## Section: Contracts and Grants with Industry

### DIAPASON: Reduced Modeling and Diagnosis of Fuel Cell Systems (ANR)

Participants : Pierre-Alexandre Bliman, Mohamad Safa, Michel Sorine, Qinghua Zhang.

This work is conducted within the framework of the ANR project Diapason (Program PAN-H 2006), which is dedicated to the diagnosis of fuel cell systems for stationary and automotive applications. It is aimed at developing supervision and diagnosis methods using the fuel cell stack itself as a sensor, with limited instrumentation. These methods are thought up for real-time use, coupled with the stack control system, or during planned maintenance operations in order to improve the system reliability and its energetic and environmental performances, and to extend its life.

Our diagnosis strategy is based on impedance spectroscopy measurements and physical modeling. The main failures which have to be detected and diagnosed are CO poisoning, membrane dehydration and membrane flooding.

Our main efforts this year have been devoted to precise modeling of the individual fuel cell. In order to take into account the critical phenomena, it has been necessary to analyze and model the following phenomena:

**Diffusion.** The impedance essays obtained by our partners in the project clearly show the characteristic finite slope in high frequency behavior usually considered as a consequence of diffusion, here in the Gas Diffusion Layers.
This aspect is usually introduced as a term in the frequency domain.
however, in order to respect the consistency of the approach, including nonlinear terms, we prefer to use a Partial Differential Equation, subsequently discretized via collocation method.

**Temporal scales of the chemical reactions.**
To simplify the models while keeping a good precision of the actual phenomena involved, we have taken into account the discrepancy between the several temporal scales involved in the the different reactions.
More precisely, we have considered that the concentration balance equations are much more rapid than the adsorption/desorption reactions, and the former ones have been simplified by singular perturbations.

**Water balance.**
A compartmental model of water exchanges inspired by work by J.B. Benziger *al.* has been used.
Simplified dynamics have been introduced here too, taking advantage of the time scale separations.

**Double layer capacity.**
This important phenomenon is typically rendered in electrochemistry by a capacitance put in parallel or in series to the other models.
In order to have the subsequent ability to get a full model aging of the reactive zones of the cell, we have worked on a physically based model.
The latter is inspired especially from a multiscale analysis due to A.A. Franco, detailing electronic and protonic flows in the compact layer, as well as water adsorption and dipolar effects to explain the capacitance effect.