The parameter identification of the Nexa 1.2 kW PEMFC's model using particle swarm optimization

Renewable Energy 82 (2015) 26e34

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The parameter identification of the Nexa 1.2 kW PEMFC's model using particle swarm optimization Reem Salim, Mahmoud Nabag, Hassan Noura*, Abbas Fardoun Department of Electrical Engineering, United Arab Emirates University, P.O.Box:15551, Al Ain, United Arab Emirates

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 June 2014 Accepted 4 October 2014 Available online 25 October 2014

People's extensive and ignorant lifestyles impose an increasing amount of destruction on the environment, which lead to an increased governmental and research interest towards the development and use of green technology such as fuel cells. Fuel cells are recently receiving a major share of research interest due to their promising features. This paper presents an offline parameter identification approach based on particle swarm optimization (PSO) to identify the mathematical modeling parameters of the Nexa 1.2 kW proton exchange membrane fuel cell (PEMFC) system. The goal of this work is not to get a new technique in modeling, but rather to obtain a very good model of the PEMFC system using a simple and fast heuristic approach that requires minimal mathematical effort. This model can then be utilized to perform further analysis and fault diagnosis studies on PEMFCs. The proposed approach uses basic fitting to determine some of the initial values for the PSO, while the rest of the initial values are set to be chosen randomly. The developed model is then successfully validated using actual experimental data sets. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Fuel cells Proton exchange membrane Parameter identification Voltage model Thermal model PSO

1. Introduction Fossil fuels have been the main source of power for humanity for many years. However, the use of fossil fuels in power generation resulted in many negative environmental consequences, which lead to the exploration of alternative power sources that are efficient energies with an unlimited fuel supply and produce zero to minimal pollutants. Although United Arab Emirates (UAE) is considered as one of the world's largest fossil fuels suppliers, and despite the fact that their fossil fuel resources are extensive; their increasing environmental and pollution awareness in the past few years is pushing the decision makers towards the exploration of green technologies. Thus, fuel cells tended to attract a lot of research interest in the past decade; therefore they are undergoing major research and testing to study their compatibility with the hot and humid climate of the Gulf region. A fuel cell (FC) is an electrochemical device that converts the chemical energy of a fuel directly into DC electrical energy. This promises power generation with high efficiency since the intermediate steps of producing heat and mechanical work typical of most conventional power generation methods are avoided.

* Corresponding author. E-mail addresses: [email protected], [email protected] (H. Noura). http://dx.doi.org/10.1016/j.renene.2014.10.012 0960-1481/© 2014 Elsevier Ltd. All rights reserved.

Moreover, fuel cells have low environmental impact because combustion is avoided. Hence, fuel cells produce power with minimal pollutants. The basic physical structure, or building block, of a fuel cell consists of an electrolyte layer sandwiched between an anode and a cathode [1]. Fig. 1 gives a schematic representation of a single fuel cell with the reactant/product gases and the ion conduction flow directions through the cell. In a typical fuel cell, fuel is fed continuously to the anode (negative electrode) and an oxidant (often oxygen from air) is fed continuously to the cathode (positive electrode). The electrochemical reactions take place at the electrodes to produce an electric current through the electrolyte, while driving a complementary electric current that performs work on the load [1]. However fuel cells are very complex systems that require a high degree of reliability. The modeling methodology presented in this paper could serve as a guide in modeling any other PEM fuel cell system. Moreover, the developed model can be utilized to design and improve the PEM fuel cell system under study as well as being used to develop a reliable fault diagnosis study. Several experiments were conducted on the 1.2 kW Nexa fuel cell system at varying load. The voltage and temperature responses of the system were then recorded. The I/V characteristics of one of the experimental data sets were matched by identifying 13 different modeling parameters using particle swarm optimization (PSO); while the system's temperature response was matched by

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work presented in Ref. [11] proposed a parameter optimization technique of PEMFC models based on a hybrid PSO in order to optimize their highly sensitive model parameters. Most of the standard PEMFC modeling equations and modeling approaches available in literature depend on several physical parameters of the system, such as the thickness of the membrane, the active membrane area, the geometric cell area and the volumes of the cathode and the anode. However, since such parameters are not always available for several reasons such as confidentiality issues with the manufacturer; an alternative formulation of the PEMFC model was employed. 3. PEM fuel cell modeling

Fig. 1. The schematic diagram of a fuel cell.

identifying 5 different parameters using PSO. Other experimental data sets were then used to validate the obtained model. The resulting model was found to highly resemble the actual voltage and temperature characteristics of the system. This paper is organized as follows: A general overview on previous studies in the area is presented in the next section followed by a brief overview on the Nexa 1.2 kW PEMFC system and the mathematical modeling equations. The proposed parameter identification process of the system's model is then presented and validated. The paper is then ended by concluding remarks. 2. Previous studies Evolutionary algorithms helped solving a lot of difficult, computationally demanding modeling and parameter identification problems in the past few decades with almost no computational effort at all. However, only a few researches in the area of parameter identification of PEMFCs using PSO exist in literature. Qi et al. [2e5] used adaptive focusing particle swarm optimization (AFPSO) based on the balance characteristic between global search and local search of PSO to optimize the mechanism model parameters of a PEMFC system. Hu et al. [6,7] on the other hand, used a neural networks based on PSO to model their PEMFC stack. In Ref. [8] the PEMFC was broken into a mechanism sub-model and a black box sub-model, and PSO was then used to optimize the parameters of the mechanism sub-model, whereas the black-box sub-model was expressed in nonlinear autoregressive exogenous (NARX) form using a wavelet network and experimental data. Chibante and Campos [9] noted that PEMFC model is characterized by technological and empirical parameters; which makes it hard to identify the model parameters that will provide precise simulation results in a wide range of operating conditions. Thus, they used PSO to extract the correct parameter values which helped minimize the difference between experimental and simulated results. The work done on Ref. [9] is similar to the approach of this paper in some aspects; however in Ref. [9], they model their fuel cell system's behavior based on fixed operating temperature conditions, whereas the presented work in this paper considers the voltage performance of the system under varying temperature values. On the other hand, Askarzadeh and Rezazadeh [10] used a modified particle swarm optimization (MPSO) to optimize an electrochemical-based PEMFC mathematical model where the inertial weight was calculated according to the distance from the particle to that of the best solution of the entire swarm. Another

The basic concept behind the operation of all types of fuel cells is the conversion of the chemical energy stored in the chemical bonds between the atoms and the molecules of a certain fuel into electrical energy. The PEMFC under study uses hydrogen gas supplied from pressurized hydrogen cylinders as the anode fuel, and atmospheric air supplied by a blower as the cathode fuel. 3.1. PEMFC output voltage For a PEMFC with the following overall reaction and with the output water in liquid form:

1 H2 þ O2 /H2 OðlÞ 2

(1)

its internal potential (the voltage across the fuel cell electrodes; also known as the reversible cell potential) is given by the following Nernst equation [12]:

Ecell ¼ E0;cell þ

 RT  0:5 ln PH2 PO 2 2F

(2)

where: E0,cell is the reference potential R is the gas constant (8.3143 J/[mol K]) T is the fuel cell temperature (K) F is Faraday constant (96,487 C/mol) PH2 is pressure of hydrogen (atm) PO2 is pressure of oxygen (atm) The reference potential E0,cell is a function of temperature and can be expressed as:

E0;cell ¼ E0;cell  kE T  298




(3)

where E0;cell is the standard reference potential at the standard state of a 25  C and 1 atm pressure, and kE is an empirical constant equal to (8.5  104 V/K). E0;cell is given by Ref. [1]:

E0;cello ¼

DG nF

(4)

where n is the number of electrons per mole of fuel and DG is the Gibbs free energy of the fuel cell reaction at the standard reference temperature and pressure and it is given by Ref. [1]:

DG ¼ DH  TDS

(5)

where H is the enthalpy and S is the entropy. The standard enthalpy and entropy of water, hydrogen and oxygen are given in Table 1. Solving (4) and (5) leads to:

 DG ¼

     1 1  T SH2 OðlÞ  SH2 þ SO2 hH2 OðlÞ  hH2 þ hO2 2 2

28

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Table 1 Standard thermodynamic properties.

H2O (l) H2 O2

Vact1 ¼ h0 þ ðT  298Þ,a

Enthalpy, H (J/mol)

Entropy, S (J/(mol K))

285,826 0 0

69.92 130.68 205.14

Vact2 ¼ T,b lnðIÞ

E0;cello

237; 153:66 J=mol ¼ 1:229J=C ¼ 1:229V ¼ 2  96; 487C=mol

(6) (7)

3.2. PEMFC voltage drops The output voltage of the PEMFC is less than the internal voltage Ecell developed inside the fuel cell due to several voltage drops, namely: activation voltage drop, ohmic voltage drop, and concentration voltage drop (see Fig. 2). Activation and concentration voltage drops occur at both the anode and the cathode, while the ohmic voltage loss represents the resistive losses throughout the entire fuel cell. Activation voltage drop: The activation voltage losses are caused by sluggish electrode kinetics. In both electrochemical and chemical reactions there is an activation energy that must be overcome by the reacting species. The activation losses are the result of complex surface electrochemical reaction steps. Each step has its own reaction rate and activation energy which controls the activation losses on the electrodes. However, the voltage drop due to the activation polarization can be approximated by the following Tafel equation [1]:

Vact;cell ¼

  RT I ln ¼ T,½a þ b lnðIÞ anF I0

(8)

where: a is the electron transfer coefficient of the reaction. n is the number of electrons participating in the reaction (2 e/ mol). I is the load current. I0 is the exchange current density. Equation (8) can also be described as a sum of two voltage drops, Vact1 and Vact2 as follows [12]:

Vact;cell ¼ h0 þ ðT  298Þ,a þ T,b lnðIÞ ¼ Vact1 þ Vact2

(10)

where h0, a and b are empirical constants. Moreover, Vact2 can also be expressed as [12]:

Vact2 ¼ Ract I ¼ ðRact0 þ Ract1 þ Ract2 ÞI DG ¼ 237; 153:66

(9)

(11)

where: Ract0 is an empirical constant. Ract1 is a current dependent polynomial. Ract2 is temperature dependent and has the form b(T  298) where b is an empirical constant. Ohmic voltage drop: Ohmic losses occur because of the resistance to the flow of ions in the electrolyte as well as the resistance to the flow of electrons through the electrode. The dominant ohmic losses through the electrolyte are usually reduced by decreasing the electrode separation and enhancing the ionic conductivity of the electrolyte. These ohmic losses are expressed as [1]:

Vohm;cell ¼ IRohm

(12)

where Rohm is the total cell resistance and it is dependent on both the fuel cell temperature and the current, thus, it can be expressed as:

Rohm ¼ Rohm0 þ Rohm1 þ Rohm2

(13)

where: Rohm0 is an empirical constant Rohm1 has the form g1I where g1 (U/A) is an empirical constant Rohm2 has the form g2(T  298) where g2 (U/K) is an empirical constant. Concentration voltage drop: During the reaction process, concentration gradients can be formed due to mass diffusions from the gas flow channels to the reaction sites (at the catalyst surfaces). At high current densities, there will be slow transportation of reactants to the reaction sites which is the main reason for concentration voltage drop [12].

Vconc;cell ¼ 

    RT C RT I ln S ¼  ln 1  nF nF Ilimit CB

(14)

where: CS is the surface concentration at the reaction sites. CB is the bulk concentration in the gas channels Ilimit is the fuel cell current limit (A) 3.3. PEMFC stack temperature The chemical reactions that occur inside the fuel cell generate heat energy which in turn causes the fuel cell's temperature to rise or fall. The thermodynamic energy balance equation of a PEMFC can be written as [12]:

qnet ¼ qchem  qelec  qsensþlatent  qloss

(15)

where qnet is the net heat energy (J), qchem is chemical energy (J), qelec is the electrical energy (J), qsensþlatent is the sensible and latent heat (J), and qloss is the heat loss (J). The heat generated from the chemical reaction is a function of the Gibbs free energy and the rate of consumption of hydrogen [11,13], as follows:

q_ chem ¼ NH2 ;consumed ,DG,N

Fig. 2. Ideal and actual fuel cell voltage current characteristics.

(16)

where DG is the Gibbs free energy (J/mol) which was calculated in (6), N is the number of cells in the PEMFC stack and NH2 ;consumed is

R. Salim et al. / Renewable Energy 82 (2015) 26e34

the rate of hydrogen consumed (mol/s) which can be represented by Ref. [12]:

NH2 ;consumed ¼

I 2F

(17)

Similarly, the rates of consumption of oxygen and water in (mol/ s) can be represented by Ref. [12]:

NO2 ;consumed ¼

(18)

I 2F

(19)

The output electrical power is given by:

q_ elec ¼ Vout ,I

(20)

The sensible and latent heat energy on the other hand is expressed as [12]:

q_ sensþlatent ¼ N_ H2 ;out ðT  Troom Þ,CH2 þ N_ O2 ;out ðT  Troom Þ,CHO2 þ N_ ðT  Troom Þ,C H2 O;generated

H2 O;l

þ N_ H2 O;generated ,HV (21) where: T is the stack temperature Troom is the room (ambient) temperature Ni is the flow rate of i in (mol/s) Ci is the specific heat capacity of i in ðJ=mol KÞ Hv is the vaporization heat of water (J/mol) Finally, the heat loss which is mainly transferred by air convection can be represented by Ref. [12]:

q_ loss ¼ hcell ðT  Troom ÞNAcell

(22)

where: Acell is the cell's area (1.2  102 m2) hcell is the convective heat transfer coefficient ðW=m2 KÞ The fuel cell temperature would rise or drop according to the net heat as follows:

dT 1 ¼ q_ dt MFC CFC net

developed EAs are: genetic algorithms (GA), particle swarm optimization (PSO), and ant colony optimization (ACO). However, in several works such as Refs. [14,15], it was found that PSO outperforms other EAs in terms of terms of success rate, solution quality and processing time. Therefore, PSO was utilized in identifying the PEMFC system modeling parameters. 4. Particle swarm optimization

I 4F

NH2 O;generated ¼

29

(23)

where: MFC is the mass of the fuel cell's stack (13 kg) CFC is the overall specific heat capacity of the stack ðJ=mol KÞ In order to identify and optimize the parameters of the Nexa 1.2 kW PEMFC system model and match its actual voltage and temperature characteristics with those of the mathematical model using a fast and effective method that requires minimal mathematical effort, evolutionary algorithms (EAs) were to be explored. Evolutionary algorithms (EAs) are generic population-based meta-heuristic optimization techniques. They use certain mechanisms inspired by biological evolution (e.g. survival of the fittest, mutation, reproduction, swarming, etc.). EAs start with a population of multiple possible candidate solutions to the optimization problem, and the fitness function determines the environment within which the solutions live. Evolution of the population then takes place after the repeated application of the algorithm's operators [13]. EAs are known to be very successful in finding/approximating solutions to all types of problems because of their generality. This lead to the employment of EAs in many fields, such as engineering, art, biology, economics, genetics, operations research, robotics, social sciences, physics, and chemistry [13]. Examples of well-

Particle swarm optimization (PSO) is an EA that was developed in 1995 by Eberhart and Kennedy [16]. It mimics the swarming behaviors of some living creatures such as flocks of birds, schools of fish, and herds of animals. The swarming behavior helps those creatures in avoiding predators and food search. This is achieved through constant communication and coordinated decision making between all the particles in the swarm [17]. PSO is conceptually simple and computationally efficient. The following steps summarize the PSO algorithm's procedure [17]: 1. Initialize a population of particles with predefined or random positions xi(1) and velocities vi(1) on a D dimensional space. 2. Evaluate the fitness function for each particle with respect to the initial D variables. 3. Compare the particles fitness values with pbest (the personal best fitness value a particle has achieved so far). If current value is better, then update pbest and set pi to equal the current position xi in the D Dimensional space. 4. Identify the particle with the best success so far and assign its fitness value to variable gbest (for global best) and its position to variable G. 5. Change the velocities and positions of each particle according to the following two equations:

vi ðk þ 1Þ ¼ fk vi ðkÞ þ c1 g1i ðpi  xi ðkÞÞ þ c2 g2i ðG  xi ðkÞÞ

(24)

xi ðk þ 1Þ ¼ xi ðkÞ þ vi ðk þ 1Þ

(25)

where i is the particle's index number. k is the iteration number vi is the velocity of the ith particle xi is the position of the ith particle pi is the personal best position of the ith particle G is the global best position of the swarm g1,2i are random numbers on the interval [0 1] f is the inertial weight function c1,2 are acceleration constants 6. Loop to step 2 until a sufficiently satisfactory fitness value or a maximum number of iterations is reached. The inertial weight f in the PSO's velocity equation decreases with every iteration. In this work, f was set to decrease according to the following function:

 ðk  1Þ  fk ¼ wi þ wf  wi Nw  1

(26)

where wi and wf are the initial and final inertial weights respectively and Nw is the iteration when the inertial weight is supposed to reach its final value [18]. By decreasing the inertial weights at the final iterations in the PSO's algorithm, the effect of the particle's velocity on the particle's position decreases while increasing the effect of the particle's best achieved fitness value so far as well as the effect of the global best

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R. Salim et al. / Renewable Energy 82 (2015) 26e34

Fig. 5. The experimental polarization curve of the Nexa 1.2 kW PEMFC system.

characteristics of this experimental data set, all the different parameters in the three voltage drops should be identified. The concentration voltage drop was directly calculated from (14) using Ilimit of 75 A, which is the maximum allowable current of the Nexa system as per the data sheet of the system. 5.1. Voltage model

Fig. 3. The Nexa 1.2 kW PEMFC system at UAE University.

achieved fitness value of the swarm. Therefore, this process helps in fine tuning the results of the PSO search at the final iterations. 5. Parameter identification Several experiments were conducted on the Nexa 1.2 kW PEMFC system of Fig. 3, and the dynamic response of the system was recorded under variable operating points. The Nexa 1.2 kW PEMFC system has 47 cells, thus, the stack's internal potential becomes:

EStack ¼ 47  Ecell

(27)

In the modeling data set, the load current was varied linearly in time from 0 to 60 A as depicted in Fig. 4. In order to match the I/V

Fig. 4. Current input to the modeling experimental data set.

The activation and ohmic voltage drops on the other hand were identified using the same methodology represented in Refs. [19,20]. By looking at the system's voltageecurrent relationship of Fig. 5 and comparing it with Fig. 2, it can be deduced that at low current values, the voltage drop seen in Fig. 5 is mainly due to activation polarization, whereas at high current values, the concentration polarization dominates the fuel cell's voltage drops. Moreover, the linear voltage drop in the middle of the graph is mainly due to ohmic (resistances) polarization. To model the activation and ohmic voltage drops, they were first plotted from the experimental data set using (28) with respect to current and then fitted into the 7th degree polynomial in (29) as depicted in Fig. 6.

Vact þ Vohm ¼ Estack  Vout  Vconc

(28)

Vact þ Vohm y6:811  1011 I 7  1:7295  108 I 6 þ 1:8013  106 I 5  9:9475  105 I4 þ 0:0031645  0:060163I 2 þ 0:76211I þ 25:54 (29)

Fig. 6. Ohmic and activation voltage drops versus current.

R. Salim et al. / Renewable Energy 82 (2015) 26e34 Table 2 PSO parameters settings used for identification in MATLAB.

31

Table 3 Optimal model parameters results of PSO.

PSO parameter

Value

Parameter

PSO optimization result

Number of particles c1 and c2 Maximum particle velocity (vmax) wi wf Nw

100 2 20 0.9 0.2 1000

Vact1 Ract

26.5230  8.9224  102 (T  298) 1.0526 þ 6.945  1011I6  1.7272  108I5 þ 1.7772  106I4  9.8133  105I3 þ 3.1430  103I2  3.5320  102I þ 1.3899  103 (T  298) 1.7941 2.3081  102I 2.0060  103 (T  298)

Rohm0 Rohm1 Rohm2

Fig. 7. The convergence plot of the PSO when initialized using basic fitting. Fig. 9. PSO model's output voltage versus experimental output voltage.

The linear part in the middle of Fig. 6 was divided by the current and fitted into a linear line to resemble the resistance of the ohmic voltage drop. The resulting linear line best fit is given below:

PSOfitness function ¼ Vout;actual  Vout;PSO ∞

(31)

Note that both the fitting polynomials of (29) and (30) neglect the temperature effect on the activation and ohmic voltage drops. Thus, those current dependent polynomials were used as initial value input to one of the PSO particles whereas the initial values of the temperature coefficients as well as the initial values of the rest of the PSO particles were set to be chosen randomly by MATLAB. The PSO can therefore find the optimal set of system parameters that best describe the Nexa 1.2 kW PEMFC system while incorporating the temperature effect on the voltage drops. Table 2 presents the PSO parameter settings used in the identification process in MATLAB. The fitness equation used to optimize the model in PSO was set to be the H∞ norm of the error between the experimental stack output voltage and the model's stack output voltage:

The PSO identification program in MATLAB was run several times to ensure the accuracy and the reproducibility of the obtained results. The PSO converged at an H∞ norm fitness value of 0.175 V in all tries. The convergence took place in about 1700 iterations as depicted in Fig. 7 which is equivalent to a convergence time of 63 s at a rate of 27 iterations per second. The fact that basic fitting was used to initialize some of the modeling parameters has a major effect on reducing the convergence time of the PSO since the number of parameters that are to be identified is large. The initialization therefore helps in guiding the PSO towards the solution space. Fig. 8 shows the convergence plot of the PSO when all particles are set to be initialized randomly by MATLAB. Note that in that case, even after 20,000 iterations, the PSO is still far away from the optimal solution. Table 3 presents the resultant optimal model parameters of the system obtained by initialized PSO, whereas Fig. 9 compares the

Fig. 8. The randomly initialized PSO convergence plot.

Fig. 10. PSO convergence plot.

Rohm y  0:028488 I þ 1:9249

(30)

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R. Salim et al. / Renewable Energy 82 (2015) 26e34 Table 4 Optimal model parameters results of PSO. Parameter

Value

CFC h K1 K2 K3

282.8416 19.6434 10.3597 0.3259 4.7337

(21), it has many unknown parameters. However, from the consumption and generation rates of (17)e(19), the sensibility and latent heat representation can be simplified into the following form:

q_ sensþlatent ¼ ðK1 þ K2 IÞðT  Troom Þ þ K3 I

(32)

where: K1 ¼ N_ H2 ;out ,CH2 þ N_ O2 ;out ,CHO2 K2 I ¼ N_ H2 O;generated ,CH2 O;l K3 I ¼ N_ H2 O;generated ,Hv Using a 4th order RungeeKutta representation of (23) with (16), (20), (22) and (32); five different parameters were identified using PSO in MATLAB and the following fitness function:

PSOfitness function ¼ kTactual  TPSO k∞

Fig. 11. PSO model's stack temperature versus experimental stack temperature.

PSO models' output voltage to the experimental output voltage. Note that the simulation results lie on top of the experimental data. Note that in the Ract representation of Table 3, the (1011) power as well as all other powers in the equation cannot be ignored since they are multiplied by powers of the current resulting in significant values that cannot be omitted. 5.2. Thermal model Temperature modeling and parameter identification are based on (23). Looking at the sensibility and latent heat representation of

(33)

The PSO particles were set to be initialized randomly by MATLAB and the parameters of the PSO were set to be the same as those presented in Table 2. The PSO was run several times to ensure reproducibility of the results, and it was found to converge at all times at an H∞ norm fitness value of (0.426 K) in about 600 iterations (around 2.6 s at rate of 230 iterations per second) as depicted in Fig. 10. Table 4 presents the resultant optimal model parameters of the system obtained by PSO, whereas Fig. 11 compares the PSO models' stack temperature to the experimental stack temperature values. Note that the simulation results lie on top of the experimental data. 6. Model validation The PSO obtained model was constructed in Simulink/MATLAB as depicted in Fig. 12. This Simulink model was then used for validation purpose using other different experimental data sets. The currents and ambient temperature values of the validation experimental data sets were loaded into the Simulink model and the model was able to successfully match the actual output voltage and stack temperature performance of the PEMFC experimental data. Two model validation examples are presented in Figs. 13e18. In the first example a step current input was used as shown in Fig.13 and the room temperature was set to be 296 K (23  C) to match the actual

Fig. 12. The Nexa 1.2 kW PEMFC system's model constructed in Simulink/MATLAB.

R. Salim et al. / Renewable Energy 82 (2015) 26e34

33

Fig. 13. Input current to the first validation example.

Fig. 16. Input current to the second validation example.

Fig. 14. Simulation and experimental voltage responses of the first validation example.

Fig. 17. Simulation and experimental voltage responses of the second validation example.

ambient conditions for when the actual experiment was conducted. The voltage response had an H∞ norm of error equal to (1.50 V) whereas its temperature response had an H∞ norm of (1.86 K). In the second example however, the current input is given in Fig. 16 and the room temperature was set to be 295 K (22  C) to match the experimental ambient temperature reading. The voltage response of this example had an H∞ norm of about (0.93 V), whereas its temperature response had an H∞ norm of (1.29 K). Table 5 summarizes the identification and validation results.

Fig. 18. Simulation and experimental temperature responses of the second validation example.

Table 5 Summary of identification and validation results.

Fig. 15. Simulation and experimental temperature responses of the first validation example.

Modeling data set Model validation# 1 Model validation# 2

Voltage response H∞ norm

Temperature response H∞ norm

0.176 V 1.50 V 0.93 V

0.426 K 1.86 K 1.29 K

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7. Conclusion and future work Fuel cells are an extremely attractive renewable energy source with the capability of someday replacing fossil fuels in the areas of power generation and transportation, while helping clean the environment by significantly lowering the world's pollution rates. However, to turn this green technology dream into reality, an accurate model that can effectively predict the fuel cell's performance in different conditions is desired. Such model can then be used to study, simulate, and monitor the behavior of PEMFCs to detect or predict any incipient faults that can affect their performance. In this paper, several experiments were conducted on the Nexa 1.2 kW PEMFC system and the parameters of the PEMFC mathematical model have been identified using basic fitting and then further optimized using PSO. This proposed method guarantees the achievement of an accurate mathematical model that highly resembles the actual system's performance quickly and with minimal computational effort. The resulting model of the work was then validated using other experimental data sets with two different types of load currents (a step current and a linear current), and was found to accurately predict the system's voltage and thermal characteristics in both validation cases. However, the obtained model in this paper is a starting step towards obtaining a complete model of the PEMFC system that takes reactant flows and pressures into consideration as well as the different interfaces. The complete model can then be used to study, simulate, and monitor the behavior of PEMFCs to detect or predict any incipient faults that can affect their performance. As a next step, this fault analysis can be utilized to improve the PEMFCs' performance while optimizing their cost and safety measures. Acknowledgments This research work was supported by United Arab Emirates University (UAEU) 31N114 and Japan Cooperation Center, Petroleum (JCCP). References [1] EG&G Services Inc.. Fuel cell handbook. 7th ed. Science Applications International Corporation, DOE, Office of Fossil Energy, National Energy Technology Laboratory; 2004. Chap. 1.

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