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Dynamic Modeling and Simulation of a PEM Fuel
Cell (PEMFC) during an Automotive Vehicle’s
Driving Cycle
Mehmet Ali Biberci
Vocational School
Cankiri Karatekin University
Cankiri, Turkey
m.alibiberci@karatekin.edu.tr
Mustafa Bahattin Celik
Faculty of Engineering
Karabuk University
Karabuk, Turkey
mcelik@karabuk.edu.tr
Abstract—Polymer Electrolyte Membrane Fuel Cells (PEMFCs)
are the most appropriate type of fuel cells for application in
vehicles due to their low operational temperature and high-power
density. In this paper, a zero-dimensional, steady state
thermodynamic modeling for an automotive 90kW PEMFC
system has been built up in order to investigate the effects of
operating parameters such as vehicle acceleration and operating
pressure on the size of the system elements, heat and water
system constitution, fuel consumption, and efficiency. A dynamic
model was formed for the fuel cell power system in MATLAB.
Power output and power losses of the system were investigated at
3atm operation pressures.
Keywords-dynamic modeling; fuel cell system; PEM; thermal
analysis;MATLAB
I. INTRODUCTION
PEM (Proton Exchange Membrane or Polymer Electrolyte
Membrane) fuel cells are considered candidates for automotive
applications due to their low operational temperature and high-
power density. Even so, fuel cell systems face substantial
barriers to commercialization due to their high price and short
lifespan. PEMFC durability is mainly compromised by the
degradation of the membrane electrode assembly during long-
term operation [1]. Generally, the fuel of a PEMFC is pure
hydrogen. The basic electrochemical reaction cell consists of
one anode and one cathode electrode where on their surface
electrochemical reactions occur and conduct ions from the one
to the other, and the external circuit between electrodes for
current flow [2-4]. Many research attempts for automotive
applications focus on PEMFCs due to their capacity of higher
power density and faster start-up compared to other fuel cell
types. Water and heat management for PEMFCs is one of the
key technical issues that must be resolved in order to be used in
automotive applications. Proper water and thermal
management is significant for optimizing the carrying out of a
fuel cell stack. Water and heat management in automotive fuel
cell systems can be classified and analyzed at cell and system
levels. The cell level fields investigate the effects of parameters
such as pressure, rate of flow, temperature, humidity, and
membrane heaviness on the performance of the fuel cell stack
[5-9]. Authors in [10] studied the PEM fuel cell engine system
which is used in transportation applications. This system
consists of a compressor, humidifiers, pressure regulator,
hydrogen storage tank, cooling system, heat exchanger and the
fuel cell stack. The system performance was looked into by
parametric studies of energy, exergy and work output values by
changing operating conditions and system parameters. The
results demonstrated that the system efficiency increases with
the increase of temperature and pressure and that an increase in
relative humidity of the system has a positive effect on the
efficiency and power product values. In addition, the results
showed that the efficiency increases with the decrease of
membrane thickness, anode stoichiometry, and cathode
stoichiometry. The model was developed in [11] in order to
study the water and thermal management and balance of the
fuel cell stack. The results showed that the decrease of air
humidity increases the ionic resistance eventually and it causes
a significant drop in the voltage. In addition, the air
stoichiometric ratio must be greater than one to remove the
produced water from the stack in order to prevent the cathode
from flooding. Furthermore, the operating temperature of the
cell significantly affects the fuel cell performance. Higher
temperature increases the need for humification and water
production cannot meet the corresponding demand.
This work presents a general zero-dimensional PEM fuel
cell model for a vehicle application. The model was developed
in order to study water and thermal management and the
balance of the fuel cell stack of an automotive PEM fuel cell
system with a maximum power of 90kW. A model of the fuel
cell power system was created to power a true automotive
vehicle (weight=1880kg, air friction coefficient=0.65, front
surface area=2.68, rolling resistance coefficient=0.012).
Dynamic modeling was carried out with all its components
(auxiliary units, fuel cell, and aerodynamic structure of the
vehicle). The analysis of the system was run on the MATLAB
program and during the ECE-15 driving cycle, the power
required for the vehicle, the fuel cell current value, the fuel cell
water and heat management, the required power amounts for
auxiliary equipment, and the amount of hydrogen consumed
etc. values were studied.
Corresponding author: Mehmet Ali Biberci
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II. SYSTEM DESCRIPTION
A. Overall PEMFC System Model
In this chapter, a common zero-dimensional PEMFC
example is presented for automotive applications. The first step
in the evolution of such a model is the innovation of the system
layout including the fuel cell stack and auxiliary equipment. As
explained below, as the operational pressure is increased the
layout from the system changes due to the cooling system
requirements of the compressed air. In this paper, system
simulations were carried out at operating pressure of 3atm.
Figure 1 demonstrates the formal diagram of an automotive
PEMFC system proposed for 3atm operating pressure. This
diagram is similar to the existing commercial PEMFC
automotive systems accessible in the market and consists of
components necessary to add reactants, remove the generated
heat, and manage the produced water. The fuel cell stack
demands three flow systems that interact with each other: air
supply system, hydrogen supply system, and water and thermal
management systems.
Fig. 1. Schematic view of a fuel cell power system
The air provision system consists of a compressor, an air
cooler (intercooler), a humidifier, and a heater. Air supply at
high pressure is provided by the compressor. The compression
process causes a temperature rise in the supplied air. To lower
the temperature of the entering air to the humidifier, the air
transits from an intercooler. The air is moisturized by the
humidifier before ingoing to the cathode side of the fuel cell
stack to ensure a suitable hydration level of the membrane. The
unused air leaving the stack can be heated by the heater and
used to increase the hydrogen temperature through a heat
exchanger in the hydrogen supply line. The hydrogen supply
system consists of a hydrogen tank, a pressure regulator valve,
a heat exchanger, a humidifier, and the unused hydrogen
recycle line. The hydrogen is stored in a tank at high pressure.
The pressure regulator valve is used to adjust the flow rate of
the hydrogen. The heat exchanger helps warming the incoming
hydrogen which is then fed to the humidifier. Like air flow,
hydrogen is moisturized by the humidifier prior to entering the
anode side of the fuel cell stack. The recycling hydrogen
system is used to accumulate the hydrogen that has not reacted
in the stack and sends it back to mix with the entering anode
flow after the humidifier. The water system and thermal
management system consist of a radiator, a fan, pumps, and a
water storage tank. The chief function of the radiator is to
maintain the fuel cell stack at its operation temperature by
dissipating heat to the coolant. The fan increases the potency of
heat convection at lower vehicle speeds. The pumps recirculate
the water and the coolant through the system and the water
storage tank is used to reconstruct and save the generated
water. The generated water is used to moisturize the reactant
gases through the humidifier [2, 12].
B. Vehicle Force and Torque Parameters
In general, the force and torque parameters of the EV
(Electrical Vehicle) powertrain are borrowed from the well-
established definitions used in ICEV (Internal Combustion
Engine Vehicle) for powertrain. Figure 2 shows the force
components that the vehicle powertrain must provide for the
vehicle to travel, which include the road load Fload and the
acceleration force Faccel. This road load consists of three main
components as described by (1): the aerodynamic drag force
Fdrag, the rolling resistance force Fresist, and the climbing force
Fclimb [11].
Fig. 2. Vehicle powertrain force
����� � ����
����
��
���
�� (1)
C. Driving Cycle
In the European Union, a vehicle is commonly tested using
two kinds of driving cycles. The first one is the urban driving
cycle known as the ECE-15 which was introduced in 1999. It
was devised to represent city driving conditions in Paris or
Rome. As shown in Figure 3, it simulates an urban trip of
4052m at an average speed of 18.7km/h and maximum speed
of 50km/h. It is particularly useful for testing the urban driving
performance of an EV [13].
Fig. 3. ECE-15 driving cycle
D. Simulation Software
A zero-dimensional and steady state PEMFC model is
developed and presented. This example was enforced in
MATLAB which contains several types of heat exchangers,
compressors, pumps, mixtures, separators, etc. that have
been developed over the years. The users can add new
elements to the library components, which is the case for the
auxiliary equipment in this study. The equations used for
modeling were either analytical or semi-empirical as
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described below. The accuracy of the theoretical results was
validated by stack data and the ECE-15 driving cycle
produced by this model matches very well the
corresponding stack data. The presented model can be used
for all types of PEMFC stacks by replacing the adjusting
parameters explained in detail below [2, 14].
III. PEM MODEL AND BASIC EQUATIONS
To establish a general, zero-dimensional model of PEMFC,
a semi-empirical solution was applied for reproducing the
experimental polarization curve of the fuel cell. The average
cell voltage can be analytically expressed by the following
expression:
����� � � − ���� − ����
� − ����� (2)
where E is the open circuit voltage. ���� , ����
�, ����� are
activation, ohmic, and concentration losses respectively. There
are numerous equations proposed in the literature for predicting
the aforementioned terms which are elaborated below [14]:
������ � �����.����� (3)
where the stack voltage ������ is simply the cell voltage
multiplied by the ����� number of cells [15],
�� � �. �����.����� � �.������ (4)
where �� is the power output of the fuel cell stack (W) [15].
A. Activation Loss
The activation losses in fuel cell voltage can be calculated
using the well-known Butler- Volmer equation [16]:
���� � � �!"#$%&' ()�
�*�����
�
�!+",-$%&'
()�
�*������� (5)
where � is the current density, �. is the reaction exchange
current density, n is the number of exchange protons per mole
of reactant, F is Faraday’s constant, and α is the charge transfer
coefficient [17].
B. Ohmic Loss
The total fuel cell ohmic losses can be written as [16]:
����
� � � / Σ1
� �/ 23 4567�������8��
3
4
567�������
3
4
567�����9 (6)
where L is the thickness of the electrolyte layer, and σ is the
conductivity, and A is the active area of the fuel cell.
C. Concentration Loss
The concentration losses can be calculated using (7) [17]:
����� � � �' ln
<
<=>
(7)
where �4 the limiting current density, which is the point where
the current density becomes large and the reactant
concentration falls to zero, so the fuel cell will not be able to
produce a higher current density than its limiting current
density.
D. Fuel Cell Thermal Efficiency
Generally, the thermodynamic fuel cell efficiency is the
relation between the electrical power produced and the total
rate of fuel energy entering the fuel cell:
����� � ?.@+&AA.�+&AA�B CD,E#.FF@CD (8)
E. Hydration Management of the Membrane
The water content in the polymer electrolyte plays a
significant role in PEMFC stack lifetime and the ionic
resistance of the membrane. Low humidification in the
membrane causes a rapid increase of the ionic resistance and
high humidification will cause too much liquid water to
overflow into the reactant channels and fill the pores in the
electrodes. In order to have high ionic conductivity in the
membrane, it should be fully hydrated. Hydration can be
achieved by the humidification of gases, or by designing the
fuel cell to allow the product water to hydrate the membrane
[14, 18]. In this study both methods are applied. Generally,
diffusion of water in the polymer electrolyte is expressed in
two terms: one is the electro osmotic drag phenomenon, which
is representative of the number of water molecules associated
with protons (H
+
) while crossing the membrane. But when the
water is generated in the cathode side this phenomenon is the
other way round. Water concentration gradient makes the water
move from the cathode to the anode side, a phenomenon called
water back diffusion [14]. Water molar flux due to electro-
osmotic drag can be defined as:
G��� B � HIFDJ .��.
.6+&AA.�+&AA
' (9)
where �� is the electro-osmotic drag coefficient in water
molecules per proton. The electro-osmotic drag coefficient ��
can be calculated from the membrane water content K� [2]:
�� � 0.0029K�O
0.05 K� − 3.4.10=>T (10)
The water content in the membrane, K� is defined as the
ratio of water molecules to the number of sulfonic acid groups
within the ionomer and is calculated from the water activity UV
[2]:
K� � 0.043
17.8 UV − 39.85UVO
36.UVZ (11)
Water activity is defined as:
UV � 8[\\]",( ) = RH (12)
where P is the pressure of the anode or the cathode. The
amount of water concentration across the membrane that is
caused by back diffusion is assumed equal to 0.9 of water
transfer by electro osmotic drag.
F. Mass Balance
Mass balance equations are applied for each composition in
the reactants separately. Water mass balance can be written as:
GB FD`abc,d�
B GB FD`e&# −fGB ��� ./����.HFD` .10=Zg
� GB FD`aEc,�h� (13)
GB FD`ij&A,d�
B GB FD`e&# − fGB ��� ./����. HFD`.10=Zg
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� GB FD`ij&A,�h� (14)
These equations represent the water mass balance on the
cathode and anode sides respectively which can be liquid or
vapor. Acell is the active cell area and
2H O
M represents the water
molecular weight. GB FD` is the water mass flow rate and
subscripts in, out and gen represent inlet, outlet and generated
respectively [14].
G. Heat Transfer Balance
The energy released in the electrochemical reaction must be
taken away from the stack in order to maintain the desired
constant temperature. The thermodynamic steady state energy
balance of the fuel cell is given as:
∑l
,
� � ∑l
,�h�
I��
l����
l��m (15)
where l
,
� is the rate of energy entering with the reactant
gases, l
,�h� is the rate of energy leaving with the unused
reactant gases, Wel is the electrical power generated, l���� ̇is
the rate of heat carried from the fuel cell to the coolant,
and ̇l��m the rate of heat dissipated by the exposed stack
surface to the environment.
H. Total System Power and System Thermal Efficiency
The efficiency of the fuel cell power system is the relation
between the net electric power output and the total rate of fuel
energy entering the fuel cell:
��8� �
\E#
\$j,
(16)
where the output electrical energy ��h� is:
��h� � �� � ��hn (17)
�
� � GFD,
�.oo�FD (18)
where the gross output power �� was calculated (4) and the
parasitic loads by all the auxiliary system equipment ��hn is the
sum of all parasitic loads, commonly:
��hn � ����p
�ph�p
�q��
������� (19)
where ����p is the power of the compressor, �ph�p is the
power of hydrogen recirculation and cooling circuit pumps,
�q�� is the power of cooling circuit fan, and ������� is the
electrical power of the heater.
IV. RESULTS AND DISCUSSION
The simulation model was implemented using the above
formulation systems within the ECE-15 driving cycle. In this
section, an automotive PEMFC system is simulated in
MATLAB. The described aboce thermodynamic models for
compressors, pumps, humidifiers, and heat exchangers are
required to operate the PEMFC system under the required
conditions. Figure 4 shows the required power output as a
function of vehicle speed for 3atm working pressure. As can be
seen, the change in speed values directly affects the required
output power. Figure 5 shows the dissipation of auxiliary
power as a function of vehicle speed at 3atm operating
pressure. The auxiliary components include a compressor, an
electric heater, a coolant pump, an injection pump, a radiator
fan, and an intercooler fan. In this way, it is possible to see that
the electrical power consummation by the fan grows faster than
the electrical power consumed by the other auxiliary
components. It is further noted that the compressed air will
need to be cooled before it enters the humidifier using the
intercooler. It is stated that the temperature of the air coming to
the humidifier drops in an air cooler.
Fig. 4. Power output as a function of vehicle speed
Fig. 5. Auxiliary equipment power requirement as a function of vehicle
speed
Fig. 6. Vehicle speed vs cumulative hydrogen fuel consumption
The electrical energy generated by a fuel cell is directly
proportional to the amount of fuel consumed, because each
mole of fuel provides specific electron moles. Figure 6 shows
the consumption of hydrogen as a function of vehicle speed.
When the vehicle speed increases, more energy is needed, so
more fuel is consumed. Figure 7 shows the efficiency value as
a function of vehicle speed indicating fuel cell thermal
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efficiency and system thermal efficiency. The fuel cell thermal
efficiency curves present the relationship between the
generated electricity and the maximum usable operation for the
vehicle drive. The curves of the fuel cell thermal efficiency are
decreased when thespeed of the vehicle increases due to the
increase in the fuel consumption of the vehicle. It is also seen
that an increase in working pressure increases the fuel thermal
efficiency due to an increase in power output at high pressure
from the fuel cell. In the system thermal efficiency curves, it
can be seen that the increase in vehicle speed from 0km/h to
50km/h reduces significantly the system’s thermal efficiency.
This is mainly due to the electrical energy consumed by the
compressor and other auxiliary components. By entering the
appropriate operating parameters, the model produced in this
study can perform system optimization and select the best
operating condition for the system.
Fig. 7. System and thermal efficiency throughout the driving cycle
Figure 8 shows the water balance of the PEMFC system,
the amount of water entering the system in the ambient air, and
the amount of water injected into the humidified gases.
Fig. 8. Water management values during ECE-15 driving cycle
The water produced in the cathode due to the
electrochemical reaction must be greater than or equal to the
amount of water exiting the system. The water in the exhaust
may be liquid or gaseous. The condition of the water depends
on the operating conditions of the fuel cell (air stoichiometric
ratio and operating pressure and temperature). Liquid water is
easily separated from the gas flow in the condenser. Figure 8
shows the amount of water (liquid and vapor) at the outlet of
the stack required for humidification as a function of vehicle
speed for 3atm pressure. As a result it is concluded that the
average value of water at the exit of the fuel cell stack consists
of 60% liquid water and 40% water vapors. At high pressures,
the vapor pressure of the water is high, so the boiling point of
the water increases. Therefore, the amount of liquid water
increases with increasing working pressure. It also appears that
the liquid water at the exit of the fuel cell is larger than the
injected water and is sufficient to moisten the reagents before
entering the fuel cell without using a condenser. Thermal
management is one of the most important features in the
development of the fuel cell stack system because heat is
produced in large quantities by an electrochemical reaction in a
PEM fuel cell. If the rate of generated heat is too high, the fuel
cell overheats and may cause membrane dehydration. Low
temperatures reduce the speed of the chemical reaction, reduce
efficiency, and can cause water condensation and electrodes to
overflow. As noted above, proper thermal management is
required to maintain the required performance and durability
temperatures of the cells and to prevent the stack from heating
up the fuel cell stack system. The heat balance of the fuel cell
stack as a function of vehicle speed is shown in Figure 9. The
sum of the generated electrical energy, the rate of energy
released by unused reactive gases and the rate of heat removal
from the fuel cell should be equal to the rate of energy entering
with the reactant gases.
Fig. 9. Energy quantities during the ECE-15 driving cycle
The size of the heat exchanger (radiator) depends on the
amount of heat to be extracted from the fuel cell stack and is
influenced by the operating pressure. Figure 10 shows that as
the speed of the required heat exchanger area increases the
power from the fuel cell stack increases and the effective area
of the radiator is also increased in order to spread the waste
heat to the environment. This means that the size of the radiator
is the main factor affecting system thermal performance. Figure
11 shows the effect of vehicle speed on the refrigerant flow. It
is seen that if the vehicle speed increases, the required power
from the fuel cell stack increases and the refrigerant flow rate
must be increased to match the increased waste heat output.
Fossil fuels used in vehicles cause environmental pollution
in many ways. At the same time, the fossil fuel reserves are
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running out [19]. In some studies, alcohol based bio fuels are
used as alternative fuels reducing the environmental pollution
to some, but not sufficient extent [20, 21]. Since fuel cell
vehicles use hydrogen as fuel, they emit only water vapors to
the environment and cause zero environmental pollution. For
this reason and because of the abundance of hydrogen in
nature, they are seen as the technology of the future. Some
researchers have simulated only one fuel cell power system,
[10, 22] while others have examined the power requirements of
the auxiliary equipment (pump, compressor, fan, etc.) required
to operate, fuel and power management, and a power
generating engine of the fuel cell [10, 12, 14]. However, a fuel
cell engine system for a passenger vehicle has not been studied
within a driving cycle. In this paper, a detailed study was
conducted by examining and simulating the fuel cell system
and thermal efficiency, the power requirements of the auxiliary
equipment, the engine cooling system, and the radiator area
required for this system. Real vehicle features were used. For
this reason, this study eliminates the large experimental costs of
the companies developing fuel cell vehicles and makes the
development studies safer. From these perspectives, this paper
paves the way on future studies that can be conducted in
different real vehicles with different driving cycles.
Fig. 10. Required radiator area according to speed values during the ECE-
15 drive cycle
Fig. 11. Cumulative coolant flow ratio during the ECE-15 drive cycle
V. CONCLUSIONS
This paper has attempted to integrate component models for
an automotive PEMFC system that includes fuel cell stack, air
supply system, hydrogen supply system, and thermal circuit.
Increase of the operating pressure of the system increases the
fuel cell thermal efficiency but has no effect on the system
thermal efficiency. The system pressure has a significant
positive impact on the power density and water balance
characteristics of the fuel cell. Increase of the vehicle speed has
a negative impact on the system efficiency and stack efficiency.
Auxiliary components are necessary to operate the PEMFC
system but decrease its efficiency. Water management is one of
the problems in systems that operate at low pressure because
they need a large amount of water for the humidification
process and the sizes of the humidifier and the condenser
increase. This parasitic power requirement increases due to the
fan condenser. Several improvements can be made to the
PEMFC system model. The existing model can investigate the
effects of stack geometry and fuel cell material properties on
the system’s performance. An improved model can be used to
simulate the vehicle performance in different realistic driving
cycles.
ACKNOWLEDGEMENT
The authors will like to thank the TUBITAK (Scientific and
Technological Research Council of Turkey) for supporting
this research.
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