A novel solar trigeneration system based on concentrating

A novel solar trigeneration system based on concentratingphotovoltaic/thermal collectors.Part 1:Design and simulation modelAnnamaria Buonomano a ,Francesco Calise a ,*,Massimo Dentice d ’Accadia a ,Laura Vanoli ba DETEC e Univ.of Naples Federico II,P.le Tecchio 80,80125Naples,ItalybDIT e Univ.of Naples “Parthenope ”Centro Direzionale IS.C4,80143Naples,Italya r t i c l e i n f oArticle history:Received 28July 2012Received in revised form 4February 2013Accepted 7February 2013Available online 15March 2013Keywords:PVTTriple-junction Solar energya b s t r a c tThis paper analyzes the thermodynamic performance of high-temperature PhotoVoltaic/Thermal (PVT )solar collectors.The collector is based on a combination of a parabolic dish concentrating solar thermal collector and a high ef ficiency solar photovoltaic collector.The PVT system under investigation allows one to produce simultaneously electrical energy and high-temperature thermal energy by solar irradiation.The main aim of this study is the design and the analysis of a concentrating PVT which is able to operate at reasonable electric and thermal ef ficiency up to 180 C.In fact,the PVT is designed to be integrated in a Solar Heating and Cooling system and it must drive a two-effect absorption chiller.This capability is quite new since conventional PVT collectors usually operate below 45 C.Among the possible high-temperature PVT systems,this paper is focused on a system consisting in a dish concentrator and in a triple-junction PV layer.In particular,the prototype consists in a parabolic dish concentrator and a planar receiver.The system is equipped with a double axis tracking system.The bottom surface of the receiver is equipped with triple-junction silicon cells whereas the top surface is insulated.In order to analyze the performance of the Concentrating PVT (CPVT )collector a detailed mathematical model was implemented.This model is based on zero-dimensional energy balances on the control volumes of the system.The simulation model allows one to calculate in detail the temperatures of the main components of the system (PV layer,concentrator,fluid inlet and outlet and metallic substrate)and the main energy flows (electrical energy,useful thermal energy,radiative losses,convective losses).The input parameters of the model include all the weather conditions (temperature,insolation,wind velocity,etc.)and the geometrical/material parameters of the systems (lengths,thermal resistances,thicknesses,etc.).Results showed that both electrical and thermal ef ficiencies are very good in a wide range of operating condi-tions.The study also includes a comprehensive sensitivity analysis in which the main design variables were varied in order to evaluate the related variations of both electrical and thermal ef ficiencies.Ó2013Elsevier Ltd.All rights reserved.1.IntroductionIt is diffusely recognized that solar energy is one of the most viable type of renewable energy sources.It is well known that solar energy availability is signi ficantly higher than the overall world-wide energy demand [1e 4].Unfortunately,for several years this renewable energy source has been largely underutilized for several reasons.First,the capital cost of solar systems was signi ficantly higher than the one of conventional systems based on fossil fuels.Then,the cost of the fossil fuels was very low due to their large availability.Finally,solar systems were penalized by a very low power density,especially when compared to the conventionalsystems based on fossil fuels.However,during the last few years,a new impulse is pushing the research regarding solar system as a consequence of the emerging policies of several governments promoting environmental-friendly energy sources,other than fossil fuels [1,5e 12].It is well known that solar energy can be used to produce electrical energy and/or thermal energy,respectively by photovol-taic collectors (PV )and heat by thermal solar collectors (SC ).Therefore,the production of both thermal and electrical energies requires the installation of two separate solar fields (PV and SC ).This circumstance is often unfeasible due to the large land surface required to supply the demanded thermal and electrical energies [1,5,9].An improvement for increasing the overall power density of both technologies consists in a combination of PV and SC effects.This occurs in photovoltaic/thermal collectors (PVT )which simul-taneously provide electricity and heat.A PVT collector consists of a*Corresponding author.Tel.:þ390817682301;fax:þ390812390364.E-mail addresses:frcalise@unina.it ,frcalise@ (F.Calise).Contents lists available at SciVerse ScienceDirectEnergyjournal h omepage:w/locate/energy0360-5442/$e see front matter Ó2013Elsevier Ltd.All rights reserved./10.1016/j.energy.2013.02.009Energy 61(2013)59e 71conventional thermal collector whose absorber is covered by asuitable PV layer [13].The absorbed thermal energy is distributed to a fluid (typically air or water),whereas the PV produces electricity [1,5].The result of this arrangement is the combined production of electricity and heat and a possible improvement of PV ef ficiency.For the majority of the PV materials,the electrical ef ficiency linearly decreases with the temperature [14].Therefore,when the fluid average temperature is relatively low (usually <40 C),the oper-ating temperature of the PV layer may be lower than the one ach-ieved by a conventional PV collector.In this case the electrical ef ficiency of the PVT would be higher than the PV one [1,5,14].For this reason,PVT systems are particularly ef ficient when low-temperature heat is demanded (e.g.,domestic hot water,floor heating,desiccant cooling etc.).The selection of PV material to be integrated in a PVT collector is a key point for an ef ficient design of such systems.In fact,the PV material must be selected as a function of the operating temperature of the PVT collector.When this tem-perature is low,crystalline Silicon cells (c-Si)are typically adopted (the typical temperature coef ficient is 0.45%/K).Conversely,for higher operating temperatures (typically >80 C)innovative PV materials (e.g.triple-junction)must be considered,since they are less sensitive to the operating temperature [1,5,14].A further possible option may consist in the use of amorphous Silicon cells (a-Si)since they are cheaper than c-Si and their temperature co-ef ficient (about 0.2%/K)is typically lower than the one of c-Si.The use of a-Si is only limited by the fact that their electrical ef ficiency is typically lower than the one of c-Si cells.A possible alternative for increasing fluid PVT outlet temperature,without decreasing PV electrical ef ficiency,may consist in the use of a heat pump (driven by PV electricity)[1,5,15].Although the basic idea of the PVT was developed about 40years ago,this product is still far from a mature commercialization [16].Thus,several researchers are investigating several novel PVT arrangements [16e 19].For example,Zhao et al.investigated a novel PVT where thermal and electrical sections are separated [20].Furthermore,the selection of the appropriate cover (tedlar,DEA,glass-to-glass,etc.)is still not established due to the need of reducing simultaneously cover re flectance and heat transfer coef ficient [21].Similarly,different studies investigated the optimal design of fluid channels.Different options are under investigation:the cooling fluid may flow between the PV and the absorber or between the absorber and the insulation (as usual in SC )[1,5].Usually,the adopted PVT cooling fluid is water [18].However,several studies are focused on the use of air [19]or a combination of air and water [17].The use of air as cooling fluid is very attractive in case of building integration (BIPVT)[22].Anyhow,the main issue regarding PVT development is the reduction of their capital cost,which is a crucial point for a possible future massive commercialization of this technology.For the same peak power,the capital cost of PVT systems can be signi ficantly reduced increasing the radiative flux incident on PV receiver.InthisA.Buonomano et al./Energy 61(2013)59e 7160case,a dramatic reduction of the PV area per kWp would be ach-ieved.This reduction also results in a proportional decrease of system capital costs.It is well known that an increase of radiative flux can be achieved by concentrating systems.Concentrating PVT collectors(CPVT)consist in PVT collectors placed in the focus of some reflectors(Fresnel,parabolic,dish,etc.)[1,5,15,23].Note also that CPVT can only convert the beam fraction of the total radiation. Therefore,when the beam-to-total radiation ratio is low,these devices may be scarcely convenient with respect to the conven-tional PVT.In fact,CPVT cannot utilize the diffuse radiation which is converted into electricity and heat by conventionalflat plate PVT systems.Furthermore,the increase of radiativeflux achieved in case of CPVT systems also allows one to raise CPVT andfluid average temperatures.In case of PVT a theoretical maximum temperature of 240 C has been estimated,although prototypal CPVT typically operate below100 C in order to preserve system reliability and operating life[23,24].However,such temperature cannot be ach-ieved by conventional c-Si cells since their voltage drops to zero around270 C[14].For high-temperature CPVT systems the most suitable PV material is the triple-junction PV whose nominal effi-ciency of40%(at25 C)drops around20%at240 C.The perspective of using high-temperature PVT is very interesting since it extends the number of possible applications.An example consists in the use of the high-temperature heat provided by the PVT to drive a heat engine[25]or an Organic Rankine Cycle(ORC)[26]or a Solar Heating and Cooling system(SHC)[23].However,commercially or pre-commercially available CPVT systems are typically a small amount of the PVT under development [16].Similarly,the availability of theoretical and experimental studies investigating CPVT performance is scarce.In particular, Mittelman et al.[23,27,28]performed some experimental and theoretical works dealing with CPVT systems.In reference[28] presented a novel miniature CPVT based on a dish concentrator (0.95m2)and a silicon PV cell.A thermal model for that system was developed in order to predict its performance.The system provides 140e180W of electricity and400e500W of heat.The cost of the system was evaluated at2.5$per peak electric Watt.The operation at high temperature of similar CPVT systems was also analyzed both for solar cooling[23]and water desalination[27]applications.A Parabolic Trough CPVT prototype was experimentally investigated by Coventry[29].In this work the author pointed out that one of the major challenges in designing CPVT systems is to achieve an acceptable radiationflux distribution.The concentration ratio of the system under investigation was37,thermal and electrical ef-ficiencies were rated respectively at58%and11%.In this study the author also concluded that the thermal efficiency of CPVT is higher than the one offlat plate solar collectors only when radiation is scarce and/or ambient temperature is low.In fact,flat plate col-lectors convert both beam and diffuse radiation,whereas CPVT can only convert the beam one.Parabolic Trough CPVT were also investigated by Li et al.[30e32]comparing the electrical and thermal efficiencies of the system varying the PV technology,for different concentration ratio.Authors concluded that GeAs cells increase electrical efficiency with respect to silicon cells.However, the thermal efficiency of GeAs results lower than the one of silicon cells.Authors also pointed out that the cost of unit area of the GeAs is3067.16$/m2versus the131.34$/m2of the silicon cell.A similar work was performed by Bernardo et al.analyzing a low concen-trating parabolic trough CPVT for the Swedish climate[33].This study presents a thermal model of the PVT subsequently validated by experimental data.The system is based on a combination of a one axis tracking parabolic concentrator and silicon cells.This prototype is distributed by the Swedish company Absolicon. Additional specific applications of CPVT technology are also inves-tigated in literature.Xu et al.[34]analyzed the integration of CPVT in the evaporator of a heat pump system.Al-Alili et al.[35]inves-tigated the use of a CPVT in a desiccant cooling system.Finally, Rosell et al.[36]investigated a low concentrating PVT system based on a linear Fresnel receiver.The system was analyzed by a mathe-matical model subsequently validated by experimental data.The rated thermal efficiency was about60%.In a previous study published by some of the authors,a detailed finite-volume model of concentrating photovoltaic/thermal(PVT) solar collectors was developed.Such collectors are equipped with a parabolic trough concentrator coupled with a linear triangular receiver.Here energetic and exergetic sensitivity analyses were carried out[37].With respect to such study,this paper is focused on the technology of concentrating parabolic dish PVT solar collectors. The paper presents a design procedure and a simulation model of a novel concentrating PVT collector.The layout of the PVT system under investigation was derived from a prototype recently pre-sented in literature[23,28]and commercially available.From this point of view,a zero-dimensional model of such prototype concentrating PVT collector was developed,validated and pre-sented by some of the authors in references[38,39].Here,a water coolant operating at low-medium temperature was taken into ac-count.With respect to such previous studies and the literature review,the main novelties of the presented work consist in:i)the design of the prototype microchannel,and ii)the type of coolant fluid(diathermic oil),working at high temperature.Such modifi-cations were adopted with the scope to improve the device overall performance and permit its integration in high-temperature solar heating and cooling systems.Furthermore,thefinal goal of this paper was the development of a new simulation model of the dish CPVT collector to be included in TRNSYS simulation environment [40],aiming at using this model for dynamic simulations of solar trigeneration systems(as sown in Section2of this paper).The prototype consisted in a parabolic dish concentrator and a planar receiver.The bottom surface of the receiver(facing the concen-trator)is equipped with triple-junction silicon cells whereas the top surface is covered by a thermal insulation.With respect to the hybrid square microchannel solar cell thermal tile of the original prototype,in this work the PV layer is placed on a metallic substrate which include thefluid channels required for the heat removal.The system is managed by a double axis tracking system,following both solar azimuth and zenith angles.Similar systems(consisting of a single and two coupled dish concentrators)were recently pre-sented by an Israeli company().In the pre-sent study a detailed0-dimensional mathematical model of the CPVT under investigation has been developed.This model is based on zero-dimensional mass and energy balances on the control volumes of the system.In particular,in order to identify the energy losses occurring during the incident solar radiation conversion to electricity and heat,one dimensional heat transfer and steady state operation assumptions have been adopted.The model was subsequently used in order to design and parametrically optimize the system.Therefore,this procedure al-lows one to identify several design parameters,such as:thermal insulation rate,fluid channel geometry,receiver geometry,etc.The simulation model also allows one to calculate in detail the tem-peratures of the main components of the system(PV layer, concentrator,fluid inlet and outlet and metallic substrate)and the main energyflows(electrical energy,useful thermal energy,radi-ative losses,convective losses).The input parameters of the model include all the weather conditions(temperature,insolation,wind velocity,etc.)and the geometrical/material parameters of the sys-tems(lengths,thermal resistances,thicknesses,etc.).The model was also used in order to evaluate both electrical and thermal ef-ficiency curves related to the beam incident radiation,fluid inlet temperature and external temperature.Finally,the same modelA.Buonomano et al./Energy61(2013)59e7161will be used in additional works for being integrated in transient simulation environments in order to evaluate the overall yearly performance of the system under investigation.2.CPVT simulation model2.1.System layoutThe idea of CPVT considered in this study is based on the work performed by Mittelman et al.[23,28]and on the prototype recently commercialized by ZenithSolar.However,the geometrical properties and the materials of the CPVT considered in this study are significantly different from those of the above-mentioned prototype.The CPVT(Fig.1)consists in a parabolic dish concen-trator,equipped with a two-axis tracking system.A planar receiver is placed in the focus of the parabola.This receiver consists of: triple-junction PV layer,metallic substrate includingfluid channels, thermal insulation(Fig.1).The side of the planar receiver facing the parabolic dish concentrator is equipped InGaP/InGaAs/Ge triple-junction solar cells[24],whereas the top side of the receiver is equipped with a thermal insulation.The receiver includes an inner channel where thefluid to be heatedflows.Therefore,the concentrated solar irradiation is converted simultaneously in electricity by the PV layer and in thermal energy by the coolingfluid.erning equationsAlthough simplified models for the calculation of CPVT perfor-mance are available in literature[41],they cannot be applied to the system under investigation due to the use of concentrating systems and triple-junction cells.Therefore,an appropriate model,based on energy balances,has been developed in this paper in order to design and simulate the CPVT under investigation.This is a0-D model since thefinal scope of this work is to create a new Type to be integrated in TRNSYS environment[40].The model of the CPVT has been developed in EES(Engineering Equation Solver) which can be easily interfaced with TRNSYS,since it allows a simple formulation of the equations as well as their fast and robust solu-tion.Therefore,the model should be sufficiently fast for being used in a quasi-stationary yearly simulation.The general assumptions adopted for the model are:thermo-dynamic equilibrium,steady state,kinetic and gravitational terms negligible in the energy balances,radiation uniformly concentrated along PV area.In addition the small thickness of the PV layer and the high conductivity in the metal substrate allow one to assume negligible temperature gradients in the PVfilm and in the substrate.In other words PV and substrate temperature are assumed uniform. All these assumptions are consistent with those typically adopted in literature[1,5,17,23,28,29,33,36,42,43].The system was assumed to operate up to180 C,since it is intended to supply hot stream to a double-effect absorption chiller for Solar Heating and Cooling applications.Therefore,diathermic oil was considered as operatingfluid.Nevertheless,since the model discussed above is general,it can be used with anyfluid.The thermo-physical properties of the oil were assumed not depending on the operating temperature,though empirical temperature-dependent correlation could be easily implemented when avail-able.Such values are summarized in Table1.Conversely,the thermo-physical properties of the air area accurately calculated using the routines included in EES software.In this study a rectangular shape for the receiver is assumed. Therefore,the frontal area of the receiver(A rec)is the square of the length of the two sides(L side,1and L side,2)of the rectangle:A rec¼L side;1$L side;2(1)Obviously,the same area will be considered for all the layers of the receiver(PVT,insulation,metallic substrate,etc.).The concentration ratio is defined as the ratio between the area of the receiver,A rec and the aperture area,A ap,of the concentrator: C PVT¼A recA ap(2)The optical efficiency(h opt)of the concentrator is assumed being constant[23].Therefore,the radiation incident on the receiver surface(PV side,facing the concentrator)is:G PVT¼A rec I b C PVT h opt(3)As usual in concentrating systems,in the previous equation only the beam incident radiation(I b)is considered.Note that,due to the double axis tracking system of the collector under investigation,the solar radiation is always perpendicular to the concentrator aperture area.In this case,no Incidence Angle Modifier(IAM)[4]must be considered.Note also that solar radiation concentrated on the PVT layer is not the sole radiation incident on the receiver.In fact,the top surface of the receiver absorbs part of the total radiation incident on its surface.In this case,the calculation of the heat absorbed by the top surface of the receiver(facing the sky)must consider the total radiation since this is a non-concentrated radiative heatflux. Therefore,the additional thermal energy absorbed by the top thermal absorber is:CPVT Upper ViewCPVT Frontal View Receiver Frontal SectionReceiver Upper SectionFluid0.60 mFig.1.CPVT layout.A.Buonomano et al./Energy61(2013)59e7162Q top ¼A top I tot a top(4)Assuming the top surface area as gray surface and considering that the area of the top surface is much lower than the one of the sky,the radiative heat transfer between the top surface (side of insulation facing the sky)and the sky can be calculated as follows [4]:Q top Àsky¼A top 3R ;top s T 4top ÀT 4sky(5)Here,the sky equivalent temperature is calculated using TRNSYS routine.Similarly,assuming the area of the concentrator much larger than the one of the PVT receiver and assuming both PVT and concentrator as gray surfaces,the radiative heat transfer between the PVT and the concentrator [4]:Q PVT Àconc ¼A PVT s 3R ;PVTT 4PVTÀT 4conc(6)The convective heat transfer between the PVT and the air is calculated as follows [44]:Q con v ;PVT ¼A PVT h c ;PVT ðT PVT ÀT a Þ(7)The convective heat transfer coef ficient,h c ,PVT ,included in the previous equation is calculated using the following correlation,relating the Nusselt,Reynolds and Prandtl numbers [44]:Nu ¼0:664Pr 13Re 12(8)The same correlation is used to calculate the heat transfer co-ef ficient between the top receiver surface and the air,h c ,top .The corresponding heat flow is [44]:Q con v ;top¼A top h c ;top ÀT top ÀT aÁ(9)The gross electrical power produced by the PV layer is:P PVT ;gross ¼C PVT A PVT I b h opt h PV(10)Note that this energy is calculated considering the concentrated beam radiation (corrected by the concentrator optical ef ficiency)incident on the PV layer,corrected by the electrical ef ficiency of the PV ,h PV .As discussed above no IAM coef ficient must be taken into account due to the double axis tracking system,included in the CPVT under investigation.The electrical ef ficiency of the triple-junction PV (h PV )is experimentally related to the concentration ratio and to the tem-perature [23].h PV ¼0:298þ0:0142ln ðC PVT Þþ½À0:000715þ0:0000697ln ðC PVT Þ ðT PVT À298Þ(11)The net power produced by the system is reduced by the amount of electricity lost in the module connections and in the inverter,considering the corresponding conversion ef ficiencies (h mod and h inv )[23].P PVT ;net ¼P PVT ;gross h mod h in v(12)Finally,the useful heat absorbed by the cooling fluid is:Q u ¼_m f ðh out Àh in Þ(13)In the previous equation,the enthalpies of the inlet and outlet cooling fluid (h in and h out )are calculated by the thermo-physical property subroutine discussed above.Therefore,the overall energy balance on a control volume including the entire receiver (from PVT to the insulation)is:Note that in this energy balance the left side is representative of the energy flows entering the control volume,whereas the terms at the right side of the equation are the energy flows exiting the control volume.Among these terms at the right side,the first one is the useful thermal energy,the second one is the electrical power produced and all the remaining terms are losses,clearly divided between radiative and convective ones.A second energy balance considers the control volume including the metallic substrate and the fluid channel (also including the fluid flowing inside).In this study,this control volume can be considered as a heat exchanger.In particular,it is here assumed that the tem-perature of the metallic substrate is homogeneous along both di-rections.In this case,the primary side of the heat exchanger is at constant temperature equal to the temperature of the metallic substrate.This assumption can be considered acceptable as a consequence of the high thermal conductivity of the metallic sub-strate [23,27,28,33,42]and allows one to develop a 0-D model of the CPVT .According to this approach,the thermal performance of the heat exchanger can be calculated using the well-known 3-NTU technique [45].For the case under consideration,the NTU number is:NTU ¼U HEX A HEX_C min¼11fluid þr subA HEX_m f c f (15)Here,the overall heat transfer coef ficient,U HEX ,is calculated taking into account both substrate and fluid thermal resistances.Similarly,the minimum heat capacity ratio,_C min ,is calculated withrespect to the fluid.The heat exchange area,A HEX ,is the lateral area of the fluid channel (see arrangement shown in Fig.1),which is proportional to the overall length of the fluid channel included in the metallic substrate,L HEX .Such length is calculated taking into account all the length of all the straight channels and considering their quantity (n ch ).A HEX ¼p d ch L HEX ¼p d ch ÀL side ;2n chÁ(16)Table 1Diathermic oil properties.Property Value Unit Speci fic heat,c p 2980J/(kg K)Viscosity,m 4558$10À6Pa sConductivity,k 0.113W/(m K)Density,r870kg/m3A.Buonomano et al./Energy 61(2013)59e 7163The number of channels has been determined as a function of the ratio (f sp )between the actual and maximum number of channels:n ch¼INTEGERL side ;1d chf sp(17)The thermal resistance of the metallic substrate,r sub ,is typically orders of magnitude lower than the one of the fluid.According to the assumption used in reference [28]and to the calculated values of Reynolds number,the fluid heat transfer coef ficient,h fluid ,is evaluated assuming a fully developed turbulent flow:Nu f ¼0:023Re 4f Pr 2f(18)Finally,the heat transfer effectiveness is [45]:3¼1Àe ÀNTU(19)Thus,the energy balance for the considered heat exchanger is:_m f ðh out Àh in Þ¼3_m f c f ðT sub ÀT in Þ(20)The third of the required five equations is derived from an en-ergy balance on a control volume including the PVT layer,and themetallic substrate.A rec T PVT ÀT subPVT Àsub ¼_mf ðh out Àh in ÞþA top T sub ÀT top top(21)Thermal resistances can be calculated as follows:r PVT Àsub ¼t PVT k PVT þtsub 2k sub(22)r top ¼t sub 2k sub þtinsulk insul(23)In other words,the previous equation shows that the conductive thermal flow coming from the PVT layer is partly used to increase the outlet temperature of the cooling fluid and is partly con-ductively exchanged with the top side of the receiver.A fourth energy balance can be considered with respect to the control volume including the top side of the substrate and the top surface of the receiver:A top T sub ÀT top r topþA top I top ¼A top I top r top þA top 3R ;top s T 4top ÀT 4skyþA top h c ;top ÀT top ÀT aÁ(24)Finally,the last energy balance considers the control volume including only the parabolic dish concentrator.In this case,the left side of the energy balance includes theradiative heat transfer with the PVT and the radiative energy absorbed by the concentrator surface.Conversely,the terms at the right side of the equations are respectively:the radiative heat transfer of the back surface (external side of the parabola)of the concentrator,the convective losses at the front surface (facing the sun)of the concentrator,and the convective heat loss at the back surface.Eqs.(14),(20),(21),(24)and (25)are a system of five equations in the above mentioned five unknowns.This system of equations is highly non-linear as a consequence of the radiative terms included in the energy balances and of the correlations for the calculations of heat transfer coef ficients.This system must be solved by conven-tional numerical iterative techniques.Note also that the model discussed above lies on the assumption of steady state.However,this assumption can be easily removed,simply adding the capacitive terms in the five energy balances described above.In that case,the algebraic system of equations turns in a system of differential equations that can be easily solved using well-known techniques also included in EES.However,re-sults from those calculations showed that these capacitive terms are usually negligible,so that the deviation of results between the steady and transient models is often small.Therefore,it can be concluded that,for the case under investigation,the steady model is preferable since it is much faster than the transient one.The overall performance of the CPVT is often evaluated using the well-known thermal and electrical ef ficiencies,which are conven-tionally related to the incident beam radiation and to the collector aperture area:h CPVT ;th ¼_mf ðh out Àh in ÞA ap I b (26)h CPVT ;el ¼C PVT A PVT I b h opt h PVA ap I b(27)2.3.Design data and model validationCPVT design parameters are reported in Table 2[23,27,28,33,42]whereas the boundary conditions are shown in Table 3.Note that these design parameters are selected with the scope of using the CPVT collector under investigation to drive a double-effect ab-sorption chiller in a solar heating and cooling system.Presently,no data is still available in literature for the CPVT analyzed in this pa-per,since the related experimental campaign is still in progress.However,some performance data are available for a similar system equipped with c-Si cells [39,46].Therefore,in order to perform a validation of the simulation model discussed in the previous sec-tions,the design parameters and the boundary conditions have been modi fied according to the peculiarities of the experimented prototype [39,46].The model showed an acceptable accuracy,being able to predict the CPVT fluid outlet temperature with an error in the same order of magnitude of the measurement uncertainty,as shown in Fig.2.A similar accuracy is also achieved for the predic-tion of the electrical production.However,the validation of theelectrical performance is not signi ficant for the present study since the prototype under investigation is equipped with c-Si cells,whereas the CPVT considered in this study used III e V cells.Nevertheless,as discussed before,Eq.(11)is derived from experi-mental data.Therefore,the electrical performance of the CPVT under investigation is intrinsicallyvalidated.A.Buonomano et al./Energy 61(2013)59e 7164。