[IEEE 2011 IEEE Industry Applications Society Annual Meeting - Orlando, FL, USA...

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Multi-Rates Fuel Cell Emulation With Spatial Reduced Real-Time Fuel Cell Modelling

Fei Gao* , Daniela Chrenko t, Benjamin Blunier* , David Bouquain* and Abdellatif Miraoui* * Universite de Technologie de Belfort-Montbeliard (UTBM), Rue Thierry Mieg, Belfort Cedex 90010, France

emails: [email protected]@[email protected]@utbm.fr t Institut Superieur de l' Automobile et des Transports Universite de Bourgogne

49 rue Mademoiselle Bourgeois, 58000 Nevers, France email: [email protected]

Abstract-This paper presents, a multi-physical fuel cell stack model. The stack model is divided into 3 sub-models describing the different physical domains: electrical, fluidic and thermal. The stacking method has been used to model the fuel cell stack from a single cell model. The proposed model has been

validated against a 1.2 kW commercial fuel cell stack with excellent agreement between simulation and experimentation. Based on the simulation results, a novel model reduction method is proposed. The reduced model is suitable for real-time simulation purpose. Moreover, a real-time model based fuel cell emulator is introduced. The emulator has 3 real-time computation cores with different rates. The 3 computation cores are interconnected with a digital communication bus. A DCIDC buck converter is designed, in order to receive the model predicted stack power conditions and emulate the real fuel cell stack power output. The experimental test results show that such an emulator is suitable for fuel cell system Hardware-in-the-Ioop (HIL) applications.

Index Terms-Fuel cell, model, Emulation, Power converter, Real-time application, Hardware-in-the-Ioop applications

I. INTRODUCTION

Fuel cell systems are considered as an attractive and clean alternative for power supply in automotive applications. During the last years, research on polymer electrolyte fuel cell (PEFC) systems has made great progress. A fuel cell is an open reactor which is fed by hydrogen or reformed gas and oxygen or air depending on the electrical needs. A fuel cell generates electricity, reaction by-products and heat from entropy variation. This heat has to be evacuated by a cooling system. In some conditions, the inlet gas has to be heated and/or humidified before entering the stack, which requires the recovery of water and heat from the outlet of the fuel cell stack.

To meet these requirements auxiliary systems are needed. They are the key factors for the efficiency and durability of a fuel cell system. Hence, the auxiliaries and control strategies have to be designed and adapted carefully to the fuel cell. Validation tests have to be performed with the fuel cell stack [1]. Even though, there are needs for real fuel cell stacks for fuel cell system auxiliaries performance tests and validations, the utilization of a fuel cell stack in such a system validation process still imposes some drawbacks: fuel cell system tests are expensive (e.g. , hydrogen consumption), the lifetime of a fuel cell stack is still limited and the fuel cell

stack can be damaged during the tests if the auxiliaries are not well designed.

In contrast, the advantages of using a fuel cell stack emulator to test auxiliaries are obvious. The power of the emulated fuel cell stack can be configured to different values using the same emulator, depending on the specific fuel cell stack to be emulated. Also limit operating scenarios, such as stack shortcircuits or stack overheats, can be emulated during the tests, without damaging a real fuel cell stack.

In order to create an emulator, an adapted fuel cell model is required. An overview of different models is given in [2]. There are models existing to describe the different types of fuel cells like DMFC [3], PEFC [4], [5], [6] or SOFC [7] and for different fuel cell stack sizes from some watts over 1 kW [2], [5], [8] up to 1 MW [3], [9]. The fuel cell model development started around 1990 [9] and found a first application for emulation based on the work of Correa et al. [5], before becoming widely used since 2000.

Most of the models only take into account electric and fluidic aspects [3], [6], [8], [10], [11]. Thermal aspects are often neglected even though they have a great influence on the system efficiency. Furthermore, the system is often described by one equivalent fuel cell representing the stack [5], [6], [7], [8], [10], even though especially the outer cells face different conditions [4]. The models take into account dynamic aspects which might incorporate different aspects like reaction kinetics [3], double layer capacity [5] or diffusion effects [4], [6]. According to their applications the models can be I-D [4], [6], [10], 2D [11] or 3D [12]. In order that a model is widely applicable it has to run on few parameters that are easy to determine [4], [7], [8]. Another aspect that is particularly important for the use of a fuel cell system model for an emulator is its capacity of real-time application [7], [10], [13].

Probably the most known fuel cell emulator has been developed by Correa et al. [14]. Nowadays, fuel cell emulators are available for different fuel cell types: DMFC [15]; PEFC [14], [16]; SOFC [17], [7]; but also for transportation applications [18] or renewable energy applications [19]. All emulators are representing the electric domain [14], [15], [16], [17], but only few take the thermal and fluidic domain into consideration [7], [20]. The models are often separated with regard to static and dynamic behaviour. The static behaviour can

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be described empirically [14], [15], physically [20] or using cubic polynomial curve fitting [17]. The dynamic behaviour is described using the double layer capacitance [14], [15], [19], by power slew rate limitation [17] or describing the fluidic processes inside the fuel cell [20].

The emulator is realized in different ways. Ordonez et al. [15] and Parker-Allotey et al. [21] proposed to use a single fuel cell and to scale up the results. This gives a high accuracy, but keeps the need of expensive auxiliary systems. Otherwise AC/DC power converters [14] are used as well as programmable DC supply [17], buck converter [16], [19] and boost converter [20].

In contrast, a novel real-time model based fuel cell emulator is proposed in this paper. In the following section, a multiphysical dynamic fuel cell stack model is presented followed by the stack spatial non-homogeneous effect discussion and model simplification method. Thereafter, a novel architecture for fuel cell emulator is introduced and validated by experimentation. The designed emulator is suitable for fuel cell system Hardware-in-the-Loop (HiL) applications and any other kind of fuel cell stack real time applications.

II. MULTI-PHYSIC FUEL CELL MODELLING

A 1-0 multi-physical dynamic PEM fuel cell stack model that covers 3 major physical domains: electrical, fluidic and thermal is presented briefly in this section. A very detailed model description with fully experimental validations can be found in [4] and [22].

A. Fuel Cell Stack Modelling Structure

The presented model has an innovated modelling structure. The three domain models are independent from each other, as shown hereafter.

The global fuel cell stack model structure is presented in Fig. 1. Each specific domain inside the fuel cell is modelled independently. To build the model of the entire fuel cell stack, the individual specific cell model is stacked. Each cell has the same physical model, but the boundary conditions of the cell N are calculated from cell N - 1 and cell N + 1.

Each specific domain model takes into account the corresponding physical behaviour (electrical, fluidic or thermal). Only state variables numerical values (in form of data vectors) are exchanged between each domain sub-model.

Specific domain State variables

Exchanges between the

domain model

Slack model (N cells)

Stack level modelling

Fig. I. Fuel cell stack model structure

This kind of modelling structure gives a great advantage for distributed model simulation. Each specific domain model

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can be simulated independently in a different computation core with different simulation time step (multi-rates). The specific domain state variables exchanges can be ensured using a data bus between the computation cores.

B. Cell Electrical Model

The single cell voltage output can be expressed as follow:

Vcell = E - Vact - Vohm (1)

where E is the electromotive force (V), Vact the cell activation losses (V) and Vohm the cell ohmic losses (V).

The cell electromotive force is obtained from the thermodynamic formula:

E = 1.229 - 0.85· 1O-3(T - 298.15)

+ �: In ( J P02 • PH2 ) (2)

where T is the temperature of the layer (K), P02 the oxygen pressure (atm) at the interface of cathode catalyst layer, PH2 the hydrogen pressure (atm) at the interface of anode catalyst layer, R the ideal gas constant (8.31 J/mol·K) and F the Faraday constant (96 485 C/mo\).

It should be noted, that the gas pressures used in equation (2) are the gas pressures at the catalyst interfaces; these pressures are not the gas pressures in the supply channels. The gas pressure drop from the supply channels through the gas diffusion layer (GDL) to catalyst layer is considered and taken into account in the fuel cell fluidic model. Thus, the gas transport losses in the GDL, generally known as "concentration losses", are not considered directly in equation (1) as they are already implicitly taken into account in the equation (2).

The cell activation losses can be expressed from the Tafel equation (from Butler-Volmer equation):

RT (i) Vact = o:nF In jo S (3)

where i is the stack current (A), S the catalyst layer section area (m2), n the number of electrons involved in the reaction, 0: the symmetry factor and jo the exchange current density (A/m2).

The cell ohmic losses are mainly due to the membrane resistance. This loss can be obtained with the membrane resistance expression applying the Joule's law:

Vohm = Rmem . i = � 18 r (T, )..(z)) dz

C. Cell Fluidic Model

(4)

The gas pressure drop in the channels due to the mechanical losses can be expressed by the Darcy-Weisbach equation:

pcvL 2 b.P = fdarcy 2 D Vs hydro

(5)

where fdarcy is the Darcy friction factor, Dhydro is the hydraulic diameter of the channels (m), Vs is the mean fluid

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velocity in the channels (m/s) and L is the length of the channel (m).

The phenomenon of the gas diffusion of each species i in the gas diffusion layers (GOL) is described by the Stefan-Maxwell equation:

where 0 is the GOL thickness (m), S is the GOL layer section (m2), Ptot is the mean gas total pressure (Pa) in the GOL layer, M is the gas molar mass (kg/mol), j stands for species other than species i, and Dij is the binary diffusion coefficient between the species i and j (m2/s).

The water balance in the membrane layer can be described by two different phenomenons: The electro-osmotic drag described by the equation (7), and the back diffusion described by the equation (8).

J - nsat >.(z)

. _2_' M drag - 11 2F H2 0 (7)

Pdry d>.(z) Jback_diJ J = -

Mn D>, d;- S MH2 0 (8)

where nsat = 22 is the electro-osmotic drag coefficient for

maximum hydration condition, Pdry is the dry density of the membrane (kg/m3), D>, the mean water diffusion coefficient in the membrane (m2/s), and Mn the equivalent mass of the membrane (kg/mol).

The total water mass flow (kg/s) in the membrane can then be expressed:

(9)

This equation is a differential equation of >.(z) derivate by z (the membrane z-axis). By giving the boundary conditions for >., the equation can be solved.

D. Cell Thermal Dynamic Model

The thermal dynamic response of a fuel cell is governed by the thermal capacity of each layer in the cell. This dynamic can be generally described as:

dTcv (pVCp) CIt = � + � conduction forced convection

+ QnaCconv_radia + Qmass + Qsources � '-v-" �

natural convection and radiation

convective mass flow

internal sources (10)

where P is the mean layer volume density (kg/m3), V is the layer volume (m3), Cp is the layer thermal capacity (J/kg-K) and Q stands for the different types of heat flows entering or leaving the layer volume (J/s): conduction, forced convection, natural convection, radiation, convective mass flow and internal heating sources.

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 change in the reaction and the activation losses. These losses can be calculated as:

Q source 1 ==

entropy change part

(11)

part

where !1S is the entropy change (J/mol·K) during the electrochemical reaction.

The fuel cell internal resistance is governed by the polymer membrane resistance. When a current passes through the fuel cell membrane, heat is produced due to the membrane resistance according to Joule's law:

Q source 2 = i2 . Rmem

E. Model Experimental Validations

(12)

The presented model is validated for a commercial air cooled 1.2 kW Ballard NEXA system. The stack properties of its 47 cells and geometry data can be found in the reference [2].

A dynamic current cycle during 300 s (5 min) has been applied to the fuel cell stack as presented in Fig. 2.

The real stack voltage response and the model results are illustrated in Fig. 3. The proposed fuel cell stack model demonstrates a great accuracy with regard to the experimental measurements. For the entire stack operating range, the maximum relative error in voltage is less than 5 %. The voltage dynamic behaviour is well reproduced by the model.

The temperature dynamic of the stack cathode air outlet from the model follows the measured data accurately even with a high dynamic current profile as shown in Fig. 4 .

50 �40

50 100 150 Time(s) 200 250

Fig. 2. Stack current profile

300

Furthermore, the model stacking method structure presented before allows the model to simulate the stack physicals spatial distribution. Fig. 5 and Fig. 6 show the individual cells voltages and temperature distribution in the stack at different times. The simulation results show that the model has a very good accuracy compared to the real stack measurements.

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55

50 i"� � 40 >

� 35 en

30

25 ' o 50 100 1 50 200 250 300

Time (s)

Fig. 3. Stack voltage responses

-Modell -Me�dJ

50 100 150 200 250 300 Time(s)

Fig. 4. Cathode air outlet temperature

In addition to the measurable physical variables in the real stack, many non-measurable stack variables, including individual membrane resistance and water content, can be obtained from the presented model. Fig. 7 shows the membrane average water content evolution of the 24th cell. It can be noted clearly that the average water content is mainly around 8, but at a fast decrease of stack current, the membrane average water content can be relatively low, because at low current, the water produced by the electrochemical reaction is no longer enough to maintain the membrane hydration.

� 0.8 "' Q)

ITime = 150 sl

fO�I '�T'ii'8�"="�

0"

02- ' 0 05 01 015 02 025 03

Axis of stack (m)

Fig. 5. Individual cell voltages in stack at 150 s

The previous comparison confirms a great temporal and spatial accuracy in different physical domains for the proposed model. Thus, the proposed model is suitable for fuel cell stack simulation purpose.

F Fuel Cell Stack Model Discussions and Simplification

In general, every single fuel cell in a stack has the same characteristic, such as geometry and material properties; but during fuel cell stack operation, each cell has its own state

70

65 p-i6D � 55 a. E 250 � ..

ITime = 120 sl

(J

45[ 40L--::-';:-:---::'":"---::-':"::-----::'::-----:-::-:----::'::" 0. 05 0.1 0.15 0.2 0.25 0.3

Axis of stack (m)

Fig. 6. Individual cell temperature in stack at 120 s

50 100 150 200 250 300 Time (s)

Fig. 7. Middle cell membrane average water content

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conditions, such as voltage and temperature, influenced by different boundary conditions from the two adjacent cells.

On the one hand, the stack model proposed in the previous section has a great advantage compared to other models: every single cell in the stack has been modelled individually. The non uniform cell state conditions can be well simulated by the stack model, as shown in Fig. 5 and Fig. 6.

On the other hand, the drawback of this kind of model is obvious: with the large number of cells in the stack, the number of physical equations to be solved simultaneously is quite large. Hence, the simulation time increases significantly. This drawback limits the real time simulation capability of the proposed model.

From the full model results shown in Fig. 5 and Fig. 6, it can be noted that the cells at the beginning and at the end of the stack form a significant non-homogeneous zone. The cells in the middle of the stack have almost the same physical results. The homogeneous zone can be observed from the 11 th cell to 38th cell in the stack (47 cells overall).

Thus, a simplification can be proposed. From the observation it can be stated, that the cells in the middle of the stack have the same physical state (homogeneous zone) during the simulation, the K cells in the homogeneous zone of the stack can be reduced to a single equivalent cell in the model, as shown in Fig. 8. The results of this equivalent cell will be duplicated K time to behave as K cells in the middle of the stack.

G. Simplified Model Validations

In the 1.2 kW Ballard fuel cell stack simulations, the results show, that the non-homogeneous zone of the stack comprises the first 10 cells and last 10 cells in the stack.

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Middle K cells First Nleft cells Last Nrlght cells

I I

1--- ---I

First Nleft cells Equivalent single cell Last Nrlght cells (Represent K

identical cells)

Fig. 8. Model simplification method

Thus, the 47 cells stack model is reduced to a 21 cells stack model during simulation, with 1 equivalent cell that represents the 27 cells in the middle of the stack. The simulation results of this equivalent cell are mUltiplied 27 times in order to have the overall result for 47 cells. In order to validate the proposed simplification method, a comparison between the full scale model and the reduced model is presented hereafter.

The spatial distributions of single cells voltages and temperatures using the homogeneous zone are shown in Fig. 9 and Fig. 10, respectively. The reduced model results show an excellent agreement with the full scale model.

A slight difference between the results can be found with regard to the temperature, due to the homogeneous zone choice. In fact, the choice to take the first 10 cells and last 10 cells as non-homogeneous zone for cell temperatures is not strictly accurate. From the full scale model result in Fig. 6, it can be noted that the non-uniform zone is larger than 20 cells. But on the other hand, the relative error in the temperature prediction in Fig. lOis less than 2 %. This slight difference can be balanced by the gained time during the simulation. Thus, the results are considered to be acceptable.

Beside the reduced model spatial validations, Fig. 11 and Fig. 12 show the temporal comparison of stack voltage and cathode air outlet temperature between the full scale model and reduced model. Again, an excellent agreement between the simulation results can be found.

Thus, the proposed model simplification method has been proved and validated.

0.8

0.75 � 150sJ 1- • - Full model I -... - Reduced model I

Homogenous zone

� 0.7 tatheell

�O.65 \ � 0.6 '

tfP"

38th cell

I --- ------_.-----------

0.55 0. 5'-------,-�-�-�-�-�-�

0.05 0.1 0.15 0.2 0.25 0.3 Axis of stack (m)

Fig. 9. Individual cell voltages comparison at 150 s

70

�60 Q)

! 50 .� .2:l 10th cell

� 40

\ 38th cell

Homogen,QUS zone

30'-----�-�-�-�-�-� 0.05 0.1 0.15 0.2 0.25 0.3

Axis of stack (m)

Fig. 10. Individual cell temperatures comparison at 120 s

60 55

�50

50

-Full model - Reduced model

100 150 200 250 300 Time (s)

Fig. II. Stack voltage temporal comparison

H. Simplified Model Advantages

Using the proposed simplification method, the model simulation speed can be accelerated significantly, while keeping the accurate stack non-homogeneous effect and model accuracy as in a full scale model. With the appropriate choice of the homogeneous zone between the model simplicity and model accuracy, the reduced multi-physical stack model can be simulated in real time for different kinds of applications.

III. MULTI-RATES FUEL CELL STACK EMULATOR

Based on the presented real time fuel cell stack model, a multi-rates fuel cell stack emulator has been designed.

A. Emulator Global Structure

The emulator structure is presented in Fig. 13. The proposed fuel cell stack model is implemented in the

real time computation cores. The detailed computation cores schema will be presented hereafter. This implemented model

�70

� 65 � 2i 60 E Q) � 55 '3 :: 50 ·ro Q) � 45 1ij u 40

o 50 100 150 200 250 300 Time (s)

Fig. 12. Cathode air outlet temperature comparison

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+

power converter +

controller

Fuel cell emulator power output

Fig. 13. Fuel cell emulator structure

can predict fuel cell stack perfonnance in the three major domains: electrical, fluidic and thennal.

A digital Control Area Network (CAN) bus is implemented in the emulator in order to handle the communication between the real time model and other parts. Retaining this fuel cell emulator architecture, the model computation part of the emulator is independent. The implemented model can predict many fuel cell stack state variables, such as coolant outlet temperature, gas outlet humidity, individual cell output voltage and so on. These state variables are always sent by the model to the CAN bus. The model also takes the fuel cell stack external operating condition variables from the CAN bus, such as load current, air inlet flow rate, hydrogen supply pressure.

A DCIDC step-down power converter with its voltage controller is connected to the CAN bus, in order to emulate the real stack electrical power output. The converter sends the measured load current value to the CAN bus for model use, receives the model predicted stack voltage value and regulates the converter output voltage to this predicted value.

As mentioned above, all the model predicted fuel cell stack state variables are sent to the CAN bus continuously. These state variables other than stack current and voltage, such as individual cell temperatures or membrane water content, are then displayed via an additional supervision monitor connected to the CAN bus.

B. Distributed Multi-rates Multi-physical Model Real-time

Computation Cores

The fuel cell emulator real time computation cores structure is detailed in Fig. 14.

According to the proposed model distributed computation capability discussed previously, the stack model has been separated into 3 different dSpace processors in the designed structure. Each processor contains one specific domain fuel cell stack model.

The data variable exchanges between the models is done by the CAN bus communication shown in the fuel cell emulator global structure. A 1 GHz dSpace real-time processor is used to compute the fuel cell thennal model, because it is the most complex dynamic model which requires more computation

Fig. 14. Multi-rates computation cores structure

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resources. Two others dSpace 250 MHz real time processors are used for electrical and fluidic model computation.

Based on the specific model complexity and dynamic behaviour time constant, a 100 fJS time step is used by the thennal model, a 500 fJS time step is used by the fluidic model and a 10 ms time step is used by the electrical model. Thus, the three dSpace processors fonn a multi-rate fuel cell stack model computation core.

C. Emulator test bench with power converter

The prototype of the designed fuel cell emulator test bench is shown in Fig. 15.

Fig. 15. Fuel cell stack emulator test bench

A buck DC/DC converter and a DC power supply are used to emulate the fuel cell stack power output. The converter controller communicates with the CAN bus via a DSP based gateway. A current regulated active load is connected to the emulator to produce the desired current profile. The same active load has also been used for the real fuel cell stack test.

Two dSpace 1104 250 MHz boards in PC and one dSpace 1005 1 GHz modular system have been connected to a CAN bus for real time model simulation and communication. A

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supervision PC receives the information from the CAN bus and displays the model predicted fuel cell state physicals in a Labview based supervision interface.

D. Emulator supervision and diagnostic

As discussed previously, all the multi-physical (electrical, fluidic and thermal) model predicted stack state variables are sent to the CAN bus. Beside the stack voltage and current information used for electrical power emulation, the other stack physicals available from the CAN bus can be also used for stack diagnostic purpose.

For the example of Ballard NEXA 1.2 kW stack: besides the stack electrical output, the manufacturer also provides OEM software to monitor other stack key physicals, such as operating time, cathode air outlet temperature, stack current and voltage, hydrogen pressure, etc.

All these physical values are also simulated in real-time by the model and can be obtained as CAN bus messages from the fuel cell emulator. Thus, a simulated stack monitoring interface can be used to replace the real stack monitoring software in the actual emulator, as shown in Fig. 16 and Fig. 17.

In addition of the real stack monitoring software, the model gives even more diagnostic possibilities; many non-measurable stack variables, including individual membrane resistance, cell layer temperatures, gas pressures at catalyst layers, can also be received through the CAN bus messages. Thus, the accessible stack states are largely extended compared to those of the real stack. Some of them, such as membrane water contents are key factors of the fuel cell stack performance. Using the fuel cell emulator instead of a real stack, these factors become available for the users.

Fig. 16. Real Nexa stack monitoring interface

IV. EMULATOR EXPERIMENTAL VALIDATIONS

The entire design of proposed fuel cell emulator has been tested and validated by experimentations.

For the load current shown in Fig. 2, the model predicted voltage and emulator controlled DC/DC converter output voltage applied to the load is presented in Fig. 18. It can be concluded that the emulator voltage output is in very good agreement with the model predicted value. Moreover, the Fig. 18 shows a zoom of the voltages between 100 s to 127 s.

l:JWUorf'CNr. OMJ:(ft'.,. lM�·'$UIJt,;amM" "1fd«-�oO�

c::.>

I I,'" .

:;SA 3..., � eO lo.,l�l�JaI,;,:m "

Fig. 17. Designed fuel cell emulator monitoring interface

. : ..... 105 110 115 Time (5)

Fig. 18. Zoom in around 110 s of model and emulator voltage

The converter output voltage follows the model prediction with a maximum voltage ripple of 1 %.

For the emulator validation purpose, a second current profile with less dynamic changes has been applied to the electrical load, as shown in Fig. 19. The comparison of the model prediction and the designed emulator output is illustrated in Fig. 20. Again, the obtained results show very good accuracy for the emulator voltage output.

It can be concluded from the experimentation that the converter output meets the model prediction accurately. Thus, the designed emulator is validated.

40

�30

Lo " TI .!!i en 10

%�--�20� 0----4�0� 0--�6�00�--�8�00� Time (5)

Fig. 19. 2nd test: stack current profile

V. CONCLUSION

In this paper, a multi-physical fuel cell stack model is presented in the first section. The model is divided into 3 submodels in different physical domains: electrical, fluidic and thermal.

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50

45

�40 Q) 0) til

'6 35

> .Y. (J

Bl 30

25

Fig. 20.

200

• Model prediction - Emulator output

400 600 Time (5)

800

Model and emulator voltage for 2nd test

The stacking method is used to model the fuel cell stack from single cell model. The model in each physical domain is relatively independent from each other. The proposed model has been validated with a Ballard 1.2 kW 47 cells commercial fuel cell stack. The experimental results show excellent agreement between the simulation and experimentation.

Based on the simulation results, a novel model simplification method is proposed. The single cell in fuel cell stack model can be divided into a homogeneous zone and a nonhomogeneous zone. In the homogeneous zone the individual cell models can be replaced by a single equivalent cell model. The simplified model is then validated against the original model. The simplified/reduced fuel cell stack model is much less time consuming and holds still a great accuracy compared to the full classical stack model. Thus, the reduced model is suitable for real-time simulation purpose.

In the second section of the paper, a real-time model based fuel cell emulator is introduced. The emulator has an innovative structure; it has 3 different real-time computation cores with different computation rates, each corresponding to a single physical domain fuel cell model. The data exchanges is done by a digital CAN (Control area network) bus connection.

A controlled DC/DC buck converter is connected to the CAN bus, in order to receive the model predicted stack power conditions and emulate the real fuel cell stack power output. The converter is designed to meet the fuel cell stack transient behaviour. The emulator is validated against experimental results. The proposed fuel cell emulator can be used for fuel cell system validation or Hardware-in-the-Ioop (HiL) applications.

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[13] X. Kong, W. Yeau, and A. M. Khambadkone, "Ann modelling of nonlinear subsystem of a pemfc stack for dynamic and steady state operation," in Proc. IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 6-10 Nov. 2006, pp. 4322-4327.

[14] J. M. Correa, F. A. Farret, J. R. Gomes, and M. G. Simoes, "Simulation of Fuel-Cell Stacks Using a Computer-Controlled Power Rectifier With the Purposes of Actual High-Power Injection Applications," IEEE Transactions on industry applications, vol. 39, no. 4, p. 7, 2003.

[15] M. Ordonez, M. T. Iqbal, and J. E. Quaicoe, "Development of a fuel cell simulator based in an experimentally derived model," 2005.

[16] T.-w. Lee, S.-H. Kim, Y-H. Yoon, S.-j. Jang, and C.-Y Won, "A 3kW Fuel Cell Generation System using the Fuel Cell Simulator," 2004.

[17] P. Acharya, P. Enjeti, and I. J. Pitel, "An Advanced Fuel Cell Simulator," 2004.

[18] L. Gauchia and J. Sanz, "A per-unit hardware-in-the-Ioop simulation of a fuel cellibattery hybrid energy system," IEEE Transactions on, pp. I-I, 2009, accepted for future publication Industrial Electronics.

[19] M. Cirrincione, M. C. Di Piazza, G. Marsala, M. Pucci, and G. Vitale, "Real time simulation of renewable sources by model-based control of dc/dc converters," in Proc. IEEE International Symposium on Industrial Electronics ISlE 2008, June 30 2008-July 2 2008, pp. 1548-1555.

[20] F. Gao, B. Blunier, D. Bouquain, A. Miraoui, and A. EI Moudni, "Polymer electrolyte fuel cell stack emulator for automotive hardwarein-the-Ioop applications," in Proc. IEEE Vehicle Power and Propulsion Conference V PPC '09, 7-10 Sept. 2009, pp. 998-1004.

[21] N.-A. Parker-Allotey, A. Bryant, and P. Palmer, 'The Application Of Fuel Cell Emulation In The Design Of An Electric Vehicle Powertrain," IEEE, p. 6, 2005.

[22] F. Gao, B. Blunier, A. Miraoui, and A. E. moudni, "Cell layer level generalized dynamic modeling of a PEMFC stack using VHDL-AMS language," International Journal of Hydrogen Energy, vol. 34, no. 13, p. 24, 2009.

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