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Proceedings 2nd International Hydrogen Energy Congress and Exhibition IHEC 2007
Istanbul, Turkey, 1315 July 2007
Dynamic Simulation of a Pem Fuel Cell System
Zehra Ural1*, Muhsin Tunay Gençoğlu2 and Bilal Gümüş3
1,3 Dept. of Elec. and Electr. Eng., Eng. and Arch. Fac., Dicle University, Diyarbakır, TÜRKĐYE
2 Dept. of Elec. and Electronics Eng., Engineering Fac., Firat University, Elazığ, TÜRKĐYE
1*zural@dicle.edu.tr 2mtgencoglu@firat.edu.tr
ABSTRACT
In the near future, some fuel cell systems could be an accessible and attractive alternative to
conventional electricity generation and vehicle drives. The polymer electrolyte membrane
(interchangeably called proton exchange membrane, PEM) fuel cell systems can be made in mW
to kW capacities; hence a wide range of applications can be covered by this type of fuel cell. This
is a major advantage of this type of fuel cell, because once the technology was developed it can
be more or less easily scaled up or down for various applications. PEM fuel cell has attracted a
great deal of attention as a potential power source for automobile and stationary applications due
to its low temperature of operation, high power density and high energy conversion efficiency.
Great progress has been made over the past twenty years in the development of PEM fuel cell
technology. However, there are still several technical challenges that need to be addressed before
commercialization of PEM fuel cell.
In this study, the dynamics of a polymer electrolyte membrane fuel cell system is modelled,
simulated and presented. Matlab –SimulinkTM is used for the modeling and simulation of the fuel
cell system. The fuel cell system model consists of the dynamics of reactant flow, fuel cell model
and power conditioning units. Also, characteristic of 1.2 W PEM fuel cell system is obtained by
experiments. Simulation and experimental results are presented in this paper. The analyses of
grid connected or stand alone applications of PEM fuel cell generator system can be achieved
with this dynamic simulation model.
3bilgumus@dicle.edu.tr
Keywords: Fuel cells, Proton Exchange Membrane (PEM), PEM Fuel Cell Model.
1. INTRODUCTION
Rapid growth in energy consumption during the last century on the one hand, and limited
resources of energy on the other, has caused many concerns and issues today. Although the
conventional sources of energy, such as fossil fuels, are currently available in vast quantities,
however they are not unlimited and sooner or later will vanish. Moreover, environmental
concerns, such as global warming, are becoming increasingly serious, and require significant
attention and planning. Renewable energy sources are the answer to these needs and concerns,
since they are available as long as the sun is burning, and because they are sustainable as they
have no or little impact on the environment.
One technology which can be based upon sustainable sources of energy is fuel cell. Fuel cells are
devices that directly convert the chemical energy stored in some fuels into electrical energy and
heat. The preferred fuel for many fuel cells is hydrogen, and hydrogen fuel is a renewable source
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of energy; hence fuel cell technology has received a considerable attention in recent years.
However, this is only one reason, among many reasons, for the recent come back to this
technology. Fuel cells can have higher efficiencies than more conventional devices that convert
chemical energy into other forms of energy such as electricity. They are inherently simpler, and
have other social, economical, and engineering advantages over other types of machines for
energy conversion [1].
Fuel cell technology plays an important role in the development of alternative energy converters
for mobile, portable and stationary applications. In the recent years there was an increasing
interest in fuel cell technology. In particular, PEM fuel cell has reached a high development
status. This development was mostly advanced by the automotive industry, because fuel cells are
suitable to substitute the fossil fuels and also to provide an environmentfriendly propulsion. But
there is also a growing market for stationary fuel cell applications [2].
PEM fuel cell is considered to be a promising power source, especially for transportation and
stationary cogeneration applications due to its high efficiency, lowtemperature operation, high
power density, fast startup, and system robustness [3]. PEM fuel cells are suitable for portable,
mobile and residential applications [4]. In most stationary and mobile applications, fuel cells are
used in conjunction with other power conditioning converters and a circuit model would be
beneficial, especially for power electronics engineers who in many cases have the task of
designing converters associated with the fuel cell for various load applications [5]. In the last
decade a great number of researches have been conducted to improve the performance of the
PEM fuel cell, so that it can reach a significant market penetration [3].
Rapid development recently has brought the PEM fuel cell significantly closer to commercial
reality. Although prototypes of fuel cell vehicles and residential fuel cell systems have already
been introduced, it remains to reduce the cost and enhance their efficiencies. To improve the
system performance, design optimization and analysis of fuel cell systems are simple and safe
construction and quick startup even at low operating temperatures.
Mathematical models and simulation are needed as tools for design optimization of fuel cells,
stacks, and fuel cell power systems. In order to understand and improve the performance of
PEMFC systems, several different mathematical models have been proposed to estimate the
behavior of voltage variation with discharge current of a PEM fuel cell. Recently, numerical
modeling and computer simulation have been performed for understanding better the fuel cell
itself [48]. Numerical models are useful to simulate the inner details of PEMFC, but the
calculation required for these models is too extensive to be used for system models. In system
studies, it is important to have an adequate model to estimate overall performance of a PEMFC in
terms of operating conditions without extensive calculations. But, few studies have focused on
the simple models, which can be used to investigate the impact of cell operating conditions on the
cell performance and can be used to design practical fuel cell total systems [4].
In this study; firstly, general information about the fuel cells, their importance and applications
are presented. Then mathematical models of the PEM fuel cell are investigated. Finally, Dynamic
modeling of the PEM fuel cell is performed. Various system dynamics such as fuel cell
electrochemistry and reactantflow are modeled, simulated and presented. On the other hand, the
characteristic of 1,2 W PEM fuel cell is obtained by experiments.
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2. MATHEMATICAL MODEL OF A PEM FUEL CELL
The fundamental structure of a PEM fuel cell can be described as two electrodes (anode and
cathode) separated by a solid membrane acting as an electrolyte (Fig.1). Hydrogen fuel flows
through a network of channels to the anode, where it dissociates into protons that, in turn, flow
through the membrane to the cathode and electrons that are collected as electrical current by an
external circuit linking the two electrodes. The oxidant (air in this study) flows through a similar
network of channels to the cathode where oxygen combines with the electrons in the external
circuit and the protons flowing through the membrane, thus producing water. The chemical
reactions occurring at the anode and cathode electrode of a PEM fuel cell are as follows:
Anode reaction: 2H2 → 4H+ +4 e
Cathode reaction: O2 + 4H+ + e → 2H2O
Total cell reaction: 2H2 + O2 → 2H2O + electricity + heat
The products of this process are water, DC electricity and heat [4].
Figure 1: Schematic of a single typical proton exchange membrane fuel cells
Electrons flowing from the anode towards the cathode provide power to the load. A number of
cells, when connected in series, make up a stack and deliver sufficient electricity.
A IV curve, known as a polarization curve, is generally used to express the characteristics of a
fuel cell (Fig. 2). The behavior of a cell is highly nonlinear and dependant on a number of
factors such as current density, cell temperature, membrane humidity, and reactant partial
pressure. The cell voltage decreases with increasing current. A PEM fuel cell generally performs
best at temperatures around 7080 0C, at a reactant partial pressure of 35 atm, and a membrane
humidity of ~ 100% [6]. VI Characteristics of a 1,2 W PEM fuel cell is shown in Fig.3.
Experimental data is obtained by variable loads.
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 70 110 160 240 320 520 770 960 1100 1270 1310 1320
Current / mA
Cell Potential / V
Figure 2: Polarization curve Figure 3: VI Characteristics of a 1,2 W PEM fuel cell.
The cell potential (Vcell), at any instance could be found using Eq. 1. When a cell delivers power
to the load, the noload voltage (E), is reduced by three classes of voltage drop, namely, the
activation (Vact), ohmic (Vohm), and concentration (Vconc) over voltages.
Vcell = E – Vact – Vohm – Vconc V
The Nerst equation (Eq. (2)) gives the open circuit cell potential (E) as a function of cell
temperature (T) and the reactant partial pressures [6];
22
.
. 2
PP
F
OH
E0 represents the reference potential at unity activity, R is the universal gas constant and P is the
total pressure inside the stack. Relevant parameter values are given in Table 1.
The activation drop can be analyzed by Tafel’s equation and the empirical model outlined in [7]
is considered in this regard. Eq. (3) gives the activation voltage drop (Eact).
Eact = 0,9514 + 0,00312T 0,000187.T.[ln(I)] + 7,4.105.T.[ln(CO2)] V
I(mA.cm2) is the cell current density, the oxygen concentration(CO2) is given as a function of
stack temperature in Eq. (4)
PO
−
(1)
E = E0 – 0,85.103 (T – 298,15) +
5 . 0
2
5 . 0
.
ln
.
PP
TR
OH
V (2)
(3)
CO2 =
)/ 498 exp( 10. 08 , 5
6
2
T
mol.cm3 (4)
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Table 1: Fuel cell model parameters [7].
Symbol Parameter Value Unit
E0
Reference potential 1,229 V
J mol1 K1
C mol1
R Universal gas constant 8,314
F Faraday constant 96485
T Stack temperature 353 K
P Cell pressure 1,2 atm
tm
Cdl
τH+
Membrane thickness 175.104
cm
Double layer capacitance 0,035x232 F
Time constant 12,78 s
cm6 A3
cm s1
αH+
DH+
Since, the activation overvoltage appears as a voltage drop in Eq. (1) and Eact in Eq. (3) is
negative throughout the whole range, Eq. (5) is used to avoid a double negation for this term.
Vact =  Eact V
The effects of double layer capacitance charging at the electrodeelectrolyte interfaces can be
expressed by Eq. (6) [6];
V
C dt.
Relational parameter 5,78
0,85x106
Diffusion coefficient
(5)
dlact
act
C
dl
act
R
dV
1
−=
V (6)
Here Cdl is the double layer capacitance and Ract is the activation resistance, found by dividing
Vact, with I.
V
R
kΩ.cm2
I
act
act=
(7)
It should be noted that, here, Ract stands for the effective resistance for a given cell current, I, and
contributes to the activation overvoltage, Vact. On the other hand, Eq (6) is used to determine Vact
at any instance of time. Therefore, these equations need to be used separately and cannot be inter
changed.
At intermediate current densities the voltage drop is almost linear and ohmic in nature.
Membrane resistance (Rmem) is found by dividing the thickness, tm, by the membrane
conductivity, σ (kΩ1.cm1).
Vohm = I.Rmem
t
R
=
kΩ.cm2
(8)
σ
m
mem
(9)
The membrane water content depends on various factors, such as water drag from the anode to
the cathode due to moving protons, external water content of the reactants, and back diffusion of
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water from the cathode to the anode [6]. Since the effect of water drag is a significant factor, it
could be hypothesized that the membrane proton concentration is a function of the cell current
density only. An empirical differential equation could be solved to determine the proton
concentration, CH+, and Eq. (10) and (11) could be used to estimate the membrane conductivity, σ
[ 7];
+
=+
dt
ττ
F
.
.
At higher current densities, the cell potential decreases rapidly due to masstransport limitations.
This linearity is termed as the concentration over potential and modeled as;
Vconc = a.e (bl) V
Here, the coefficient a (V), and b (cm2 mA1) vary with temperature and given as;
a = 1,1.104 – 1,2.106. (T273)
b = 8.103
Eq. (1)(12) could be solved for cell potential, Vcell, as a function of current density, cell
temperature, reactant pressure, and membrane hydration [7]. If all the cells are in series, stack
output is the product of cell potential and number of cells in the stack (N).
Vstack = Vcell x N
It is assumed that reactant flow at the anode and cathode is laminar, that the inlet gases are
saturated at the given cell temperature.
Assuming that all the gases are ideal, the ideal gas law could be extended for dynamic analysis
and the principles of mole conservation could be used to model the reactant flows with the
general equation given below;
I
mm
dtTR..
V is the anode or cathode volume (m3), Pg is the gas (oxygen, hydrogen or vapor) pressure (atm),
.
m is the reactant inlet flow rate (mol.s1),
out
m
, is the reactant outlet flow rate (mol.s1), n is the
number of electrons involved for each mole of reactant.
To determine instantaneous conditions inside the cell, the conservation of gas reactants are
calculated using the following formulas.
Anode flow model equations;
+
+
+
++
H
H
H
HH
IC dC
α
3
.1
(10)
++
=
HHCD
TR
2
σ
(11)
(12)
(13)
Fn
dP
V
out in
g
..
±−=
(14)
in
.
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7
F
I
mm
dt
dP
T
.
R
.
m
V
outH inH
Ha
. 2
2
.
2
.
2
−−=
−−
(15)
)(
2
2
amb
P
Ha
outH
Pk
−=
−
222
2
.
..
HHH
inH
CF PC FRm
Cathode flow model equations;
dP
TR.
.
Pkm
=
−
=
−
F
I
mm
dt
V
outO inO
Oc
. 4
2
.
2
.
2
−−=
−−
(16)
)(
2
2
ambOc
outO
P
−
222
2
.
..
OOO
in
dP
O
CFPC FRm
V
=
−
F
I
mm
dtT
.
R
.
m
Table 2: Reactant flow model parameters
Symbol Parameter
Pamb
Ambient pressure
Va
Anode volume
ka
Anode flow constant
Vc
Cathode volume
kc
Cathode flow constant
PCH2
Percentage of H2 (purity)
CFH2
H2 flow rate conversion factor (SLMP to mol s1)
PCO2
Percentage of O2 (purity)
CFO2
O2 flow rate conversion factor (SLMP to mol s1)
PCH2OC
Cathode vapour content
Associated parameters are given in Table 2 [7].
3. DYNAMIC MODELLING OF THE PEM FUEL CELL SYSTEM
A fuel cell system mainly consists of a fuel processing unit (reformer), fuel cell stack and power
conditioning unit. A simple representation of a fuel cell system is given in Fig. 4. The fuel cell
uses hydrogen as input fuel and produced DC power at the output of the stack [8].
C outOHC inOH
COHc
. 2
2
.
2
.
2
+−=
−−−−
−
(17)
)(
2
2
ambCOHc
C outOH
PPk
−=
−
−−
Value
1
0,0159
0,004
0,0025
0,01
99%
6,85x104
21%
6,084.104
1%
Unit
atm
m3
mol s1atm1
m3
mol s1atm1





Figure 4: Basic fuel cell system components
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A PEM fuel cell system block diagram is shown in Fig. 5. The fuel cell system model consists of
the dynamics of reactant flow, fuel cell model and power conditioning unit. The fuel cell
subsystem which contains membrane resistance subsystem is shown in Figure 6. The fuel cell’s
inputs are hydrogen, oxygen and vapor pressures, cell current density of the stack. Hydrogen,
oxygen and vapor pressures could be found Eq. (15), (16) and (17). These terms could be used in
Eq. 2. to determine the open circuit cell potential. The cell potential products number of cells in
the stack. So, the stack voltage is obtained by this product. Also, the stack voltage is input of the
power conditioning unit. The power conditioning subsystem Simulink implementation is shown
in Figure 7. The power conditioning unit occurs of a single phase inverter to convert DC power
into AC, a 5 kVA transformer in order to increase low output voltage in 220 V, 50 Hz grid
power.
Power (W)
Iloadrms(A)
Vloadrms(V)
Vstack(V)
Iload(A)
Vload(V)
Power Conditioning
8
H2 flow(SLMP)
pH2
Istack
pO2
pH2O
Vcell (V)
Fuel Cell
Air flow (mole/sec)
I stack (A)
pH2O(atm)
Cathode H2O flow
120
Air flow(SLMP)
Air flow (SLMP)
I stack (A)
pO2(atm)
Air flow (mole/sec)
(Cathode) O2 flow
H2 flow (SLMP)
I stack (A)
pH2(atm)
(Anode) H2 Flow
signal rms
35
signal rms
Figure 5: Simulink blocks for a PEM fuel cell system.
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F
T
pH2
pO2
pH2O
E
Eo
Vohm
Co2
Vconc
Vohm
Vact
Vact
1
Vcell
(V)
u(1)*u(2)
eqVohm
f(u)
eqVconc
f(u)
eqO2 conc
f(u)
eqEact
350
T
Ract
C R
f(u)
Nerst
Temp
Iload
Rmem (kohmcm2)
Membrane Resistance
I/Cdl
C
F
f(u)
Eotemp
Cdl
Cdl
K
A~mA/cm2
1
s
1
4
pH2O
3
pO2
2
Istack
1
pH2
Figure 6: Single Fuel Cell Model (Fuel Cell Subsystem)
2
Vload(V)
1
Iload(A)
+

pulses
A
B
Single phaese
inverter
Signal(s) Pulses
PWM Generator
50 Hz
5 kVA
34/220 V
+

v
+
i

+

v
signal
+

+

v
1
Vstack(V)
Figure 7: Power Conditioning Subsystem
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4. SIMULATION RESULTS
MatlabSimulinkTM is used to simulate the PEM fuel cell system. Additional limiters are placed
in various key locations in order to prevent problems arising from algebraic loops and extreme
numerical values. The simulation is done for 1.5 s. The hydrogen flow rate is maintained at 8
standard litre per minute (SLMP). The air flow rate is fixed at 120 SLMP [7]. Simulation results
for 00.2 s time interval are given in figures 811 and 01.5 s time interval are given in figures 12
17. System output voltage for alternative and effective values for 4.5 kW, cos φ= 0.90 and 3 kW,
cos φ= 0.80 lagging loads are given in Figure 8, 10, 12, 14. Alternative and effective current
values for 5 kW, cos φ= 0.90 and 3 kW, cos φ= 0.80 lagging loads are given in Figure 9, 11, 13,
15. The load is connected the transformer output. This load is changed variable real and reactive
power values.
400
output voltage(ac)
output voltage(rms)
0 0.02 0.040.06 0.080.10.12 0.140.160.18 0.2
400
300
200
100
0
100
200
300
Time (s)
System Output Voltage (V)
0 0.020.04 0.06 0.080.1 0.120.14 0.160.18 0.2
40
30
20
10
0
10
20
30
40
Time (s)
Load Current (A)
load current(ac)
load current(rms)
Figure 8: Voltage Output (4.5 kW, cosφ 0.9) Figure 9: Load Current (4.5kW, cosφ 0.9)
400
output voltage(ac)
output voltage(rms)
0 0.02 0.040.06 0.080.1 0.12 0.14 0.160.18 0.2
400
300
200
100
0
100
200
300
Time (s)
System Output Voltage (V)
0 0.020.04 0.06 0.080.10.12 0.14 0.160.180.2
30
20
10
0
10
20
30
Time (s)
Load Current (A)
load current(ac)
load current(rms)
Figure 10: Voltage Output (3 kW, cosφ 0.8)
Figure 11: Load Current (3 kW, cosφ 0.8)
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0 0.51 1.5
400
300
200
100
0
100
200
300
400
Time (s)
System Output Voltage (V)
output voltage(ac)
output voltage(rms)
0 0.51 1.5
40
30
20
10
0
10
20
30
40
Time (s)
Load Current (A)
load current(ac)
load current(rms)
Figure 12: Voltage Output (4,5 kW, cosφ 0.9) Figure 13: Load Current (4.5kW, cosφ 0.9)
400
output voltage(ac)
output voltage(rms)
0 0.51 1.5
400
300
200
100
0
100
200
300
Time (s)
System Output Voltage (V)
0 0.51 1.5
30
20
10
0
10
20
30
Time (s)
Load Current (A)
laod current(ac)
load current(rms)
Figure 14: Voltage Output (3 kW, cosφ 0.8)
6000
Figure 15: Load Current (3 kW, cosφ 0.8)
0 0.51 1.5
0
1000
2000
3000
4000
5000
Time (s)
Power (VA)
0 0.51 1.5
0
1000
2000
3000
4000
5000
6000
Time (s)
Power (VA)
Figure 16: Power Demand (4.5 kW, cosφ 0.9) Figure 17: Power Demand (3 kW, cosφ 0.8)
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Variation in power demand is represented by figures in case of lagging power factor is changed
(Figure 1617).
5. CONCLUSIONS
In this paper the dynamic simulation of a PEM fuel cell system and simulation results are
presented. Studies have been done with a 5 kW PEM fuel cell system. As a result of this study
PEM fuel cell system is suitable for distributed generation. Further analysis should be done three
phase fuel cell system and controlled power conditioning systems design.
ACKNOWLEDGEMENT
The authors would like to thank The Commission of Dicle University Scientific Research
Projects (DUBAP) for financial support towards this study.
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