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    Simulation Model of a Solar-Hydrogen Generation System

    Abdulhamid El-sharifSchool of Mechanical and System Engineering Newcastle University

    Email: [email protected]

    Abstract

    This paper describes the work undertaken in order to model a solarhydrogen generation system using the commercially available software

    package IPSEpro. New library component models are described based onthermal and exergy analysis. The library includes the key systemcomponents subroutines for photovoltaic, water electrolyser, and a fuelcell. The entire system is designed to meet the environmental conditions ofa small community in Libya for which the necessary data has beenobtained. The effect of the main operation parameters for each componentand the entire system with variable ambient conditions, on irreversibility,and system performance is studied. It appears that the environmentconditions such as solar intensity, ambient temperature and the operation

    parameters have a large effect on the system performance, the rate ofelectricity output and hydrogen production.

    KEY WORDS : Solar, Hydrogen, Fuel Cell, Libya, IPSEpro, Exergy,Photovoltaic, Electrolyser.

    1. Introduction

    The search for reliable, long-lasting sources of energy has been an ever challenging taskfor mankind. This search is more urgent today than ever before, due to the heavydependence of modern life on energy from fossil fuels (i.e. petroleum, natural gas andcoal), which are being depleted. In addition, their combustion products are causing theglobal pollution problems. Many engineers and scientists agree that the solution to theseglobal problems would be to replace the existing fossil fuel system by the hydrogenenergy system [1]. The hybrid energy systems design is mainly dependent on the

    performance of its individual system. In order to predict its performance, individualcomponents should be modeled first and then their combination can be evaluated to meetthe demand reliably. If the power output prediction from these individual components isaccurate enough then the resultant combination will deliver power at the least cost [2].One of the most interesting developments of energy systems based on the utilization ofhydrogen is their integration with renewable sources of energy. In fact, hydrogen canoperate as a storage and carrying medium of these primary sources. The design andoperation of the system could change noticeably, depending mainly on the type ofcomponents, management strategy, control system, size and availability of the primarysource [3]. Hydrogen produced from renewable energy (e.g. solar) sources is a veryefficient and clean fuel. The main problem of solar energy plants is the variances of PV

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    output power under different solar radiation. To overcome this problem, PV power plantsare integrated with power sources or storage systems such as hydrogen generators,storage and fuel cells [4]. The technology, manufacturing, and marketing of many of therenewable hydrogen system components are in the early stage of development; costs must

    be revised periodically as the market continues to grow [5]. Many researchers focusedtheir studies on such systems by following three main directions: (a) experimental studieson an established system; (b) simulation and optimization of their operation parametersand efficiencies; and (c) real time control [6]. In the following section a brief descriptionof some of these researches will be presented.

    El-shatter, Eskandar and El-hagry [4] designed and simulated a hydrogen photovoltaic(PV) fuel cell generation system. M. L. Doumbia, K. Agbossou and E.Granger [7] studiedthe behavior of renewable energy systems with hydrogen storage using a dynamicsimulation model, Mat lab/Simulink software. Ulleberg, S.O. Morner [8] presented a

    parametric study of solar hydrogen system using the TRANSYS program, in order to better understand how to design solar hydrogen systems. Exergy and energy analysis fora 1.2 KW p nexa PEM fuel cell unit in a solar based hydrogen production system wasundertaken by Yilanci, Dincer and Ozturk [9]. Mohamed Ibrahim [10] developed asimulation analysis for a solar hydrogen system based on a voltage current designcharacteristics study. He suggested that the inclusion of thermal models of systemcomponents into the design code must be considered. Anand S. Joshi, Ibrahim Dincer,and Bale V. Reddy [11] investigated the performance characteristics of a photovoltaic-thermal (PV/T) system based on energy and exergy efficiencies. Ali Volkan Akkaya,Bahri Sahin and Huseyin Erdein [12] studied the effect of the operation condition of asimple fuel cell system on its performance based on exergy analysis. M. Mattei, G.

    Notton, C. Cristafari, M. Muselli, and P. Poggi [13] used a simple model to predict the performance of a photovoltaic module versus environmental variables. Ayoub M. Kazem[14, 15] applied a comprehensive exergy analysis on a large scale electrolyser and a PEMfuel cell at variable operation parameters using a simple thermodynamic model. Instead,M. Ay, A. Midilli and I. Dincer [16] used a detailed thermodynamic-exergy model toinvestigate the performance of a PEM fuel cell.

    A small number of software programs are available commercially to use for simulationand optimization of a solar hydrogen system such as HYDROGEMS and HOMER. Noneof the available software is based on the exergy analysis code. Furthermore, most of themare based on empirical relations or data from (I-V) curves of the components. The main

    purpose of this research is to develop a new library of simple and general models basedon energy and exergy analysis for a solar hydrogen system using the commerciallyavailable energy tool software package IPSEpro. A parametric study is undertaken toinvestigate the effects of the operation condition on the performance of each componentand the entire system. The entire system is designed, optimized and simulated to meet therequired demand of a small community in Libya.

    2. Thermodynamic analysisEnergy and exergy analysis are applied in this research to investigate the performance ofthe system components and the entire system. Energy analysis is based on the first law of

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    thermodynamics (Eq.1) and exergy analysis is based on the second law ofthermodynamics (Eq.2). Exergy is defined as the maximum amount of work which can be

    produced by a system or a flow of matter or energy as it comes to equilibrium with areference environment [11]. Exergy deals with the quantity and quality of energy, unlikeenergy which deals with the quantity only [15]. The exergy analysis consumption duringa process is proportional to the entropy generated due to irreversibility. For exergyanalysis, the characteristics of a reference environment (dead state) must be specified[11]. In this research, the actual environment condition is taken as the reference state. Thefollowing section describes the main equations used in developing new library models ofsolar hydrogen system components (photovoltaic, electrolyser, and fuel cell) using anIPSEproMDK package. For a steady state-flow system, the energy and exergy balancesfor a flow of matter through a system can be calculated as

    0=+ W Qmenmen out out

    out inin

    in (1)

    0=+ I exexmexmex wQout out

    out inin

    in (2)

    2.1 Photovoltaic

    The solar energy absorbed by the PV modules is converted to electric energy and alsothermal energy. The thermal energy is dissipated to the ambient as a heat loss; byconvection, conduction, and radiation. The rate of the heat transfer process depends onthe design of the PV system. To achieve the efficiency of a PV module its operatingtemperature T c must be determined, which for simplicity could be assumed homogenouson the plate. T c depends on the ambient conditions. The higher surface temperature couldcause a reduction in PV efficiency. Therefore, the cells may be cooled artificially by

    passing air or water on the back side of the module (PV/T) system, especially in hotregions. The output power of the PV system, however, fluctuates depending on solarradiation and surface temperature. Then, a storage system must be used to deliver therequired power at lower radiation levels and during the night [4].The electro-thermal mathematical model of a solar cell can be described by the followingequations [8, 11, 16]:The power output isPel = I V (3)Moreover, the maximum output power is given byPmax = (I V) max = V oc Isc FF (4)

    The energy conversion efficiency is given bysta = (V mp Imp / P in)sta = (V oc Isc FF / P in)sta (5)Where the energy inclined on the photovoltaic surface isPin= S A (6)The exergy output of the photovoltaic system can be calculated asexoutput = V oc Isc [ (V oc Isc - V m . I m ) + Q loss (1 - T a/Tc ) ] , and (7)Q loss ( heat loss) = h ca A (T c - T a ) ,The convective and radiative heat transfer coefficienthca= 5.7+3.8( ) (8)

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    Energy input of the photovoltaic system (exergy of solar energy) can be calculatedapproximately asex solar = ex input = S A (1 T a / T sun ) (9)Then, the exergy efficiency of the photovoltaic system can be defined as

    pv,ex = [ V m Im - ( 1- T a / T c ) [h ca A (T c - T a ) ] ]/ ex solar (10)The irreversibility of the system (exergy destruction) could be calculated as

    I= (1- pv,ex ) ex solar (11)The total area of a photovoltaic system could be calculated asA=C n mn A c* 1.54 where (1.54 is a space factor) (12)The PV system parameters values are affected by the ambient conditions and the actualvalus could be calculated by the following equations

    act=[sta (1- ( Tc- T r )] + [ log(S )] (13)The cell temperatureTc = T a +( T C,NOCT - T R,NOCT ) (S / 0.8) (14)Pel,act = act S A (15)Voc_act = V oc_sta [(V oc_ t V oc_sta (Tc T r )] (16)Isc_act = I sc_sta (S / S sta) [1+I sc_ t Isc_sta (T c T r )] (17)F F act = P el,act / (V oc_act Isc_act ) (18) The energy efficiency, the maximum electric efficiency and the exergy efficiency of thePV/T system are expressed respectively as

    en = [V oc_act Isc_act + Q loss] / S A (19)el-max = (V oc_act Isc_act ) / S A (20)

    ex-pvt = [ V m Im + ( 1- T a / T c ) h ca A (T c - T a ) ]/ ex solar (21)

    2.2 Fuel Cell

    A fuel cell is an electrochemical energy converter that converts the chemical energy of afuel and an oxidant to electrical current (DC). In the case of a H 2 O 2 fuel cell, H 2 is thefuel and O 2 is the oxidant and the only product is pure water. Fuel cells in general have ahigher efficiency than conventional engines. A simple thermodynamic model is used forthe energy and exergy analysis of the fuel cell with the following assumptions [17].

    -The fuel cell is operating under specified temperature, pressure, voltage and power.-The flow of reactants is steady, incompressible, and laminar.-The theoretical amount of hydrogen is calculated based on the power produced.-All gases are ideal gases.-Kinetic and potential exergy are neglected.-Chemical exergy values are taken from literature as standard values.-20% of the total heat generated by the fuel cell is lost via convection and radiation fromthe fuel cell [18].-The water mass flow rate for humidification the reactant is negligible, as it has a smallexergy amount and does not affect the analysis result [19].

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    According to equations 1 and 2, the irreversibility of a fuel cell could be calculated asI=(1-(T a / Tc) Q loss W net +[(m H2 ex t_H2in ) +( mo 2 ex t_o2in )] [(m H2_out ex t_H2out ) +( mo 2_outex t_o2out )]- [m w ex t_w] (22)The exergy efficiency is

    ex = 1- I / [(m H2 ex t_H2in ) +( mo 2 ex t_o2in )] (23)Qgen = (1.481-V c) C n W c / V c (24)Q loss = 0.2 Q gen (25)Wnet = P el - W acc (26)Pel = W c Cn (27)The total exergy of stream of matter isex t = ex ph + ex ch (28)The chemical exergy is taken from literature, and the physical exergy for H 2,O2 , iscalculated respectively as

    ex ph_H2 = 14.2091 T o [(T H2 / To) 1 - ln (T H2 / To) ]+ 4.12418 T o ln(P H2 / P o) (29)ex ph_o2 = 0.9216 T o [(To 2 / To) 1 - ln (To 2 / To) ]+ 0.25983 T o ln(Po 2 / P o) (30)The physical exergy for water is ex ph_w = (h w h wo)T o(Sw S wo) (31)The energy efficiency related to the low heating value of hydrogen is given as

    en = W net / 142000 m H2_in (32)The hydrogen, oxygen and water mass flow rate for an individual unit is calculatedrespectively asmH2_in = 1.05 E -05 S t_H2 ( C n W c / V c ) (33)mH2_out = ( S t_H2 -1) m H2_in (34)mo2_in = 8.29 E -05 S t_o2 ( C n W c / V c ) (35)mo2_out = ( S t_o2 -1) mo2_in (36)

    mw = 9.34 E -05 ( C n W c / V c ) (37)The power output of a fuel cell integrated in a solar hydrogen system where the hydrogenamount is known and coming from an electrolyser directly or from a tank can becalculated asPel = m H2_in V c / 1.05 E -05 S t_H2 (38)

    2.3 Electrolyser

    Hydrogen can be produced by many methods and many factors affecting its productionsuch as source availability, cost, hydrogen quality and purity. It can be produced fromfossil sources as well as from renewable sources. One of the most important technologies

    is water electrolytic, which is proposed for this research project. Hydrogen is produced bythe decomposition of water into hydrogen and oxygen by passing an electric current between two electrodes separated by an electrolyte. Alkaline and proton exchangemembrane, PEM, are the two main types of electrolysers, which are well developed. Asimple thermodynamic model for energy and exergy analysis of an electrolyser, similar tothe one used for the fuel cell, is applied, except with the following changes.Qgen = (V c -1.481) (P in_el W acc) / V c (39)The total heat generated at steady state is assumed to dissipated as heat by radiation andconviction [20] Q loss = Q gen (40)W c = (P in_el - W acc) / C n (41)

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    en = 142000 m H2_in / W net (42)And

    I=(1-(T a / T c) Q loss + W net - (m H2 ex t_H2in ) -( mo 2 ex t_o2in )+ (m w ex t_w) (43)3. Case study

    A small community in Misurata-Libya (32.38N, 15.09E), located at about 200 km east ofTripoli, was chosen as a case study for the research. The community was estimated to beconsisted of 100 families with 5 members as an average. The average hourly totaldemand was calculated as 2.5 KW/h, taking into consideration the environment andculture of the Libyan society. An extra 20 KW/h was assumed for the efficiency losses ofthe electric equipment and general community enquiries. The solar radiation data forMisurata is very limited, but because of the very close altitude of Misurata to Tripoli, thedata for Tripoli was used. The maximum amount of radiation is always received by a

    surface normal to its direction. So, the design of a solar PV system needs informationabout the solar radiation being intercepted by the tilted surface and site meteorologicaldata. As systems-tracking are expensive, a fixed system at a proper tilt angle (adjustedmonthly, seasonally or yearly), will maximize the solar radiation being collected. The tiltangle measured for Tripoli is 31 o [21] and for Misurata is taken as 30 o [22]. The yearlyaverage wind speed for Misurata is 5 m/s [22]. The average ambient temperaturemeasured for 2009 for Misurata was 294.65 K [23]. The average yearly total radiation forTripoli for 2004 was 0.665 KW/m 2 [21]. For this research it is taken as 0.675KW/m 2. Thetotal hourly solar radiation for Misurata for a typical day in January and June (2009) istaken from [24]. All the data obtained for Misurata was compared with the data measuredfor Tripoli and it is gives good agreement.

    4. Model configuration analysis, results and discussion

    In this section, the new models library developed for a solar hydrogen system is presented. This library, integrated with the applied library existing in the IPSEprosoftware package, was used to evaluate solar hydrogen components individually througha parametric study for its main operation parameters. A stand alone solar hydrogensystem was designed to meet the energy demand of a small community in Libya. Theentire system was optimized and simulated to investigate the effect of the mainenvironment conditions on the units and the systems performance.

    4.1 Photovoltaic

    A new model library using IPSEproMDK was developed based on a detailed electro-thermodynamic model presented in section 2.1. The print screen of this model library isshown in Figure 1. The model library was validated using a photovoltaic-module typeP220-60 produced by a2peak company, framed glass/tedlar for a grid-connected PVsystem (205-235W p). The simulation results of the units performance are indicated inFigure 2. The results agreed with the manufactures data sheet [25]. Actual data obtainedfor a typical day in June and January (2009) respectively for Misurata was applied toinvestigate the effect of the ambient conditions on the performance of the module. Theaverage measured annual ambient temperature was taken as 288K and 298K for January

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    and June respectively [23]. The calculated hourly total solar radiation from 7:38 to 17:38on a typical day in both months was obtained from [24]:

    Figure 1: Print screen of PV IPSEproMDK model library

    Figure 2: Simulation results screen of PV unit (IPSEpro) Figure 3 shows the effect of the variation of the total solar radiation on PV performance,during a typical day in June. The total solar radiation varies from 0.164 KW/m 2 to 0.980KW/ m 2. The exergy efficiency of the PV modules varies from 9.5% to14% at 12:38 and17:38 respectively. At the same time, the power conversion efficiency, also called theelectric efficiency, varies from 12% to 14%, and the exergy efficiency (PV/T) systemreduced from 16% to 15%. Figure 4 shows the variation of the PV cell temperature withirreversibility during the day. It is clear from the figure that the cell temperature increaseswith increasing solar radiation and this reduces the exergy efficiency of the module andincreases the energy and (PV/T) efficiencies. This is because the heat loss (irreversibility)

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    from the module surface and the ambient temperature is increasing. Also, the electricityoutput varies from 260 KW to 1380 KW by increasing the cell temperature from 308 K to329 K at midday, as shown in Figure 5.

    Figure 3: Variation of solar radiation, efficiencies with time on a typical day in June.

    Figure 4: Variation of PV cell temperature and irreversibility with time.

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    Figure 5: Variation of PV electricity output with time.Figure 6 shows the variation of the electricity output in January. The trend of the resultsagreed with the experimental and simulation results in the literature [11, 13].

    Figure 6: Effect of cell temperature on PV output with time in January.

    4.2 Fuel cell

    Figure 7 shows simulation results for a fuel cell using the developed library(IPSEproMDK). A parametric study to validate the model and evaluate the fuel cells

    performance has been achieved. The analysis was performed on an experiment tested 10KW PEM fuel stacks developed by Energy Partener Inc. The fuel cell consisted of 40cells with an active cell area of 780 cm 2, capable of generating 10 KW power output at 40% efficiency at 3 bar and 338.15 K[15].

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    Figure 7: Simulation results screen of PEM fuel cell unit (IPSEpro).

    Figure 8 shows the effect of the cell voltage on the exergy efficiency and irreversibility ofthe fuel cell. It appears that the irreversibility increasing from 4.7 to 30 KW and theexergy efficiency increase from 27% to 69%, which is due to increasing the cell voltagefrom 0.4 V to 1.1 V. Also, the energy efficiency increases from 26% to73%, leading toreduce the hydrogen flow rate amount needed for the same power generated.

    Figure 8: Effect of fuel cell voltage on efficiencies and irreversibility.

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    Figure 9 shows the effect of the pressure ratio (P c/Po) and the temperature ratio (T c/ T o)on the physical exergy of the hydrogen. It is found that increasing the pressure andtemperature increases the physical exergy of the hydrogen, which leads to increasing thefuel cell exergy efficiency. The results obtained in this analysis are in a good agreementwith the results in the published literature [15, 17].

    Figure 9: Effect of pressure and temperature on, hydrogen physical exergy.

    4.3 Electrolyser

    The developed electrolyser model library was evaluated using actual data from ahydrogen and renewable integration project installed at West Beacon Farm,Leicestershire, UK, known as the HARI-project. The alkaline electrolyser unit in the

    project was modeled by the IFE (Institute of energy technology, Norway) and the HARI- project evaluation team [26]. The unit consisted of 1 stack, 32 cells, 0.1 m 2 area operatedat 65 OC, 450 A, 25 bar, 1.815 V, 26.1 KW, and the hydrogen and oxygen output were6,3 Nm 3/h respectively. The efficiency existing at these conditions is 79.6 %. Theobtained results using IPSEpro for the same conditions give an identical output andresults, as shown in Figure 10.

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    Figure 10: Simulation results screen of electrolyser unit (IPSEpro). A parametric study has been carried out to investigate the performance of the unit underdifferent operation conditions. Figure 11 shows the variation of the exergy and energyefficiency and the irreversibility with varying cell voltage. It appears that theirreversibility increases as the cell voltage increases, leading to a decrease in exergyefficiency from 99% at 1.6V to 69% at 2.2V and the energy efficiency from 89% at 1.6Vto 65% at 2.2 V.

    Figure 11: Effect of voltage on electrolyser efficiencies and irreversibility.

    4.4 The case study

    The developed library models, integrated with the existing applied library at IPSEpro,were used to optimized, designed and simulated a stand alone solar hydrogen system for asmall community in Libya. Accessory work for the auxiliary equipments was assumed to

    be 31 KW and 10 KW for the electrolyser and the fuel cell respectively. A print screen ofthe simulation analysis for the designed system is presented in Figure 12. The total areaof PV needed to produce the proper amount of electricity for the community is 19767 m 2 and needed the 7700 module from the selected type in this study. The total PV outputelectricity is 1118 KW, which is enough to produce the demand for the day time. Theannual measured average sun shine duration for Misurata is 9 h [20]. During the night the

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    fuel cell will cover the demand. The electrolyser is coupled directly to the PV and the fuelcell to produce the proper amount of hydrogen.

    Figure 12: Simulation model of a stand alone solar hydrogen system (IPSEpro).

    The total system exergy and energy efficiency are 3.78% and 14.82% respectively. Theexergy destruction factor for the PV is 92.3% and 6.13%, 1.48% for the fuel cell and theelectrolyser respectively. It is clear that the most important exergy destruction occurs atthe PV followed by the fuel cell. This is due to the great irreversibility and heat lossvalues at these units.

    5. Conclusions

    In this paper, new model libraries for a solar hydrogen system using the IPSEproMDK package are presented. A parametric study has been carried out to investigate the performance of a solar hydrogen system and its components.

    The PV exergy efficiency decreases as the solar radiation and ambient temperatureincreases due to increasing cell temperature and irreversibility while the output electricityincreases. The PV/T system has a higher efficiency than the PV system, due to thecooling of the cell surface.

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    It is recommended to operate the fuel cell at high pressure, temperature and voltage toreduce its irreversibility, increase its efficiency and reduce the amount of hydrogenconsumed for the same power.

    Operating the electrolyser at low voltage will reduce the irreversibility, leading to anincrease in efficiency and the hydrogen production rate.

    A stand alone solar hydrogen system was designed and optimized to meet the demands ofa small community in Misurata. The community consisted of 100 families with anaverage consumption of 270 KW/h. A 19767 m 2 area is needed to produce 1118 KW/hfor the selected PV solar module to meet the communitys demand day and night. Themost important exergy destruction (irreversibility) occurs at the PV unit followed by thefuel cell. More investigations and development are needed to reduce these values.

    6. Future Work

    This research will continue for the following:-More investigations will be carried out on various operation parameters of eachcomponent and the entire system with variable ambient conditions.-New model libraries for hydrogen and oxygen tanks; auxiliary equipment will bedeveloped using IPSEproMDK package.-More validation on the system components and the entire system will be carried out.-An exergy economic code for the system components will be created within thedeveloped IPSEpro libraries and an exergy economic analysis for the system will beachieved.

    Acknowledgment

    I would like to thank Prof. Brian Agnew for his assistance and support during this work.

    References

    1. T. Najat Veziroglu, Sumer Sahin, 21 st Centurys energy: Hydrogen energysystem. Energy conversation and management, 49, (2008), p. 1820-1831.

    2. M. K. Deshmukh & S. S. Deshmukh, Modeling of hybrid renewable energysystems. Renewable and Sustainable Energy Reviews, 12(1), 2008, p. 235-249.

    3. Massimo Santarelli, Michele Cali & Sara Macagnc, Design and analysis ofstandalone hydrogen energy systems with different renewable sources.International Journal of hydrogen Energy, 29, 2004, p. 1571-1586.

    4. Th. F. El-shatter, M. N. Eskander & M. T. El-Hagry, Hybrid PV fuel cell systemdesign and simulation. Renewable Energy, 27, 2002, p. 479-485.

    5. Sachin S. Deshmukh & Robert F. Boehm, Review of modeling details torenewable powered hydrogen systems. Renewable and Sustainable EnergyReview, 12(9), 2008, p. 2301-2330.

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    6. P. L. Zrvas, H. Sarmvies & J. A. Paljuos, N.C.G. Market Model-based optimalcontrol of a hybrid power generation system consisting of photovoltaic and fuelcells. Journal of Power Sources, 181, 2008, p.327.

    7. M. L. Doumbia, K. Agbossou, & E. Granger, Simulink Modeling and Simulationof Hydrogen Based Photovoltaic. Wind Energy system. Eurocon 2007, TheInternational Conference on Computer as a tool, Warsaw, September, p. 9-12.

    8. O. Ulleberg & S. O. Morner, Transys simulation models for solar-hydrogensystems. Solar Energy, 59, (4-6), 1997, p. 271-279.

    9. A. Yilanci, I. Dincer & H. K. Ozturk, Performance analysis of a PEM fuel cell unitin a solar-hydrogen system. International Journal of Hydrogen Energy, 33, (24),2008, p.7538-7552.

    10. Mohamed Ibrahim, Solar Energy and the use of hydrogen as an energy vector inlibya, 2003, PhD thesis, , Electric Engineering department, UMIST University.

    11. Anand S. Joshi, Ibrahim Dincer & Bale V. Reddy, Thermodynamic assessment of photovoltaic systems, Solar Energy 83, 2009, p. 1139-1149.

    12. Ali Volkan Akkaya, Bahri Sahin & Hasan Huseyin Erdien, Exergitic performancecoefficient analysis of a simple fuel cell system, International Journal of HydrogenEnergy, 32, 2007, p. 4600-4609.

    13. M. Mattei, G. Notton, C. Cristafari, M. Muselli & P. Poggi, Calculation of the polycrystalline PV module temperature using a simple method of energy balance.Renewable Energy, 31, 2006, p. 553-567.

    14. Ayoub M. Kazem, Exergetic efficiency of a PEM electrolyzer at variable operationtemperature and pressures, International journal of exergy, 1, 1, 2004, p. 47-59.

    15. Ayoub M. Kazem, Exergy analysis of a PEM fuel cell at variable operationconditions, Energy conversion and management, 45, 2004, p. 1949-1961.

    16. Handbook of photovoltaic science and engineering, Antonio Luque, StevenHeqedas, Wiely, C2003.

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    18. M. M. Hussain, J. J. Baschuk, X. Li. & I. Dincer, Thermodynamic analysis of aPEM fuel cell power system, International journal of thermal science, 44, 9, 2005,

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    20. P. M. Dieguer, A. Ursua, P. Sanchis, C. Sopena, E. Gaelbezu & L. M. Gandia,Thermal performance of a commercial alkaline water electrolyzer: Experimentalstudy and mathematical modeling, International Journal of Hydrogen Energy, 33,2008, p. 7338-7354.

    21. Solar energy centre data, Libya.22. Meteorological data from general meteorological foundation, Misurata office.23. World Weather, Tu Tiempo.net, available at: www.tuitmpo.net/en/climate 24. European Commission, Joint research centre, PVGIS, available at:

    www.sunbird.jrc.it/pvgis/apps/pvest.php 25. a2peak power co. ltd., Taiwan R.O.C., available at: www.a2peak.com.tw

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    26. Hydrogen demonstration project evaluation, Final report for IEA (Internationalenergy agency), HIA (Hydrogen implementing agreement), Task18, subtask B, byUlleberg. etl. November 2007.

    Nomenclature

    A The surface area, m 2 TR Reference temperature at NOCT (K)Ac Cell area T o Reference temperature (K)P Pressure (bar) T sun Sun temperature (6800 K)Pel Electric power (KW) T a Ambient temperature (K)Ph Physical exergy (KJ/ kg) T c Cell temperature (K)Cn Number of cells connected in series T r Temperature at sta conditions (K)Ch Chemical exergy (KJ/kg) V c Voltage of the cell (V)

    ex Exergy (KJ/kg) V oc The open circuit voltage (V)en Energy (KJ/kg) W Works (KW)el Electricity (KW) W c Work cell (KW)FF The fill factor W acc Accessory work (KW)h Enthalpy (KJ/kg. K) W net Work net (KW)I Irreversibility (KW)Isc The short circuit current (A) efficiency m Mass, kg/s Solar radiation coefficientmn Module number t Temperature coefficient(K)

    NOCT PV conditions at 0.8 KW/m 2, T R (K) Wind velocity (m/s)Qgen Heat generated (KW) w WaterQ Heat (KW) sta Standard condition at 1KW/m 2, 25 OCSgen Entropy generation (KW)S Entropy (KJ/kg.K)St Stoichometric ratio (kg/kg)S Solar radiation (KW/m 2)