fuel cell

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



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)



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.



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.

fuel cell

Engineering

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