184
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
PEM Fuel Cell Stack Modeling for Real-Time
Emulation in Hardware-in-the-Loop Applications
Fei Gao, Student Member, IEEE, Benjamin Blunier, Member, IEEE, Marcelo Godoy Simões, Senior Member, IEEE,
and Abdellatif Miraoui, Senior Member, IEEE
Abstract—In this paper, a multiphysical proton exchange membrane fuel cell stack model, which is suitable for real-time emulation is presented. The model covers three physical domains:
electrical, fluidic, and thermal. A Ballard 1.2 kW 47 cells fuel cell
stack model is introduced. The corresponding fuel cell system auxiliary models are given based on experimental tests. Based on the
modeling equations, the fuel cell dynamic phenomena in different
physical domains are analyzed and the corresponding time constant expressions are given. Using the real-time stack model, a fuel
cell stack emulator based on a buck converter is used to emulate
the fuel cell stack electrical part. The experimental results show
that the emulator can reproduce the real-stack behavior with a
great agreement. Such a fuel cell stack emulator can be used for
hardware-in-the-loop applications, in order to test and validate the
fuel cell system design.
Index Terms—Fuel cells, power electronics, real-time systems,
simulation.
I. INTRODUCTION
UEL cells technology, recently, a very active research field
because of many possible applications in distributed generation solutions. Fuel cell systems are complex multiphysical
systems, which covers three major physical domains: electrical,
fluidic, and thermal. A stand-alone proton exchange membrane
(PEM) fuel cell stack itself cannot be used directly as an energy supply and require stack control and energy management.
The fuel cell dc output voltage is highly dependent to the current, which imposes a high-output voltage variation. The voltage
variation range is not acceptable for most of the dc electrical devices. Moreover, if the electrical device needs an ac supply, the
fuel cell system must be connected to an inverter to provide
alternating current [1].
One of the key challenges of fuel cell systems is the design
of an appropriate power converter for conditioning the power
output. During the design phase, the converter needs to be tested
and adjusted with the real-fuel cell stack, and then, it must be
validated. However, the design and the development of fuel cell
F
Manuscript received March 29, 2010; revised May 25, 2010; accepted June
1, 2010. Date of publication July 19, 2010; date of current version February 18,
2011. Paper no. TEC-00133-2010.
F. Gao, B. Blunier, and A. Miraoui are with the Department of Electrical
Engineering, Transport and Systems Laboratory (SeT), Université de Technologie de Belfort-Montbéliard (UTBM), Belfort Cedex 90010, France (e-mail:
fei.gao@utbm.fr; benjamin.blunier@utbm.fr; abdellatif.miraoui@utbm.fr).
M. G. Simões is with the Colorado School of Mines, St. Golden, CO 804011887 USA (e-mail: msimoes@mines.edu).
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.2010.2053543
auxiliary systems, such as testing of air compressor control,
power and energy management, and performance optimization
may damage a fuel cell very easily. In addition, fuel cell test costs
(hydrogen consumption and the need of safety installations) are
still relatively high, in addition of the requirement of safety and
special installations to conduct experiments with a real-fuel cell.
The aforementioned drawbacks support the interest in designing a PEM fuel cell real-time model-based emulator for
hardware-in-the-loop (HiL) applications. In fuel cell system
power converter design as well as in other developments, the
fuel cell auxiliaries can be tested and improved with the realtime fuel cell emulator initially without any risks for the fuel
cell stack, with low cost of operation.
A fuel cell model-based emulator requires that the output
physical quantities, such as voltage of a real stack must be
reproduced accurately by the emulator. The computation time
of the emulator should be in real time for HiL tests. Therefore,
the model complexity is a compromise between accuracy and
computational speed. In addition, as mentioned earlier, the realtime model should be multiphysical model in order to simulate
the different physical phenomena occurring in the fuel cell stack.
Different approaches for fuel cell models are found in the
literature [2]–[9], but few of them considered the detailed fluidic
and thermal behaviors. Most of the proposed models are singledomain models. Some of them considered the fluidic domain in
the fuel cell. But the complete electrical, fluidic, and thermal
phenomena are never included in a single model as proposed in
this paper.
Moreover, many real-time PEM fuel cell emulators have been
proposed [10]–[15]. A common drawback of these emulators is
that the fuel cell models used for the emulator are too simplified
and do not represent accurately all the system physics and nonlinearities. Most of these proposed emulators consider only the
electrical system level or an electrical equivalent model. In fact,
a fuel cell is a multiphysical system and other physical domains,
such as fluidic and thermal phenomena should be considered in
the model.
In this paper, a complex multiphysical model is shortly presented in a first part. This model can predict the fuel cell stack
behavior in different physical domains. With the model equations, a fuel cell dynamic phenomena analysis is done. The
proposed multiphysical model is then implemented in a realtime system for simulation. The design of the fuel cell emulator
using a dc/dc buck converter is detailed in a second part. The
experimentation in the last section shows that the emulator can
reproduce the fuel cell power output very accurately and fuel
cell physical quantities in different domains can be supervised
during the emulator operation.
0885-8969/$26.00 © 2010 IEEE
GAO et al.: PEM FUEL CELL STACK MODELING FOR REAL-TIME EMULATION IN HARDWARE-IN-THE-LOOP APPLICATIONS
TABLE I
TABLE OF INDEXES USED IN EQUATIONS
185
model presented hereafter. Thus, a concentration losses term is
not necessary in (1) for this model.
The dynamic activation losses voltage Vact (V) due to the
“double-layer effect” in the electrical domain is as follows:
d
i
1
Vact =
Vact
1−
(3)
dt
Cdl
ηact
where Cdl is the single-fuel cell double-layer capacitance (F).
The cell static activation losses ηact (V) can be obtained from
the well-known Butler–Volmer potential equation
αnF
−( 1 −α ) n F
i = j0 S e R T η a c t − e R T η a c t
(4)
II. MULTIPHYSIC FUEL CELL SYSTEM MODEL
A multiphysical PEM fuel cell stack model used for fuel
cell real-time simulation is summarized in this section. More
detailed model equations with fully experimental validation are
presented in [16] and [17].
More informations for the sources of the physical equations
presented hereafter in modeling sections can be found in detail
in [16]. Table I gives all the indexes used model equations in the
following sections.
A. Cell Electrical Model
The single-cell voltage output can be computed using the
following equation:
Vcell = Ecell − Vact − Vohm
(1)
where Ecell is the single-cell electromotive force (V), Vact is the
cell activation losses at catalyst layer (V), and Vohm is the cell
resistive losses (V).
The cell electromotive force can be obtained from the Nernst
equation as follows:
Ecell = E0 − 0.85 × 10−3 (T − Tc )
RT +
ln
PO 2 × PH 2
2F
(2)
where T is the temperature of the cell (K), E0 is the reversible
nearest potential for single cell (1.229 V), Tc is the temperature
correction offset (298.15 K), PO 2 is the oxygen pressure (atm)
at the interface of cathode catalyst layer, PH 2 is the hydrogen
pressure (atm) at the interface of anode catalyst layer, R is the
ideal gas constant (8.31 J/mol), and F is the Faraday constant
(96 485 C/mol).
It should be noted that the gas pressures used in the model are
the pressures at the interface of the catalyst layers of the anode
and cathode sides. The well-known “concentration losses” in a
fuel cell are due to the pressures drop through the gas diffusion
layer (GDL) (i.e., from the gas channels to the catalyst interface).
If the channels pressures are used in (2), the equation should take
into account a concentration losses correction term in addition
to (1). But in the proposed model, the pressures of the species
at the catalyst layer can be directly obtained due to the fluidic
where i is the stack current (A), S is the catalyst layer section
area (m2 ), n is the number of electrons involved in the reaction,
α is the symmetry factor, and j0 is the exchange current density
(A/m2 ).
When ηact is large, (4) becomes the well-known Tafel
equation
i
RT
ηact =
ln
.
(5)
αnF
j0 S
The cell resistive losses Vohm are mainly due to the membrane resistance. These losses can be obtained by computing
the membrane resistance expression using the Joule’s law
i δ m em
Vohm = Rm em i =
r(Tm em , λ(z))dz
(6)
S 0
where δm em is the membrane thickness (m) and r(T, λ(z)) is
the membrane local resistivity (Ωm).
B. Cell Fluidic Model
The fluidic dynamic response of fuel cells is generally due
to the gas pressure dynamic in the fuel cell channels (cooling,
cathode, and anode), which is given by the mass balance
Mgas VCh
RT
d
PCh
dt
=
Ch
q̇fluid
(7)
in/out
where Vch is the volume of the channels (m3 ), Mgas is the gas
molar mass (kg/mol), Pcv is the gas pressure in the channels (Pa),
and qfluid is the fluid mass flow(s) (kg/s) entering or leaving the
channels.
The gas pressure drop in the channels due to the mechanical
losses assuming a laminar flow can be expressed by the Darcy–
Weisbach equation
ΔP =
64 ρch L
V2
Re 2 Dhydro S
(8)
where Dhydro is the channels hydraulic diameter (m), Vs is the
mean fluid velocity in the channels (m/s), ρch is the channels
gas density (kg/m3 ), L is the length of the channel (m), and Re
is the fluid Reynolds number.
In the other side, the gas mass flow rate (kg/s) through the
GDL is directly related to the stack current, as described by the
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
following equations:
as follows:
MO 2 i
4F
MH 2 i
=
2F
MH 2 O i
.
=
2F
q̇O 2 =
q̇H 2
q̇H 2 O,pro d
(9)
δGDL RT Pa (qb /Mb ) − Pb (qa /Ma )
Ptot S
Dab
(10)
(12)
where δGDL is the GDL thickness (m), S is the GDL layer
section area (m2 ), Ptot is the mean gas total pressure (Pa) in
the GDL layer, M is the gas molar mass (kg/mol), b stands for
species other than species a, and Dab is the binary diffusion
coefficient between the species a and b (m2 /s).
In the membrane layer, the water content can be written as
follows [18]:
⎧
⎨ 0.0043 + 17.81 · aH 2 O − 39.85 · a2H 2 O
(13)
+36 · a3H 2 O ,
[0 < aH 2 O 1]
λ=
⎩
14 + 1.4 · (aH 2 O − 1), [1 < aH 2 O 3]
where aH 2 O is the water activity, calculated from the partial water vapor pressure PH 2 O (Pa) and the water saturation pressure
Psat (Pa).
The water balance in the membrane layer can be described
by two different phenomena: the electroosmosic drag described
by (14), and the back diffusion described by (15).
Jdrag =
(14)
Jbd
(15)
where nsat = 22 is the electroosmotic drag coefficient for maximum hydration condition, ρdry is the dry density of the membrane (kg/m3 ), D( λ) is the mean water diffusion coefficient in
the membrane (m2 /s), δm em is the membrane thickness (m), λA
is the membrane water content of anode side, λC is the membrane water content of cathode side, and Mn is the equivalent
mass of the membrane (kg/mol).
The total water mass flow (kg/s) in membrane can be then
expressed as follows:
qH 2 O,net = Jdrag + Jbd .
+
Q̇fc
forced convection
Q̇nc r
natural convection and radiation
(11)
b= a
i
nsat λA + λC
·
·
· MH 2 O
11
2
2F
ρdry
λA − λC
=
· Dλ ·
· S · MH 2 O
Mn
δm em
dTCV
= Q̇cond +
dt
conduction
The multigas diffusion of each species (oxygen, hydrogen,
nitrogen, and water vapor) in the GDL can be described by the
Stefan–Maxwell equation
ΔPa =
(ρ V Cp )
(16)
C. Cell Thermal Model
The thermal dynamic response of a fuel cell is due to the
thermal capacity of each layer in the cell. This dynamic for
each thermal control volume (CV) can be generally described
+
+
Q̇ ass
m
convective m ass flow
Q̇src
(17)
internal sources
where ρ is the mean layer volume density (kg/m3 ), V is the
layer volume (m3 ), Cp is the layer thermal capacity (J/kg), and
Q̇ stands for the different types of heat flow entering or leaving
the layer volume (J/s): conduction, forced convection, natural
convection, radiation, convective mass flow, and internal heating
sources.
The heat flows between solid materials layers in the fuel cell
stack are transferred by conduction according to the Fourier’s
Law
Q̇cond =
λm Scontact
(Tlayer1 − Tlayer2 )
δ
(18)
where λm is the material thermal conductivity (W/mK), S is the
contact area (m2 ), and δ is the material thickness (m).
The heat exchanges between the solid material and the forced
fluid flow is described by the Newton cooling law
Q̇fc = hfc Scontact (Tfluid − Tsolid )
(19)
where hfc is the forced convection heat transfer coefficient
(W/m2 K).
In addition, considering the fuel cell bipolar plate size and
the number of cells in one stack, the heat exchanges due to the
natural convection and radiation is be considered
Q̇nc
r
= hnc r Sext (Tamb − Tsolid )
(20)
where hnc r is the combined natural convection and radiation
heat transfer coefficients (W/m2 K), Sext is the external area of
the bipolar plate (m2 ), and Tamb is the external temperature (K).
The convective mass transport brings an additional heat flow
into each layer
(q̇fluid Cp,fluid ) (Tfluid − Tlayer ) .
(21)
Qm ass =
fluid
When the fuel cell stack produces electricity from the electrochemical reactions, the heat is also generated at the same time.
The main heat sources in the fuel cell are due to the irreversible
losses in the electrochemical reaction and the resistive losses
from the membrane resistance.
The main irreversible losses occur in the cathode catalyst
layer: the entropy changes in the reaction and the activation
losses. These losses can be calculated as follows:
T ΔS
+ i · Vact
Q̇src 1 = −i ·
2F activation
entropy change
where ΔS is the entropy change (J/mol).
(22)
GAO et al.: PEM FUEL CELL STACK MODELING FOR REAL-TIME EMULATION IN HARDWARE-IN-THE-LOOP APPLICATIONS
Fig. 1.
Fig. 2.
Cathode air compressor outlet flow rate with fitting curve.
The fuel cell internal resistance is generally due to the polymer membrane resistance. Another heat source due to the resistive losses can be obtained according to the Joule’s Law
Q̇src 2 = i2 · Rm em .
187
Cooling fan speed at different stack temperatures.
TABLE II
COOLING FAN SPEED AND STACK TEMPERATURE
(23)
D. Fuel Cell Stack Model
The model is set and validated for an air cooled 1.2 kW 47
cells Ballard Nexa stack supplied by compressed air and pure
hydrogen. The entire fuel cell stack is modeled by stacking N
single-cell models together. Every single-cell model in the stack
has the same physical model equations as presented earlier, but
has different boundary conditions. The boundary conditions of
cell k are obtained from the adjacent cells (k − 1 and k + 1).
E. Fuel Cell Auxiliaries Model
In addition to the fuel cell stack itself, the vision Ballard Nexa
stack system needs some other auxiliary components, such as
electronic control broad, air compressor, and cooling fan. In
order to model the entire fuel cell stack system, the models of
these components are needed. From the experimental data, the
air compressor and cooling fan empirical mathematic model can
be obtained.
1) Air Compressor Empirical Model: In order to keep the air
stoichiometry, the air compressor outlet flow rate (inlet of the
cathode channels) of the Ballard Nexa fuel cell system depends
directly on the stack current.
The relation between the stack current and the cathode air
flow rate is obtained by experimentation as presented in Fig. 1.
From experimental data, the relationship between the stack
current and the cathode air inlet flow rate can be approximated
by an empirical fourth-order polynomial equation
Nair
inlet
= 6.04 × 10−5 · i4 − 4.71 × 10−3 · i3
+ 9.65 × 10−2 · i2 + 1.05 × i + 16.1 (24)
where Nair inlet is the air inlet flow rate (slpm) in the cathode
channels.
2) Cooling System Empirical Model: The Ballard Nexa fuel
cell system is cooled by a controlled cooling fan. The relation-
ship between the fuel cell stack temperature and fan speed is
shown in Fig. 2.
From the experimental measurement, it can be clearly concluded that the fan speed control is divided into a constant speed
zone (straight lines at the bottom) and regulated zone (the curve
at high temperature), depending on the stack temperature, as
shown in Table II.
According to the manufacture datasheet, the Ballard Nexa
stack cooling fan maximum flow rate is about 3600 slpm. From
the experimental data, the empirical air cooling fan model of the
Ballard Nexa fuel cell system can be then obtained.
F. Fuel Cell Dynamic Phenomena Analysis
In a fuel cell stack, different dynamic phenomena exist in
electrical, fluidic, and thermal domains, as described in the previous section. In electrical domain, the dynamic is due to the
double layer capacitance at the catalyst interface. In the fluidic
domain, the dynamic is due to the channels volume and the
water balance through the cathode and the anode. In the thermal domain, the dynamic is due to the heat generation and heat
capacity of material.
Each dynamic of each domain expression can be approximated by a first-order system. Thus, from the equation analysis,
the “time constant” expression of each dynamic phenomenon
can be obtained. It should be noticed that the transient time of a
first-order system is about four times its time constant.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
1) Electrical Dynamics (Double Layer Capacitance): From
the electrical dynamic (3)–(5), the time-constant expression in
the fuel cell electrical domain is the following:
i
Cdl RT
ln
τelectrical =
.
(25)
αn F i
j0 S
In the Ballard Nexa 1.2 kW fuel cell stack, the double layer
capacitance of the single cell is measured using experimental
method. The value of this capacitance is about 150 F/m2 . From
the Ballard Nexa fuel cell stack characteristic data given in [16],
the electrical time constant in the Ballard Nexa fuel cell stack is
found to be around 0.16 s.
2) Fluidic Dynamics (Gas Channels Dynamics): The first
kind of dynamics in the fluidic domain are due to the channels
gas volume.
The cooling, cathode, and anode channels pressure time constant in the fluidic domain can be obtained from (7)–(11) [16]:
τfluidic
channels
=
32L2 μgas
.
2
Dhydro
Pch
(26)
In the Ballard Nexa 1.2 kW fuel cell stack, from the fuel cell gas
supply channels geometry and gas property [16], the cooling
channels pressure time constant is found to be around 8.14 μs,
the cathode channels pressure time constant is about 6.92 ms
and the anode channels pressure time constant is about 25.1 ms.
The anode time constant is much bigger than the cathode side,
because the anode supply channels are longer in the Ballard
Nexa system.
3) Fluidic Dynamics (Membrane Water Diffusion): The second kind of dynamics in the fluidic domain are due to the membrane water diffusion [see (13)–(16)] and water vapor partial
pressure balance in the cathode and anode channels.
This membrane water diffusion dynamic time constant in
fluidic domain can be calculated according to the following
equation:
τfluidic
=
where
Csrc =
0.011δm em i2
iΔS
+
.
2F
(0.5193λ − 0.326) S
In the Ballard Nexa 1.2 kW fuel cell stack, from the fuel
cell stack properties data given in [16], the fuel cell temperature
dynamic time constant can be estimated to be between 37.15
and 124.3 s. Thus, the cell temperature transients can last about
497 s (8 min and 17 s).
5) Discussions: From the previous dynamic analysis, the
Ballard Nexa 1.2 kW fuel cell stack dynamic phenomena can
be summarized in Table III.
It can be concluded that the thermal transient in the fuel cell
is the most significant dynamic. The water diffusion through the
membrane can be relatively fast or slow, because the water flux
in the membrane depends on several variable physical quantities,
such as membrane water content, stack current, cathode vapor
pressure, and anode vapor pressure. But none of the electrical
and fluidic dynamic transients last more than 1 s. Thus, from the
point of view of a long-term model-based fuel cell simulation,
the thermal dynamic phenomena is the most important because
the thermal dynamic transient time is much bigger than those in
the electrical and fluidic domains.
III. FUEL CELL STACK EMULATOR DESIGN
m em
Psat Vano de
9.5955 · R T (Dλ ρdry S/δm em Mn ) + (nsat i/44 F )
(27)
where Psat is the water saturation pressure (Pa).
In the Ballard Nexa 1.2 kW fuel cell stack, assuming the
nominal operating temperature 338.15 K, a maximum stack
current of 40 A, the membrane properties given in [16] and the
membrane water content, the membrane water dynamic time
constant can be approximated between 0.0082 and 0.12 s.
4) Thermal Dynamics (Stack Thermal Capacities): The
thermal dynamics in the fuel cell are mostly due to the material thermal capacity and different heat fluxes, as mentioned
in (17)–(23).
From these equations, the cell level temperature time constant
in the thermal domain can be obtained
τtherm al =
TABLE III
DIFFERENT DYNAMIC TRANSIENT TIMES IN BALLARD NEXA SYSTEM
ρcell Vcell Cp
hfc Scontact + hnc r Sext +Csrc
(28)
Based on the real-time model simulation, the design of a fuel
cell emulator is introduced hereafter. The fuel cell stack voltage is emulated by a classical controlled dc/dc buck converter
connected to the proposed multiphysical fuel cell system model.
A. Real-Time Model Implementation
The governing physical equations presented in the previous
section of fuel cell modeling can describe the fuel cell phenomena in different physical domains. However, these equations cannot be used directly for real-time simulation purpose
in their present form. An appropriate equation arrangement and
a suitable solution algorithm should be considered for program
implementation.
For the portability and compatibility reason, the presented
model is decided to be coded in C-language-based S-function
for MATLAB/Simulink environment. In order to use a generic
ordinary differential equations system solver algorithm (ODE
solver), the model should be rearranged to a well-known
GAO et al.: PEM FUEL CELL STACK MODELING FOR REAL-TIME EMULATION IN HARDWARE-IN-THE-LOOP APPLICATIONS
nonlinear state-space representation as follows:
ẋ = A(x, u) · x + B(x, u) · u
y = C(x, u) · x + D(x, u) · u
189
(29)
where x is the model dynamic state-variable vector, ẋ is the
time derivative of state vector x, u is the input variable vector
of model, y is the output vector of model, and A, B, C, and D
are the nonlinear coefficients matrix obtained from the proposed
physical equations in nonlinear model.
The state vector of present model contains all dynamic variables in each cell (please refer to dynamic equations in modeling
section), which can be described in (30).
⎫
⎞
⎛
Vact
⎪
⎪
⎟
⎪
⎜ Pch (O2 , H2 , H2 O) ⎪
⎪
⎟
⎬
⎜
···
⎟
⎜
states of cell 1 ⎟
⎜
⎟
⎜ Tcv (channels, GDL, ⎪
⎪
⎟
⎜
⎪
x = ⎜ catalyst, membrane) ⎪
⎟ . (30)
⎪
⎭
⎟
⎜
···
⎟
⎜
⎜
···
}
states of cell 2 ⎟
⎟
⎜
⎠
⎝
···
···
}
states of last cell
Each cell in stack has the same state-variable structure with
different numerical values, because the physical equations that
describe each cell are the same, but the boundary conditions of
each cell are different. Thus, the derivative state vector ẋ can be
expressed as follows:
⎫
⎛
⎞
dVact /dt ⎪
⎪
⎜ dPch /dt ⎪
⎟
⎬
⎜
⎟
derivative states of cell 1 ⎟
...
⎜
⎜
⎟
⎪
⎜ dTcv /dt ⎪
⎟
⎪
⎭
ẋ = ⎜
⎟ . (31)
...
⎜
⎟
⎜
···
} derivative states of cell 2 ⎟
⎜
⎟
⎝
⎠
···
···
} derivative states of last cell
The model input vector describes the external boundary conditions applied to the fuel cell stack model in different physical
domains. These boundary conditions can be described as follows:
⎛
⎞
istack
⎜ q̇O 2 ⎟
⎜
⎟
⎜ PH 2 ⎟
⎜
⎟
u = ⎜ PH 2 O ⎟ .
(32)
⎜
⎟
⎜ q̇co oling ⎟
⎝
⎠
Pamb
Tamb
And at last, the output vector y contains all the desired fuel
cell variables (dynamic or static) for further use at outside of
simulation. An example of y can be seen in the following:
⎛
⎞
Vcell
⎜ Rm em ⎟
⎜
⎟
⎜ Pch ⎟
⎜
⎟
y = ⎜ q̇H 2 O,net ⎟ .
(33)
⎜
⎟
⎜ Tcatho de ⎟
⎝
⎠
Tano de
Tm em
Fig. 3.
Real-time fuel cell model current solving algorithm.
The correspond nonlinear matrix A, B, C, and D can be then
obtained using the formula of the physical equations presented
in modeling section.
These vectors in (29) is coded using C-language specific 1-D
and 2-D table structure. The nonlinear mathematical operations
are done by C-based mathematical library.
Once the model structure is generalized, an appropriate ODE
solver algorithm should be applied for the current model, in
order to resolve this complex differential equations system.
For the nonlinear model stability consideration, an implicit
solver, which is proposed by MATLAB/Simulink environment,
is used to resolve numerically and iteratively the presented statespace fuel cell stack model. The solver flow diagram for the
current real-time model is presented in the Fig. 3.
This proposed solver algorithm with the previous state-space
model codes are then implemented in a commercial Opal-RT
QNX-based real-time processor board via the real-time workshop interface.The Opal-RT system provides also a digital control area network (CAN) bus communication board. The values
of output vector y from the model is sent to CAN communication driver at each time step, these values are then sent to
the CAN bus of fuel cell emulator that will be described in
the following section. The 2.8-GHz processor embedded in the
Opal-RT system gives the real-time computation capacity for
the current complex mathematical fuel cell stack model.
B. Emulator Structure With Digital Communication Bus
The actual fuel cell emulator structure is given in Fig. 4.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Fig. 5.
Fig. 4.
Fuel cell emulator structure.
The fuel cell stack model communicates with the dc/dc buck
power converter via a digital CAN bus. A 150-MHz DSP is
used as a gateway between CAN message and converter driver,
this DSP is used also as converter controller (see Section III-E
for more details). The converter is connected to an active load.
The actual current value in the load is measured by a current
sensor connected at the output of the power converter. The measured current value is then sent to the CAN bus and to the
real-time model to compute the corresponding voltage reference. With the given load current, the corresponding fuel cell
stack output voltage is computed by the fuel cell model and its
value is sent back to the dc/dc converter. Then, the embedded
controller regulates the converter voltage to meet the desired
voltage output.
The gate driver/insulated gate bipolar transistor (IGBT) for
this converter is an available commercial Semikron unit. The
gate driver is matched to the transistor. The converter design
for optimization of switching losses, or anything related to the
gate driver is not considered in this paper, because this paper
deals with the low-frequency bandwidth of the fuel cell transient response and gate driver/transistor switching is subject of
circuit design, which is considered to be properly done by the
manufacturers.
It has to be noted that, all the model predicted quantities
(electrical, fluidic, and thermal) are sent to the CAN bus continuously, despite they are required by the emulator or not (e.g., in
the actual emulator, only the stack voltage value is required for
the dc/dc converter). These state variables, such as individual
cell temperatures or membrane water content, which can be got
from the CAN bus, can be used in the fuel cell stack supervision
interface.
C. Buck Converter Design for the Emulator Power Interface
A typical dc/dc buck converter is used to control the power
of the fuel cell emulator, as shown in Fig. 5.
As discussed in the previous sections, the thermal dynamic
is the most important dynamic behavior. The temperature transients can last some minutes, which is much longer than others
dynamics. Thus, for a fuel cell stack emulation, the thermal dynamics should be able to be reproduced by the dc/dc converter.
DC/DC buck converter diagram.
The power output of the designed converter is set to 1.2 kW
with a voltage ranging from 20 to 50 V and a current between 1
and 50 A. Even all other kind of dynamics can be well predicted
by the real-time model, the voltage dynamics due to transient
phenomena below 100 ms cannot be easily reproduced by a
conventional buck converter with a 10-kHz pulsewidth modulation (PWM) and a maximum voltage ripple requirement of
about 1% [19]. Thus, only phenomena with dynamic transient
times larger than 100 ms have been considered. It means that
the converter has to be able to answer ten times faster than the
reference voltage variations caused by fuel cell transient, i.e., in
less than 10 ms (cutoff frequency larger than 100 Hz).
D. Converter L and C Conditioning
1) Converter Inductance: The converter inductance value
is calculated from the converter minimum current, in order
to ensure that the converter is always working in continuousconduction mode (CCM). CCM is required for a linear operation
of the converter, and the minimum current is guaranteed by the
auxiliary power required to run a fuel cell.
In order to match the fuel cell stack voltage range, the expected converter output voltage is between 20 and 50 V. Thus,
the expected duty cycle range of IGBT is between 30% and
80%.
In order to calculate the values of the output filter (inductance
and capacitance) for the buck converter, the PWM period time
TPW M (s), the converter supply voltage Vd (V), and the converter
minimum current Im in (A) are required. Knowing these values,
the minimum value of inductance can be obtained [19]
L>
10−4 × 60
TPW M Vd
= 0.75 × 10−3 (H).
=
8Im in
8×1
(34)
Thus, L = 1 mH is chosen for the converter.
2) Converter Capacitance: The converter capacitance value
should be chosen to meet the converter dynamic response needs.
With the fixed inductance value L (H) and the converter minimum cutoff frequency fc,m in (Hz), the maximum value of the
converter capacitance can be obtained
2
2
1
1
√
√
=
C
2πfc,m in L
2π × 100 × 10−3
= 2533 × 10−6 (F).
(35)
On the other hand, the capacitance is also used to filter the
converter output voltage ripple. Generally, the dc/dc converter
GAO et al.: PEM FUEL CELL STACK MODELING FOR REAL-TIME EMULATION IN HARDWARE-IN-THE-LOOP APPLICATIONS
191
output voltage ripple should be less than 1% of the output voltage
ΔVO m ax 1% · VO (m in) = 0.01 × 20 = 0.2(V).
(36)
Thus, the minimum capacitance value can be obtained [19]
C>
=
2
VO (m ax) TPW
M
8LΔVO m ax
50 × 10−8
= 312.5 × 10−6 (F).
8 × 10−3 × 0.2
(37)
From (35) and (37), C = 680 μF is chosen for converter.
E. Buck Converter Real-Time Control Implementation
The buck converter (IGBT switch) is controlled by a classic
proportional integral (PI) closed loop with an antiwindup feedback. The PI loop controls the converter voltage output from the
reference voltage calculated by the multiphysical model. The
controller is embedded in a 150-MHz DSP board. The same
DSP is used also as a gateway of the CAN bus and the power
converter. The DSP receives the desired voltage value from the
model via the CAN bus, computes the corresponding duty cycle
value, and then, generates the PWM output for the driver of the
converter.
The inductance and capacitance values were chosen to match
the dynamics of the fuel cell response, based on experimental
evaluation of a fuel cell transient response, as discussed in previous section. The PI controllers were fine tuned and debugged
using the real-time prototyping interface of dSpace, and extensive experimentation confirmed the stability and optimized
response. More detail in this subject can be found in [20].
The controller parameters Kp , Ki , and Kt (antiwindup)
are adjusted during experimentation using the experimental
Ziegler–Nichols tuning rule [21].
It should be noted that the converter conditioning and design
are not the major concern of this paper. For further reading, a
more analytically and detailed fuel cell-related power converter
design can be found in a recent paper [22].
IV. EXPERIMENTAL RESULTS AND DISCUSSIONS
Fig. 6.
Experimental setup for the fuel cell stack model validation.
Fig. 7.
Experimental setup (designed emulator, load, and power supply).
A. Experimental Setup
The experimental platform of Ballard Nexa stack is presented
in Fig. 6.
The Ballard Nexa stack is a ultra compact fuel cell system
that has 47 individual cells connected in series. The embedded
control board communicates via RS232 with the supervision
software provided by Ballard. This software can provide some
important stack parameters during the stack operation, such
as stack current, stack voltage, cathode temperature, gas pressure, fan speed, etc. In addition to this supervision software,
two supplementary experimental devices were added in this test
platform. First, a National Instrument 60 channels differential
voltage measurement DAQmx system is implemented on the
stack to measure the individual cells voltage. The measured
voltages data are collected and treated in a Labview environment. Second, a professional forward looking infrared (FLIR)
infrared camera is set on the top of the stack to measure the
individual cells temperature. This camera capture infrared images of the stack every second during the stack operation. These
images can be then treated by a dedicated FLIR software to
extract the temperature of predefined measurement points. The
synchronization between the Ballard software, the Labview environment, and the FLIR camera is done by the synchronized
real-time clock in each device.
The stack is connected to an electronic load. The load is
running under current control mode. Different current profiles
are set by the load, this profiles can be applied automatically to
the stack during operation.
The photograph of the experimental emulator setup is shown
in Fig. 7. The CAN bus-based supervision interface can record
the data sent by the model or measured on the power converter.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Fig. 8.
Stack current profile.
Fig. 9.
Stack voltage responses.
The same electronic load is connected to the emulator for
the emulator tests. The load reproduces exactly the same prerecorded current profiles than the ones used in the real-stack tests.
Thus, the emulator can be compared to the real stack using
exactly the same current profiles.
B. Results and Discussions
The model and the emulator have been validated temporally
and experimentally with the Ballard Nexa 1.2 kW 47 cells fuel
cell stack system.
The test stack current profile of about 900 s is shown in Fig. 8.
This profile, covering currents from 5 to 35 A, is also applied
to the proposed multiphysical fuel cell stack model for model
validations. Based on the stack current, the model fuel cell stack
voltage value is then used by the buck converter controller in
order to emulate the real-stack power output characteristics.
The real-stack voltage, the predicted stack voltage by the
model and the emulator converter output voltage are shown and
compared in Fig. 9. From Fig. 9, it can be concluded that the
model prediction is very close to the experimental measurement.
The max prediction error is less than 1.2 V, which gives less than
Fig. 10.
Zoom-in at 50s: stack voltage (model, real stack, and emulator).
Fig. 11.
Individual cell voltages at 230 s.
4% of relative error. It can be also found that the emulator output
voltage based on the model prediction is very close to the model
predicted one over the whole current range. A zoom-in at about
50 s (first transient) for these three curves is given in Fig. 10 in
order to give a clearer comparison.
In addition to the real-stack electrical power output emulation
with the dc/dc converter, the model itself can predict much more
fuel cell state variables then the stack voltage. Beside the model
temporal prediction, the spatial distribution of the fuel cell stack
physicals can be also obtained from the proposed model. Fig. 11
shows the stack individual cell voltages prediction at 230 s. The
predicted value have a good accuracy compared to experimental
data.
In the thermal domain, the measured temperatures of individual cells are compared to the model predicted ones, as shown in
Fig. 12(a) and (b). The stack spatial and temporal evolution is
well reproduced by the model. The slight differences between
the simulation and the experimentation are due to the measurement method: the measured cell temperature is the single-cell
bipolar plate surface temperature, but in the model, the temperature is the single-cell average temperature. The given model is
a 1-D fuel cell model; thus, the nonuniform temperature distribution is not considered in the other two axes.
GAO et al.: PEM FUEL CELL STACK MODELING FOR REAL-TIME EMULATION IN HARDWARE-IN-THE-LOOP APPLICATIONS
Fig. 12.
Fig. 13.
193
Cell temperature evolution. (a) Measured cell temperatures evolution. (b) Simulated cell temperatures evolution.
Cathode air outlet temperature.
A more accurate model validation in the thermal domain is
given in Fig. 13. The measured cathode air outlet temperature
is compared to the model result. It can be concluded that the
thermal transient behavior is accurately predicted by the model.
V. CONCLUSION
In this paper, a dynamic multiphysical fuel cell stack model
is presented. The model emcompasses electrical, fluidic, and
thermal domains. The modeling approach has been validated
against a Ballard Nexa 1.2 kW fuel cell system. Based on experimental data, the system auxiliaries empirical models, such as
cathode air compressor and cooling system, is also introduced.
The model is developed for real-time simulation purposes in
HiL applications. A cross-domain fuel cell dynamic behavior
analysis is presented and the dynamic time-constant analytical
expressions are given. The results show that in the fuel cell stack,
the thermal dynamics are the most significant ones. Based on the
real-time model and dynamic behavior analysis, a novel fuel cell
emulator structure with a CAN communication bus is proposed.
The fuel cell stack power output is emulated using a dc/dc buck
converter. The converter is designed to meet the real-fuel cell
dynamic responses.
However, due to the power converter switching frequency
and the error requirements, the dynamics that have a transient
time less than 100 ms are, therefore, not taken into account
for the final fuel cell emulator power output, because these
dynamics are difficult to be reproduced by a conventional power
converter. It should be noted that these dynamics are relatively
short compared to the significant thermal dynamic effect for
long-time period.
According to the results in Table III, if all the dynamic effects in a fuel cell would be reproduced by the emulator, the
power converter should be able to respond in 1 μs with a good
accuracy (1 MHz) from low power up to some kilowatts. A typical conventional converter cannot achieve this goal. For future
improvements, a new converter with nonlinear control method
should be considered and tested.
The model results show a great accuracy with experimental
measurements in different domains and the real-time model
itself can predict nonmeasurable physical quantities during the
fuel cell operation. The emulator power output has also been
validated for a real-stack data with a very good agreement. Such
an emulator is of great interest for real-time HiL applications
and it is envisioned that this emulator can contribute for real
experiments, studies, and design with realistic results without a
fuel cell stack and all the required installations and auxiliaries
required for a fuel cell to operate.
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Benjamin Blunier (S’07–M’08) received the M.S.
and M.Sc. degrees in electrical and control system engineering from the University of Technology
of Belfort-Monbteliard (UTBM), Belfort, France, in
2004.
Since 2008, he has been an Assistant Professor
at UTBM, where he is currently a Researcher and
a Teacher. He is the author of the first textbook in
French Fuel Cells : Pile à Combustible : Principes,
Technologies Modélisation et Application (France:
Ellipses-Technosup, 2007). His research interests include electric and hybrid vehicles, fuel cells, and especially on their modeling
and air management.
Fei Gao (S’09) was born in Beijing, China, in 1983.
He received the M.Sc. degree in electrical and control
system engineering from the University of Technology of Belfort-Montbeliard, Belfort, France, in 2007,
where he is currently working toward the Ph.D. degree in electrical engineering.
His current research interests include fuel
cells, system modeling, and hardware-in-the-loop
applications.
Marcelo Godoy Simões (S’89–M’95–SM’98) received the B.S. and M.Sc. degrees in electrical engineering from the University of Sao Paulo, Sao Paulo,
Brazil, in 1985 and 1990, respectively, the Ph.D. degree in electrical engineering from the University of
Tennessee, Knoxville, TN, in 1995, and the LivreDoclncia (D.Sc.) degree in mechanical engineering
from the University of Sao Paulo, in 1998.
He is currently an Assistant Professor with the
Power Electronics Laboratory, Engineering Division,
Colorado School of Mines, Golden, CO, where he has
been engaged in establishing research and education activities in the development of intelligent control for high-power-electronics applications in renewable
and distributed energy systems. He is the Director of the Advanced Control of
Energy Power System Research Center, Colorado, and a Visiting Professor with
the Universit de Technologie de Belfort-Montbliard, Belfort, France. He has
authored or coauthored more than 50 journal papers and 100 conference papers
in his academic career. He is the author of the books Alternative Energy Systems: Design and Analysis With Induction Generators (Boca Raton, FL: CRC
Press, 2005) and Integration of Alternative Sources of Energy (Piscataway, NJ:
Wiley/IEEE Press, 2007).
Dr. Simões was the recipient of a National Science Foundation (NSF) Faculty Early Career Development in 2002, the NSFs most prestigious award for
new faculty members. He has organized several IEEE activities (Power Electronics Specialists Conference 2005, Power Electronics Education Workshop
2005, and Future Energy Challenge), and also organized and founded the IEEE
Power Electronics Denver Chapter. He has been engaged with IEEE in several capacities. He is currently an Associate Editor of the IEEE TRANSACTIONS
ON POWER ELECTRONICS, Chair for the IEEE Industry Applications Society
(IAS) Industrial Automation and Control Committee, and Vice-Chair for the
IAS Manufacturing Systems Development and Applications Department, and
also participates in the new Intelligent Grid Technical Committee of the IEEE
Industrial Electronics Society.
Abdellatif Miraoui (M’07–SM’09) was born in
Morocco, in 1962. He received the M.Sc. degree from
Haute Alsace University, Cedex, France, in 1988, and
the Ph.D. degree and the Habilitation to Supervise Researches from Franche-Comte University, Besancon,
France in 1992 and 1999, respectively.
Since 2000, he has been a Professor of electrical
engineering at University of Technology of BelfortMontbeliard (UTBM), Belfort, France, where he has
been the Director of the Electrical Engineering Department since 2001 and Vice-President of Research
Affairs since 2008. He is also the Head of “Energy Conversion and Command”
Research Team and the editor of the International Journal on Electrical Engineering Transportation. His research interests include fuel cell energy, integration of ultra capacitor in transportation, design and optimization of permanent
magnet machines, and electrical propulsion/traction.
Dr. Miraoui is a member of IEEE Power Electronics Society, Industrial Electronics Society, and IEEE Vehicular Technology Society.