Design and Dynamic Modeling of a Fuel Cell/Ultra Capacitor Hybrid Power System

Ben Slama Sami

Physical department Faculty of Sciences of Tunis (FST)

El Manar, Tunisia Benslama.sami@gmail.com

Ben Chaabene Abderrahmen Research Unit C3S

ESST MontFleury, Tunisia

abd.chaabene@yahoo.fr

Cherif Adnane Physical department

Faculty of Sciences of Tunis (FST) El Manar, Tunisia

adnane.cher@fst.rnu.tn

Abstract—The aim of this paper is firstly to describe the design than to introduce a new approach of dynamic modeling and simulation results of a Fuel cell/Ultra capacitor (FC/ULC) hybrid power system. The developed model is represented in the state space, so it can be used to implement a suitable control strategy. The given design shows that the transient behavior, effect of the Fuel Cell, is eliminated by the use of the Ultra capacitor through the Flyback converter (FlBC). Thus, the output voltage from the source is maintained with a certain range and meets power demand of the load at high efficiency.

Keywords— Proton Exchange Membrane Fuel Cell; ultra capacitor; FlyBack Converte;Simulation.

The Electrical and Hybrid Unit (EHU) are possible solutions to reduce the air pollution and fossil fuel and can provide many benefits. Thus, the FCs (Fuel Cells) have been found to be promising energy sources toward building a sustainable and environment friendly energy economy especially that the world is facing the global warming problem. Furthermore, due to sluggish dynamic responses of the fuel cell in transient events, problems with the load will result. In such cases, it is necessary to combine the FC with other electrical energy storage devices to satisfy the transient events and the load demand [1].

The Ultra Capacitor (ULC) can be defined as a super capacitor or electric double layer capacitor, which is a large capacitance device. In addition, the ULC is more efficient than the battery due to the limitation on a life cycle, the prompt storage and stored energy consumption. So, when the batteries have low power densities and limited lifetime in highly cyclic applications, ULC can be used [2]. However it was not until the nineties that the interest in ULC was renewed in the context of hybrid electric vehicles [3]. An ever increasing power requirement for automotive applications have rendered the standard battery design obsolete leading to the design of pulsed batteries and battery-ultra capacitor hybrid systems for high power applications[4].

Some approaches in the literatures have shown interests to assessment, modeling and control of the FC-ULC based on classical methods. L. Guo, K. Yedavali, and D. Zinger (2010)

[5] have described a model of power system for a fuel cell hybrid switcher locomotive. Additionally, they proposed control strategy of a power system. In addition, the power control system regulates the sharing of power demand between the fuel cell and auxiliary storage units including batteries and ULC. Teng-Fa,Po-Hung and Hung-Cheng (2009) [6] proposed a new approach of dynamic model of hybrid power systems based on renewable energy using FC and ULC. Thus, the FC and ULC can be integrated to ensure that the system performs under all conditions. While, A. Drolia, P. Jose, and N. Mohan (2003) [7] developed a model approach to connect ULC to FC Powered Electric Vehicle and Emulating FC Electrical Characteristics using a Switched Mode converter (SMC). However, the solution is to provide the additional energy required by (the) increased load by means of secondary source of energy like ULC until FC responds to the increased load current. L. Gauchia and A. Bouscayrol (2009) [8] have described a model of Fuel Cell, Battery and Super capacitor Hybrid System for an Electric Vehicle (SHSEV). Their works consist in the combining of the electrochemical energy systems to obtain a hybrid energy storage system and to present the Energetic Macroscopic Representation (EMR) of the multisource power system.

The particularity of this work consists in the development of a new nonlinear model based on a MIMO approach expressed in the state space of PEMFC/ULC, which are coupled with TWO DC/DC converters in order to supply the load. In addition, the Flyback converter (FlBC) stores the energy during the switch ON time duration and transfers it during the switch OFF time duration, instead of transferring it in a forward fashion.

The paper is organized as follows. In section 2, we describe the whole global hybrid power system and we present the developed models of each part of this system. Section 3 is devoted to the analysis of the simulation results. Finally, we conclude the paper in section 4.

U.S. Government work not protected by U.S. copyright

I. DESCRIPTION AND MODELING OF FC-ULC HYBRID SYSTEM

A. Design of the global system The Hybrid power system that we present is composed of:

• A Subsystem A

• A Subsystem B

• A Subsystem C

The system configuration is shown in Fig. 1. It is composed of five compartments which are the PEMFC, the Fuel-Boost Converter (FBC), the ULC, the Sup-Boost Converter (SBC) and the FlBC. The primary energy source of the plant is the PEMFC which is directly connected to the FBC. It is a static energy conversion device that converts the chemical reaction of fuels directly into electrical energy and regenerates the stored electricity by recombining hydrogen and oxygen. The second energy is the ULC. It is directly connected to the SBC and used in power requiring short duration peak power. In addition, ULC is not reversible; this means it recharges from PEMFC current which is assured by the FBC. So, it is usually used as a secondary power source for improving the performance and efficiency of the overall system. However, the FlBC is connected independently from the two boosts converters.

The reformer obtains hydrogen starting from a fuel with hydrocarbon. So, the amount of components of the system will depend mainly on the total power of the stack. In any case, for a value of voltage and current desirable to supply the load, a DC-DC converter is installed in series with the PEMFC and ULC. In fact, the detected variables are the Fuel cell current (IFC), the fuel cell voltage (UFC), the ULC current (IUL) and the ULC voltage (UUL).

Figure 1. Design of the global system

B. Circuit model of the subsystem A In the studied subsystem in Fig. 2, we describe and model

the two components which are the PEMFC and the FBC. The PEMFC has long been known as a converter of hydrogen in

energy (electrical + thermal) having a high efficiency, as proven by the comprehensive research done on this technology worldwide. The reasons are well-known: the response to the environmental pressure (clean use), to the problems arising from the centralized production of electricity, the need for having energy alternatives (hydrogen vector) and certain technological requirements such as the applications space, underwater, portable electronic devices, power supply of isolated sites and Microsystems. It must be noted that, the choice of the technology of fuel cell with exchanging membrane of protons is done due to these interesting performances (weak weight, robust, solid electrolyte, fast starting, broad range of power of 1W to 10MW, etc.). Thus, it is significant to study this technology to be able to control it and extend its application [9].

The boost circuits produce the output voltage by charging an input inductor with current, from an input voltage source, then discharging the inductor into an output capacitor. The model of a “subsystem A” was studied and developed using matlab/Simulink. PEMFC converts chemical energy at middle temperature (20°-80°). The chemical reactions occurring at the oxidation and reduction electrode of a PEMFC can be summarized in the Table. I.

TABLE I. ELECTROCHEMICAL REACTIONS IN PEMFC

However, the electrical model of subsystem A is depicted in Fig.2 [4].

Figure 2. Electrical model of subsystem A

Reactions Equations

Hydrogen 2 4 42H H e+ −⇒ +

Oxygen2 22O H H O++ ⇒

Overall reaction 2 2 22 2H O H O+ ⇒

1) Anode Voltage

The relationship between the voltage VAN and the current IFC of the fuel cell is given by the following (1).

( ) 1

11

ANAN FC

AN

AN

Vd V Idt R

C

α

α

⎧ ⎡ ⎤= −⎪ ⎢ ⎥

⎪ ⎣ ⎦⎨⎪ =⎪⎩

(1)

The equation (1) is simplified to a first order transfer function (see (2)).

1

1

1

11

11

AN FC

AN

AN

kV Is

kRR

α

α

α

α

τ

τα

⎧=⎪ +⎪

⎪=⎨

⎪⎪

=⎪⎩

(2)

2) Cathode Voltage

The voltage of the cathode can be defined as in (3).

(3)

Equation (3) is simplified to a first order transfer function, given by (4).

1

1

1

11

11

CAT FC

CAT

CAT

kV I

s

kRR

β

β

β

β

τ

τβ

⎧=⎪ +⎪

⎪⎪ =⎨⎪⎪

=⎪⎪⎩

(4)

3) Fuel Cell Curent

We can rewrite IFC as only a function of VAN, VCAT, Vb and DFB which can be expressed in (5).

( ) ( )2 1FC Open CAT AN m FC FB bd I V V V R I D Vdt

α ⎡ ⎤= − − − − −⎣ ⎦ (5)

Where: α2 =1/LFC.

Equation (5) is simplified to a first order transfer function, given by (6).

( ) ( )2

2

11FC Open CAT AN FB b

kI V V V D V

sα

ατ⎡ ⎤= − − − −⎣ ⎦−

(6)

Where: τα2=1/RM*α2 and kα2=1/Rm

The parameters of subsystem” A” are given in Appendix.

The voltage of a single cell can be defined in (7).

F C N ernst A N ohm C A TU E V V V= − − −

(7)

For N cells connected in series, forming a stack, the voltage can be calculated by (8):

.s F CV N U= (8)

Where ENernst is the average thermodynamic potential of each unit cell and it represents its reversible voltage. The ENernst is given by (9).

[ ] ( ) ( )13 51.229 0.85.10 298.15 4.31.10 ln ln222

E T T p poNernst H− −= − − + +⎡ ⎤

⎢ ⎥⎣ ⎦ (9)

C. Circuit model of the subsystem B The UC’s banks are used in power application requiring

short peak power. For the same reason, an ULC exhibits operating characteristics that are distinct from those of a conventional capacitor [10]. An UC is an energy storage device with a construction similar to that of a battery. Compared with batteries, UC’s have at least two orders of magnitude higher specific owners and much longer lifetime. Because they are capable of millions of cycles, they are virtually free of maintenance. Their great rated currents enable fast discharges and fast charges as well. Their quite low specific energy, compared to batteries, is in most cases the factor that determines the feasibility of their use in a particular high power application [11] [12].

In addition, the ULC can not only be charged and discharged more than one million times but also be stored with ten times more energy than conventional electrolytic capacitors. It must be noted that the ULC has the merits of a rapid charge and discharge of energy and a longer life cycle, because of the electrostatic nature of the capacitor rather than the chemical reaction. Besides, a ULC has an extremely high capacitance with superior durability and maintenance-free characteristics [13]. While designing the desired size of UC, the amount of energy consumed/drown from the UC bank Euc in extreme condition is deducted [14].

The energy of UC can be defined as in (10).

( )2 212uc Cu i fE C v v= − (10)

( ) 1

11

CATCAT FC

CAT

CAT

Vd V Idt R

C

β

β

⎧ ⎡ ⎤= −⎪ ⎢ ⎥

⎪ ⎣ ⎦⎨⎪ =⎪⎩

The voltage state of UC bank can be described as in (11). [15]

( ) *expsu Cu

tV t ViR C

⎛ ⎞−= ⎜ ⎟⎝ ⎠

(11)

When the energy is released from the UC, the magnitude of the voltage is decreased and vice versa. However, the electrical model of subsystem B is given by the following Fig. 3.

Figure 3. Electrical model of subsystem B

Mathematically, the voltage of ULC is defined as:

( ) 1UL UL

Cu

d V Idt C

= (12)

The equation (12) is simplified to a first order transfer function, given by (13).

CuUL UL

kV Is

= (13)

Where: kCu =1/C Cu

The current of ULC is given by (14).

( ) ( )3 1ULUL su UL UB b

d IV R I D V

dtα= − − −⎡ ⎤⎣ ⎦ (14)

Equation (14) is simplified to a first order transfer function, given by (15).

( ) ( )( )3

3

11U L U L U B b

kI V D Vs

α

ατ= − −

+ (15)

Where: α3 =1/LUL, k α3=1/Rsu and τα3=1/Rsu*LUL.

The parameters of “subsystem B” are given in Appendix. The relationship between the voltage Vb and the currents, voltage and duty cycle D i=FB, UB is given by (16).

( ) ( ) ( )1 1L UL UL load FC FCd Vb D I I D Idt

α= − − + −⎡ ⎤⎣ ⎦ (16)

Equation (16) is simplified to a first order transfer function, expressed by (17).

( ) ( ) ( )1 11

L

L

b F C F C U B U L

kV D I D Iα

ατ= − + −⎡ ⎤⎣ ⎦+

(17)

1) The state space of FC-ULC hybrid system

The state space of the FC-ULC will be described as follows.

TCAT

AN

FC

UL

UL

b

VVI

XIVV

•

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

(18)

TFC

UB

Du

D⎡ ⎤

= ⎢ ⎥⎣ ⎦

(19)

[ ]TLoady i= (20)

The Steady-State of the nonlinear model is expressed as:

( )..

ssX AX B x uy C X

⎧⎪ = +⎨

=⎪⎩

i

(21)

( )( )

( ) ( )

1 1 1

1 1 1

3 3 3

4

0 0 0 00 0 0 0

2 1 2 0 2 2 00 0 0 10 0 0 0 00 0 1 1 0 0

FC ss m

su LU ss

FC ss UL ss

kk

D RA

R D

D D

α

β

α αβ β

α α α αα α α

αα α

−

−

− −

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥− + − − −

=⎢ ⎥− − −⎢ ⎥⎢ ⎥⎢ ⎥

− − −⎢ ⎥⎣ ⎦

(22)

2

2

0 0 0 00 0 0 0

b ss FC ss

UL ss b ss

V IB

I Vα α

α α− −

− −

−⎡ ⎤= ⎢ ⎥− −⎣ ⎦

(23)

(24)

[ ]0 0 0 0 0C α= −

Where α=1/C.

The steady state values of PEMFC/ULC hybrid power system are given in Appendix.

D. Circuit model of the subsystem C In the studied subsystem D (see Fig.5), we describe and

model the FlBC. The latter has become one of the most common DC–DC converters in the world of low power switch mode power supplies (SMPS). The low number of components (capacitors, current sense resistors and magnetics) makes, the FBC converter an excellent solution for low power and high voltage applications. In addition, the most important advantage is that it becomes possible to have multiple outputs with a simple modification on the transformer (adding another secondary winding) and adding few extra components (a diode and a filter capacitor). Another important advantage is that it has natural isolation between input and output, which is required by many standards for the design of power supplies [16] [17]. Thus, the method of FBC operation is to store the energy during the switch ON time duration and transfer it during the switch OFF time duration, instead of transferring it in a forward fashion. Therefore, the transformer in a FBC converter is not really a transformer, but two coupled inductors. There are two possible operating conduction modes for the Flyback converter. The Discontinuous-Mode Operation (DMO) means that all the energy (neglecting losses) stored in the input inductor during the ON time period of the main switch is transferred to the output capacitor and the load [18].

Figure 4. Electrical model of subsystem C

During the first subinterval, when the MOSFET conducts and the diode is off, the relation between current and voltage can be expressed as follows:

( )

( ) ( )

( )

( ) ( )

( )

F

FC L

ULUL

F

FC L

m FC

UL ULF

I t I tU t

I tR

U Vd i

L U tdt

d U UCdt R

⎧⎪ =⎪⎪ −

=⎪⎪⎪ =⎨⎪⎪ =⎪⎪⎪ = −⎪⎩

(25)

During the second subinterval, when the MOSFET is off

and the diode is on. The relation between current and voltage is defined as follows:

(26)

II. SIMULATION RESULTS In this section, we evaluate the efficiency of our Hybrid

Power System PEMFC/ULC through conducting simulations measuring some parameters such as current, voltage and power. First, we have studied the dynamic behavior of the PEMFC/ULC. The study of the FlBC converter is done subsequently.

A. The PEMFC system In order to evaluate the global system illustrated in Fig.1,

we have simulated the non-linear model of our Hybrid Power System PEMFC/ULC by using MATLAB-SIMULINK environment. It must be noted that the single stack fuel cells can be operated in the permissible range of 25V to 38V for constant fuel input in order to maintain the stability of the system. Furthermore, the temperature T is applied to provide a variable FC operating condition. This step changes the temperature value from 60ºC to 80ºC.

The variations of the voltage, current and the power vs. time supplied by PEMFC are illustrated in Fig.5 and Fig.6 Through these curves, we observe the increment of the power and voltage due to (8), with the number of cells (called N) equal to 48.

( ) ( )

( ) ( )

( )

.

.

0F

Lm UL

UL ULF L

FC

d IL U t n

dtd U UC I t n

dt R

I t

⎧=⎪

⎪⎪

= − −⎨⎪⎪ =⎪⎩

0 500 1000 1500 2000 2500 30000.5

0.6

0.7

0.8

0.9C

ell V

olta

ge

0 500 1000 1500 2000 2500 30000

10

20

30

Time(ms)

Fue

l Cel

l Cur

rent

0 500 1000 1500 2000 2500 300025

30

35

40

The

Fue

l Cel

l Vol

tage

0 500 1000 1500 2000 2500 30000

200

400

600

The

FU

EL

CE

LL P

ower

0 500 1000 1500 2000 2500 30000

10

20

30

Time(ms)

Impo

ut C

urre

nt

10 20 30 40 50 60 70 800

20

40

60

80

100

120

Time(s)

Vol

tage

Figure 5. Dynamic behavior of Cell voltage and current vs. time

Figure 6. Dynamic behavior of PEMFC vs. time

The PEMFC supply power to the load and ULC backup the difference power between the supplied power from fuel cell and the load demand power by using the FlBC. The ULC accomplish to stabilizing the DC bus during the low power of fuel cell and during the transient time. The voltage generated by ULC is shown in Fig. 7. Hence, the global system outputs were stabilized at a finite time.

Figure 7. ULC voltage vs. time

B. The Flyback converter system In this section, we describe the dynamic behavior of the

Flyback converter (see Fig.8). So, multiple outputs can be

obtained using a minimum number of parts. Each additional output requires only an additional winding, diode, and capacitor. Thus, the peak transistor voltage is the sum of the input voltage and the reflected load voltage, expressed by UUl/n. A snubbed circuit may be required to clamp the magnitude of this ringing voltage to a safe level that is within the peak voltage rating of the transistor.

Figure 8. The current and voltage outputs of the Flyback.

III. CONCLUSION In this paper, we developed a MIMO state space non-linear model

of the FC/ULC hybrid power system, and also we have designed all its components. As can be seen by simulations, the variations of the output current and voltage within the transients’ behavior was eliminated. The developed model has to be validated by experimental results than used for control purposes.

APPENDIX The parameters used in the study:

1- The subsystem A

CCAT = CAN=2.1989F, RCAT=2.0396e-3Ω, RAN=4.7589e-4Ω, Rm=1.2798e-3Ω, LFC=50e-6H, α1=0.45F-1, kα1=210.132 Siemens, τα1=10.575e-3, β1=0.45, kβ1=0.49e+3, τ β1=4.531e-3s, α2=0.02, k α2=0.787 e+3 Siemens, τ α2=4e+4s.

2- The subsystem B

LUC=50e-6H, Rsu 0.019 Ω, Rpu=2.0396e-8 Ω, Ccu=58F, kCu=58F-1, α3=0.02, k α3=52.54Siemens, τα3=1.05e+7s.

3- The steady state

FC ssI − =37A, b ssV − =48V, FC ssD − =0.48, UL ssD − =0.39,

UL ssI − =31.20A.

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0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

10

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Fly

back

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0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-2

0

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vol

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