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World Applied Programming, Vol (3), Issue (7), July 2013. 264-281  ISSN: 2222-2510 2222-2510 ©2013 WAP journal. www.tijournals.com

An Intelligent, Fast and Robust Maximum Power Point Tracking for Proton Exchange Membrane Fuel Cell Iman Soltani

Mohammad Sarvi

Haniyeh Marefatjou

Faculty of Technical & Engineering Imam Khomeini International University Iran [email protected]   [email protected]  

Faculty of Technical & Engineering Imam Khomeini International University Iran [email protected]  

Faculty of Technical & Engineering Imam Khomeini International University Iran [email protected]  

Abstract: Abstract of paper goes g oes here. In this section, author is supposed to include three important parts. In the first part, it talks about the purposes of writing the paper. In the second part, methodologies that are been used in paper, should be talked. Finally, in the third part, a brief overview of results should be presented. The length of abstracts is 1/20 of whole papers. Pay attention that it shouldn't be extended from 300 words. (Font: Times  New Roman 10pt) Ability Ability of fuel cell sys systems tems to produce power is limite limited d so it is necessary to force the system to 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 point tracking (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. In this paper, many types of PSO include simple or conventional PSO, Improved PSO (IPSO), Quantum inspired PSO (QPSO), Vector Evaluated PSOmethods (VEPSO) and Particle Swarm Optimization Timedetermine Varying Acceleration Coefficients (PSOTVAC) are used to track MPP of FC. The MPPTwith algorithm the duty cycle of the DC/DC boost converter in order to achieve MPPT. The results of the proposed methods are compared with the conventional perturbation and observation (P&O) method. The results show that the  proposed methods have better charact characteristic eristic and perform performance ance ((fast fast response and high accurate) in comparison with P&O. Also among of the proposed PSO based algorithms, conventional PSO has the fast response where PSOTVAC 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 electrical energy. FCs have advantages such as high efficiency, zero or low emission (of pollutant gases), and flexible modular structure [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. Owing to the limited ability of FC systems to produce power from available fuel flow, it is necessary to force the FC to operate at 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-DC converter and a certain amount of current which corresponds to MPP is extracted from FC. There are several methods to search 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), incremental conductance, 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, sliding mode control approach and other MPPT techniques for photovoltaic system may be found in [11]. Among them Perturbation and Observation (P&O) [6] is the most commonly used method because of its simple algorithm. MPPT methods 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 the tracker’s input resistance [21], voltage and current based MPPT [22], adaptive extremum seeking control [23]. The  particle swarm optimization 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 different conditions. In another work [25], an Adaptive Perceptive Particle Swarm Optimization (APPSO) is proposed for the same constant bus voltage application. However, due to additional dimensional search space, the number of particles needs to be increased compared to its original counterpart [24]. The efficiency of a fuel cell as power generating system can 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 by some 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 cell also a fuel cell's output power have nonlinear behavior with variations voltage and current. The MPP is changed with changing 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 Varying Acceleration Coefficients (PSOTVAC) methods are used to track MPP of FC. In order to perform the accuracy and  performancee of the proposed method  performanc method,, the well-kn well-known own P&O algorithm results are compare compared d with the propose proposed d MPPT methods. Also this paper presents a detailed study of the MPPT controller to insure a high proton exchange membrane fuel cell (PEMFC) system performance which can be selected for practical implementation issue. A simulation work dealing with MPPT controller, a DC/DC boost conve converter rter feeding a resistive l oad is achieved. Significant extracted results are given to verify the validity of the proposed various types of Particle Swarm Optimization scheme. In these works different types of Particle Swarm Optimization for MPPT in PEMFC, is presented and analyzed. The rest of this paper is organized as follows: In section 2, modeling of proton exchange membrane fuel cell is introduced. MPPT concept is outlined in section 3. Section 4, presents a brief introduction of PSO algorithm. The proposed MPPT methods are  presented in section section 5. T The he results are p presented resented and discusse discussed d in sectio section n 6.  I.1. Modeling Modeling of Pro Proton ton Exchange Membran Membranee Fuel Cell The proportional relationship between the flow of gas through a valve and the partial pressure can be stated as following: [6]

qH 2 P H 2



K an

 K  H 

2

 M  H 2

 

(1)

and

qO2 PO2



K an  M O2

 K O

2

(2)

 

-1

Where qH2  is molar flow of hydrogen (kmol S ), PH2 is hydrogen partial pressure (atm), is KH 2 hydrogen valve molar 1

constant kmol atmS 

      

 

hydrogen  kg kmol  

 ,

K an  is anode valve constant

    1       kmol kg atmS   

, MH2  is molar mass of

  .  

1

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

d dt

P H2



RT  V an

r   ( qHin 2  qHou2t  qH  2)

(3)  

in Where R is the universal gas constant ((1 mol)(kmol K -1)), T is absolute temperature (K), Van is anode volume (1), q H  2 is q r  q out  hydrogen input flow (kmolS-1),  H  2 is hydrogen output flow (kmol S-1),  H  2  is hydrogen flow that reacts (kmol S-1). The amount of hydrogen consumed in the reaction can be calculated from the following electrochemical principle:

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q Hr 2



 NI 

2F 

 2kr I 

(4)  

Where N is the number of the series wound fuel cells in the stack, I is the stack current (A), F is Faraday’s constant   1 1 (C k m o l ), K r r   is is model constant ( 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 pressure can be rewritten in the s domain as:

1



P H 2

k  H 2

1    H 2 s

 2k r I )

(q Hin 2

 

(5)

 

Where

  H  2

V an



k H 2 RT 

(6)  

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

1

k O

(7) 2

 1   O s (q

PO 2

in2 O

 k r I )

Where

 O 2



   

2

V ca kO2 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 reactants–hy reactants–hydrogen drogen and oxygen–   become depleted depleted in the fuel cell stac stack, k, and bot both h partial pres pressures sures drop according accordingly. ly. To protect the fuel cell plant from reactants starvation, commonly excessive amounts of hydrogen and oxygen are

q

in O2 

in k r  I   , q H  2





2k r  I   provided for the st ack.

A higher excess ratio leads to higher partial pressures, and then a higher fuel cell voltage. However, too much excess flow is a problem as it dries out the memb membrane rane and cconsumes onsumes much more parasitic power. [2-10] presented a high quality study on how to control the excess ratio. They designed several airflow controllers to regulate the input flow rate so s o that it is always twice as much as the reaction rate. To focus on the MPPT control problem, this paper will not go into details on the excess ratio control issue but simply supply the fuel cell with a constant flow rate that is sufficient for consumption [6].  I.2. Polarization Polarization curv curvee model The fuel cell voltage as a function of current density in a steady state can be represented by a polarization curve, which is influenced influenc ed by such parameters as the cell temperature, oxygen partial pressure, hydrogen partial pressure and membrane water content. When current is drawn from a fuel cell, the cell voltage V Cell  decreases from its equilibrium thermodynamic potential  E nernst    (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: (9)



Cell

 E 

nernst 

     act 

266

ohmic



con  

 

 Iman Soltani, Soltani, et al. World World Applied Applied Programming, Programming, Vol Vol (3), No (7) (7),, July 2013 2013.. 

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

 E nernst   1.229  8.5  10

4

T    298   .15  4.308 10 5 T ln P H 2  0.5 ln PO 2   

(10)

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

 act    1   2T     3 T ln Co 2

  4 ln I   

(11)

where _(i = 1–4) are parametric coefficients for each cell model. C O2 is the concentration of dissolved oxygen at the − gas/liquid interface interface (mol cm 3), which can be calculated by means of

C O 2



PO 2

5.08 10  exp    498T  6

 

(12)

Ohmic overvoltage ηohmic results from the resistance of the polymer membrane in electron and proton transfers. It can be expressed as (13)    IR   ohmic

m

The ohmic resistance R m is given by

 Rm  

r m t m  A

 

(14)

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

             

  I  A 181.61  0.03  I   0.0062 T   A 303  r m   m  0.634  3  I  exp 4.18 T   303  A T  2



2.5

   

(15)

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

0.043  17.81am  39.85am2  36a m3 ,  m   14  1.4(am  1),

0  am

1   1  am  3

(16)

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

am

  1 P P 1  aan  aca   v ,an v ,ca 2

2

Psat 

 

(17)

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

log 10 Psat   2.1794  0.02953T   9.1813  10 5 T 2

267

 1.4454  10 7 T 3  

(18)

 

 Iman Soltani, Soltani, et al. World World Applied Applied Programming, Programming, Vol Vol (3), No (7) (7),, July 2013 2013.. 

The value of  λ  λm m varies between 0 and 14, which is equivalent to the relative humidity of 0% and 100%. Under supersaturated conditions, however, the maximum possible value of λ of λm m can be as high as 23. In addition, λ addition, λm m can also be influenced by the membrane preparation procedure, the relative humidity of the feed gas, the stoichiometric ratio of the feed gas, and the age of the membrane [6]. Hence, in this paper,  λm  λm is considered as an adjustable parameter with a  possible  possib le value between 0 and 23. Concentrat Concentration ion overvoltage ηcon results from the concentration gradient of reactants as they are consumed in the reaction. The equation for concentration overvoltage is shown by [6]

  RT  ln      1  i I  nF     A  l  

 con

(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 Fig.1 shows PEM ffuel uel cell sim simulation ulation mo model. del. Table 1. Parameters of FC model [11]

Parameter

Value

-1

F(Ckmol ) -1 R(jkmol K)  N 2 A(cm )

96484600 8314.47 35 232 -8

-1 K r =N/4F

9.07×10-5 4.22×10 2.11×10-5 3.37 6.47 0.0178 -0.944 0.00354 7.8×10-8 -4 -1.96×10 2.0

K H H2 2(kmols atm) Ko2(kmols-1atm) τH2(s) τO2(s) Tmem(cm) ζ1  ζ2  ζ3  ζ4  IL(Acm-2)

I

P H2

PO2

Polarization curve  model

V cell

Tcell

Figure 1. PEM fuel cell block diagram.

II. 

 

FUEL CELL MAXIMUM POWER POINT TRACKING 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 these methods metho ds [[12]. 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-chemical reaction and the external load impedance. The system’s operating point is at the intersection of the fuel cell’s I–P curve and the load line. There exists a unique operating point, called the maximum power point (MPP), at which the fuel cell  producess its max  produce maximum imum p power, ower, as illustrated in Fig. 2. Acco According rding to the power transfer theory theory,, the power deliv delivered ered to the load 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 dc–dc converter topologies, the boost converter is considered because of its simplicity, low cost and high efficiency as well as increasing of the load voltage. The terminal voltage of fuel cell is controlled by varying of DC/DC converter duty cycle. The MPPT controller determines a control signal D (duty cycle of DC/DC converter) that maximum power is obtained from FC in normal condition and in the presence of disturbances such as load and system parameter variations .

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

III.  PSO ALGORITHM PRINCIPLE  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 evolutionary computations. 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 possible solutions) as well as the movement towards a promising area in order to get to a global optimum.

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v ji 1 i 1  j

s

 wv ji  c1r 1 pbest   c2 r 2 g best   j

i   j

i 1  j

s v

 (20)

 

(21)

Where, C1  and C2 are the balance factors between the effect of self-knowledge and social knowledge in moving the  particle towards the target. Usually the value 2 is suggested for b both oth factors in the literature, rand is a random number  between 0 and 1, and different at each iteration,  best position within the swarm, swarm,

 is inertia weight,

w

 is the best position of a particle,

 pbest 

 is the

g best 

v ji  is the velocity of jth particle in ith  iteration, and S  ji  is the position of jth particle in ith 

iteration. The typical movement of particles in the optimization process is shown in Fig. 4.

Figure 4. Movement of particle in the optimization process.

Since, in the above algorithm, there is the possibility of particles movement to out of the problem space [27], an upper velocity bound for particle movement is specified. Flowchart of PSO algorithm is shown in Fig.5. One of the PSO  problemss is its tendency to a fast and p  problem premature remature conve convergence rgence in mid op optimum timum points points.. A lot of effort has been mad madee so far to solve this problem. For instance, in [15] the best value for w in Eq. 20 is set to 0.9. A passive swarm model can be added to the PSO in order to increase its efficiency, which is the PSO with passive congregation PSOPC. This term is the same as randomly selected particle from the current swarm and particle [16]. In PSOPC, grouping has two types: 1) Aggregation: which itself has two kinds. The first kind is passive aggregation in which a passive group is with a physical process; like planktons swarm floating on the water that the water flow keeps them together. The second kind is active aggregation in which the aggregation is performed by an absorbent source. The absorbent source may be food or water. 2) Congregation: This is different from aggregation. That is, the absorbent supply and not external and physical factors is the group forced by it. This type is also divided in two kinds: 1) Passive congregation in which there is an attraction from one particle to others but is not shown a social behavior. 2) Social congregation congregatio n in which there is a social behavior among the particles and they are strongly str ongly related to each other. Since in some groups there may be a selfish behavior in information sharing, e.g. fish school, a selfish behavior may lead in forming a passive group. Improved Particle swarm optimizer (IPSO) is based on PSOPC. Moreover, it uses a harmony search. It utilize a mechanism call fly-back in order to employ the constraints [17]. Quantum Quantum-inspired -inspired version of the PSO (QPSO) algorithm permits all particles to have a quantum behavior instead of the classical Newtonian dynamics assumed so far in all versions of the PSO. Hence, instead of the Newtonian random walk, some sort of “quantum motion” is imposed in the search process. When the QPSO is tested against a set of benchmarking functions, it demonstrates superior performance as compared to the classical PSO but under the condition of large population sizes. One of the most attractive features of the QPSO algorithm is the reduced number of control parameters. Strictly speaking, there is only one parameter required to be tuned in the QPSO [18]. [18].Vector Evaluated PSO (VEPSO) is a novel algorithm based on a multi-objective interaction sort of the PSO [19].VEPSO is a co evolutionary multi-objective variant of the popular PSO.

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Start

Initialize particles with random position and velocity vectors

For each particle`s position (P) evaluate fitness

If fitness(p) than fitness(Pbest) than Pbest=p

Set best of Pbest as Gbest  Update particles velocity and position

Figure 5. Flow chart of particle swarm optimization.

 

IV. PSO-TVAC CONCEPT   In the PSO, proper control of the two stochastic acceleration components: the cognitive component (c1) which corresponds to the personal thinking of each particle and the social component ( c2) which describes the collaborative effect of the particles, to obtain the global optimal solution is very important accurately and successfully. It should be noted that it is desirable that for cheering the particles to wander through the entire search space, without clustering around local optima during the early stages of the swarm-based optimization. On the other hand, in order to find the optimal solution effectively it is very important to enhancement convergence toward the global optima during the latter  processes [35]. Thus, a novel parame parameter ter automatio automation n strategy for the PSO concep conceptt called PSO with time vary varying ing acceleration coefficients is proposed, in this paper. The motivation for using this method is enhancement the global search in the early stage of the optimization stages and cheering the particles to converge toward the global optima at the end of it. All parameters including inertia weight and acceleration coefficients are varied with time (iterations) in Equation (20). Thus, in the PSO-TVAC the velocity is updated as follows: i 1  j

v

  iter  i i 1 1 1  f  i i  j  j  C  w  v   c  c  iter max  c    rand ()  Pbest   S   i  j

  iter   c2 f   c2 i   c2 i  iter max   i i  rand ()  Gbset  j  S  j    w  wmax

C  

2 2      

2

 4 

 wmin  . ,

(22)

 

wmax

 iter 

iter max

 

 wmin  

where

271

(23)

4.1     4.2   (24)

 

 Iman Soltani, Soltani, et al. World World Applied Applied Programming, Programming, Vol Vol (3), No (7) (7),, July 2013 2013.. 

where, C is constriction factor, c1i, c1 f and c2i, c2 f are initial and final values of c1 and c2, respectively. Under this situation, the inertia weight is linearly decreasing as time grows and by changing the acceleration coefficients with time the cognitive component is reduced and the social component is increased [36]. The large and small value for cognitive and 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 the optimization optim ization performance in comparison with classic PSO. Using the above concepts, t he whole PSO-TVAC algorithm can be described as follows: -  -  -  - 

For each particle, the position and velocity vectors will be randomly initialized with the same size as the  problem dimension wit within hin their allow allowable able range ranges. s. 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. Cheaper : There is need to adjust a few parameter settings for different problems than the PSO. o 

V. 

THE PROPOSED PSO BASED MAXIMUM POWER POINT TRACKING 

In order to investigate the performance of proposed models, the performance of the proposed method is compared with conventional tracking method.  In the many conventional  maximum power point (MPP) tracking  methods usually the slope of P-V curve has been used. The slope is zero at the MPP, positive on the left of the MPP, and negative on the right. Based on negative or positive slope, error has been defined to achieve zero slop. Fig 6 shows the P-I curve of fuel cell 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 a FC 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 the optimization, a solution vector of Voltage with k particles needs to be defined defined as follows in (25).  (25). 

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The objective function is the generated power 'P', which is the summation of power generated by each cell. Assuming that there is 'M' number of agents involved in the search process, the terminal voltage vector 's k ' changes in the following order and also computes the power 'P(s k )'at each stage.

...  s1

k   s2k   s3k   s M   ...   k 1 k 1 k 1  s1  s2  s M   ... k 

(25)

This process is continued until the global optimum is reached and in reached iteration the position and velocities are updated as per the relationships defined by Eqs. 21-22. In real time operation, the objective function 'F ' often changes due to load or system parameter variation. In this condition, the agents must be reinitialized to search for the new MPP again, if the initialization process is not implemented for the change in operating point due to load variations, 'P  best ' and 'g best ' cannot be updated automatically. As a result, the agents stop searching for new maximum power point. The PSO algorithm reinitializes the agents whenever the following two conditions are satisfied.

Psi1   Psi        Psi  F obj



 

Psi1

 Ps

i

swarm size

(26)

(27)

 

Equations 26 and 27 form the basis for convergence detection of agent and sudden change in input gas, respectively. After finding the output of exact amount power and voltage of fuel cell can be calculated Duty Cycle. The MPP tracker adjusts the operating point of the fuel cell to the maximum power ( Pmax ) by tuning of boost converter duty cycle.The DC/DC boost converter transfer function is obtained by considering of its steady state operation as follows:

 D  1 

V FC (iFC ) V o

(28)  

With the optimal duty cycle, DC - DC converter is set and can reach the maximum power point. Where d  is the duty cycle, V O   is the DC/DC boost converter output voltage and V FC    is the output Fuel cell voltage. The optimum duty cycle ( d opt ) is calculated from Eq.(28) with substitution of V FC     V mp  The flowchart of the PSO MPPT algorithm is shown in Fig.7.By changing the duty cycle of the boost converter appropriately we can match the source impedance with that of the load impedance for achieving MPPT. The results are indicative of the out performance of the proposed method. The main features of PSO based MPPT method can be summarized as: 1)  2)  3)  4) 

MPPT with variation of temperature MPPT with variation vari ation of inputs(Hydrogen gas, oxygen gas ) High accuracy Fast response

The proposed system is simulated in different conditions, and the results demonstrate appropriate performance of the system and controllers.

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Start In Initialization itialization o f particles

Evaluate fitness function(i.e FC out power) f i(t-1) and f i(t)

Finding of the pi,best:pi,best=MAX{f i(t-1),f i(t))}, i=1,2,...,N

Finding of the g best:g best=MAX{ pi,best   i=1,2,...,N}

Updating Upda ting of the velocities and position according (21) and (22)

No

Convergence critenia satisfied?

Yes

Outp utput: ut:Gbes Gbestt Imp,fgbest Vmp=Pmp/Imp

Pmp

End 

  Figure 7. The flowchart of the PSO MPPT algorithm

VI.  SIMULATIONS AND DISCUSSIONS  In order to investigate the performance of the proposed PSO based MPPT, a system includes a PEMFC, a DC/DC converter, a resistive load and MPPT control are considered, analyzed and simulated in MATLAB/SIMULINK environment (as shown show n in Fig.3 ). In order to obtain an operating operatin g point close to the MPP, the PEMFC’s PEMFC’s system usually employs a DC/DC converter into the control system. Simulations are performed for three following cases: Case 1: Constant 1: Constant temperature and λm  Case 2: Pulsed 2: Pulsed variation of λm  Case 3: Pulsed variation of fuel cell temperature

Case 1: Constant temperature and λ  In order to investigate the accuracy of the proposed MPPT algorithm and to compare its performance with P&O and

types of PSO MPPT method, the membrane water content ( λm) is considered equal to 14 and temperature is assumed

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equal to 343°K. 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 proposed methods have better pe performance rformance in comparison with 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 ( λm). 2000

    ) 1500    w     (     R     E     W     O     P1000

500

50

100

150

200

250

300

350

400

450

500

550

600

 

TIME(ms) Figure 8. Output Power of FC .

50 40

    ) 30     A     (     I 20 10 0 0

100

200

300

400

500

600

TIME(ms)

 

Figure 9. Output Current of FC.

43

42     )    v41     (     V 40 39

50

100

150

200

250

300

350

400

TIME(ms) Figure 10. Output Voltage of FC.

275

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1800 1750

    ) 1700    w     (     R     E1650     W     O     P1600

P&O QPSO IPSO VEPSO PSOTVAC PSO

1550

1500   0

100

200

3 00

4 00

5 00

60 0

TIME(ms)

1710 1700 1690

    )    w1680     ( 1670     R     E     W1660     O     P1650

P&O QPSO IPSO

1640

VEPSO PSOTVAC

1630

PSO

1620   1 00

1 20

1 40

160

1 80

2 00

2 20

240

2 60

TIME(ms) (b)

 

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

2000     )     )    w1000     (    r    e    w    o     P     ( 0     P

-1000 

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

45

50

55

60

65 70 I(Current(A))

75

80

85

90

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

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2500

Landa=16 Landa=12

2000

    ) 1500    w     (     P1000 500 0 

45

50

55

60

65

70

75

80

85

90

95

I(A)

 

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=343°K and

Applied Method Average PFC  value(w) Time to max(s) Accuracy(%)

PSOTVAC 1719 3.45 98.67

VEPSO 1716 3.56 98.50

IPSO 1711 3.54 98.22

QPSO 1713 3.34 98.33

PSO 1710 3.23 98.16

   12 . P&O 1694 21.6 97.24

Analytical 1742 100

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

 m for the PSOTVAC method. Figs. 16, 17, 18, 19

shows the time evolution of P_FC under fast variation of the FC

and20 also show this case for PSO, VEPSO, P&O, QPSO, IPSO methods, respectively. These results show that the VEPSO and QPSO method have more accurate and better response than P&O and conventional PSO methods and IPSO.

10 0

200

300

4 00

500

600

 

TIME(ms)

Figure 14. Variations of

 m

1750

1750

    C     A     V     T     O     S1700     P      r    e    w    o     P

    O     S     P      r    e1700    w    o     P

1650

1 00

15 0

200

250

30 0

350 TIME

4 00

4 50

500

5 50

600

1650 100

 

Figure 15. Time evolution of PEM_FC under fast 



150

200

250

300

350 TIME

400

450

500

550

600

Figure 16. Time evolution of PEM_FC under fast 

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 

CELL  m

VARIATION OF THE FUEL

variation of the fuel Cell m for the PSOTVAC method.

 FOR THE PSO 

METHOD. 1750

1720

    O     S1700     P     E     V      r    e    w1680    o     P

1700     O     P      r    e1650    w    o     P 1600

1660 100

150

200

250

300

350 TIME

400

450

500

550

600

 

1550

500

1000

1500

2000

2500

TIME

Figure 17. The time evolution of PEM_FC under fast

 m

variation of the Fuel Cell method.

 

Figure 18. The time evolution of PEM_FC under fast

 for the VEPSO

 m

variation of the Fuel Cell

 for the P&O method.

1720

1750

1700     O     S     P     I      r    e1680    w    o     P 1660

    O     S     P     Q   - 1700    r    e    w    o     P

1650 10 0

150

200

250

300

350 400 TIME

450

500

550

600

6 50

 

1640

Figure 19. The time evolution of PEM_FC under fast variation of the Fuel Cell

100

150

200

250

300

350 TIME

400

450

500

550

600

 

Figure 20. The time evolution of PEM_FC under fast

 m  for the QPSO method.

variation of the Fuel Cell

 m

 for the IPSO method.

Case 3: Pulsed variation of temperature In order to investigate the performance of the proposed method under variable the membrane water content (λ  (λ m), a  pulsed  pulse d variat variation ion for T is cons considered idered (a (ass show shown n in Fig Fig.21). .21). T The he simulati simulation on res results ults are sh shown own in F Fig.2 ig.22(a). 2(a). T This his figu figure re show showss the output power of FC for comparison of the conventional P&O method b y the proposed methods. In Fig. 22(b) a zoom window of Fig.22 (a) is presented. The proposed methods have lower rise time than the P&O method. Furthermore, the  proposed methods can track the peak power more more accurate.

360 decrease

   e    r 350    u     t    a    r    e    p340    m    e     t

increase

330

320

100

150

200

250

300

350

400

450

TIME(ms) Figure 21.  Time variations of PEM FC temperature.

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2000

1500     )    w     (    r    e    w    o     P 1000

QPSO IPSO VEPSO PSO PSOTVAC

500   0

100

200

300 TIME

400

500

600

1740 1720 1700

    )    w     (    r    e 1680    w    o     P1660 QPSO 1640

IPSO VEPSO

1620

PSO PSOTVAC  

2 50

26 0

270

28 0

290 TIME

3 00

310

3 20

330

3 40

    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 fuel cell. In this paper PSO, IPSO, VEPSO, PSOTVAC and QPSO based MPPT for fuel cell systems are presented and its results are compared with conventional P&O strategy. A system includes a PEMFC, a DC/DC boost converter, a resistive load and MPPT controller are considered, analyzed and simulated in MATLAB/SIMULINK environment. Simulations are performed for several cases (constant condition and variation of λ m  and temperature). The proposed MPPT algorithms are accurate which have a fast dynamic response under rapid changing of the fuel cell temperature and λ m. Furthermore PSOTVAC method show the more accurate among the studied methods and PSO method has the fast response among the studied methods.

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NOMENCLATURE:   E  NERNST  

 NERNST VOLTAGE (V)

 

ACTIVATION VOLTAGE (V )

V  ACT 

 

OHMIC VOLTAGE (V )

V O HMIC 

PARAMETRIC C OEFFICIENTS 

 i  (I =1,2,3,4)  

V CC ON    N  O

CONCENTRATION OVER VOLTAGE(V )

 

HYDROGEN

P H2

 

PO2

PRESSURE (P A)

OXYGEN PRESSURE ( P A)

T  

TEMPERATURE(K )  

3 CONCENTRATION OF DISSOLVED OXYGEN( mol mol .cm  )

CO2  R M  

E SISTANCE(  ) OHMIC R ESISTANCE

 

MEMBRANE R ESISTIVITY ESISTIVITY( cm )

 R M 

 A 

2

CELL ACTIVE AREA ( cm )

 

MEMBRANE THICKNESS ( cm )

T   M 

TABLE I.

F  

 m  

 

 I   L

 A)  LIMITING CURRENT ( A

FARADAY CONSTANT, 96487  CHARGE=MOL  MEMBRANE WATER CONTENT 

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 Nehrir.H, Caishen C aisheng g Wang Wang,, Shaw, S.R, 2006. “Fuel cells: promising promising devices for distribu distributed ted generation generation”, ”, IEEE Power and Energy Magazine, Vol. 4, Issue 1, pp. 47-53. Caisheng Wang, Hashem Nehrir, Steven R. Shaw, 2005. “Dynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuits”,IEEE Trans Energy Conversion, Vol. 20, No.2. J. Larminie and A. Dicks, 2001. “Fuel Cell Systems Explained” New York, Wiley. R.F.Mann, J.C. Amphlett, M.A.I. Hooper, H.M. Jensen, B.A. Peppley, P.R.Roberge, 2000. “Development and application of a generalised steady-state electrochemical model for a PEM fuel cell”, J. Power Sources,Vol. 86, No.1–2, pp. 173–180. M.Y. El-Sharkh, A. Rahman, M.S. Alam, P.C. Byrne, A.A. Sakla, T.Thomas, 2004. “A dynamic model for a stand-alone PEM fuel cell power plant for residential applications”, J. Power Sources, Vol. 138, No. 1–2, pp. 199–204. Zhong Zhi-dan, Huo Hai-bo, Zhu Xin-jian,Cao Guang-yi, Ren Yuan, 2008. “Adaptive maximum power point tracking control of fuel cell power plants”, J. Power Sources, Vol. 176, pp. 259–269. O. Wasynczuck, 1983. “Dynamic Behavior of a Class of Photovoltaic Power Systems”, IEEE Trans. Apparatus and Systems, Vol. PAS-102, No. 9, pp. 3031-3037. K. Hussein, I.Muta, T.Hoshino, and M. Osakada, 1995. “Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Conditions”, IEE Proc.-Generation, Transmission, Distribution, Vol. 142, No.1, pp. 59-64. T.Noguchi, S.Togashi, R.Nakamoto, 2002. “Short-Current Pulse-Based Maximum-Power-Point Tracking Method for Multiple Photovoltaic and Converter Module System”, IEEE Trans. on Industrial Electronics, Vol. 49, pp. 217-223.

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