current.