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World Applied Programming, Vol (3), Issue (7), July 2013. 264-281 ISSN: 2222-25102013 WAP journal. www.tijournals.com

264

An Intelligent, Fast and Robust Maximum Power PointTracking for Proton Exchange Membrane Fuel Cell

Iman Soltani Mohammad Sarvi Haniyeh MarefatjouFaculty of Technical & Engineering

Imam Khomeini InternationalUniversity

Iran

Faculty of Technical & EngineeringImam Khomeini International

UniversityIran

Faculty of Technical & EngineeringImam Khomeini International

UniversityIran

[email protected] [email protected] [email protected]

Abstract: Abstract of paper goes here. In this section, author is supposed to include three important parts. In thefirst part, it talks about the purposes of writing the paper. In the second part, methodologies that are been usedin paper, should be talked. Finally, in the third part, a brief overview of results should be presented. The lengthof abstracts is 1/20 of whole papers. Pay attention that it shouldn't be extended from 300 words. (Font: Times

New Roman 10pt) Ability of fuel cell systems to produce power is limited so it is necessary to force the systemto operate in conditions which match up with fuel cell (FC) maximum power point (MPP). MPP of FC is

changed with variation of its inputs and load. Therefore a MPP tracker which utilizes a maximum power pointtracking (MPPT) algorithm is necessary for tracking of MPP. This paper presents a particle swarm optimization(PSO) based MPPT algorithm for tracking of Proton Exchange Membrane fuel cell MPP (PEMFC) system. Inthis paper, many types of PSO include simple or conventional PSO, Improved PSO (IPSO), Quantum inspiredPSO (QPSO), Vector Evaluated PSO (VEPSO) and Particle Swarm Optimization with Time VaryingAcceleration Coefficients (PSOTVAC) methods are used to track MPP of FC. The MPPT algorithm determinethe duty cycle of the DC/DC boost converter in order to achieve MPPT. The results of the proposed methodsare compared with the conventional perturbation and observation (P&O) method. The results show that the

proposed methods have better characteristic and performance (fast response and high accurate) in comparisonwith P&O. Also among of the proposed PSO based algorithms, conventional PSO has the fast response wherePSOTVAC has the more accurate than other analyzed methods.

Keywords: Particle Swarm Optimization (PSO), Fuel Cell, Maximum Power Point Tracking, Energy storage

I. INTRODUCTION Fuel cells (FCs) are static electric power sources that convert the chemical energy of fuel directly into the electricalenergy. FCs have advantages such as high efficiency, zero or low emission (of pollutant gases), and flexible modularstructure [1, 2]. A large number of internal parameters can impact on produced voltage of FC [2-5], but in any condition,there is just one unique point on V-I curve which represents MPP. In this point, FC produces its maximum power. Owingto the limited ability of FC systems to produce power from available fuel flow, it is necessary to force the FC to operateat MPP. This can avoid excessive fuel consumption and low efficiency operation. A maximum power point tracking(MPPT) tracks the MPP of FC using a MPPT algorithm. The MPPT algorithm determines duty cycle of a DC-DCconverter and a certain amount of current which corresponds to MPP is extracted from FC. There are several methods tosearch MPP of optimum value of a function [6-9,10].

A good study about different MPPT methods such as Hill-climbing/ Perturb and Observe (P&O), incrementalconductance, fractional open-circuit voltage, fractional short-circuit current, fuzzy logic control, neural network, ripple

correlation control , current sweep, DC-Link capacitor droop control, load current or load voltage maximization, slidingmode control approach and other MPPT techniques for photovoltaic system may be found in [11]. Among themPerturbation and Observation (P&O) [6] is the most commonly used method because of its simple algorithm. MPPTmethods vary in complexity, implementation hardware, popularity, convergence speed and sensed parameters [12].Many MPPT methods have been applied to fuel cell for exacting maximum available powers from fuel cell modules,e.g., P&O [13-17], adaptive MPPT control [18], Moto compressor control technique [19], adaptive fuzzy logic controller[20], MPPT algorithm based on resistance matching between the direct methanol fuel cells internal resistance and thetrackers input resistance [21], voltage and current based MPPT [22], adaptive extremum seeking control [23]. The

particle swarm optimization (PSO) method has a simple structure that can be effectively used for MPP tracking. Hence

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several authors have attempted apply it; for example, in [24], PSO is applied in the constant bus voltage application.Despite its effectiveness, the algorithm developed by the authors cannot guarantee the tracking of GP for all differentconditions. In another work [25], an Adaptive Perceptive Particle Swarm Optimization (APPSO) is proposed for thesame constant bus voltage application. However, due to additional dimensional search space, the number of particlesneeds to be increased compared to its original counterpart [24]. The efficiency of a fuel cell as power generating systemcan be significantly improved by using optimum operating conditions.

In this paper two areas of significant interest are: first, the optimization of the electrochemical process, characterized bysome parameters with unknown values, which must be precisely determined in order to obtain accurate simulated results;and second, power electronic converters requires an adequate control in order to know the load applied to the fuel cellalso a fuel cell's output power have nonlinear behavior with variations voltage and current. The MPP is changed withchanging in behavior. In this paper, many types of PSO include simple or conventional PSO, Improved PSO (IPSO),Quantum inspired PSO (QPSO), Vector Evaluated PSO (VEPSO) and Particle Swarm Optimization with Time VaryingAcceleration Coefficients (PSOTVAC) methods are used to track MPP of FC. In order to perform the accuracy and

performance of the proposed method, the well-known P&O algorithm results are compared with the proposed MPPTmethods. Also this paper presents a detailed study of the MPPT controller to insure a high proton exchange membranefuel cell (PEMFC) system performance which can be selected for practical implementation issue. A simulation workdealing with MPPT controller, a DC/DC boost converter feeding a resistive load is achieved. Significant extracted resultsare given to verify the validity of the proposed various types of Particle Swarm Optimization scheme. In these worksdifferent types of Particle Swarm Optimization for MPPT in PEMFC, is presented and analyzed. The rest of this paper isorganized as follows: In section 2, modeling of proton exchange membrane fuel cell is introduced. MPPT concept isoutlined in section 3. Section 4, presents a brief introduction of PSO algorithm. The proposed MPPT methods are

presented in section 5. The results are presented and discussed in section 6.

I.1. Modeling of Proton Exchange Membrane Fuel CellThe proportional relationship between the flow of gas through a valve and the partial pressure can be stated as following:[6]

2

22

2 H

H

an

H

K M

K PqH

(1)

and

2

22

2 O

O

an

OK

M K

PqO (2)

Where qH 2 is molar flow of hydrogen (kmol S -1), PH 2 is hydrogen partial pressure (atm), is KH 2 hydrogen valve molar

constant 1atmS kmol , K an is anode valve constant

1atmS kgkmol , MH 2 is molar mass of

hydrogen

1kmolkg .

For hydrogen, the derivative of the partial pressure can be calculated by using the following perfect gas equation:

2 2 2 2( )in out r

H H H H an

d RT P q q qdt V

(3)

Where R is the universal gas constant ((1 mol)(kmol K -1)) , T is absolute temperature (K), V an is anode volume (1), 2in

H q is

hydrogen input flow (kmolS -1), 2out

H q is hydrogen output flow (kmol S -1), 2r

H q is hydrogen flow that reacts (kmol S -1). Theamount of hydrogen consumed in the reaction can be calculated from the following electrochemical principle:

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22

2r

H r NI

q k I F

(4)

Where N is the number of the series wound fuel cells in the stack, I is the stack current (A), F is Faradays constant

(C1k m o l ), K r is model constant

1( ( ) )k m o l s A .

When the output flow is replaced by Eq.1 and the Laplace transform is applied to Eqs.3 and 4, hydrogen partial pressurecan be rewritten in the s domain as:

2

2

2

2

1

( 2 )1

H in H H r

H

k P q k I

s

(5)

Where

2

2

an H

H

V k RT

(6)

By the same means, the equations for oxygen partial pressure can be derived as:

2

2

2

2

1

( )1

O inO O r

O

k P q k I

s

(7)

Where

2

2

caO

O

V k RT

(8)

Eq.5 describes the relationship between stack current and hydrogen partial pressure, and Eq.7 the shows relationship between stack current and oxygen partial pressure. As the load draws current, the reactantshydrogen and oxygen become depleted in the fuel cell stack, and both partial pressures drop accordingly.

To protect the fuel cell plant from reactants starvation, commonly excessive amounts of hydrogen and oxygen are

I k q I k q r in H r inO 2, 22 provided for the stack.A higher excess ratio leads to higher partial pressures, and then a higher fuel cell voltage. However, too much excessflow is a problem as it dries out the membrane and consumes much more parasitic power. [2-10] presented a high qualitystudy on how to control the excess ratio. They designed several airflow controllers to regulate the input flow rate so thatit is always twice as much as the reaction rate. To focus on the MPPT control problem, this paper will not go into detailson the excess ratio control issue but simply supply the fuel cell with a constant flow rate that is sufficient forconsumption [6].

I.2. Polarization curve modelThe fuel cell voltage as a function of current density in a steady state can be represented by a polarization curve, which is

influenced by such parameters as the cell temperature, oxygen partial pressure, hydrogen partial pressure and membranewater content. When current is drawn from a fuel cell, the cell voltage CellV decreases from its equilibrium

thermodynamic potential nernst E (open circuit voltage). This voltage drop consists of activation loss act , ohmic loss

ohmic and concentration loss con .The basic expression for the cell voltage is:

conohmicact nernst Cell E V (9)

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Reversible thermodynamic potential nernst E is described by the Nernst equation .With literature values for the standard-state entropy change, the expression is [6]:

2254 ln5.0ln10308.415.298105.8229.1 O H nernst PPT T E (10)

Activation overvoltage act is described by the Tafel equation, which can be expressed as:

I CoT T act lnln 42321 (11)

where _( i = 14) are parametric coefficients for each cell model. C O2 is the concentration of dissolved oxygen at thegas/liquid interface (mol cm

3), which can be calculated by means of

T P

C OO 498exp1008.5 62

2 (12)

Ohmic overvoltage ohmic results from the resistance of the polymer membrane in electron and proton transfers. It can be

expressed asmohmic IR (13)

The ohmic resistance R m is given by

A

t r R mmm (14)

where r m is membrane resistivity ( cm) to proton conductivity, t m membrane thickness (cm), A cell active area (cm 2).Membrane resistivity depends strongly on membrane humidity and temperature, and can be described by the followingempirical expression [6] .

T T A I

A I T A I r

m

m 30318.4exp3634.0

3030062.003.016.1815.22

(15)

where m is the membrane water content. The membrane water content is a function of the average water activity a m:

31),1(4.114

10,3685.3981.17043.0 32

mm

mmmmm

aa

aaaa (16)

The average water activity is related to the anode water vapor partial pressure Pv, an and the cathode water vapor partial pressurePv, ca:

sat

cavanvcaanm P

PPaaa ,,

21

21

(17)

The saturation pressure of water Psat can be figured out with the following empirical expression:

372510 104454.1101813.902953.01794.2log T T T Psat (18)

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The value of m varies between 0 and 14, which is equivalent to the relative humidity of 0% and 100%. Undersupersaturated conditions, however, the maximum possible value of m can be as high as 23. In addition, m can also beinfluenced by the membrane preparation procedure, the relative humidity of the feed gas, the stoichiometric ratio of thefeed gas, and the age of the membrane [6]. Hence, in this paper, m is considered as an adjustable parameter with a

possible value between 0 and 23. Concentration overvoltage con results from the concentration gradient of reactants asthey are consumed in the reaction. The equation for concentration overvoltage is shown by [6]

Ai I

nF RT

lcon 1ln (19)

where iL is the limiting current. It denotes the maximum rate at which a reactant can be supplied to an electrode.

Parameters of a typical fuel cell are shown in Table 1. These parameters are used for analysis and simulation in this paper. Fig.1 shows PEM fuel cell simulation model.

Table 1. Parameters of FC model [11]

ValueParameter

96484600F(Ckmol-1

) 8314.47R(jkmol -1K)35 N

232A(cm 2)9.0710 -8K r =N/4F4.2210 -5K H2(kmols -1atm)2.1110 -5Ko2(kmols -1atm)

3.37H2(s)6.47O2(s)

0.0178Tmem (cm)-0.9441

0.003542 7.810 -83

-1.9610 -44 2.0I

L(Acm -2)

Polarization curve

model

I

P H2

P O2

T cell

V cell

Figure 1. PEM fuel cell block diagram.

II. FUEL CELL M AXIMUM POWER P OINT T RACKING CONCEPT

A maximum power point tracker, tracks the maximum power point of FC using a MPPT algorithm. In the literature,there are many maximum power point tracking (MPPT) algorithms. Perturb and Observe (P&O) method is one of thesemethods [12].

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When a fuel cell is directly connected to an external load, its output power depends on both the internal electro-chemicalreaction and the external load impedance. The systems operating point is at the intersection of the fuel cells IP curveand the load line. There exists a unique operating point, called the maximum power point (MPP), at which the fuel cell

produces its maximum power, as illustrated in Fig. 2. According to the power transfer theory, the power delivered to theload is maximized when the fuel cell internal impedance equals the load impedance.

Figure 2. Typical fuel cell polarization and power curves.

Block diagram of the fuel cell MPPT system is shown in Fig.3. This system includes of a fuel cell, a DC/DC converter,a MPPT controller and load. With respect to dcdc converter topologies, the boost converter is considered because of itssimplicity, low cost and high efficiency as well as increasing of the load voltage. The terminal voltage of fuel cell iscontrolled by varying of DC/DC converter duty cycle. The MPPT controller determines a control signal D (duty cycle ofDC/DC converter) that maximum power is obtained from FC in normal condition and in the presence of disturbancessuch as load and system parameter variations .

Figure 3. Block diagram of the fuel cell MPPT system.

III. PSO ALGORITHM P RINCIPLE Kennedy and Eberhart [26], developed the PSO algorithm based on the behavior of swarms in the nature, such as birds,fish, and etc. The PSO has particles driven from natural swarms with communications based on evolutionarycomputations. PSO combines self-experiences with social experiences. In this algorithm, a candidate solution is

presented as a particle. It uses a collection of flying particles (changing solutions) in a search area (current and possiblesolutions) as well as the movement towards a promising area in order to get to a global optimum.

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where, C is constriction factor, c1i, c1 f and c2i, c2 f are initial and final values of c1 and c2, respectively. Under thissituation, the inertia weight is linearly decreasing as time grows and by changing the acceleration coefficients with timethe cognitive component is reduced and the social component is increased [36]. The large and small value for cognitiveand social component at the optimization process starting is permitted the particles to move around the search space,instead of moving toward the population best. In contrast, using a small and large cognitive and social component,respectively the particles are permitted to converge toward the global optima in the latter part of the optimization. Thus,PSO-TVAC is easier to understand and implement and its parameters have more straightforward effects on theoptimization performance in comparison with classic PSO. Using the above concepts, the whole PSO-TVAC algorithmcan be described as follows:

- For each particle, the position and velocity vectors will be randomly initialized with the same size as the problem dimension within their allowable ranges.

- Evaluate the fitness of each particle ( Pbest ) and store the particle with the best fitness ( Gbest ) value.- Update velocity and position vectors according to (21) and (22) for each particle.- Repeat steps 2 and 3 until a termination criterion is satisfied. Comparing the classic PSO, PSO-TVAC has the

following advantages:o Faster : PSO-TVAC can get the quality results in significantly fewer fitness evaluations and constraint

evaluations.o Cheaper : There is need to adjust a few parameter settings for different problems than the PSO.

V. T HE P ROPOSED PSO BASED MAXIMUM P OWER POINT TRACKING In order to investigate the performance of proposed models, the performance of the proposed method is compared withconventional tracking method. In the many conventional maximum power point (MPP) tracking methods usually theslope of P-V curve has been used. The slope is zero at the MPP, positive on the left of the MPP, and negative on theright. Based on negative or positive slope, error has been defined to achieve zero slop. Fig 6 shows the P-I curve of fuelcell in per unit and the positive or negative slope at the left or right side of MPP.

Figure 6. Power-Voltage characteristic fuel cell

The described PSO algorithm in preceding section is applied to realize the maximum power point tracking control of aFC system, where the P-V characteristic exhibits multiple local maximum power points.

In this work, a PSO algorithm is applied to track the MPP using the Competitive technique. In order to start theoptimization, a solution vector of Voltage with k particles needs to be de ned as follows in (25).

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equal to 343K. The FC output power, output current and output voltage are shown in Figs. 8, 9 and 10, respectively.The results of conventional P&O and the proposed methods are shown in Fig.11. Comparisons of these methods are

presented in Table 2. The Fig.11 and Table 2 show that the proposed methods have better performance in comparisonwith P&O. The all of proposed methods have lower rise time and settling time than the P&O method. Furthermore,the proposed methods can track the peak power more accurate than P&O. Fig.12 shows the power-current (P-I)characteristic of fuel cell in four different temperatures (310K, 330K, 350K, 360K). Fig.13 shows power-current (P-I)characteristic of fuel cell in two different value of the membrane water content ( m).

50 100 150 200 250 300 350 400 450 500 550 600500

1000

1500

2000

P O W E R ( w )

TIME(ms)

Figure 8. Output Power of FC .

0 100 200 300 400 500 6000

10

20

30

40

50

I ( A )

TIME(ms)

Figure 9. Output Current of FC.

50 100 150 200 250 300 350 400 450 500 550 60039

40

41

42

43

V ( v )

TIME(ms)

Figure 10. Output Voltage of FC.

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0 100 200 300 400 500 6001500

1550

1600

1650

1700

1750

1800

P O W E R ( w )

P&OQPSOIPSOVEPSOPSOTVACPSO

TIME(ms)

100 120 140 160 180 200 220 240 2601620

1630

1640

1650

1660

1670

1680

1690

1700

1710

P O W E R ( w )

P&O

QPSO

IPSOVEPSO

PSOTVAC

PSO

TIME(ms)

Figure 11. (a) Output power of FC with P&O and the proposed methods, (b) a zoom window of (a).

45 50 55 60 65 70 75 80 85 90 95-1000

0

1000

2000

I(Current(A))

P ( P o w e r ( w ) )

T=310kT=330kT=350kT=360k

Figure 12. The power-current (P-I) characteristic of fuel cell in different temperatures.

(b)

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45 50 55 60 65 70 75 80 85 90 950

500

1000

1500

2000

2500

I(A)

P ( w )

Landa=16Landa=12

Figure 13. The power-current (P-I) characteristic of Fuel cell in different m .

Table 2. Comparison of P&O and application PSO results at T=343K and 12 .

Applied Method PSOTVAC VEPSO IPSO QPSO PSO P&O AnalyticalAverage P FC value(w) 1719 1716 1711 1713 1710 1694 1742

Time to max(s) 3.45 3.56 3.54 3.34 3.23 21.6 -Accuracy(%) 98.67 98.50 98.22 98.33 98.16 97.24 100

Case 2: Pulsed variation of m In this section, temperature of FC is constant but m is changed. Fig.14 shows time variations of cell m . Also Fig.15

shows the time evolution of P_FC under fast variation of the FC m for the PSOTVAC method. Figs. 16, 17, 18, 19and20 also show this case for PSO, VEPSO, P&O, QPSO, IPSO methods, respectively. These results show that theVEPSO and QPSO method have more accurate and better response than P&O and conventional PSO methods and IPSO.

100 200 300 400 500 600

TIME(ms)

Figure 14. Variations of m

.

100 150 200 250 300 350 400 450 500 550 6001650

1700

1750

TIME

P o w e r - P

S O T V A C

Figure 15. Time evolution of PEM_FC under fast

100 150 200 250 300 350 400 450 500 550 6001650

1700

1750

TIME

P o w e r - P

S O

Figure 16. Time evolution of PEM_FC under fast

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0 100 200 300 400 500 600500

1000

1500

2000

TIME

P o w e r ( w )

QPSOIPSOVEPSOPSOPSOTVAC

250 260 270 280 290 300 310 320 330 340

1620

1640

1660

1680

1700

1720

1740

TIME

P o w e r ( w )

QPSO

IPSO

VEPSOPSO

PSOTVAC

Figure 22. (a) The time evolution of P_FC under fast variation of the Fuel Cell temperature in constant membrane water content 12 for both the proposed and the P&O methods; (b) a zoom window of (a).

VII. CONCLUSION The main purpose of this paper is to present a PSO based MPPT controller for capturing of maximum power from fuelcell. In this paper PSO, IPSO, VEPSO, PSOTVAC and QPSO based MPPT for fuel cell systems are presented and itsresults are compared with conventional P&O strategy. A system includes a PEMFC, a DC/DC boost converter, aresistive load and MPPT controller are considered, analyzed and simulated in MATLAB/SIMULINK environment.Simulations are performed for several cases (constant condition and variation of m and temperature). The proposedMPPT algorithms are accurate which have a fast dynamic response under rapid changing of the fuel cell temperature and m. Furthermore PSOTVAC method show the more accurate among the studied methods and PSO method has the fastresponse among the studied methods.

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NOMENCLATURE :

E NERNST NERNST VOLTAGE (V)

V ACT ACTIVATION VOLTAGE (V )

V O HMIC OHMIC VOLTAGE (V )

i (I =1,2,3,4) PARAMETRIC COEFFICIENTS

V C ON CONCENTRATION OVER VOLTAGE (V )

P H2

HYDROGEN PRESSURE (P A)

PO2

OXYGEN PRESSURE (P A)

T TEMPERATURE (K )

CO2

CONCENTRATION OF D ISSOLVED OXYGEN ( 3.mol cm )

R M OHMIC R ESISTANCE ( )

R M

MEMBRANE R ESISTIVITY ( cm )

A CELL ACTIVE AREA ( 2cm )

T M MEMBRANE THICKNESS (cm )

TABLE I. I L

LIMITING CURRENT ( A)

F FARADAY CONSTANT , 96487 CHARGE =MOL

m MEMBRANE WATER CONTENT

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