exergetic performance assessment of a solar photovoltaic thermal (pv/t) air collector
TRANSCRIPT
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Energy and Buildings 42 (2010) 2184–2199
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xergetic performance assessment of a solar photovoltaic thermal (PV/T)ir collector
. Sarhaddi ∗, S. Farahat, H. Ajam, A. Behzadmehrepartment of Mechanical Engineering, Shahid Nikbakht Faculty of Engineering, University of Sistan & Baluchestan, Zahedan 98164-161, Iran
r t i c l e i n f o
rticle history:eceived 2 November 2009eceived in revised form 16 March 2010ccepted 8 July 2010
eywords:olar photovoltaic thermal (PV/T) air
a b s t r a c t
In this paper, an attempt is made to evaluate the exergetic performance of a solar photovoltaic thermal(PV/T) air collector. A detailed energy and exergy analysis is carried out to calculate the thermal andelectrical parameters, exergy components and exergy efficiency of a typical PV/T air collector. Somecorrections are done on related heat loss coefficients. An improved electrical model is used to estimatethe electrical parameters of a PV/T air collector. Further, a modified equation for the exergy efficiency of aPV/T air collector is derived in terms of design and climatic parameters. A computer simulation program
ollectorxergy efficiencyomputer simulation
is also developed to calculate the thermal and electrical parameters of a PV/T air collector. The results ofnumerical simulation are in good agreement with the experimental measurements noted in the previousliterature. Finally, parametric studies have been carried out. It is observed that the modified exergyefficiency obtained in this paper is in good agreement with the one given by the previous literature. It isalso found that the thermal efficiency, electrical efficiency, overall energy efficiency and exergy efficiencyof PV/T air collector is about 17.18%, 10.01%, 45% and 10.75% respectively for a sample climatic, operating
and design parameters.. Introduction
Renewable energies are going to be a main substitute for fossiluels in the coming years for their clean and renewable nature. Solarnergy is one of the most significant renewable energy sourceshat world needs. The major applications of solar energy can belassified into two categories: solar thermal system, which con-erts solar energy to thermal energy, and photovoltaic (PV) system,hich converts solar energy to electrical energy. Usually, these sys-
ems are used separately. In the solar thermal system, externallectrical energy is required to circulate the working fluid throughhe system. On the other hand, in the PV system, the electricalfficiency of the system decreases rapidly as the PV module tem-erature increases. Therefore, in order to achieve higher electricalfficiency, the PV module should be cooled by removing the heat inome way. In order to eliminate an external electrical source and toool the PV module, the PV module should be combined with theolar air/water heater collector. This type of system is called solar
hotovoltaic thermal (PV/T) collector. The PV/T collector produceshermal and electrical energy simultaneously. Besides the higherverall energy performance, the advantage of the PV/T collectorystem lies in the reduction of the demands on physical space and∗ Corresponding author. Tel.: +98 541 2426206; fax: +98 541 2447092.E-mail address: [email protected] (F. Sarhaddi).
378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.enbuild.2010.07.011
© 2010 Elsevier B.V. All rights reserved.
the equipment cost through the use of common frames and brack-ets as compared to the separated PV and solar thermal systemsplaced side-by-side.
The main part of a building integrated photovoltaic thermal(BIPVT) system is PV/T air collector. The energy payback time (EPBT)of a PV/T air collector lies between 10 and 15 years depending oninsulation and the performance of it. If the performance of a PV/T aircollector can be increased, the energy payback time can be reduced.Therefore, the performance evaluation of a PV/T air collector isimportant. The performance of a PV/T air collector parametricallydepends on climatic, operating and design parameters such asambient temperature, solar radiation intensity, wind speed, solarcell temperature, back surface temperature, inlet and outlet airtemperature, inlet air velocity, open-circuit voltage, short-circuitcurrent, maximum power point voltage, maximum power pointcurrent, the length and width of PV/T air collector, overall heattransfer coefficient, etc. It can be evaluated in terms of the first andsecond law of thermodynamics. Its evaluation based on the firstand second law of thermodynamics is known as energy efficiencyand exergy efficiency, respectively.
The energy analysis has some deficiencies [1,2]. Fundamentally,
the energy concept is not sensitive with respect to the assumeddirection of the process, e.g., energy analysis does not object if heatis considered to be transferred spontaneously in the direction ofincreasing temperature. It also does not distinguish the quality ofenergy, e.g., 1 W of heat equals 1 W of work or electricity. Energy
F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199 2185
Nomenclature
a ideality factor (eV)A area (m2)BIPVT building integrated photovoltaic thermalc calculated valueCf the conversion factor of thermal power plantCp specific heat capacity of air (J/kg K)Cp,cell specific heat capacity of silicon solar cell (J/g K)CFD computational fluid dynamicsdx elemental length of flow duct (m)E power (W)EAHE earth air heat exchangerEPBT energy payback timeEVA ethyl vinyl acrelateEx exergy rate (W)G solar radiation intensity (W/m2)h heat transfer coefficient (W/m2 K)hp1 penalty factor due to the presence of solar cell mate-
rial, glass and EVAhp2 penalty factor due to the presence of interface
between tedlar and working fluidi counter parameterI circuit current (A)I irreversibility rate (W)IPVTS integrated photovoltaic thermal solarI–V current–voltagek the Boltzmann constant (J/K)K thermal conductivity (W/m K)L dimensions of solar module, the length of PV/T air
collector, thickness (m)m measured valueMAPE mean absolute percentage error (dimensionless)MBE mean bias error (dimensionless)mcell mass of PV module (g)m mass flow rate of air (kg/s)n number of calculated and measured values (dimen-
sionless)Nc number of cells in PV moduleNm number of modules in series per stringNs number of stringP pressure (Pa)PV photovoltaicPV/T photovoltaic/thermal collectorq electron charge (C)Q heat transfer rate (W)R gas constant (kJ/kg K), resistance (�)R2 coefficient of determination (dimensionless)RMSE root mean square error (dimensionless)S the rate of solar energy incident on the PV surface
(W)Sgen entropy generation rate (W/K)SRC standard rating conditionst time interval (second)t-stat t-statistic (dimensionless)T temperature (K)T0 reference environmental temperature (K)Ub an overall back loss coefficient from flowing air to
ambient (W/m2 K)UL an overall heat loss coefficient from the PV/T air col-
lector to the environment (W/m2 K)Ut an overall heat transfer coefficient from solar cell to
ambient through glass cover (W/m2 K)
UT a conductive heat transfer coefficient from solar cellto flowing air through tedlar (W/m2 K)
UtT an overall heat transfer coefficient from glass-to-tedlar through solar cell (W/m2 K)
Utf an overall heat transfer coefficient from glass to airthrough solar cell and tedlar (W/m2 K)
V circuit voltage (V), wind speed (m/s)W the width of PV/T air collector (m)
Greek symbols˛ absorptivity, current temperature coefficient
(mA/◦C), statistical significant level1 − ˛ confidence level (=99%)(˛�)eff the product of effective absorptivity and transmit-
tivityˇ packing factor, voltage temperature coefficient
(V/◦C)� dimensionless diode curve-fitting factorı duct depth (m)� difference in current, temperature, time, voltageε emissivity, semiconductor band gap energy (eV)� efficiency (%)� density (kg/m3) Stefan-Boltzmann’s constant (W/m2 K4)� transmittivity
Subscripts1 length2 widtha averageamb ambientb backbs back surface of tedlarc solar cellcal calculatedcell cell, moduleconv convectioncrit criticalc.v. control volumed ductD diodedes destroyedel electricalen energyex exergyexp experimentalf fluid flowfin finalg glassi insulation, ith parameterin inletini initiallos lossL light currentmod modulemp maximum power pointnew newo reverse saturationoc open-circuitout outletQ heat transferov overallrad radiative
2186 F. Sarhaddi et al. / Energy and Buil
rec recoveredref references seriessc short-circuitsh shuntsi siliconsim simulatedsky skysun sunsup suppliedt topT tedlarth thermal
aeicsrHsuy
sc
sw
o
ogasom
su
Pso
ott
oe
behc
ar
u usefulw wind, work
nalyses on their own incompletely interpret some processes [1,2],.g., environmental air, when isothermally compressed, maintainsts energy (e.g., enthalpy) equal to zero, whereas the exergy of theompressed air is greater than zero. The energy analysis does nothow internal irreversibilities [1,2]; it cannot be a sufficient crite-ion in order to evaluate the performance of a PV/T air collector.owever, exergy data are more practical and realistic in compari-
on with the respective energy values [1,2]. Thus, exergy analysissually provides a more realistic view of process than energy anal-sis.
A significant amount of theoretical as well as experimentaltudies on the energy or exergy performance evaluation of PV/Tollector systems has been carried out in the last 35 years.
Wolf [3], Kern and Russell [4] as early as in the 1970s have pre-ented the main concept of PV/T collector with the use of eitherater or air as the coolant.
Takashima et al. [5] have carried out a theoretical exergy studyn a PV-roof cooled by natural convection.
Fujisawa and Tani [6] have compared the annual performancef a flat-plate solar water-heating collector, a PV module, a single-lazed PV/T collector with monocrystalline silicon solar cells, andn unglazed one. The energetic evaluation of the measured datahowed that the single-glazed PV/T collector is the best. In termsf exergy analysis, unglazed PV/T collector gives the best perfor-ance.Polivoda [7] has calculated the energy and exergy efficiency of
olar thermal and photovoltaic systems and PV/T systems and givenseful results.
Bosanac et al. [8] have briefly carried out exergy analysis of aV/T system and reported that maximum exergy efficiency of a PV/Tystem is about 12% against an overall maximum energy efficiencyf 60%.
Saitoh et al. [9] have compared the energy and exergy efficiencyf a brine-cooled PV/T collector with a PV panel and a solar collec-or in Hokkaido (in northern Japan) and given similar equations asaken from Fujisawa and Tani [6].
Ajam et al. [10] have compared the energy and exergy efficiencyf a solar air heater and found optimal operating and design param-ters of the heater.
Sahin et al. [11] have carried out the exergy analysis of a PV arrayased on chemical potential components. They have also obtainedxergy components and PV array exergy efficiency. Finally, they
ave compared energy, electrical, exergy efficiencies under givenlimatic and operating conditions.Joshi and Tiwari [12] have carried out the energy and exergynalysis of a PV/T parallel-plate air collector for the cold climateegion of India (in Srinagar). They have reported the instantaneous
dings 42 (2010) 2184–2199
energy and exergy efficiency of a PV/T air collector varies between55–65% and 12–15%, respectively.
Hepbasli [13] has carried out a review on exergy analysis of sev-eral solar energy systems especially photovoltaic thermal systemsand given similar expressions as taken from Fujisawa and Tani [6]and Saitoh et al. [9].
Nayak and Tiwari [14] have presented the performance of a PVintegrated greenhouse system for New Delhi climatic condition andreported that the exergy efficiency of the system is 4%.
Farahat et al. [15] have carried out the exergetic optimization ofa flat plate water solar collector and given useful results.
Joshi et al. [16] have compared the thermal performance of aglass-to-tedlar PV/T air collector and a glass-to-glass PV/T air col-lector and shown that a glass-to-glass PV/T air collector has a betterthermal performance than a glass-to-tedlar PV/T air collector.
Joshi et al. [17] have carried out the performance analysis ofboth PV and PV/T system in terms of exergy efficiency and reportedthat the thermal energy due to solar radiation is actually a heatloss to the PV system whereas it is a useful heat for a PV/T system.They have also shown that the electrical (exergy) efficiency of a PVsystem can be improved if the heat can be removed from the PVsurface.
Torío et al. [18] have done a review on exergy analysis of severalsolar energy systems especially photovoltaic thermal systems andgiven similar expressions as taken from Saitoh et al. [9].
Dubey et al. [19] have evaluated the energetic and exergetic per-formance of a PV/T air collector with air duct above the absorberplate and the one with air duct below the absorber plate. They haveinvestigated the effect of design and operating parameters and fourweather conditions on the performance of above-mentioned PV/Tair collectors for five different cities of India and found that the lat-ter one gives better results in terms of thermal energy, electricalenergy and exergy gain.
Nayak and Tiwari [20] have studied the yearly effectiveness ofPV/T collector and earth air heat exchanger (EAHE) integrated witha greenhouse in terms of the energy and exergy analysis. They havecalculated yearly thermal exergy and energy which are 1006.2 kWhand 24,728.8 kWh, respectively.
Sarhaddi et al. [21] have optimized a PV array based on exergyanalysis and given useful results.
Agrawal and Tiwari [22] have carried out an energy and exergyanalysis in order to select an appropriate BIPVT system suitable forthe cold climatic conditions of India. They have reported that fora constant mass flow rate of air, the system connected in series ismore suitable for the buildings fitted with BIPVT systems as rooftop.This system produces an annual electrical and thermal exergies of16,209 kWh and 1531 kWh with an average overall thermal effi-ciency of 53.7%.
Corbin and Zhai [23] have developed a computational fluiddynamics (CFD) model for a novel BIPVT collector and validatedit experimentally. They have indicated that PV cell efficiency canbe raised up to 5.3% and the outlet water temperature of collectoris suitable for domestic hot water use.
Sukamongkol et al. [24] have investigated the dynamic perfor-mance of a condenser heat recovery with a PV/T air collector toregenerate desiccant for reducing energy use of an air conditioningroom, experimentally. They have indicated that the use of a hybridPV/T air heater, incorporated with the heat recovered from the con-denser to regenerate the desiccant for dehumidification, can savethe energy use of the air conditioning system by approximately18%.
The exergy efficiency of a PV/T air collector used in the previ-ous literature [5–9,12–14,17–20,22], has some deficiencies; first,it does not include the pressure exergy terms of airflow and theexergy components of chemical potential in PV module. Second,it has a significant error at low solar radiation intensity. At low
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F. Sarhaddi et al. / Energy an
olar radiation intensity, it gives PV/T exergy efficiency equals thelectrical efficiency of the reference conditions (�ex ≈ �el,ref = 0.12).
In this paper, the exergetic performance of a solar PV/T air col-ector will be evaluated. A detailed energy and exergy analysis wille carried out to calculate the thermal and electrical parameters,xergy components and exergy efficiency of a typical PV/T air col-ector. The thermal and electrical parameters of a PV/T air collectornclude solar cell temperature, back surface temperature, outlet airemperature, open-circuit voltage, short-circuit current, maximumower point voltage, maximum power point current, etc. Some cor-ections will be done on related heat loss coefficients. An improvedlectrical model will be used to estimate the electrical parametersf a PV/T air collector such as open-circuit voltage, short-circuiturrent, maximum power point voltage, maximum power pointurrent, electrical power, etc. Further, a modified equation for thexergy efficiency of a PV/T air collector will be derived in terms ofesign and climatic parameters. A computer simulation programill be developed to predict the thermal and electrical parameters
f a PV/T air collector. Finally, parametric studies will be carriedut; also, the effect of climatic, design and operating parametersn exergy efficiency will be studied.
. Analysis
The exergy efficiency of a PV/T air collector is parametricallyependent on its energy analysis. Hence, firstly the energy analysisf a PV/T air collector will be carried out. Then the exergy compo-ents and exergy efficiency of a PV/T air collector will be computednd studied.
.1. Energy analysis
Following assumptions are considered in order to write thenergy balance equation for each component of a PV/T air collectorystem [12,14,16,19,20,22]:
The system is in quasi-steady state condition.
ig. 1. (a) The cross-sectional view of a PV/T air collector, (b) thermal resistance circu12,14,16,19,20,22].
dings 42 (2010) 2184–2199 2187
• The transmittivity of ethyl vinyl acrelate material (EVA) is nearly100%.
• The temperature variation along the thickness is negligible.• The airflow through air duct is uniform for the forced mode of
operation for streamline flow.
Fig. 1 shows the cross-sectional view of a PV/T air collector, itsequivalent thermal resistant circuit and an elemental length ‘dx’ offlow duct [12,14,16,19,20,22].
The thermal parameters and thermal efficiency of a PV/T air col-lector are obtained if the energy balance equation is written for eachcomponent of a PV/T air collector [12,14,16,19,20,22]:
Energy balance for glass-tedlar PV module:
�g[˛cˇcG + ˛T(1 − ˇc)G]W dx
= [Ut(Tcell − Tamb) + UT(Tcell − Tbs)]W dx + �gˇc�elGW dx, (1)
[The rate of solar energy available on PV module]
= [An overall heat loss from the top surface of PV cell to
ambient] + [An overall heat transfer from PV cell to the back
surface of tedlar] + [The rate of electrical energy produced],
where Tcell, Tamb, Tbc, G, W, dx, ˛c, ˛T, ˇc, �g and �el are solar cell tem-perature, ambient temperature, back surface temperature, solarradiation intensity, the width of PV/T air collector, the elementallength of flow duct, the absorptivity of solar cell, the absorptivityof tedlar, the packing factor of solar cell, the transmitivity of glasscover and the electrical efficiency of PV cell, respectively. Further,UT is a conductive heat transfer coefficient from solar cell to flowingair through tedlar and it is given by[ ]−1
UT = LsiKsi+ LT
KT, (2)
where Lsi, Ksi, LT and LT are the thickness of silicon solar cell, theconductivity of silicon solar cell, the thickness of tedlar and theconductivity of tedlar, respectively.
it diagram for a PV/T air collector and (c) an elemental length ‘dx’ of flow duct
2 d Buil
acwc
U
wo
h
w
a
h
wBo[
T
U
wtsiN
m
tft
m
woii
U
wdo
b
T
Tf(x) =(
Tamb + hp1hp2(˛�)effG
UL
)(1 − exp
(−WULx
mCp
))
+ Tf,inexp
(−WULx
mCp
). (20)
The outlet air temperature (Tf,out) of the flowing air can beobtained from the above equation with the boundary conditionTf = Tf,out, at x = L such as follows
Tf,out =(
Tamb + hp1hp2(˛�)effG
UL
)(1 − exp
(−WULL
mCp
))
+ Tf,in exp
(−WULL
mCp
), (21)
188 F. Sarhaddi et al. / Energy an
Ut is an overall heat transfer coefficient from solar cell tombient through glass cover. In the previous studies [3–24], thisoefficient has been assumed as a constant factor or a variableith little effect, whereas it is not constant. Ut includes conduction,
onvection and radiation losses and it is given by
t =[
Lg
Kg+ 1
hconv,t+ 1
hrad
]−1
, (3)
here Lg and Kg are the thickness of glass cover, the conductivityf glass cover, respectively.
The convective heat transfer coefficient (hconv,t) is given by [25]
conv,t = 2.8 + 3Vw, (4)
here Vw is wind speed on the top surface of PV/T air collector.The radiative heat transfer coefficient between PV/T air collector
nd surroundings is obtained from [26]
rad = εg(Tsky + Tcell)(T2sky + T2
cell), (5)
here εg and are PV/T air collector emissivity and the Stefan-oltzmann’s constant, respectively and the effective temperaturef the sky (Tsky) is calculated from the following empirical relation26].
sky = Tamb − 6. (6)
Energy balance for the back surface of tedlar:
T(Tcell − Tbs)W dx = hf(Tbs − Tf)W dx, (7)
[An overall heat transfer from PV cell to the back surface of tedlar]
= [The rate of heat transfer from the back surface of tedlar to
flowing air],
here Tf and hf are flowing air temperature and convective heatransfer coefficient inside the air duct, respectively. In the previoustudies [3–24], hf has been assumed as a constant factor. However,n this research hf is calculated according to flow regime and itsusselt number.
Energy balance for flowing air through the air duct (Fig. 1 c):
˙ Cp
(dTf
dx
)dx + Ub(Tf − Tamb)W dx = hf(Tbs − Tf)W dx, (8)
[The heat carried away with the flowing air] + [An overall heatransfer from flowing air to ambient] = [The rate of heat transferrom the back surface of tedlar to flowing air], where m and Cp arehe mass flow rate and heat capacity of flowing air, respectively.
The mass flow rate of flowing air is defined as
˙ = �VinAd, (9)
here Vin, Ad and � are inlet air velocity, the cross-sectional areaf air duct and the density of flowing air, respectively. Further, Ubs an overall back loss coefficient from flowing air to ambient andt is given by
b =[
Li
Ki+ 1
hconv,b
]−1
, (10)
here Li, Ki and hconv,b are the thickness of back insulation, the con-uctivity of back insulation and convective heat transfer coefficientn the back surface of PV/T air collector, respectively.
From Eqs. (1) and (7), expressions for solar cell temperature and
ack surface temperature are obtained as followscell = (˛�)effG + UtTamb + UTTbs
Ut + UT, (11)
dings 42 (2010) 2184–2199
Tbs = hp1(˛�)effG + UtTTamb + hfTf
UtT + hf, (12)
where
(˛�)eff = �g[˛cˇc + ˛T(1 − ˇc) − ˇc�el], (13)
hp1 = UT
UT + Ut, (14)
UtT =[
1Ut
+ 1UT
]−1= UtUT
UT + Ut. (15)
An ordinary differential equation for the flowing air temperature(Tf) is obtained if Eq. (12) is substituted into Eq. (8) such as follows
dTf
dx+
(WUL
mCp
)(Tf − Tamb) = Whp1hp2(˛�)effG
mCp. (16)
Here,
hp2 = hf
UtT + hf, (17)
Utf =[
1hf
+ 1UtT
]−1= UtThf
UtT + hf, (18)
UL = Ub + Utf, (19)
where UL is an overall heat transfer coefficient from PV/T air collec-tor to surrounding. In the previous studies [3–24], this coefficienthas been assumed as a constant factor, whereas it is not constant.UL includes all of conduction, convection and radiation losses fromthe PV/T air collector to the atmosphere.
An expression for the flowing air temperature can be obtainedby integrating Eq. (16) with the boundary condition Tf = Tf,in, at x = 0such as follows
where L is the length of air duct. The average air temperature overthe length of air duct below PV module is obtained as follows
F. Sarhaddi et al. / Energy and Buil
F
T
o
Q
�
iePm
m
�
rlc(teovvacp
ea
yn(w
ig. 2. Equivalent electrical circuit in the five-parameter photovoltaic model [27].
¯f = 1L
∫ L
x=0
Tf(x) dx
=[
Tamb + hp1hp2(˛�)effG
UL
][1 − (1 − exp(−WULL/mCp))
WULL/mCp
]
+ Tf,in(1 − exp(−WULL/mCp))WULL/mCp
. (22)
The rate of useful thermal energy of the PV/T air collector isbtained as follows
˙ u = mCp(Tf,out − Tf,in) = mCp
UL[hp1hp2(˛�)effG
− UL(Tf,in − Tamb)]
[1 − exp
(−WULL
mCp
)]. (23)
The thermal efficiency of the PV/T air collector is defined as
th = Qu
WLG= mCp
WLUL
[hp1hp2(˛�)eff − UL(Tf,in − Tamb)
G
]
×[
1 − exp
(−WULL
mCp
)]. (24)
Since the presence of the electrical efficiency of PV module (�el)n Eq. (13), the thermal parameters of PV/T air collector and itslectrical parameters are dependent. The thermal parameters of aV/T air collector will be improved if the electrical efficiency of PVodule is calculated in a precise way.In the previous studies [3–24], the electrical efficiency of a PV
odule has been calculated from the following equation
el = �el,ref[1 − 0.0045(Tcell − Tamb,ref)]. (25)
The subscript ‘ref’ indicates the value of parameters at theeference conditions. Eq. (25) has some deficiencies; first, atow solar radiation intensity, it gives PV module electrical effi-iency equals the electrical efficiency of the reference conditions�el ≈ �el,ref = 0.12). The equivalence of the solar cell and ambientemperature is the reason of this fact. Second, Eq. (25) cannotstimate the electrical parameters of a PV/T air collector such aspen-circuit voltage, short-circuit current, maximum power pointoltage, maximum power point current, etc. Knowing the outputalue of current or voltage in a PV system affects PV modulesrrangement (series or parallel). On the other hand, some exergyomponents of a PV/T air collector are dependent to the electricalarameters. This subject will be shown in the next section.
In this research, the electrical efficiency of a PV module and itslectrical parameters is calculated from the electrical simulation ofPV module.
The proof of governing equations on PV module electrical anal-sis is not included in order to have a brief note. A PV module isonlinear device and can be represented by its current–voltageI–V) characteristic curve. There are several mathematical models,hich can describe I–V characteristic curve [27]. Five-parameter
dings 42 (2010) 2184–2199 2189
photovoltaic model (Fig. 2) for I–V characteristic curve is defined as[27]
I = IL − Io
[exp
((V + IRs)
a
)− 1
]− (V + IRs)
Rsh, (26)
a = �kTcell
q, (27)
where, I and V represent current and voltage at load, q, k, � , a, IL, Io,Rs and Rsh are electron charge, the Boltzmann constant, dimension-less diode curve-fitting factor, ideality factor, light current, diodereverse saturation current, series resistance and shunt resistance,respectively. The second terms on the right hand side of Eq. (26)indicate diode current (ID).
In order to calculate five reference parameters (aref, IL,ref, Io,ref,Rs,ref and Rsh,ref), five pieces of information are needed at referenceconditions. These five pieces of information are defined as follows[27]:
At short circuit current : I = Isc,ref, V = 0.
At open circuit voltage : I = 0, V = Voc,ref.
At the maximum power point : I = Imp,ref, V = Vmp,ref.
At the maximum power point :[
d(IV)dV
]mp
= 0.
At short circuit :[
dI
dV
]sc
= −1Rsh,ref
.
Reference conditions or standard rating conditions (SRC) aredefined as follows [28]:
The solar cell temperature at reference conditions :
Tcell,ref = 25 ◦C.
The solar radiation intensity at reference conditions :
Gref = 1000 W/m2.
Substituting the above five pieces of information into Eq. (26),the following equations are obtained
Isc,ref = IL,ref − Io,ref
[exp
(Isc,refRs,ref
aref
)− 1
]− Isc,refRs,ref
Rsh,ref, (28)
0 = IL,ref − Io,ref
[exp
(Voc,ref
aref
)− 1
]− Voc,ref
Rsh,ref, (29)
Imp,ref = IL,ref − Io,ref
[exp
(Vmp,ref + Imp,refRs,ref
aref
)− 1
]
− Vmp,ref + Imp,refRs,ref
Rsh,ref, (30)
[d(IV)dV
]mp
= 0, (31)
[dI
]1
dV sc= −
Rsh,ref, (32)
where Voc, Vmp, Isc and Imp are open-circuit voltage, maximumpower point voltage, short-circuit current and maximum powerpoint current, respectively.
2190 F. Sarhaddi et al. / Energy and Buil
Fp
svrcdf
I
�
�
�
I
V
wfcm
pcc
re
�
wi
S
wn
A
ig. 3. Representation of a general current–voltage characteristic curve and itsarameters [30].
The Eqs. (28)–(32) are a set of nonlinear equations that can beolved with numerical methods. Solving Eqs. (28)–(32) gives thealue of five parameters (aref, IL,ref, Io,ref, Rs,ref and Rsh,ref), at theeference conditions (Tcell,ref = 25 ◦C, Gref = 1000 W/m2). In order toalculate the model parameters at new climatic and operating con-itions (Gref, Tcell,new), a set of translation equations is used such asollows [27,29]
a
aref= Tcell
Tcell,ref, (33)
IoIo,ref
=(
Tcell
Tcell,ref
)3
exp
[εNc[1 − (Tcell,ref/Tcell)]
aref
], (34)
L =(
G
Gref
)[IL,ref + ˛(Tcell − Tcell,ref)], (35)
T = Tcell − Tcell,ref, (36)
I = ˛(
G
Gref
)�T +
[(G
Gref
)− 1
]Isc,ref, (37)
V = ˇ�T − Rs�I, (38)
new = Iref + �I, (39)
new = Vref + �V, (40)
here ε, Nc, ˛ and ˇ are semiconductor band gap energy (1.12 eVor silicon solar cell), cells number in series, current temperatureoefficient and voltage temperature coefficient, respectively. PVodule manufacturers usually give temperature coefficients [28].The new values of maximum power point voltage and maximum
ower point current are obtained from solved I–V characteristicurve and Eq. (31) simultaneously at new climatic and operatingonditions (Fig. 3) [30].
The electrical efficiency of a PV module can be defined as theatio of actual electrical output power to input the rate of solarnergy incident on the PV surface as follows [13,14,16,19–22]:
el = VmpImp
S= Eel
S, (41)
here Eel is outlet electrical power and the rate of solar energyncident on the PV surface (S) is given by
˙ = GNsNmAmod, (42)
here Nm and Ns are number of modules in series per string andumber of strings, respectively. PV module area (Amod) is given by
mod = L1L2, (43)
dings 42 (2010) 2184–2199
where L1 and L2 are the length of PV module and the width of PVmodule, respectively. Here we convert the conventional electricalefficiency to thermal efficiency equivalent through the followingequation:
�el,th = �el
Cf, (44)
where Cf is the conversion factor of the thermal power plant andits value may be taken as 0.36 for countries such as India [31].
The overall energy efficiency of a PV/T air collector can becalculated by adding the thermal efficiency (Eq. (24)) and ther-mal efficiency equivalent of electrical efficiency (Eq. (44)) as[12,14,16,19,20,22]
�en,ov = �th + �el,th = �th +(
�el
Cf
). (45)
2.2. Exergy analysis
Exergy analysis is a technique that uses the conservation of massand conservation of energy principles together with the secondlaw of thermodynamics for the analysis, design and improvementof energy and other systems. Exergy is defined as the maximumamount of work that can be produced by a system or a flow of massor energy as it comes to equilibrium with a reference environment[32].
The general form of exergy balance equation for a control vol-ume is written as [32–34]
Exfin − Exini = ExQ − Exw + Exin − Exout − Ic.v., (46)
where Exini, Exfin, Exin, Exout, ExQ, Exw and Ic.v. are the exergy rateof initial mass in control volume, the exergy rate of final mass incontrol volume, the exergy rate of inlet mass, the exergy rate ofoutlet mass, heat transfer exergy rate, work exergy rate and irre-versibility rate in control volume, respectively.
The exergy rate of inlet and outlet mass:The exergy rate of inlet mass to control volume is given by
[32–34]
Exin = mCp
[Tf,in − Tamb − Tambln
(Tf,in
Tamb
)]
+ mRTambln
(Pf,in
Pamb
). (47)
The exergy rate of outlet mass from control volume is given by[32–34]
Exout = mCp
[Tf,out − Tamb − Tambln
(Tf,out
Tamb
)]
+ mRTambln
(Pf,out
Pamb
), (48)
where R, Pamb, Pf,in and Pf,out are gas constant, ambient pressure,agent fluid pressure at entrance and exit from PV/T air collector,respectively.
The heat transfer exergy rate includes solar radiation intensityexergy rate. According to the Petela theorem, it is given by [1,2]
ExQ,sun = S
[1 − 4(Tamb/Tsun)
3+ (Tamb/Tsun)4
3
], (49)
where, Tsun is the sun’s temperature in Kelvin.The work exergy rate includes only the outlet electrical power of
PV module [11,17,21]:
Exw = VmpImp = Eel. (50)
d Buildings 42 (2010) 2184–2199 2191
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I
coki
g
E
tet
E
wt
amTi
E
wrcc[
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ec
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P
F. Sarhaddi et al. / Energy an
The irreversibility rate in control volume includes the rate of exter-al exergy losses from control volume and the rate of internalxergy losses (exergy destructions) in control volume [17,34,35]:
˙c.v. = Exlos + Exdes. (51)
The amount of exergy goes out of control volume or system andannot be used, is called exergy loss. On the other hand, the amountf exergy caused by for example flow friction or mixture of twoinds of liquids, etc. and does not go out of control volume or systems named exergy destruction [17].
The rate of external exergy losses caused by heat leakage rate areiven by [10,15,21]:
˙ xlos = UL(NsNmAmod)(Tcell − Tamb)[
1 −(
Tamb
Tcell
)]. (52)
The rate of internal exergy losses (exergy destructions rate):According to the Gouy–Stodola theorem, the exergy destruc-
ions rate in control volume are equal to the product of referencenvironmental temperature to the entropy generation rate in con-rol volume [32–35]
˙ xdes = T0Sgen, (53)
here T0, Sgen are the reference environmental temperature andhe entropy generation rate in control volume, respectively.
The exergy rate of initial and final mass in control volume:Since, the inlet and outlet mass flow rate are equal, there is no
ccumulation of mass in control volume, therefore initial and finalass in control volume is constant and equal to PV module mass.
he exergy rate changes of initial and final mass in control volumes defined as [11,17,21]
˙ xfin − Exini =(
mcellCp,cell
�t
)[Tcell − Tamb − Tambln
(Tcell
Tamb
)]
− (VocIsc − VmpImp)Tcell
Tsun, (54)
here mcell and �t are PV module mass and time interval,espectively. The first terms on the right hand side of Eq. (54) indi-ate physical exergy changes and the second terms show exergyhanges due to the variations of chemical potential in PV module11,17,21].
The specific heat capacity of silicon solar cell (Cp,cell) is calculatedrom [36]
p,cell = 0.844 + 1.18 × 10−4Tcell − 1.55 × 104T−2cell. (55)
The exergy efficiency of PV/T air collector:Exergy efficiency is defined as the ratio of total output exergy
ate (recovered) to total input exergy rate (supplied) [30–33]:
ex = Exrec
Exsup= 1 − Ic.v.
Exsup= 1 −
[∑(Exlos + Exdes)
Exsup
]. (56)
Substituting Eqs. (47)–(54) into Eq. (46) and considering exergyfficiency definition (Eq. (56)), the exergy efficiency of a PV/T airollector is obtained:
ex = Exfin − Exini + Exout − Exin + Exw
ExQ,sun= 1 −
(Exlos + Exdes
ExQ,sun
),
(57a)
�ex = 1 − [UL(NsNmAmod)(Tcell − Tamb)[1 − (Tamb/Tcell)] + T0 Sgen]4
S[1 − 4(Tamb/Tsun)/3 + (Tamb/Tsun) /3]= (mcellCp,cell/�t)[Tcell − Tamb − Tamb ln(Tcell/Tamb)] − (VocIsc − VmpImp)Tcell/Tsun
S[1 − 4(Tamb/Tsun)/3 + (Tamb/Tsun)4/3]+ m
Eq. (57b) is a modified equation for the exergy efficiency of aV/T air collector in terms of thermal, electrical, design parameters
Fig. 4. . The schematic diagram of Joshi et al.’s experimental setup [16].
and climatic conditions. It includes all of the exergy componentsof a PV/T air collector. On the other hand, the electrical parametersare appeared in this equation directly.
In the previous studies [5–9,12–14,17–20,22], the exergy effi-ciency of a PV/T air collector has been calculated from the followingequation
�ex = �th
[1 −
(Tamb
Tf,out
)]+ �el
= Qu[1 − (Tamb/Tf,out)](WLG)
+ �el,ref[1 − 0.0045(Tcell − Tamb,ref)].
(58)
Eq. (58) has some deficiencies; first, Eq. (58) does not includethe pressure exergy terms of airflow and the exergy components ofchemical potential in PV module. Second, Eq. (58) has a significanterror at low solar radiation intensity. At low solar radiation inten-sity, it gives PV/T exergy efficiency equals the electrical efficiencyof the reference conditions (�ex ≈ �el,ref = 0.12). The equivalence ofthe solar cell and ambient temperature and the negligible amountof Qu are the reasons of this fact.
3. System description
The energy and exergy models obtained in the previous sectionshave been validated with the experimental results of Joshi et al.[16].
The experimental setup of Joshi et al. [16] include twomonocrystalline silicon PV modules (2 × 75 W) integrated with anair duct. The electrical energy generated with PV modules is storedin a battery. Two DC fans blow air into air duct. These DC fans con-sume a small amount of electricity from the battery itself, whichis neglected during the simulation. Fig. 4 shows the schematic dia-gram of Joshi et al.’s [16] experimental setup.
The experiments have been carried out on the above-mentionedPV/T air collector at Solar Energy Park, IIT Delhi (India). The mea-
Cp[Tf,out − Tf,in − Tamb ln(Tf,out/Tf,in)] + mRTamb ln(Pf,out/Pf,in) + VmpImp
S[1 − 4(Tamb/Tsun)/3 + (Tamb/Tsun)4/3].
(57b)
2192 F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199
Table 1The values of climatic, operating and design parameters during validation process and parametric studies of PV/T air collector[12,14,16,19,20,22,27–29].
Solar PV/T air collector parameters Value
PV module type Siemens SP75, monocrystalline siliconThe length of PV module, L1 1.2 mThe width of PV module, L2 0.527 mThe number of modules in series per string, Nm 1The number of strings, Ns 2The short-circuit current at the reference conditions, Isc,ref Ns × 4.8 A (for total PV array)The open-circuit voltage at the reference conditions, Voc,ref Nm × 21.7 V (for total PV array)The maximum power point current at the reference conditions, Imp,ref Ns × 4.4 A (for total PV array)The maximum power point voltage at the reference conditions, Vmp,ref Nm × 17 V (for total PV array)The solar radiation intensity at the reference conditions, Gref 1000 W/m2
The ambient temperature at reference conditions, Tamb,ref 298.15 KThe solar cell temperature at reference conditions, Tcell,ref 298.15 KThe electrical efficiency at the reference conditions, �el,ref 0.12The sun temperature, Tsun 5760 KThe current temperature coefficient, ˛ 2.06 mA ◦CThe voltage temperature coefficient, ˇ −0.077 V ◦CThe semiconductor band gap energy, ε 1.12 eVThe thickness of glass cover, Lg 0.003 mThe conductivity of glass cover, Kg 1 W/m KThe transmitivity of glass cover, �g 0.95The emissivity of PV/T air collector, εg 0.88The absorptivity of solar cell, ˛c 0.85The thickness of silicon solar cell, Lsi 300 × 10−6 mThe conductivity of silicon solar cell, Ksi 0.036 W/m KThe absorptivity of tedlar, ˛T 0.5The thickness of tedlar, LT 0.0005 mThe conductivity of tedlar, KT 0.033 W/m KThe thickness of back insulation, Li 0.05 mThe conductivity of back insulation, Ki 0.035 W/m KThe length of air duct, L 1.2 mThe width of PV/T air collector, W 0.45 mThe duct depth, ı 0.05 mThe packing factor of solar cell, ˇc 0.83
s5escc
amob
m
ca
c
T
4
4
tsc
The wind speed, Vw
The time interval, �tThe ambient pressure, Pamb
The conversion factor of the thermal power plant, Cf
urements have been recorded during a clear day from 8:00 a.m. to:00 p.m. on May 2004 and experimental data have been recordedvery an hour. The measured data include the solar radiation inten-ity, ambient temperature, inlet and outlet air temperature, solarell temperature, back surface temperature, inlet air velocity, open-ircuit voltage, short-circuit current and outlet electrical power.
Solar radiation intensity has been measured by a pyranometert the same incident plane of the PV modules. All the temperatureeasurements have been done with the calibrated thermocouples
r thermometers to ensure the accuracy. Ambient temperature haseen measured in the shade.
A digital anemometer has been used to measure the air flow in/s at different locations, i.e., air entering and leaving the duct.A digital clamp meter has been used to measure the various
urrents (e.g., short-circuit current, battery current, etc.) in Amperend voltages (e.g., battery voltage, open-circuit voltage, etc.) in V.
Additional information about the experiment method and itsonditions are found in Ref. [16].
The design parameters of the PV/T air collector are described inable 1.
. Results and discussion
.1. Experimental validation
The experimental results of Joshi et al. [16] for a PV/T air collec-or make it possible to verify the results obtained by our computerimulation. The simulated values of outlet air temperature, solarell temperature, back surface temperature, open-circuit voltage,
1 m/s3600 s101 kPa0.36
short-circuit current, outlet electrical power, thermal efficiency,electrical efficiency and overall energy efficiency in present workhave been validated by their corresponding experimental valuesin Ref. [16]. Further, a comparison between the simulated val-ues of outlet air temperature, solar cell temperature, back surface,temperature, outlet electrical power, thermal efficiency, electricalefficiency and overall energy efficiency in present work and theircorresponding calculated values in Ref. [16] have been carried out.
The experimental and calculated values of the above-mentionedparameters have been obtained from the figures and tables of Ref.[16].
The climatic, operating and design parameters of the PV/T aircollector during validation process are described in Table 1. Theycorrespond to the experimental system described by Joshi et al.[16], except that they did not report the wind speed observed overthe course of their tests. This affects the convective heat transfercoefficient between the PV/T air collector surface and the ambientair.
In Table 1, a wind speed of 1 m/s is assumed to have a compar-ison with the experimental data. On the other hand, additionallyperformed calculations for different wind speeds are also reportedin the next section.
In order to compare the simulated results with the experimentalmeasurements, five kinds of error have been calculated by follow-ing equations [37]:
4.1.1. Coefficient of determination (R2)The coefficient of determination can be used to test determining
the linear relation between calculated and measured values, which
F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199 2193
ture, i
c
R
mov
4
vd
M
4
M
tbv
4
e
R
wvc
Fig. 5. The variations of solar radiation intensity, ambient tempera
an be obtained from the following equation [37]:
2 =∑n
i=1(ci − ca)(mi − ma)√[∑ni=1(ci − ca)2] [∑n
i=1(mi − ma)2] , (59a)
where ci, mi, ca, ma and n are the ith calculated value, the itheasured value, the average of the calculated values, the average
f the measured values and the number of calculated and measuredalues, respectively.
.1.2. Mean absolute percentage error (MAPE)The mean percentage error is expressed as the absolute average
alue of percentage deviation between estimated and measuredata and is given by [37]
APE =∣∣∣∣∑n
i=1[100 × (ci − mi)/mi]
n
∣∣∣∣ . (59b)
.1.3. Mean bias error (MBE)The mean bias error is given by [37]
BE = 1n
∑n
i=1(ci − mi). (59c)
The MBE provides information on the long-term performance ofhe correlations by allowing a comparison of the actual deviationetween calculated and measured values term by term. The idealalue of MBE is ‘zero’.
.1.4. Root mean square error (RMSE)The root mean square error can be computed from the following
quation [37]√1∑n 2
MSE =n i=1(ci − mi) . (59d)
hich provides information on the short-term performance. Thealue of RMSE is always positive, representing ‘zero’ in the idealase.
nlet air temperature and inlet air velocity during the test day [16].
4.1.5. t-statistic (t-stat) methodTo determine whether or not the equation estimates are statis-
tically significant, i.e., not significantly different from their actualcounterparts, at a particular confidence level, Stone [38], proposedthe t-statistic as [39]:
t − stat =√
(n − 1)MBE2
RMSE2 − MBE2. (59e)
Using published data in the literature, Stone [38], demonstratedthat MBE and RMSE separately do not represent a reliable assess-ment of the model’s performance and can lead to the false selectionof the best model from a set of candidate ones.
In order to determine whether a model’s estimates are statisti-cally significant, one has simply to determine a critical (t-stat)critvalue obtainable from standard statistical tables, e.g., (t-stat)crit,(˛/2)at the ˛ level of significance, and (n − 1) degrees of freedom. Forthe model’s estimates to be judged statistically significant at the(1 − ˛) confidence level, the calculated value must be between theinterval defined by −(t-stat)crit and (t-stat)crit (acceptance regionunder the reduced normal distribution curve). Values outside thisinterval, the so-called critical region, are those for which we rejectthe hypothesis that the parameter selection has improved themodel.
In all the above-mentioned statistical tests of accuracy, exceptR2, the smaller the value, the better is the model performance [39].
The variations of solar radiation intensity, ambient temperature,inlet air temperature and inlet air velocity during the test day areshown in Fig. 5.
The simulated values of outlet air temperature, solar celltemperature, back surface temperature and the correspondingexperimentally measured data during the test day are shown inFig. 6.
The calculated values of these parameters presented by Joshi etal. [16] are also shown in the same figure for comparison. In this
figure, the subscript ‘sim’ indicates the simulated values of parame-ters in the present work and the subscript ‘cal’ shows the calculatedvalues of parameters by Joshi et al. [16]. The error values of theseparameters with respect to the experimental measurements aregiven in Table 2.
2194 F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199
F eratud
gt2oit
a
itFeis
TT
ig. 6. The simulated and calculated values of outlet air temperature, solar cell tempuring the test day.
According to this figure and Table 2, it is observed that there is aood agreement between the experimental and simulated values ofhese parameters. The t-stat values of the simulated parameters are.88, 6.41 and 6.14, respectively. On the other hand, the t-stat valuesf the calculated parameters are 6.59, 6.47 and 7.92, respectively. Its observed from Fig. 6 that our simulated results are more precisehan the calculated results of Ref. [16].
The simulated and experimental values of open-circuit voltagend short-circuit current during the test day are shown in Fig. 7.
The error values of these parameters with respect to the exper-mental measurements are given in Table 2. The t-stat values ofhese parameters are 7.8 and 0.28, respectively. It is observed from
ig. 7 that there is a good agreement between the simulated andxperimental values of these parameters. The electrical model usedn Ref. [16] (Eq. (25)) cannot estimate open-circuit voltage andhort-circuit current.able 2he R2, MAPE, MBE, RMSE and t-stat values of the PV/T air collector parameters.
Solar PV/T air collector parameter
The simulated outlet air temperature, Tf,out,sim
The calculated outlet air temperature, Tf,out,cal
The simulated solar cell temperature, Tcell,sim
The calculated solar cell temperature, Tcell,cal
The simulated back surface temperature, Tbs,sim
The calculated back surface temperature, Tbs,cal
The simulated open-circuit voltage, Voc,sim
The simulated short-circuit current, Isc,sim
The simulated electrical power, Eel,sim
The calculated electrical power, Eel,cal
The simulated electrical efficiency, �el,sim
The calculated electrical efficiency, �el,cal
The simulated thermal efficiency, �th,sim
The calculated thermal efficiency, �th,cal
The simulated overall energy efficiency, �en,ov,sim
The calculated overall energy efficiency, �en,ov,cal
The simulated exergy efficiency given by Eq. (57b), �ex,Eq. (57b),sim
The simulated exergy efficiency given by Eq. (58), �ex,Eq. (58),sim
The experimental exergy efficiency described by Eqs. (57b) and (58), �ex,Eqs. (57b,58),exp
re, back surface temperature and the corresponding experimentally measured data
Fig. 8 shows the simulated values of maximum power pointvoltage and maximum power point current and the simulatedand experimental values of outlet electrical power during the testday.
The experimental values of maximum power point voltage andmaximum power point current are not mentioned in Ref. [16].Further, the electrical model used in Ref. [16] (Eq. (25)) cannotestimate the electrical parameters of PV/T air collector. However,the electrical model used in the present work is able to predi-cate the electrical parameters. The simulated and experimentalvalues of outlet electrical power during the test day are shownin the same figure. A comparison between the simulated values
of outlet electrical power obtained from Eq. (25) and the experi-mental values of outlet electrical power is also carried out in thisfigure. The respective values of t-stat error are 6.54% and 8.54%,respectively. It is observed from Fig. 8 that there is a good agree-Error value
R2 MAPE MBE RMSE t-stat
0.9897 1.7437 0.7583 1.0934 2.88760.9836 4.0948 −1.7128 1.8815 6.59880.9753 13.6237 6.7519 7.4540 6.41380.9536 18.7014 9.2308 10.1724 6.47860.9832 8.7925 4.3916 4.8870 6.14520.9768 17.1168 8.4621 9.0486 7.92210.9456 2.0311 −0.3776 0.4045 7.80710.9724 2.4751 0.0376 0.3944 0.28740.9993 4.8543 −2.7482 3.0232 6.54480.9999 9.9449 −5.6817 6.0213 8.54900.9728 4.8774 −0.0050 0.0051 11.84220.9978 9.9266 −0.0102 0.0102 47.69810.6994 24.2758 0.0152 0.0252 2.27060.8037 12.2245 −0.0149 0.0231 2.50890.8223 0.8167 0.0015 0.02414 0.20520.8123 6.5772 −0.0264 0.0351 3.41080.9640 2.7403 −0.0030 0.0033 6.47230.9879 3.2761 −0.0035 0.0038 6.64460.8967 0.5771 5.3 × 10−4 0.0025 0.6378
F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199 2195
-circu
meutE
et
a
Ft
Fig. 7. The simulated and experimental values of open
ent between the simulated and experimental values of outletlectrical power. Further, it is observed that the simulated val-es of outlet electrical power in present work are more precisehan the simulated values of outlet electrical power obtained fromq. (25).
Fig. 9 shows the experimental and simulated values of overall
nergy efficiency, thermal efficiency and electrical efficiency duringhe test day.The calculated values of these efficiencies presented by Joshi etl. [16] are also shown in the same figure for comparison. According
ig. 8. The simulated values of maximum power point voltage, maximum power point cuhe test day.
it voltage and short-circuit current during the test day.
to this figure, it is observed that there is a good agreement betweenthe experimental and simulated values of these efficiencies. Fur-ther, the t-stat values of the simulated efficiencies are 0.2%, 2.27%and 11.84%, respectively. On the other hand, the t-stat values ofthe calculated efficiencies are 3.41, 2.5 and 47.69, respectively. Itis observed that our simulated results are more precise than the
calculated results of Ref. [16].The simulated and experimental values of exergetic efficiencydescribed by Eqs. (57b) and (58) during the test day are shown inFig. 10.
rrent and the simulated and experimental values of outlet electrical power during
2196 F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199
ficien
itdmgti(
e
Fig. 9. The experimental and simulated values of overall energy ef
The respective t-stat values are 6.47 and 6.64, respectively. Its observed from Fig. 10 that there is a good agreement betweenhe simulated and experimental values of the exergetic efficiencyescribed by Eqs. (57b) and (58). A comparison between the experi-ental values of exergetic efficiency given in Eq. (57b) and the one
iven by Eq. (58) is also carried out in the same figure. It is clear
hat from Fig. 10 there is a good agreement between the exper-mental values of two exergy efficiencies with a t-statistic errort-stat) = 0.63.According to Figs. 9 and 10, it is observed that the behavior ofxergy efficiency with respect to the variations of climatic, operat-
Fig. 10. The simulated and experimental values of exergetic effic
cy, thermal efficiency and electrical efficiency during the test day.
ing and design parameters is so similar to the electrical efficiencyof PV/T air collector. The exergy shows the quality of energy. Thequality of thermal energy (thermal exergy) in a PV/T air collector islow (�ex,th ≤ 2 % ), therefore the exergy efficiency value of a PV/T aircollector is near to its electrical efficiency value (�ex ≈ �el ≈ 10 % ).
The good agreement between experiment and simulation that
are shown in the previous figures (Figs. 6–10) indicates that theassumption of a wind speed as 1 m/s in the calculations is reason-able.The simulated parameters errors compared with those obtainedby the experimental measurement is explained as follows:
iency described by Eqs. (57b) and (58) during the test day.
F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199 2197
Table 3The typical results of computer simulation program.
Value
Input parameters to computer simulation programThe climatic, operating and design parameters of
solar PV/T air collectorTable 1
The ambient temperature conditions, Tamb 300 KThe inlet air temperature, Tf,in ≈ Tamb 300 KThe inlet air velocity, Vin 1 m/sThe ambient pressure, Pamb 101 kPaThe inlet fluid pressure, Pf,in ≈ Pamb 101 kPaThe solar radiation intensity, G 700 W/m2
The number of modules in series per string, Nm 1The number of strings, Ns 1
Output parameters from computer simulation programThe exergy efficiency, �ex 10.75%The thermal efficiency, �th 17.18%The electrical efficiency, �el 10.01%The overall energy efficiency, �en,ov 45%The outlet air temperature, Tf,out 308.76 KThe solar cell temperature, Tcell 330.19 KThe back surface temperature, Tbs 327.28 KThe average air temperature, Tf 304.6 KThe rate of useful thermal energy, Qu 64.96 WThe rate of solar energy incident on the PV surface,
S442.68 W
The open-circuit voltage, Voc 18.78 VThe short-circuit current, Isc 3.406 AThe maximum power point voltage, Vmp 14.53 VThe maximum power point current, Imp 3.051 AThe light current, IL 3.407 AThe diode reverse saturation current, Io 1.026 × 10−5 AThe series resistance, Rs 0.295 ˝The shunt resistance, Rsh 582.109 ˝The ideality factor, a 1.47 eVThe overall heat transfer coefficient, UL 4.18 W/m2 KThe heat capacity of flowing air, Cp 1.005 kJ/kg KThe product of effective absorptivity and
transmittivity, (˛�)eff
0.672
The penalty factor due to the presence of solar cell 0.787
•
•
TC
lector systems is carried out in Table 4. According to this Table, it isobserved that agent fluid has a great effect on the exergy efficiencyand the exergy efficiency can be increased if an incompressible fluid
material, glass and EVA, hp1
The penalty factor due to the presence of interfacebetween tedlar and working fluid, hp2
0.376
the temperature coefficients of current and voltage have beenassumed constant. In practical cases, they have slight fluctuationdue to the solar radiation intensity and PV module temperaturevariations;
the experimental and calculated results of Ref. [16] has beenobtained from the figures of Ref. [16] by interpolation and curve-fitting methods. This subject decreases the precision of measureddata;able 4omparison of the exergy efficiency values for some solar collector systems.
Solar collector type Exergy efficiency (%)
The coverless PV/T water collector (Fujisawa andTani [6])
11–12.87%
The glazed PV/T water collector (Bosanac et al. [8]) 8–13%The glazed PV/T water collector (Saitoh et al. [9]) 13.3%The double glazed air heater (Ajam et al. [10]) 2%The PV array (Sahin et al. [11]) 3–9%The unglazed PV/T air collector integrated
greenhouse (Nayak and Tiwari [14])4%
The double glazed flat-plate water collector(Farahat et al. [15])
3.9%
The (glass-to-glass) PV/T air collector (Dubey et al.[19])
10.45%
The unglazed PV/T air collector integratedgreenhouse with earth air heat exchanger(EAHE) (Nayak and Tiwari [20])
5.5%
The BIPV/T air collector (Agrawal and Tiwari [22]) 2.12%The unglazed PV/T air collector (present work) 10.75%
Fig. 11. The variations of exergy efficiency described by Eqs. (57b) and (58) withrespect to inlet air temperature.
• wind speed is not constant and has a direct effect on the overallheat loss coefficient that can decrease the precision of calculatedoverall heat loss coefficient in the computer simulation;
• the product of effective absorptivity and transmittivity, (˛�)eff,has been assumed constant while it is changing during theday with the change of solar incidence angle on PV/T collectorsurface.
4.2. Parametric studies
The values of climatic, operating and design parameters in theparametric studies of PV/T air collector are described in Table 1.The typical results of computer simulation program for a sampleconditions have been given in Table 3.
A comparison between the exergy efficiency values of PV/T col-
(water) is used in PV/T collector system.
Fig. 12. The variations of exergy efficiency described by Eqs. (57b) and (58) withrespect to inlet air velocity.
2198 F. Sarhaddi et al. / Energy and Buildings 42 (2010) 2184–2199
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wn
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1tEatgasdp
Fi
ig. 13. The effect of solar radiation intensity on the exergy efficiency described byqs. (57b) and (58).
In order to plot the next figures some parameters are assumedhich are mentioned above each figure. The rest of parameterseeded to plot the next figures are used from Table 1.
The variations of exergy efficiency described by Eqs. (57b) and58) with respect to inlet air temperature are plotted in Fig. 11.
It is observed that the behavior of two exergy efficiencies withespect to inlet air temperature variations is the same and they haveslight change (∼10.8% and ∼10.7%, respectively).
Fig. 12 shows the variations of exergy efficiency described byqs. (57b) and (58) with respect to inlet air velocity.
It is observed that increasing inlet air velocity from 0.001 to5 m/s, the exergy efficiency given by Eq. (58) increases from ∼9.8%o ∼11.3%. On the other hand, the exergy efficiency described byq. (57b) increases from ∼10% to ∼11.1% initially and then afterttaining the inlet air velocity of about Vin ≈ 4.5 m/s, it decreaseso ∼8.5%. This indicates the optimum value of inlet air velocity foriven climatic and design parameters (Table 1). The increase of inlet
ir velocity increases pressure drop in air duct, therefore the pres-ure exergy terms in Eq. (57b) increases and it causes a significantrop in the exergy efficiency of PV/T air collector. The amount ofressure exergy terms in Eq. (57b) is always negative.ig. 14. The variations of exergy efficiency described by Eqs. (57b) and (58) accord-ng to the changes of wind speed.
Fig. 15. The variations of exergy efficiency described by Eqs. (57b) and (58) withrespect to duct length.
Fig. 13 shows the effect of solar radiation intensity on the exergyefficiency described by Eqs. (57b) and (58).
It is observed that the exergy efficiency described by Eq. (57b)increases from ∼7.5% to ∼11.7% initially and then it decreases to∼10% after the solar radiation intensity reaches about 170 W/m2.This indicates the optimum value of solar radiation intensity forgiven climatic and design parameters (Table 1). On the other hand,the exergy efficiency given by Eq. (58) decreases from ∼11.9%to ∼10.3% while increasing solar radiation intensity from 10 to1000 W/m2. According to Fig. 13, it is observed that the exergy effi-ciency given by Eq. (58) has a significant error at low solar radiationintensity. At low solar radiation intensity, Eq. (58) gives PV/T exergyefficiency in such way that is almost near the amount of the elec-trical efficiency of the reference conditions (�ex = 11.9 % ≈ �el,ref).The equivalence of the solar cell and ambient temperature and thenegligible amount of Qu are the reasons of this fact.
Fig. 14 shows the variations of exergy efficiency described byEqs. (57b) and (58) according to the changes of wind speed.
The exergy efficiencies described by Eqs. (57b) and (58) increasefrom ∼10.5% to ∼11.65% and ∼10.61% to ∼11.3%, respectively whilewind speed is increasing from 0 to 10 m/s. It is observed that thebehavior of two exergy efficiencies with respect to wind speedvariations is same.
The variations of exergy efficiency described by Eqs. (57b) and(58) with respect to duct length are shown in Fig. 15.
The exergy efficiency given by Eqs. (58) increases from ∼10.67%to ∼11.02% when duct length increases from 1.2 to 6 m. The increaseof duct length increases the rate of useful thermal energy and out-let air temperature in Eq. (58), therefore exergy efficiency increases.On the other hand, the increase of duct length also increases pres-sure drop in air duct. This subject is not considered by Eq. (58).
The exergy efficiency described by Eqs. (57b) has a slight changewith respect to duct length variations (∼10.75%). The increase ofduct length increases the rate of air flow exergy and the pressureexergy terms in Eq. (57b), therefore exergy efficiency remains con-stant. The amount of pressure exergy terms in Eq. (57b) is alwaysnegative.
It is assumed that PV/T air collectors are connected in series. Fora number of PV/T air collectors connected in series, the outlet tem-
perature of the first collector will be the inlet for second collector,the outlet temperature of the second will be the inlet for the thirdand so on.
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F. Sarhaddi et al. / Energy an
. Conclusion
In this paper, the exergetic performance assessment of a PV/Tir collector was carried out. A detailed energy and exergy analysisas carried out to calculate the thermal and electrical parame-
ers, exergy components and exergy efficiency of a typical PV/Tir. Some corrections were done on related heat loss coefficients inrder to improve the thermal model of a PV/T air collector. A betterlectrical model was used to increase the calculations precision ofV/T air collector electrical parameters. Further, a modified equa-ion for the exergy efficiency of a PV/T air collector was derivedn terms of design and climatic parameters. Finally, validation,umerical simulations and parametric studies were carried out.n the basis of present study, the following conclusions have beenrawn:
The numerical simulation results of this study are in good agree-ment with the experimental measurements noted in the previousliterature. Further, it is observed that the simulation resultsobtained in this paper is more precise than the one given by theprevious literature.The electrical model used in this paper gives better results thanthe one given by the previous literature.The modified exergy efficiency obtained in this paper is in goodagreement with the one given by the previous literature (for inletair velocity less than 4.5 m/s).The behavior of modified exergy efficiency with respect to thevariations of climatic, operating and design parameters is so sim-ilar to the electrical efficiency of PV/T air collector.The agent fluid has a great effect on the modified exergy effi-ciency and the modified exergy efficiency can be increased if anincompressible fluid (water) is used in PV/T collector system.The exergy efficiency used in the previous literature has somedeficiencies such as it does not include the exergy of pressureterms and it has a significant error at low solar radiation intensity.The modified exergy efficiency has a slight change with respectto inlet air temperature or duct length.Increasing inlet air velocity or solar radiation intensity, the mod-ified exergy efficiency increases initially and then decreases afterattaining inlet air velocity or solar radiation intensity of about amaximum point.While increasing wind speed, the modified exergy efficiencyincreases.
cknowledgments
The authors acknowledge Prof. A. D. Sahin [11] for respondingur inquiries.
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