The necessity for reliable simulation models, able to support the fuel cell systems development activity, has increased continuously during the last years. The present work proposes a model which integrates the finite element method in a dynamic simulation, in order to achieve higher accuracy and the possibility to investigate the influence of various parameters on the fuel cell dynamics. The model is implemented using MATLAB/SIMULINK and consists of two interacting main subsystems that calculates the fuel cell power response and the stack thermal behavior. The first simulates the mass transport and electrochemical phenomena using a model implemented in FEMLAB, and considers as input parameters the stack geometry, reactants pressure, flow rate and composition, and the stack average temperature. The last parameter is also evaluated by the second model, implemented also in FEMLAB, which considers the stack geometry, cooling air flow rate and ambient temperature. Both models were validated using the experimental data acquired on a Ballard Nexa $1.5kWe$ proton exchange membrane (PEM) system. The results prove that integrated model simulates with accuracy the dynamics of the proton exchange membrane fuel cell type (PEMFC) system and the interaction between the stack and the auxiliaries. The proposed model was used as a predictive tool for two situations. In the first simulation, with a relative fast dynamic, the model demonstrates that the cooling fan control strategy is essential for transient conditions characterized by a significant load decreasing. In the second, the model estimates the variation of the PEMFC main parameters on a $24h$ cycle, confirming its reliability.

1.
Cheddie
,
D.
, and
Munroe
,
N.
, 2005, “
Review and Comparison of Approaches to Proton Exchange Membrane Fuel Cell Modeling
,”
J. Power Sources
0378-7753,
147
, pp.
72
84
.
2.
Amphlett
,
J. C.
,
Mann
,
R. F.
,
Peppley
,
B. A.
,
Roberge
,
P. R.
, and
Rodrigues
,
A.
, 1996, “
A Model Predicting Transient Responses of Proton Exchange Membrane Fuel Cells
,”
J. Power Sources
0378-7753,
61
, pp.
183
188
.
3.
Pukrushpan
,
J. T.
,
Stefanopoulou
,
A. G.
, and
Peng
,
H.
, 2002, “
Modeling and Control for PEM Fuel Cell Stack System
,” American Control Conference, TP09-2.
4.
Pukrushpan
,
J. T.
,
Peng
,
H.
, and
Stefanopoulou
,
A. G.
, 2002, “
Simulation and Analysis of Transient Fuel Cell System Performance Based on a Dynamic Reactant Flow Model
,” ASME International Mechanical Engineering Congress & Exposition.
5.
Yerramalla
,
S.
,
Davari
,
A.
,
Feliachi
,
A.
, and
Biswas
,
T.
, 2003, “
Modeling and Simulation of the Dynamic Behavior of a Polymer Electrolyte Membrane Fuel Cell
,”
J. Power Sources
0378-7753,
124
, pp.
104
113
.
6.
El-Sharkh
,
M. Y.
,
Rahman
,
A.
,
Alam
,
M. S.
,
Byrne
,
P. C.
,
Sakla
,
A. A.
, and
Thomas
,
T.
, 2004, “
A Dynamic Model for Stand-Alone PEM Fuel Cell Power Plant for Residential Applications
,”
J. Power Sources
0378-7753,
138
, pp.
199
204
.
7.
Zhang
,
Y.
,
Ouyang
,
M.
,
Lu
,
Q.
,
Luo
,
J.
, and
Li
,
X.
, 2004, “
A Model Pedicting Performance of Proton Exchange Membrane Fuel Cell Stack Thermal Systems
,”
Appl. Therm. Eng.
1359-4311,
24
, pp.
501
513
.
8.
Golbert
,
J.
, and
Lewin
,
D. R.
, 2004, “
Model-Based Control of Fuel Cells: (1) Regulatory Control
,”
J. Power Sources
0378-7753,
1335
, pp.
135
151
.
9.
Pathapati
,
P. R.
,
Xue
,
X.
, and
Tang
,
J.
, 2005, “
A New Dynamic Model for Predicting Transient Phenomena in a PEM Fuel Cell System
,”
Renewable Energy
0960-1481,
30
, pp.
1
22
.
10.
Shan
,
Y.
, and
Choe
,
S. Y.
, 2005, “
A High Dynamic PEM Fuel Cell Model With Temperature Effects
,”
J. Power Sources
0378-7753,
145
, pp.
30
39
.
11.
Marr
,
C.
, and
Li
,
X.
, 1999, “
Composition and Performance Modeling of Catalyst Layer in a Proton Exchange Membrane Fuel Cell
,”
J. Power Sources
0378-7753,
77
, pp.
17
27
.
12.
He
,
W.
, and
Nguyen
,
T. V.
, 2000, “
Two Phase Flow Model of the Cathode of PEM Fuel Cells Using Interdigitated Flow Fields
,”
Mat. Int. Electrochem. Phenom.
,
46
(
10
), pp.
2053
2064
.
13.
Dannenberg
,
K.
,
Ekdunge
,
P.
, and
Lindbergh
,
G.
, 2000, “
Mathematical Model of the PEMFC
,”
J. Appl. Chem.
0021-8871,
30
, pp.
1377
1387
.
14.
Eldrid
,
S.
,
Shahnam
,
M.
, and
Prinkey
,
M. T.
, and
Dong
,
Z.
, 2003, “
3D Modelling of Polymer Electrolyte Membrane Fuel Cells
,”
First International Conference on Fuel Cell Science
,
Engineering and Technology
,
Rochester, NY
, pp.
195
202
.
15.
Ferguson
,
A.
, and
Ugursal
,
V. I.
, 2004, “
Fuel Cell Modeling for Building Cogeneration Applications
,”
J. Power Sources
0378-7753,
137
, pp.
30
42
.
16.
Senn
,
S. M.
, and
Poulikakos
,
D.
, 2004, “
Polymer Electrolyte Fuel Cells With Porous Materials as Fluid Distributors and Comparisons With Traditional Channeled Systems
,”
Trans. ASME
0097-6822,
126
, pp.
410
418
.
17.
FEMLAB 3—Chemical Engineering Module User’s Guide, 2004, Version 3.1, Comsol AB, October.
18.
FEMLAB 3—Chemical Engineering Module Model Library, 2004, Version 3.1, Comsol AB, October.
19.
Pharoah
,
J. G.
, 2005, “
On the Permeability of Gas Diffusion Media Used in PEM Fuel Cells
,”
J. Power Sources
0378-7753,
144
, pp.
77
82
.
20.
Lee
,
C. S.
,
Yun
,
C. H.
,
Kim
,
B. M.
,
Jang
,
S. C.
, and
Yi
,
S. C.
, 2005, “
Effect of Gas Permeability in a Porous Flow Channel on the Cell Current in a Polymer Electrolyte Fuel Cell (PEFC) System
,
J. Ceram. Proc. Res.
1229-9162,
6
(
2
), pp.
188
195
.
21.
Hines
,
A. L.
, and
,
R. N.
, 1985, “
Mass Transfer
.”
Fundamentals and applications
,
Prentice-Hall
, Englewood Cliffs, NJ.
22.
Coulson
,
J. M.
, and
Richardson
,
J. F.
, 1990,
Coulson & Richardson’s Chemical Engineering
,
4th ed.
,
Pergamon Press
, New York, Vol.
1
.
23.
Fogler
,
H. S.
, 2006,
Elements of Chemical Reaction Engineering
,
4th ed.
,
Prentice-Hall
, Englewood Cliffs, NJ.
24.
Broka
,
K.
, and
Ekdunge
,
P.
, 1997, “
Modelling the PEM Fuel Cell Cathode
,”
J. Appl. Electrochem.
0021-891X,
27
, pp.
281
289
.
25.
Song
,
D.
,
Wang
,
Q.
,
Liu
,
Z.
,
Navessin
,
T.
, and
Holdcroft
,
S.
, 2004, “
Numerical Study of PEM Fuel Cell Cathode With Non Uniform Catalyst Layer
,”
Electrochim. Acta
0013-4686,
50
, pp.
731
737
.
26.
Wang
,
Q.
,
Song
,
D.
,
Navessin
,
T.
,
Holdcroft
,
S.
, and
Liu
,
Z.
, 2004, “
A Mathematical Model and Optimization of the Cathode Catalyst Layer Structure in PEM Fuel Cells
,”
Electrochim. Acta
0013-4686,
50
, pp.
725
730
.
27.
Sun
,
W.
,
Peppley
,
B. A.
, and
Karan
,
K.
, 2005, “
An Improved Two Dimensional Agglomerate Cathode Model to Study the Influence of Catalyst Layer Structural Parameters
,”
Electrochim. Acta
0013-4686,
50
, pp.
3359
3374
.
28.
Siegel
,
N. P.
,
Ellis
,
M. W.
,
Nelson
,
D. J.
, and
von Spakovsky
,
M. R.
, 2003, “
Single Domain PEMFC Model Based on Agglomerate Catalyst Geometry
,”
J. Power Sources
0378-7753,
115
, pp.
81
89
.
29.
Grujicic
,
M.
, and
Chittajallu
,
K. M.
, 2004, “
Design and Optimisation of Polymer Electrolyte Membrane (PEM) Fuel Cells
,”
Appl. Surf. Sci.
0169-4332,
227
, pp.
56
72
.
30.
Futerko
,
P.
, and
Hsing
,
I. M.
, 2000, “
Two-Dimensional Finite Element Method Study of the Resistance of Membranes in Polymer Electrolyte Fuel Cells
,”
Electrochim. Acta
0013-4686,
45
, pp.
1741
1751
.
31.
Nexa™ (310-0027) Power Module User’s Manual, 2003, Ballard Power Systems, Inc., Vancouver, Canada.
32.
Ferguson
,
A.
, and
Ugursal
,
V. I.
, 2004, “
Fuel Cell Modelling for Building Cogeneration Applications
,”
J. Power Sources
0378-7753,
137
, pp.
30
42
.