Research Journal of Applied Sciences, Engineering and Technology 4(22): 4845-4850, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: May 13, 2012
Accepted: May 29, 2012
Published: November 15, 2012
Analysis of Effective Parameters of a PEMFC Considering Optimal Operation
1
Saber Arabi Nowdeh, 2Mohammad Bagher Nasrollahnejad, 3Mahsa Khayyatzadeh
and 4Sina Kashani
1,2
Department of Electrical Engineering, Behbahan Branch, Islamic Azad University, Behbahan, Iran.
3
Department of Electric and Computer Engineering, Tabriz University, Tabriz, Iran.
4
Department of Mechanical Engineering, Islamic Azad University, Gorgan Branch,
Kordkuy Center, Golestan, Iran.
Abstract: Fuel Cell (FC) is electrochemical systems capable to convert the oxygen and hydrogen chemical
energy to electrical energy. FC is as a promising alternative due its suitable efficiency, low pollution to the
environment, high reliability and durability and excellent dynamic response. In this study we have
implemented simple PEMFC in GAMS environment considering its input hydrogen molar flow rate
consumption. Then the impact of effective operational parameters is investigated on optimal operation and
output power of PEMFC. This study can ensure PEMFC optimal operation and maximizing its generated
power considering obtained results from modeling and different effects of each operational parameter.
Keywords: Fuel Cell (FC), GAMS, modeling, optimal operation, Proton Exchange Membrane (PEM)
INTRODUCTION
FC is electrochemical systems capable to convert
the chemical energy of oxygen and hydrogen to
electrical energy during which some heat and water is
generated as well. The use of FC based on power
generation is expected to become more widespread in
future due to better power quality, reliability, portability
and ecological constraints. These characteristics and the
possibility of refueling the cell with different fuels are
increasing the interest or the applications as electric
power sources. The commonly available FC includes
polymer membrane, alkaline, phosphoric acid, molten
carbonate and solid oxide based FCs. Due to its low
operating temperature and fast start up characteristic,
the PEMFC is most attractive for residential use among
the various types of FC (Chiu et al., 2004).
A FC based on power system consists of a
reformer, FC stack and power conditioner, able to adapt
the operating conditions to the requirements of the load.
FC generates DC power, normally (Pathapati et al.,
2005).
In many literature is developed PEMFC measuring
and control system but they didn’t focus on measuring
sensors and evaluation the operational parameters
impact on PEMFC generated power considering
consumption of hydrogen molar flow rate. In this study
a PEMFC 500-W BCS stack is modeled in GAMS
environment. Then in sensitivity analysis is investigated
cell operational parameters impact on PEMC output
power versus hydrogen molar flow rate consumption
and the effective parameters on PEMFC optimal
peration are determined. The aim of this sensitivity
analysis is to find the effective parameters for better
control, improvement the optimal output power
generation and higher efficiency of a PEMFC.
PEMFC MODELING
FC converts oxygen and hydrogen chemical energy
to electrical energy during which some heat and water
is generated as well. Typical scheme of FC system and
equivalent electrical circuit model shown in Fig. 1-2
(Friede et al., 2004).
The output voltage in each cell is little, so some
cells connected in series to gain a bigger output voltage
and that is called FC stack. The operation of FC is
described by polarization curve and in a constant state
which shows FC voltage based on the current (Buasri
and Salameh, 2006).
The basic areas which affect the overall
polarization are Ohmic, activation and Concentration
Polarization (Dongjing and Li, 2007).
PEMFC voltage: According to polarization curve, FC
voltage can be defined by:
VFC  Enernst  Vact  Vohmic  Vcon
(1)
The thermodynamic potential of the FC that
represents its reversible voltage can be calculated by:
Corresponding Author: Saber Arabi Nowdeh, Department of Electrical Engineering, Behbahan Branch, Islamic Azad
University, Behbahan, Iran
4845
Res. J. Appl. Sci. Eng. Technol., 4(22): 4845-4850, 2012
Fig. 1: Typical scheme of FC system
Fig. 2: Equivalent electrical circuit model
E n e r n s t  1 .2 2 9  0 .8 5  1 0  3 ( T  2 9 8 .1 5 ) 
4 .3 0 8 5  1 0  5 T  ln ( PH 2 )  0 .5 ln ( PO 2 ) 
(2)
Ohmic polarization: Ohmic voltage drop occurs due to
resistive losses in the FC and can be obtained as
follows:
V
ohm
 I
F C
(R
M
 R
C
)
(3)
where, iFC refers to FC current. RC represents resistance
of FC electrodes against movement of electrons and
RM is resistance of FC membrane against ions passing,
which can be expressed by:
RM   M (l A)
M
181 . 6 ((1  0 .03 (i FC A )  0 . 062 (T 303 ) 2 ( i FC A ) 2 .5 )

((  0 .634  3(i FC A )) exp( 4 . 18 ((T  303 ) T )))
where, ρM represents cell membrane specific resistivity
(Ω.m), A is cell active area (cm2) and l is membrane
thickness (cm).
Activation polarization: Activation voltage drop
occurs due to slow reactions on the surface of
electrodes which calculated by:
Vact   1 2T 3T ln(CO2 ) 4T ln(IFC )
where, CO2 refers to oxygen concentration rate on the
catalyst surface which can be defined as follow:
(4)
CO2 
(5)
4846 (6)
PO2
5.08  10 6 exp( 
498
)
T
(7)
Res. J. Appl. Sci. Eng. Technol., 4(22): 4845-4850, 2012
0.8
0.012
0.008
0.006
0.004
0.002
0
1
3
5
7
9
0.6
VFC (V)
WFC (kmol/s)
0.010
0
11 13 15 17 19 21 23
Time (hours)
500
400
0.8
0.6
PFC (W)
Voltage (V)
0.005
0.01
WFC (kmol/s)
0.015
600
1.2
Enernst
Vact
Vohm
Vcon
VFC
0.4
0.2
0
0.005
0.010
WFC (Kmol/s)
where, Jmax represents maximum current density in
FC.
According to all voltage drops in FC, for n cells
forming a stack, output power of FC stack is calculated
as follows:
(9)
where, NFC is the number of cells in series.
PEMFC current: The current of FC can be described
as a linear function of hydrogen flow rate to FC and can
be calculated as follow (El-Sharkh et al., 2004):
I F C  ( 2 F N F C )(W H 2 M
H2
)
0
0.002
0.004
0.008
0.006
W (kmol/s)
0.010
0.012
FC
(8)
PF C  N F C  V F C  I F C
200
0
0.015
Concentration polarization: Concentration voltage
drop occurs due to reduction in density of reaction
materials which is called mass transport losses and can
be calculated by:
Vcon   B ln(1  ( J J max ))
300
100
Fig. 4: Different polarization curves of FC
(10)
Fig. 6: FC output power vs. hydrogen molar flow rate
consumption
In this study the profile of hydrogen molar flow
rate variation for PEMFC consumption is considered
during a fully day as Fig. 3.
Static behavior of PEMFC is modeled using Eq. (1)
to (10). Based on PEMFC electrical circuit model, its
mathematical modeling is established in GAMS
environment to describe the types of voltage drops and
PEMFC output voltage corresponding PEMFC
hydrogen molar flow rate consumption.
In this study a 500W BCS stack is applied and the
base parameters are presented in Table 1 (Jeferson
et al., 2006).
Considering PEMFC electrical circuit model and
its mathematical modeling in GAMS environment, all
polarization voltage and output voltage obtained from
modeling shown as Fig. 4.
According Fig. 4, it is clear that PEMFC output
voltage decrease in the beginning and ending with
comparatively great drop.
The curves of PEMFC output voltage and output
power density as a function cell’s molar flow rate
consumption obtained for base parameters as Fig. 5-6.
4847 0
Fig. 5: FC output voltage vs. hydrogen molar flow rate
consumption
1.4
0
0.4
0.2
Fig. 3: The hydrogen molar flow rate variation during a fully
day
600
600
500
500
400
400
PFC (W)
PFC (W)
Res. J. Appl. Sci. Eng. Technol., 4(22): 4845-4850, 2012
300
T = 303K
200
Ref (T = 333K)
100
0
0.002
0.004
0.008
0.006
WFC (kmol/s)
0.010
0
0.012
Fig. 7: FC behavior under different temperature
500
PFC (W)
400
300
200
100
0
0
0.002
0.004
0.9 Ref pressure
Ref pressure
1.1 Ref pressure
0.012
0.008
0.010
0.006
W (kmol/s)
0.002
600
500
400
300
Ref (100% A)
200
95% A
100
0
0
0.002
0.004
0.008
0.006
WFC (kmol/s)
0.010
0.012
Fig. 10: FC behavior under different cell active area
FC
Fig. 8: FC behavior under different hydrogen partial pressure
SENSITIVITY ANALYSIS
In this section the impact of PEMFC operational
parameters like temperature, pressure, membrane
humidity and cell active area (Correa et al., 2005)
investigated on polarization curve, output power and its
optimal operation. The obtained results depicted in Fig.
7-8. According to Fig. 7-8, we can say that increase
(decrease) of FC’s operational temperature and
hydrogen partial pressure will cause increase (decrease)
in FC output voltage and power (FC polarization
curves). The reason of increase due to operational
temperature is that higher temperatures improve mass
transfer within the FC and results in a net decrease in
cell. Also, reason of increase due to hydrogen partial
Table 1: Typical FC parameter of 500W BCS stack
Typical FC parameters of 500W BCS stack
Number of cells in FC stack (NFC)
Cell active area (A)
Maximal current density (Jmax)
Operation temperature (T)
Value
32
64 cm2
469 mA/cm2
333 K
178 μm
Membrane thickness ( l )
Partial pressure of hydrogen (PH2)
Partial pressure of oxygen (PO2)
Equivalent resistance to proton conduction (RC)
Parameter corresponding to Vact (ξ1)
1 atm
0.2095 atm
0.0003 Ω
-0.948
Parameter corresponding to Vact (ξ2)
Parameter corresponding to Vact (ξ3)
Parameter corresponding to Vact (ξ4)
Membrane humidity (φ)
B
Faraday’s constant (F)
Universal gas constant (R)
0.00286+0.0002 ln (A)+0.000043 ln (CH2)
0.000076
-0.000193
23
0.016 V
96 484 600 C/kmoL
8314.47 J/(kmoL K)
4848 0
Fig. 9: FC behavior under different MH
PFC (W)
600
200
100
T = 363K
0
300
Ref (100% MH)
95% MH
0.004 0.006
0.008 0.010 0.012
WFC (kmol/s)
Res. J. Appl. Sci. Eng. Technol., 4(22): 4845-4850, 2012
Table 2: The impact of FC operational parameters variation on its output power
Operational
Temperature
Partial Pressure
Parameter
(OT) (%)
(PP) (%)
1% increase
0.96
0.327
1% decrease
1.325
0.365
PFC (W)
400
300
200
100
0
0.27
0
0.1
0.2
0.3
0.35
0.4
0.5
VFC (V)
CONCLUSION
0.6
0.7
0.8
Fig. 11: PEMFC optimal power range
pressure is that the rate of the chemical reaction
isproportional to the partial pressures of the hydrogen
and the oxygen.
We have done simulations of FC output voltage
and power with different MH (Fig. 9). The obtained
result shows that decrease in MH will cause decrease in
FC’ output voltagse and power. Then decrease in cell
active area on FC’ output and power is investigated
(Fig. 10). Result shows that decrease in cell active area
will cause decrease in polarization curve, output voltage
and power.
The impact of FC operational parameters variation
on its output power for 1% increase and decrease
presented in Table 2.
From obtained results and according Table 2, it can
be concluded that the operational temperature
measurements impact of PEMFC has more impact on
designing and FC optimal operation while partial
pressures, membrane humidity and cell active area are
less significant impacts on output power of PEMFC.
PEMFC OPTIMAL POWER RANGE
FC operation is in low voltage output and high
current output. In this condition, the corresponding
output current is nearly saturated point. The efficiency
of FC increases corresponding to the cell voltage
increasing but decreases with FC power increasing. So
the efficiency and power are conflicting entirely. FC
system designers must find the desired operating range
according to whether efficiency or power is paramount
for the given application. According to Fig. 11, the
optimal power range is from nearly 0.27 to 0.35 V of
This study presents the electrochemical model of
PEMFC and establishes the GAMS mathematical
modeling based on it. Detailed researches on
polarization curves have been carried through to boost
FC performances. Impact of FC parameters investigated
on its output power and optimal operation. Some
parameters which is not so accurate in some papers but
very important are pointed out. We have found that
temperature has significant impact on PEMFC’s
characteristics whereas impact of partial pressures,
membrane humidity and cell active area is lower. Based
on the obtained results, we can define design criteria for
measurement and control equipment in FC systems
with different complexity to ensure optimal operation
with optimal output power and output voltage.
REFERENCES
Buasri, P. and Z.M. Salameh, 2006. An electrical circuit
model for a Proton Exchange Membrane Fuel Cell
(PEMFC). IEEE Power Engineering Society
General Meeting, Electr. Eng., Massachusetts
Univ., Lowell, MA.
Chiu, L.Y., B. Diong and R.S. Gemmen, 2004. An
improved small-signal model of the dynamic
behavior of pem fuel cells. IEEE Trans. Ind. Appl.,
40(4): 970- 977.
Correa, J.M., F.A. Farret, V.A. Popov and M.G.
Simoes, 2005. Sensitivity analysis of the modeling
parameters used in simulation of proton exchange
membrane fuel cells. IEEE Trans. Energ. Conver.,
20(1): 211-218.
Dongjing, L. and W. Li, 2007. Dynamic and steadystate performance of pem fuel cells under various
loading conditions. IEEE Power Engineering
Society General Meeting, 24-28 June, Tainan, pp:
1-8.
El-Sharkh, M.Y., A. Rahman, M.Y. Alam, P.C. Byrne,
A.A. Sakla and T. Thomas, 2004. A dynamic
model for a stand-alone PEM fuel cell Power plant
for residential applications. J. Power Sour., 138:
199-204.
4849 Cell Active Area
(CAA) (%)
0.617
cell voltage in this study corresponding to hydrogen
molar flow rate consumption.
600
500
Membrane
Humidity
(MH) (%)
0.214
Res. J. Appl. Sci. Eng. Technol., 4(22): 4845-4850, 2012
Friede, W., S. Rael and B. Davat, 2004. Mathematical
model and characterization of the transient
behavior of a PEM fuel cell. IEEE Trans. Power
Electron., 19(5): 1234-1241.
Jeferson, M.C., A.F. Felix, A.P. Vladimir and G.S.
Marcelo, 2006. Sensitivity analysis of modeling
parameters used in simulation of proton exchange
membrane fuel cells. IEEE Trans. Energ. Conver.,
20(1): 211-218.
Pathapati, P., X. Xue and J. Tang, 2005. A new
dynamic model for predicting transient phenomena
in a pem fuel cell system. Renewab. Energ., 30(1):
1-22.
4850