Applied Energy 120 (2014) 115–124

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Applied Energy

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

Optimizing limited solar roof access by exergy analysis of solarthermal, photovoltaic, and hybrid photovoltaic thermal systems

http://dx.doi.org/10.1016/j.apenergy.2014.01.0410306-2619/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: 601 M&M Building, 1400 Townsend Drive,Houghton, MI 49931-1295, USA. Tel.: +1 906 487 1466.

E-mail address: pearce@mtu.edu (J.M. Pearce).

M.J.M. Pathak a, P.G. Sanders b, J.M. Pearce b,c,⇑a Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canadab Department of Materials Science and Engineering, Michigan Technological University, Houghton, MI, USAc Department of Electrical & Computer Engineering, Michigan Technological University, Houghton, MI, USA

h i g h l i g h t s

� Rigorous theoretical exergy modeldeveloped to compare solar energysystems.� Compared photovoltaic solar thermal

hybrid (PVT) systems.� Also side by side photovoltaic and

thermal (PV + T) systems.� Also photovoltaic (PV) systems and

solar thermal (T) systems.� PVT systems are superior in exergy

performance in representativeclimates.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 April 2013Received in revised form 9 January 2014Accepted 11 January 2014Available online 14 February 2014

Keywords:ExergyPVTSolar energySolar thermalPhotovoltaicPhotovoltaic thermal hybrid

a b s t r a c t

An exergy analysis was performed to compare a conventional (1) two panel photovoltaic solar thermalhybrid (PVT x2) system, (2) side by side photovoltaic and thermal (PV + T) system, (3) two modulephotovoltaic (PV) system and (4) a two panel solar thermal (T x2) system with identical absorber areasto determine the superior technical solar energy systems for applications with a limited roof area. Threelocations, Detroit, Denver and Phoenix, were simulated due to their differences in average monthlytemperature and solar flux. The exergy analysis results show that PVT systems outperform the PV + Tsystems by 69% for all the locations, produce between 6.5% and 8.4% more exergy when matched againstthe purely PV systems and created 4 times as much exergy as the pure solar thermal system. The resultsclearly show that PVT systems, which are able to utilize all of the thermal and electrical energy generated,are superior in exergy performance to either PV + T or PV only systems. These results are discussed andfuture work is outlined to further geographically optimize PVT systems.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Fossil fuels cannot indefinitely sustain the energy needs of theearth’s growing human population due not only to finite supplies,

116 M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124

but also the adverse effects of anthropogenic greenhouse gas emis-sions on global climate [1,2]. It is therefore necessary to look foralternative renewable forms of energy [3–6] such as solar energy,which have previously been shown to be a sustainable solution tosociety’s energy needs [7,8]. Currently there are two common sys-tems that utilize the sun’s energy for human use: (1) the solar pho-tovoltaic (PV) cell, which converts sunlight directly into electricityand (2) the solar thermal (T) collector, which converts solar energyinto thermal energy. As the levelized cost of PV has dropped quickly[9] to become competitive with conventional grid electricity in spe-cific regions, available roof top space with open solar access tendsto drop precipitously in those same regions as they are covered withPV. Thus, when attempting to meet all of a building’s internal elec-tricity and heat loads with energy from the sun, roof area becomes asignificant limiting factor [10]. A hybrid solar system, called a solarphotovoltaic thermal hybrid system (PVT), provides a potentialsolution to this challenge [11–13]. PVT systems exploit the heatgenerated from the PV system, which is normally wasted, to pro-duce useful thermal energy along with the electricity from the PV.

There have been several methods to compare PVT systems usingeconomics, carbon dioxide emissions, energy produced and exergyefficiency [14–18]. Both Erdil et al. [19] and Kalogirou et al. [20] cal-culated the economic feasibility of a PVT system and concluded thattheir systems were cost effective. However, economic analysis isusually used to determine the cost viability of the system, but is lim-ited because of the arbitrary nature of the current economic system[21,22]. The proposal of using carbon dioxide (CO2) emissions, par-ticularly the dynamic life-cycle emissions [4], as a way to rate energysystems is useful particularly in the context of stabilizing global CO2

concentrations. However, trying to make a system more energyefficient would reduce the CO2 emissions of the system in a givenlocation, which eventually reduces the complexities of varying geo-graphic emission intensities due to fuel mix in a region [4]. Energyanalysis has shown that PVT systems produce more energy thaneither a PV or thermal collector system per unit area [23]. Throughthis work, studies have tested using different flow rates, glazesand designs to determine if PVT systems are superior [24–27]. How-ever, like the other two comparisons, energy lacks the ability to com-pare electrical energy and thermal energy since energy analysis onlylooks at the quantity of the energy and not the quality as well. Exer-gy, defined as the maximum useful energy in a specific referencestate, typically the surroundings, analyzes both the quantity andquality. This further allows for an improved analysis and optimiza-tion of systems since exergy, unlike energy, is not conserved, butrather destroyed by irreversibilities in real processes [28].

There have been several studies comparing PV, T and PVT sys-tems using exergy. However in these studies, the exergy analysisuses a simplified model by multiplying the Carnot cycle by thethermal energy efficiency [29,30]. Other exergy analysis work hasfocused on specific systems to try to optimize operating settings[31–33]. A meticulous exergy analysis comparing PV, thermaland PVT systems has not been undertaken. Thus, this paper pro-vides a more rigorous theoretical exergy model by building on pre-vious detailed exergy models [31–33] but going further to comparea conventional two panels PVT (PVT x2) system to a side-by-side(PV + T) system, two modules PV (PV x2) only system, and a twopanels T (T x2) only system to determine the technically superiorsystem for applications with limited roof area. In this study all foursolar energy systems were analyzed for the same total area to en-sure an unbiased comparison in three locations with varying cli-matic conditions: Detroit, Denver and Phoenix.

2. Nomenclature

Table 1 contains the nomenclature for the equations inSection 3–6. The equations used in these appendices are from the

renowned account of solar engineering of thermal processes [34]unless otherwise stated.

3. Material and methods

Models, detailed in the sections following, of the four solar en-ergy systems (PVT x2, PV + T, PV x2, and T x2) shown in Fig. 1, werecreated and analyzed in Scilab, an open-source numerical simula-tion tool [35]. The National Renewable Energy Laboratory NationalSolar Radiation Data Base 1991–2005 update Typical Meteorologi-cal Year 3 (TMY 3) data was used for the three locations: DetroitCity Airport (725375), Denver Intl AP (725650) and Phoenix SkyHarbor Intl AP (722780) [36].

All three locations are Class I data sets with the highestquality of solar modeled data with a complete data set. Thesethree locations were chosen due to their distinct and representa-tive average ambient temperatures and irradiance values, withDetroit representing both low temperatures and low solar flux(9.2 �C and 3.63 kWh/m2/d), Denver presenting low temperaturesand high solar flux (8.2 �C and 4.58 kWh/m2/d), and Phoenix rep-resenting both high temperatures and high solar flux (16.9 �Cand 5.48 kWh/m2/d) [37]. The hourly air temperature, windspeed and solar irradiation were used in the simulation. Thewind speed was recorded at ten meters off the ground andtherefore the systems are assumed to be at that elevation. Asshown in Fig. 1 each individual system (PVT x2, PV + T, PV x2,and T x2) has the same total area. The following sub-sectionsdescribe the evolution of the models to analyze the systems.The PVT system was model as an air heater with a PV panelas the absorber since air systems are typically preferred due tothe lower operating costs and minimal use of material [38].The solar thermal system was modeled as a tube and sheetsystem but with air as the fluid to have the same medium asthe PVT system for a more direct comparison.

4. PV model

4.1. Solar photovoltaic cell model

In this simulation, the solar PV cells are modeled with afive-parameter equivalent electric circuit which describes thecell as a diode [39,40]. The starting equation for the model ofthe solar cell describes the solar cell as a diode and can be seenin Eq. (1).

I ¼ IL � ID �V þ IRs

Rsh¼ IL � Io e

VþIRsa � 1

h i� V þ IRs

Rshð1Þ

where I is the current, IL is the leakage current, Io is the reverse sat-uration current, V is the voltage, Rs is the series resistance and a isthe modified ideality factor. A circuit depiction of Eq. (1) can befound in Fig. 2.

To solve for the five parameters, the initial conditions wereapplied to Eq. (1). At the short circuit current conditions, thecurrent, I, is equal to the reference short circuit current (Isc, ref)and the voltage is equal to zero. Furthermore, the slope of thecurrent with respect to the voltage is equal to the negativeinverse of the shunt resistance (Rsh). In the open circuit condi-tions, the current equals zero and the voltage equals the refer-ence open circuit voltage (Voc,ref). At the maximum powercondition, the current equals the reference maximum powercurrent (Imp,ref) and the voltage equals the reference maximumpower voltage (Vmp,ref). Furthermore the change in the maximumpower is zero.

When these conditions are applied to the diode equation, Eq.(1), the following five equations are produced (2–6).

Table 1Nomenclature.

a Modified ideality factor (V) Greek SymbolsA Area (m2) b Collector tilt (degree)Cb Bond conductance (W/m) d Declination: sun’s angular position at noon with respect

to the plane of the equatorCp Specific heat capacity of air (kJ/kg K) D Difference in temperature, pressureD Diameter (m), pipe diameter (m) e EmissivityEg Material bandgap (eV) g EfficiencyEx Exergy l Viscosity (kg/s m)fr Friction factor lI,sc Short circuit current temperature coefficientF Fin efficiency factor q Density (kg/m3)F0 Collector efficiency factor r Stefan–Boltzmann’s constant (W/m2 K4)F00 Collector flow factor / Latitude of the location being studiedFR Collector heat removal factor Subscriptsh Heat transfer coefficient (W/m2 K) 1 LengthI Current (A) 2 WidthIV Current voltage abs Absorber/Platek Thermal conductivity (W/m K) , Boltzmann’s constant (m2 kg/s2 K) amb AmbientL Dimensions of the solar module, length of system, thickness, duct length (m) b Back_m Air mass flow rate (kg/s) cell Cell

N Number of glass covers f FluidNu Nusslet number g Glassp Flow pressure (Pa) h HydraulicP Perimeter (m) in InletPV Photovoltaic i InnerPV/T Photovoltaic solar thermal hybrid s L Loss, LightQu Useful gain (W) m MeanR Resistance (X) mp Maximum power pointRe Reynolds number o Reverse saturationS Solar radiation intensity (W/m2) oc Open circuitT Temperature (K) p PanelUb Overall back loss coefficient (W/m2 K) pv PhotovoltaicUe Overall edge loss coefficient (W/m2 K) pv/t Photovoltaic solar thermal systemUL Overall loss coefficient (W/m2 K) r RadiationUt Overall top loss coefficient (W/m2 K) ref ReferenceV Voltage (V) , Velocity (m/s) s SeriesW Distance between diameter of pipe (m) sc Short circuity Empirically determined coefficient establishing the upper limit for module

temperature at low wind speeds and high solar irradiancesh Shunt

z Empirically determined coefficient establishing the rate at which moduletemperature drops as wind speed increases

th Thermal

w Windpm Mean Plate

M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124 117

Isc;ref ¼ IL;ref � Io;ref e

Isc;ref Rs;ref

aref � 1

264

375� Isc;ref Rs;ref

Rsh;refð2Þ

1Rsh;ref

¼

Io;ref

arefe

Isc;ref Rs;ref

aref � 1

264

375� 1

Rsh;ref

1þ Io;ref Rs:ref

arefe

Isc;ref Rs;ref

aref � 1

264

375� Rs;ref

Rsh;ref

ð3Þ

0 ¼ IL;ref � Io;ref e

Vsc;ref

aref � 1

264

375� Vsc;ref

Rsh;refð4Þ

Imp;ref ¼ IL;ref � Io;ref e

Vmp;ref þ Imp;ref Rs;ref

aref � 1

264

375

� Vmp;ref þ Imp;ref Rs;ref

Rsh;refð5Þ

Imp;ref

Vmp;ref¼

Io;ref

arefe

Vmp;ref þ Imp;ref Rs;ref

aref � 1

264

375� 1

Rsh;ref

1þ Io;ref Rs:ref

arefe

Vmp;ref þ Imp;ref Rs;ref

aref � 1

264

375� Rs;ref

Rsh;ref

ð6Þ

Solving Eqs. (2)–(6) produces the reference values for the Io, IL, a, Rs

and Rsh. These variables are then used to calculate the operatingcondition values. The equations used to solve for the operating val-ues are the following Eqs. (7)–(11).

aaref¼ Tcell

Tcell;refð7Þ

where Tcell is the PV cell’s temperature in Kelvin.

Rsh

Rsh;ref¼ Sref

Sð8Þ

where S is the irradiance in W/m2.

IL ¼S

Sref½IL;ref þ lI;scðTcell � Tcell;ref Þ� ð9Þ

where lIsc is the current temperature coefficient in A/�C.

Fig. 1. Equal area solar energy systems: (a) PVT x2, (b) PV + T, (c) PV x2 and (d) T x2.

Fig. 2. Five parameter photovoltaic model equivalent electric circuit.

118 M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124

Eg ¼ Eg;ref ½1� CðTcell � Tcell;ref Þ� ð10Þ

where Eg is the band gap of the solar cell in electron volts (eV). Inthis case, it is the band gap of silicon.

Io ¼ Io;refTcell

Tcell;ref

� �3

e

Eg;ref

kTcell;ref

� �� Eg

kTcell

� �� �264

375 ð11Þ

Rs is assumed to be independent of both temperature and irradi-ance. These variable results allowed for the calculation of Voc, Isc,Vmp and Imp. The Eqs. (12) and (13) were used to solve Voc and Isc

and the Vmp and Imp. For solving for the Isc and Voc just replace theVmp with the Voc and the Imp with the Isc.

Imp ¼ IL � Io eVmp þ ImpRs

a � 1

24

35� Vmp þ ImpRs

Rshð12Þ

Imp

Vmp¼

Ioa e

Vmp þ ImpRs

a � 1

24

35� 1

Rsh

1þ IoRsa e

Vmp þ ImpRs

a � 1

24

35� Rs

Rsh

ð13Þ

A Heliene 72 M 300 W (1.984 � 0.984 m) module was used in thesimulation because it is a recent model and is a longer module,which is required for a condition in the thermal modeling on thePVT system [41]. Using the EES code provided by Klein, the datasheet parameters were entered and the reference values, Io, Il, aand Rs and Rsh were calculated [40]. Using these reference values,

the temperature and irradiance dependent Imp and Vmp were deter-mined. Multiplying the Imp and Vmp produced the maximum power,which when divided by the total solar exergy (Exin) derived by Pe-tela, produced the exergy efficiency for the solar panel [42,43]. Eq.(14) gives the efficiency of the PV panel.

epv ¼VmpImp

Exinð14Þ

where the Exin, Petela derived total solar exergy entering the systemis given in Eq. (15) [39].

_Exin ¼ 1� 34

Tamb

Tsunþ 1

3Tamb

Tsun

� �4 !

SAp ð15Þ

where the Tamb and Tsun are the ambient and sun temperature inKelvin.

4.2. Solar PV panel temperature

The temperature of the PV module was determined using theempirically derived equation from Sandia National Laboratoriesand was found to have ±5 �C accuracy in predicting the tempera-ture of the panel, which is equivalent to a 3% error in the poweroutput of the solar panel [44]. The system type chosen was glass/cell/polymer sheet on an open rack mount. The wind speeds usedto determine the empirical coefficients were at the standardmeteorological height of 10 m, which matches the wind speed in-put values for this simulation. The air properties were interpolatedbased off the average air temperature in the system [45,46].

To determine the temperature of the back of the panel, Eq. (16)was used [44].

Tm ¼ SeyþzVw þ Tamb ð16Þ

where y is dimensionless and z is s/m, are the empirically deter-mined coefficients with the values of �3.56 and �0.075 for theglass/cell/polymer sheet open rack module type and Vw is the windvelocity is m/s. To determine the temperature of the cell, Eq. (17)was implemented [44].

Tcell ¼ Tm þS

SrefDT ð17Þ

where DT is the temperature difference between the panel’s backsurface (Tm) and the cell’s temperature at an irradiance value of(Sref) 1000 W/m2. In the case of the module being considered, thetemperature difference value is 3 �C.

5. Solar thermal model

5.1. Thermal design

The solar thermal system was modeled using the Duffie andBeckman equations for a tube and sheet system [34]. The solarthermal model is modeled with eight 4 cm tubes running underthe absorber. The coolant used is air with a flow rate for the systemof 0.056 kg/s (100 kg/h m2), which was chosen based off the ASH-RAE standards for testing of solar air collectors [47]. This flow ratewas chosen to be in the middle of the range of the ASHRAE flowrates of 0.01–0.03 m3/s m2. The inlet temperature is assumed tobe the ambient temperature.

To determine the efficiency of the solar collector, the overallheat loss from the system is needed. The physical constants werecalculated using interpolation from a physical constant table ofvalues using the average temperature as the temperature the con-stants were at [45]. The overall heat loss of the system was calcu-lated using Eqs. (18)–(24). Eq. (18) was employed to calculate thetop heat losses (Ut) as a starting temperature for the simulation.

M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124 119

Ut ¼N

CTpm

Tpm � Tamb

N þ f

� �e þ1

hw

0BBB@

1CCCA�1

þrðT2

pm þ T2ambÞðTpm þ TambÞ

1eabs þ 0:00591Nhw

þ 2Nþf�1þ0:133eabseg

� Nð18Þ

where N is the number of glass covers, Tpm and Tamb are the temper-ature of the plate and ambient temperature (K), b is the collector tilt(degrees), eg and eabs are the emissivity of the glass and absorberand hw is the wind heat transfer coefficient (W/m2 K), which canbe found using Eq. (19) [34,48].

hw ¼ 2:8þ 3Vw ð19Þ

The coefficients f, C, and e in Eq. (18) are calculated usingEqs. (20)–(22).

f ¼ ð1þ 0:089hw � 0:1166hweabsÞð1þ 0:07866NÞ ð20Þ

C ¼ 520ð1� 0:000051b2Þ ð21Þ

e ¼ 0:43 1� 100Tpm

� �ð22Þ

The bottom, Ub, and side, Ue, losses were calculated using Eqs. (23)and (24).

Ub ¼kL

ð23Þ

Ue ¼kL A� �

edge

Apð24Þ

where k is the thermal conductivity (W/m K), L is the thickness (m)and A is the area of that edge (m2).

The total loss of the system is the sum of Ut, Ub and Ue as in Eq.(25)

UL ¼ Ub þ Ue þ Ut ð25Þ

Using UL the fin collector efficiency factor F0 was calculated usingEq. (26).

F 0 ¼1

UL

W 1UL ½DþðW�DÞF� þ 1

Cbþ 1

pDihf

h i ð26Þ

where W is the pipes center to center distance (m), D and Di is theouter and inner diameter of the pipe (m), Cb is the bond conduc-

tance which is assumed to be very large 1Cb¼ 0

� (W/m K), hf is

the heat transfer coefficient between the fluid and the pipe wall(W/K) which can be calculated using Eq. (27).

hf is the heat transfer coefficient between the fluid and the pipewall (W/K) which can be calculated using Eq. (27).

hf ¼ Nuk

Dhð27Þ

where Nu is the Nusselt number found by using Eq. (28). Eq. (28)was derived for a fully developed turbulent airflow with one sideheated and the other side insulated [33]. In this use of the equationthe heated side is the top and the bottom is insulated.

Nu ¼ 0:0158Re0:8 ð28Þwhere Re is the Reynolds number which can be calculated using Eq.(38) found in Section 5.2.

F is the fin efficiency factor which can be calculated from Eq.(28) [48–50].

F ¼ tanh½mðW � DÞ=2�mðW � DÞ=2

ð29Þ

where m can be calculated using Eq. (30).

m ¼ffiffiffiffiffiffiUL

dk

rð30Þ

where d is the thickness of the plate (m) and k is the thermalconductivity of the plate (W/m K).

Using the collector efficiency factor F0 found by Eq. (26), the heatremoval factor was determined from Eq. (31) [48–50].

FR ¼_mCp

APUL1� e�

ApULF0_mCp

� �ð31Þ

The actual useful energy gain Qu was then calculated using theEq. (32).

Qu ¼ ApFR½S� ULðTin � TambÞ� ð32Þ

Using the Qu the mean temperature of the plate and the fluids out-flow were calculated with Eq. (33) and (34) [48–50].

Tabs�m ¼ Tin þQu=Ap

ULFRð1� FRÞ ð33Þ

Tout ¼ Tin þQ u

_mCpð34Þ

5.2. Exergy model

The change in exergy ðD _ExthÞ for the thermal system is derivedfrom the difference in the exergy of the flow at the inlet and outlet[31–33]. This is given by the Eq. (34).

D _Exth ¼ _mCp Tout � Tin � TamblnTout

Tin

� �� �� 1:5

_mTambDpqTin

� �ð35Þ

where _m is the mass flow rate (kg/s), Cp is the specific heat capacity(s/kg K), Tout, Tin and Tamb are the outlet, inlet and ambient temper-ature (K) respectively, q is the density (kg/m3) and Dp is thefrictional pressure drop (Pa). The 1.5 factor found in Eq. (34) is toaccount for the fan and motor efficiency losses (74% and 90%respectively) as derived in the paper by Hegazy [51]. The frictionalpressure drop of the fluid Dp was calculated using Eq. (36).

Dp ¼ frqLV2

2Dhð36Þ

where L is the length of the duct (m), V is the velocity (m/s), Dh isthe hydraulic diameter as seen in Eq. (37).

Dh ¼4Af

Pfð37Þ

where Af is the cross sectional area (m2) and P is the wetted perim-eter (m) and f is the friction which can be calculated using Eq. (38).

frðReÞ ¼64Re

0:316Re�0:25

( )Re 6 2200otherwise

ð38Þ

where Re is the Reynolds number that was calculated from Eq. (38)

Re ¼_mDh

Af lð39Þ

where l is the Viscosity (kg/s m).The total rate of exergy of the solar input ð _ExinÞ is the same

equation used for the PV (Eq. (15)) derived by Petela [42,43]. Therate of exergy of the system was divided by the total rate of solarexergy to produce the exergy efficiency of the thermal system. Thisis given in Eq. (40).

eth ¼D _Exth

_Exin

ð40Þ

Fig. 3. A comparison of a PV + T, PV x2, T x2 and PVT x2 systems at Detroit (DET),Denver (DV) and Phoenix (PHX) at the Spring Equinox.

120 M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124

6. PVT model

The PVT model was designed as a single panel air heater withthe PV module directly on the absorber plate. The thermal equa-tions can be found in Sections 5.1 and 6.2 [34,45,46]. The totalexergy of the PVT model is the sum of the exergy of the PV moduleand thermal system of the PVT system.

6.1. PV component model of PVT

The same solar PV panel was used in the PVT model as in the PVmodel. The maximum voltage and current and exergy efficiencywere calculated as discussed in Section 3.1. The only difference isthat Sandia National Laboratory empirical equation to determinethe temperature of the panel was not used because it is only de-signed for PV panels. Thus the temperature of the panel was deter-mined using the air heater equations, which would better matchthe PVT panel/absorber temperature [34].

6.2. Thermal component model of PVT

The PVT model was designed as an air heater [34] with an air gapof 1 cm and a flow rate of 0.056 kg/s (100 kg/h m2). These weredetermined to produce a high outlet temperature while maintain-ing the purpose of cooling the PV panel [52]. The inlet temperatureis again assumed to be the ambient temperature. The exergyanalysis of the PVT model for the thermal side was in a calculatedsimilar way to that used for the flat plate collector in Section 4.2with the following modifications. The top heat loss for a single paneair heater was calculated using Eq. (41) instead of Eq. (18) [53].

Ut ¼1

1hwþhrTp�Tamb

þ 1hrTp�Tg

þ Lp

kp

ð41Þ

where hrTp-Tamb and hrTp-Tg are calculated from Eq. (42) which is theradiation coefficient [52].

hr1�2 ¼rðT2

1 þ T22ÞðT1 þ T2Þ

1e1þ 1

e2� 1

ð42Þ

where T1 and T2 are two object temperatures (K), e1 and e2 are theemissivity of two objects and r is the Boltzmann constant.

The collector efficiency factor F0 was calculated using Eq. (43)instead of Eq. (26) [48–50,52].

F 0 ¼ 11þ UL

h1þ 11

h2þ 1

hr

ð43Þ

Assuming the temperature of the absorber and the bottom of the ducthas the same temperature; h1 and h2 are the same [34], where h1 andh2 are the convective heat transfer from the duct to the airflow. Theconvection was calculated using Eq. (28). It was also assumed thatthe duct had a constant temperature, which causes the radiationcoefficient equation, Eq. (42), to be simplified to Eq. (44).

hr ¼rT3

p1e1þ 1

e2� 1

ð44Þ

where Tp is the temperature of the absorber plate and e1 and e2 arethe emissivity of the two objects and r is the Boltzmann constant.

7. Results and discussion

The simulations were run for the PV + T (side by side), PV x2, Tx2 and PVT x2 systems of equal area for Detroit, Denver and Phoe-nix. Figs. 3–6 show a 24-h exergy efficiency for specific days: the

spring equinox, summer solstice, autumn equinox and winter sol-stice for each location and system combination respectively.

From Figs. 3–6, it was seen that the PVT x2 system outperformsboth the PV + T, PV x2 and the T x2 systems. However, at first andlast light of the day, the PV x2 system typically surpasses the PVTx2 system. This is because at these times of the day, the irradianceis significantly lower, which causes the change in air coolanttemperature in the PVT system to increase very little. This resultsin the exergy of the thermal side of the PVT system to be slightlynegative, causing the PVT overall exergy to be lower than the PVx2 system. This suggests that it may be beneficial to not start thethermal system until the PV module reaches a certain temperatureat which the thermal component produces a positive exergy. Thisalso indicates that optimizing the PVT system for its locationwould further improve the system’s performance. However, thethermal extraction from the PV panels in the PVT system is quiteeffective during the summer solstice, as seen in Fig. 5, as there isa significant drop in the exergy performance of the PV x2 systemand an unnoticeable drop in the PVT system. As the PVT systemis exposed to hotter temperatures, the PV module will becomeslightly cooler than a standard non-cooled PV module, and will alsoextract a larger additional exergy from the thermal removal. Thissuggests that, in the hotter climates, a PVT system would be thehighly preferred system as long as there is an adequate thermalload.

Both the PV + T and T x2 have significantly lower exergy out-puts compared to the PV x2 and the PVT systems. This is becausethe low grade heat produced by the T systems is less useful, whichthus produces less exergy. Since both systems have a large portionof their exergy produced from the thermal systems, the systemswill have a lower overall exergy output.

It is interesting to note how the hourly exergy produced by anyof the systems is affected by the irradiance and wind speed. Anexample of this can be found in Fig. 5 with the T x2. The irradianceis the highest for this day and there is no wind resulting in a spikein the Denver data point when compared to the points before andafter where there is a similar irradiance but wind speeds are 2 and5 m/s respectively. Higher wind speeds cause heat loss that resultsin a lower exergy output for the thermal systems. These observa-tions of the superior performance of the PVT systems can be fur-ther supported by looking at the average monthly exergyefficiency for the whole year at each location. Figs. 7–9 show theexergy efficiency as a function of month for Detroit, Denver andPhoenix for the four systems respectively.

Fig. 4. A comparison of a PV + T, PV x2, T x2 and PVT x2 systems at Detroit (DET),Denver (DV) and Phoenix (PHX) at the Fall Equinox.

Fig. 5. A comparison of a PV + T, PV x2, T x2 and PVT x2 systems at Detroit (DET),Denver (DV) and Phoenix (PHX) at the Summer Solstice.

Fig. 6. A comparison of a PV + T, PV x2, T x2 and PVT x2 systems at Detroit (DET),Denver (DV) and Phoenix (PHX) at the Winter Solstice.

Fig. 7. A comparison of the average monthly exergy efficiency for the PV + T, PV x2,T x2 and PVT x2 systems in Detroit.

Fig. 8. A comparison of the average monthly exergy efficiency for the PV + T, PV x2,T x2 and PVT x2 systems in Denver.

Fig. 9. A comparison of the average monthly exergy efficiency for the PV + T, PV x2,T x2 and PVT x2 systems in Phoenix.

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Table 2Standard deviation of annual monthly exergy efficiency of the systems.

PVT x2 PV + T PV x2 T x2 Latitude (�N)

Detroit 1.73 0.97 2.21 0.61 42.4Denver 1.47 0.85 1.94 0.53 39.8Phoenix 1.42 0.91 1.74 0.34 33.5

Table 3The yearly total exergy (MW h) for the PVT x2, PV + T, PV x2, and T x2 systems atDetroit, Denver and Phoenix.

Yearly total exergy [MW h]

PVT x2 PV + T PV x2 T x2

Detroit 1.71 1.01 1.60 0.42Denver 1.74 1.03 1.63 0.44Phoenix 1.77 1.05 1.63 0.46

122 M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124

As seen from Figs. 7–9, the effects of the different temperaturesand irradiances can be seen in the different weather patterns of thethree chosen locations. Detroit has the lowest winter tempera-tures, which causes the PV to perform better and achieve higherexergy efficiency for the PVT, PV and PV + T systems as seen inFig. 7. In addition, Detroit’s summer months produce similarefficiencies to the other locations seen in Figs. 8 and 9. Therefore,Detroit exhibits the largest efficiency change from the winter tothe summer. This can be seen in Table 2 where the annual standarddeviation of exergy efficiency of each system found in Figs. 7–9.

Detroit has the largest deviations for all systems which can beattributed to the highest latitude producing the greatest changein solar irradiance throughout the year. This demonstrates that thissystem could be better optimized to suit the significant change inseasonal weather conditions. From Table 2, the different weatherpatterns are apparent with the different systems deviations. Mostsystems are more consistent in Phoenix where the irradiancewould differ the least due to the lower latitude with the exceptionof the PV + T system, which deviated the least in Denver. Thiswould suggest the thermal and PV panels complement each otherbest in Denver and that the other systems could be betteroptimized.

In Fig. 8, Denver has a higher irradiance than Detroit, but it alsohas higher wind speeds, especially in the winter months, causinggreater thermal losses which lower the thermal exergy efficiencyof the PVT system. Furthermore, as will be seen from Fig. 8, somemonths produce more favorable conditions when all three inputs(ambient temperature, irradiance and wind speed) change atdifferent rates. An example of this is in February and April whenthe wind speed remains constant or drops slightly, the ambienttemperatures rise a bit and the irradiance jumps significantly fromthe previous month simultaneously. This allows the thermalcomponent to perform better because the change in air flow tem-perature increases greatly. In the case of Phoenix, see Fig. 9, thetemperature is always higher, the wind speeds are always lowerand the irradiance is always higher than at the other two locations.This produces an annual standard deviation of 0.91 and 1.42 for theexergy efficiency for the PV + T and PVT systems compared to thedeviation of 1.74 for the PV system as seen in Table 2. During thecooler months, the PV components of the two systems performbetter. However, during the hotter months, the thermal compo-nent performs better. Thus, there is a slight boost in exergy whichcauses less of an exergy efficiency drop than the PV only system.Finally, the PV system by itself performs the worst in Phoenixdue to the higher temperatures. The opposite is true for the ther-mal only system, which has a standard deviation of 0.34.

From Figs. 7–9, the PVT system is clearly the superior system forall locations based on the exergy analysis. The reason the PVT sys-tem outperforms the PV + T and T x2 system is that a flat plate col-lector (half/all the total area) produces low grade heat, which iswell designed for its application of preheating homes, but is notvery useful energy (low exergy). For comparison the high exergyelectricity provided by the PV could be used in a high coefficientof performance heat pump system to deliver low exergy preheat-ing for the same home. Furthermore, the PVT x2 system has twoPV panels, instead of one in the PV + T and none in the T x2 setup, which gives the PVT system a significant exergy boost given

that electricity is more useful energy (high exergy). With this inmind, even when comparing PVT system to PV only system, whichboth have high exergy outputs, the PVT system still outperformsthe PV x2 system. This would suggest that with the limited opti-mally-positioned roof space, PVT with the highest exergy systemdensity would be the best choice. Even in the months where thePV system produced similar efficiencies to the PVT system werethe coldest months of January and December, where the percent-age difference was less than 2%, this difference still translates to5–7% more annual exergy produced by the PVT system. Thisslightly lower exergy gain is because during the colder months,the thermal component of the PVT system produces a lower exergyoutput since the change in air flow temperature is lower due tolower irradiance values. Furthermore, the temperatures of the PVpanel and PVT system are similar which leads to similar exergyefficiencies. However, when analyzing the hotter months, espe-cially in Phoenix, the PVT system and PV x2 system percentage dif-ference increased to over 3%, translating to 8–10% more annualexergy produced. This is due to the exact opposite situation as de-scribed for the colder months. Table 3 displays the yearly amountof exergy produced by all four systems for the three locations.

From Table 3, it was seen that the PVT system produces almosttwice as much exergy as the PV + T system and four times as muchexergy as the T x2 over the course of the entire year for all threelocations. In comparison with the PV x2 system, the PVT systemproduces 6.5%, 7.2% and 8.4% more exergy for the Detroit, Denverand Phoenix locations respectively. This further demonstrates thatthe PVT system should be chosen if there is limited optimal roofspace to produce the maximum amount of exergy. It also suggeststhat there is a need to optimize the PVT system for each location:the Denver and Phoenix locations produce 2.1% and 3.7% moreexergy than the Detroit due to the higher irradiance, but Detroitis more efficient. Such optimization might include changing theflow rates, reducing the thermal losses and using different PVmaterials to better suit higher operating temperatures.

8. Future work

The primary limitation of this work is the assumption that all theexergy is used for the simulated systems. In solar thermal systems inparticular this may not always be a valid assumption. Thus, it is leftfor future work to refine this base case to take into account primarilythermal loads, but also depending on electrical grid conditions, theelectric loads. Such electrical grid conditions could include the useof battery storage either in the form of traditional batteries or utiliz-ing the batteries in plug-in cars [54,55]. For most rooftop con-strained applications, the assumption of full consumption of theexergy produced may be reasonable. However, a practical optimiza-tion would require the matching of electrical and thermal loads forspecific building usage. Depending on the loads, the optimal systemcould change substantially for a given application.

Another important consideration is the location, since it greatlyaffects the performance of the system. It would therefore beinteresting to provide an exergy efficiency map of the PVTsystems for all of North America or for other regions to determine

M.J.M. Pathak et al. / Applied Energy 120 (2014) 115–124 123

efficiency patterns and location performance of the PVT system.Alongside location, possible building integrated PVT systems(BIPVT) instead of typical PVT panels should be analyzed to betterunderstand the opportunities for PV to be utilized in the façade of abuilding [56].

PVT technology is at a relatively early stage of technologicaldevelopment. Optimizing the system’s components, such as thematerials, could improve the performance for a given application.There have been many different studies on the PV material whichcould be harnessed to better optimize the system. Detailed workon the thermal and structural performance of a PV module andunderstand the spectral irradiance effect on the PV would assistin the design of the correct PVT for a specified location [57,58].Thin film PV panels such as hydrogenated amorphous silicon (a-Si:H) materials could be used in replacement of crystalline silicon(c-Si) in PVT systems since it offers a promising solution to PVTsystem integration [59]. a-Si:H can be deposited directly onto theabsorber plate making an integral system [60], has a superior tem-perature coefficient (0.1%/�C) [61] to c-Si-based PV and running thesystem at a higher operating temperature [62], which would havethe added benefit of annealing the Staebler–Wronski Effect (SWE)defects and achieving a higher electrical performance. Preliminarystudies of a-Si:H PV under PVT operating temperatures showedoperating a-Si:H-based PV at 90 �C (i.e. a PVT operating tempera-ture), with thicker i-layers than the cells currently used incommercial production, provided a greater power outputcompared to the thinner cells operating at either PV or PVT operat-ing temperatures [63]. In addition, the solar thermal side of thePVT can be used to create high-temperature annealing pulses(spike annealing), which were found to provide a greater than10% energy gain when compared to a cell that was only degradedunder normal PV conditions [64]. These preliminary results show-ing the promise of a-Si:H as a PVT material should be followed upwith an appropriate exergy analysis.

This could then be used to focus on optimizing the entire PVTsystem as an integrated optimized system, rather than the existingtradeoffs between the two sub-systems, and would clearly have animpact on the overall system exergy efficiency. This would allowthe thermal component to perform better than current designswhilst not hampering the PV performance [65].

9. Conclusions

This study found that for solar energy collecting systems withidentical absorber areas, PVT hybrid systems surpassed the exergyefficiency of both PV + T (side by side) and purely PV systems inthree representative regions in the U.S. The PVT system outper-formed the PV + T system by 69% and the T x2 system by almost400% in all the locations. Similarly, the PVT system performed6.5%, 7.2% and 8.4% better than the PV only system for the Detroit,Denver and Phoenix locations respectively. It is clear that for appli-cations with limited roof area PVT systems are superior choices.This research also suggests that greater optimization is requiredfor PVT systems. To further improve the exergy performance ofPVT systems, geographical optimization should be further investi-gated with potential improvements found in the PV material, flowrate and improved thermal loss reductions.

Acknowledgements

This research was supported by the Natural Sciences andEngineering Research Council of Canada and the Solar BuildingsResearch Network. The authors would like to acknowledge helpfuldiscussions with S.J. Harrison.

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