Applied Energy 87 (2010) 1376–1385

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Modelling and simulation of the utilization of a PEM fuel cellin the rural sector of Venezuela

Alfonso Contreras a,*, Fausto Posso b, Esther Guervos a

a Department of Chemistry Applied to Engineering, UNED, Madrid 28040, Spainb Science Department, ULA-Táchira, San Cristóbal 5001, Venezuela

a r t i c l e i n f o

Article history:Received 14 January 2009Received in revised form 22 May 2009Accepted 31 May 2009Available online 25 July 2009

Keywords:PEM cellsModellingSimulation

0306-2619/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.apenergy.2009.05.040

* Corresponding author.E-mail addresses: acontreras@ind.uned.es (A.

(F. Posso).

a b s t r a c t

We studied the use of Proton Exchange Membrane (PEM) fuel cells in rural villages of Venezuela lacking apermanent and reliable energy supply. For this purpose, we formulated a semi-empirical mathematicalmodel representing the main technical and economic features involved in the operation of the PEM cells.The simulation of the resulting non-linear model spans a 20-year time horizon, considering how costs areaffected by the expected increase in the energy demand of the rural population, to which it is applied andthe decrease in the unit costs of the cell on account of technological improvements and mass productionof the cell. These villages are located in the parish of Trinidad de la Capilla, in the central-west part of thecountry. They were selected on the basis of various social and economic factors involving percentage ofrural population and the Human Development Index. The results show that the main operating variables,current density, efficiency and generated voltage, show the typical behaviour of this type of cell, whereas,from the economic point of view, the cost of the electricity produced by the cell stack decreases to con-stant values, both for the same year and interanually, due to the economy of scale and because the invest-ment costs and the costs of the hydrogen used offset one another. The use of PEM cells, besides meetingthe energy requirements of this Venezuelan rural parish, is viable in principle, as it contributes in a largeway to improving the quality of life and sustainable development of these isolated and depressed regions,which, due to their distance from the electrical grid and their surface area, are not covered by it, andprobably will not be in the near future.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The End Use stage is the last in the structure of any H2-basedenergy system and serves to harness its energy in the different sec-tors of society to meet the energy requirements in question, andtherefore its full development will, to a large extent, determinethe successful penetration and massive use of H2 as an energy vec-tor in the immediate future [1]. This explains the interest ofresearchers from universities, research facilities, energy compa-nies, multinational agencies and even states themselves, in devel-oping services technologies related with the different ways ofharnessing the energy contained in this unique chemical elementthat are economically viable [2]. Of all the technologies proposed,fuel cells are regarded as one of the most competitive and promis-ing, with a wide array of potential applications throughout allsectors of society, in particular in automotive transport and thedistributed generation of electricity from alternative energysources for residential use, both in urban areas and in remote or

ll rights reserved.

Contreras), fausto@ula.ve

isolated places [3,4]. In this respect, it is in the rural regions ofthe developing countries that lack permanent and reliable energyservices, where renewable and hybrid energy systems that includefuel cells as final conversion technologies are being used increas-ingly more frequently, raising the quality of life of these vast re-gions and contributing to their sustainable development [5].

We are carrying out research in this context with the main pur-pose of studying the viability of developing an H2-based energysystem in Venezuela for residential use in rural regions of thecountry. Due to the scope of the study, we considered it appropri-ate to divide it into various stages, each of which corresponds to anaspect of the proposed energy system: Production, Storage, Trans-portation and Distribution and End Uses.

In the first of these, the production of H2 via electrolysis usinghydro-electricity is studied. This is the means of production cho-sen, taking into account Venezuela’s large potential for hydraulicenergy, if fully utilized, would be equivalent to an output of 3 mil-lion barrels of oil a day [6]. Barely 25% of this potential is used togenerate 12,000 MW of electricity in large hydroelectric power sta-tions, with highly competitive production costs compared to othercountries in the region. This in turn enables a low price structure tobe offered to end-users, with an average price for 2005 of 0.035 $/

Nomenclature

AC cell area, cm2

CC costs of the cells, $CCA annualized cost of the cells, $/yearCCV converter cost, $CCVA annualized converter cost, $/yearCE cost of the electricity, $/kWCEH annual energy consumption per household, kWh/yearCEQA annualized equipment cost, $/yearCHA annual cost of H2, $/ yearCH cost of H2, $/ N m3 H2

CH2 annual consumption of H2, N m3 H2/yearCHR actual annual consumption of H2, N m3 H2/yearCIA annualized investment cost, $/yearCEQ equipment costs, $CINV investment costs, $

COMA cost of O and M by yearCUC cell unit cost, $CUC0 unit base cost of the cell, $CUCV converter cost unit, $/kWDC current density, mA/cm2

EEA annual electrical energy, kW h/yearEFI fuel cell voltage efficiency, adimg theoretical efficiency of the fuel cell, adimNC number of cells in stackNH number of rural households in a rural centre of popula-

tionPOA AC output power, kWPOC DC output power, kWVC cell voltage, Vt time, years

A. Contreras et al. / Applied Energy 87 (2010) 1376–1385 1377

kW h [7]. While it is pointed out that producing H2 by electrolysisusing hydroelectricity as the primary source, may be an economi-cally feasible option, which is in a position to compete with the tra-ditional option of refining natural gas when the price of electricityis less than 0.05 $/kW h [8,9], there is no doubt that this means ofobtaining renewable H2 is the most appropriate one for Venezuela.This is corroborated by the results of this study, which obtained aproduction cost for H2 of 0.3762 $/N m3 H2 for the year 2005 [10]. Ifwe compare this figure with those given in references for similarvalues of hydrogen production, it can be seen that the values foundin the Venezuelan case are much smaller, even for cases in whichfar larger production is involved, and therefore with a greater im-pact of economy of scale. It may therefore be concluded that theproposed method for obtaining hydrogen is, by comparison, highlyadvantageous in the case of Venezuela.

As the Production and End Use stages do not coincide, either interms of time or place, the H2 that is produced has to be stored andtransported. Therefore, in the second stage, we have looked at thetechnical and economic aspects of storing H2 compressed gas, andthe best way to do so, taking into account the amounts of H2 to behandled and the proposed end uses [11]. The analysis was made fora range of storage pressures of 100–400 bar, and for the storageperiods of 5, 10 and 15 days. The results for all the cases consideredhere, show that there is an operating point with a minimum totalcost that corresponds to a pressure of around 150 bar, due to thebehaviour of investment costs, which defines the evolution of thetotal cost. Furthermore, economy of scale means total costs are re-duced when the stored quantity is increased. On the other hand,total costs continue to increase with the storage time. The resultsof the model for Venezuela are comparable to those reported byAmos [12] for the same operating conditions and similar storageperiods.

With regard to the Transportation and Distribution of H2, con-sidered in the third stage, we propose compressed gas cylinderswith a 50 l geometric volume, at a pressure of 200 bars, distributedby road and in lorries [13]. In order to estimate the cost of trans-port and distribution, a non-linear mathematical model was devel-oped in which a General H2 Distribution Scheme is proposed thattakes into account the features and peculiarities of the Venezuelanrural sector and the large number of end-users. This means therehave to be several H2 distribution routes, depending on the ruralpopulation that is served and the distance to be travelled. Lastly,simulations of these routes were carried out, obtaining in each casethe investment, O&M and total transport and distribution costs,depending on the H2 that is transported and the chosen methodof transport. The results show that, due to economy of scale, the

overall cost can be reduced as the number of homes served and/or journey distance increases. Finally, we see that the investmentcosts are the largest portion of the overall cost, whereas in termsof the operating costs, it is the cost of the truck that is the mainitem.

One important point regarding the application of all the modelsdeveloped during these stages, was the choice of rural area inwhich the villages are located, as their size and location determinethe H2 production, storage, transport and distribution require-ments. They also determine, of course, the associated costs. To se-lect the area, we used various demographic and socio-economicindicators for the rural parishes in the country, taken from officialstudies [14,15], and related to: (a) the percentage of rural popula-tion; (b) the lack of energy supplies; (c) the Human Developmentindex (HDI) [16]; and (d) the existing road infrastructure. As forthe definition of a rural village, we used the onet employed bythe Venezuelan National Institute of Statistics, according to whicha rural area is one which contains villages and settlements withfewer than 2500 inhabitants, including dispersed inhabitants [17].

The criterion used for the selection process was to find a regionwith a high proportion of rural population and with figures for theother indicators that were far lower than the national average. Thismeant that the potential introduction of an energy system using H2

as the energy vector was fully justified by its positive impact onquality of life and sustainable development in that region, if wetake a number of aspects into account [18]. In environmentalterms, it noticeably reduces the local pollution levels caused byinadequate combustion of wood and fossil fuels such as kerosene,which is commonly used in the region [14]; in economic terms, bysupplying safe energy sources, increasing the level and quality oflocal employment, increasing the income per head in an area witha far lower income than the national average [14]; and, in socialterms, by reducing poverty levels, preserving cultural identity,and helping to reduce migration from rural areas to the towns,which is a huge social phenomenon in Venezuela [17].

The full achievement of these benefits is undoubtedly linked toan appropriate choice of technology for the final conversion pro-cess. With this in mind, fuel cells have the advantage that, whenused with electric cookers, they are capable of supplying all thenecessary energy required to satisfy the basic needs of a typicalrural household: electricity for various purposes and heat for cook-ing food.

This goes a long way to explaining why the use of PEM cells forresidential purposes, as a part of the renewable and hybrid energysystems that use H2 as a carrier, has been studied in differentlocations:

1378 A. Contreras et al. / Applied Energy 87 (2010) 1376–1385

� In small rural communities with fewer than 50 households[19,20], where the main purpose is to demonstrate technicalfeasibility and establish the conditions that ensure the financialviability of the energy system, the most widely used renewableprimary source is photovoltaic solar energy.

� In isolated households located in remote areas or on islands [21–25], comparisons are made between different types of primarysources and storage options which lead to better performanceor a minimal cost of the energy system.

� In buildings [26–28], where the purpose has been to assess, intechnical and economic terms, the alternative of replacing thetraditional energy supply with energy systems that use H2 asthe storage medium, the results show that such a system isnot currently viable, although in the medium-term it willbecome competitive. The environmental benefits of such areplacement should be highlighted.

Finally, we would like to point out the work carried out by [29],which took place in a very similar context to ours and with thesame purpose. The study consists of a technical and economic anal-ysis of the use of renewable energies in two rural communities inBhutan, using H2 as the energy vector. It demonstrates technicaland economic viability by comparing the costs of the various op-tions studied with the traditional option of laying out an electricalgrid. However, this analysis is somewhat limited, as it is basedexclusively on information provided by manufacturers, so thatconclusions are fundamentally qualitative.

Because of all the above, the purpose of this paper is to devel-op a mathematical model of the technical and economic aspectsinvolved in operating PEM fuel cells, so as to determine thecosts of using it in rural sectors of Venezuela to meet theirinhabitants’ energy needs through the generation of heat andelectricity. The simulation is performed for a 20-year horizon,considering how costs are affected by the expected technologicalimprovements in the fuel cells and by the estimated growth inthe energy consumption of the rural population to whom it willbe applied.

2. Selecting the type of fuel cell

As already mentioned, the H2 will be used in Venezuelan ruralhouseholds to generate heat for cooking food and electricity forlighting and for running different electric household appliances.Taking this into account, a preliminary selection of the most appro-priate transformation technologies results in the following op-tions: a. A combination of burners fuelled directly by H2 forcooking uses and fuel cells for the electricity generation; and, b.The exclusive use of fuel cells for running electric cookers andthe other electric appliances. For the final selection, taking intoaccount features such as the efficiency, applicability, costs, techno-logical complexity and ease of access to them [30]; and consideringthe level of general education and the socio-economic conditionsof the Venezuelan rural population [14], we have chosen optionb, that is to say, only using fuel cells as the transformationtechnology.

Depending on the electrolyte that is used, fuel cells are classi-fied as alkaline, polymer, phosphoric acid and solid oxide. Selectinga type of fuel cell for a specific application will depend largely onoperating conditions, the nature of the application and on the out-put power required [24]. In our case, we have decided to use PEMtype cells, based on the following considerations:

1. It is the most suitable for generating small-scale distributed sta-tionary power and adapts efficiently to variable load operations,as is the case of residential applications [31].

2. It operates at high current densities and low temperatures, thislatter fact permitting faster start-up and shutdown with lessthermal wear of its components, resulting in longer durability[32,33].

3. It is more compact, lightweight and smaller than the othertypes of fuel-cells, making it less complex to assemble and han-dle [34].

4. It poses fewer corrosion problems because it does not needhighly corrosive bases and acids [35].

Nevertheless, its main disadvantages must also be mentioned:

1. This technology is not fully developed yet, as certain obstacleshave to be overcome relating to the thermal treatment anddehydration of the polymer membrane, the change of scalefrom a simple cell to a cell stack, and the high sensitivity toCO contamination of the catalyser.

2. The production costs are relatively high, although there is a realpossibility of being able to obtain a major reduction in costs ifthey are mass produced [36].

3. Along with the above, the reliability of the cells is considered tobe the main obstacle to their commercialization [37].

3. Mathematical model of the H2 end use

Conceptually speaking, the mathematical model to be devel-oped for the case in hand is semi empirical, because it combinesthe empirical correlations obtained for specific operating condi-tions and a certain phenomenological knowledge [38]. In our casethe model is built from prior results described in the literature[39,40], Venezuelan rural sector energy demand projections[14,15], and information on PEM type fuel cell manufacturers[41–43]. Structurally, the model is divided into two parts: an en-ergy model that studies the fuel cell energy conversion processin terms of the relationship between two of its key operating vari-ables: current density and voltage, for which we shall use a zero-dimension model, as we consider it to be sufficiently well-suitedto the purposes of our study [38]; and an economic model thatestimates the fuel, investment and operational costs of each pointof operation determined by the current density/voltage pair. Whenrequired by the calculation, the Higher Heating Value of the H2 willbe used.

3.1. Energy model

The energy model serves to establish the mathematical repre-sentation of the fuel cell current density vs. voltage relationshipfor an output power determined by demand, and this informationis then used to calculate the number of cells of the conversion sys-tem, the cell operating efficiency and consumption of H2.

3.1.1. Polarization equationThis is the most important indicator of the fuel cell operational

performance because it provides the voltage generated in the cellfor a given current density and for a fixed operating conditions.When the cell is in operation, different kinds of phenomena takeplace, causing the cell potential to be lower than the ideal orreversible potential. The value of this, 1.229 V, is obtained fromthermodynamic considerations of the electrochemical conversionprocess [39]. These phenomena, called overpotentials, are: activa-tion overpotential, ohmic overpotential and concentration overpo-tential. Therefore, any mathematical model which is proposed forrepresenting the current density vs. voltage relationship must takeinto account such irreversibilities. In this respect, following a

A. Contreras et al. / Applied Energy 87 (2010) 1376–1385 1379

judgmental documentary review of the different mathematicalmodels that have been proposed for expressing the said relation-ship, in terms of exponential, logarithmical and linear expressions[22,35,38–40,44–46], for our study we have selected the Santarellimodel [22], developed for PEM cells with a maximum theoreticaloutput power of 1.2 kW, of the same order as the one estimatedfor our study, as the power required for a typical rural householdto satisfy its basic energy needs, POA, for the year the study begins,is close to 0.8 kW, a value calculated on the basis of the historicalevolution of energy consumption in the Venezuelan rural sec-tor [47] and the most likely daily timetable. Last of all, themodel adapts quite well to the experimental results and to thoseobtained by other more complex models. Its expression is asfollows:

VC ¼ E� ðDC þ inÞr � A lnDC þ in

io

� �þ B ln 1� DC þ in

il

� �ð1Þ

where the first term represents the ideal potential, while the otherthree represent the ohmic, activation and concentration overpoten-tials, respectively.

3.1.2. Number of cellsThe voltage and current obtained in an individual cell are too

small to be harnessed directly, so the cells must be grouped in ser-ies, parallel and mixed stacks of different sizes until the desiredoutput power is reached. The number of cells required is obtainedfrom the ratio between the maximum theoretical power and realoutput power for a point of operation and a specified area of theelectrode [26].

NC ¼POA

DCVCACð2Þ

Eq. (2) shows that the number of cells in the stack decreases asthe current density increases, and this has a heavy bearing oncosts. The number of cells in a stack can vary from dozens to sev-eral hundred and can even form a network of stacks. In our case, forthe sake of calculation simplicity, we will consider that each ruralhousehold will only have one stack. As for the surface area of theelectrode, we will use a value of 100 cm2, equal to the one usedin [48] for a PEM fuel cell with a maximum output power of1 kW, an adequate value for our purposes, for the reasons givenin Section 3.1.1.

3.1.3. PEM fuel cell efficiencyThe efficiency of the fuel cell energy conversion is an important

aspect of its operation and has a significant bearing on the eco-nomic aspects of its use [39]. In its most general form, the effi-ciency is defined as the ratio between the useful or availableenergy in the cell, and the enthalpy change between the reactantsand products of the electrochemical reaction [49]. The useful en-ergy is represented by the change of the Gibbs Free Energy, andtherefore is expressed as follows:

g ¼ DGDH

ð3Þ

It can be proved [34], that the maximum theoretical efficiencyachievable in the fuel cell in normal conditions with respect tothe Higher Heating Value of H2, is 0.83, much higher than the effi-ciency obtained in traditional energy conversion devices. In prac-tice, what is used in design and costs calculations is the so-calledVoltage Efficiency [34,49], which relates the actual or operatingvoltage with the ideal voltage or thermodynamic voltage, and itsvalue of 1.482 V corresponds to the maximum (electric and ther-mal) energy obtainable from the electrochemical reaction [39].Therefore, the expression of this efficiency is:

EFI ¼ VC

1:482 V¼ 0:675 VC ð4Þ

The direct dependency of the PEM fuel cell efficiency on VC hasseveral implications. First of all, the cell is more efficient for partialload operations, as occurs in residential applications, which consti-tutes one of the main differences with other energy conversion de-vices such as internal combustion engines and heat engines;furthermore, as the system becomes less efficient, a larger amountof H2 is required to obtain a fixed output power.

3.1.4. Consumption of H2

This value is obtained from the ratio between the annual elec-trical energy produced by the fuel cells and their efficiency, suchthat:

CH2 ¼EEA

gHHVð5Þ

With respect to EEA, we have already indicated that we will only usefuel cells to meet the energy requirements of rural households. Inthis case, the annual total production of electrical energy necessaryis directly proportional to the annual energy consumption of a typ-ical Venezuelan rural household, which we calculated in [8], suchthat:

EEA ¼ CEHNH ð6Þ

Furthermore, in Eq. (5) it has been assumed that all the H2 isconsumed, as occurs in the normal operation of traditional conver-sion devices. However, in the fuel cells not all the H2 is convertedand therefore a certain amount of H2 is not consumed. Conse-quently, the equation must include a factor that describes whatpercentage of the input H2 is used, as such:

CHR ¼ CH2=FU ð7Þ

3.1.5. Output signal conversion and adjustmentFor domestic use purposes, the DC power generated in the fuel

cell must be converted into its AC equivalent, and the potential mustbe adapted to a 110 V single-phase type output value, this being thevoltage used in the Venezuelan electricity grid. Both requirementsare met by using a signal converter and adjuster whose simplestmathematical representation is of the linear type [34]:

POA ¼ FCAPOC ð8Þ

In short, the energy model is represented by Eqs. (1)–(8) and itdemonstrates the importance of the cell voltage because it directlydetermines the cell stack size and operating efficiency, and indi-rectly the amount of H2 required to meet a given output power.

3.2. Economic model

The variable commonly used for economically evaluating fuelcell operation is the electricity generation cost, calculated usingthe annuity or life cycle method [50]. In this respect, the proposedmodel calculates the annual total cost of electricity generation asthe sum of the fuel costs, the investment costs and the operationalcosts with respect to the electricity obtained by the fuel cell systemin the same period. The fuel costs are equivalent to the costs of pro-ducing the H2 required to operate the cells, the investment costsare represented by the cost of the individual cells and the cost ofcoupling them in different-sized groups depending on the outputpower, while the operation and maintenance costs are consideredas a fraction of the annualized investment costs. Finally, we havealready said that the annual production of electrical energy de-pends directly on the energy consumption of the rural householdsto be supplied.

1380 A. Contreras et al. / Applied Energy 87 (2010) 1376–1385

3.2.1. Fuel costsThe H2 cost mainly depends on the production technology used

and on the amount produced. In our analysis we consider that theH2 is produced by electrolysis from hydroelectricity as the primarysource and whose unit cost in Venezuela we have calculated in [8].A more exhaustive study of the production costs of electrolytic H2

as part of an energy system should consider the effect of usingelectrolysers that work at a much higher than atmospheric pres-sure, because, although the investment costs of the Productionstage increase, the costs of the Storage stage are reduced [51].However, our procedure of studying the various different stagesof the energy system separately means that studying these optionsis beyond the scope of this paper. Finally, the amount of H2 re-quired is obtained from Eq. (7), and therefore:

CHA ¼ CHRCH ð9Þ

3.2.2. Investment costsIn order to evaluate the effect of the investment costs, they

must be divided into fixed costs and variable costs [23,26], accord-ing to their dependence on the cell stack size. The fixed costs,which we will refer to as equipment costs, do not change withthe number of cells and are the costs of the reactant and productinlet and outlet devices; the costs of the cell humidification costsand of the measuring and control elements; in addition to the costsof assembling the stack, and installing and coupling the system[26]. The variable costs, which we will refer to as cell costs, CC, de-pend on their unit value and their number, in accordance with theexpression:

CC ¼ CUCNC ð10Þ

Furthermore, the investment costs must include the cost of thesignal converter/adjuster, which depends on the output power[24], as follows:

CCV ¼ CUCVPOA ð11Þ

Therefore, the expression for the investment costs is:

CINV ¼ CEQ þ CC þ CCV ð12Þ

To calculate the annual investment cost, we will use a capital recov-ery factor such that [26]:

F ¼ dð1þ dÞn

ð1þ dÞn � 1ð13Þ

0

20

40

60

80

100

120

2000 2005 2010 t (ye

CU

P($

/kW

)

Fig. 1. Temporal variation of the u

In Eq. (13) we will distinguish between the useful life of theequipment, estimated as 20 years and the useful life of the cells,much shorter, which we consider to be 5 years [26]. Therefore,the corresponding annualized costs are:

CEQA ¼ FEQ CEQ ð14ÞCCA ¼ FCCC ð15Þ

In the case of the converter/adjuster, we have considered a usefullife similar to that of the equipment, such that annually:

CCVA ¼ FEQ CCV ð16Þ

Therefore, the annual investment is expressed as follows:

CIA ¼ CEQA þ CPA þ CCVA ð17Þ

3.2.3. O and M costsThe O and M costs have been taken as a percentage of the annu-

alized investment costs and equal 2.5%, a value reported in the bib-liography for cases similar to ours [20,25]. Due to the low cost ofthe electric cookers, we will consider them part of the annual Oand M costs. Such that the expression for these costs is:

COMA ¼ 0:025CIA þ CEC ð18Þ

3.3. General equation of the End Use Model

Therefore, we can conclude that the End Use Model developedabove is expressed by the following equation, which calculatesthe cost of the electricity produced with respect to the annualquantity of electrical energy generated by the cell stack:

CE ¼CHA þ CIA þ COMA

EEAð19Þ

4. Application of the End Use Model in the Venezuelan ruralsector

The End Use Model is now going to be used to calculate thecosts of electricity generation using PEM fuel cells in Venezuelanrural centres of population. The simulation spans a 20-year timehorizon, taking into account the following: (a) 2001 was chosenas year one of the study, – base year – to make it coincide withthe year that the last population and housing census was con-ducted in Venezuela. Consequently, the study is based on official,up-to-date statistics about the Venezuelan rural sector; (b) The

2015 2020 2025ars)

OptimisticConservative

nit costs of the PEM fuel cell.

Table 1Model parameter values.

Parameter Value

Coefficient of tafel activation overpotential (A) 0.06 VCoefficient of concentration overpotential (B) 0.05 VReversible voltage (E) 1.229 VInternal and fuel crossover equivalent current density (in) 2 mA/cm2

Exchange current density (io) 0.067 mA/cm2

Limiting current density (il) 900 mA/cm2

Area specific resistance micro-hydro turbine (R) 30 � 106 kX/cm2

Capital recovery factor (F) FEQ = 0.0944FC = 0.2439

Higher heating value of the H2 (HHV) 3.54 N m3/kW hDC/AC conversion factor (FCA) 0.98Cost of the electric cooker (CEC) 50 $/cookerH2 utilization factor (FU) 80%Cell area (AC) 100 cm2

Base cost of the fuel cell for 2001 (CUCO) $ 100Exponential parameter (s) 0.1 years–1Annual discount rate (d) 10%Lifespan (n) 20 yearsUnit cost adjustment factor (b) 0.2Year the study began (t0) 2001

A. Contreras et al. / Applied Energy 87 (2010) 1376–1385 1381

base value of the equipment costs and of the cell unit costs also re-fer to 2001, and are assumed to equal $ 1000 and $ 100, respec-tively [52]; (c) The equipment costs must increase year on yearas a result of the expected increase in the annual consumption ofenergy in each household of the rural sector. This increase in thecosts is assumed to be 3% a year, of the same order as the estimatedgrowth in energy consumption in the residential sector of Venezu-ela [47]; (d) The unit cost of the cells is expected to decrease intime due to technological improvements and to their mass produc-tion. In order to study this decrease, different scenarios have beenassumed, and here we will use two: the first, more conservativescenario, establishes a linear decrease of 2% a year in the unit costof the cells CUC [26]; the second, more optimistic scenario, assumesa larger decrease with a nonlinear power-type representation [53]:

CUC ¼ CUC0bsðt�t0Þ ð20Þ

In Eq. (20) CUCO represents the base cost for first year of thestudy, t0. The variation of CUC for each scenario and in the simula-tion period is displayed in Fig. 1.

0

20

40

60

80

100

120

140

160

180

0 100 200 300 400

DC(m

NC

Fig. 2. Variation in the nu

4.1. Selected rural centres of population

Taking into account that Venezuela is politically divided into 23states or provinces, 330 municipalities and 1680 parishes [14], forour selection we made direct and inclusive comparisons. In otherwords, first we chose a state, then a municipality and then a parish.As a result of this procedure, we selected the state of Portuguesa, inthe central-west part of the country. We then chose the municipal-ity of Guanarito, and finally the parish of Trinidad de la Capilla, as itwas the one that best met our selection criteria. This parish has arural population percentage of 72%, of which 80% has no energysupply, which means that 539 households do not have permanentenergy services, and mainly use wood or highly pollutant and inef-ficient fossil fuel sources for cooking, as well as not having electric-ity [14].

4.2. The Parameters of the final use model

In order to apply the model to the selected rural centres ofpopulation, the value of the different parameters that appear init must be established. As the case may be, these correspond tothose indicated in [22] for the construction of the polarizationcurve (Eq. (1)), or to those used in papers in the bibliographyon PEM fuel cells for residential use and/or with similar operatingconditions [22,48,52]. For the price of the electric cooker, we haveassumed a mean value of the commercial offering in Venezuela,taking into account the output power interval considered in thisstudy (see Table 1).

5. Results and discussion

First of all, we will present and analyze the results of the energymodel. The calculations have been made for each year of the cellstack lifecycle and each pair of values (DC, VC), obtained from thePolarization Curve. Fig. 2 displays the variation in the number ofcells with respect to the current density for the entire study inter-val. It is observed that for a fixed year, the number of cells in thestack decreases continuously because a smaller useful transfer areais required. This decrease is sharper for the lower values of DC,tending asymptotically to constant values. This behaviour is re-peated for the whole interval studied, and it is noted that as timepasses, the amount of cells increases in order to meet the annual

500 600 700 800 900

A/cm2)

20012005201020152020

mber of cells with DC.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 100 200 300 400 500 600 700 800 900 1000

DC (mA/cm 2 )

EFI

Fig. 3. Fuel cell efficiency vs. DC.

0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400 500 600 700 800 900

DC(mA/cm2)

CH

2(N

m3 /

year

-hou

se)

20012005201020152020

Fig. 4. Change in the consumption of H2 with the DC.

0

0.5

1

1.5

2

2.5

3

3.5

0 100 200 300 400 500 600 700 800 900

DC(mA/cm2)

CE($

/kW

h)

20012005201020152020

Fig. 5. Cost of electricity with DC. Conservative scenario.

1382 A. Contreras et al. / Applied Energy 87 (2010) 1376–1385

A. Contreras et al. / Applied Energy 87 (2010) 1376–1385 1383

increase of power due to the larger amount of energy consumed bythe rural households.

The variation of the efficiency of the fuel cell is shown in Fig. 3,and we noticed that the efficiency of the cell stack is reduced as theDC increases, and as the potential generated by the cell diminishes.

If we now consider H2 consumption, this increases within onesame year as the DC increases. Hydrogen consumption also in-creases from one year to another for a fixed value of DC, due tothe increase in the output power. Both patterns of behaviour aredisplayed in Fig. 4.

As regards the results obtained from the economic model, let usconsider first the results of the conservative scenario displayed inFig. 5. It may be seen that for one same year, the cost of electricitydecreases with the DC to constant values as a result of which theincrease in the H2 costs, due to a larger amount being required,is offset by the decrease in the investment costs due to the de-crease in the number of cells. Furthermore, for a fixed value ofthe DC, the lowest cost of electricity is obtained for 2020, due tothe economy of scale effects generated by the larger electricity pro-duction that is required. The same behaviour is seen in the opti-mistic scenario, which is displayed in Fig. 6, the difference beingthat the cost values obtained are markedly lower as a consequenceof the sharp decrease in the unit costs of the fuel cells.

The difference of costs between the two scenarios is displayedbetter in Fig. 7, which shows that the differences increase towardsthe end of the considered interval of time.

0

0.5

1

1.5

2

2.5

3

3.5

0 100 200 300 400

DC(m

CE($

/kW

h)

Fig. 6. Cost of electricity with

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2000 2005 2010

T (ye

CE($

/kW

h)

Fig. 7. Temporal variation of th

The values for the cost of electricity might be considered highcompared to those obtained in other studies on energy suppliesfor isolated households [21,22]. However, in situations such asthe one studied here, the energy supply to rural regions with alow standard of living, and in developing countries, the usual pro-cedure of assessing the viability of an energy proposal based exclu-sively on quantification, and comparison in monetary terms of itscosts and benefits, is not the most appropriate. This is because, inthis case, there are intangible benefits which are therefore hardto quantify and, still less, to express in monetary terms. Indeed,how can one quantify in monetary terms the improvement in theenvironmental conditions, quality of life and social influence ofthese villages. How can one include in a costing formula the wel-fare of a rural family that has been supplied with light and heatwith which to cook their food. Therefore, these results have to beviewed in a wider manner, taking into account the purpose ofthe study.

One possible alternative to what is proposed in this studywould be to extend the electrical grid until it entirely covered allthe rural villages in the parish of Trinidad de la Capilla. In that case,one would have to consider, on the one hand, the costs and, on theother, the environmental impact. With regard to the former, as it isdifficult to obtain reliable values for the cost of transmission anddistribution in Venezuela, we have used the value of 10,000 $/kmused in [19,5]. To these costs, one must add the cost of mainte-nance for the entire transmission system. We also have to take into

500 600 700 800 900

A/cm2)

20012005201020152020

DC. Optimistic scenario.

2015 2020 2025

ars)

Optimistic

Conservative

e costs. DC = 500 mA/cm2.

1384 A. Contreras et al. / Applied Energy 87 (2010) 1376–1385

account the environmental impact of the power lines and otherdistribution equipment, as they have to cover an area of 800km2. Should the costs incurred by this impact, i.e. by externalissues, be quantifiable, the total costs would also have to be added,so that this option involves a number of obstacles. This has meantit has not been possible to implement, and nothing appears to indi-cate it will be implemented in the medium-term future. All in all,the use of fuel cells in the rural sector of Venezuela would, inprinciple, be viable if one takes into account not only the economicfeatures, but also social and human development aspects.

6. Conclusions

The use of PEM cells in the rural sector of Venezuela was stud-ied by formulating and manipulating a mathematical model.

Conceptually speaking, the model developed is semi-empiricaland structurally it is formed by an energy model and an economicmodel. The energy model studies the energy conversion process interms of the current density vs. voltage relationship, which it thenuses to calculate the main design variables of the cell system:number of cells, efficiency and H2 consumption. The economicmodel estimates the fuel, investment and operational costs of eachpoint of operation. The resultant End Use Model is used to calculatethe costs of utilizing H2 in Venezuelan rural centres of populationto meet their energy needs through the generation of heat andelectricity. The simulation spans a 20-year time horizon from theyear 2001, which is when the last population and housing censuswas conducted in Venezuela. The simulation also considers the an-nual linear increase in equipment costs, as a result of the increasein the expected energy demand; and the decrease in the cell unitcosts due to technological improvements and its mass production,for which two possible scenarios have been considered: a conser-vative scenario expressed by a linear decrease and another moreoptimistic scenario in which a sharper decrease in costs is as-sumed. The results show that for both scenarios the cost of theelectricity produced by the cells decreases asymptotically for thesame year because the investment costs and the H2 costs offsetone another, and interanually, due to the economy of scale effects.The decrease in the cost of electricity production is sharper for theoptimistic scenario. The tangible and intangible beneficial effectsof the use of fuel cells, which can be summarized as a majorimprovement in the quality of life of the rural populations ifVenezuela, mean the use of PEM cells is, in principle, viable as afinal use technology for supplying the required energy to the ruralsector of Venezuela.

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