International Journal of Engineering & Computer Science IJECS-IJENS Vol:13 No:03 31
137003-9292-IJECS-IJENS © June 2013 IJENS I J E N S
Review And Analysis Of MATLAB® Simulink
Model Of PEM Fuel Cell Stack 1Faheem Khan, 2Arshad Nawaz, 3Malik Ansar Muhammad, 4Muhammad Ali Khadim.
Electrical Engineering Department.
Sarhad University of Science and Information Technology
Peshawar, Pakistan
Abstract— Modern world face problems like energy crises,
global warming and ozone depletion due to toxic pollutants. The
technology of the fuel cell is able to tackle these challenges. That
is the reason fuel cell is considered as environmental friendly and
efficient technology of future. Among various types of fuel cell,
PEM fuel cell is the most diffused and popular type of market
due to its sound features such as low operating temperature,
quick variation according to load, high efficiency and better
power density. In this paper, Matlab®-Simulink model of PEM
fuel cell stack is used to analyze the phenomenon occurring in
PEM fuel cell stack and the factors that affect the efficiency of
the fuel cell stack. Moreover the behavior of fuel cell stack is
observed under varying load and varying flow rate of fuel and
oxidants.
Index Term-- PEM Fuel cell, Matlab-Simulink, Model
I. INTRODUCTION
Fossil fuel resources are decreasing with time due to which
prices of conventional hydrocarbon fuel increases in the
international market thus most countries of the world is
investing in renewable energies.[1] Now unlike conventional
fossil fuel run power generation system, we need a power
source that is energy efficient, produce low pollutants and
being supplied by unlimited low cost fuel.[2]
Fuel cells are electrochemical devices that convert chemical
energy of a fuel directly to electric energy, without any
moving parts. [1] - [2]
In the near future the fuel cell technology will be the most
eco-friendly source of power production. The value of fuel
cell has increased in the last decade because of zero toxic
emissions. In the past few decades different types of fuel cell
technologies have been developed, some of them are as
under.[3]
1) Solid oxide fuel cell
2) Direct methanol fuel cell
3) PEM fuel cell
4) Phosphoric acid fuel cell
5) Molten carbonate fuel cell
The PEM fuel cell has a wide range of applications from
transportation to distributed power generation and from
residential power to portable power.[4]
II. PEM FUEL CELL WORKING PRINCIPLE
PEM fuel cell consists of catalyst porous electrodes and
between them an ion conductive electrolyte is present
(Nafion®).
The Redox reaction occurring in the PEM fuel cell is given
below:
Reaction at anode: H2 → 2H+ + 2e-
Reaction at cathode: 2H+ + 2e- + ½ O2→ H2O
Overall reaction: H2 + ½ O2→ H2O
Fig. 1. Showing the working principle of PEM Fuel cell
The above figure (1) showing how the Redox reaction
occurs in PEM fuel cell. The redox reaction gives us heat,
water and electrical energy. The quantity of electrical energy
produced depends on the Gibbs free energy of the above
reaction.
𝐸𝑜 =−∆𝐺
𝑛𝐹
G, n and F are constants so the voltage of a single PEM fuel
cell can be calculated. [5]
𝐸𝑜=1.229volts at STP
III. MATHEMATICAL MODEL
Modeling is very helpful in the development and improvement
of any technology. Fuel cell modeling is therefore important
for the improvement of efficiency and cost control of fuel cell
technology. The fuel cell model must have some
characteristics like being able to solve problems present in the
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fuel cell, able to improve efficiency and model must be firm
and accurate.
Some important factors that affect the fuel cell performance
must be included in any fuel cell model. The factors such as
pressure, temperature, humidity, composition and flow rate of
fuel and oxidants and number of cells in stack.
IV. MATLAB SIMULINK MODEL
Matlab Simulink generic model of PEM fuel cell stack has
been studied in this paper. [6]
V. SIMPLIFIED MODEL
The simplified model is that model which is operating at
nominal temperature and pressure conditions. This model is
called simplified model on the basis of its level of detail. In a
simplified model, only current and voltage signals are
available. Other signals like flow rate, fuel utilization and
stack efficiency is set to zero.
The equivalent circuit on which the model is based is given
below:
Fig. 2. Representing Simplified Model
The diode is used to prevent the reverse current into the stack.
VI. DETAILED MODEL
The detailed model includes flow rates of fuel and oxidants,
Pressure, composition of the fuel and oxidants and
temperature. By variation of the above factors under signal
variation pan in Simulink, Change in the following is
observed:
Open circuit voltage (Eo)
Exchange current (Io)
Tafel slope (A)
Equations for the calculation of the above Open circuit
voltage, Exchange current and Tafel slop is given in Equation
section.
The equivalent circuit of detailed model is same as for
Simplified model but there are more parameters included and
the values for Open circuit voltage, Exchange current, and
Tafel slope are updated.
The detailed model is interpreted in three blocks also shown in
Figure (3) below
Fig. 3. Representing Detailed Model Of PEM Fuel Cell Stack
Block A:
In Block (A) factors like fuel flow rate, Air flow rate, Partial
Pressure of fuel, Partial pressure of air, Operating
Temperature, Percentage of hydrogen in fuel, Percentage of
oxygen in the air and Feedback form Fuel cell current are
varied on the basis of which the fuel and air utilization are
obtained .
Block B:
In Block (B) the open circuit voltage and Exchange current is
obtained based on the fuel and air utilization from block (A).
Block C: In Block (C) Tafel slop values are obtained by taking under
consideration parameters like Charge transfer coefficient α,
Gibbs free energy ∆G and reaction equilibrium constant
(Kc).Obtained from Polarization curve from Manufacturer
datasheet moreover other parameters like low heating value
efficiency of stack , temperature , pressure , composition of
fuel and air.
VII. EQUATIONS
1) Open circuit Voltage
𝑬𝒐𝒄 = 𝑲𝒄𝑬𝒏 (1)
2) Exchange Current:
𝒊𝒐 =𝒛𝑭𝒌(𝑷𝑯𝟐
+𝑷𝑶𝟐)
𝑹𝒉𝒆−
∆𝑮
𝑹𝑻 (2)
3) Tafel Slop:
𝑨 =𝑹𝑻
𝒛𝜶𝑭 (3)
4) Utilization of hydrogen (UfH2) and oxygen (UfO2) are
determined in Block (A)
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The fuel and air utilization in this section is based on Absolute
values.
𝑼𝒇𝑯𝟐=
𝟔𝟎𝟎𝟎𝟎𝑹𝑻𝑵𝑰𝒇𝒄
𝒛𝑭𝑷𝒇𝒖𝒆𝒍𝑽𝒊𝒎𝒑(𝒇𝒖𝒆𝒍)𝒙% (4)
𝑼𝒇𝑶𝟐=
𝟔𝟎𝟎𝟎𝟎𝑹𝑻𝑵𝑰𝒇𝒄
𝟐𝒛𝑭𝑷𝒂𝒊𝒓𝑽𝒍𝒎𝒑(𝒂𝒊𝒓)𝒀% (5)
5) The partial pressure of oxygen, Hydrogen, water and the
Nernst voltage is determined as:
Partial pressure is the Pressure of specific gas in a mixture of
gases in this model IDEAL GAS is considered so Pressure of
gas is the partial pressure.
Nernst voltage(𝐸𝑛) Is basically the cell voltage obtained from
the standard cell voltage minus factors which effect standard
cell voltage.
The values we get from the following equations for Partial
Pressure and Nernst voltage calculation is used to calculate
new values of open circuit voltage & Exchange current.
𝑷𝑯𝟐= (𝟏 − 𝑼𝒇𝑯𝟐
) 𝒙%𝑷𝒇𝒖𝒆𝒍 (6)
𝑷𝑯𝟐𝑶 = (𝒘 + 𝟐𝒚%𝑼𝒇𝑶𝟐)𝑷𝒂𝒊𝒓 (7)
𝑷𝑶𝟐= (𝟏 − 𝑼𝒇𝑶𝟐
) 𝒚%𝑷𝒂𝒊𝒓 (8)
𝑬𝒏 = 𝟏. 𝟐𝟐𝟗 + (𝑻 − 𝟐𝟗𝟖)(−𝟒𝟒.𝟒𝟑)
𝒛𝑭+
𝑹𝑻
𝒛𝑭𝑰𝒏(𝑷𝑯𝟐
)(𝑷𝑶𝟐)𝟐
𝟏 𝒘𝒉𝒆𝒏 𝑻 ≤ 𝟏𝟎𝟎℃ (9)
𝑬𝒏 = 𝟏. 𝟐𝟐𝟗 + (𝑻 − 𝟐𝟗𝟖)−𝟒𝟒.𝟒𝟑
𝒛𝑭+
𝑹𝑻
𝒛𝑭𝑰𝒏 (
𝑷𝑯𝟐𝑷𝑶𝟐
𝟏𝟐
𝑷𝑯𝟐𝑶) 𝒘𝒉𝒆𝒏 𝑻 > 𝟏𝟎𝟎℃ (10)
6) The nominal rate at which conversion of gases occurs
calculated as follows:
Equation 11 and 12 are for calculation of, rate of utilization of
fuel and oxidants.
Unlike Equation (4-5) Nominal values of current, voltage,
partial pressure are used and percentage of Hydrogen in the
fuel and Oxygen in the air is not considered.
𝑼𝒇𝑯𝟐=
𝜼𝒏𝒐𝒎∆𝒉𝒐 (𝑯𝟐𝑶(𝒈𝒂𝒔))𝑵
𝒛𝑭𝑽𝒏𝒐𝒎 (11)
𝑼𝒇𝑶𝟐=
𝟔𝟎𝟎𝟎𝟎𝑹𝑻𝒏𝒐𝒎𝑵𝑰𝒏𝒐𝒎
𝟐𝒛𝑭𝑷𝑨𝒊𝒓𝒏𝒐𝒎𝑽𝒊𝒎𝒑(𝑨𝒊𝒓𝒏𝒐𝒎).𝟎.𝟐𝟏 (12)
Assumption for Fuel and air at stack input:
If no fuel and air are present at the input of the stack it is
assumed that the stack is working at a fixed rate of fuel and air
utilization.
The stack is always supplied with bit more gases than stack
requirements. Flow rate regulator adjusts the supply of gases
according to the current. Current delivered by the stack is
limited by the flow rate of fuel and air.
Fuel cell dynamics:
The model also includes fuel cell dynamics; this is done by
including Flow dynamics and Response time(𝑇𝑑).
Charge Double Layer
The charge Double layer affects the Activation voltage (
𝑁𝐴𝐼𝑛(𝐼𝑓𝑐
𝐼𝑜) ), Charge double layer is the process in which
complex double layer of charges form between electrode and
electrolyte. The charge double layer factor is included in the
generic model by response time (𝑇𝑑) At 95%.
7) Modified Nernst voltage:
For modeling the effects of oxygen depletion, Voltage
undershoot ( 𝑉𝑢 ) and peak utilization of oxygen is used, Due
to which the Nernst voltage equation is also modified as
follows.
𝑬𝒏 = {𝑬𝒏 − 𝑲 (𝑼𝒇𝑶𝟐
− 𝑼𝒇𝑶𝟐(𝒏𝒐𝒎)) 𝑼𝒇𝑶𝟐
> 𝑼𝒇𝑶𝟐 (𝒏𝒐𝒎)
𝑬𝒏 𝑼𝒇𝑶𝟐≤ 𝑼𝒇𝑶𝟐
(𝒏𝒐𝒎)
(13)
𝑲 =𝑽𝒖
𝑲𝒄(𝑼𝒇𝑶𝟐 (𝒑𝒆𝒂𝒌)−𝑼𝒇𝑶𝟐(𝒏𝒐𝒎)
) (14)
VIII. SIMULATION ANALYSIS
Based on the simplified and detailed model of PEM fuel cell
stack .Simulation of circuit which models 45VDC, 6KW PEM
fuel cell stack connected with 100V DC/DC boost converter
fed to RL load is done. The outputs are observed under two
conditions.
Nominal fuel utilization.
Maximum fuel utilization.
For the first ten seconds the nominal fuel utilization is
maintained using a flow rate regulator. The Voltage and
current curve of fuel cell and DC/DC converter is observed at
scope as shown below.
International Journal of Engineering & Computer Science IJECS-IJENS Vol:13 No:03 34
137003-9292-IJECS-IJENS © June 2013 IJENS I J E N S
Fig. 4. Representing the scope results of current and voltage of the stack and
DC/DC converter.
After ten seconds the flow rate regulator is removed fuel flow
rate is increased to the maximum level.
This cause effects on stack efficiency, the fuel and air
consumption. Curves of stack efficiency, fuel and air
utilization and flow rate is shown on scope below.
Fig. 5. Representing the scope results of Flow rate, utilization of fuel, stack
consumption and efficiency.
XI. CONCLUSION In this paper MATLAB-Simulink Generic Model of PEM fuel
cell stack is analyzed. By analysis of this model it is found
that it is a concise model of PEM fuel cell. In this model PEM
fuel cell is broadly analyzed by keeping under consideration
almost all the parameters which affect the performance of
PEM fuel cell such as Flow rate, utilization of fuel and air,
Partial pressure of fuel and air, Humidity & Temperature of
stack, stack consumption of air and fuel. Further, the operation
of PEM Fuel cell stack is done under two conditions of
absolute and Nominal values of fuel and air utilization.
NOMENCLATURE
R Universal gas constant, 8.3145 J / (Mol K); F Faraday’s constant, 96485 A.s/Mol; T Stack temperature (K); En Nernst voltage (V); N Number of series fuel cells in the stack;
ΔG The size of the activation barrier which depends
on The type of electrode and catalyst used;
Kc Voltage constant at nominal condition of Operation;
z Number of moving electrons; α Charge transfer coefficient; k Boltzmann's constant = 1.38 × 10
–23 (J/K);
h Planck's constant = 6.626 × 10–34
(J.s);
𝑃𝐻2 Hydrogen partial pressure in the stack (ATM);
𝑃𝑓𝑢𝑒𝑙 Absolute supply pressure of fuel (ATM); 𝑃𝑎𝑖𝑟 Absolute supply pressure of air (ATM);
pairnom Nominal absolute air supply pressure (Pa);
Vlpm (fuel) Fuel flow rate (l/min); Vlpm (air) Air flow rate (l/min); x Percentage of hydrogen in the fuel (%); y Percentage of oxygen in the oxidant (%); w Percentage of water vapor in the oxidant (%); ηnom Nominal LHV efficiency of the stack (%); Vnom Nominal voltage (V);
𝑃𝑂2
Oxygen partial pressure inside the stack (ATM);
𝑃𝐻2𝑂
Partial Pressure of water vapors inside the stack
Inom Nominal current (A); I0 Exchange current (A);
Tnom Nominal operating temperature (K);
K Voltage undershoot constant; UfO2 (nom) Nominal oxygen utilization; E Nernst instantaneous voltage (V); E0 Open cell voltage (V); IFC Fuel cell stack current (A); Vlpm (air) nom Nominal air flow rate (l/min); Δh
0 (H2O (gas)) = 241.83 × 10
3 J/Mol.
PEM Proton exchange membrane
REFERENCES [1] C. Spiegel, “Pem Fuel Cell Modeling And Simulation Using Matlab
-.”
[2] G. Bucci, E. Fiorucci, F. Ciancetta, and F. Veglio, “Experimental Characterization and Modeling of PEM Fuel Cells under Dynamic
Load Variations,” vol. 5, no. 2, pp. 75–84, 2010.
[3] G. Bucci, F. Ciancetta, S. Member, E. F. Member, and F. Vegliò, “An Experimental Approach to the Modeling of PEM Fuel Cells in
Dynamic Conditions.”
[4] B. C. Vr-s, “AN INTRODUCTION TO FUEL CELLS AND HYDROGEN TECHNOLOGY Brian Cook Heliocentris 3652 West
5th Avenue Canada,” no. December, 2001.
[5] J. More, C. Kunusch, P. F. Puleston, and M. a Mayosky, “Characterization and experimental results in PEM fuel cell
electrical behaviour,” Society, vol. 35, no. 11, pp. 5876–5881, Jun.
2010. [6] MATLAB® Documentation (2009), Simpower Systems Demos. The
Mathworks, Inc.
BIOGRAPHY First author: Faheem Khan was born 28/May/1990 in Peshawar , Pakistan. And presently an undergraduate final year student of electrical power
engineering from Sarhad university of science and IT Peshawar , KPK,
Pakistan.
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