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T hybrid air collector
Applied Energy 86 (2009) 697–705
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Analytical expression for electrical efficiency of PV/T hybrid air collector Swapnil Dubey *, G.S. Sandhu, G.N. Tiwari Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India
a r t i c l e
i n f o
Article history: Received 22 May 2008 Received in revised form 26 July 2008 Accepted 5 September 2008 Available online 18 October 2008 Keywords: Photovoltaic Electrical efficiency Solar radiation Thermal energy
a b s t r a c t The overall electrical efficiency of the photovoltaic (PV) module can be increased by reducing the temperature of the PV module by withdrawing the thermal energy associated with the PV module. In this communication an attempt has been made to develop analytical expression for electrical efficiency of PV module with and without flow as a function of climatic and design parameters. The four different configurations of PV modules are considered for the present study which are defined as; case A (Glass to glass PV module with duct), case B (Glass to glass PV module without duct), case C (Glass to tedlar PV module with duct), case D (Glass to tedlar PV module without duct). Further, experiments were carried out for all configurations under composite climate of New Delhi. It is found that the glass to glass PV modules with duct gives higher electrical efficiency as well as the higher outlet air temperature amongst the all four cases. The annual effect on electrical efficiency of glass to glass type PV module with and without duct is also evaluated. The annual average efficiency of glass to glass type PV module with and without duct is 10.41% and 9.75%, respectively. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Photovoltaic (PV) directly convert solar radiation into electricity with peak efficiency in the range of 9–12%, depending on specific solar cell type. More than 80% of the solar radiation falling on photovoltaic (PV) cells is not converted to electricity, but either reflected or converted to thermal energy. This leads to an increase in the PV cell’s working temperature and consequently, a drop of electricity conversion efficiency. In view of this, hybrid photovoltaic and thermal (PV/T) systems are introduced to simultaneously generate electricity and thermal power. In PV/T system applications the production of electricity is the main priority, therefore it is necessary to operate the PV modules at low temperature, the carrier of thermal energy associated with the PV module may be either air or water. Kern and Russel [1] present the design and performance of water and air cooled PV/T systems, while Hendrie [2] and Florschuetz [3] include PV/T modelling in their works. Numerical methods predicting PV/T system performance are developed by Raghuraman [4], computer simulations are studied by Cox and Raghuraman [5], a low cost PV/T system with transparent type a-Si cells is proposed by Lalovic et al. [6] and results from an applied air type PV/T system are given by Loferski et al. [7]. Garg and Adhikari [8] present a variety of results regarding the effect of design and operational parameters on the performance of air type PV/T systems.
* Corresponding author. Tel.: +91 9868929291. E-mail address: [email protected] (S. Dubey). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.09.003
Hagazy [9] and Sopian et al. [10] investigated glazed photovoltaic/thermal air system for a single and a double pass air heater for space heating and the drying purposes. Kalogirou [11] has carried out monthly performance of an unglazed hybrid PV/T system under forced mode of operation for climatic condition of the Cyprus. He observed an increase of the mean annual efficiency of the PV solar system from 2.8% to 7.7% with thermal efficiency of 49%. Lee et al. [12] and Chow et al. [13] give interesting modelling results on air cooled PV modules. Jones and Underwood [14] have studied the temperature profile of the photovoltaic (PV) module in a non-steady state condition with respect to time. They conducted experiment for cloudy as well clear day condition. They observed that the PV module temperature varies in the range of 300–325 K (27–52 °C) for an ambient air temperature of 297.5 K (24.5 °C). The main reasons for reduction of the electrical efficiency of the PV module is packing factor (PF) of PV module, ohmic losses between two consecutive solar cells and the temperature of the module. The overall electrical efficiency of the PV module can be increased by increasing the packing factor (PF) and reducing the temperature of the PV module by withdrawing the thermal energy associated with the PV module, [15,16]. Packing factor is the ratio of total area of solar cells to the area of PV module. To increase the efficiency of PV a sun-tracking design is presented by Mohamad [17], the movement of a photovoltaic module was controlled to follow the Sun’s radiation using a programmable logiccontroller (PLC) unit. He has found that the daily output power of the PV was increased by more than 20% in comparison with that of a fixed module. Based on the I–V curves of a photovoltaic (PV) module, a novel and simple model is proposed to predict the PV
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Nomenclature b L C h hp1, hp2 I(t) IL Isc K _ m T Utc,a UTc,f Ub UL VL Voc
width of PV module (m) length of PV module (m) specific heat (J/kg °C) heat transfer coefficient (W/m2 °C) penalty factor due to the glass cover of PV module (dimensionless) incident solar intensity (W/m2) load current (A) short circuit current (A) thermal conductivity (W/m K) rate of flow of air (kg/s) temperature (°C) an overall heat transfer coefficient from solar cell to ambient through glass cover (W/m2 °C) an overall heat transfer coefficient from solar cell to flowing air through glass cover/tedlar (W/m2 °C) an overall back loss coefficient from flowing air/plate to ambient (W/m2 °C) an overall heat transfer coefficient for glass to glass and glass to tedlar modules (W/m2 °C) load voltage (V) open circuit voltage (V)
module performance for engineering applications. PV module performance is mainly depends upon solar-irradiance intensity and PV module temperature [18]. Tiwari et al. [19] have validated the theoretical and experimental results for photovoltaic (PV) module integrated with air duct for composite climate of India and concluded that an overall thermal efficiency of PV/T system is significantly increased due to utilization of thermal energy from PV module. Tripanagnostopoulos [20] presented a new type of PV/T collector with dual heat extraction operation with aspects and improvements of hybrid PV/T solar energy systems. Design of PV integrated solar-collector for natural circulation of water is presented by He et al. [21]. The methodology for the analytical treatment of the reliability of PV systems is proposed by Hamdy et al. [22]. The method depends upon the logic of the fault-tree technique. The reliabilities of the different components of a PV system are used to predict the reliability of the overall system. The performance analysis of a photovoltaic heat pump is presented by Jie et al. [23], in this system the PV/T collector is coupled with a solar assisted heat pump and works as an evaporator and found that the photovoltaic solar assisted heat pump (PV-SAHP) has better coefficient of performance (COP) and photovoltaic efficiency than the separate units. The COP of the PV-SAHP reached 8.4 and the average value was around 6.5, whereas the average photovoltaic efficiency was around 13.4%. Muntasser et al. [24] describes the Photovoltaic marketing in developing countries and examine marketing opportunities for PV technologies in less-developed countries, which were previously dominated by the industrialized countries and concludes by making a global policy package proposal, in terms of an appeal on the global community concerned with PV to propagate this proposal more convincingly, perhaps to emanate from an internationally recognized ‘‘forum”, like a PV conference and exhibition, with cooperation and participation of PV manufacturers, suppliers, industrialized countries, NGOs, financial institutions and developing countries. Recently, Zondag [25] carried out rigorous review on research work of a PV–thermal collector and system, carried out by various scientists till 2006. His review includes the history and importance of photovoltaic hybrid system and its application in various sectors. It also includes characteristics equations, study of design parameters, and marketing, etc.
V, v
go g
air velocity (m/s) efficiency at standard test condition (I(t) = 1000 W/m2 and Ta = 25 °C) (dimensionless) temperature dependent efficiency (dimensionless)
Subscripts a ambient c solar cell eff effective f fluid (air) inlet fluid fi outgoing fluid fo g glass p blackened plate T tedlar Greek symbols absorptivity product of effective absorptivity and transmittivity b packing factor s transmitivity
a (as)eff
In this paper, two types of PV module, glass to glass and glass to tedlar, with and without duct are considered for the study. The solar intensity based analytical expression of electrical efficiency of PV modules are derived and performance are evaluated by considering four types of weather condition of New Delhi, which are defined as: Type a: The ratio of daily diffuse to daily global radiation is less than or equal to 0.25 and sunshine hours greater then or equal to 9 h. Type b: The ratio of daily diffuse to daily global radiation between 0.25 and 0.50 and sunshine hours between 7 and 9 h. Type c: The ratio of daily diffuse to daily global radiation between 0.50 and 0.75 and sunshine hours between 5 and 7 h. Type d: The ratio of daily diffuse to daily global radiation is greater than or equal to 0.75 and sunshine hours less then or equal to 5 h. Data of solar radiations for different climates are obtained from Indian Metrological Department (IMD), Pune. The both type of PV module is manufactured by Central Electronics Ltd. (CEL), Sahibabad, Ghaziabad (UP).
2. Thermal analysis of PV modules Two types of PV module, glass to glass and glass to tedlar with and without duct are considered for the present study. PV modules are tilted at 30°, equal to the latitude of New Delhi. The cut sectional views of PV modules with duct are shown in Fig. 1. Wooden duct is embedded below the PV modules for air circulation having a cross section of 0.605 m 1.0 m 0.04 m. In case of with flow/ duct air is flowing in forced mode with the help of a DC fan of 12 V, which is run by PV module. In order to write the energy balance equation of photovoltaic modules, the following assumptions have been made: One dimensional heat conduction is good approximation for the present study. The glass cover is at uniform temperature. There is stream line flow of air through the duct.
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g ¼ go 1 bo T c T a
ð1cÞ
(ii) For blackened absorber plate:
h
i
ap ð1 bc Þs2g IðtÞ b dx ¼ hp;f ðT p T f Þ þ U bp;a ðT p T a Þ b dx
ð2aÞ
2
3 2 3 The rate of solarenergy The rate of heat 6 available on blackened 7 6 transferfrom 7 6 7 6 7 6 7¼6 7 4 surfacefrom non packing 5 4 blackened plate 5 area of PV module to flowing fluid 2 3 An overall heat þ 4 loss from plate 5 to ambient From Eq. (2a), the expression for plate temperature is
Tp ¼
ap ð1 bc Þs2g IðtÞ þ hp;f T f þ U bp;a T a U bp;a þ hp;f
ð2bÞ
(iii) For air flowing through the duct: The energy balance of flowing air through absorber pipe is given by
dT f dx ¼ hp;f ðT p T f Þ þ U Tc;f ðT c T f Þ b dx dx 2 3 2 3 The rate ofheat The mass flow 6 transfer from 7 4 rate offlowing 5 ¼ 6 7 4 blackened plate to 5 fluid flowing fluid 2 3 An overall heat 4 þ transfer from cell 5 to flowing fluid _ aCa m
Fig. 1. (a) Cut sectional view of glass to glass PV module with duct. (b) Cut sectional view of glass to tedlar PV module with duct.
The system is in quasi-steady state. The ohmic losses in the solar cell are negligible. The energy balance equations for glass to glass and glass to tedlar PV modules are as follows. 2.1. Case A: glass to glass PV module with duct (Fig. 1a) (i) For solar cells of PV module: Following Dubey and Tiwari [26], the energy balance equation for solar cell of PV module can be written as
ð1aÞ
3 2 3 An overall heat The rate of heat 6 lossfrom top 7 6 7 6 7 6 7 4 energy available 5 ¼ 6 7 þ 4 transfer from cell 5 4 surface of cell 5 on solar cell to flowing fluid to ambient 2 3 The rate of 6 7 þ 4 electrical energy 5 2
The rate of solar
The solution of Eq. (3) with the help of Eqs. (1b) and (2b) and initial conditions namely, at T f jx¼0 , Tf = Tfi1 and at T f jx¼L , Tf = Tfo1, we get,
T fo ¼
ac sg bc IðtÞb dx ¼ U tc;a ðT c T a Þ þ U Tc;f ðT c T f Þ b dx þ sg gac bc IðtÞb dx 3
2
ðasÞGG;eff IðtÞ bU L;GG L þ T a 1 exp _ aCa m U L;GG bU L;GG L þ T fi exp _ aCa m
Z 1 L T f dx L 0
3 2 bU L 1 exp m_L;GG ðasÞGG;eff IðtÞ a Ca 5 þ T fi ¼ þ T a 41 bU L;GG L U L;GG _ a Ca m
bU L 1 exp m_L;GG a Ca bU L
Tf ¼
L;GG
From Eq. (1a), the expression for cell temperature is
ð1bÞ
U tc;a þ U bc;f
An expression for temperature dependent electrical efficiency of a PV module Schott [27] and Evans [28] is given by
g¼
n
If Tfi = Ta and T f ¼ T f , then from Eqs. (1b), (1c), and (4b), the expression for temperature dependent electrical efficiency can be obtained as L . where X o ¼ bUm_LGG a Ca
bo Tc;f oÞ go 1 Utc;asgþU ac bc þ UUL;GG hp1 ac bc þ hp2 ap ð1 bc Þsg 1 1expðX Xo Tc;f
1
go bo sg bc ac IðtÞ U tc;a þU Tc;f
ð4bÞ
_ a Ca m
sg ac bc ð1 gÞIðtÞ þ U tc;a T a þ U Tc;f T f
h
ð4aÞ
The average air temperature over the length of air duct below PV module is obtained as
produced
Tc ¼
ð3Þ
U hp1 oÞ 1 þ UTc;f 1 1expðX Xo L;GG
o
i IðtÞ ð5Þ
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U T ðT c T bs Þb dx ¼ hT ðT bs T f Þb dx
2.2. Case B: glass to glass PV module without duct (i) For solar cells of PV module: Following Dubey and Tiwari [26], the energy balance equation for solar cell of PV module can be written as
sg ac bc þ sg ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U b ðT c T a Þ b dx ð6aÞ þ sg gac bc IðtÞb dx 2
2
3
An overall heat
Tc ¼
An overall heat The rate of heat transfer 4 transfer from cell to 5 ¼ 4 from back surface of the 5 back surface of tedlar tedlar to flowing fluid Using Eqs. (8b) and (9a), the expression for back surface temperature of PV module can be obtained as
g¼
go 1 1
bo ðasÞGG;eff IðtÞ U tc;a þU b
ð6bÞ
i ð7Þ
bo go sg ac bc IðtÞ U tc;a þU b
ð9bÞ
ð10Þ
The solution of Eq. (11a) with the help of Eqs. (9b) and (10) and initial conditions namely, at T f jx¼0 , Tf = Tfi1 and at T f jx¼L , Tf = Tfo1, we get,
T fo ¼
From Eqs. (1c) and (6b), the expression for the efficiency of glass to glass PV module can be obtained as
h
hp1 sg ½ac bc þ aT ð1 bc Þ ac gbc IðtÞ þ U tT T a þ hT T f U tT þ hT
dT f dx þ U b ðT f T a Þb dx ¼ hT ðT bs T f Þb dx dx 2 3 2 3 The mass flow An overall heat transfer 4 rate offlowing 5 þ 4 from flowing fluid to 5 fluid ambient 2 3 The rate of heat transfer ¼ 4 from back surface of the 5 tedlar to flowing fluid
i
U tc;a þ U b
3
_ aCa m
produced
ðasÞGG;eff sg gac bc IðtÞ þ U tc;a T a þ U b T a
ð9aÞ
2
(iii) For the air flowing below the tedlar:
From Eq. (6a), the expression for cell temperature is
h
3
T bs ¼
3
The rate of solar 7 6 6 7 6 lossfrom top 7 7 4 energy available 5 ¼ 6 7 6 4 surface of cell 5 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 þ 4 loss from back side 5 þ 4 electrical energy 5 of the cell
2
hp1 hp2 ðasÞGT;eff IðtÞ þ Ta U L;GT bU L;GT L þ T fi exp _ aCa m
bU L;GT L 1 exp _ aCa m
ð11aÞ
The average air temperature over the length of air duct below PV module is obtained as
3 2 bU L
Tf ¼
2.3. Case C: glass to tedlar PV module with duct (Fig. 1b)
1 exp m_L;GT hp1 hp2 ðasÞGT;eff IðtÞ a Ca 5 þ T a 41 bU L;GT L U L;GT 0 _ a Ca m
bU L 1 exp m_L;GT a Ca ð11bÞ þ T fi bU L 1 L
Z
L
T f dx ¼
L;GT
(i) For solar cells of PV module: Following Tiwari and Sodha [29], the energy balance equation for solar cell of PV module can be written as
go 1 g¼
3
back surface of tedlar
ð12Þ
L . where X o ¼ bUm_LGG a Ca
2.4. Case D: glass to tedlar PV module without duct
3
2
An overall heat 7 6 6 lossfrom top 7 6 7 7 6 energy available 7 ¼ 6 7 4 5 6 6 surface of cell 7 5 4 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 7 6 7 þ6 4 transfer from cell to 5 þ 4 electrical energy 5 The rate of solar
(i) For solar cells of PV module: Following Tiwari and Sodha [29], the energy balance equation for solar cell of PV module can be written as
sg ½ac bc þ aT ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U b ðT c T a Þb dx ð13aÞ þ sg gac bc IðtÞb dx 2
produced
From Eq. (8a), the expression for cell temperature is
Tc ¼
If Tfi = Ta and T f ¼ T f , then from Eqs. (1c), (8b), (9b), and (11b), the expression for temperature dependent electrical efficiency can be obtained as
bo sg ½ac bc þ aT ð1 bc ÞIðtÞ U T hp1 U T hT hp1 hp2 1 expðX o Þ 1þ þ 1 U tc;a þ U T Xo hT þ U tT ðhT þ U tT ÞU L;GT bo go sg ac bc IðtÞ U T hp1 U T hT hp1 hp2 1 expðX o Þ 1 1þ þ 1 U tc;a þ U T Xo hT þ U tT ðhT þ U tT ÞU L;GT
sg ½ac bc þ aT ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U T ðT c T bs Þb dx ð8aÞ þ sg gac bc IðtÞb dx 2
_ a Ca m
sg ½ac bc þ aT ð1 bc Þ ac gbc IðtÞ þ U tc;a T a þ U T T bs U tc;a þ U T
(ii) For the back surface of the tedlar:
ð8bÞ
The rate of solar
3
2
An overall heat
3
7 6 6 7 6 loss from top 7 7 4 energy available 5 ¼ 6 4 surface of cell 5 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 þ 4 loss from back side 5 þ 4 electrical energy 5 of the cell produced
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
From Eq. (13a), the expression for cell temperature is
h Tc ¼
ðasÞGT;eff
i sg gac bc IðtÞ þ U tc;a T a þ U b T a U tc;a þ U b
2.6. Correlation coefficient and root mean square percent deviation
ð13bÞ
From Eqs. (1c) and (13b), the expression for the efficiency of glass to glass PV module can be obtained as
h
g¼
ÞGT;eff IðtÞ go 1 bo ðaUstc;a þU b
1
i ð14Þ
bo go sg ac bc IðtÞ U tc;a þU b
In addition to the above equations the relations used for defining the design parameters (Table 1) and different configuration of glass to glass and glass to tedlar PV modules with and without duct are given in Appendix.
To compare the theoretical and experimental results the correlation coefficient (r) and root mean square percent deviation (e) have been evaluated by using the following expressions:
P P P N X i Y i ð X i Þð Y i Þ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ffi r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P P P N X 2i ð X i Þ2 N Y 2i ð Y i Þ2
ð16aÞ
And
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ðei Þ e¼ N
ð16bÞ
where
Xi Y i 100 Xi
ei ¼
gexp
0:8 V oc Isc IL V L ¼ Am IðtÞ
ð15Þ
where 0.8 is the fill factor or power factor, it measure of sharpness of the knee in I–V curve. It indicates how well a junction was made in the cell and how low the series resistance has been made. It can be lowered by the presence of series resistance and tends to be higher whenever the open circuit voltage is high.
2 Solar intensity, W/m
Experimental efficiency of PV module can be calculated as
900
40
800
35
700
30
600
25
500
20
400
15
300
I(t)
200
10
Ta
5
100 0
Ambient temperature,˚C
2.5. Electrical efficiency of PV module
0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
go sg
0.605 m 7.6 W/m2 K 1.0 m 0.0058 kg/s 1005 J/kg K 7.44 W/m2 K 0.9 0.8 0.5 0.83 0.0045 0.12 0.95
Glass to glass with duct hp1 hp2 Kg Lg UTc,f UL,GG Ubp,a
0.536 0.934 1.1 W/m K 0.003 m 8.59 W/m2 K 4.56 W/m2 K 0.62 W/m2 K
ac ap aT bc bo
Glass to glass without duct Ub
2
3.36 W/m K
Glass to tedlar with duct hp1 hp2 KT LT UT UtT UL,GT Ubf,a
0.898 0.54 0.033 W/m K 0.0005 m 66 W/m2 K 6.68 W/m2 K 4.42 W/m2 K 0.62 W/m2 K
Glass to glass without duct Ub
3.23 W/m2 K
Glass to glass withduct
Glass to tedlar withduct
Glass to glass without duct
Glass to tedlar without duct
12.0 11.0 10.0 9.0 8.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 3. Hourly variation of electrical efficiency considering with and without duct.
Efficiency (Glass to glass)
Efficiency (Glass to tedlar)
Cell temp. (Glass to glass)
Cell temp. (Glass to tedlar)
12.0
90.0
11.5
80.0
11.0
70.0
10.5 60.0
10.0
50.0
9.5
40.0
9.0 8.5
Cell temperature,˚C
Values
b ho L _a m Ca Utc,a
Eletrical efficiency, %
Parameters
Fig. 2. Hourly variation of solar intensity and ambient temperature for the month of April, 2008.
Electrical Efficiency, %
Table 1 Design parameters of glass to glass and glass to tedlar, with and without duct of PV modules
30.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 4. Hourly variation of electrical efficiency and cell temperature considering with duct.
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
b
With Duct (Glass to Glass) 12.0
e= 3.92 r = 0.838
Theoretical Experimental
12.0
11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
Without Duct (Glass to Glass)
Electrical Efficiency, %
Electrical Efficiency, %
a
Theoretical
e= 4.19 r = 0.827
Experimental 11.0 10.0 9.0 8.0
16:00
09:00
10:00
11:00
d
With Duct (Glass to Tedlar) 12.0
Theoretical
Electrical Efficiency, %
Electrical Efficiency, %
c
e= 3.41 r= 0.806
Experimental 11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
Time (Hours)
14:00
15:00
Without Duct (Glass to Tedlar) 12.0
e= 3.87 r= 0.849
Theoretical Experimental
11.0 10.0 9.0 8.0 09:00
16:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
Time (Hours)
Fig. 5. (a) Hourly variation of electrical efficiency considering with duct. (b) Hourly variation of electrical efficiency considering without duct. (c) Hourly variation of electrical efficiency considering with duct. (d) Hourly variation of electrical efficiency considering without duct.
decrease in efficiency of module. In case B and D (modules without duct) efficiency is nearly same. Hourly variation of electrical
V = 0.5 m/s (GG)
V = 0.5 m/s (GT)
V = 1 m/s (GG)
V= 1 m/s (GT)
V= 2 m/s (GG)
V= 2 m/s (GG)
a type b type
a
75 70 65 60 55 50 45 40 35
c type d type
12.0
11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
b Daily avg. electrical efficiency, %
Avg. air temperature,˚C
The variation of solar intensity and ambient temperature for a typical day in the month of April 2008 for New Delhi condition is shown in Fig. 2. The values of various parameters (design parameters) of PV modules are given in Table 1. In this paper, the results of the four cases, case A (Glass to glass PV module with duct), case B (Glass to glass PV module without duct), case C (Glass to tedlar PV module with duct), case D (Glass to tedlar PV module without duct) are discussed in details. Experimental electrical efficiency of PV module for all the four cases are evaluated by using Eq. (15) and the variations are shown in Fig. 3. Glass to glass type PV module with duct gives higher efficiency than the glass to tedlar type PV module. This is due to the radiation falling on non-packing area of glass to glass module is transmitted through the glass cover, however, in case of glass to tedlar all the radiation is absorbed by the tedlar and then heat is carried away by the conduction. So that the temperature of the solar cell is higher in case of glass to tedlar type PV module, result in
Electrical Efficiency, %
3. Result and discussion
12.0 11.17 11.0
10.0
10.65
9.73
9.86
9.0 Type a
Type b
Type c
Type d
Weather conditions 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 6. Hourly variation of average air temperature over the length of duct by varying the mass flow rate; glass to glass (GG) and glass to tedlar (GT).
Fig. 7. (a) Hourly variation of electrical efficiency for a, b, c, d type weather conditions considering glass to glass PV module with duct. (b) Daily average of electrical efficiency for a, b, c, d type weather conditions considering glass to glass PV module with duct.
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
a Monthly avg. electrical efficiency, %
11.0
Annual Avg. = 10.41 %
10.5
10.0
9.5
9.0 JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Month of year
b Monthly avg. electrical efficiency, %
10.5
Annual Avg. = 9.75 % 10.0
9.5
9.0
8.5
8.0 JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Month of year Fig. 8. (a) Monthly average of electrical efficiency considering a, b, c, d type weather conditions for glass to glass PV module with duct. (b) Monthly average of electrical efficiency considering a, b, c, d type weather conditions for glass to glass PV module without duct.
efficiency and cell temperature for case A and case B with duct are shown in Fig. 4. Figure shows that as the temperature increases efficiency decreases and as the temperature decreases efficiency increases, as expected. This result is in accordance with the results reported by earlier researchers, Zondag et al. [15] and Chow [16]. Eqs. (5) and (6) has been used for calculating the theoretical efficiency of glass to glass type PV module with and without duct. Experimental results are validated with the theoretical results and the variations are shown in Fig. 5a and b. Similarly, Eqs. (12) and (14) has been used for calculating the theoretical efficiency of glass to tedlar type PV module with and without duct. The variations between experimental and theoretical results are shown in Fig. 5c and d. The correlation coefficient (r) and root mean square percent deviation (e) is also evaluated using Eqs. (16a) and (16b), respectively which are shown in the same figure. It is observed that there is a fair agreement between theoretical and experimental values of all the four cases. The correlation coefficient (r) and root mean square percent deviation (e) is varies from 4.19 to 3.41 and 0.849 to 0.806, respectively. Eqs. (4b) and (11b) has been used for evaluating the average air temperature over the length of air duct by varying the mass flow rate for case A and case C. It is observed that the average air temperature is higher in case of A than case C, due to the solar radiation is transmitted through the glass cover (non-packing area) and absorbed by the blackened plate (below the module). In this case the heat is convected to the flowing air by two ways from back
surface of PV module as well as from top surface of the blackened plate. The variation is shown in Fig. 6. Hourly variation of electrical efficiency of glass to glass type PV module with duct for a, b, c, and d type weather conditions is shown in Fig. 7a. Figure shows that as the solar intensity decreases (from a type to d type) the temperature of solar cell is also decreases and efficiency increases. The same results are also obtained for daily average efficiency of a, b, c, and d type weather conditions which is shown in Fig. 7b. Monthly average electrical efficiency by considering a, b, c, d type weather conditions of New Delhi for glass to glass type PV module with and without duct are calculated and the variation is shown in Fig. 8a and b. The annual average efficiency of PV module with and without duct is 10.41% and 9.75%, respectively. The monthly average efficiency is calculated by multiplying the number of days belongs to each type of weather condition of that month and taking the average of all days of that month. And then the average of 12 months gives the annual average efficiency of PV module.
4. Conclusion 1. In this paper, four different configurations of two types of PV modules, glass to glass and glass to tedlar are studied. 2. The percentage difference between electrical efficiency (Dg) of glass to glass and glass to tedlar type PV modules with and without duct are 0.24% and 0.086%, respectively.
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3. The percentage difference between electrical efficiency (Dg) of glass to glass type PV modules with and without duct is 0.66%. 4. This 0.66% difference of electrical efficiency could be very large if it is used in large PV plants and simultaneously fulfilling the requirement of electricity generation and thermal heating with better efficiency.
Appendix A
(iv) Glass to tedlar PV module without duct:
ðasÞGT;eff ¼ sg ½ac bc þ aT ð1 bc Þ U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 LT 1 þ Ub ¼ K T hi hi ¼ 2:8 þ 3v;
v ¼ 0:2 m=s
In modelling equations, we used following relations for defining the design parameters, which are shown in Table 1. (i) Glass to glass PV module with duct:
The values of ac, aT, bc, go, ap and sg are taken from Duffie and Beckman [30], Tiwari [31] and Tiwari and Sodha [32].
ðasÞGG;eff ¼ hp1 ðasÞ1;eff þ hp2 ðasÞ2;eff
References
Here, ðasÞ1;eff ¼ sg ac bc ð1 gÞ and ðasÞ2;eff ¼ ap ð1 bc Þs2g . hp1 and hp2 is the penalty factors due to glass cover of PV module, which are defined as
hp;f U Tc;f and hp2 ¼ U tc;a þ U Tc;f U p;a þ hp;f 1 Lg 1 ¼ þ K g ho
hp1 ¼ U tc;a
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 Lg 1 þ U Tc;f ¼ K g hi hp;f ¼ hi ¼ 2:8 þ 3v; U Tc;f U tc;a U tT ¼ U Tc;f þ U tc;a U bp;a hp;f UT ¼ U bp;a þ hp;f
v ¼ 2 m=s
U L;GG ¼ U tT þ U T (ii) Glass to glass PV module without duct:
ðasÞGG;eff ¼ sg ac bc þ sg ð1 bc Þ U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 Lg 1 þ Ub ¼ K g hi hi ¼ 2:8 þ 3v;
v ¼ 0:2 m=s
(iii) Glass to tedlar PV module with duct:
ðasÞGT;eff ¼ sg ½ac bc þ aT ð1 bc Þ ac gbc hp1 and hp2 is the penalty factors due to glass cover and tedlar of T and hp2 ¼ Utc;ahTþhT PV module, which are defined as, hp1 ¼ Utc;aUþU T
U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; 1 LT UT ¼ KT
V ¼ 0:5 m=s
hT ¼ 2:8 þ 3v; v ¼ 2 m=s U tc;a U T U tT ¼ U tc;a þ U T U tT hT U t;f ¼ U tT þ hT U L;GT ¼ U t;f þ U bf;a
[1] Kern Jr. EC, Russell MC. Combined photovoltaic and thermal hybrid collector systems. In: Proceedings of the 13th IEEE photovoltaic specialists, Washington, DC, USA, 1978. p. 1153–7. [2] Hendrie SD. Evaluation of combined photovoltaic/thermal collectors. In: Proceedings of international conference ISES, Atlanta, Georgia, USA, May 28– June 1, vol. 3. 1979. p. 1865–9. [3] Florschuetz LW. Extention of the Hottel–Whillier model to the analysis of combined photovoltaic/thermal flat plate collectors. Sol Energy 1979;22:361–6. [4] Raghuraman P. Analytical predictions of liquid and air photovoltaic/thermal, flat-plate collector performance. J Sol Energy Eng 1981;103:291–8. [5] Cox III CH, Raghuraman P. Design considerations for flat-plate photovoltaic/ thermal collectors. Sol Energy 1985;35:227–41. [6] Lalovic B. A hybrid amorphous silicon photovoltaic and thermal solar collector. Solar Cells 1986/1987;19:131–8. [7] Loferski JJ, Ahmad JM, Pandey A. Performance of photovoltaic cells incorporated into unique hybrid photovoltaic/thermal panels of a 2.8 kW residential solar energy conversion system. In: Proceedings of 1988 annual meeting, American Solar Energy Society, Cambridge, Massachusetts, USA, 1988. p. 427–32. [8] Garg HP, Adhikari RS. Conventional hybrid photovoltaic/thermal (PV/T) air heating collectors: steady-state simulation. Renew Energy 1997;11:363–85. [9] Hegazy AA. Comparative study of the performances of four photovoltaic/ thermal solar air collectors. Energy Convers Manage 2000;41:861–81. [10] Sopian K, Liu HT, Kakac S, Veziroglu TN. Performance of a double pass photovoltaic thermal solar collector suitable for solar drying systems. Energy Convers Manage 2000;41(4):353–65. [11] Kalogirou SA. Use of TRYNSYS for modelling and simulation of a hybrid PV thermal solar system for Cyprus. Renew Energy 2001;23:247–60. [12] Lee WM, Infield DG, Gottschalg R. Thermal modelling of building integrated PV systems In: Proceedings of 17th PV solar energy conference. Munich, 22–26 October, 2001. p. 2754–7. [13] Chow TT, Hand JW, Strachan PA. Building-integrated photovoltaic and thermal applications in a subtropical hotel building. Appl Therm Eng 2003;23:2035–49. [14] Jones AD, Underwood CP. A thermal model for photovoltaic systems. Sol Energy 2001;70(4):349–59. [15] Zondag HA, de Vries DW, van Helden WGJ, van Zolengen RJC, Steenhoven AA. The yield of different combined PV–thermal collector designs. Sol Energy 2003;74(3):253–69. [16] Chow TT. Performance analysis of photovoltaic–thermal collector by explicit dynamic model. Sol Energy 2003;75:143–52. [17] Al-Mohamad A. Efficiency improvements of photo-voltaic panels using a suntracking system. Appl Energy 2004;79:345–54. [18] Zhou W, Yang H, Fang Z. A novel model for photovoltaic array performance prediction. Appl Energy 2007;84:1187–98. [19] Tiwari A, Sodha MS, Chandra A, Joshi JC. Performance evaluation of photovoltaic thermal solar air collector for composite climate of India. Sol Energy Mater Sol Cells 2006;90(2):175–89. [20] Tripanagnostopoulos Y. Aspects and improvements of hybrid photovoltaic/ thermal solar energy systems. Sol energy 2007;81:1117–31. [21] He W, Chow TT, Ji J, Lu J, Pei G, Chan L. Hybrid photovoltaic and thermal solarcollector designed for natural circulation of water. Appl Energy 2006;83:199–210. [22] Hamdy MA, Beshir ME, Elmasry SE. Reliability Analysis of Photovoltaic Systems. Appl Energy 1989;33:253–63. [23] Ji J, Chow TT, Pei G, He W, He H. Performance analysis of a photovoltaic heat pump. Appl Energy 2008;85:680–93. [24] Muntasser MA, Bara MF, Quadri HA, EL-Tarabelsi R, La-azebi IF. Photovoltaic marketing in developing countries. Appl Energy 2000;65:67–72. [25] Zondag HA. Flat-plate PV–thermal collectors and systems: a review. Renew Sustain Energy Rev 2008;12(4):891–959. [26] Dubey S, Tiwari GN. Thermal modelling of a combined system of photovoltaic thermal (PV/T) solar water heater. Sol Energy 2008;82:602–12.
S. Dubey et al. / Applied Energy 86 (2009) 697–705 [27] Schott T. Operational temperatures of PV modules. In: Proceedings of 6th PV solar energy conference, 1985. p. 392–6. [28] Evans DL. Simplified method for predicting PV array output. Sol Energy 1981;27:555–60. [29] Tiwari A, Sodha MS. Parametric study of various configurations of hybrid PV/ thermal air collector: experimental validation of theoretical model. Sol Energy Mater Sol Cells 2007;91:17–28.
705
[30] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley & Sons; 1991. [31] Tiwari GN. Solar energy fundamentals, design, modelling and applications. New Delhi: Narosa Publishing House; 2004. [32] Tiwari A, Sodha MS. Performance evaluation of solar PV/T system: an experimental validation. Sol Energy 2006;80(7):751–9.
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Analytical expression for electrical efficiency of PV/T hybrid air collector Swapnil Dubey *, G.S. Sandhu, G.N. Tiwari Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India
a r t i c l e
i n f o
Article history: Received 22 May 2008 Received in revised form 26 July 2008 Accepted 5 September 2008 Available online 18 October 2008 Keywords: Photovoltaic Electrical efficiency Solar radiation Thermal energy
a b s t r a c t The overall electrical efficiency of the photovoltaic (PV) module can be increased by reducing the temperature of the PV module by withdrawing the thermal energy associated with the PV module. In this communication an attempt has been made to develop analytical expression for electrical efficiency of PV module with and without flow as a function of climatic and design parameters. The four different configurations of PV modules are considered for the present study which are defined as; case A (Glass to glass PV module with duct), case B (Glass to glass PV module without duct), case C (Glass to tedlar PV module with duct), case D (Glass to tedlar PV module without duct). Further, experiments were carried out for all configurations under composite climate of New Delhi. It is found that the glass to glass PV modules with duct gives higher electrical efficiency as well as the higher outlet air temperature amongst the all four cases. The annual effect on electrical efficiency of glass to glass type PV module with and without duct is also evaluated. The annual average efficiency of glass to glass type PV module with and without duct is 10.41% and 9.75%, respectively. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Photovoltaic (PV) directly convert solar radiation into electricity with peak efficiency in the range of 9–12%, depending on specific solar cell type. More than 80% of the solar radiation falling on photovoltaic (PV) cells is not converted to electricity, but either reflected or converted to thermal energy. This leads to an increase in the PV cell’s working temperature and consequently, a drop of electricity conversion efficiency. In view of this, hybrid photovoltaic and thermal (PV/T) systems are introduced to simultaneously generate electricity and thermal power. In PV/T system applications the production of electricity is the main priority, therefore it is necessary to operate the PV modules at low temperature, the carrier of thermal energy associated with the PV module may be either air or water. Kern and Russel [1] present the design and performance of water and air cooled PV/T systems, while Hendrie [2] and Florschuetz [3] include PV/T modelling in their works. Numerical methods predicting PV/T system performance are developed by Raghuraman [4], computer simulations are studied by Cox and Raghuraman [5], a low cost PV/T system with transparent type a-Si cells is proposed by Lalovic et al. [6] and results from an applied air type PV/T system are given by Loferski et al. [7]. Garg and Adhikari [8] present a variety of results regarding the effect of design and operational parameters on the performance of air type PV/T systems.
* Corresponding author. Tel.: +91 9868929291. E-mail address: [email protected] (S. Dubey). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.09.003
Hagazy [9] and Sopian et al. [10] investigated glazed photovoltaic/thermal air system for a single and a double pass air heater for space heating and the drying purposes. Kalogirou [11] has carried out monthly performance of an unglazed hybrid PV/T system under forced mode of operation for climatic condition of the Cyprus. He observed an increase of the mean annual efficiency of the PV solar system from 2.8% to 7.7% with thermal efficiency of 49%. Lee et al. [12] and Chow et al. [13] give interesting modelling results on air cooled PV modules. Jones and Underwood [14] have studied the temperature profile of the photovoltaic (PV) module in a non-steady state condition with respect to time. They conducted experiment for cloudy as well clear day condition. They observed that the PV module temperature varies in the range of 300–325 K (27–52 °C) for an ambient air temperature of 297.5 K (24.5 °C). The main reasons for reduction of the electrical efficiency of the PV module is packing factor (PF) of PV module, ohmic losses between two consecutive solar cells and the temperature of the module. The overall electrical efficiency of the PV module can be increased by increasing the packing factor (PF) and reducing the temperature of the PV module by withdrawing the thermal energy associated with the PV module, [15,16]. Packing factor is the ratio of total area of solar cells to the area of PV module. To increase the efficiency of PV a sun-tracking design is presented by Mohamad [17], the movement of a photovoltaic module was controlled to follow the Sun’s radiation using a programmable logiccontroller (PLC) unit. He has found that the daily output power of the PV was increased by more than 20% in comparison with that of a fixed module. Based on the I–V curves of a photovoltaic (PV) module, a novel and simple model is proposed to predict the PV
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Nomenclature b L C h hp1, hp2 I(t) IL Isc K _ m T Utc,a UTc,f Ub UL VL Voc
width of PV module (m) length of PV module (m) specific heat (J/kg °C) heat transfer coefficient (W/m2 °C) penalty factor due to the glass cover of PV module (dimensionless) incident solar intensity (W/m2) load current (A) short circuit current (A) thermal conductivity (W/m K) rate of flow of air (kg/s) temperature (°C) an overall heat transfer coefficient from solar cell to ambient through glass cover (W/m2 °C) an overall heat transfer coefficient from solar cell to flowing air through glass cover/tedlar (W/m2 °C) an overall back loss coefficient from flowing air/plate to ambient (W/m2 °C) an overall heat transfer coefficient for glass to glass and glass to tedlar modules (W/m2 °C) load voltage (V) open circuit voltage (V)
module performance for engineering applications. PV module performance is mainly depends upon solar-irradiance intensity and PV module temperature [18]. Tiwari et al. [19] have validated the theoretical and experimental results for photovoltaic (PV) module integrated with air duct for composite climate of India and concluded that an overall thermal efficiency of PV/T system is significantly increased due to utilization of thermal energy from PV module. Tripanagnostopoulos [20] presented a new type of PV/T collector with dual heat extraction operation with aspects and improvements of hybrid PV/T solar energy systems. Design of PV integrated solar-collector for natural circulation of water is presented by He et al. [21]. The methodology for the analytical treatment of the reliability of PV systems is proposed by Hamdy et al. [22]. The method depends upon the logic of the fault-tree technique. The reliabilities of the different components of a PV system are used to predict the reliability of the overall system. The performance analysis of a photovoltaic heat pump is presented by Jie et al. [23], in this system the PV/T collector is coupled with a solar assisted heat pump and works as an evaporator and found that the photovoltaic solar assisted heat pump (PV-SAHP) has better coefficient of performance (COP) and photovoltaic efficiency than the separate units. The COP of the PV-SAHP reached 8.4 and the average value was around 6.5, whereas the average photovoltaic efficiency was around 13.4%. Muntasser et al. [24] describes the Photovoltaic marketing in developing countries and examine marketing opportunities for PV technologies in less-developed countries, which were previously dominated by the industrialized countries and concludes by making a global policy package proposal, in terms of an appeal on the global community concerned with PV to propagate this proposal more convincingly, perhaps to emanate from an internationally recognized ‘‘forum”, like a PV conference and exhibition, with cooperation and participation of PV manufacturers, suppliers, industrialized countries, NGOs, financial institutions and developing countries. Recently, Zondag [25] carried out rigorous review on research work of a PV–thermal collector and system, carried out by various scientists till 2006. His review includes the history and importance of photovoltaic hybrid system and its application in various sectors. It also includes characteristics equations, study of design parameters, and marketing, etc.
V, v
go g
air velocity (m/s) efficiency at standard test condition (I(t) = 1000 W/m2 and Ta = 25 °C) (dimensionless) temperature dependent efficiency (dimensionless)
Subscripts a ambient c solar cell eff effective f fluid (air) inlet fluid fi outgoing fluid fo g glass p blackened plate T tedlar Greek symbols absorptivity product of effective absorptivity and transmittivity b packing factor s transmitivity
a (as)eff
In this paper, two types of PV module, glass to glass and glass to tedlar, with and without duct are considered for the study. The solar intensity based analytical expression of electrical efficiency of PV modules are derived and performance are evaluated by considering four types of weather condition of New Delhi, which are defined as: Type a: The ratio of daily diffuse to daily global radiation is less than or equal to 0.25 and sunshine hours greater then or equal to 9 h. Type b: The ratio of daily diffuse to daily global radiation between 0.25 and 0.50 and sunshine hours between 7 and 9 h. Type c: The ratio of daily diffuse to daily global radiation between 0.50 and 0.75 and sunshine hours between 5 and 7 h. Type d: The ratio of daily diffuse to daily global radiation is greater than or equal to 0.75 and sunshine hours less then or equal to 5 h. Data of solar radiations for different climates are obtained from Indian Metrological Department (IMD), Pune. The both type of PV module is manufactured by Central Electronics Ltd. (CEL), Sahibabad, Ghaziabad (UP).
2. Thermal analysis of PV modules Two types of PV module, glass to glass and glass to tedlar with and without duct are considered for the present study. PV modules are tilted at 30°, equal to the latitude of New Delhi. The cut sectional views of PV modules with duct are shown in Fig. 1. Wooden duct is embedded below the PV modules for air circulation having a cross section of 0.605 m 1.0 m 0.04 m. In case of with flow/ duct air is flowing in forced mode with the help of a DC fan of 12 V, which is run by PV module. In order to write the energy balance equation of photovoltaic modules, the following assumptions have been made: One dimensional heat conduction is good approximation for the present study. The glass cover is at uniform temperature. There is stream line flow of air through the duct.
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
g ¼ go 1 bo T c T a
ð1cÞ
(ii) For blackened absorber plate:
h
i
ap ð1 bc Þs2g IðtÞ b dx ¼ hp;f ðT p T f Þ þ U bp;a ðT p T a Þ b dx
ð2aÞ
2
3 2 3 The rate of solarenergy The rate of heat 6 available on blackened 7 6 transferfrom 7 6 7 6 7 6 7¼6 7 4 surfacefrom non packing 5 4 blackened plate 5 area of PV module to flowing fluid 2 3 An overall heat þ 4 loss from plate 5 to ambient From Eq. (2a), the expression for plate temperature is
Tp ¼
ap ð1 bc Þs2g IðtÞ þ hp;f T f þ U bp;a T a U bp;a þ hp;f
ð2bÞ
(iii) For air flowing through the duct: The energy balance of flowing air through absorber pipe is given by
dT f dx ¼ hp;f ðT p T f Þ þ U Tc;f ðT c T f Þ b dx dx 2 3 2 3 The rate ofheat The mass flow 6 transfer from 7 4 rate offlowing 5 ¼ 6 7 4 blackened plate to 5 fluid flowing fluid 2 3 An overall heat 4 þ transfer from cell 5 to flowing fluid _ aCa m
Fig. 1. (a) Cut sectional view of glass to glass PV module with duct. (b) Cut sectional view of glass to tedlar PV module with duct.
The system is in quasi-steady state. The ohmic losses in the solar cell are negligible. The energy balance equations for glass to glass and glass to tedlar PV modules are as follows. 2.1. Case A: glass to glass PV module with duct (Fig. 1a) (i) For solar cells of PV module: Following Dubey and Tiwari [26], the energy balance equation for solar cell of PV module can be written as
ð1aÞ
3 2 3 An overall heat The rate of heat 6 lossfrom top 7 6 7 6 7 6 7 4 energy available 5 ¼ 6 7 þ 4 transfer from cell 5 4 surface of cell 5 on solar cell to flowing fluid to ambient 2 3 The rate of 6 7 þ 4 electrical energy 5 2
The rate of solar
The solution of Eq. (3) with the help of Eqs. (1b) and (2b) and initial conditions namely, at T f jx¼0 , Tf = Tfi1 and at T f jx¼L , Tf = Tfo1, we get,
T fo ¼
ac sg bc IðtÞb dx ¼ U tc;a ðT c T a Þ þ U Tc;f ðT c T f Þ b dx þ sg gac bc IðtÞb dx 3
2
ðasÞGG;eff IðtÞ bU L;GG L þ T a 1 exp _ aCa m U L;GG bU L;GG L þ T fi exp _ aCa m
Z 1 L T f dx L 0
3 2 bU L 1 exp m_L;GG ðasÞGG;eff IðtÞ a Ca 5 þ T fi ¼ þ T a 41 bU L;GG L U L;GG _ a Ca m
bU L 1 exp m_L;GG a Ca bU L
Tf ¼
L;GG
From Eq. (1a), the expression for cell temperature is
ð1bÞ
U tc;a þ U bc;f
An expression for temperature dependent electrical efficiency of a PV module Schott [27] and Evans [28] is given by
g¼
n
If Tfi = Ta and T f ¼ T f , then from Eqs. (1b), (1c), and (4b), the expression for temperature dependent electrical efficiency can be obtained as L . where X o ¼ bUm_LGG a Ca
bo Tc;f oÞ go 1 Utc;asgþU ac bc þ UUL;GG hp1 ac bc þ hp2 ap ð1 bc Þsg 1 1expðX Xo Tc;f
1
go bo sg bc ac IðtÞ U tc;a þU Tc;f
ð4bÞ
_ a Ca m
sg ac bc ð1 gÞIðtÞ þ U tc;a T a þ U Tc;f T f
h
ð4aÞ
The average air temperature over the length of air duct below PV module is obtained as
produced
Tc ¼
ð3Þ
U hp1 oÞ 1 þ UTc;f 1 1expðX Xo L;GG
o
i IðtÞ ð5Þ
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U T ðT c T bs Þb dx ¼ hT ðT bs T f Þb dx
2.2. Case B: glass to glass PV module without duct (i) For solar cells of PV module: Following Dubey and Tiwari [26], the energy balance equation for solar cell of PV module can be written as
sg ac bc þ sg ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U b ðT c T a Þ b dx ð6aÞ þ sg gac bc IðtÞb dx 2
2
3
An overall heat
Tc ¼
An overall heat The rate of heat transfer 4 transfer from cell to 5 ¼ 4 from back surface of the 5 back surface of tedlar tedlar to flowing fluid Using Eqs. (8b) and (9a), the expression for back surface temperature of PV module can be obtained as
g¼
go 1 1
bo ðasÞGG;eff IðtÞ U tc;a þU b
ð6bÞ
i ð7Þ
bo go sg ac bc IðtÞ U tc;a þU b
ð9bÞ
ð10Þ
The solution of Eq. (11a) with the help of Eqs. (9b) and (10) and initial conditions namely, at T f jx¼0 , Tf = Tfi1 and at T f jx¼L , Tf = Tfo1, we get,
T fo ¼
From Eqs. (1c) and (6b), the expression for the efficiency of glass to glass PV module can be obtained as
h
hp1 sg ½ac bc þ aT ð1 bc Þ ac gbc IðtÞ þ U tT T a þ hT T f U tT þ hT
dT f dx þ U b ðT f T a Þb dx ¼ hT ðT bs T f Þb dx dx 2 3 2 3 The mass flow An overall heat transfer 4 rate offlowing 5 þ 4 from flowing fluid to 5 fluid ambient 2 3 The rate of heat transfer ¼ 4 from back surface of the 5 tedlar to flowing fluid
i
U tc;a þ U b
3
_ aCa m
produced
ðasÞGG;eff sg gac bc IðtÞ þ U tc;a T a þ U b T a
ð9aÞ
2
(iii) For the air flowing below the tedlar:
From Eq. (6a), the expression for cell temperature is
h
3
T bs ¼
3
The rate of solar 7 6 6 7 6 lossfrom top 7 7 4 energy available 5 ¼ 6 7 6 4 surface of cell 5 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 þ 4 loss from back side 5 þ 4 electrical energy 5 of the cell
2
hp1 hp2 ðasÞGT;eff IðtÞ þ Ta U L;GT bU L;GT L þ T fi exp _ aCa m
bU L;GT L 1 exp _ aCa m
ð11aÞ
The average air temperature over the length of air duct below PV module is obtained as
3 2 bU L
Tf ¼
2.3. Case C: glass to tedlar PV module with duct (Fig. 1b)
1 exp m_L;GT hp1 hp2 ðasÞGT;eff IðtÞ a Ca 5 þ T a 41 bU L;GT L U L;GT 0 _ a Ca m
bU L 1 exp m_L;GT a Ca ð11bÞ þ T fi bU L 1 L
Z
L
T f dx ¼
L;GT
(i) For solar cells of PV module: Following Tiwari and Sodha [29], the energy balance equation for solar cell of PV module can be written as
go 1 g¼
3
back surface of tedlar
ð12Þ
L . where X o ¼ bUm_LGG a Ca
2.4. Case D: glass to tedlar PV module without duct
3
2
An overall heat 7 6 6 lossfrom top 7 6 7 7 6 energy available 7 ¼ 6 7 4 5 6 6 surface of cell 7 5 4 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 7 6 7 þ6 4 transfer from cell to 5 þ 4 electrical energy 5 The rate of solar
(i) For solar cells of PV module: Following Tiwari and Sodha [29], the energy balance equation for solar cell of PV module can be written as
sg ½ac bc þ aT ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U b ðT c T a Þb dx ð13aÞ þ sg gac bc IðtÞb dx 2
produced
From Eq. (8a), the expression for cell temperature is
Tc ¼
If Tfi = Ta and T f ¼ T f , then from Eqs. (1c), (8b), (9b), and (11b), the expression for temperature dependent electrical efficiency can be obtained as
bo sg ½ac bc þ aT ð1 bc ÞIðtÞ U T hp1 U T hT hp1 hp2 1 expðX o Þ 1þ þ 1 U tc;a þ U T Xo hT þ U tT ðhT þ U tT ÞU L;GT bo go sg ac bc IðtÞ U T hp1 U T hT hp1 hp2 1 expðX o Þ 1 1þ þ 1 U tc;a þ U T Xo hT þ U tT ðhT þ U tT ÞU L;GT
sg ½ac bc þ aT ð1 bc ÞIðtÞb dx ¼ ½U tc;a ðT c T a Þ þ U T ðT c T bs Þb dx ð8aÞ þ sg gac bc IðtÞb dx 2
_ a Ca m
sg ½ac bc þ aT ð1 bc Þ ac gbc IðtÞ þ U tc;a T a þ U T T bs U tc;a þ U T
(ii) For the back surface of the tedlar:
ð8bÞ
The rate of solar
3
2
An overall heat
3
7 6 6 7 6 loss from top 7 7 4 energy available 5 ¼ 6 4 surface of cell 5 on PV module to ambient 2 3 2 3 An overall heat The rate of 6 7 6 7 þ 4 loss from back side 5 þ 4 electrical energy 5 of the cell produced
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
From Eq. (13a), the expression for cell temperature is
h Tc ¼
ðasÞGT;eff
i sg gac bc IðtÞ þ U tc;a T a þ U b T a U tc;a þ U b
2.6. Correlation coefficient and root mean square percent deviation
ð13bÞ
From Eqs. (1c) and (13b), the expression for the efficiency of glass to glass PV module can be obtained as
h
g¼
ÞGT;eff IðtÞ go 1 bo ðaUstc;a þU b
1
i ð14Þ
bo go sg ac bc IðtÞ U tc;a þU b
In addition to the above equations the relations used for defining the design parameters (Table 1) and different configuration of glass to glass and glass to tedlar PV modules with and without duct are given in Appendix.
To compare the theoretical and experimental results the correlation coefficient (r) and root mean square percent deviation (e) have been evaluated by using the following expressions:
P P P N X i Y i ð X i Þð Y i Þ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ffi r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P P P N X 2i ð X i Þ2 N Y 2i ð Y i Þ2
ð16aÞ
And
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ðei Þ e¼ N
ð16bÞ
where
Xi Y i 100 Xi
ei ¼
gexp
0:8 V oc Isc IL V L ¼ Am IðtÞ
ð15Þ
where 0.8 is the fill factor or power factor, it measure of sharpness of the knee in I–V curve. It indicates how well a junction was made in the cell and how low the series resistance has been made. It can be lowered by the presence of series resistance and tends to be higher whenever the open circuit voltage is high.
2 Solar intensity, W/m
Experimental efficiency of PV module can be calculated as
900
40
800
35
700
30
600
25
500
20
400
15
300
I(t)
200
10
Ta
5
100 0
Ambient temperature,˚C
2.5. Electrical efficiency of PV module
0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
go sg
0.605 m 7.6 W/m2 K 1.0 m 0.0058 kg/s 1005 J/kg K 7.44 W/m2 K 0.9 0.8 0.5 0.83 0.0045 0.12 0.95
Glass to glass with duct hp1 hp2 Kg Lg UTc,f UL,GG Ubp,a
0.536 0.934 1.1 W/m K 0.003 m 8.59 W/m2 K 4.56 W/m2 K 0.62 W/m2 K
ac ap aT bc bo
Glass to glass without duct Ub
2
3.36 W/m K
Glass to tedlar with duct hp1 hp2 KT LT UT UtT UL,GT Ubf,a
0.898 0.54 0.033 W/m K 0.0005 m 66 W/m2 K 6.68 W/m2 K 4.42 W/m2 K 0.62 W/m2 K
Glass to glass without duct Ub
3.23 W/m2 K
Glass to glass withduct
Glass to tedlar withduct
Glass to glass without duct
Glass to tedlar without duct
12.0 11.0 10.0 9.0 8.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 3. Hourly variation of electrical efficiency considering with and without duct.
Efficiency (Glass to glass)
Efficiency (Glass to tedlar)
Cell temp. (Glass to glass)
Cell temp. (Glass to tedlar)
12.0
90.0
11.5
80.0
11.0
70.0
10.5 60.0
10.0
50.0
9.5
40.0
9.0 8.5
Cell temperature,˚C
Values
b ho L _a m Ca Utc,a
Eletrical efficiency, %
Parameters
Fig. 2. Hourly variation of solar intensity and ambient temperature for the month of April, 2008.
Electrical Efficiency, %
Table 1 Design parameters of glass to glass and glass to tedlar, with and without duct of PV modules
30.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 4. Hourly variation of electrical efficiency and cell temperature considering with duct.
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S. Dubey et al. / Applied Energy 86 (2009) 697–705
b
With Duct (Glass to Glass) 12.0
e= 3.92 r = 0.838
Theoretical Experimental
12.0
11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
Without Duct (Glass to Glass)
Electrical Efficiency, %
Electrical Efficiency, %
a
Theoretical
e= 4.19 r = 0.827
Experimental 11.0 10.0 9.0 8.0
16:00
09:00
10:00
11:00
d
With Duct (Glass to Tedlar) 12.0
Theoretical
Electrical Efficiency, %
Electrical Efficiency, %
c
e= 3.41 r= 0.806
Experimental 11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
Time (Hours)
14:00
15:00
Without Duct (Glass to Tedlar) 12.0
e= 3.87 r= 0.849
Theoretical Experimental
11.0 10.0 9.0 8.0 09:00
16:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
Time (Hours)
Fig. 5. (a) Hourly variation of electrical efficiency considering with duct. (b) Hourly variation of electrical efficiency considering without duct. (c) Hourly variation of electrical efficiency considering with duct. (d) Hourly variation of electrical efficiency considering without duct.
decrease in efficiency of module. In case B and D (modules without duct) efficiency is nearly same. Hourly variation of electrical
V = 0.5 m/s (GG)
V = 0.5 m/s (GT)
V = 1 m/s (GG)
V= 1 m/s (GT)
V= 2 m/s (GG)
V= 2 m/s (GG)
a type b type
a
75 70 65 60 55 50 45 40 35
c type d type
12.0
11.0
10.0
9.0 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours)
b Daily avg. electrical efficiency, %
Avg. air temperature,˚C
The variation of solar intensity and ambient temperature for a typical day in the month of April 2008 for New Delhi condition is shown in Fig. 2. The values of various parameters (design parameters) of PV modules are given in Table 1. In this paper, the results of the four cases, case A (Glass to glass PV module with duct), case B (Glass to glass PV module without duct), case C (Glass to tedlar PV module with duct), case D (Glass to tedlar PV module without duct) are discussed in details. Experimental electrical efficiency of PV module for all the four cases are evaluated by using Eq. (15) and the variations are shown in Fig. 3. Glass to glass type PV module with duct gives higher efficiency than the glass to tedlar type PV module. This is due to the radiation falling on non-packing area of glass to glass module is transmitted through the glass cover, however, in case of glass to tedlar all the radiation is absorbed by the tedlar and then heat is carried away by the conduction. So that the temperature of the solar cell is higher in case of glass to tedlar type PV module, result in
Electrical Efficiency, %
3. Result and discussion
12.0 11.17 11.0
10.0
10.65
9.73
9.86
9.0 Type a
Type b
Type c
Type d
Weather conditions 09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
Time (Hours) Fig. 6. Hourly variation of average air temperature over the length of duct by varying the mass flow rate; glass to glass (GG) and glass to tedlar (GT).
Fig. 7. (a) Hourly variation of electrical efficiency for a, b, c, d type weather conditions considering glass to glass PV module with duct. (b) Daily average of electrical efficiency for a, b, c, d type weather conditions considering glass to glass PV module with duct.
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a Monthly avg. electrical efficiency, %
11.0
Annual Avg. = 10.41 %
10.5
10.0
9.5
9.0 JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Month of year
b Monthly avg. electrical efficiency, %
10.5
Annual Avg. = 9.75 % 10.0
9.5
9.0
8.5
8.0 JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Month of year Fig. 8. (a) Monthly average of electrical efficiency considering a, b, c, d type weather conditions for glass to glass PV module with duct. (b) Monthly average of electrical efficiency considering a, b, c, d type weather conditions for glass to glass PV module without duct.
efficiency and cell temperature for case A and case B with duct are shown in Fig. 4. Figure shows that as the temperature increases efficiency decreases and as the temperature decreases efficiency increases, as expected. This result is in accordance with the results reported by earlier researchers, Zondag et al. [15] and Chow [16]. Eqs. (5) and (6) has been used for calculating the theoretical efficiency of glass to glass type PV module with and without duct. Experimental results are validated with the theoretical results and the variations are shown in Fig. 5a and b. Similarly, Eqs. (12) and (14) has been used for calculating the theoretical efficiency of glass to tedlar type PV module with and without duct. The variations between experimental and theoretical results are shown in Fig. 5c and d. The correlation coefficient (r) and root mean square percent deviation (e) is also evaluated using Eqs. (16a) and (16b), respectively which are shown in the same figure. It is observed that there is a fair agreement between theoretical and experimental values of all the four cases. The correlation coefficient (r) and root mean square percent deviation (e) is varies from 4.19 to 3.41 and 0.849 to 0.806, respectively. Eqs. (4b) and (11b) has been used for evaluating the average air temperature over the length of air duct by varying the mass flow rate for case A and case C. It is observed that the average air temperature is higher in case of A than case C, due to the solar radiation is transmitted through the glass cover (non-packing area) and absorbed by the blackened plate (below the module). In this case the heat is convected to the flowing air by two ways from back
surface of PV module as well as from top surface of the blackened plate. The variation is shown in Fig. 6. Hourly variation of electrical efficiency of glass to glass type PV module with duct for a, b, c, and d type weather conditions is shown in Fig. 7a. Figure shows that as the solar intensity decreases (from a type to d type) the temperature of solar cell is also decreases and efficiency increases. The same results are also obtained for daily average efficiency of a, b, c, and d type weather conditions which is shown in Fig. 7b. Monthly average electrical efficiency by considering a, b, c, d type weather conditions of New Delhi for glass to glass type PV module with and without duct are calculated and the variation is shown in Fig. 8a and b. The annual average efficiency of PV module with and without duct is 10.41% and 9.75%, respectively. The monthly average efficiency is calculated by multiplying the number of days belongs to each type of weather condition of that month and taking the average of all days of that month. And then the average of 12 months gives the annual average efficiency of PV module.
4. Conclusion 1. In this paper, four different configurations of two types of PV modules, glass to glass and glass to tedlar are studied. 2. The percentage difference between electrical efficiency (Dg) of glass to glass and glass to tedlar type PV modules with and without duct are 0.24% and 0.086%, respectively.
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3. The percentage difference between electrical efficiency (Dg) of glass to glass type PV modules with and without duct is 0.66%. 4. This 0.66% difference of electrical efficiency could be very large if it is used in large PV plants and simultaneously fulfilling the requirement of electricity generation and thermal heating with better efficiency.
Appendix A
(iv) Glass to tedlar PV module without duct:
ðasÞGT;eff ¼ sg ½ac bc þ aT ð1 bc Þ U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 LT 1 þ Ub ¼ K T hi hi ¼ 2:8 þ 3v;
v ¼ 0:2 m=s
In modelling equations, we used following relations for defining the design parameters, which are shown in Table 1. (i) Glass to glass PV module with duct:
The values of ac, aT, bc, go, ap and sg are taken from Duffie and Beckman [30], Tiwari [31] and Tiwari and Sodha [32].
ðasÞGG;eff ¼ hp1 ðasÞ1;eff þ hp2 ðasÞ2;eff
References
Here, ðasÞ1;eff ¼ sg ac bc ð1 gÞ and ðasÞ2;eff ¼ ap ð1 bc Þs2g . hp1 and hp2 is the penalty factors due to glass cover of PV module, which are defined as
hp;f U Tc;f and hp2 ¼ U tc;a þ U Tc;f U p;a þ hp;f 1 Lg 1 ¼ þ K g ho
hp1 ¼ U tc;a
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 Lg 1 þ U Tc;f ¼ K g hi hp;f ¼ hi ¼ 2:8 þ 3v; U Tc;f U tc;a U tT ¼ U Tc;f þ U tc;a U bp;a hp;f UT ¼ U bp;a þ hp;f
v ¼ 2 m=s
U L;GG ¼ U tT þ U T (ii) Glass to glass PV module without duct:
ðasÞGG;eff ¼ sg ac bc þ sg ð1 bc Þ U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; V ¼ 0:5 m=s 1 Lg 1 þ Ub ¼ K g hi hi ¼ 2:8 þ 3v;
v ¼ 0:2 m=s
(iii) Glass to tedlar PV module with duct:
ðasÞGT;eff ¼ sg ½ac bc þ aT ð1 bc Þ ac gbc hp1 and hp2 is the penalty factors due to glass cover and tedlar of T and hp2 ¼ Utc;ahTþhT PV module, which are defined as, hp1 ¼ Utc;aUþU T
U tc;a ¼
Lg 1 þ K g ho
1
ho ¼ 5:7 þ 3:8V; 1 LT UT ¼ KT
V ¼ 0:5 m=s
hT ¼ 2:8 þ 3v; v ¼ 2 m=s U tc;a U T U tT ¼ U tc;a þ U T U tT hT U t;f ¼ U tT þ hT U L;GT ¼ U t;f þ U bf;a
[1] Kern Jr. EC, Russell MC. Combined photovoltaic and thermal hybrid collector systems. In: Proceedings of the 13th IEEE photovoltaic specialists, Washington, DC, USA, 1978. p. 1153–7. [2] Hendrie SD. Evaluation of combined photovoltaic/thermal collectors. In: Proceedings of international conference ISES, Atlanta, Georgia, USA, May 28– June 1, vol. 3. 1979. p. 1865–9. [3] Florschuetz LW. Extention of the Hottel–Whillier model to the analysis of combined photovoltaic/thermal flat plate collectors. Sol Energy 1979;22:361–6. [4] Raghuraman P. Analytical predictions of liquid and air photovoltaic/thermal, flat-plate collector performance. J Sol Energy Eng 1981;103:291–8. [5] Cox III CH, Raghuraman P. Design considerations for flat-plate photovoltaic/ thermal collectors. Sol Energy 1985;35:227–41. [6] Lalovic B. A hybrid amorphous silicon photovoltaic and thermal solar collector. Solar Cells 1986/1987;19:131–8. [7] Loferski JJ, Ahmad JM, Pandey A. Performance of photovoltaic cells incorporated into unique hybrid photovoltaic/thermal panels of a 2.8 kW residential solar energy conversion system. In: Proceedings of 1988 annual meeting, American Solar Energy Society, Cambridge, Massachusetts, USA, 1988. p. 427–32. [8] Garg HP, Adhikari RS. Conventional hybrid photovoltaic/thermal (PV/T) air heating collectors: steady-state simulation. Renew Energy 1997;11:363–85. [9] Hegazy AA. Comparative study of the performances of four photovoltaic/ thermal solar air collectors. Energy Convers Manage 2000;41:861–81. [10] Sopian K, Liu HT, Kakac S, Veziroglu TN. Performance of a double pass photovoltaic thermal solar collector suitable for solar drying systems. Energy Convers Manage 2000;41(4):353–65. [11] Kalogirou SA. Use of TRYNSYS for modelling and simulation of a hybrid PV thermal solar system for Cyprus. Renew Energy 2001;23:247–60. [12] Lee WM, Infield DG, Gottschalg R. Thermal modelling of building integrated PV systems In: Proceedings of 17th PV solar energy conference. Munich, 22–26 October, 2001. p. 2754–7. [13] Chow TT, Hand JW, Strachan PA. Building-integrated photovoltaic and thermal applications in a subtropical hotel building. Appl Therm Eng 2003;23:2035–49. [14] Jones AD, Underwood CP. A thermal model for photovoltaic systems. Sol Energy 2001;70(4):349–59. [15] Zondag HA, de Vries DW, van Helden WGJ, van Zolengen RJC, Steenhoven AA. The yield of different combined PV–thermal collector designs. Sol Energy 2003;74(3):253–69. [16] Chow TT. Performance analysis of photovoltaic–thermal collector by explicit dynamic model. Sol Energy 2003;75:143–52. [17] Al-Mohamad A. Efficiency improvements of photo-voltaic panels using a suntracking system. Appl Energy 2004;79:345–54. [18] Zhou W, Yang H, Fang Z. A novel model for photovoltaic array performance prediction. Appl Energy 2007;84:1187–98. [19] Tiwari A, Sodha MS, Chandra A, Joshi JC. Performance evaluation of photovoltaic thermal solar air collector for composite climate of India. Sol Energy Mater Sol Cells 2006;90(2):175–89. [20] Tripanagnostopoulos Y. Aspects and improvements of hybrid photovoltaic/ thermal solar energy systems. Sol energy 2007;81:1117–31. [21] He W, Chow TT, Ji J, Lu J, Pei G, Chan L. Hybrid photovoltaic and thermal solarcollector designed for natural circulation of water. Appl Energy 2006;83:199–210. [22] Hamdy MA, Beshir ME, Elmasry SE. Reliability Analysis of Photovoltaic Systems. Appl Energy 1989;33:253–63. [23] Ji J, Chow TT, Pei G, He W, He H. Performance analysis of a photovoltaic heat pump. Appl Energy 2008;85:680–93. [24] Muntasser MA, Bara MF, Quadri HA, EL-Tarabelsi R, La-azebi IF. Photovoltaic marketing in developing countries. Appl Energy 2000;65:67–72. [25] Zondag HA. Flat-plate PV–thermal collectors and systems: a review. Renew Sustain Energy Rev 2008;12(4):891–959. [26] Dubey S, Tiwari GN. Thermal modelling of a combined system of photovoltaic thermal (PV/T) solar water heater. Sol Energy 2008;82:602–12.
S. Dubey et al. / Applied Energy 86 (2009) 697–705 [27] Schott T. Operational temperatures of PV modules. In: Proceedings of 6th PV solar energy conference, 1985. p. 392–6. [28] Evans DL. Simplified method for predicting PV array output. Sol Energy 1981;27:555–60. [29] Tiwari A, Sodha MS. Parametric study of various configurations of hybrid PV/ thermal air collector: experimental validation of theoretical model. Sol Energy Mater Sol Cells 2007;91:17–28.
705
[30] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley & Sons; 1991. [31] Tiwari GN. Solar energy fundamentals, design, modelling and applications. New Delhi: Narosa Publishing House; 2004. [32] Tiwari A, Sodha MS. Performance evaluation of solar PV/T system: an experimental validation. Sol Energy 2006;80(7):751–9.