IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 1, MARCH 2009 283
Modeling and Dynamic Characteristic Simulation
of a Proton Exchange Membrane Fuel Cell
J. Jia, Member, IEEE, Q. Li, Y. Wang, Senior Member, IEEE, Y. T. Cham, Senior Member, IEEE, and M. Han
Abstract—In order to investigate the output characteristic of a
proton exchange membrane fuel cell (PEMFC) based on the elec-
trical empirical model, a novel dynamic model of the PEMFC has
been developed with MATLAB/Simulink, which is distinct from
the models that have been published previously. By using a fuel cell
test system of the Fuel Cell Application Centre (FAC) at Temasek
Polytechnic, the transient electrical responses of PEMFC were con-
ducted and analyzed under various operating conditions. A good
match is found between simulation results and experimental data.
The comprehensive results of simulation manifested that the model
is effective and operational. This model will be very useful to op-
timize the structure design, improve the operation performance,
and develop the real-time control system of PEMFC.
Index Terms—Dynamic model, dynamic simulation, proton ex-
change membrane fuel cell (PEMFC), transient electrical response.
NOMENCLATURE
A Activation area of the membrane.
B Constant determined by the proton ex-
change membrane fuel cell (PEMFC) and
its working status.
C Equivalent capacitance.
C
H
+ Liquid phase concentration of H
+
.
C
H
2
Liquid phase concentration of hydrogen.
C
H
2
O
Liquid phase concentration of water.
C
O
2
Dissolved oxygen concentration in the in-
terface of the cathode catalyst.
E
Nernst
Thermodynamic potential.
F Faraday’s constant.
ΔG Gibbs free energy change.
ΔG
c
Gibbs free energy change of the chemical
sorption under standard status.
i Current of the equivalent circuit.
i
C
Current of the equivalent capacitance C.
J Current density.
J
max
Maximum current density.
K
0
a
Inherent velocity constant of anode
reaction.
Manuscript received January 4, 2008; revised August 8, 2008. First published
January 27, 2009; current version published February 19, 2009. Paper no.
TEC-00508-2007.
J. Jia and Y. Wang are with the School of Electrical and Electronic Engineer-
ing, Nanyang Technological University, Singapore 639798, Singapore (e-mail:
jiajunbo@tp.edu.sg; eyywang@ntu.edu.sg).
Q. Li is with the School of Electrical Engineering, Southwest Jiaotong Uni-
versity, Chengdu 610031, China (e-mail: liqi0800@gmail.com).
Y. T. Cham and M. Han are with the School of Engineering, Temasek
Polytechnic, Singapore 529757, Singapore (e-mail: chamyt@tp.edu.sg;
minghan@tp.edu.sg).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2008.2011837
K
0
c
Inherent velocity constant of cathode
reaction.
l Thickness of the membrane.
N Number of cells.
P
consumed
Power consumed by stack.
P
H
2
Effective partial pressure of hydrogen.
P
O
2
Effective partial pressure of oxygen.
P
stack
Output power of stack.
r
M
Resistivity of Nafion series proton ex-
change membrane.
R Gaseous constant.
R
a
Equivalent resistance.
R
act
Activation equivalent resistance.
R
c
Contact resistances both between the mem-
brane and electrodes as well as the elec-
trodes and the bipolar plates.
R
con
Concentration equivalent resistance.
R
M
Equivalent membrane impedance.
R
total
Equivalent resistance of fuel cell stack.
ΔS Standard mole entropy change.
t Time in seconds.
T Temperature in Kelvin.
T
ref
Reference temperature.
ν
d
Overall voltage drop across R
a
.
V
act
Activation losses.
V
con
Concentration losses.
V
ohmic
Ohmic losses.
V
stack
Output voltage of stack.
α
c
Activation coefficient.
λ Water content of the membrane.
τ Time constant of the equivalent circuit.
ξ
i
(i =1,..., 4) Model coefficients obtained by exper-
imental data fitting based on electro-
chemistry, thermodynamics, and fluid
mechanics.
I. INTRODUCTION
W
ITH the world facing the global warming problem, fuel
cells are one of the promising energy technologies for
sustainable future due to their high energy efficiency and en-
vironment friendliness. Compared with the other types of fuel
cells, a proton exchange membrane fuel cell (PEMFC) shows
promising results with its advantages such as low temperature,
high power density, fast response, and zero emission if it is run
with pure hydrogen, and it is suitable for use in portable power
supply, vehicles, and residential and distributed power plants.
For a better understanding of the characteristics and evalua-
tion of the performance of PEMFCs, and therefore, optimization
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