1
Shell Eco Racer – Modelling and design of a
fuel cell propulsion system
A. Chr. Olesen, J. R. Jensen, and M. R. Cerqueda
Aalborg University Denmark
Abstract—This paper concerns the modelling, simulation and
design of a High Temperature Polymer Electrolyte Membrane
fuel cell propulsion system for the AAU Shell eco marathon race.
Simulations in MatLab Simulink are used to evaluate whether a
system with or without a capacitor gives the best performance
and highest energy efficiency. Both models are implemented with
a PI controller that maintains a constant temperature in the fuel
cell stack. Further, the system without capacitor is tested experimentally to validate the Matlab Simulink model. Finally it is
shown that when having a limit on the peak voltage, a capacitor
can improve the system efficiency, but not necessarily the mileage.
Index Terms— HT-PEM Fuel Cell, Modelling, Simulation, Shell
Eco Racer.
I.
INTRODUCTION
T
he Shell Eco Marathon race is an educational project that
was founded as a competition to enhance energy efficiency and thus the sustainability of vehicles. It is scheduled
that Aalborg University (AAU) is going to participate in the
spring of 2009 in the prototype category. The vehicle in question is based on a High Temperature Polymer Electrolyte
Membrane fuel cell (HT PEMFC) which sets certain requirements to the power electronic system. A sketch of the system
is shown in Figure 1.
pattern has been established by (1). It minimizes the power
needed to drive the race while keeping an average speed of
8.33 m/s, which is the minimum average velocity allowed.
This power consumption divided by the efficiency of the electrical parts is used in the simulation and the experiment.
The objective of this research study is to determine which
fuel cell system configuration gives the highest energy efficiency and mileage when taking the constraint with regard to
maximum operating voltage into account. The rules stated by
Shell prescribe that the voltage cannot exceed 50 V. Moreover, temperature control, air stoichiometry and the fan characteristics’ are taken into account in the comparisons done.
The comparisons are based on an available 1 kW fuel cell
stack from the Danish company Serenergy.
Two system configurations have been proposed, one with a
capacitor in parallel to the fuel cell and another without. Both
are supposed to be temperature controlled by a PI controller to
maintain as high a possible temperature in the fuel cell stack
and thus efficiency, without destroying the fuel cell membranes (2)
The main idea behind using a capacitor in parallel is that it
should reduce the operation time at a low voltage, i.e. at low
efficiency, by keeping the voltage more stable. Further, by
keeping the voltage more stable, the mean voltage can be
pushed closer to the limit of 50 V, than without a capacitor
with the present stack design.
The fuel cell system consists, besides the fuel cell and the
capacitor, of a fan, thermo couples and a PI controller. Further, it is assumed conservatively that the racer weighs 150 kg
without capacitor as no car been built yet.
II. TECHNOLOGY
Figure 1: The power electronic system consisting of a fuel cell, capacitor,
inverter and an electric motor.
Until now, the following parts have been designed: The aerodynamic shape of the vehicle, the mechanical structure, the
drive motor as well as a power and motor controller. Among
the ongoing projects is the inverter. Further, a velocity drive
The current state-of-the-art fuel cell prototype vehicle that
participated at the Shell Eco Marathon race in May 2008 is
developed by the University of Applied Sciences in Offenburg, Germany. Their vehicle drove with an equivalent gasoline mileage (EGM) of 3198 km/l. It uses a Nexa 1.2 kW rated
LTPEM from Ballard, consisting of 47 cells. The supporting
power electronic system consists in addition to a capacitor in
parallel of a self developed electronic steering, energy management and Hub motor with integrated electronics.
The chassis/wheels/steering weighs 25 kg, fuel cell 15 kg
and the electric motor 13 kg, equivalent to a total weight with
driver of approximately 103 kg. The average drag coefficient
of the car was measured to 0.17 with a projected area of 0.237
2
m². These specifications give a mean power consumption
during the race of 50 W. (2)
Recent development with regard to PEM has been concentrated on HTPEM. The advantages of operating at high temperatures are among others improved electrochemical reaction
rates, simplified water management and cooling. (3) The disadvantage of HTPEM is that they possess a lower thermodynamic efficiency than LTPEM. Thus, parasitic losses are minimized at the expense of efficiency and control simplification.
Further, to improve fuel cell systems many researchers have
proposed a hybridization by utilizing reversible energy storage, i.e. a super capacitor in parallel. The benefits include
better transient power demand response and the possibility of
recovering kinetic energy during regenerative braking. In
addition it increases the degrees of freedom in the power flows
and thus offers opportunities for the optimization of the vehicle efficiency. (4)
III. PHYSICAL MODELS
The power demand to drive the vehicle is calculated by
knowing the slopes of the track, the torque and the different
forces to overcome, inertia, drag and gravitation. It is given by
the three equations:
dv
dt
ds
dt
dE
dt
=
τ − r ⋅ ( Fdrag + Fincline + Froll )
⎛ ⎛ J wheel + m ⎞ ⎞
⎟⎟
⎝ ⎝ r2
⎠⎠
r ⋅⎜3⋅⎜
=v
=
(1.1)
τ ⋅v
r
, which when calculated over the entire race with the physical
values; the projected area of the vehicle parallel to the driving
direction, 0.283 m2, the drag coefficient, 0.05, the rolling resistance coefficient, 0.005, and the vehicle mass of 150 kg.
These yield the power depicted in Figure 3.
Mechanical model
The controller regulating the driving profile proposed by (1) is
quite simple. It always calculates which velocity the racer
should do just to finish the race with the lowest allowable
average speed. This calculated speed is set as reference speed
for the regulator. Moreover a torque saturation of 3.85 Nm has
been set not to overload the motor. The racer should be fitted
with a brake only and when it is applied or the maximum safe
speed is reached the motor is disconnected, the regulator is
shut off and the integrator is zeroed. The velocity profile with
the torque for the entire race is shown in Figure 2
Figure 3: The power needed to drive the racer. x-axis is time [s], and y-axis is
power [W].
This power demand is used to feed the models and the experiments described in the following.
Simulink
To be able to simulate the different system configurations in
MatLab Simulink the following models are needed:
Figure 2: Optimal speed profile. x-axis is time [s], and y-axis is [Nm] for
torque (pink) and [m/s] for speed (black).
Of course, this is the ideal cycle; the real one could be a bit
different due to overtaking or other obstacles. The speed profile is compared to the critical values due to the risk of sliding
and overturning calculated at the narrowest turns. The maximum allowed speed in the narrowest turn is 12 m/s which, by
looking at the speed profile never should be reached.
•
•
•
•
•
•
Fuel cell
Thermal
Fan
Electrical circuit
PI controller
Voltage controller
The fuel cell model used was proposed by (6). It is a semiempirical model that determines the voltage dependent on the
current drawn by taking the activation, ohmic and diffusion
3
overvoltage into consideration. The governing equation is as
follows:
V = N cell (V0 − ηact − ηohmic − ηdiff
⎛
Ru T
⎝
4α c F
V = N cell ⎜ V0 −
ln
i + i0
i0
)
− iRohmic −
(1.2)
Rdiff i ⎞
⎟
λ −1⎠
(1.3)
Where Ncell is the number of cells, V0 is the open circuit voltage (OCV), αc is the cathode transfer coefficient, i0 is the exchange current density, i is the current, Rohmic and Rdiff are the
ohmic and the diffusion resistance. The four last variables are
calculated by experimentally determined regressions that depend on the stack mean temperature.
The thermal model monitors the change in energy of the
fuel cell and hereby calculates the change in temperature. This
is done based on a conservation of energy analysis of a thermal lumped system. Thus temperature gradients are neglected
in the modelling to make a feasible simulation. These have
been measured in the range of 10-20 °C (Andreasen 2008).
These gradients are neglected since they only cover a small
volume of the fuel cell stack and thus when modelling, the
lumped assumption is reasonable.
The governing equation for the stack energy balance is:
m ⋅ cp ⋅
( (
dT
dt
( (
= m h of + h − ho
− m h + h − h
o
f
o
))
H2O
))
( (
H2
( (
+ m h of + h − h o
− m h + h − h
o
f
o
))
air , out
))
air , in
The model proposed without a capacitor is quite simple. It
consists of a fuel cell model developed by (7), a fan model, a
thermal model, the PI controller and the power load. An overview of the system and the interactions between the parts can
be seen in Figure 4.
Figure 4: An overview of the system without a capacitor
The PI controller was tuned in the model by simulating it with
a step in power demand of 100 W. It was assessed as being the
largest possible stepwise change in load to encounter during
the race. Moreover, it was set as a criterion that the temperature oscillation should be within one degree.
System with capacitor
Voltage vs. Current:
I = 0.000965659V 4 − 0.00258361V 3 + 0.0249245V 2 ...
(1.5)
Voltage vs. pressure loss through the fuel cell (7):
(1.6)
Volume flow vs. pressure loss (7).
ΔP = 1.309V 2 + 3.365V
System without capacitor
(1.4)
Where m is mass of the fuel cell, ṁ are the mass flows, h is the
enthalpy pr. mass, Q is heat loss, V is the fuel cell voltage and
I is the fuel cell current.
The fan model determines the air stoichiometry and fan
power consumption based on a voltage signal from the PI
controller and the hydrogen consumption. It does this partially
by the following experimentally determined regressions that
are fitted to the blower Micronel D601T/Q mounted on a 1
kW Serenergy fuel cell stack:
ΔP = 0.0008145Q 2 + 0.2798Q
IV. SIMULINK MODELS
...
− Q − V ⋅ I
−0.076647V + 0.15272
The controller is setup as a PI only. The derivative gain is
omitted since it is very sensitive towards noise that is present
from the temperature feedback of the thermo couple.
The voltage controller is designed for the capacitor system;
it is designed to shut of the fuel cell if the capacitor has been
charged enough to be able to supply power the rest of the race.
(1.7)
The electrical circuit consist of the fuel cell, the load and a
capacitor that takes losses into account, by having a resistance
in parallel and series.
The system with capacitor is more complex. It consists of a
new fuel cell model, which is setup with a non-linear solver
that determines the current based on the voltage. In addition,
the system has a thermal model, a fan model, an electrical
circuit with the capacitor and the voltage controller inside, the
PI controller and the power load. An overview of the system
and its interactions is seen in Figure 5.
4
Figure 5: An overview of the system with a capacitor
For the PI controller, the same values as before are used. The
change in load that the fuel cell with a capacitor in parallel
would encounter would be smaller, thus the PI controller
should be better than needed.
The capacitor size used was chosen based on a simplified
system. This was done to decrease the simulation time during
a parameter variation. In this system, the fuel cell model consisted of two linear regressions representing the actual polarisation curve instead of solving the non-linear equations described in the preceding section. This simplification made the
model much faster, however the output results were still
matching the more complex non-linear model.
Different sizes of capacitors were tested, first in a big range
and afterwards a smaller range, closer to the optimal. It was
chosen to take the difference between maximum and minimum operation voltage into account. Also, the change in the
efficiency was taken into account. There is not exactly a clear
optimal size. Therefore, the smaller and lighter that followed
the requirements was chosen. The capacitor size was determined to be 40 F, which means that a super capacitor is
needed.
V. EXPERIMENTS
One experiment on a FC stack was conducted two times to
increase the reliability. The experiments were conducted to
test the fuel cell system, though isolated from the inverter and
electrical motor as close to the real race conditions as possible.
The entire setup is shown in Figure 6.
heating, the load and the blower. A PI-controller regulates the
temperature of the stack at the desired temperature; in the
experiments at 160 °C.
Firstly the stack was heated to 110°C by the heating foil
placed on top of the stack. Hereafter the hydrogen valve was
opened and the pressure reduction valve made sure that there
was a constant pressure of 1.2 bar. The purge valve was
opened for 1-2 seconds evacuating air from the anode side. A
constant load of 300 W was applied until the temperature
reached 160°C. The load was disconnected and the value of
the flow meter was read. The power graph calculated was
loaded into the variable load that acted as the racer driving the
entire race. After 3054 seconds the simulated race was over
and the flow meter was read again.
The same experiment was conducted twice to minimize the
errors and the results were nearly similar.
To find out if there was any leakage in the system a small
test was conducted. The fuel cell was pressurized with the fan
shut off and with no load applied to it. It was left like this for 5
minutes and the flow meter was read. The results are shown in
the preceding section.
Table 1
Apparatus Flow meter Thermocouples Red‐y compact 6 Nl/min from Vögtlin (See datasheet on the enclosed CD) 1 kW HTPEM stack with 65 cells from Sere‐
nergy Micronel D603T 12 V (See datasheet on the enclosed CD) AGA W40B‐1.5B. Max input: 40 bar, output 0.1‐1.5 bar Bürkert 6011 direct magnet valve (See data‐
sheet on the enclosed CD) Transistor Devices RBL 4000W (See datasheet on the enclosed CD) Data acquisition National Instruments NI cRIO‐9004 Fuel cell Axial blower Pressure reduction valve Purge valve/Inlet valve Variable Load Heating foil Implemented in the stack maximum effect 800 W The apparatus for the experiment
VI. RESULTS AND DISCUSSION
Simulink results
Figure 6: The experimental setup of fuel cell system
The set-up is controlled by a LabView programme that monitors all the inputs and controls the signals to the valves, the
Both simulations were done with an OCV of 0.95V. This
value was based on measurements on a new fuel cell stack
from Serenergy (8). The temperature was set to 180°C. Since a
capacitor is used it increases the weight of the vehicle. It was
found that a capacitor of 40 F weighs 10 kg (9). Thus, with a
super capacitor the car weighs 160 kg.
Without capacitor an EGM of 1977 km was obtained, as
seen in Table 2. This equals a thermodynamic efficiency of
58.8 % or a hydrogen consumption of 3.436 g. During the
simulation the voltage oscillated between 46.7 and 56.8 V
with a mean of 50.5 V. The temperature of the stack was kept
5
constant at 180°C; only small changes were seen. The fan had
an average power consumption of 0.072 W for keeping the
temperature stable.
With a capacitor the EGM was 1954 km. This equals an efficiency of 59.80 % and a hydrogen consumption of 3.476 g.
The voltage oscillation was between 47.49 and 50.76 V and
with a mean of 49.03 V. Likewise, as before the temperature is
kept constant within a margin of 0.1°C and the mean fan
power demand was quite small 0.078 W.
Table 2
Efficiency, EGM and hydrogen consumption for with and without capacitor
Efficiency [%]
Without capacitor 58.8
With capaci‐
tor 59.80 Difference
‐1
EGM [km] 1977 1954 23 Hydrogen [g]
3.436
3.476 ‐0.04
Mean power demand [W] Voltage var. [V]
77.8
81.63 ‐3.83
46.7 – 56.3 47.49 – 50.76
‐0.98 – 5.45
Mean voltage [V]
50.5
49.03 1.47
Mean fan power [W]
0.072
0.078 ‐0.006
Fuel cell and capacitor voltage
Without capacitor
With capacitor
58
Voltage [V]
56
54
52
50
48
46
0
500
1000
1500
Time [s]
2000
2500
3000
Figure 7: The voltage of the system with and without a capacitor
It appears that the system with a capacitor is more efficient.
An increase of 1 % showed possible. However, since the mean
power demand is 3.83 W higher, a decrease in EGM of 23 km
is observed. Consequently, a capacitor does not improve the
EGM because of the weight increase. However, with a capacitor the rules are almost obeyed, i.e. it peaks 0.76 V above the
limit. In contrary, without a capacitor, it peaks 6.3 V above.
To make the system without capacitor obey the rules, the
number of cells should be lowered quite significantly or a
resistance should be inserted in the fuel cell; hence lowering
the efficiency as well as the EGM. However, simulations show
when lowering the maximum voltage to the allowed, by removing cells, the model without capacitor still gives a higher
EGM.
The increase in efficiency with a capacitor agrees well with
the expectation that an increase in minimum voltage is equivalent to an increase in efficiency. It should be noted however
that the mean voltage actually decreases. This indicates that
though operating at a high voltage in average, the system
without capacitor only produces low amounts of power at high
voltage and high efficiency. Thus, the end-efficiency is
dragged more down by the periods where the fuel cell is operated at low voltages, low efficiency and high power demand.
A plot of both voltages as a function of time is seen in Figure
7. It should be noted that both models do not obey the rules
with the given fuel cell parameters. However, the model with
a capacitor almost operates below the maximum voltage. If the
actual OCV measured on the stack was used in modeling, the
system would fulfill the rules.
It should be noted that the comparison is done without taking uncertainty propagation in the models into account. Since
the difference in efficiency is relative small, the uncertain of
the models could easily be in the same range as the variation.
Thus, this small difference would not be a good criterion to
choose the implementation of a capacitor on. Therefore, future
work should include an uncertainly propagation analysis to be
sure of the capacitor efficiency results.
Experimental results
As can be seen in Figure 8 the voltage is lower than in the
simulation.
Experimental Voltage
56
54
52
50
Voltage [V]
60
48
46
44
42
40
0
500
1000
1500
2000
Tme [s]
2500
3000
3500
Figure 8: Experimental fuel cell voltage as a function of time
As the Open Circuit voltage was taken from (7) and not necessarily corrected for the particular stack used in this project it
was chosen to reduce it by 0.048 which was the difference in
mean between the simulated and the experimental results. This
changed the value from 0.95 to 0.902V. The simulation was
6
run again. In Figure 9 the experimental and simulated voltages
can be seen together with the mean of the simulation.
Stack Voltage Experimental and Simulation
58
Average
Instant
Experiment
56
54
Changed conditions
52
Voltage [V]
The experiments follow the simulation results quite nicely
when comparing the voltage and current; but when comparing
the mileage there is a big difference. This is thought to be due
to leakage in the FC stack.
50
48
46
44
42
40
0
500
1000
1500
Time [s]
2000
2500
3000
Figure 9: The experimental and the simulated voltage as a function of time
The two graphs are following each other quite nicely except in
the outer regions where the voltage is high and low. In the
high voltage region the simulation is cut off in a straight line.
This is due to the saturation in the power demand which has a
lower limit of 0.3W. This value was estimated as being a minimum power production.
The reason that the experimental results do not follow the
simulation in the lower voltage region is more difficult to
explain, this could be due to the kinetics of the FC, it takes a
little while for the reaction to follow the power demand. However HTPEM Fuel Cells have shown to have very short time
response time (10) so an explanation could be the dynamics of
the variable load. Since it is operated in power- mode the
internal components have to vary the voltage and the current
simultaneously which may impose some dynamics.
Leakage result
This revealed that around 0.63 liters of hydrogen was fed in to
the system per minute. The red-Y flow meter also showed an
approximately 0.61 L/m several minutes after. In the 3054
seconds the experiment ran this constituted app. 32 liters. This
is a major source of error since it is not known how much
hydrogen is being used in the reaction and how much is leaked
to the surroundings, but it could be a very feasible explanation
for the higher hydrogen use in the experiment than in the simulation.
The calculated efficiencies for the system depend on the power demand from the car, i.e. the weight and drive pattern. If it
rains or the wind changes etc. the calculated power profile will
not be true. In the case of increased head wind the power demand will go up. As the friction coefficient in the over-turning
calculations were on dry road, rain would increase the risk of
accidents; in this situation the torque saturation of the controller should be lowered.
There can also be some failures in the system. Of course, if
the fuel cell is disconnected, or it fails, the car is going to stop.
If the PI controller for the fan breaks, the temperature of the
fuel cell may rise, so the membrane gets in danger of degrading. To prevent this there has to be some kind of security system to protect it; for example the hydrogen could be shut off,
if the temperature exceeds a certain maximum value.
VII. CONCLUSION
The modeling results show a small improvement in thermodynamic efficiency with a 40 F super capacitor in parallel of a 1
kW Serenergy HT PEMFC stack with the given power demand. However, the efficiency increase is not significant,
partially because the difference in modeling the capacitor with
a large or small loss is in the same range, and partially since
the uncertainty propagation also may be in the same range.
Further, the efficiency increase does not mean a better result
in the race with regard to equivalent gasoline mileage; actually
the energy consumption is larger with the capacitor because of
the extra weight. The capacitor only seams useful as a common one in the order of micro farads to supply energy in small
periods where fast transient power demands arise.
Though the voltage is higher without a super capacitor it
could be lowered and still drive longer.
In addition, it should be noted that this was only proven for
a given power demand and fuel cell. Thus, it could change
with circumstances.
Table 3
Experimental results
VIII. ACKNOWLEDGMENTS
Experiment 1 Experiment 2 Efficiency [%] 33.01 32.5 EGM [km] 1267 1248 Hydrogen [g] 5.361 5.445 Hydrogen [l] 65.83 64.82 The authors would like to thank Ph.d.-student Søren Juhl Andreasen for exhibiting great flexibility in the experimental
development -and execution.
7
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