1 Proceedings 2 nd International Hydrogen Energy Congress and Exhibition IHEC 2007 Istanbul, Turkey, 13-15 July 2007 Dynamic Simulation of a Pem Fuel Cell System Zehra Ural 1* , Muhsin Tunay Gençoğlu 2 and Bilal Gümüş 3 1,3 Dept. of Elec. and Electr. Eng., Eng. and Arch. Fac., Dicle University, Diyarbakır, TÜRKĐYE 2 Dept. of Elec. and Electronics Eng., Engineering Fac., Firat University, Elazığ, TÜRKĐYE 1* [email protected]2 [email protected]3 [email protected]ABSTRACT In the near future, some fuel cell systems could be an accessible and attractive alternative to conventional electricity generation and vehicle drives. The polymer electrolyte membrane (interchangeably called proton exchange membrane, PEM) fuel cell systems can be made in mW to kW capacities; hence a wide range of applications can be covered by this type of fuel cell. This is a major advantage of this type of fuel cell, because once the technology was developed it can be more or less easily scaled up or down for various applications. PEM fuel cell has attracted a great deal of attention as a potential power source for automobile and stationary applications due to its low temperature of operation, high power density and high energy conversion efficiency. Great progress has been made over the past twenty years in the development of PEM fuel cell technology. However, there are still several technical challenges that need to be addressed before commercialization of PEM fuel cell. In this study, the dynamics of a polymer electrolyte membrane fuel cell system is modelled, simulated and presented. Matlab –Simulink TM is used for the modeling and simulation of the fuel cell system. The fuel cell system model consists of the dynamics of reactant flow, fuel cell model and power conditioning units. Also, characteristic of 1.2 W PEM fuel cell system is obtained by experiments. Simulation and experimental results are presented in this paper. The analyses of grid connected or stand alone applications of PEM fuel cell generator system can be achieved with this dynamic simulation model. Keywords: Fuel cells, Proton Exchange Membrane (PEM), PEM Fuel Cell Model. 1. INTRODUCTION Rapid growth in energy consumption during the last century on the one hand, and limited resources of energy on the other, has caused many concerns and issues today. Although the conventional sources of energy, such as fossil fuels, are currently available in vast quantities, however they are not unlimited and sooner or later will vanish. Moreover, environmental concerns, such as global warming, are becoming increasingly serious, and require significant attention and planning. Renewable energy sources are the answer to these needs and concerns, since they are available as long as the sun is burning, and because they are sustainable as they have no or little impact on the environment. One technology which can be based upon sustainable sources of energy is fuel cell. Fuel cells are devices that directly convert the chemical energy stored in some fuels into electrical energy and heat. The preferred fuel for many fuel cells is hydrogen, and hydrogen fuel is a renewable source
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Proceedings 2nd International Hydrogen Energy Congress and Exhibition IHEC 2007 Istanbul, Turkey, 13-15 July 2007
Dynamic Simulation of a Pem Fuel Cell System
Zehra Ural
1*, Muhsin Tunay Gençoğlu
2 and Bilal Gümüş
3
1,3 Dept. of Elec. and Electr. Eng., Eng. and Arch. Fac., Dicle University, Diyarbakır, TÜRKĐYE 2 Dept. of Elec. and Electronics Eng., Engineering Fac., Firat University, Elazığ, TÜRKĐYE
In the near future, some fuel cell systems could be an accessible and attractive alternative to conventional electricity generation and vehicle drives. The polymer electrolyte membrane (interchangeably called proton exchange membrane, PEM) fuel cell systems can be made in mW to kW capacities; hence a wide range of applications can be covered by this type of fuel cell. This is a major advantage of this type of fuel cell, because once the technology was developed it can be more or less easily scaled up or down for various applications. PEM fuel cell has attracted a great deal of attention as a potential power source for automobile and stationary applications due to its low temperature of operation, high power density and high energy conversion efficiency. Great progress has been made over the past twenty years in the development of PEM fuel cell technology. However, there are still several technical challenges that need to be addressed before commercialization of PEM fuel cell. In this study, the dynamics of a polymer electrolyte membrane fuel cell system is modelled, simulated and presented. Matlab –SimulinkTM is used for the modeling and simulation of the fuel cell system. The fuel cell system model consists of the dynamics of reactant flow, fuel cell model and power conditioning units. Also, characteristic of 1.2 W PEM fuel cell system is obtained by experiments. Simulation and experimental results are presented in this paper. The analyses of grid connected or stand alone applications of PEM fuel cell generator system can be achieved with this dynamic simulation model.
Rapid growth in energy consumption during the last century on the one hand, and limited resources of energy on the other, has caused many concerns and issues today. Although the conventional sources of energy, such as fossil fuels, are currently available in vast quantities, however they are not unlimited and sooner or later will vanish. Moreover, environmental concerns, such as global warming, are becoming increasingly serious, and require significant attention and planning. Renewable energy sources are the answer to these needs and concerns, since they are available as long as the sun is burning, and because they are sustainable as they have no or little impact on the environment.
One technology which can be based upon sustainable sources of energy is fuel cell. Fuel cells are devices that directly convert the chemical energy stored in some fuels into electrical energy and heat. The preferred fuel for many fuel cells is hydrogen, and hydrogen fuel is a renewable source
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of energy; hence fuel cell technology has received a considerable attention in recent years. However, this is only one reason, among many reasons, for the recent come back to this technology. Fuel cells can have higher efficiencies than more conventional devices that convert chemical energy into other forms of energy such as electricity. They are inherently simpler, and have other social, economical, and engineering advantages over other types of machines for energy conversion [1].
Fuel cell technology plays an important role in the development of alternative energy converters for mobile, portable and stationary applications. In the recent years there was an increasing interest in fuel cell technology. In particular, PEM fuel cell has reached a high development status. This development was mostly advanced by the automotive industry, because fuel cells are suitable to substitute the fossil fuels and also to provide an environment-friendly propulsion. But there is also a growing market for stationary fuel cell applications [2]. PEM fuel cell is considered to be a promising power source, especially for transportation and stationary cogeneration applications due to its high efficiency, low-temperature operation, high power density, fast startup, and system robustness [3]. PEM fuel cells are suitable for portable, mobile and residential applications [4]. In most stationary and mobile applications, fuel cells are used in conjunction with other power conditioning converters and a circuit model would be beneficial, especially for power electronics engineers who in many cases have the task of designing converters associated with the fuel cell for various load applications [5]. In the last decade a great number of researches have been conducted to improve the performance of the PEM fuel cell, so that it can reach a significant market penetration [3]. Rapid development recently has brought the PEM fuel cell significantly closer to commercial reality. Although prototypes of fuel cell vehicles and residential fuel cell systems have already been introduced, it remains to reduce the cost and enhance their efficiencies. To improve the system performance, design optimization and analysis of fuel cell systems are simple and safe construction and quick startup even at low operating temperatures. Mathematical models and simulation are needed as tools for design optimization of fuel cells, stacks, and fuel cell power systems. In order to understand and improve the performance of PEMFC systems, several different mathematical models have been proposed to estimate the behavior of voltage variation with discharge current of a PEM fuel cell. Recently, numerical modeling and computer simulation have been performed for understanding better the fuel cell itself [4-8]. Numerical models are useful to simulate the inner details of PEMFC, but the calculation required for these models is too extensive to be used for system models. In system studies, it is important to have an adequate model to estimate overall performance of a PEMFC in terms of operating conditions without extensive calculations. But, few studies have focused on the simple models, which can be used to investigate the impact of cell operating conditions on the cell performance and can be used to design practical fuel cell total systems [4]. In this study; firstly, general information about the fuel cells, their importance and applications are presented. Then mathematical models of the PEM fuel cell are investigated. Finally, Dynamic modeling of the PEM fuel cell is performed. Various system dynamics such as fuel cell electrochemistry and reactant-flow are modeled, simulated and presented. On the other hand, the characteristic of 1,2 W PEM fuel cell is obtained by experiments.
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2. MATHEMATICAL MODEL OF A PEM FUEL CELL The fundamental structure of a PEM fuel cell can be described as two electrodes (anode and cathode) separated by a solid membrane acting as an electrolyte (Fig.1). Hydrogen fuel flows through a network of channels to the anode, where it dissociates into protons that, in turn, flow through the membrane to the cathode and electrons that are collected as electrical current by an external circuit linking the two electrodes. The oxidant (air in this study) flows through a similar network of channels to the cathode where oxygen combines with the electrons in the external circuit and the protons flowing through the membrane, thus producing water. The chemical reactions occurring at the anode and cathode electrode of a PEM fuel cell are as follows: Anode reaction: 2H2 → 4H+ +4 e- Cathode reaction: O2 + 4H+ + e- → 2H2O Total cell reaction: 2H2 + O2 → 2H2O + electricity + heat The products of this process are water, DC electricity and heat [4].
Figure 1: Schematic of a single typical proton exchange membrane fuel cells
Electrons flowing from the anode towards the cathode provide power to the load. A number of cells, when connected in series, make up a stack and deliver sufficient electricity. A I-V curve, known as a polarization curve, is generally used to express the characteristics of a fuel cell (Fig. 2). The behavior of a cell is highly non-linear and dependant on a number of factors such as current density, cell temperature, membrane humidity, and reactant partial pressure. The cell voltage decreases with increasing current. A PEM fuel cell generally performs best at temperatures around 70-80 0C, at a reactant partial pressure of 3-5 atm, and a membrane humidity of ~ 100% [6]. V-I Characteristics of a 1,2 W PEM fuel cell is shown in Fig.3. Experimental data is obtained by variable loads.
Figure 2: Polarization curve Figure 3: V-I Characteristics of a 1,2 W PEM fuel cell.
The cell potential (Vcell), at any instance could be found using Eq. 1. When a cell delivers power to the load, the no-load voltage (E), is reduced by three classes of voltage drop, namely, the activation (Vact), ohmic (Vohm), and concentration (Vconc) over voltages. Vcell = E – Vact – Vohm – Vconc V (1) The Nerst equation (Eq. (2)) gives the open circuit cell potential (E) as a function of cell temperature (T) and the reactant partial pressures [6];
E = E0 – 0,85.10-3 (T – 298,15) +
5.0
2
5.0
22
.
.ln
.2
.
PP
PP
F
TR
OH
OH V (2)
E0 represents the reference potential at unity activity, R is the universal gas constant and P is the total pressure inside the stack. Relevant parameter values are given in Table 1. The activation drop can be analyzed by Tafel’s equation and the empirical model outlined in [7] is considered in this regard. Eq. (3) gives the activation voltage drop (Eact). Eact = -0,9514 + 0,00312T- 0,000187.T.[ln(I)] + 7,4.10-5.T.[ln(CO2)] V (3) I(mA.cm-2) is the cell current density, the oxygen concentration(CO2) is given as a function of stack temperature in Eq. (4)
CO2 = )/498exp(10.08,5 6
2
T
PO
− mol.cm-3 (4)
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Table 1: Fuel cell model parameters [7]. Symbol Parameter Value Unit
E0 Reference potential 1,229 V
R Universal gas constant 8,314 J mol-1 K-1
F Faraday constant 96485 C mol-1
T Stack temperature 353 K
P Cell pressure 1,2 atm
tm Membrane thickness 175.10-4 cm
Cdl Double layer capacitance 0,035x232 F
τH+ Time constant 12,78 s
αH+ Relational parameter 5,78 cm6 A-3
DH+ Diffusion coefficient 0,85x10-6 cm s-1
Since, the activation overvoltage appears as a voltage drop in Eq. (1) and Eact in Eq. (3) is negative throughout the whole range, Eq. (5) is used to avoid a double negation for this term. Vact = - Eact V (5) The effects of double layer capacitance charging at the electrode-electrolyte interfaces can be expressed by Eq. (6) [6];
dlact
act
dl
act
CR
V
Cdt
dV
.
1−= V (6)
Here Cdl is the double layer capacitance and Ract is the activation resistance, found by dividing Vact, with I.
I
VR actact = kΩ.cm2 (7)
It should be noted that, here, Ract stands for the effective resistance for a given cell current, I, and contributes to the activation overvoltage, Vact. On the other hand, Eq (6) is used to determine Vact at any instance of time. Therefore, these equations need to be used separately and cannot be inter-changed. At intermediate current densities the voltage drop is almost linear and ohmic in nature. Membrane resistance (Rmem) is found by dividing the thickness, tm, by the membrane conductivity, σ (kΩ-1.cm-1). Vohm = I.Rmem (8)
σm
mem
tR = kΩ.cm2 (9)
The membrane water content depends on various factors, such as water drag from the anode to the cathode due to moving protons, external water content of the reactants, and back diffusion of
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water from the cathode to the anode [6]. Since the effect of water drag is a significant factor, it could be hypothesized that the membrane proton concentration is a function of the cell current density only. An empirical differential equation could be solved to determine the proton concentration, CH+, and Eq. (10) and (11) could be used to estimate the membrane conductivity, σ [ 7];
+
+
+
++ +=+
H
H
H
HH IC
dt
dC
τ
α
τ
3.1 (10)
++= HH CDTR
F.
.
2
σ (11)
At higher current densities, the cell potential decreases rapidly due to mass-transport limitations. This linearity is termed as the concentration over potential and modeled as; Vconc = a.e (bl) V (12) Here, the coefficient a (V), and b (cm2 mA-1) vary with temperature and given as; a = 1,1.10-4 – 1,2.10-6. (T-273) b = 8.10-3 Eq. (1)-(12) could be solved for cell potential, Vcell, as a function of current density, cell temperature, reactant pressure, and membrane hydration [7]. If all the cells are in series, stack output is the product of cell potential and number of cells in the stack (N). Vstack = Vcell x N (13) It is assumed that reactant flow at the anode and cathode is laminar, that the inlet gases are saturated at the given cell temperature. Assuming that all the gases are ideal, the ideal gas law could be extended for dynamic analysis and the principles of mole conservation could be used to model the reactant flows with the general equation given below;
Fn
Imm
dt
dP
TR
Voutin
g
..
..
±−= (14)
V is the anode or cathode volume (m3), Pg is the gas (oxygen, hydrogen or vapor) pressure (atm),
.
inm is the reactant inlet flow rate (mol.s-1), outm.
, is the reactant outlet flow rate (mol.s-1), n is the
number of electrons involved for each mole of reactant. To determine instantaneous conditions inside the cell, the conservation of gas reactants are calculated using the following formulas. Anode flow model equations;
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F
Imm
dt
dP
TR
VoutHinH
Ha
.2.2
.
2
.2 −−= −− (15)
)( 22
.
ambHaoutH PPkm −=−
2222
.
.. HHHinH CFPCFRm =−
Cathode flow model equations;
F
Imm
dt
dP
TR
VoutOinO
Oc
.4.2
.
2
.2 −−= −− (16)
)( 22
.
ambOcoutO PPkm −=−
2222
.
.. OOOinO CFPCFRm =−
F
Imm
dt
dP
TR
VCoutOHCinOH
COHc
.2.2
.
2
.2 +−= −−−−
− (17)
)( 22
.
ambCOHcCoutOH PPkm −= −−−
Table 2: Reactant flow model parameters Symbol Parameter Value Unit Pamb Ambient pressure 1 atm Va Anode volume 0,0159 m3
Associated parameters are given in Table 2 [7]. 3. DYNAMIC MODELLING OF THE PEM FUEL CELL SYSTEM
A fuel cell system mainly consists of a fuel processing unit (reformer), fuel cell stack and power conditioning unit. A simple representation of a fuel cell system is given in Fig. 4. The fuel cell uses hydrogen as input fuel and produced DC power at the output of the stack [8].
Figure 4: Basic fuel cell system components
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A PEM fuel cell system block diagram is shown in Fig. 5. The fuel cell system model consists of the dynamics of reactant flow, fuel cell model and power conditioning unit. The fuel cell subsystem which contains membrane resistance subsystem is shown in Figure 6. The fuel cell’s inputs are hydrogen, oxygen and vapor pressures, cell current density of the stack. Hydrogen, oxygen and vapor pressures could be found Eq. (15), (16) and (17). These terms could be used in Eq. 2. to determine the open circuit cell potential. The cell potential products number of cells in the stack. So, the stack voltage is obtained by this product. Also, the stack voltage is input of the power conditioning unit. The power conditioning subsystem Simulink implementation is shown in Figure 7. The power conditioning unit occurs of a single phase inverter to convert DC power into AC, a 5 kVA transformer in order to increase low output voltage in 220 V, 50 Hz grid power.
Power (W)
Iload-rms(A)
Vload-rms(V)
Vstack(V)Iload(A)
Vload(V)
Power Conditioning
8
H2 flow(SLMP)pH2
Istack
pO2
pH2O
Vcell (V)
Fuel Cell
Air f low (mole/sec)
I stack (A)pH2O(atm)
Cathode H2O flow
120
Air flow(SLMP)
Air f low (SLMP)
I stack (A)
pO2(atm)
Air f low (mole/sec)
(Cathode) O2 flow
H2 f low (SLMP)
I stack (A)pH2(atm)
(Anode) H2 Flow
signal rms
35
signal rms
Figure 5: Simulink blocks for a PEM fuel cell system.
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F
T
pH2
pO2
pH2O
EEo
Vohm
Co2
Vconc
Vohm
Vact
Vact
1
Vcell
(V)
u(1)*u(2)
eq-Vohm
f(u)
eq-Vconc
f(u)
eq-O2 concf(u)
eq-Eact
350
T
Ract
-C- R
f(u)
Nerst
Temp
IloadRmem (kohm-cm2)
Membrane Resistance
I/Cdl
-C-F
f(u)
Eo-temp
Cdl
Cdl
-K-
A~mA/cm2
1
s
-1
4
pH2O
3
pO2
2
Istack
1
pH2
Figure 6: Single Fuel Cell Model (Fuel Cell Subsystem)
2
Vload(V)
1
Iload(A)
+
-
pulses
A
B
Single phaese
inverter
Signal(s) Pulses
PWM Generator50 Hz
5 kVA
34/220 V
+
-v
+i
-
+
-v
signal+
-
+
-v
1
Vstack(V)
Figure 7: Power Conditioning Subsystem
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4. SIMULATION RESULTS
Matlab-SimulinkTM is used to simulate the PEM fuel cell system. Additional limiters are placed in various key locations in order to prevent problems arising from algebraic loops and extreme numerical values. The simulation is done for 1.5 s. The hydrogen flow rate is maintained at 8 standard litre per minute (SLMP). The air flow rate is fixed at 120 SLMP [7]. Simulation results for 0-0.2 s time interval are given in figures 8-11 and 0-1.5 s time interval are given in figures 12-17. System output voltage for alternative and effective values for 4.5 kW, cos φ= 0.90 and 3 kW, cos φ= 0.80 lagging loads are given in Figure 8, 10, 12, 14. Alternative and effective current values for 5 kW, cos φ= 0.90 and 3 kW, cos φ= 0.80 lagging loads are given in Figure 9, 11, 13, 15. The load is connected the transformer output. This load is changed variable real and reactive power values.
Figure 10: Voltage Output (3 kW, cosφ 0.8) Figure 11: Load Current (3 kW, cosφ 0.8)
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0 0.5 1 1.5-400
-300
-200
-100
0
100
200
300
400
Time (s)
System O
utput Voltage (V)
output voltage(ac)
output voltage(rms)
0 0.5 1 1.5-40
-30
-20
-10
0
10
20
30
40
Time (s)
Load C
urrent (A
)
load current(ac)
load current(rms)
Figure 12: Voltage Output (4,5 kW, cosφ 0.9) Figure 13: Load Current (4.5kW, cosφ 0.9)
0 0.5 1 1.5-400
-300
-200
-100
0
100
200
300
400
Time (s)
System O
utput Voltage (V)
output voltage(ac)
output voltage(rms)
0 0.5 1 1.5-30
-20
-10
0
10
20
30
Time (s)
Load C
urrent (A
)
laod current(ac)
load current(rms)
Figure 14: Voltage Output (3 kW, cosφ 0.8) Figure 15: Load Current (3 kW, cosφ 0.8)
0 0.5 1 1.50
1000
2000
3000
4000
5000
6000
Time (s)
Power (V
A)
0 0.5 1 1.50
1000
2000
3000
4000
5000
6000
Time (s)
Power (V
A)
Figure 16: Power Demand (4.5 kW, cosφ 0.9) Figure 17: Power Demand (3 kW, cosφ 0.8)
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Variation in power demand is represented by figures in case of lagging power factor is changed (Figure 16-17).
5. CONCLUSIONS
In this paper the dynamic simulation of a PEM fuel cell system and simulation results are presented. Studies have been done with a 5 kW PEM fuel cell system. As a result of this study PEM fuel cell system is suitable for distributed generation. Further analysis should be done three phase fuel cell system and controlled power conditioning systems design. ACKNOWLEDGEMENT
The authors would like to thank The Commission of Dicle University Scientific Research Projects (DUBAP) for financial support towards this study. REFERENCES
[1] Akbari, M. H., PEM Fuel Cell Systems for Electric Power Generation: An Overview,
International Hydrogen Energy Congress and Exhibition IHEC 2005, Istanbul, Turkey, 2005. [2] Lemes, Z., Vath, A., Hartkopf, Th., Mancher, H., Dynamic fuel cell models and their application in hardware in the loop simulation, Journal of Power Sources, 154, (2006), 386-393. [3] W.Q. Tao, C.H. Min, X.L. Liu, Y.L. He, B.H. Yin, W. Jiang, Parameter sensitivity examination and discussion of PEM fuel cell simulation model validation Part I. Current status of modeling research and model development, Journal of Power Sources, (2006). [4] Maher A.R. Sadiq Al-Baghdadil, Modelling of proton exchange membrane fuel cell performance based on semi-empirical equations, Renewable Energy, 30, (2005), 1587-1599. [5] Fmoun, P., Member, S., Gemmen, R. S., Electrochemical Circuit Model of a PEM Fuel Cell, IEEE, 2003. [6] Larminie, J., Dicks, A., Fuel Cell System Explained, John Wiley & Sons Ltd, West Sussex, England, 2001. [7] Khan, M., J., Iqbal, M. T., Dynamic Modelling and Simulation of a Fuel Cell Generator, Fuel Cells, 2005, 5, No 1.
[8] Tanrioven, M., Alam, M.S., Reliability modeling and analysis of stand-alone PEM fuel cell power plants, Renewable Energy, 31, (2006), 915-933.
