In this paper, the modelling of an energy generation system based on polymer electrolyte membrane fuel cell (PEMFC) system through a parameter varying approach (LPV model), that takes in to account model parameter variation with the operating point, is presented. This model has been obtained through a Jacobian linearization of the PEMFC non-linear dynamic model that was previously calibrated using real data from lab. In order to illustrate the use of the LPV model obtained its application to model-based fault detection is used. For this purposes a set of common fault scenarios, which could appear during a normal PEMFC operation, is used as case study.