Fuel cell systems represent a promising alternative energy converter. In the past years, researches have been conducted for their modeling, control, and diagnosis. The model should accurately reproduce the behavior without being too complex. Due to the highly multiphysical interactions and coupling within the fuel cell, using a graphical representation for developing this model seems well suited. This paper presents a review of recent literature on graphical representation of proton exchange membrane fuel cell (PEMFC). Three main graphical representations are discussed: bond graph (BG), EMR, and equivalent electrical circuit. Their fields of application will be shown as well.

References

References
1.
Barbir
,
F.
,
2012
,
PEM Fuel Cells Theory and Practice
,
Academic Press
,
Cambridge, MA
.
2.
Jouin
,
M.
,
Gouriveau
,
R.
,
Hissel
,
D.
,
Péra
,
M. C.
, and
Zerhouni
,
N.
,
2013
, “
Prognostics and Health Management of PEMFC-State of the Art and Remaining Challenges
,”
Int. J. Hydrogen Energy
,
38
(
35
), pp.
15307
15317
.
3.
Biyikoglu
,
A.
,
2005
, “
Review of Proton Exchange Membrane Fuel Cell Models
,”
Int. J. Hydrogen Energy
,
30
(
11
), pp.
1181
1212
.
4.
Springer
,
T.
,
Zawodzinski
,
T.
, and
Gottesfeld
,
S.
,
1991
, “
Polymer Electrolyte Fuel Cell Model
,”
J. Electrochem. Soc.
,
138
(
8
), pp.
2334
2342
.
5.
Amphlett
,
J. C.
,
Baumert
,
R. M.
,
Mann
,
R. F.
,
Peppley
,
B. A.
, and
Roberge
,
P. R.
,
1995
, “
Performance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel Cell I. Mechanistic Model Development
,”
J. Electrochem. Soc.
,
142
(
1
), pp.
1
8
.
6.
Costamagna
,
P.
,
2001
, “
Transport Phenomena in Polymeric Membrane Fuel Cells
,”
Chem. Eng. Sci.
,
56
(
2
), pp.
323
332
.
7.
Lee
,
J.
,
Lalk
,
T.
, and
Appleby
,
A.
,
1998
, “
Modeling Electrochemical Performance in Large Scale Proton Exchange Membrane Fuel Cell Stacks
,”
J. Power Sources
,
70
(
2
), pp.
258
268
.
8.
Hontanon
,
E.
,
Escudero
,
M.
,
Bautista
,
C.
,
Garcia-Ybarra
,
P.
, and
Daza
,
L.
,
2000
, “
Optimisation of Flow-Field in Polymer Electrolyte Membrane Fuel Cells Using Computational Fluid Dynamics Techniques
,”
J. Power Sources
,
86
(
1–2
), pp.
363
368
.
9.
Barre
,
P. J.
,
Bouscayrol
,
A.
,
Delarue
,
P.
,
Dumetz
,
E.
,
Giraud
,
F.
,
Hautier
,
J. P.
,
Kestelyn
,
X.
,
Lemaire-Semail
,
B.
, and
Semail
,
E.
,
2006
, “
Inversion-Based Control of Electromechanical Systems Using Causal Graphical Descriptions
,”
32nd Annual Conference on IEEE Industrial Electronics
(
IECON’06
), Paris, Nov. 6–10, pp.
5276
5281
.
10.
Djeziri
,
M. A.
,
Merzouki
,
R.
,
Bouamama
,
B. O.
, and
Dauphin-Tanguy
,
G.
,
2007
, “
Robust Fault Diagnosis by Using Bond Graph Approach
,”
IEEE/ASME Trans. Mechatron.
,
12
(
6
), pp.
599
611
.
11.
Boulon
,
L.
,
Hissel
,
D.
,
Bouscayrol
,
A.
, and
Péra
,
M. C.
,
2008
, “
Multi Physics Modelling and Representation of Power and Energy Sources for Hybrid Electric Vehicles
,”
IEEE Vehicle Power and Propulsion Conference
(
VPPC '08
),
Harbin
,
China
, Sept. 3–5.
12.
Chartrand
,
G.
,
1985
,
Introductory Graph Theory
,
Dover
,
Mineola, NY
.
13.
Tsuge
,
Y.
,
Shiozaki
,
J.
,
Matsuyama
,
H.
, and
O'Shima
,
E.
,
1995
, “
Fault Diagnosis Algorithms Based on Signed Directed Graphs and Its Modifications
,”
Indian Chem. Eng. Symp. Ser.
,
92
, pp.
1
6
.
14.
Mosterman
,
P.
, and
Biswas
,
G.
,
1999
, “
Diagnosis of Continuous Valued Systems in Transient Operating Regions
,”
IEEE Trans. Syst. Man Cybern. A
,
29
(
6
), pp.
554
565
.
15.
Geitner
,
G.
,
2006
, “
Power Flow Diagrams Using a Bond Graph Library Under Simulink
,”
32nd Annual Conference on IEEE Industrial Electronics
(
IECON’06
), Paris, Nov. 6–10, pp. 5282-5288.
16.
Samantaray
,
K.
,
Medjaher
,
K.
,
Boumama
,
B. O.
,
Staroswiecki
,
M.
, and
Dauphin-Tanguy
,
G.
,
2005
, “
Diagnostic Bond Graph for Online Fault Detection and Isolation
,”
Simul. Model. Pract. Theory
,
14
(
3
), pp.
237
262
.
17.
Ould-Bouamama
,
B.
, and
Dauphin-Tanguy
,
G.
,
2006
, “
Modelisation par bond graph. application aux systemes energetiques
,”
Tech. Ing.
,
TIB216DUO
, p.
BE8281
.
18.
Karnopp
,
D.
, and
Rosenberg
,
R.
,
1991
,
Systems Dynamics: A Unified Approach
,
Wiley
,
Hoboken, NJ
.
19.
Chatti
,
N.
,
Bouamama
,
B. O.
,
Gehin
,
A.
, and
Merzouki
,
R.
,
2014
, “
Signed Bond Graph for Multiple Faults Diagnosis
,”
Int. Sci. J. Eng. Appl. Artif. Intell.
,
36
, pp.
134
147
.
20.
Ould-Bouamama
,
B.
,
Chatti
,
N.
, and
Gehin
,
A. G.
,
2014
, “
SBG for Health Monitoring of Fuel Cell System
,”
ICREGA’14—Renewable Energy: Generation and Application
,
Springer
,
New York
, pp.
73
85
.
21.
Hautier
,
J. P.
, and
Faucher
,
J.
,
1996
, “
Le graphe informationnel causal
,”
Bull. Union Physiciens
,
90
, pp.
167
189
.
22.
Lhomme
,
W.
,
2007
, “
Gestion d’énergie de véhicule hybrides basée sur la représentation énergétique macroscopique
,” Ph.D. thesis,
University of Lille
,
Lille, France
.
23.
Hissel
,
D.
,
Turpin
,
C.
,
Boulon
,
L.
,
Bouscayrol
,
A.
,
Péra
,
M.-C.
, and
Rael
,
S.
,
2008
, “
A Review on Existing Modeling Methodologies for PEM Fuel Cell Systems
,”
Fundamentals and Development of Fuel Cells Conference (FDFC’08)
,
Nancy
,
France
, Dec. 10–12.
24.
Bouscayrol
,
A.
,
Guillaud
,
X.
,
Hautier
,
J. P.
, and
Delarue
,
P.
,
2000
, “
Macromodelisation pour les conversions electromecaniques: application a la commande des machines electriques
,”
Rev. Int. Genie Electr.
,
3
, pp.
257
282
.
25.
Bouscayrol
,
A.
,
Delarue
,
P.
, and
Guillaud
,
X.
,
2005
, “
Power Strategies for Maximum Control Structure of a Wind Energy Conversion System With Synchronous Machine
,”
Renewable Energy
,
30
(
15
), pp.
2273
2288
.
26.
Boulon
,
L.
,
Hissel
,
D.
,
Bouscayrol
,
A.
,
Péra
,
M.-C.
, and
Delarue
,
P.
,
2008
, “
Maximal and Practical Control Structure of a PEM Fuel Cell System Based on Energetic Macroscopic Representation
,”
Fundamentals and Development of Fuel Cells Conference (FDFC’08)
,
Nancy
,
France
, Dec. 10–12, p. 11.
27.
Hernandez
,
A.
,
Hissel
,
D.
, and
Outbib
,
R.
,
2010
, “
Modeling and Fault Diagnosis of a Polymer Electrolyte Fuel Cell Using Electrical Equivalent Analysis
,”
IEEE Trans. Energy Convers.
,
25
(
1
), pp.
148
160
.
28.
Noiying
,
P.
,
2013
, “
Modélisation locale d'une cellule de pile à combustible pour l’étude de systèmes électriques
,” Ph.D. thesis,
University of Lorraine
,
Lorraine, France
.
29.
Larminie
,
J.
, and
Dicks
,
A.
,
2003
,
Fuel Cell Systems Explained
,
2nd ed.
,
Wiley
,
Hoboken, NJ
.
30.
Hissel
,
D.
,
Péra
,
M. C.
,
Bouscayrol
,
A.
, and
Chrenko
,
D.
,
2008
, “
Représentation énergétique macroscopique d'une pile à combustible
,”
Rev. Int. Genie Electr.
,
11
, pp.
4
5
.
31.
Peraza
,
C.
,
Diaz
,
J. G.
,
Arteaga-Bravo
,
F. J.
,
Villanueva
,
C.
, and
Gonzales-Longatt
,
F.
,
2008
, “
Modeling and Simulation of PEM Fuel Cell With Bond Graph and 20Sim
,”
American Control Conference
(
ACC
), Seattle, WA, June 11–13, pp.
5104
5108
.
32.
Rabih
,
S.
,
Turpin
,
C.
, and
Astier
,
S.
,
2008
, “
Bond Graph Model of a PEM Fuel Cell Stack
,”
International Conference on Renewable Energies and Power Quality
, (
ICREPQ'08
), Santander, Spain, Mar. 12–14, Paper No. 291.
33.
Saisset
,
R.
,
Fontes
,
G.
,
Turpin
,
C.
, and
Astier
,
S.
,
2006
, “
Bond Graph Model of a PEM Fuel Cell
,”
J. Power Sources
,
156
(
1
), pp.
100
107
.
34.
Hung
,
Y. H.
,
Lin
,
P. H.
,
Wu
,
C. H.
, and
Hong
,
C. W.
,
2008
, “
Real-Time Dynamic Modeling of Hydrogen PEMFCS
,”
J. Franklin Inst.
,
345
(
2
), pp.
182
203
.
35.
McCain
,
B. A.
, and
Stefanopoulou
,
A. G.
,
2006
, “
Order Reduction for a Control-Oriented Model of the Water Dynamics in Fuel Cells
,”
4th International ASME Conference on Fuel Cell Science, Engineering and Technology
, (
FUELCELL2006
), Irvine, CA, June 19–21, pp.
151
159
, ASME Paper No. FUELCELL2006-97075.
36.
Chatti
,
N.
,
Ould-Bouamama
,
B.
,
Gehin
,
A.-L.
, and
Merzouki
,
R.
,
2013
, “
Merging Bond Graph and Signed Directed Graph to Improve FDI Procedure
,”
European Control Conference
, (
ECC
), Zurich, Switzerland, July 17–19, pp.
1457
1472
.
37.
Schott
,
P.
, and
Baurens
,
P.
,
2006
, “
Cell Operation Characterization Using Simulation
,”
J. Power Sources
,
156
(
1
), pp.
85
91
.
38.
Schott
,
P.
,
Poirot
,
J.-P.
, and
Baurens
,
P.
,
2001
, “
Modélisation et simulation de la source d'energie à pile à combustible du véhicule hydrogen
,”
Ann. Chim. Sci. Mater.
,
26
(
4
), pp.
27
42
.
39.
Gerard
,
M.
,
Poirot-Crouvezier
,
J.-P.
,
Hissel
,
D.
, and
Pera
,
M.-C.
,
2010
, “
Oxygen Starvation Analysis During Air Feeding Faults in PEMFC
,”
J. Hydrogen Energy
,
35
(
22
), pp.
12295
12307
.
40.
Benchouia
,
N. E.
,
Elias
,
H. A.
,
Khochemane
,
L.
, and
Mahmah
,
B.
,
2014
, “
Bond Graph Modeling Approach Development for Fuel Cell PEMFC Systems
,”
Int. J. Hydrogen Energy
,
39
(
27
), pp.
15224
15231
.
41.
Bressel
,
M.
,
Hilairet
,
M.
,
Hissel
,
D.
, and
Ould-Bouamama
,
B.
,
2015
, “
Dynamical Modeling of Proton Exchange Membrane Fuel Cell and Parameters Identification
,”
6th International Conference on Fundamentals and Development of Fuel Cells (FDFC)
, Toulouse, France, Feb. 3–5.
42.
Mzoughi
,
D.
,
Allagui
,
H.
,
Khili
,
N.
, and
Mami
,
A.
,
2015
, “
Bond Graph Modeling and Control of a Single PEM Cell
,”
6th International Renewable Energy Congress
(
IREC
),
Sousse
,
Tunisia
, Mar. 24–26.
43.
Francois
,
B.
,
Hissel
,
D.
, and
Iqbal
,
M.
,
2005
, “
Dynamical Modelling of a Fuel Cell and Wind Turbine DC-Linked Power System
,” 8th International Conference on Modeling and Simulation of Electric Machines, Converters and Systems (
ELECTRIMACS 2005
), Hammamet, Tunisia, Apr. 17–20.
44.
Chrenko
,
D.
,
Péra
,
M. C.
, and
Hissel
,
D.
,
2007
, “
Fuel Cell System Modeling and Control With Energetic Macroscopic Representation
,”
IEEE International Symposium on Industrial Electronics
(
ISIE 2007
),
Vigo
,
Spain
, June 4–7, pp.
169
174
.
45.
Boulon
,
L.
,
Pera
,
M.-C.
,
Delarue
,
P.
,
Bouscayrol
,
A.
, and
Hissel
,
D.
,
2009
, “
Causal Fuel Cell System Model Suitable for Transportation Simulation Applications
,”
ASME J. Fuel Cell Sci. Technol.
,
7
(
1
), p.
011010
.
46.
Solano-Martinez
,
J.
,
Hissel
,
D.
,
Pera
,
M. C.
, and
Amiet
,
M.
,
2011
, “
Practical Control Structure and Energy Management of a Testbed Hybrid Electric Vehicle
,”
IEEE Trans. Veh. Technol.
,
60
(
9
), pp.
4139
4152
.
47.
Baert
,
J.
,
Pouget
,
J.
,
Hissel
,
D.
, and
Péra
,
M. C.
,
2011
, “
Energetic Macroscopic Representation of a Hybrid Railway Powertrain
,”
IEEE Vehicle Power and Propulsion Conference
(
VPPC
), Chicago, IL, Sept. 6–9.
48.
Ettihir
,
K.
,
Boulon
,
L.
,
Agbossou
,
K.
,
Kelouwani
,
S.
, and
Hammoudi
,
M.
,
2012
, “
Design of an Energy Management Strategy for PEM Fuel Cell Vehicles
,”
IEEE International Symposium on Industrial Electronics
(
ISIE
),
Hangzhou
,
China
, May 28–31, pp.
1714
1719
.
49.
Gauchia
,
L.
,
Bouscayrol
,
A.
,
Sanz
,
J.
,
Trigui
,
R.
, and
Barrade
,
P.
,
2011
, “
Fuel Cell, Battery and Supercapacitor Hybrid System for Electric Vehicle: Modeling and Control Via Energetic Macroscopic Representation
,”
IEEE Vehicle Power and Propulsion Conference
(
VPPC
), Chicago, IL, Sept. 6–9.
50.
Boscaino
,
V.
,
Miceli
,
R.
, and
Capponi
,
G.
,
2013
, “
A Circuit Model of a 5kW Fuel Cell
,”
International Conference on Clean Electrical Power
, (
ICCEP
),
Alghero
,
Italy
, June 11–13, pp.
447
452
.
51.
Wingelaar
,
P. J. H.
,
Duarte
,
J. L.
, and
Hendrix
,
M. A. M.
,
2005
, “
Dynamic Characteristics of PEM Fuel Cells
,”
IEEE 36th Power Electronics Specialists Conference
, (
PESC '05
),
Recife
,
Brazil
, June 16, pp.
1635
1641
..
52.
Famouri
,
P.
, and
Gemmen
,
R. S.
,
2003
, “
Electrochemical Circuit Model of a PEM Fuel Cell
,”
IEEE Power Engineering Society General Meeting
,
Toronto
,
ON, Canada
, July 13–17.
53.
Fontes
,
G.
,
Turpin
,
C.
, and
Astier
,
S.
,
2010
, “
A Large-Signal and Dynamic Circuit Model of a H2/O2 PEM Fuel Cell: Description, Parameter Identification and Exploitation
,”
IEEE Trans. Ind. Electron.
,
57
(
6
), pp.
1874
1881
.
54.
Wang
,
C.
,
Nehrir
,
M. H.
, and
Shaw
,
S. R.
,
2005
, “
Dynamic Models and Model Validation for PEM Fuel Cell Using Electrical Circuits
,”
IEEE Trans. Energy Convers.
,
20
(
2
), pp.
442
451
.
55.
Becherif
,
M.
,
Hissel
,
D.
,
Gaagat
,
S.
, and
Wack
,
M.
,
2011
, “
Electrical Equivalent Model of a Proton Exchange Membrane Fuel Cell With Experimental Validation
,”
Renewable Energy
,
36
(
10
), pp.
2582
2588
.
56.
Noiying
,
P.
,
Hinaje
,
M.
,
Rael
,
S.
, and
Davat
,
B.
,
2011
, “
Electrical Modeling of PEMFC Based on an ID Analogic Description of Mass Transport
,”
IEEE Vehicle Power and Propulsion Conference
(
VPPC
), Chicago, IL, Sept. 6–9.
57.
Beer
,
C. D.
,
Barendse
,
P.
,
Pillay
,
P.
,
Bullecks
,
B.
, and
Rengaswamy
,
R.
,
2013
, “
Electrical Circuit Analysis of CO Poisoning in High Temperature PEM Fuel Cell for Rapid Fault Diagnostics
,”
IEEE Energy Conversion Congress and Exposition
(
ECCE
), Denver, CO, Sept. 15–19, pp.
4623
4630
.
You do not currently have access to this content.