Analysis and Characterization of PEMFC Power Systems with Bond Graph

Analysis and Characterization of PEMFC Power Systems with Bond Graph

Nedjem eddine.Benchouia1, Aoual Elias.Hadjadj2, Lakhdar. Khochemane 1, Bouziane.Mahmap 1Mechanical Department, Faculty of Technology, University 20Aout1955, P.O.Box.26

El-Hadaiek Road, Skikda, 21000 , Algeria

2Electromechanical Department, Faculty of science engenireeng, University of Badji Mokhtar P.O.Box.12, Annaba, Algeria,

3Bioenergy and Environment Division, Research Center of Renewable Energies Development.

P.O. Box. 62 Observer Road, Bouzaréah, Algiers, Algeria.

Abstract

This paper addresses the problem of bond graph methodology as a graphical approach for modeling fuel cell systems. The system consists of a Proton Exchange Membrane Fuel Cell (PEMFC) stack, an interleaved boost converter.

Simulation results illustrate the simplified system response obtained using implementation of the governing equations in MATLAB/Simulink or a bond graph implementation in the simulation program 20- sim.

Keywords: PEM fuel cell, boost, modeling, dynamic, Bond graph, simulation.

1. Introduction

   In recent years, an energetic approach original was set up to model the fuel cell via the tool Bond Graph (BG) [5]. BG to define and model the energy exchanges within a system and any physical realm.

   The bond graph formalism is a graphical approach to modeling, based on the concept of power and incorporating ideas from network theory in a general setting [1][2].

   Bond graph modeling is a multi-domain approach that has been applied in a variety of disciplines, covering all areas of engineering but also many others such as biological systems [3].

   Fuel cells are known to have higher efficiency than conventional power plants [4]. Fuel cells are environmentally friendly (environmentally clean), have extremely low emission and they produce very low noise [4].

   Modelings of fuel cells have become increasingly important. This in order to achieve integration simulates the fuel cell in an electrical system. These models must be comprehensive enough to take into

   account all the electrochemical phenomena brought into play while being simple enough to allow the simulation of the complete system

   In this work we have tried to present the bond graph modeling of the conversion chain. Our goal is first to create a direct model (simulation) having as inputs the molar flow qH2, qO2 output power of the system taking into account its environment.

   The paper is organized as: the section II discusses the dynamic behavior of H-Tec 1.2W PEM fuel cell model and details out the design of a simple DC/DC boost converter used to provide a regulated voltage for varying loads. The section III evaluates the performance of PEM fuel cell system with DC/DC boost converter using simulink and simulation results is brought out.

2. Modeling of the Power system

   The topology of the Fuel cell system is that given in Figure 1.

   DC

   DC Load

   Stack Fuel cell

   (Cder Algiers) Boost Load

   Figure.1.Bond graph à mot of the FC system .

   Before starting the modeling of the whole system, we model each component alone.

   1. Dynamic model of PEMFC

      Based on the work presented in [6,7,8], The actual cell potential decreases from its equilibrium potential due to irreversible losses. The output voltage of the

      single cell is given by (1) according to the PEMFC output characteristics empirical equation [7].

      Based on Eqs.(1) to (5), the developed model for fuel cell is shown Figure.2.

      Vcell Ecell act ohm dif )

      (1)

      Where; Vcell fuel cell voltage, Ecell Thermodynamic potential of the fuel cell, act, con, ohmic are losses, introduced into the fuel cell.

      The ideal performance of a fuel cell is defined by its Nernst equation, in the case of PEMFC:

      E E

      PH

      RT 2

      RT 2

      • ln

        PO1/ 2

        (2)

        N 0 2F

        PH O

        2

        2

        Many model have been proposed to simulate the fuel cell in the literature [10, 13].This model is built by utilizing the relationship between the output voltage and potential pressure of hydrogen, oxygen.

        The relationship between the modular flows of any gas through the valve is proportional to its partial pressure inside the channel [10]. For hydrogen, this relationship can be expressed as follows

        Figure.2. Dynamic model of the FC system [8].

   2. Dynamic Boost converter model

      A boost dc/dc converter can be used to convert the fuel cell output voltage to the desired dc bus voltage.

      qH 2

      pH 2

      kan k

      M

      M

      H

      H

      2

      H 2

      (3)

      The boost converter is given in Figure.3 with a

      switching period T and a duty cycle . Again, assuming

      continuous conduction mode of operation, the state space equations when the main switch is ON And when

      With,pH2 hydrogen partial pressure ( atm),kan anode

      valve constant (Kmol Kg (atm s)-1),

      MH2 molar mass of hydrogen (kg kmol -1),kH2

      the switch is OFF [11].

      During the on state, switch S is closed, which makes the input voltage (V ) appear across the inductor, which in

      hydrogen valve molar constant (kmol (atm s)-1).

      i

      turns results in change in inductor current (iL) during

      The molar flow of hydrogen that reacts can be found from the basic electrochemical relationship between hydrogen flow and the fuel cell system current [9]

      NI

      a time interval t. Rate of change of current is given by [14]:

      V L diL i d

      qH r 2K I

      t (7)

      2 2F r

      (4)

      At the end of the on-state the increase in inductor current is given by [14] :

      The hydrogen partial pressure can be obtained by applying Laplace transform on (3) and (4) [9],

      IL on

      T

      1. dI L

         ViT

         L

         (8)

         2

         2

         pH 1/ KH (qin

         • 2K I )

         During the off-state, the switch s is open, so the

         2

         Where:

         (1 S ) H 2 r

         H

         H

         2

         (5)

         inductor current flows through the load, the evolution of iL assuming voltage drop across diode is zero and a large capacitor is:

         H 2

         Van

         H

         H

         RTK

         2

         (6)

         Vi V0

         L diL

         dt

         (9)

         With, KH2 Valve molar constant for hydrogen (kmol/s atm), H2 Response time for hydrogen

         Variation of iL during the Off-period is:

         (s),similar operation can be done oxygen partial pressure.

         ILoff

         ( 1)T

         0 dI L

         (Vi V0 )( 1)T

         L

         (10)

         The energy stored in each component at the end of commutation cycle T is the equal to that at the beginning of the cycle. That means overall change in current is zero [14]:

         Table.1. Boost converter equations

         off

         off

         ILon IL 0

         Jonction1 f1 f2 f3 f4 e2 e1 e3 e4				Jonction0 f6 f5 f7 f8 e6 e5 e7 e8
         Elément I : L	f	2	p2 L	Elément I:C	e q6 6 C
         Elément R : RL e3 RL . f3				Elément TF e4 m.e5 f5 m. f4
         Elément R : Rc e7 Rc . f7				Elément R : RLd e8 RLd . f8

         Jonction1 f1 f2 f3 f4 e2 e1 e3 e4				Jonction0 f6 f5 f7 f8 e6 e5 e7 e8
         Elément I : L	f	2	p2 L	Elément I:C	e q6 6 C
         Elément R : RL e3 RL . f3				Elément TF e4 m.e5 f5 m. f4
         Elément R : Rc e7 Rc . f7				Elément R : RLd e8 RLd . f8

         (11)

         This can be written as [11, 14]:

         V0

         Vi

         1

         1

         (12)

         The above equation reveals that the output voltage will be always greater than input voltage.

         V 0

         Vi

      2. m

      1

      (13)

      With the equation (13), we can modeled the converter by Bond graph, supposed is transformer (TF).

      After rearrangement we can write the equations as state variable.

      RL (1 )

      d p2 L c

      P 1

      2

      2

      V fc

      dt q6

      1 1

      1 q6

      0

      L R C R C

      c ld

      (14)

      Figure.3.a: DC-DC Boost Converter.

      Figure.3 b. Bond graph of Boost converter.

      This bond graph model has allowed us to ask analytically all equations of the system without reducing the causal path:

3. Simulation results

   When we have constructed the model by means of Bond Graph, The mathematical expressions for the fuel cell system and power converters were simulated in environment Matlab- simulink [16].

   1. Simulation of PEMFC subsystem

Figure.4 shows changes in fuel cell voltage and current for varying loads. The equivalent capacitor will basically change the stack electrical constant, then, it will change the time response. As observed in Figure, the fuel cell voltage and current takes about 3ms for the base parameter (C = 3 F).

Shows the input molar flow of fed hydrogen after gas processing response and this hydrogen flow will be fed to PEM stack unit. From Figure 5, we can see that the gas reaction process requires a short time of delay to response.

Figures.5.Hydrogen, oxygen gases input flow qH2, qO2.

4.8

Stack voltage (v)

Stack voltage (v)

4.6

4.4

4.2

4

0 1 2 3 4 5 6 7 8 9 10

3.2 Simulation of power converter subsystem

The output voltages and output currents for 5Vto12V (Boost) dc-dc converter during a load constant are shown in Figures.6.a to 6.b, respectively.

			Outp	ut voltage Boost conver	ter 5v-12v

			Outp	ut voltage Boost conver	ter 5v-12v

25

20

Times (ms)

1

x 10 15

Output voltage(v)

Output voltage(v)

4

4

10

5

0.8

0

Stack current (A )

Stack current (A )

0.6

-5

0 2 4 6 8 10 12

Time(s)

4

x 10

0.4

0.2

Figure.6.a) Output voltage of the Boost converter.

0

1 2 3 4 5 6 7 8 9 10

0.18

Times (s)

Figures.4.Transient state of load current and output voltage.

0.012

4

x 10

0.16

0.14

Output Current(A )

Output Current(A )

0.12

0.1

0.08

0.06

qH2 flow rateof hydrogen (mol.s)

qH2 flow rateof hydrogen (mol.s)

0.04

0.01

			Outp	ut current Boost conver	ter 5v-12v

			Outp	ut current Boost conver	ter 5v-12v

0.008

0.02

0

0 2 4 6 8 10 12

Time(s)

4

x 10

0.006

0.004

0.002

0

0 10 20 30 40 50 60

Times (s)

Figure.6.b) Output current of the Boost converter.

0.025

qO2 flow rate of oxygen (mol.s)

qO2 flow rate of oxygen (mol.s)

0.02

0.015

0.01

0.005

0

0 10 20 30 40 50 60

Times (s)

Parame ters	Val ue	Unit	Parame ters	Value	Uni t
T	298, 15	K	Rm	0,126	S
F	964 87	C/m ol	C	3F
R	8,31 4	J/(k mol K) /td>	Rc	0,0003
Eo	1,22 9	V	B	0,016	V
N	4		rH-O	1,168	/
Kr	1,03 64 x 10-5	kmol /(s A)	L	230	m
Uopt	0,85		1th̩orique	Р0,949	V
KH2	4,22 x 10- 5		1experimen tal	– 1,053	V
KO2	2,11 x 10- 5	kmol /(s atm)	2	0,02866l n(A) + 4,3.10- 5ln(CH2)
H2	3,37	kmol /(s atm)	3	7,6×10-5
O2	6,74	S	4	1,93×10- 4
f	0,8	S	Jlim	0,0496	A/c m2
C	3F

Parame ters	Val ue	Unit	Parame ters	Value	Uni t
T	298, 15	K	Rm	0,126	S
F	964 87	C/m ol	C	3F
R	8,31 4	J/(k mol K)	Rc	0,0003
Eo	1,22 9	V	B	0,016	V
N	4		rH-O	1,168	/
Kr	1,03 64 x 10-5	kmol /(s A)	L	230	m
Uopt	0,85		1th̩orique	Р0,949	V
KH2	4,22 x 10- 5		1experimen tal	– 1,053	V
KO2	2,11 x 10- 5	kmol /(s atm)	2	0,02866l n(A) + 4,3.10- 5ln(CH2)
H2	3,37	kmol /(s atm)	3	7,6×10-5
O2	6,74	S	4	1,93×10- 4
f	0,8	S	Jlim	0,0496	A/c m2
C	3F

Table.2. PEMFC Parameters [7], [this model].

Table.3. Parameters of Boost converter

Boost Parameters	Value	Unit
L	75	H
RL	80	m
RC	5	m
C	1.68	F
Fs	100	kHz
Vfc	5	v
Load resistance	120
Reference voltage	12	v
Duty cycle	0.6

1. Conclusion

   This paper presents a study of dynamic behavior of 1.2W PEM fuel cell. The dynamic limitations of the stack fuel cell model are analyzed based on their dynamic behavior of characteristic curves. To regulate the fuel cell terminal voltages a simple DC/DC boost converter is interfaced with PEM fuel cell system. It is observed that the design of simple DC/DC boost converter gives better performance.

   The future developments will consist in connecting buck converter, a battery to the system and proposed the control structure.

   ACKNOWLEDGMENT

   The authors would like to thank the aid given by Dr Mahmah. B and members of Bioenergy and Environment Division.

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