Analytical expressions for temperature dependent electrical efficiencies of thin film BIOPVT systems

Applied Energy 146 (2015) 442–452

Contents lists available at ScienceDirect

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

Analytical expressions for temperature dependent electrical efficiencies of thin film BIOPVT systems Ankita Gaur ⇑, G.N. Tiwari Center for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

h i g h l i g h t s  Analytical expressions for electrical efficiency of thin film BIOPVT systems are derived.  Studies are performed for thin film BIOPVT systems with and without air duct.  Characteristic curves, energy and exergy analysis have been carried out for these systems.  BIOPVT systems without air duct exhibit lower efficiency and higher room temperature.  Number of air changes and mass flow rates are observed to affect the room temperature.

a r t i c l e

i n f o

Article history: Received 10 June 2014 Received in revised form 28 November 2014 Accepted 27 January 2015 Available online 13 March 2015 Keywords: a-Si BIOPVT systems Solar energy Exergy

a b s t r a c t Analytical expressions for the electrical efficiencies (gm Þ of building integrated opaque photovoltaic thermal (BIOPVT) systems based on thin film photovoltaic (PV) modules have been derived. The expressions are valid for different climatic conditions and different design parameters of the building. The systems based on a-Si, CdTe and CIGS thin film solar modules have been analyzed for their energy, exergy and characteristics performance with and without air duct, for a typical day of Srinagar, India. The module daily average electrical efficiency (gm Þ and average room temperature (T r Þ of a BIOPVT system based on a-Si solar modules without air duct were found to be 7.25% and 18.7 °C respectively, whereas with air duct the gm and T r of the same system have been found to be 7.57% and 15.2 °C respectively. The num_ f Þ have been found to have a significant effect on T r . ber of air changes (NÞ and mass flow rates (m Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Regular increment in energy demand and its insufficient supply has now become a world wide problem. Global warming and rapid depletion of conventional sources of energy, force the researchers to develop renewable energy sources. Photovoltaics (PV) is an important renewable energy technology, which converts the solar light into electricity and it itself has the potential to meet all the energy demands, but the high cost and inefficient energy harvesting are limiting the proper utilization of this technology. The one way to improve the efficiency of this technology would be the minimization of energy losses and proper utilization of energy wastage. Only a fraction of incident energy on PV modules gets converted into electricity and the rest of it is wasted via reflection and heating. The energy wastage via reflection can be minimized by the use of antireflection layers and the energy wastage via heat can be harvested through heat extraction and its utilization in ⇑ Corresponding author. E-mail address: [email protected] (A. Gaur). http://dx.doi.org/10.1016/j.apenergy.2015.01.106 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

other suitable applications. The PV systems, which are designed to harvest the thermal energy as well, are known as photovoltaic thermal (PVT) systems. The building integration of PVT systems makes these systems more useful and it reduces the expenses for building construction and makes the buildings to look more beautiful. When integrated with buildings the PVT systems are known as building integrated PVT (BIPVT) systems [1]. The BIPVT technology has now become an important technology as it contributes to the energy demand of the building itself and the generated energy can also be fed/sold to the grid. For the heat extraction a coolant fluid like water or air is circulated at the bottom of the panel and it takes the heat away from the panel. The heat energy of this hot fluid is utilized for other applications. On the other hand the heat dissipation causes a reduction in module temperature, resulting in longer durability as the high temperature reduces module efficiency and causes degradation [2]. The BIPVT systems can be used as roof or as the facade in the building [3]. There are many reports in the literatures where the analysis regarding total building energy consumption, including heating, cooling and artificial lighting loads, and the economic

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

443

Nomenclature A B b C H h hp1 ; hp2 IðtÞ K L L1 ma _f m N Pr Re T U tc;a U Tc;f U p;r ðUAÞt V V1

area (m2) breadth of wall (m) width of PV module (m) specific heat of air (J kg1 K1) height of wall (m) heat transfer coefficient (W m2 K1) penalty factors due to glass cover and PV module (dimensionless) incident solar radiation (W m2) thermal conductivity (W m1 K1) length (m) length of PV module (m) mass of air (kg) mass flow rate of air (kg s1) number of air change per hour Prandtl number (dimensionless) Reynolds number (dimensionless) temperature (°C) overall heat transfer coefficient from solar cell to ambient through glass cover (W m2 K1) overall heat transfer coefficient from solar cell to flowing air through glass cover (W m2 K1) overall heat transfer coefficient from brick and insulation to room air (W m2 K1) overall heat transfer coefficient from room to ambient air through walls and windows (W K1) volume of a room (m3) air velocity (m s1)

analysis have been performed [4–7]. From a holistic viewpoint, Bazilian and Prasad summarized the potential applications of these systems [8]. Analysis on the performance of a photovoltaic-Trombe wall in outdoor environmental chamber has also been carried out [9]. There are many reports where such systems have been studied in different conditions in different ways [10–18]. Chow et al. [19] studied a PVT facade hotel building in Macau, with a 24-h air-conditioned room and found that the climate conditions and system operating modes affect significantly the PV productivity. The design parameters like fin efficiency, lamination requirements and thermal conductivity between the PV module and the supporting structure also affect the electrical and thermal efficiencies of a BIPVT system [20]. Majority of the PV module production is based on crystalline silicon (c-Si) wafer technology and usually possess a hard glass cover or tedlar sheet, which have shortage in availability and causes high price of the modules. The thin film solar panels are relatively cheaper and can simply be rolled and attach to any curved or flat surface. Though c-Si BIPVT systems have high energy and exergy efficiencies, but from the economic point of view, thin film BIPVT systems are better options. Therefore intense research is being done on thin film solar cells and the thin film PV market has grown significantly in the past few years. Gaur and Tiwari [21] presented the modeling of a-Si thin film PV module and validated the same experimentally. Depending on the transparency of the PV modules and the back plates, the BIPVT systems can be classified into semi-transparent and opaque BIPVT systems. In the present paper the focus has been on the performance analysis of opaque BIPVT (BIOPVT) systems only. Though some reports are already there in the literature on performance analysis of c-Si BIOPVT systems, but these reports lack the temperature effect on module efficiency [22–24]. Vats et al. [22] analyzed the c-Si based semi-transparent BIPVT (BISPVT) systems without considering the temperature effect on module efficiency. They found that from the space heating and

Greek symbols a absorptivity (dimensionless) b packing factor (dimensionless) s transmissivity (dimensionless) ðasÞeff product of effective absorptivity and transmissivity q density (kg m3) m kinematic viscosity (m2 s1) g efficiency (dimensionless) Subscripts a ambient air b brick c solar cell eff effective f fluid (air) fi inlet fluid fo outgoing fluid m module PVroof roof of PV modules b insulated roof or insulated wall (brick and insulation material) r room E EVA (Ethyl vinyl acetate, topmost coating of thin film PV module)

higher electrical yield point of view BISPVT system is more suitable than BIOPVT system. Since the thin film PV modules are usually fabricated on metallic sheet and are opaque, so in this paper, instead of BISPVT systems, a performance analysis of BIOPVT systems based on thin film solar modules has been carried out with and without air duct. The effects of temperature variation, climatic conditions and design parameters have been taken into account. Fig. 1(a) and (b) respectively show the schematic design of a thin film BIOPVT system, integrated with the roof of the building with and without air duct. In Fig. 1(a) the PV panel is integrated to the roof of the room with a distance (air gap). Air channel is made between back plate of aluminium sheet of PV module and the roof made of bricks and insulation materials (sand, cement and polystyrene and straw fiber). Whereas in Fig. 1(b) the PV panel itself is roof of the room. Here the PV modules are prepared on the

Fig. 1. Schematic view of thin film BIOPVT roof system (a) with duct and (b) without duct.

444

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

whether temperatures are usually very low and power supplies/ means for room heating are not easily available. We have done the analysis for a place Srinagar (Indian hill station), where the climate is too cold and cloudy. Therefore the buildings should be designed to make maximum use of sunlight, and thereby keep its interiors as warm as possible. We have performed the necessary calculations keeping these points in our mind. For this purpose the calculations were carried out for a typical day of 17th January 2013 in Srinagar, India which is a recommended average day for the coldest month January in India [25]. 2. Theory and modeling Fig. 1c. Schematic representation of opaque thin films PV modules, inclined at an angle of 34° from horizontal.

metallic plates and the module is encapsulated by an EVA encapsulant only, which is very thin and considered to be highly transparent. Fig. 1(c) shows the schematic cross-sectional view of the PV modules and Fig. 1(d) shows the schematic view when the module is integrated to the roof with a duct formation. In both the system PV modules are installed at angle of 34° to the horizontal which corresponds to latitude of the Srinagar, India. For BIOPVT system without duct, when the solar radiation falls on it, due to very low thicknesses some of the heat of the incident radiation is transmitted through the solar cells and is absorbed by the back sheet of the module which causes heating of the PV module. This heat enters into the room through convection. Whereas in case of BIOPVT system with air duct, inlet and outlet vents are there at the top and bottom of the duct for the air flow. The cooler air entering through bottom inlet takes the heat of PV module and escapes through outlet vent and the hot air enters into the room. For smooth circulation of air, fan is provided at the outlet but not shown in figures. Usually the solar radiation entering in the living space is stored in the form of thermal energy in the building components such as floors, walls then this energy transmits into the room space and the room gets heated. In this way in both the cases, BIOPVT systems with and without air duct, the thermal energy of PV modules are utilized for space heating. Further this reduces the temperature of PV module and increases the electrical efficiency. The effects of module temperature ðT m Þ, air temperature ðT r Þ and design parameters viz. cross section area of duct, duct thickness ðtÞ, duct height ðdÞ, fluid velocity ðv 1 Þ and the number of air changes ðNÞ, on the module efficiency have been investigated. For these studies d has been varied from 0.01 to 0.2 m, whereas v 1 and N have been changed from 0.1 to 2.0 m/s, and from 2 to 10 respectively. The values of rest of the design parameters are given in Table 1. BIOPVT systems in particular, would have a great impact on room heating therefore the overall thermal and exergy gain calculations have been carried out for a place where the

The efficiencies of thin film BIOPVT systems integrated to roof with and without air duct have been calculated from energy balance equations. To write the energy balance equations the following assumptions were made: (a) Negligible ohmic losses in solar cells and PV modules. (b) The system is in quasi-steady state. (c) One dimensional heat conduction (a good approximation for the present study). (d) The surface of PV module is at uniform temperature. (e) There is no temperature stratification in the room air due to force mode of operation. (f) The room is thermally insulated and the physical properties of air are constant over operating temperatures. 2.1. Energy balance equations 2.1.1. Thin film BIOPVT systems with air duct The energy balance equations for different components of the BIOPVT systems with duct would be written as, 2.1.1.1. For thin film PV roof.

am ð1  RE ÞIðtÞbdx ¼ ½U t;ma ðT m  T a Þ þ hmp ðT m  T p Þ þ gm IðtÞbdx 2

Rate of solar energy

3

2

Overall heat

3

7 6 6 7 6 transfer from top 7 7 4 available on the 5 ¼ 6 4 surface of PV module 5 PV module to ambient 3 2 Rate of heat 6 transfer from 7  Rate of electrical  7 6 þ6 7þ 4 PV module to 5 energy produced

ð1Þ

back surface where U t;ma ¼

h

LEVA K EVA

þ h10

i1

, hmp ¼

h i1 Lp Kp

As the thickness of EVA ðLEVA Þ is very less compared to thermal conductivity ðK EVA Þ, therefore U t;ma  h0 . The term on the left hand side of Eq. (1) corresponds to the rate of solar energy available on the PV module whereas the first term on the right hand side corresponds to the overall heat transfer from the top surface of PV module. The second and third terms on the right hand side of Eq. (1) represent the rate of heat transfer from PV module to back surface and the rate of electrical energy produced respectively. 2.1.1.2. For Al carrier panel (back surface).

hmp ðT m  T p Þbdx ¼ hpf ðT p  T f Þbdx 2 3 Rate of heat transfer   Rate of heat transfer from 6 7 4 from PV module to 5 ¼ back surface to air back surface Fig. 1d. Cross section view of a BIOPVT system integrated to roof of a room.

ð2Þ

445

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452 Table 1 Design parameters of a room and opaque PV module for thin film BIOPVT system. Parameters

Values

b L1 PV roof area Lr  Br  Hr V

3m 3.6 m 10.8 m2 3.6 m  3 m  3.2 m 35 m3

Roof inclination Ca

34° 1005 J kg1 K1 1.17 kg m3 9 m2 14.97 m2 9.9 m2 9.9 m2 0.722 22.26  103 W m1 K1 25.64 kg 1 m s1

qa A1 A3 A2 A4 Pr K Ma Va

Parameters

bm b0 (/°C) gm0 (%) Am (m2) v Lb Kb Lcm K cm Ls Ks

sg Kg Lg RE

2.1.1.3. For flowing air.

þ KLcm þ KLss þ h1i cm

i1

CIGS 0.85 1 0.0045 10 0.72

Using Eqs. (2) and (5), the back surface temperature ðT p Þ is found to be given by

Tp ¼

hpf T f þ hp1 ðasÞeff þ U tp T a ; hpf þ U tp h

h

ð6Þ U

mp t;ma where hp1 ¼ Ut;mamp , U tp ¼ U t;ma and ðasÞeff ¼ am ð1  RE Þ  gm . þhmp þhmp

Substituting the values of T m and T p from Eqs. (5) and (6) in Eq. (3) and on integration one gets

where A ¼

ð7Þ

b½hp2 ½ðasÞeff IðtÞhp1 þT a U tp þU pr T r  

mf cf

;B ¼

h

bU L

pf and hp2 ¼ U tp þh . The



mf cf

pf

solution of Eq. (7) gives

Tf ¼

ð3Þ Lb Kb

CdTe 0.85 1 0.002 8.2 0.72

dT f þ BT f ¼ AðxÞ; dx

 dT f hpf ðT p  T f Þbdx ¼ mf cf dx þ U pr ðT f  T r Þbdx dx     rate of heat transfer heat carried away by ¼ from back surface to air air with distance   An overall heat transfer from þ air to room

h

a-Si 0.85 1 0.0026 7.8 1.17 9.49  106 m2 s1 0.12 m 0.69 W m1 K1 0.04 m 0.6 W m1 K1 0.04 m 0.049 W m1 K1 0.95 1.1 W m1 K1 0.003 m 0.15

am

where hpf ¼ KL 0:332Re0:5 Pr0:33 and Re ¼ vma L. Here Reynolds number Re is calculated to be 3  105, which is less than 5  105 and indicates that the flow is laminar so this hpf is for laminar flow only. The term on the right hand side of Eq. (2) corresponds to the rate of heat transfer from PV module to back surface and the term on the right hand side corresponds to the rate of heat transfer from back surface to air.

where U pr ¼

Values

. The term on left hand side repre-

sent the rate of heat transfer from back surface to air whereas the first and second terms on the right hand side represent the hest carried away by air and overall heat transfer from air to room.

A ð1  expðBxÞÞ þ T f i expðBxÞ B

On applying the boundary  T f x¼L; T f ¼ T fo one gets

Tf 0 ¼

ð8Þ

conditions

 Tf 

x¼0;

T f ¼ T fi

hp1 hp2 ðasÞeff þ U tp hp2 T a þ U pr T r ð1  expðhÞÞ þ T r UL  expðhÞ

2.1.1.4. For room air.

ð9Þ

LL where U L ¼ U pr þ U pf ; h ¼ bU and T r ¼ T fi . The average fluid (air) 

dT r mf cf ðT fo  T fi Þ ¼ M a C a þ ðUAÞt ðT r  T a Þ þ 0:33NVðT r  T a Þ dt     Heat carried away by rate of thermal energy ¼ air stored in room 2 3 2 3 rate of thermal energy rate of thermal energy 6 7 6 7 þ 4 lost from room to ambient 5 þ 4 lost from room to ambient 5 

through walls

where ðUAÞt ¼ U i A1 þ U i A2 þ U i A3 þ U i A4 and U i ¼

h

Lb Kb

þ KLcm þ KLss þ h1i cm

i1

.

The term on left hand side correspond to the heat carried away be air whereas the first term on right hand side corresponds to the rate of thermal energy stored in room. The second and third terms on right hand side correspond to rate of thermal energy lost from room to ambient through wall and rate of thermal energy lost from room to ambient through windows. From Eq. (1) the T m would be given by

am ð1  RE ÞIðtÞ  gm IðtÞ þ U t;ma T a þ hmp T p U t;ma þ hmp

mf cf

temperature through the air gap between thin film opaque PV module and blackened absorber roof (see Fig. 1(a)) is given by

Tf ¼

through windows ð4Þ

Tm ¼

and

:

ð5Þ

  hp1 hp2 ðasÞeff þ U pf T a þ U pr T r 1  expðhÞ 1 h UL   1  expðhÞ þ Tr h

ð10Þ

where U pf ¼ U tp hp2 . Using Eqs. (9) and (10), (4) gives

dT r þ a T r ¼ f ðtÞ ; dt where

a ¼

F R U pf þðUAÞt þ0:33NV Ma C a

F R ½hp1 hp2 ðasÞeff IðtÞþU pf T a þ½ðUAÞt þ0:33NVT a . Ma C a

ð11Þ h U

; U pf ¼ U tppfþhtp

pf

and

f ðtÞ ¼

Using the initial boundary condition

at t = 0, T r ¼ T r0 , the solution of Eq. (11) gives

Tr ¼

f ðtÞ ð1  expðatÞÞ þ T r0 expðatÞ a

ð12Þ

The temperature dependent electrical efficiency of a PV module can be written as [26,27],

446

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

gm ¼ g0 ½1  b0 ðT m  T 0 Þ

ð13Þ

Now using Eqs. (5), (6) and (10) and substituting the value of ðT m  T 0 Þ in Eq. (13) we get the following expression for module efficiency g

 0 h  i ii U F hp1 hp2 F R Hð1expðhÞÞ U þ UprL þ pfUL R 1expðhÞ 1 U 1  1expðhÞ ðUAÞeff h h      am ð1  RE ÞIðtÞ hmp hp1 hp1 hp2 H 1  expðhÞ  1  b0 1þ þ 1 hpf þ U tp U UL h     U pr U pf F R 1  expðhÞ hp1 hp2 F R Hð1  expðhÞÞ T a hmp U tp U t;ma þ þ þ þ UL UL U hpf þ U tp h ðUAÞeff      HU pf F r 1  expðhÞ U pr U pf F R 1  expðhÞ þH ð1  expðhÞÞ þ 1 þ UL UL UL h h     T r0 H U pr U pf F R 1  expðhÞ þ expðhÞ  T 0 ð14Þ þ UL U UL h

gm ¼ h

g0 b0 IðtÞ

h

h h 1 þ h mpþUp1tp pf

hmp hpf hpf þU tp

.

gm ¼

h

1 UL

½am ð1  RE ÞIðtÞ þ h0 T a  þ U b;mr



dT r þ aT r ¼ f ðtÞ; dt

2

ð17Þ

ð18Þ

ra Am where a ¼ ðUAÞt þ0:33NVþU ; ðUAÞt ¼ U i A1 þ U i A2 þ U i A3 þ U i A4 and Ma C a ra Am þðUAÞt þ0:33NVT a . Using the initial boundf ðtÞ ¼ hAm ½am ð1RE ÞIðtÞgm IðtÞþ½U Ma C a

ary condition at time t ¼ 0; T r ¼ T r0 , the solution of Eq. (18) gives

f ðtÞ ð1  expðatÞÞ þ T r0 expðatÞÞ: a

n

h U ra

o

i

am ð1  RE ÞIðtÞ þ T a ð1  expðatÞÞ þ T r0 expðatÞ  T 0

ð19Þ

i

n o hU ð 1  expðatÞ Þ 1  gU0 bL 0 1 þ Ub;mr ra



heat transfer from

h U

ð20Þ

U

b;mr where U ra ¼ h00þUb;mr and h ¼ h0 þU

3

b;mr

Rate of soalr energy 6 7 ¼ 4 top surface of PV module 5 available on PV module to ambient 2 3 An overall heat transfer   Rate of electrical 6 7 þ 4 from PV module to room 5 þ energy produced air through back surface

b;mr

3. Electrical and thermal energy for thin film BIOPVT system with and without air duct 3.1. Electrical energy

ð15Þ The term on left hand side of Eq. (15) corresponds to the rate of solar energy available on the PV module whereas the first term on right hand side corresponds to the heat transfer from top surface of PV module to ambient. The second and third terms on the right hand side of Eq. (15) represent the overall heat transfer from PV module to room air through back surface and the rate of electrical energy produced respectively. 2.1.2.2. For room air.

The hourly electrical energy (W) of a BIOPVT system would be given by

Eel;hourly ¼ gm  APV;roof  IðtÞ

ð21Þ

Now the daily electrical energy in kW h would be given by

Eel;daily ¼

N1 X Eel;hourly;i i¼1

1000

ð22Þ

where N i is the number of sun shine hours per day. 3.2. Thermal energy

dT r Ma C a þ ðUAÞt ðT r  T a Þ þ 0:33NVðT r  T a Þ ¼ U b;mr ðT m  T r ÞAm dt 2 3 2 3 The rate of thermal The rate of thermal energy 6 7 6 7 4 energy stored in 5 þ 4 lost from room to ambient 5 2

h0 þ U b;mr

Substituting the value of ðT m  T 0 Þ from Eqs. (17) and (19) in Eq. (13) we get the following expression for module efficiency,

am ð1  RE ÞIðtÞAm ¼ ½h0 ðT m  T a Þ þ U b;mr ðT m  T r Þ þ gm IðtÞAm

a room

am ð1  RE ÞIðtÞ  gm IðtÞ þ h0 T a þ U b;mr T r

where U L ¼ h0 þ U b;mr . The integration of Eq. (16) gives

Tr ¼

2.1.2. Thin film BIOPVT systems without duct 2.1.2.1. For thin film PV roof.

h

Tm ¼

h h H þ p1ULp2

where ðUAÞeff ¼ F R U pf þ ðUAÞt þ 0:33NV and H ¼

g0 1  b0

the rate of thermal energy lost form room to ambient through window respectively. The term on right hand side of Eq. (16) represents the overall heat transfer from cell to room air. From Eq. (15) the T m would be given by

3

through walls

The rate of thermal energy   An overall heat transfer 6 7 þ 4 lost from room to ambient 5 ¼ from cell to room air through windows ð16Þ The first, second and third terms on the left hand side of Eq. (16) correspond to the rate of thermal energy stored in room, rate of thermal energy lost from the room to ambient through wall and

The rate of useful thermal energy (W) obtained from a thin film BIOPVT system with duct would be given by 



Q hourly ¼ mf C f ðT fo  T r Þ þ U pr ðT p  T r ÞAPVroof

ð23Þ

On the other hand the rate of useful thermal energy without duct would be given by 

Q hourly ¼ U Tm;r ðT m  T r ÞAPVroof

ð24Þ

The daily thermal energy (kW h) is obtained by summing the hourly thermal energy for number of sun shine hours per day and could be written as

447

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

6

I(t) Ta

800

5 4

600 3 400 2 200

1

0

Ambient Tempreature (Ta) (oC)

Solar Intensity, I(t) (W/m2)

1000

0 8

10

12

14

16

Table 2a _ f Þ on the T r ; T m and gm of thin film Effect of air duct height ðdÞ and mass flow rate ðm BIOPVT system integrated to roof with duct (at v = 2 m/s). Air duct height d, (m)

Mass flow rate _ f , (kg/s) m

0.001 0.005 0.010 0.03 0.05 0.10 0.15 0.2

0.004 0.021 0.0427 0.126 0.21 0.421 0.631 0.85

Average ambient temp. ðT a Þ = 2.6 °C N=0

N=2

T fo

T r (°C) T m °(C) gm (%) T r (°C) T m (°C) gm (%)

6.06 12.02 14.54 16.85 17.4 17.83 17.97 18.05

5.36 11.32 13.84 16.15 16.7 17.13 17.27 17.35

36.3 34.45 33.12 32.9 32.15 32.11 32.10 32.10

7.39 7.5 7.52 7.59 7.59 7.6 7.6 7.6

4.67 8.64 10.38 12.0 12.39 12.69 12.79 12.84

35.74 33.84 32.69 31.5 31 30.9 30.45 30.25

7.41 7.55 7.58 7.6 7.6 7.62 7.67 7.67

18

Time (Hours) Fig. 2. Hourly variation of solar intensity ðIðtÞÞ, and ambient temperature ðT a Þ on an inclined roof for a typical day of January 2013 in Srinagar, India.

Q ;daily ¼

N1 X Q ;hourly;i i¼1

ð25Þ

1000

3.3. Overall thermal energy of thin film BIOPVT systems For the overall thermal energy the electrical energy is also converted into equivalent thermal energy using

Eth;daily ¼

Eel;daily 0:38

ð26Þ

where the denominator on the right hand side of Eq. (26) represents the power generation efficiency of a conventional power plant and has been considered to be 0.38 [28]. The equivalent thermal energy is obtained by summing the daily equivalent thermal energy and the daily thermal energy as

Q ov erall;thermal ¼ Q dailyl þ Eth;daily

ð27Þ

Now the overall thermal efficiency ðgov erall ;thermal Þ would be given by [29],

gov erall;thermal ¼ gthermal þ

gelectrical

ð28Þ

0:38



where; gthermal ¼

Q daily IðtÞAPVroof

ð29Þ

3.4. Overall exergy efficiency of thin film BIOPVT systems Exergy of a system is defined as the maximum theoretical work done during the interaction of the system with its environment, until the equilibrium state is reached [30]. Since the room air is heated by PV module, so considering the PV system to be a heat source and the surrounding air as heat sink, the thermal energy of the room air can be transformed into work and/or into electrical contribution. To convert the thermal efficiency into equivalent electrical efficiency, we used the Carnot efficiency factor [31]. The daily exergy for thin film BIOPVT systems integrated to the roof with air duct would be given by

  T a þ 273 : Exth;daily ¼ Q th;daily 1  T fo þ 273 However that without air duct would be given by

  T a þ 273 : Exth;daily ¼ Q th;daily 1  T r þ 273

Exdaily ¼ Exth;daily þ Eel;daily :

ð32Þ

The daily overall exergy efficiency of thin film BIOPVT system with air duct would be given by



Tm without duct

Tm with duct

8.0

60

50

40

7.5

30

7.0 20

 T a þ 273 : T fo þ 273

ð33aÞ

On the other hand the daily overall exergy efficiency without air duct would be given by

Temperature (oC)

Efficiency (%)

8.5

Efficiency without duct Efficiency with duct

ð31Þ

The overall exergy of the system would be given by the sum of the daily exergy and daily electrical energy as,

gov erall;exergy ¼ gelectrical þ gthermal 1  9.0

ð30Þ



gov erall;exergy ¼ gelectrical þ gthermal 1 

 T a þ 273 : T r þ 273

ð33bÞ

Table 2b Effect of number of air changes ðNÞ on the T r T m and gm of thin film BIOPVT system integrated to roof without duct. At average ambient temp. ðT a Þ = 2.6 °C

6.5

Tr without duct

Tr with duct

10

6.0 09:00 10:00 11:00

12:00 13:00 14:00 15:00

Time (Hour) Fig. 3. Hourly variation in T r ; T m and gm for a-Si thin film BIOPVT system with and without air duct.

N

T fo

T r (°C)

T m (°C)

gm (%)

0 2 4 6 8 10

15.29 12.28 10.55 9.42 8.63 8.05

14.62 11.61 9.88 8.75 7.96 7.38

25.59 25.46 25.4 25.36 25.34 25.33

7.70 7.71 7.713 7.714 7.714 7.714

448

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

Table 3 Calculated values of average room air ðT r Þ, module temperature ðT m Þ and average electrical efficiency ðgm Þ for various air duct height ðdÞ and fluid velocity ðv 1 Þ. Air duct height d(m)

Fluid velocity v 1 (m/s)

Mass flow rate _ f (kg/s) m

T fo (°C)

T r (°C)

Tm (°C)

gm (%)

TLL ¼

(a) d = 0.01 m 0.01 0.01 0.01 0.01 0.01

0.10 0.50 1.00 1.50 2.00

.0041 .021 0.042 0.063 .084

5.27 10.63 14.52 17.08 18.99

4.58 9.94 13.83 16.39 18.30

31.68 32.28 33.83 35.51 37.17

7.66 7.65 7.62 7.5 7.56

(b) d = 0.03 m 0.03 0.03 0.03 0.03 0.03

0.10 0.50 1.00 1.50 2.00

.012 .063 .126 .189 .252

6.88 13.12 16.73 19.05 20.76

6.3 12.54 16.15 18.47 20.18

31.82 33.08 35.04 36.95 38.76

7.66 7.64 7.60 7.57 7.53

(c) d = 0.05 m 0.05 0.05 0.05 0.05 0.05

0.10 0.50 1.00 1.50 2.00

.021 .105 0.21 0.31 0.42

7.71 13.80 17.27 19.5 21.8

7.134 13.22 16.69 18.92 20.6

31.90 33.32 35.35 37.29 39.13

7.66 7.63 7.60 7.56 7.53

(d) d = 0.10 m 0.10 0.10 0.10 0.10 0.10

0.10 0.50 1.00 1.50 2.00

0.042 0.21 0.42 0.63 0.84

8.53 14.36 17.71 19.87 21.50

7.95 13.78 17.13 19.29 20.92

31.99 33.52 35.6 37.57 39.42

7.66 7.63 7.59 7.56 7.52

(e) d = 0.15 m 0.15 0.15 0.15 0.15 0.15

0.10 0.50 1.00 1.50 2.00

.063 .315 .63 .94 1.2

8.86 14.55 17.85 19.99 21.59

8.28 13.97 17.27 19.41 21.01

32.03 33.59 33.69 37.67 39.51

7.65 7.63 7.59 7.55 7.52

(f) d = 0.20 m 0.20 0.20 0.20 0.20 0.20

0.10 0.50 1.00 1.50 2.00

.084 0.42 0.84 1.26 1.68

9.03 14.66 17.93 20.08 21.65

8.45 14.07 17.35 19.5 21.08

32.05 33.63 35.74 37.72 39.57

7.65 7.63 7.59 7.55 7.52

8.0

Electrical Efficiency (%)

7.9

without duct with duct

7.8

values of TLL should me minimum. It is the measure of variation in temperature of room air with time. For AC rooms (Air Conditioner rooms) the value of TLL is zero. For non-AC rooms (rooms without Air Conditioner) it must approaches to zero. TLL of a system can be written as,

7.7 7.6

T r max  T r min ; T r max þ T r min

ð34Þ

where T r max is the maximum room temperature and T r min is the minimum room temperature. The room temperature variation also depends on its occupancy so we should consider the unoccupied hours but in the present studies we have not considered the room vacant any time but occupied all the time. 4. Methodology Climatic data for the solar radiation IðtÞ on horizontal surface and the ambient temperature ðT a Þ on 17th January 2013 in Srinagar was obtained from the Indian Meteorological Department (IMD), Pune. The following methodology was used to evaluate the performance of thin film BIOPVT systems with and without air duct:  The hourly variation in solar radiation on an inclined roof was calculated following the Liu and Jordan method [32,33].  The designed parameters for thin film BIOPVT systems with and without air duct, used for the calculations have been tabulated in Table 1.  For the known climatic conditions and designed parameters, the gm for thin film BIOPVT systems with duct was calculated using Eq. (14). T r was calculated from Eq. (12) and then for that T r , the T m was calculated using Eq. (5). In case of without duct the gm was calculated from Eq. (20) and the T r and T m were obtained from Eqs. (19) and (17) respectively. Note: Eqs. (14) and (20) are valid only for the condition ðT m  T 0 Þ > 25 °C.  On the basis of analytical studies the T r and gm were computed _ f ; N; d and v 1 . for different values of different parameters viz. m  Electrical energies and thermal energies with and without air duct have been obtained from Eqs. (22) and (25) respectively.  For both the systems with and without air duct, the overall thermal energies and overall electrical energies have been computed from Eqs. (27) and (32) respectively.  The overall thermal efficiencies of thin film BIOPVT systems with and without air duct have been calculated using Eq. (28) whereas the overall exergy efficiencies have been calculated from Eq. (33).

7.5

5. Results and discussion

7.4 7.3 7.2 7.1 7.0 0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

(Tm-Ta)/It Fig. 4. Variation in electrical efficiency of a-Si thin film BIOPVT system with and without duct as a function of ðT m  T a Þ=It .

3.5. Index of thermal load leveling Thermal load leveling (TLL) is a parameter which describes the thermal comfort index of a system having values always less than 1. It indicates fluctuation in T r with time. For best load leveling, the

To solve the mathematical equations, a computer program ‘MathCad 8’ has been used. Fig. 2 shows the hourly variation of IðtÞ and T a on an inclined roof (34° from horizontal). IðtÞ first increased and then decreased with time and was maximum 866.46 W/m2 at 12:00 noon. Similarly the ambient temperature first increased and then decreased and was maximum 4.9 °C at 13:00 h. The investigations were carried out on different type of thin film BIOPVT systems, though the values of the parameters for different systems were different but the characteristics and results were quite similar therefore to avoid repetition of results, the results of only one type of thin film BIOPVT systems are presented. The results presented here are for a-Si based thin film BIOPVT systems. Fig. 3 shows the hourly variations in T r ; T m and gm for a-Si thin film BIOPVT systems with and without air duct. With air duct the T r and T m were found to be lower than those without air duct, however the with duct configuration resulted in

449

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

Room Temperature (°C)

(a)

20

15

10

5

0 10

1 8

0.8 6

0.6 4

0.4 2

0.2

Number of air changes (N)

(b)

0

(c)

18

18 16

Room Temperature (°C)

16

Room Temperature (°C)

Mass flow rate (Kg/sec)

0

14 12 10 8 6

14 12 10 8 6 4

4 2

2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mass flow rate (Kg/sec)

0

1

2

3

4

5

6

7

8

9

10

Number of air changes (N)

_ f on T r for a-Si thin film BIOPVT system with duct in 3Dimension. (b) Effect of m _ f on T r in 2D (XZ view). (c) Effect of N on T r in 2D (YZ view). Fig. 5. (a) Effect of N and m

higher gm . The lower T r on the application of duct happens because of indirect heating of the room air where an insulating roof exists between the module and the room air (see Fig. 1(a)). Also the loss in energy of air due to its circulation causes lower T r . Apart from that the air circulation through the duct causes more heat dissipation from the module that causes lower T m . As the gm is a function of temperature, the lower T m with duct causes higher gm . Without air duct the module average daily electrical efficiency and average T r were found to be 7.25% and 18.7 °C respectively, whereas with duct they were found to be 7.57% and 15.2 °C respectively. Fig. 4 shows the characteristics curves for a-Si thin film BIOPVT systems with and without air duct which show the variation in gm as a function of ðT m  T a Þ/IðtÞ. These characteristics curves are similar to the Hottel–Whiller–Bliss equations of a flat plat collector [16]. Due to different T m with and without air duct, the characteristics curves are observed a little bit shifted from each other. At a given intensity the BIOPVT system with air duct exhibited higher gm because of lower T m . For both the systems gm is observed to decrease linearly with increment in ðT m  T a Þ/IðtÞ and can be attributed to higher T m . Fig. 5(a) shows the variation _ f for a-Si thin film BIOPVT system integrated in T r with N and m to roof with duct (v = 2 m/s) in 3 dimension. XZ and YZ (2D)

views have been shown in Fig. 5(b) and (c) respectively. WhenN _ f of 0.0427 kg/s, the T r dropped was changed from 0 to 2 at m _ f was increased from from 13.84 °C to 10.38 °C and as the m 0.004 to 0.85 kg/s, the T r increased by 11.9 °C. No significant _ f on the T m and gm was observed (see effect of N and m Table 2a). For an increment in N from 0 to 10, T m decreased by 0.26 °C. As this reduction was very small, no significant effect was observed on gm . This cab be attributed to the facts that (i) the heat associated with PV module is removed instantaneously even at 0.004 kg/s and (ii) the PV module is not in direct contact _ f > 0:21 kg/s, there was no variation in T r with the room air. For m and can be attributed to internal circulation of room air between room and the duct. Further, the T r was observed to decrease by 7.6 °C as the value of N was increased from 2 to 10. Similarly in case of without air duct as the N was increased from 0 to 2 then T r was observed to decrease by 3.01 °C. For an increment in N from 2 to 10, the T r decreased by 4.38 °C (Table 2b). The reduction in T r with increment in N is caused by the energy loss by rapid circulation of the air, however the less reduction in T r with similar change in N for a system without air duct can be attributed to the direct contact of the PV modules with the room air. Therefore, for the room heating, N should be minimum.

450

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

(a)

22 20

Room Temperature (°C)

18 16 14 12 10 8 6 4 0.2

0.15

0.1

0.05

0

0.5

1

Duct hight (m)

2

Fluid velocity (m/s)

(c) 22

20

20

Room Temperature (°C)

(b) 22 Room Temperature (°C)

1.5

18 16 14 12 10 8 6

18 16 14 12 10 8 6

4

4 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

0.02 0.04 0.06 0.08 0.1

Fluid velocity (m/s)

0.12 0.14 0.16 0.18 0.2

Duct Hight (m)

Fig. 6. (a) 3D presentation of the effect of air duct height (d) and fluid velocity (v1) on room temperature (T r ) of a-Si thin film BIOPVT system. (b) Effect of fluid velocity (v1) on room temperature (T r ) in 2D (XZ view of (a)). (c) Effect of air duct height (d) on room temperature (T r ) in 2D (YZ view of (a)).

Table 3 shows the daily average values of gm ; T r , and T m calcu_ f . Table 3(a) shows the vallated for different values of d; v 1 and m ues of gm ; T r , and T m calculated for d = 0.01 m but with different _ f . Similarly the other sub-tables show the correvalues of v 1 and m sponding values of gm ; T r , and T m for different values of d and v 1 _ f . An increment of 13.72 °C was observed in T r as m _ f was and m increased from 0.0041 kg/s (at 0.1 m/s) to 0.084 kg/s at (2 m/s). Fig. 6(a)–(c) shows the effect of d and v 1 on T r in 3D form. The 2D representations have been shown in Fig. 6(b) and (c). It can be seen from Table 3(a) and (f), that for d = 0.01 m and _ f = 0.084 kg/s, T r is observed to be 18.30 °C (Table 3(a)), but when m _ f ; T r changed to 8.45 °C the d was changed to 0.2 m for the same m (Table 3(f)). This shows that the T r is 9.85 °C higher for d = 0.01 m _ f . This is due to high air velocity than that of 0.1 m for the same m (2 m/s) in 0.01 m duct height, which causes fast heat transfer from PV module. The TLL has also been calculated using Eq. (33) for all the materials and the values are given in Table 4. This indicates minimum fluctuations in T r with thermal heating of room air. The value of TLL should me minimum for best load leveling and for both the systems with and without air duct, the TLL values were obtained to be in the range of 0.50–0.60. Fig. 7 shows the annual electrical and thermal energy for different thin film BIOPVT systems with and without air duct. The

Table 4 TLL for thin film BIOPVT system with and without air duct. Thin film BIOPVT systems

T rmax (°C) T rmin (°C) TLL

With air duct at air mass flow rate of 0.0421 kg/s

Without air duct

a-si

CdTe

CIGS

a-si

CdTe

CIGS

10.53 2.6 0.59

19.3 5.3 0.56

19.27 5.4 0.56

10.46 3.1 0.53

21.2 7.5 0.5

20.7 6.8 0.5

BIOPVT systems without duct have shown significant higher thermal and marginally lower electrical energies compared to those with duct and can be attributed to higher T m and lower gm of the systems without duct. Among the thin film BIOPVT systems with and without air duct, the one based on CIGS has shown the highest electrical energy whereas the one based on a-Si has shown the highest thermal energy. Fig. 8 shows the overall thermal energy of the BIOPVT systems with and without air duct. The BIOPVT systems without duct have shown the higher overall thermal energy compared to those with duct. CIGS BIOPVT systems have shown to exhibit higher thermal energy whereas those based on a-Si have shown lower thermal energy. The reason behind this is that CIGS

451

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

40

9

Energy (kWh)

8

Electrical with duct

Electrical without duct

Thermal with duct

Thermal without duct

7 6 5 4 3 2 1

Overall thermal efficiency (%)

10

35

with duct

30 25 20 15 10 5 0

0 a-Si

CdTe

a-Si

CIGS

Fig. 7. Electrical and thermal energy of different thin film BIOPVT systems with and without duct.

CIGS

Fig. 10. The overall thermal efficiency of different thin film BIOPVT systems with and without air duct.

30

15 with duct

25

Overall exergy efficiency (%)

Thermal energy (kWh)

CdTe

Thin film BIOPVT System

Thin film BIOPVT System

without duct

20 15 10 5 0 a-Si

CdTe

CIGS

without duct

Fig. 8. Overall thermal energy of different thin film BIOPVT systems with and without air duct.

10 9 without duct

with duct

8 7

with duct

12

9

6

3

0 a-Si

Thin film BIOPVT System

Overall Exergy (kWh)

without duct

CdTe

CIGS

Thin film BIOPVT System Fig. 11. The overall exergy efficiency of different thin film BIOPVT systems with and without air duct.

thermal efficiency and overall exergy efficiency for thin film BIOPVT system with and without duct. It is observed that the thin film BIOPVT systems without air duct exhibit marginally lower exergy and significant higher thermal energy efficiencies than those with duct. The CIGS BIOPVT systems have shown the highest thermal and exergy efficiencies.

6

6. Conclusions

5 4

The conclusion of the present study can be presented in the following bulletin points.

3 2 1 0 a-Si

CdTe

CIGS

Thin film BIOPVT System Fig. 9. The overall exergy of different thin film BIOPVT systems with and without air duct.

has a higher value of equivalent thermal energy whereas a-Si has lower value of the equivalent thermal energy. Fig. 9 shows the overall exergy of the thin film BIOPVT systems with duct and without air duct. The CIGS based BIOPVT systems exhibit highest overall exergy whereas those based on a-Si exhibit lowest overall exergy. Similarly Figs. 10 and 11 respectively show the overall

 For a-Si BIOPVT system the average daily gm and T r without air duct are found to be 7.25% and 18.7 °C respectively, whereas with duct gm and T r are found to be 7.57% and 15.2 °C respectively. _ f have been observed to have a significant effect on T r .  N and m _ f of 0.0427 kg/s T r for d = 0.01 m is achieved higher  For a given m than that for d = 0.2 m.  Thin film BIOPVT system without duct exhibited marginally lower electrical energy and significant higher thermal energy than those with duct.  CIGS system produces maximum electrical energy and a-Si system produces higher thermal energy hence CIGS system is suitable for electricity generation and a-Si system is suitable for space heating applications.

452

A. Gaur, G.N. Tiwari / Applied Energy 146 (2015) 442–452

 Thin film BIOPVT systems without duct exhibited marginally lower overall exergy efficiency and significant higher overall thermal efficiency compared to those with duct. CIGS have shown highest overall thermal and overall exergy efficiencies.  As a whole in terms of thermal and electricity production performance simultaneously, thin film BIOPVT systems without air duct are more suitable for cold climatic conditions as they develop higher room temperature. Compared to duct system the system without duct produces higher thermal energy at a marginal lower cost of electrical energy.

Acknowledgement One of the authors (A.G.) is thankful to Department of Science and Technology, New Delhi, India for providing INSPIRE fellowship to pursue the present research work. References [1] Agrawal B, Tiwari GN. Developments in environmental durability for photovoltaics. UK: Pira International Ltd.; 2008. [2] Dubey S, Sarviya JN, Seshadri B. Temperature dependent photovoltaic (PV) efficiency and its effect on PV production in the world a review. Energy Procedia 2013;33:311–21. [3] Tiwari GN, Dubey S. Fundamentals of photovoltaic modules and their applications. Cambridge (UK): RSC Publishers; 2010. [4] Bazilian MD, Prasad D. Modelling of a photovoltaic heat recovery system and its role in a design decision support tool for building professionals. Renew Energy 2002;27:57–68. [5] Ji J, Yi H, He W, Pei W. PV-Trombe wall design for buildings in composite climates. J Solar Energy Eng 2007;129:431. [6] Wong PW, Shimoda Y, Nonaka M, Inoue M, Mizuno M. Semi-transparent PV: thermal performance, power generation, daylight modelling and energy saving potential in a residential application. Renew Energy 2008;33:1024–36. [7] Fung TYY, Yang H. Study on thermal performance of semi-transparent building integrated photovoltaic glazings. Energy Build 2008;40:341–50. [8] de Boer BJ, van Helden WGJ. PV MOBI-PV modules optimized for building integration. In: 9th International conference on solar energy in high latitudes. Northsun, Leiden (Netherlands); 2001. [9] Li DHW, Lam TNT, Chan WWH, Mak AHL. Energy and cost analysis of semitransparent photovoltaic in office buildings. Appl Energy 2009;86(5): 722–9. [10] Varitiainen E. Daylight modelling and optimization of solar facades, doctoral dissertation. Finland: Helsinki University of Technology; 2001. [11] Infield D, Eicker U, Fux V, Mei L, Schumacher J. A simplified approach to thermal performance calculation for building integrated mechanically ventilated PV facades. Build Environ 2006;41:893–901.

[12] Khedari J, Waewsak J, Supheng W, Hirunlabh J. Experimental investigation of performance of a multi-purpose PV-slat window. Solar Energy Mater Solar Cells 2004;82:431–45. [13] Alzoubi HH. Optimizing lighting, thermal performance, and energy production of building facades by using automated blinds and PV cells. US:University of Michigan, Doctoral Dissertation, University of Michigan; 2005. [14] Yang H, Burnett J, Zhu Z. Building-integrated photovoltaics: effect on the cooling load component of building facades. Build Serv Eng Res Technol 2001;22(3):157–65. [15] Chow TT, He W, Ji J. An experimental study of facade-integrated photovoltaic/ water-heating system. Appl Therm Eng 2007;27(1):37–45. [16] Sandberg M, Moshfegh B. Buoyancy-induced air flow in photovoltaic facades – effect of geometry of the air gap and location of solar cell modules. Build Environ 2002;37:211–8. [17] Mei L, Infield D, Eicker U, Fux V. Thermal modeling of a building with an integrated ventilated PV facade. Energy Build 2003;35:605–17. [18] Ordenes M, Marinoski DL, Braun P, Rüther R. The impact of building integrated photovoltaics on the energy demand of multi-family dwellings in Brazil. Energy Build 2007;39:629–42. [19] Chow TT, Hand JW, Strachan PA. Building-integrated photovoltaic and thermal applications in a subtropical hotel building. Appl Therm Eng 2003;23(16): 2035–49. [20] Anderson TN, Duke M, Morrison GL, Carson JK. Performance of building integrated photovoltaic/ thermal (BIPVT) solar collector. Solar Energy 2009;83:445–55. [21] Gaur A, Tiwari GN. Performance of a-Si thin film PV modules with and without water flow: an experimental validation. Appl Energy 2014;128:184–91. [22] Vats K, Tiwari GN. Performance evaluation of a building integrated semitransparent photovoltaic thermal system for roof and façade. Energy Build 2012;45:211–8. [23] Vats K, Tiwari GN. Energy and exergy analysis of building integrated semitransparent photovoltaic thermal (BISPVT) system. Appl Energy 2012; 96:409–16. [24] Vats K, Tomar V, Tiwari GN. Effect of packing factor on the performance of building integrated semitransparent photovoltaic thermal (BISPVT) system with air duct. Energy Build 2012;53:159–65. [25] Tiwari GN. Solar energy: fundamentals, design, modeling and applications. Narosa Publishing House; 2004. [26] Skoplaki E, Palyvos JA. On the temperature dependence of photovoltaic module electrical performance: a review of efficiency/power correlation. Solar Energy 2009;83:614–24. [27] Evans DL. Simplified method for predicting PV array output. Sol Energy 1981; 27:555–60. [28] Huang BJ, Lin TH, Hung WC, Sun FS. Performance evaluation of solar photovoltaic/thermal systems. Solar Energy 2001;70(5):443–8. [29] Agrawal B, Tiwari GN. Optimizing the energy and exergy of building integrated photovoltaic thermal (BIPVT) systems under cold climatic conditions. Appl Energy 2010;87:417–26. [30] Fujisawa T, Tani T. Annual exergy evaluation on photovoltaic–thermal hybrid collector. Solar Energy Mater Solar Cells 1997;47:135–48. [31] Mishra RK, Tiwari GN, Solanki SC. Photovoltaic modules and their applications: a review on thermal modelling. Appl Energy 2011;88:2287–304. [32] Liu BYH, Jordan RC. The interrelationship and characteristics distribution of direct and diffuse and total solar radiation. Sol Energy 1960;4(1):1–19. [33] Jordan DC, Kurtz SR. NREL/JA-5200-51664 June 2012.