1-s2.0-S0196890413008121-main

Energy Conversion and Management 79 (2014) 415–430

Contents lists available at ScienceDirect

Energy Conversion and Management

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

Performance analysis of a co-generation system using solar energyand SOFC technology

0196-8904/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.12.036

⇑ Corresponding author. Tel.: +60 183631302.E-mail addresses: [email protected], [email protected] (R.K. Akikur).

R.K. Akikur a,⇑, R. Saidur a,b, H.W. Ping a, K.R. Ullah a

a UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R&D UM, University of Malaya, 59990 Kuala Lumpur, Malaysiab Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 September 2013Accepted 16 December 2013Available online 11 January 2014

Keywords:Co-generationSolar energySolid oxide fuel cellSolid oxide steam electrolyzerHydrogen production

Due to the increasing future energy demands and global warming, the renewable alternative energysources and the efficient power systems have been getting importance over the last few decades. Amongthe renewable energy technologies, the solar energy coupling with fuel cell technology will be the prom-ising possibilities for the future green energy solutions. Fuel cell cogeneration is an auspicious technologythat can potentially reduce the energy consumption and environmental impact associated with servingbuilding electrical and thermal demands. In this study, performance assessment of a co-generation sys-tem is presented to deliver electrical and thermal energy using the solar energy and the reversible solidoxide fuel cell. A mathematical model of the co-generation system is developed. To illustrate the perfor-mance, the system is considered in three operation modes: a solar-solid oxide fuel cell (SOFC) mode,which is low solar radiation time when the solar photovoltaic (PV) and SOFC are used for electric and heatload supply; a solar-solid oxide steam electrolyzer (SOSE) mode, which is high solar radiation time whenPV is used for power supply to the electrical load and to the steam electrolyzer to generate hydrogen (H2);and a SOFC mode, which is the power and heat generation mode of reversible SOFC using the storage H2

at night time. Also the effects of solar radiation on the system performances and the effects of tempera-ture on RSOFC are analyzed. In this study, 100 kW electric loads are considered and analyzed for thepower and heat generation in those three modes to evaluate the performances of the system. This studyis also revealed the combined heat and power (CHP) efficiency of the system. The overall system effi-ciency achieved for the solar-SOFC mode is 23%, for the solar-SOSE mode is 20% and for the SOFC modeis 83.6%. Besides, the only electricity generation efficiency for the solar-SOFC mode is 15%, for the solar-SOSE mode is 14% and for the SOFC mode is 44.28%. An economic analysis is presented based on theannual electricity generation from the system and the system has shown the good economic viabilityin this study with a unit cost of energy (COE) about 0.068 $/kW h.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The World Bank and International Energy Agency reported thatthe world will require twice installation capacity over the next40 years for the new-electrical power to meet the anticipated de-mands. In an another estimation the World Business Council re-ported that for the Sustainable Development, 40% of the worldprimary energy will be used for cooling, heating and providingpower. Most of this energy is from electricity which is generatedat centralized power stations; where at present up to 70% of avail-able energy already lost. Although, the finite sources like naturalgas, coal, and unprocessed oil, are the major sources of energythose are supplying large portion of energy on this planet, butthe increasing rate of populations and energy demands are

growing faster than the energy generation. Hence to meet theclimbing energy demands the world cannot depend only on thelimited conventional sources [1,2].

This paper presents a complete renewable based sustainablecogeneration system to produce combined electricity and thermalenergy using hybrid solar energy and solid oxide fuel cell technol-ogy. The importance of solar energy, solid oxide fuel cell as well ascogeneration system is described in next subchapters.

1.1. Solar energy

The solar energy is an unlimited source of energy which is orig-inated from the sun. When the light and heat from the sun are useddirectly without changing the form, then the technology refers as adirect or passive technology of solar energy and when it used byconverting the form of energy, that is called indirect or activetechnology of solar energy. The photovoltaic technology is the

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Nomenclature

Aap aperture area, m2

Ac area of the receiver cover, m2

Ar area of the receiver, m2

Cp specific heat, kJ/kg Kda anode thickness, lmdc cathode thickness, lmD diameter, mEact,c activation energy for cathode, J/molEact,a activation energy for anode, J/molF the Faraday constant, C/molh specific enthalpy, kJ/kghc convection heat coefficient, kW/m2 Khr radiation heat coefficient, kW/m2 KI current, AJ current density, A/m2

kc incidence angle modifierL electrolyte thickness, lmn electrode porosityNus Nusselt numberP pressure, barQ heat rate, kWr average pore radiusR the universal gas constant, J/mol KS solar radiation, W/m2

T temperature, �C or KUL overall heat loss coefficient of the solar collector, kW/

m2 KUo heat loss coefficient between the ambient and receiver

of the solar collector, kW/m2 KV voltage, Vw collector width, m_W power, kW

Greek lettersr Stefan–Boltzmann constant, kW/m2 K4

q density, kg/m3

ca pre-exponential factor for anode exchange current den-sity, A/m2

cc pre-exponential factor for cathode exchange currentdensity, A/m2

ecv emittance of the receiver coverri irreversibility lossa absorbance of the receiverg efficiencys transmittance of the glass coverqc reflectance of the mirrorc intercept factor

Subscriptsi inlet

Acronymsamb ambientHEX Heat exchangermp maximum poweroc open circuit voltagePTSC parabolic trough solar collectorsref referenceRSOFC reversible solid oxide fuel cellSOSE solid oxide steam electrolyzerSOFC solid oxide fuel cellSC short circuit

416 R.K. Akikur et al. / Energy Conversion and Management 79 (2014) 415–430

renowned indirect way and the solar thermal system is the directway to harvest the abundant energy [2,3]. Approximately 60% oftotal emitted energy from the sun reaches the surface of earth.Considering 10% conversion efficiency of 10%, about 0.1% of this en-ergy can generate 3000 GW power; which is four times larger thanthe world’s total generation capacity. Among the renewablesources solar energy is the most clean and amicable for the envi-ronment. As a consequence, it is getting more concentration to playan important contributor in electricity generation system [4,5].

Although, the solar energy system is still more expensive thanthe conventional energy system, but the solar energy system costreduces progressively due to the improvement of modern and reli-able PV technologies. The solar energy cost has dropped over thelast few decades in such a way that the solar module cost wasaround US$27,000/kW in 1982, US$4,000/kW in 2006 and the so-lar-PV installation cost was approximately US$16,000/kW in1992, US$6,000/kW in 2008. Regardless of, the acceptance of solarenergy and R&D works have been tremendously increasingbecause of the worldwide supportive movements and policiesimplemented by the governments [2].

In this study, the solar PV is used for water steam electrolysisand electrical loads. The parabolic trough solar collectors (PTSC)are used for supplying high temperature water steam to producehydrogen. The PTSC is chosen for this study because it is the mostestablished technology among the solar thermal technologies [6].

1.2. Solid oxide fuel cell

The hydrogen production by the endothermic electrochemicalreactions of water can be possible in reverse fuel cell operation.

If the required electrical and heat input could be provided by thenon-fossil fuel, CO2 emission free sources (like, solar, wind, hydro,biomass, and geothermal) the sustainable H2 production by waterelectrolysis would be more promising in economical and cleanli-ness point of view [7]. The main advantage of H2 production athigh temperature is, significantly low electrical energy requiredto electrolyze the water compared to the low temperature system.The total energy requirements for H2 production are less sensitiveof the operating temperature; as a consequence high temperaturefuel cell offers more opportunities to use the industrial waste heat[8,9].

The fuel cell technologies are getting importance for global en-ergy supplies instant of centralized power plants in a small to largescale power generation because, it is more environmental friendlyas well as higher efficient compared to the fossil fuel based powerplant. Among the fuel cell technologies the solid oxide fuel cell(SOFC) has been recognized as a promising clean energy technol-ogy which produces electricity by the chemical reactions of fueland oxygen at higher efficiency (45–65%). The various range of fuelutilization makes the SOFC more attractive. The gaseous hydrogen,natural gas, products of coal gasification can be used as a fuel ofSOFC. It becomes possible for the high operating temperature(600–1000 �C), which helps internal fuel reforming [10–13]. Addi-tionally, the SOFC produces steam at high temperature that can beharnessed for further uses such as combined cycle or space anddomestic water heating. This hybrid operation of SOFC can raisethe overall system efficiency above 80% [14,15].

The production of H2 as well as electricity by a single solid oxidefuel cell makes it economically sound. Some novel studies havealso been done on dual mode operations of SOFC. For example,

R.K. Akikur et al. / Energy Conversion and Management 79 (2014) 415–430 417

Ni et al. [16] have presented a theoretical model of SOFC in dualmode operations and developed successfully. Jie Guan et al. [17]have developed a high performance reversible SOFC. They havetested 10 RSOFC stacks over 1000 h alternating the modes. Theproject was successful for producing hydrogen and electricity withhigh efficiency. Recently lots of studies have been done to improvethe performance of RSOFC such as Rao et al. [18] have proposed aco-doped BaZrO3 (BZC-x) samples of a single phase air electrodefor reversible solid oxide cells and found the polarization resis-tance promisingly lower. Nguyen et al. [19] have built a two-cellplanar stack in the Jülich F-design with solid oxide cells and dem-onstrated the reversible operation between fuel cell and electroly-sis modes. They have found that the mixed-conducting oxygenelectrodes LSCF were presented as good candidates for reversibleoxygen electrodes in high temperature electrolysis cells. Zhanget al. [20] have developed a designed apparatus for testing of singlesolid oxide cells in both fuel cell and electrolysis modes of opera-tion. Laguna-Bercero et al. [21] have presented an electrochemicalperformance of LSCF and LSM/YSZ composites as oxygen electrodesfor RSOFC. Both LSCF and LSM/YSZ were shown as good applicantsas reversible oxygen electrodes using Scandia stabilized zirconiabased cells. He et al. [22] have studied on a RSOFC, where theRSOFCs with thin proton conducting electrolyte films of BaCe0.5Z-r0.3Y0.2O3-d were fabricated and their electro-performance wascharacterized with various reacting atmospheres.

1.3. Co-generation system

Co-generation system is not a new concept which came in the1880s from industrial plants when as a primary energy source inindustry was steam. Before 20th century, main electricity genera-tion system was coal fired boiler and steam generator based andthe exhaust steam from this system was used for industrial heatingapplications. The co-generation system gained more attention justafter the oil crisis in 1973 because of the lower fuel consumptionand environment pollution. In addition, the co-generation systemcan provide both electricity and thermal energy using a singlesource of fuel with high efficiency. The efficiency of co-generationsystem is over 80%, where the average efficiency of a conventionalfossil fuel system is 30–35%. Consequently the generation cost be-comes lower in cogeneration system. Because of these advantages,today many countries like Europe, USA, Canada and Japan are tak-ing leading contribution to establish cogeneration system not onlyin industrial but also residential sector. Now-a-days, it can provideelectricity and heat for small to large scale applications, such forhospital, office building, hotel, and single or multifamily residentialbuildings [23].

The renewable energy is doing a great contribution in a cogen-eration system to provide green energy solution around the world.Among the renewable energy sources the contribution of solar en-ergy is more noticeable than the other sources. Various technolo-gies and studies have been proposed utilizing the solar energy ina cogeneration system. Rheinländer and Lippke [24], Pearce [25],Prengle et al. [26], Moustafa et al. [27], Mcdonald [28], Mittelmanet al. [29], Qiu and Hayden [30], have considered solar energy intheir study to establish the cogeneration system.

The solid oxide fuel cell has been implemented and investigatedin a cogeneration system by the many researchers not only in largepower system but also in a building integrated system over the lastfew decades. For example, Zink et al. [31] have studied on a build-ing integrated CHP system and funded the superiority of SOFC tosupply electricity and heat according to the economic and environ-mental analysis. Naimaster and Sleiti [32] have presented amedium level cost economical SOFC based CHP system for an officebuilding. Wakui et al. [33] carried out a study on 0.7 kW SOFC-CHPsystem with a plug-in hybrid electric vehicle. Han Xu et al. [34]

have developed a 1 kW residential CHP system considering planarcounter-flow SOFC. Lee and Strand [35] have analyzed on the mod-eling algorithm for the simulation of SOFC cogeneration systemand parametric studies carried out to investigate the effect of eachcell parameter on system performance. Verda and Calí Quaglia [36]have modeled a distributed power generation and cogenerationsystem and investigated possible improvements of SOFC to in-crease the plant performance. Rokni [11] presented a hybrid sys-tem with SOFC and steam turbine where the cyclic efficiency ofthe system has been improved considerably higher than theconventional system.

This study proposed and investigated a new concept of a cogene-ration system for green energy supply. The system differs from oth-ers in such a way that the solar energy in both direct and indirectforms is used and stored as a H2 gas instead of battery bank for con-tinuous power and heat supply using reversible solid oxide fuel celltechnology. This study illustrates the performance of the proposedmodel considering the three modes of operation through importantoutput parameters. These parameters are H2 generation efficiency,energy efficiency, net electrical power, electrical to heating ratioand the unit cost of energy. The investigation considers the effectof changing different operating variables on these parameters. Thevariables are the solar radiation, the operating temperature of RSOFCfor both modes and the H2 utilization of SOFC.

2. System description

The proposed co-generation system comprises of PTSC, solarphotovoltaic, RSOFC and heat exchanger (HEX) as shown inFig. 1. The parametric values of those subsystems have been givenin Table 1 to analyze the proposed cogeneration system.

The solar energy based co-generation system or any other sys-tem, the energy input varies with the time. At morning, after a cer-tain period the solar radiation increases from zero to its maximumpoint at noon and then decreases from maximum point to zero atsunset. As a consequence, for a continuous operation of solar basedsystem, another auxiliary system is required. Nowadays hydrogenstorage system is a promising solution for a large system as a costeffective and ecofriendly manner [8,20]. In this study, hydrogen isproduced and stored using solar energy for steam electrolysis dur-ing the daytime to ensure the continuous power supply at nighttime. The operating modes of the co-generation system consider-ing H2 storage, reversible SOFC and hybrid solar energy aredescribed next.

The operation can be described in three modes such as: solar-SOSE mode, SOFC mode and solar-SOFC mode. The systemoperation in these three modes are described below.

2.1. Solar-SOSE mode

The higher solar radiation time in the day is solar-SOSE mode.During the time, the system operation is described below:

– Water is supplied from the water storage tank to the PTSCwhere it absorbs the heat energy provided by the solarcollectors.

– Then the steam is heated by the HEX-1 before being fed into theelectrolyzers, when the steam gains at least 800 �C then goes tothe cathode of the RSOFC or if the steam gains lower than800 �C, it goes through the heater. In this mode the RSOFCworks as an electrolyzer.

– The solar PV is providing the electricity to electrolyze the steamfor producing the hydrogen and oxygen. The solar PV is alsoproviding the required electricity for the electric load duringthis mode of operation.

Fig. 1. Block diagram of the system operation in hydrogen production mode.


– The produced H2 with unreacted steam and the O2 pass throughthe HEX-1 and releases heat for the steam. After that the H2 andthe steam are condensed and go to the hydrogen storage tankand water storage tank respectively.

2.2. SOFC mode

After the sunset, during the night time and until sunrise theSOFC provides electricity for the load using the storage hydrogenas a fuel. The operation of SOFC mode is shown in Fig. 2 anddescribed below:

– The hydrogen from the hydrogen storage tank is initially heatedby the preheater then goes to the anode of SOFC.

– The air (O2) is supplied to the cathode.– The produced electricity goes to the load and the steam passes

through the HEX-2 and releases efficient heat energy that isabsorbed by the input H2 when drives through the HEX-2.

2.3. Solar-SOFC mode

– The system operation time in a solar-SOFC mode is few hoursafter the sunrise, and few hours before the sunset; the solarenergy collected by the PV modules is used for the loads supplyand by the collectors used for thermal storage. Besides, theadditional power for the load is delivered by the SOFC. Theoperation of the SOFC has been described in SOFC mode. Forthe heat load, PTSC can provide heat energy in this mode ofoperation and the heat is stored in heat storage tank.

3. Mathematical model development

The mathematical descriptions of each subsystem of the co-generation system are described in this section. In the presentstudy, some basic assumptions are employed to simplify theanalysis of the system in the followings are [35,40]:

1. The mass flow of the input fuel gas and all the reactionproducts of fuel cell are stable.

2. Incoming fuel and air are uniformly distributed to eachindividual cell in the stack at SOFC mode.

3. The air supplied to the cathode is composed of 21% oxygenand 79% nitrogen.

4. The temperatures of both the anode outlet gas and cathodeoutlet gas are equal to the operating temperature of the cellstack at both SOSE and SOFC mode of operation. The currentand voltage of every cell unit are the same.

5. Pressure at the anode and the cathode of the SOFC is consid-ered constant and equal.

6. Radiation heat transfer between gas channels and solidstructure is negligible.

7. Contact resistances are negligible.8. Pressure change at SOFC is negligible.9. Liquid H2O is fed to the PTSC in a reference environment

condition, i.e. 298.15 K and 1 atm.10. Heat losses inside the pipe are negligible.

3.1. Parabolic trough solar collector

In order to describe a parabolic trough geometrically, the parab-ola has to be determined, the section of the parabola that is coveredby mirrors and length of the trough. Four parameters are usuallyused to characterize the form and the size of a parabolic trough col-lector (shown in Fig. 3): trough length (L), focal length (f), aperturewidth (w), i.e. the distance between one rim and the other, andrim angle (w), i.e. the angle between the optical axis and the line be-tween the focal point and the mirror rim. The characteristics of PTSCused for solar collector analysis have been given in Table 1.

The mathematical analysis of the parabolic trough solar collec-tor (PTSC) is presented in this sub-chapter [6,37].

The delivered useful power of the collector is calculated by thefollowing equation

_Qu ¼ _mrðCpr;oTr;o � Cpr;i

Tr;iÞ ð1Þ

Table 1Values of input parameters in the present CHP model.

Parameter Value Reference

Solar thermal subsystem [37]Stefane Boltzmann constant, r 5.67 � 10�8

Emittemce, e 0.87Reflectance of the mirror 0.931Intercept factor 0.93Transmittance of the glass cover 0.94Absorbance of the receiver 0.94Incidence angle modifier 1Collector width, w(m) 3.5Collector length, Lc (m) 20Collector outer diameter Dc,o(m) 0.09

Solar photovoltaic subsystem [38]Temp. coefficient of open circuit voltage at

reference solar irradiance, (V/C)0.248

Temp. coefficient of short-circuit current atreference solar irradiance, (A/C)

0.0054

Reference solar radiation, Sref(W/m2) 1000Reference temperature, Tref (�C) 45Ambient temperature, Tab(�C) 25Open-circuit voltage, Voc (V) 62Short-circuit current, Isc (A) 5.4Voltage at maximum power point, Vmp(V) 50Current at maximum power point, Imp (A) 5Module rated power, P (Watt) 250Module surface area, m2 1.73

Solid oxide fuel cell subsystem [39]Pressure, P (bar) 1The pre-exponential factors of cathode, cc (A/m2) 1.344 � 1010

The pre-exponential factors of anode, ca (A/m2) 2.051 � 109

The activation energy level at the cathode, Eact,c

(J/mol)1.00 � 105

The activation energy level at the anode, Eact,a

(J/mol)1.20 � 105

Electrode tortuosity, 1 5.0Electrode porosity n 0.4Average electrode pore radius, r (lm) 0.5Constant, k (J/K) 1.38 � 10�23

Electrolyte thickness, L (lm) 50The thickness of anode, da(lm) 500The thickness of cathode, dc (lm) 50For model validationElectrolyte thickness, L (lm) 1000The thickness of anode, da(lm) 100The thickness of cathode, dc (lm) 100


The power also can be calculated by

_Q u ¼ AapFRðSr;ar � ðAr=AapÞULðTr;i � T0ÞÞ ð2Þ

where the aperture area of the collector Aap, the receivers absorbedradiation Sr,ar, the heat removal factor FR and the overall heat lossco-efficient between the ambient and the receiver of the collectorUL can be defined by Eqs. (3)–(6).Aap ¼ ðw� Dc;oÞLc ð3Þ

Sr;ar ¼ Sgr ð4Þ

FR ¼_mrCpr

ArUL1� exp �ArULF1

_mrCpr

� �� ð5Þ

UL ¼Ar

ðhc;ca þ hr;caÞAcþ 1

hr;cr

� ��1

ð6Þ

gr ¼ qccsaKc ð7Þ

In Eq. (3) w, Dc,o and Lc represent the collector width, the cover outerdiameter and the length respectively. In Eq. (4) gr is the receiverefficiency that can be presented by Eq. (7). In Eq. (5), Cpr

and F1

are the working fluid’s specific heat in the receiver and collector’sefficiency factor that can defined as

F1 ¼ U0=UL ð8Þ

In Eq. (6) the convention heat coefficienthc,ca, the radiation heat coef-ficient hr,ca between the cover and the ambient, and the radiation heatcoefficient hr,cr between the cover and receiver are defined as

hc;ca ¼ ðNus kair=Dc;oÞ ð9Þ

hr;ca ¼ ecvrðTc þ TaÞ T2c þ T2

a

� �� ð10Þ

hr;cr ¼rðTc þ Tr;avÞ T2

c þ T2r;av

� �1=er þ ðAr=AcÞð1=ecv � 1Þ

0@

1A ð11Þ

In Eq. (8), U0 is the overall heat coefficient that can be calculated byEq. (12).

U0 ¼1

ULþ Dr;o

hc;r;in Dr;iþ Dr;o

2krlnðDr;o=Dr;iÞ

� �� 1

ð12Þ

where hc,r,in is the convective heat transfer coefficient inside the re-ceiver tube that is defined as,

hc;r;in ¼Nusrkr

Dr;ið13Þ

In Eqs. (10) and (11), Tc is the glass cover temperature, that can befound by iterative process and the equation is explained in Ref. [6].

The amount of solar energy absorbed by the working fluid cir-culating in the receiver is calculated by_Qsolar ¼ AapFRSColr ð14Þ

where Colr is the total number of the solar collector’s rows.

3.2. Solar photovoltaic

Solar cell is basically a p–n junction fabricated in a thin wafer orlayer of semiconductor. The majority of modules use crystalline siliconcells or thin-film cells on cadmium telluride or silicon. The construc-tional geometry of solar module has shown in Fig. 4. The electromag-netic radiation of solar energy can be directly converted to electricitythrough photovoltaic effect. The solar PV module’s characteristics aregiven in Table 1; those are used for solar-PV subsystem’s analysis.

To design an optimum solar photovoltaic module system for aparticular site, the mathematical equations are presented belowbased on a stochastic method [38,41].

The total power generated by the photovoltaic array is

WPV ¼ VPV Itotal ð15Þ

where Itotal can be defined as

Itotal ¼ ILoad þ ISOSE ð16Þ

where ISOSE is the delivered current by the photovoltaic array forsteam electrolysis.

The total current delivered by the PV can be calculated by solv-ing the following equations

Itotal ¼ ISC 1� C1 expV � DVC2VOC

� �� 1

� �� þ DI ð17Þ

where ISC is the short circuit current of module, VOC is the open circuitvoltage and DV, DI are the change of voltage and current of the mod-ule that can be determined by Eqs. (20) and (21). Furthermore, theconstants C1 and C2 in Eq. (17) can be calculated by Eqs. (18) and (19).

C1 ¼ 1� Imp

ISC

� �exp � Vmp

C2VOC

� �ð18Þ

C2 ¼Vmp=VOC � 1

lnð1� Imp=ISCÞð19Þ

Fig. 2. Block diagram of the system operation in heat and power generation mode.

Fig. 3. Parabolic trough solar collector with geometrical parameters.

Fig. 4. The physical structure of a PV module as well as panel.


In Eqs. (18) and (19), Vmp and Imp are the voltage and the currentat maximum power point.

DI ¼ aS

Sref

� �DT þ S

Sref� 1

� �ISC ð20Þ

DV ¼ �bDT � RSDI ð21Þ

T ¼ Tamb þ 0:02S ð22Þ

DT ¼ T � Tref ð23Þ

In Eqs. (20)–(22), a, b are the temperature coefficients, where Rs andS are the series resistance and the tilt insolation respectively.

3.3. Solid oxide fuel cell

The planar SOFC with co-flow geometry as shown in Fig. 5 isconsidered as the basic configuration. The typical SOFC dimensionsare given in Table 2. The working temperature of SOFC is high, so

yttria stabilized zirconia (YSZ) appears to be the best option ofelectrolyte because of its high ionic conductivity and low cost. Inaddition, YSZ is physically and chemically compatible with theother electrode materials. Typically, the anode is made of nickel-yttria-stabilized zirconia (Ni-YSZ) cermet and the cathode islanthanum strontium manganite (LSM) [42,43].

In dual mode operation, the reversible solid oxide fuel cell(RSOFC) can operate efficiently. The RSOFC can produce a com-pletely renewable based power and hydrogen when the steamelectrolysis and the power generation are coupled. The chemicalreactions and the fundamental working process of a RSOFC in dualmode are shown in Eqs. (24) and (25) and Fig. 6 respectively [17].Mathematical descriptions of RSOFC in both modes are presentedbelow [16,44].

For water electrolysis:

H2Oþ ElectricityþHeat! H2 þ O2 ð24Þ

For power generation:

Fig. 5. Geometrical view of a typical SOFC; (a) Three-dimensional drawing of asingle-cell planar SOFC and (b) Configuration of unit cell planar SOFC.

Table 2Typical solid oxide fuel cell dimensions [42].

Element Size (mm)

Wch Channel width 2lch Channel height 2lint Interconnect height 3Wrib Rib width 0.5W Unit cell width 3Wt Cell width 15L Cell length 15ta Air electrode thickness 50 � 10�3

tf Fuel electrode thickness 50 � 10�3

te Electrolyte thickness 180 � 10�3


H2 þ 1=2O2 ! H2Oþ ElectricityþHeat ð25Þ

3.3.1. Hydrogen productionIn an electrolyzer mode of RSOFC, the steam is fed to the cath-

ode (porous hydrogen electrode). An electrical potential is appliedbetween two electrodes, when the potential is sufficient to splitthe steam, the water molecules are diffused to the cathode-electro-lyte interface and separated into hydrogen gas and oxygen ions.The hydrogen gas is collected from the cathode and the oxygenions go to the anode through the solid electrolyte. The oxygen ionsare oxidized to oxygen gas and the produced oxygen is transportedthrough the pores of anode to the anode surface. The reactions ofwater in RSOFC have been shown in Fig. 6.

The total energy demand (DH) for RSOFC in SOSE mode can becalculated by the following equation

DH ¼ DGþ TDS ð26Þ

where TDS is the thermal energy of H2 in J/mol and D G is the elec-trical energy demand (free Gibson energy change). Fig. 7 shows thatthe electrical energy demand decreases with increasing of thermalenergy but the total demands do not change significantly.

The total electrical energy for the RSOFC in hydrogen produc-tion mode is defined by

_WSOSE ¼ VSOSEJSOSE ð27Þ

where VSOSE is the output potential of RSOFC and JSOSE is the currentdensity, which is provided by the other source; in this study solarphotovoltaic has been selected.

In hydrogen production mode, the output potential VSOSE is thesummation of Nernst potential (E), concentration over potentials at

cathode and anode gSOSEconc;i

� �, ohmic over potential (gohmic), and

activation over potentials at anode and cathode (gact,i).

VSOSE ¼ Eþ gSOSEconc;i þ gohmic þ gact;i ð28Þ

i ¼ a; c

The Nernst potential can be determined by the Nernst equation.That can be written as

E ¼ E0 þRT2F

lnP0

H2P0

O2

� �1=2

P0H2O

264

375 ð29Þ

where E0 is the standard potential which is calculated by Eq. (30), Ris the universal gas constant (8.3145 J/mol K), T is the operatingtemperature of the fuel cell in Kelvins, F is the Faraday constant(94685.0 C/mol), and P0

H2; P0

H2O and P0O2

are the partial pressure ofhydrogen, water and oxygen on the electrode surfaces respectively.The details calculation of the partial pressures of SOFC can be foundelsewhere in Ref. [45].

E0 ¼ 1:253� 2:4516� 10�4T ð30Þ

The ohmic over potential is related with the current density, theelectrolyte thickness L, and the operating temperature T as the fol-lowing equation

gohmic ¼ JLu ð31Þ

u ¼ 2:99� 10�5 exp103;00

T

� �ð32Þ

The activation over potentials can be determined by the Butler–Vol-mer equation.

gact;i ¼RTF

sinh�1 J2Jo;i

!ð33Þ

i ¼ a; c

J0;i ¼ ci exp � Eact;i

RT

� �ð34Þ

The concentration overpotential at anode can be determined by

gSOSEconc;a ¼

RT4F

ln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP0

O2

� �2þ JRTlda=2FBg� �rP0

O2

0BB@

1CCA ð35Þ

where l is the dynamic viscosity of oxygen. The flow permeabilityBg can be expressed by the Kozeny–Carman relationship as [46],

Bg ¼e3

72nð1� eÞ2ð2rÞ2 ð36Þ

The concentration overpotential of the hydrogen electrode orcathode can be determined by

gSOSEconc;c ¼

RT2F

ln1þ JRTdc=2FDeff

H2OP0H2

1� JRTdc=2FDeffH2OP0

H2O

!ð37Þ

In Eq. (37) DeffH2O is the effective diffusion coefficient of steam in

porous SOSE electrode, which can be calculated by the moleculardiffusion and the Knudsen diffusion mechanisms using theBosanquet formula [47,48] as following

1

DeffH2O

¼ nn

1DH2�H2O

þ 1DH2O;k

� �ð38Þ

where n/n is the ratio of cathode tortuosity to porosity, n/(nDH2�H2OÞis the reciprocal of effective molecular diffusion coefficient for aH2O–H2 binary system, and n/(nDH2O;kÞ is the reciprocal of effectiveKnudsen diffusion coefficient for steam; those calculations can befound in references [47,48].

The outlet flow of H2 and O2 can be calculated by

Fig. 6. The fundamental working principle of ROSFC.

0

50

100

150

200

250

300

400 600 800 1000 1200 1400

Ene

rgy

dem

and

(kJ/

mol

H2)

Temperature (K)

Electrical Energy

Tharmal Energy

Total energy

Fig. 7. The energy demands for H2 production with varying temperatures [39].


_NH2 ;out ¼J

2F¼ _NH2O;utilized ð39Þ

_NO2 ;out ¼J

4Fð40Þ

The inlet steam flow rate of RSOFC is a known parameter, hence theoutlet flow rate of H2O can be determined by

_NH2O;out ¼ _NH2O;in �J

2Fð41Þ

3.3.2. Power generationThe fundamental operations of RSOFC in power generation

mode are shown in Fig. 6. In power generation mode as the inputhydrogen and oxygen (air) are fed to the porous anode and cath-ode of RSOFC respectively. The oxygen in cathode diffusesthrough the electrode and goes to the electrode interface, whereit is transformed into oxygen ions electro-chemically after react-ing with the electrons that comes through the external circuit.Then the oxygen ion passes through the densed ion conductingelectrolyte to the anode. In anode, the hydrogen atoms diffusethrough the porous anode where they react with the coming oxy-gen ions and produce the steam with free electrons. These elec-trons go to the anode through an external circuit resulting inelectrical power [44].

So the output power in power generation mode can be ex-pressed as

_WSOFC ¼ VSOFCJSOFC ð42Þ

Where JSOFC is the produced current density which is related to theamount of the utilized hydrogen can be shown by

JSOFC ¼ 2 _NH2 ;utilizedF ð43Þ

The fuel utilization ratio, air utilization ratio and excess aircoefficient can be calculated by Eqs. (44)–(46) [49]

Uf ¼_NH2 ;utilized

_NH2 ;inlet

ð44Þ

Ua ¼_NO2 ;utilized

_NO2 ;inlet

ð45Þ

kair ¼2 _NO2 ;inlet

_NH2 ;inlet

ð46Þ

where the oxygen utilization is the half of hydrogen utilization_NO2 ;utilized ¼ ð _NH2 ;utilizedÞ=2

The output voltage of a fuel cell depends on the polarizationlosses as following

VSOFC ¼ E� gSOFCconc;i � gohmic � gact;i ð47Þ

where the Nernst Equation (E), the ohmic over potential (gohmic), theactivation over potentials at the anode and cathode (gact,i) can becalculated by the same equations (Eqs. (29), (31), (33)), those areused for hydrogen production mode.

The concentration overpotential modeling equations in SOFCmode were developed by Chan and Xia [50] and also studied byNi et al. [44]

gSOFCconc;a ¼ �

RT2F

ln1� ðRT=2FÞ Jda=Deff

H2P0

H2

� �1þ ðRT=2FÞ Jda=Deff

H2P0

H2O

� �24

35 ð48Þ

gSOFCconc;c ¼ �

RT4F

lnðp0=dO2 Þ � p0=dO2

� �� P0

O2

� �exp ðRT=4FÞ JdO2 dc=Deff

O2p0

� �h iP0

O2

24

35

ð49Þ

dO2 ¼Deff

O2 ;k

DeffO2 ;kþ Deff

O2�N2

ð50Þ

Similar as DeffH2O (Eq. (38)), the effective hydrogen diffusion coeffi-

cient DeffH2

, the effective oxygen diffusion coefficient DeffO2

, the effectiveKnudsen diffusion coefficient of oxygen Deff

O2 ;k, and the effective oxy-

gen–nitrogen binary diffusion coefficient DeffO2�N2

can be calculated.

3.3.3. Heat supply and generation3.3.3.1. Heat input. The heat energy supplied to the electrolyzer forsteam electrolysis depends on the heat generation by the irrevers-ibility losses [39]. The overpotentials of SOSE involve directly forgenerating the heat as the following equation

ri ¼ 2F gSOSEconc;i þ gohmic þ gact;i

� �ð51Þ

When ri P TDS, the external heat is not needed for the water split-ting reaction, thus Qheat,SOSE = 0.

If ri < TDS, the external heat is needed and the heat energyinput can be determined by

Qheat;SOSE ¼ ½TDS� ri� _NH2O;utilized ð52Þ


The required heat input for the steam electrolysis is stabilized atconstant temperature by the heater. The steam from the PTSC varieswith the solar radiation, as a consequence to heat up the steam atdesired temperature the heat exchanger-1 and the heater are used.

The amount of heat energy provided by the PTSC is determinedby Eq. (2) using the concept of absorbed radiation and the fluid exittemperature can be determined by

_Q u ¼ _mCpðT0 � TiÞ ð53Þ

3.3.3.2. Heat output. From the Steady Flow Energy Equation the en-ergy is balanced by the following equation [51].

Q in þWin ¼ Q out þWout þ DH ð54Þ

Or

Q out � Qin ¼ DG� DHfc � DHref ð55Þ

where DG and DHref are the Gibbs energy and the enthalpy of fuelcell reaction [51].

The total heat output and the heat gain are reduced by heat lossesfrom the external preheater, fuel cell stack and losses up to the heatexchanger. The usable heat output and heat gain are further reducedby the effectiveness of the heat exchanger. Net usable heat gain fromcomplete fuel cell system at SOFC mode can be evaluated bysubtracting the heat output of heat exchanger and the externalpreheating heat input; that can be expressed by Eq. (56).

Q usable;net ¼ ðQ fc;net þ Q H2cr� QlossÞehcx � Q ep ð56Þ

where Qfc,net, QH2crand Qep are the net heat gain within fuel cell

stack, the heat from combustion of recirculated hydrogen and theexternal preheating heat input, those can be evaluated by Eqs.(57)–(59). And ehcx is the heat exchanger effectiveness, Qloss is theheat losses by the surrounding. If the system is well isolated thenQloss = 0

Net heat gain within fuel cell stack can be explained by

Q fc;net ¼ Q fcr þ Q rvl � Q arr ð57Þ

where Qfcr, Qrvl and Qarr are the heat generated from fuel cell reac-tion, the heat recovery from voltage losses and the heat absorbedby reforming reaction respectively. Those can be calculated by Eq.(60) [52], (61) and for the hydrogen as an input fuel no reformationis needed, thus for this study Qarr = 0.

When unutilized fuel is recirculated and burned to preheatinternally, the heat from combustion of recirculated hydrogen is,

Q H2cr¼ _NH2 ð1� Uf Þð�DHfrÞ ð58Þ

Here _NH2 is the mass flow of H2 and D Hfr is the heat required by thereforming process from the enthalpy of reaction.

Q ep ¼ _NH2 ðCp11T11 � Cp10T10Þ ð59Þ

In Eq. (59) Cp11 and Cp10 are the specific heat of H2 at the state of 11and 10 in Fig. 1.

Q fcr ¼ _NH2 Uf ðDG� DHfrÞ ð60Þ

Q rvl ¼ _NH2 Uf ervlð1� gvÞð�DGÞ ð61Þ

In Eq. (61) ervl and gv are the effectiveness of heat recovery fromvoltage losses and the voltage efficiency.

3.3.3.3. Heat transfer. The heat can be transferred in SOFC in threeprocess; convection, radiation and conduction [53]. In this modelfor a planar SOFC, the radiation heat transfer is assumed negligible.Convection is a process of heat transfer that occurs between a sur-face and a liquid or gas that can flow freely due to a temperaturegradient. According to the Newton’s law of cooling, the interaction

between the phases through convection heat transfer can be deter-mined as,

_Qconv ¼ hAiðDTÞ ð62Þ

where A is the surface area across which heat is transferred, DT isthe temperature difference over which heat is transferred and h isthe heat transfer co-efficient that can be determined using the Nus-selt number with local properties equation as following

h ¼ kDh

Nu ð63Þ

The thermal conductivity of the gas (k) can be evaluated by the fol-lowing approximation:

k ¼X

XikjðToutÞ ð64Þ

Conduction is a process of heat transfer that occurs by atomic mo-tion due to a temperature gradient. The conduction heat transfer isgoverned by Fourier’s Law that can be expressed as below

_Qcond ¼ kAðDTÞ

Lð65Þ

where A is the surface area across which heat is transferred and L isthe length over which heat is transferred.

3.3.4. Efficiency calculationThe efficiency of SOSE is determined by

gSOSE ¼ LHVH2_NH2 ;out

_WSOSE þ Q heat;SOSE þ Q heat;H2O

ð66Þ

The efficiency of PTSC can be defined as

gPTSC ¼ FR g0 � ULTi � Ta

GBC

� �� ð67Þ

where C is the concentration ratio and C ¼ AaAr

.The maximum efficiency of solar-PV can be evaluated by

gPVmax ¼

Pm

S� Acð68Þ

where Pm is the maximum power output from PV and Ac is the areaof collector.

The efficiency of a system can be founded by

gsys ¼Useful energy

Energy inð69Þ

The useful energy at solar-SOSE mode is, the power delivered by so-lar-PV for the electric load and the amount of H2 production bySOSE. Whereas, the energy input is the total sun energy on the sur-face area of PV and PTSC. On the other hand at initial operation con-dition the power for heater to worm the steam at requiredtemperature is considered as an energy input. So Eq. (69) can be ex-pressed as following to calculate the system efficiency at solar-SOSEmode.

gsolarþSOSEsys ¼

WPVout;load þ _NH2 ;outLHVH2

WPVinput þ PPTSC

input þ Q heat;SOSE

ð70Þ

The electrical efficiency of the SOFC in fuel cell mode is calculatedby

gSOFCel ¼ WSOFC;net

_NH2 ;inlet LHVH2

ð71Þ

where the net electric power from the SOFC operation is

WSOFC;net ¼ _WSOFC �Wblower ð72Þ

The heat efficiency of SOFC defines as


gSOFCheat ¼

Q usable;net

H2;consumptionLHVH2

ð73Þ

The combined overall efficiency or system efficiency of SOFC is,

gSOFCOverall ¼ gSOFC

el þ gSOFCheat ð74Þ

The overall efficiency at solar-SOFC mode is,

gsolarþSOFCsys ¼

WPVout;load þWSOFC

el þWSOFCheat þ Q water

heat

WPVinput þ PPTSC

input þ _NH2 ;inlet LHVH2

ð75Þ

3.4. Heat exchanger

In this study, counter flow heat exchangers are used to extractthe heat energy from the hot fluids [54]. According to the rangesof temperature, three types of heat exchanger are available, thoseare categories as low temperature (stainless steel heat exchanger;T < 600 �C), medium temperature (nickel based heat exchanger;650 �C < T < 850 �C) and high temperature (ceramic based heat ex-changer; T > 850 �C) [55]. Fig. 8 shows the counter flow tube heatexchanger with the inner diameter (Di) of 25 mm and the outerdiameter (Do) of 45 mm respectively.

The heat exchanger performance evaluates by the effectivenumber of transfer units (e-NTU) method. The actual heat ex-change rate (Q) between two fluid steams can be evaluated by

Q ¼ eeff Q max ð76Þ

where eeff is the effectiveness factor that is mainly depends on theaverage heat transfer rate and the heat transfer area. And Qmax isthe theoretical maximum heat exchange rate between the two fluidstreams that can be determined according to the specific heatcapacity of the two fluid streams.

For counter flow heat exchangers, the effectiveness is related tothe number of transfer units.

(NTU) and capacitance ratio through the following equation:

eeff ¼1� exp½�NTUð1� CrÞ�

1� Cr exp½�NTUð1� CrÞ�ð77Þ

Here, Cr is the capacitance heat ratio that can be calculated by

Cr ¼Cmin

Cmaxð78Þ

In Eq. (78) Cmin and Cmax are the minimum and maximum heat capac-itance rates that can be determined from the heat capacity rates ofcold and hot gas steams; those are presented in Eqs. (79) and (80).

Cc ¼X

_Nccp;c ð79Þ

Ch ¼X

_Nhcp;h ð80Þ

In Eq. (76) the theoretical maximum heat transfer rate Qmax isdefined as

Fig. 8. Counter flow heat exchanger.

Qmax ¼ CminðTh;i � Tc;iÞ ð81Þ

Based on the energy balance, the output steams temperature of theheat exchanger can be calculated by

Th;o ¼ Th;i �QCh

ð82Þ

Tc;o ¼ Tc;i þQCc

ð83Þ

3.5. System cost analysis

The economic analysis of the system has been carried out in thisstudy focusing on the estimation of unit cost of the produced en-ergy ($/kW h). The annual total cost can be calculated by thesum of investment, operation and maintenance cost [56].

Cat ¼ Cai þ Co&m ð84Þ

The annual investment cost Cai can be calculated from the total pur-chasing cost Cpc disregarding the individual component replace-ment cost during its lifespan n:

Cai ¼ Cpc CRF ð85Þ

where CRF (capital recovery factor) can be determined,

CRF ¼ ið1þ iÞn

ð1þ iÞn � 1ð86Þ

where i is the annual interest rate (%).The unit cost of energy Cu($/kW h) can be evaluated by

Cu ¼Cat

Eecð87Þ

where Eecis the annual net usable electrical energy from the system,which is the sum of electrical energy provided by the solar-PV andthe fuel cell.

4. Model validations

The solar-PV subsystem is validated by comparing the analyti-cal results with the manufacture’s data given in Table 1 [38]. Themaximum power, the short circuit current and the open circuitvoltage of the module are 250 W, 5.4 A, 62 V respectively at1000 W/m2 of solar radiation according to the manufacture’s data[38]. In this study, the I–V characteristics of solar-PV at 1000 W/m2 of solar radiation in Fig. 9, shows a good agreement with themanufacturer’s datasheet.

The PTSC subsystem is validated by the experimental study ofDudley et al. [57]. The design data for the black chrome receivermaterial case for a vacuum space between the receiver and its cov-er from Dudley et al. have considered to examine the PTSC model.The model has shown a good agreement with the experimental re-sult (shown in Fig. 10). The difference in the calculations as com-pared to the experimental results is attributed to theapproximation used to calculate the heat loss coefficients.

The fuel cell subsystem for hydrogen production is validated bythe experimental work of Momma et al. [58]. They have clearly sta-ted the laboratory setup and test procedures in literature and thedetails can support the analytical analysis. The experimental workwas considered electrolyte supported planar SOSE. The materialsand the thickness for electrolyte, cathode, anode were yttria stabi-lized zirconia (YSZ), nickel-YSZ, strontium doped lanthanum (LSM-YSZ) and 1000, 100, 100 lm respectively. The tests were conductedat a constant pressure of 1 bar, steam molar fraction of 60%, andvarious operating temperature from 1173 to 1273 K. In this study,the parametric values in Table 1 and the equations for electrolyzer

0

50

100

150

200

250

300

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70

Cur

rent

(A

)

Pow

er (

W)

Voltage (V)

1000 W/m2

ISC= 5.4 A

MPP( 50V, 5A)

VOC= 62V

Fig. 9. Validation of the solar-PV module by comparison of the manufacturers’ data.

0

10

20

30

40

50

60

70

80

90

100

100 150 200 250 300

Hea

t L

oss

(W/m

2 )

Average temperature above ambient (0C)

Experiment

Present Model

Fig. 10. Validation of the solar collector’s model.

0.0

0.5

1.0

1.5

2.0

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Cel

l pot

enti

al, V

(V

)

Current density, J (A/m2)

T=1173 K

T=1223 K

T=1273 K

T=1273 K

T=1223 K

T=1173 K

Experiment [58]

Present model

Fig. 11. Comparison between analytical results and experimental data for modelvalidation-effect of operating temperature and current density on RSOFC potentialin SOSE mode.


mode has been considered and calculated the overpotentials of thefuel cell. The theoretically calculated overpotentials have beencompared with the experimental result in Fig. 11. The Figure showsa good agreement with the experimental work. The model for theSOFC mode developed by Chan and co-workers [50,59] is well ac-cepted (Eqs. (48)–(50)); therefore, no validation is needed farther.

5. Result and discussion

In this section and sub section parametric, energy and economicanalysis are conducted according to the operation mode of CHPsystem. The effects of solar radiation on the model for hydrogenproduction, electric power as well as heat generation are analyzed.The dual mode performance of RSOFC and the effects of parametricchanges are also presented.

5.1. Parametric analysis of the system

In this study 250 W solar modules are considered for the systemanalysis. The electricity generated from solar PV is utilized for theelectric load supply and the steam electrolysis during the highersolar radiation time. The power delivered by solar-PV varies withsolar radiation’s intensity. The effects of solar radiation on powergeneration of solar-PV are shown in Fig. 12 that have been calcu-lated by using the equations in solar subsection and taking the datafrom Table 1. The variations of solar radiation have also effect onthe thermal energy generation by the PTSC, which can be evaluatedby solving Eq. (2). As a result, the existing fluid temperature insidethe PTSC’s tube changes with the radiation, shown in Fig. 13.

According to the literature, cathode supported RSOFC is recom-mended for higher electricity generation, on the other hand, anodesupported RSOFC is for higher hydrogen production [16]. The an-ode supported RSOFC has been selected where the H2O flow rateof 0.05 mol/s for 1 m2 of active area to figure out the temperatureeffects. For hydrogen production from steam electrolysis, temper-ature is one of the key parameters. The temperature effects on asingle cell have been investigated taking the parametric value ofRSOFC in Table 1 into consideration. The cell potential of SOSE isthe summation of the overpotentials, which rises with increasingof temperature as shown in Fig. 14. It is because, the ohmic andthe activation overpotentials significantly increase with increasingtemperature, although the concentration overpotential increasesbut its effect is lower compared to the other overpotentials.

In order to calculate the heat requirement, it is necessary toknow the heat generation by the SOSE cell through irreversibility(ri). After solving Eq. (52) it has been found that the heat generatedby irreversibility varies with the operating temperature. For exam-ple, Fig. 15 shows at low operating temperature (873 K) the addi-tional heat requirement is not needed above the current densityof 500 A/m2 but for the higher operating temperature (1273 K)

additional heat is needed for SOSE up to current density of17,000 A/m2.

During the night time (from few hours before the sun set to fewhours after the sun rise) the RSOFC works as a SOFC mode whereH2 and O2 are supplied as input. The rate of O2 utilization is relatedwith the H2, by the equation _NO2 ;utilized ¼ ð _NH2 ;utilizedÞ=2. Fig. 16 showsthe fuel cell output voltage and the useful electric power changeswith the variation of H2 flow rate at different temperature. Thetemperature changes, instantaneously reflected on the cell’s poten-tial as well as the power, because the current density, J (A/m2) islimited by the cell’s operating temperature. The cell potential de-creases more rapidly at low temperature than the high tempera-ture because both the activation and the ohmic overpotentialincrease with increasing of temperature due to the higher reactionrate. On the other hand, if the temperature rises, polarization mayincrease due to material constraints. The cell can provide morepower at high temperature than the low operating temperature.The electrical efficiency of SOFC has been calculated by solvingEq. (71). Fig. 17 shows the effects of current density variation onelectrical efficiency at different temperature; where, the smallchange of current density the significant changes of electrical effi-ciency at low temperature is occurred.

5.2. Performance analysis of the system

The performance of the co-generation system is analyzed con-sidering 100 kW electric loads and evaluated the amount of heatenergy generated by the fuel cell at SOFC mode. The required

0

50

100

150

200

250

300

350

400

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000

Exi

stin

g fl

uid

tem

pera

ture

, (0 C

)

The

use

ful p

ower

fro

m t

he c

olle

ctor

, (kW

)

Solar radiation, (W/m2)

Power

Temperature

Fig. 13. The variations of the useful power delivered by the PTSC and the existingfluid temperature gain with the changes of solar radiation.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 2000 4000 6000 8000 10000

Cel

l pot

enti

al, V

(V

)


873 K1073 K1273 K

Operating Temperature

Fig. 14. The effects of current density variation on cell potential at differentoperating temperature at electrolyzer mode of operation.

0

100

200

300

400

500

600

700

800

900

1000

0 5000 10000 15000 20000 25000

The

rmal

ene

gy (

kJ/m

ol H

2 )

2

T S at 1273 K2F total at 1273 KT S at 873 K2F total at 873 K

Δ

Δη

η


amount of heat and electricity for H2 production at SOSE mode hasbeen calculated. The considerations and the findings in threemodes of operation are shown in Tables 6 and 7 respectively. Thedetail operation conditions like temperature, enthalpy and entropyof each state of the system based on the operation modes are givenin Tables 3–5 which are considered on system’s operation time.

The RSOFC is considered with the cell area of 0.1 m2 and thethickness of 2.3 mm. The operating voltage of stack is 48 V andthe current density of a single cell is 2500 A/m2. As a consequencethe total required number of cells in series and parallel are 66 and88 respectively in order to analyze the 100 kW electric load supply.At constant pressure of 1 bar and 900 �C operating temperaturewith 80% fuel utilization, the system needs hydrogen flow rate of0.0024 kg/s and oxygen flow rate of 0.0193 kg/s to meet the electri-cal demands. The amount of H2O production rate from the chemi-cal reaction of H2 and O2 is 0.0172 kg/s. The heat energy for H2

preheating is taken from the heat delivered by the SOFC. For0.0024 kg/s of H2 flow rate, 25.8 kW of heat energy is needed togain the temperature at 1000 K. The heat efficiency has been calcu-lated considering the heat for H2 preheating as a loss. As a result,the heat to power ratio has been reduced and found of 0.917.The system efficiencies are conducted in SOFC mode using the effi-ciency equations and the system’s heat, electrical and overall effi-ciencies are found 39.32%, 44.28% and 83.60% respectively. Theheat generation efficiency of the SOFC is relatively more affectedby the cell operating temperature compared to the electricity gen-eration efficiency. The heat generation efficiency decreases withincreasing of temperature, it is because the heat generation fromthe fuel cell reaction decreases substantially with increasing oftemperature. Consequently the heat to power ratio and the overallefficiency of the system are decreased (shown in Fig. 18). Fig. 19shows the fuel utilization effects on the system’s electrical, heat,and CHP efficiency at 1173 K operating temperature, where theelectrical efficiency of the system increases with the increasing fuelutilization. On the other hand the heat efficiency decreases and thedecreasing rate is more substantial than the increasing electricalefficiency, as a result the CHP efficiency is decreased with theincreasing fuel utilization.

In solar-SOSE mode, to produce the same amount of H2 that isused in SOFC mode (0.00241 kg/s), the required electrical and heatenergy demands have been calculated; those are 148.1 kW and51.5 kW respectively (given in Table 7). To produce 0.00241 kg/sH2 the system needs 0.026 kg/s H2O steams as an input at 900 �Coperating temperature. The required electricity to electrolyze thesteam is provided by the photovoltaic. The solar-PV has been de-signed according to the power requirement for the steam electrol-ysis and the electric loads. Using the value of parameters in Table 1for solar subsection, it is found that total 306 kW of PV module isneeded for 100 kW of electrical loads and for 0.00241 kg/s of H2

0

50

100

150

200

250

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60 70 80

Pow

er (

W)

Cur

rent

(A

)

Voltage (V)

900 W/m2

700 W/m2

500 W/m2

Fig. 12. The variations of voltage, current and power of PV with solar radiations.

Current density, J (A/m )

Fig. 15. Comparison of the thermal energy demand and the heat generation causedby irreversible losses at different operating temperature with the variation ofcurrent density.

production. The efficiencies of PV, PTSC and electrolyzer have beendetermined of 14%, 60% and 85.1% correspondingly. The electricaland the thermal energy provided by the PV and the PTSC are di-rectly related with the solar radiation, therefore with the changesof solar radiation the rate of H2 production and the rate of H2Oreaction are changed (shown in Fig. 20). The temperature gain ofwater from PTSC also depends on the flow rate of water insidethe tubes, tubes length, diameter and width. The heat energy ofH2O for H2 production is initially provided by the PTSC after thatthe steam gains more thermal energy from the HEX-1, where theelectrolyzer’s outlet products (H2, H2O, and O2) release the heat

0

1

2

3

4

5

6

7

8

9

10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Ele

ctri

c en

ergy

out

put

(kJ

/ s)

Out

put

pote

ntia

l (V

)

Input Hydrogen flow (mol/s)

Cell potential at 1273 KAt 1073 KAt 873 KPower at 1273 KAt 1073 KAt 873 K

Fig. 16. Effects of H2 flow rate variation on cell potential and power output of SOFCat different cell operating temperatures.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5000 10000 15000 20000 25000

Eff

icie

ncy,

(%

)


At 873 K

At 1073 K

At 1273 K

Fig. 17. Effects of the variation of the cell current density on electrical efficiency atdifferent cell temperature.

Table 3Thermodynamic characteristic of the various states in solar-SOSE mode.

State no. Phase _m (kg/s) T (�C) h (kJ/kg) s (kJ/kg K)

1 Water liquid 0.026 30 125.74 0.4372 Water Steam 0.026 339.23 3074.5 8.213 Super steam 0.015 900 4398 9.784 H2 + H2O

steam0.00241 + 0.0052 900 – –

5 Oxygen gas 0.017 900 1.2 0.0086 H2+H2O

steam0.00241 + 0.0052 400 – –

7 Water liquid 90 419.17 1.308 Hydrogen 0.00241 90 a a

a The enthalpy and entropy at this state is very low.

Table 4Thermodynamic characteristic of the various states in SOFC mode.


9 Hydrogen gas 0.00241 30 0.017 –10 Hydrogen gas 0.00241 – – –11 Hydrogen gas 0.00241 800 34.135 0.17112 Oxygen gas 0.00964 800 1.2 0.00813 Water steam 0.0172 900 4398 9.7814 Water liquid 0.0172 100 125.74 0.437

Table 5Thermodynamic characteristic of the various states in solar-SOFC mode.


9 Hydrogen gas 9.29 � 10�4 30 0.017 –10 Hydrogen gas 9.29 � 10�4 800 34.135 0.17111 Hydrogen gas 9.29 � 10�4 800 34.135 0.17112 Oxygen gas 3.72 � 10�3 800 1.2 0.00813 Water steam 6.65 � 10–3 900 4398 9.7814 Water liquid 6.65 � 10�3 100 125.74 0.437

Table 6The parametric values consideration used to investigate the performance of thesystem for 100 kW electric loads.

Parameter Value Parameter Value

Cell area of RSOFC 0.01 m2 Heat exchangereffectiveness

0.8

Cell thickness of RSOFC 2.3 mm DC/AC converterefficiency

95%

Operating temperatureof RSOFC

900 �C Output hydrogen flowrate at solar and H2

mode

0.00241kg/s

Pressure 1 barFuel utilization ratio 80% Average solar

radiation at solar andSOFC mode

250 W/m2

Effectiveness of heatrecovery fromvoltage losses

75% Average solarradiation at solar andH2 mode

850 W/m2

Input H2 flow rate atSOFC mode

0.00241kg/s

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0

10

20

30

40

50

60

70

80

90

100

800 900 1000 1100 1200 1300

Hea

t/P

ower

rat

io

Ove

rall

ener

gy e

ffic

ienc

y, (

%)

Operating temperature, (K)

Efficiency

Heat to power ratio

Fig. 18. Effects of operating temperature of SOFC on the overall efficiency and heat/power ratio of fuel cell.

0

10

20

30

40

50

60

70

80

90

100

60% 65% 70% 75% 80% 85% 90% 95%

Ene

rgy

effi

cien

cy (

%)

Fuel utilization ratio

Electrical

Heat

CHP

Fig. 19. Effects of fuel utilization ratio on the Electrical, Heat and CHP efficiency ofSOFC.


energy. The heat exchangers have been designed by solving Eqs.(76)–(83) with 25 mm of inner tube diameter and 45 mm of outertube diameter. Total 18 kW of heat energy can be added from the

Table 7The calculated parameters value of the system for 100 kW electric loads.

Parameter Value Parameter Value

At SOFC mode At solar-SOSE modeNet heat gain within the

fuel cell stack88.51 kW Water input flow

rate0.026 kg/s

Heat output from heatexchanger

117.43 kW Output oxygen flowrate

0.017 kg/s

Net usable heat gain fromcomplete fuel cellsystem

91.65 kW Heat fromirreversibility losses

10.2 kJ/mol

Heat efficiency 39.32% Heat energy inputneeded

51.5 kW

Electrical efficiency 44.28% Net energydelivered by PTSC

33.68 kW

Overall efficiency 83.60% Temperature gain ofwater from PTSC

339.23 �C

At solar-SOFC mode The power requiredfor steamelectrolysis

148.10 kW

Power delivered by thePV for load supply

67.3 kW Power delivered bythe PV forelectrolysis

155.9 kW

Power delivered by theSOFC for load supply

33.42 kW Efficiency of PV 14%

H2 supply to the stack 9.29 � 10�4

kg/sEfficiency of SOSE 85.1%

O2 supply to the stack 3.72 � 10�3

kg/sEfficiency of PTSC 60%

H2O out from the stack 6.65 � 10�3

kg/sSystem overallefficiency

20%

Net heat gain within fuelcell stack

34.13 kW

Net usable heat gain fromcomplete fuel cellsystem

35.34 kW

Combined efficiency ofSOFC

85.17%

Efficiency of PV 13%Overall efficiency 23%

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 100 200 300 400 500 600 700 800 900

kg/s

Solar Radiation, (W/m2)

H2 output

O2 output

H2O reaction rate

Fig. 20. The variation of H2 and O2 generation and H2O input flow requirement withthe change of solar radiation.

3.7119.62

35.5251.41

67.2983.16

99.02114.85

97.9483.95

69.9655.97

41.9727.98

13.990.00

0

20

40

60

80

100

120

140

50 100 150 200 250 300 350 400

Tot

al p

ower

, (kW

)

Solar radiation, (W/m2)

PV SOFC

2.15 1.84 1.53 1.23 0.92 0.61 0.31 0.00

H2 flow rate 10-3, (kg/s)

Fig. 21. The variations of input H2 flow rate and power generation of SOFC with thesolar radiation changes that depends on the PV output power to meet the 100 kWelectric load.

Table 8Combined power and heat energy generation performance comparison withliterature.

Parameters Reference model [31] Proposed model

Fuel CH4 H2

Fuel utilization, % 85 80DC power output, kW 95.5 100Max. heating, kW 96.4 91.65Electrical efficiency, % 43.3 44.28Thermal efficiency, % 43.7 39.32 45.6a

Combined efficiency, % 87 83.6 89.9a

a Considering the heat exchanger efficiency 90%.


HEX-1 considering the temperature of H2, H2O and O2 about 900 �Cat the electrolyzer output.

In solar-SOFC mode of operation, the power from SOFC dependson the power delivered by the solar PV. A calculation has beendone and the result is illustrated in Table 7, considering the aver-age lower solar radiation of 250 W/m2. Fig. 21 shows the variationsof SOFC’s power generation that changes with the solar radiationwhich also indicates that the input H2 flow rate depends on the so-lar radiation. The SOFC is operated as partial load in this mode, as aresult the combined efficiency of the fuel cell is little higher thanthe SOFC mode. The PTSC can provide high quality of water steam(122 �C) at 250 W/m2 of solar radiations for 0.026 kg/s of waterflow rate during the operation.

The performance comparison of presented cogeneration systemwith a building integrated SOFC system has been illustrated [31].The building integrated SOFC system was used for absorption heat-ing and cooling applications considering 110 kW SOFC developedby Siemens–Westinghouse [31]. The characteristics of the systemare shown in Table 8 and compared with the proposed model.The presented CHP system shows lower thermal efficiency as wellas overall system efficiency than the literature model, because inmodel analysis the efficiency of heat exchanger was around 80%.If this system is considered with the heat exchanger efficiency of90% (same as literature model), the proposed system shows moreefficient (Table 8).

5.3. Economic analysis

The economic analysis has been conducted in this subsectionconsidering the parameters value given in Table 9. For economicanalysis, the system operation has been considered 8 h in day time

for power and hydrogen production and around 7.7 h in night timefor power and heat generation using the produced H2. In this anal-ysis the components capacity has been considered for 100 kW elec-tric powers. In order to evaluate the cost of energy, the economicassumptions in Table 9 and Eqs. (83)–(86) have been used.

The cost of SOFC and solar-PV are usually the major cost of thesystem. For solar-PV the major cost is due to the photovoltaic mod-ule. The unit price of these components ranges from 0.54 $/Wp upto 3.35 $/Wp depending on the manufacturer, performance andwarranty. For the analysis an average value of solar-PV of 1.34 $/Wp is used [60]. Total 306 kW of solar-PV is needed to provideelectricity for the electric load and the electrolyzer. The averageannual solar radiation data in Ref. [6] has been considered to eval-uate the yearly electricity generation by the solar-PV. According tothe data, the solar-PV provides annually 963.01 MW h electricity

Table 9Economic assumptions [60,55,31].

Fuel cell 1000 $/kWO&M cost for fuel cell 4% IC of SOFCSolar PVa 1.34 $/WO&M cost for solar PV 0% ICPTSC systema 368.5 $/m2

O&M cost for solar thermal 5% IC of PTSC systemHeat exchangera 5360 $/m2

Converter 57.14 $/kWAir flow system 2% IC of SOFCSOFC module lifetime 5 yearsSolar PV module lifetime 25 yearsSolar PTSC lifetime 25 yearsPlant lifetime 20 yearsAnnual interest rate 5%Carbon price 0 $/ton CO2

a 1 Euro = USD 1.34 (Year 2013).


for the electric loads and the electrolyzers. The cost of PTSC withthe supporting structure, reflecting mirror, receiver, tracking sys-tem and foundation is anticipated a value of 368.5 $/m2. The oper-ation and maintenance (O&M) cost has been considered 5% ofinvestment cost (IC) of PTSC, which covers the water cost that isused to extract the heat energy from PTSC.

The SOFC cost has been considered 1000 $/kW, which was the2010 goal set forth by US DOE SECA program [31] and 4% of invest-ment cost (IC) of SOFC as the operation and maintenance cost. Thecost of electric heater is covered by the O& M cost of SOFC, whichis used in both H2 production and power generation mode. The elec-tricity consumption of electric heater has been calculated in SOSEmode that is 13kW h/year. The pre-heater in SOFC mode is used onlyat start up time of fuel cell otherwise at full mode operation of SOFC,it has no activity because the heat exchanger-2 can provide the re-quired heat for input fuel (H2). The high temperature heat exchanger(HEX) has been used in this study, which cost is higher compared tothe lower temperature HEX. The calculation shows that the HEX-2(5.66 m2) is larger than the HEX-1 (1.24 m2), because the heat trans-fer rate of HEX-2 between the hot and cold fluid is high. Obviously, byincreasing the sizes of HEX the cost of it also increases. The entireindividual component’s controlling cost has been included in O&Mcost of that component. The annual electrical and thermal energyproductions of the fuel cell have been found 273.75 MW h/yearand 257.58 MW h/year respectively. In the physical form, the ther-mal energy and the electrical energy can be treated equally andexpressed in terms of kW h but the economic value between thermalenergy and electrical energy cannot be treated equally as they arepriced differently in market.

After considering all the components, 2920 h/year for electro-lyzer and 2815.2 h/year for fuel cell mode of operation, total capitalcost of $592,327 is needed for the proposed system. The annualinvestment cost of $47,529.85 has been found taking the annualinterest rate of 5% for 20 years of plant life into consideration. Fi-nally, the cost of electricity (COE) of the system has been foundabout 67.6 $/MW h (0.068 $/kW h).

6. Conclusion

A mathematical model has been developed to simulate the elec-trical power and the heat energy generation in a co-generation sys-tem. The model has been conducted by considering the solarenergy in thermal and photovoltaic form with the reversible solidoxide fuel cell (RSOFC) to produce the H2 at higher solar radiationtime as well as to generate the electrical power and the heat en-ergy at night time utilizing the storage H2. The cogeneration sys-tem model has been analysed with considering three modes ofoperation: solar-SOSE, SOFC and solar-SOFC. The effects of temper-ature on the RSOFC and the effects of solar radiation on the solar-

PV and the PTSC have been discussed taking different parametersvalue from literature. After that, considering 100 kW of electricloads, the performances and the economic analysis of the systemaccording to the operation modes have been presented. The follow-ing findings can be concluded from the analysis:

i. The SOFC mode provides the highest net electrical as well asoverall energy efficiency compared to other modes. Themain reason behind this efficiency increase is lower numberof components is used in SOFC mode. The lowest efficiencywas found at solar-SOSE mode because of inefficient solar-PV, although the efficiency of H2 production is high. Anothercause of low efficiency of the system at solar-SOSE and solar-SOFC mode is the solar radiation intensity (W/m2) on the PVmodules and the collectors’ surface, since the radiation isconsidered as the input energy of the system in order to cal-culate the efficiency.

ii. The CHP efficiencies for the SOFC, the solar-SOSE and thesolar-SOFC mode are 83.6%, 20% and 23% respectively. Onthe other hand the only electrical efficiency for the SOFC,the solar-SOSE and the solar-SOFC are 44.28%, 14% and 15%respectively.

iii. Additionally, the system provides heat energy at high tem-perature that can be harnessed for further uses such as forcombined cycle or, for space and domestic water heating.It will make the system more efficient and economical. Inthis study, the heat to power ratio has been found 0.917 atSOFC mode and 1.09 at solar-SOFC mode. The more heatenergy can be joined from the PTSC at day time.

iv. The temperature changes, instantaneously affected the mostpart of RSOFC. The RSOFC system with higher operating tem-perature for the both H2 generation in electrolyzer mode andthe power and heat generation in fuel cell mode is more ben-eficial than lower operating temperature system.

v. The solar radiation changes are highly reflected on the H2

production in solar and H2 mode because the H2 productionrate relies on the electrical input that is provided by the PVand the thermal energy input that is provided by the PTSC.The power generation of SOFC at solar-SOFC mode is alsochanged with solar radiation.

vi. Annually 2920 h in electrolyzer mode and 2815.2 h in fuelcell mode of operation have been considered for the systemperformance and the economic analysis, where the annualcost of electricity is found 0.068 $/kW h.

7. Recommendations

In this study, the cogeneration system’s performances havebeen evaluated considering the average solar radiation data fromthe literature. The actual performance analysis of the system basedon the geographical weather data will be analyzed further, becausethe costs vary geographically due to the climatic conditions and lo-cal economic circumstances such as electricity tariffs. Although, inpresent study only the electricity cost ($/kW h) of the system hasbeen conducted but the thermal energy generated by the SOFChas not been considered for cost calculation because the economicvalue between thermal energy and electrical energy cannot betreated equally. Also for thermo-economic analysis the system willbe needed exergy analysis as well. Hence, the presented cogenera-tion system can be further extended with more details and optimi-zations in future. After analysing the solar energy and the SOFCtechnology based system, it can be recommended that the pro-posed system will be competitive energy solution for small to largescale applications such as in hospital, office building, hotel, singleor multifamily residential buildings as well as the remote areafar from the grid connection.


Acknowledgments

The authors would like to acknowledge the University of Ma-laya for financial support. This research was carried under theHIR-MOHE Project No. UM.C/HIR/MOHE/ENG/22.

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