A one-dimensional, dynamic, two-phase, isothermal and finite-difference model of proton exchange membrane fuel cell (PEMFC) systems has been developed. It is distinct from most existing models which are either fast but imprecise, such as lumped-parameter models, or detailed but computationally intensive, such as computational fluid dynamics models. This model, partially validated using experimental polarisation curves, provides a comprehensive description of cell internal states while maintaining a low computational burden. Additionally, a new physical quantity, named the limit liquid water saturation coefficient ($s_{lim}$), is introduced in the overvoltage calculation equation. This quantity replaces the limit current density coefficient ($i_{lim}$) and establishes a connection between the voltage drop at high current densities, the amount of liquid water present in the catalyst layers of the cell, and the operating conditions. At high current densities, a significant amount of liquid water is generated, which limits the accessibility of reactants to certain triple point zones within the catalyst layers by covering them. This, in turn, increases overpotential. It has also been observed that $s_{lim}$ is influenced, at minimum, by the gas pressure imposed by the operator.