An advanced PEM fuel cell mathematical model is described and realised in four ancillaries in the Matlab -Simulink environment. Where possible, the model is based on parameters with direct physical meaning, with the aim of going beyond empirically describing the characteristics of the fuel cell. The model can therefore be used to predict enhanced performance owing to, for instance, improved electrode materials, and to relate changes in the measured performance to internal changes affecting influential physical parameters. Some simplifying assumptions make the model fairly light in computational demand and therefore amenable to extension to simulate an entire fuel-cell stack as part of an energy system. Despite these assumptions, the model emulates experimental data well, especially at high current density. The influences of pressure, temperature, humidification and reactant partial pressure on cell performance are explored. The dominating effect of membrane hydration is clearly revealed. (C) 2016 Elsevier Ltd. All rights reserved.