Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system

Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system

Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx Contents lists available at ScienceDirect Engineering Science and Te...

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Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

Contents lists available at ScienceDirect

Engineering Science and Technology, an International Journal journal homepage: www.elsevier.com/locate/jestch

Full Length Article

Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system Deepali Atheaya a,⇑, Arvind Tiwari b, G.N. Tiwari a a b

Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 11 00 16, India Department of Electrical Engineering, College of Engineering, Qassim University, P.O. Box-6677, Buraydah 51452, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 19 January 2016 Revised 28 June 2016 Accepted 28 June 2016 Available online xxxx Keywords: Photovoltaic thermal Thermal modeling Instantaneous thermal efficiency

a b s t r a c t The main advantage of PVT-CPC system is to generate both thermal and electrical energy at a low cost. Hence, an analytical expression of electrical and thermal efficiency of fully covered photovoltaic thermal compound parabolic concentrator (PVT-CPC) system has been derived as a function of climatic and design parameters. Further, an experiment has been performed for a typical day during the summer month namely 3rd and 4th May, 2016 at IIT, Delhi (India) for [case (A)] conventional CPC system and [case (B)] fully covered PVT-CPC system for thermal validation. The theoretical and experimental results for the outlet fluid temperature and electrical efficiency were verified with correlation coefficient (r) of 0.99. This indicates a close agreement between the theoretical and experimental results for thermal and electrical energy. Ó 2016 The Authors. Publishing services by Elsevier B.V. on behalf of Karabuk University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Today there is an energy demand wor ldwide and researchers are trying to get a viable solution for the undergoing energy crisis. Solar energy has been utilized to get clean energy [1,2]. Photovoltaic thermal (PVT) technologies can be one of solutions to meet the energy shortage effectively [3]. PVT module is used to generate electrical and thermal energy for space heating, residential and industrial applications. Rabl [4] firstly designed a trough shaped cylindrical collector for concentrating solar intensity to obtain high temperatures. A photovoltaic thermal (PVT) collector was explored theoretically and tested by Gibart [5] by using a concentrated solar radiation. The results showed better thermal and electrical performance of the collector as compared to conventional flat thermal collector. Based on solar trough concentration, an experiment of a two phase photovoltaic thermal collector was conducted by Tan et al. [6]. The results indicated that as the temperature of solar cell attained 73 °C, the working medium output temperature was raised by 12.06 °C. An asymmetric compound parabolic photovoltaic concentrator (ACPPVC) was designed, fabricated and tested in the outside environment with and without concentrators by Abbreviations: CPC, compound parabolic concentrator; PVT, photovoltaic thermal. ⇑ Corresponding author. E-mail address: [email protected] (D. Atheaya).

Mallick et al. [7]. It was observed that ACPPVC produced 1.62 times more power in comparison with conventional concentrator. A small concentrating photovoltaic and thermal system was analyzed by Kribus et al. [8]. This system concentrated solar energy about 500 times. Kong et al. [9] designed a similar concentrated photovoltaic thermal system to achieve a uniformly concentrated radiation. A thermal analysis of high concentration thermal system was also carried out by Chen et al. [10]. It was observed that for high concentration ratio and mass flow rate, the electrical efficiency increases with decrease in thermal efficiency. Xu et al. [11] studied experimentally a solar PV thermal system with permanent truncated parabolic concentrators. In their system, a refrigerant R134a flowed in the aluminum tubes below the PV cells to extract the solar radiation for evaporation of refrigerant. Further, the refrigerant was condensed to heat water in a condenser. A flux concentrating rate of fixed parabolic concentrator was reported as 1.6 times more power output as compared to PV cells without concentrator. Kunnemeyer et al. [12] investigated the performance of a V-trough photovoltaic thermal concentrator and reported that by concentrating solar intensity on the PV cells and cooling them, better electrical output can be achieved. A design of an air gap lens walled compound parabolic concentrator photovoltaic thermal (ALCPC-PVT) system was proposed and tested by Li et al. [13]. An improved overall system efficiency of 65.5% was reported by them. Mohsenzadeh and Hosseini [14] studied and tested a photovoltaic thermal system integrated with reflectors and vacuum tube solar

Peer review under responsibility of Karabuk University. http://dx.doi.org/10.1016/j.jestch.2016.06.014 2215-0986/Ó 2016 The Authors. Publishing services by Elsevier B.V. on behalf of Karabuk University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: D. Atheaya et al., Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system, Eng. Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.06.014

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

Nomenclature A Aa Ar b cf bo dx F0 FR h Lr PF 1 PF 2 PF c Lp Li Lg It Id Ib U t;ca U t;cp U t;pa _f m

area (m2) total aperture area (m2) total receiver area (m2) breadth of receiver (m) specific heat of fluid (J/kg K) breadth of aperture area (m) elemental length (m) flat plate collector efficiency factor flow rate factor, dimensionless heat transfer coefficient (W=m2 K) total length of the receiver area (m) first penalty factor due to glass cover second penalty factor due to absorber/receiver plate penalty factor due to glass cover for the portion covered by glazing receiver plate thickness (m) insulation thickness (m) glass cover thickness (m) total radiation (W/m2) diffuse radiation (W/m2) beam radiation (W/m2) overall heat transfer coefficient from solar cell to ambient through glass cover (W/m2 K) overall heat transfer coefficient from solar cell to plate (W/m2 K) total (top and bottom) overall heat transfer coefficient from plate to ambient (W/m2 K) mass flow rate of water in (kg/s)

water heaters. The results indicated an increase in electrical and thermal energy output of the system. Recently, a study of photovoltaic thermal double pass and flat and compound parabolic concentrators system (PVT-CPC) was carried out by Elsafi and Gandhidasan [15] and the PVT-CPC system showed the best performance. Atheaya et al. [16] proposed a partially covered PVT-CPC system. It was found that partially covered PVT-CPC system has a superior thermal performance than fully covered PVT-CPC system. Further, fully covered PVT-CPC gives better electrical power. The main purpose of this work is to compare the performance of conventional compound parabolic concentrator system and fully covered photovoltaic thermal compound parabolic concentrator system by using the characteristic equation/curve to meet the electrical and thermal energy demand of users. Now, the prime objective of this present paper is experimental validation of the thermal model developed by Atheaya et al. [16].

2. Brief description of experimental set up 2.1. Conventional CPC system [case (A)] An experimental set up of conventional CPC system was installed at the roof top of the building of IIT, Delhi (28°370 N 77°140 E). The sketch of the experimental arrangement for [case (A)] has been shown in Fig. 1. The conventional CPC system was mounted on a mild steel frame. The absorber plate was made up of copper and it had a selective coating of black chrome plating to enhance the absorptivity of plate. A glass plate was fixed at the top of it. A casing of aluminum material was fabricated and both the absorber plate and the glass were fitted inside the casing to reduce thermal losses. Water is allowed to flow below the absorber plate in the copper tubes and its inlet and outlet pipe arrangement has been shown in the Fig. 2. The capacity of water tank was

U L1

overall heat transfer coefficient from blackened surface to ambient ðW=m2 KÞgo efficiency at standard test condition (It ¼ 1000 W/m2, T o ¼ 25 °C) bo temperature coefficient of efficiency (K1) Greek letters a absorptivity bc packing factor q reflectivity s transmittivity gi instantaneous thermal efficiency ðasÞeff product of effective absorptivity and transmittivity g thermal efficiency Subscript a c eff f fi fo g m p

ambient solar cell effective fluid inlet fluid outlet fluid glass module plate

30 l and it was placed on a stand and connected to the inlet of the system. The water flowed from water tank to the pipe and then moved parallel into four smaller tubes and finally gets collected at the outlet. The reflectors of the CPC were made up of stainless steel polished material due to its high corrosion resistance, enhanced strength and high reflectivity. The reflectors were fitted with the whole aluminum casing with the help of three mild steel strips (32 mm  5 mm) which were placed at three different places on both reflectors for support. A floating valve was placed inside the tank to maintain the water level at a particular height to ensure constant mass flow rate. The copper tube in plate was insulated from below by using glass wool to reduce bottom losses. Firstly, the experiment was performed at the conventional CPC system on 3rd May, 2016 in New Delhi. 2.2. Fully covered PVT-CPC system [case (B)] The sketch of an experimental arrangement of fully covered PVT-CPC system has been illustrated in Fig. 3. In this case, a semitransparent PV module (101 cm  51 cm) was fixed to the top of glass as shown in Fig. 4. The PV module was sealed by placing plastic rectangular sheets and putty sealant The Figs. 5–7 shows the actual photograph of the top view, front view and side view of fully covered PVT-CPC system. The experiment was performed for fully covered PVT-CPC system on 4th May, 2016 in New Delhi. 3. Thermal modeling The assumptions for writing the energy balance equations for cases (A) and (B) are as follows:  Both the conventional CPC and fully covered PVT-CPC systems are considered in the quasi steady state.

Please cite this article in press as: D. Atheaya et al., Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system, Eng. Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.06.014

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Supply mains

Watertank ) teel ss s e l n tai r (S cto e l f Re

Floating valve

Glass (top layer) absorber plate (second layer) tor lec Ref Outlet

Inlet Insulation (fourth layer) Aluminum frame

Mild steel (stand)

arrangement of water flowing below the plate (third layer)

Foundation

Fig. 1. Sketch of experimental arrangement of conventional CPC system.

Water tank Glass

Reflectors

Water inlet

Water Outlet

Absorber plate below glass

Mild steel stand

Temperature indicator

Fig. 2. Photograph of experimental arrangement of conventional CPC system.

 For both systems, the ohmic losses are neglected.  For both systems, there is no temperature gradient across thickness of PV module and glass material.  The heat capacity of glass and PV module are neglected.  Heat conduction is one dimensional.

qap sg Ib Aa ¼ F 0 hpf ðT p  T f ÞAr þ U t;pa ðT p  T a ÞAr (ii) Flowing fluid

_ f cf m

dT f dx ¼ F 0 hpf ðT p  T f Þbdx dx

ð2Þ

Eqs. (1) and (2) can be solved with initial condition T f ¼ T 0fi at x ¼ 0 as follows:

3.1. Thermal modeling of conventional CPC system, [case (A)]

Tf ¼ Following Atheaya et al. [16], the energy balance equations have been written as follows:

ð1Þ

   0  PF c ðasÞc;eff Ib F U l;c bx þ T a 1  exp _ f cf U l;c m  0  F U bx l;c þ T 0fi exp _ f cf m

ð3Þ

(i) Receiver Please cite this article in press as: D. Atheaya et al., Experimental validation of a fully covered photovoltaic thermal compound parabolic concentrator system, Eng. Sci. Tech., Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.06.014

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

Watertank Supply mains

) teel ss s e l in Sta or ( t c e l Ref

Floating valve

PV module (top layer) glass(second layer) or lect Ref Outlet

Inlet insulation (fourth layer)

Mild steel (stand) Aluminum frame arrangement of water flowing below the plate (third layer)

Foundation

Fig. 3. Sketch of an experimental arrangement of fully covered PVT-CPC system.

(i) For semi-transparent PV component

qac sg bc Ib Aa ¼ ½U t;ca ðT c  T a Þ þ U t;cp ðT c  T p ÞAr þ qgm Ib Aa

ð5Þ

(ii) For blackened tube in plate type absorber

qap s3g ð1  bc ÞIb Aa þ U t;cp ðT c  T p ÞAr ¼ F 0 hpf ðT p  T f ÞAr Reflector Stainless steel (polished)

PV module

Air gap

Clamps

Glass

Absorber plate(Copper)

In the above expressions ‘‘bc ” is the packing factor of PV module and it is the ratio of total area of solar cells to the area of PV module. (iii) For fluid flowing beneath the absorber

_ f cf m Copper tubes

Aluminum frame

Fig. 4. Front view sketch of fully covered PVT-CPC system.

Tc ¼

The outlet water temperature of conventional CPC system (T f ¼ T fo1 at x ¼ Lr ) can be evaluated as follows:



  0  PF c ðasÞc;eff Ib F U l;c b  Lr ¼ þ T a 1  exp _ f cf U l;c m  0  F U b  L r l;c þ T 0fi exp _ f cf m

T fo1 ¼



ð7Þ

ð4aÞ



PF c ðasÞc;eff Ib F U l;c Ar þ T a 1  exp _ f cf m U l;c  0  F U A r l;c þ T 0fi exp _ f cf m 0

ð8Þ

ðasÞ2;eff Ib þ PF 1 ðasÞ1;eff Ib þ U L1 T a þ F 0 hpf T f

ð9Þ

F 0 hpf þ U L1

By using Eq. (7), Eqs. (8) and (9) have been rewritten as:

_ f cf m



ðasÞ1;eff Ib þ U t;ca T a þ U t;cp T p U t;ca þ U t;cp

where ðasÞ1;eff ¼ qðaC bC sg  gm Þ AAar and

Tp ¼

Therefore, the outlet water temperature (Tfo1) at the exit of conventional CPC system has been calculated from



dT f dx ¼ F 0 hpf ðT p  T f Þbdx dx

From Eqs. (5) and (6) T c , T p (solar cell temperature and plate temperature) have been evaluated as follows:

Insulation

T fo1

ð6Þ

dT f 0 dx ¼ bF ½PF 2 ðasÞm;eff Ib  U l;m ðT f  T a Þdx dx

The solution of above equation  T f x¼0 ¼ T fi , is given as follows:

with

initial

condition



Tf ¼ ð4bÞ

with (Ar ¼ b  Lr ). 3.2. Thermal modeling of fully covered PVT-CPC system, [case (B)] The energy balance equations have been written for the proposed system:

   PF 2 ðasÞm;eff Ib bU l;m F 0 x þ T a 1  exp _ f cf m U l;m  0  bU l;m F x þ T fi exp _ f cf m

ð10Þ

ð10aÞ

Thus, the average fluid temperature underneath the PV module (T f ) by integrating above equation is given by

Tf ¼

1 Lr

Z

Lr

T f dx

ð11Þ

0

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

5

PV module

Reflectors

101cm

40cm Fig. 5. Photograph of top view of experimental arrangement of fully covered PVT-CPC system.

Water tank Reflector PV module Water exit

Temperature indicator Inlet water Clamps

Foundation

Mild Steel Stand

Fig. 6. Photograph of front view of experimental arrangement of fully covered PVT-CPC system.

Evans [17] and Schott [18], the solar cell efficiency (gc ) of solar cell is as follows:

or,

" #      PF 2 ðasÞm;eff Ib F_ rm F rm F rm 1  0 þ T a 1  0 þ T fi 0 Tf ¼ U l;m F F F _ f cf m l;m Ar

where F rm ¼ U

h

1  exp

n

F 0 U l;m Ar _ f cf m

ð12Þ

oi

By substituting the expression for T f from Eq. (12) in Eq. (9), one gets an expression for T p (average plate temperature). After obtaining an expression for T p ; an expression for an average solar cell temperature (T c ) can be evaluated from Eq. (8). Further, following

gc ¼ go ½1  bo ðT c  T o Þ

ð13Þ

For the values of T c (Eq. (8)), the solar cell efficiency (gc ) has been evaluated. Further, an analytical expression for electrical efficiency of a solar cell of PV module can be derived by substituting average solar cell temperature (T c ) expression in Eq. (13). An analytical expression for the solar cell efficiency (gc ) is given by

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

Reflector

Inlet water

Mild steel frame

Foundation

Fig. 7. Photograph of side view of experimental arrangement of fully covered PVT-CPC system.

2

3 9   82 A U t;cp PF 1 qðaC bC sg Þð Aa Þ U t;cp ðasÞ2;eff Aa r > > q ð a b s þ þ 0 0 > C g C Ar F hpf þU L1 ðF hpf þU L1 Þ 7 > >6 > > 6 7 > > > > > I 6 7 > > þ b > > h n   o i 4 5 > > 0

> > U t;cp F hpf PF 2 > > Aa F rm > > 1   ð a s Þ þ PF  qa b s > > 0 0 1 C g C 2;eff A F > ðF hpf þUL1 ÞUl;m > r > > > > h i : > > 0

> > U F h U h F T U t;cp U L1 > > t;cp t;cp pf rm fi pf F rm < = þ U t;ca þ F 0 h þU þ ðF 0 h þU Þ 1  F 0 T a þ ðF 0 h þU Þ

6 6 6 6 6 6 6 6 6 6 go 6 61  bo > > 6 > > 6 > > 6 > > 6 > > 6 > > 6 > > 6 > > 6 > > 4 > :

pf

L1

L1

pf

pf

n

1

U

U t;cp F 0 hpf PF 2

PF

qsg go bo bc ðAAar Þ 1þðF 0 ht;cpþU1 ÞþðF 0 h pf

L1

pf þU L1 ÞU l;m

L1

ð14Þ

o ½1FFrm0  Ib

U t;ca þU t;cp

Following Tiwari et al. [19], the electrical efficiency, gm of PV component has been evaluated as follows:

gm ¼ sg bc gc

ð15Þ

The water temperature at the outlet of fully covered PVT-CPC system (T f ¼ T fo at x ¼ Lr ) from Eq. (12) is as follows:

T fo ¼

7 7 7 7 7 7 7 7 7 7  To7 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 5 > ;

U t;ca þU t;cp

gc ¼

3

   0  PF 2 ðasÞm;eff Ib F U l;m Ar þ T a 1  exp _ f cf U l;m m  0  F U l;m Ar þ T fi exp _ f cf m

Receiver plate temperature and glass temperature (Tp and Tg) Solar intensity (It, Ib and Id) _ f) Mass flow rate (m Open circuit voltage (Voc) and short circuit current (Isc) Load voltage(VL) and current(Isc).

4.1. Methodology

ð16Þ

4. Experimental observations The following hourly parameters were measured during the experiment: i. An ambient temperature (Ta) ii. An inlet and outlet water temperature (Tfi and Tfo1)

iii. iv. v. vi. vii.

The conventional CPC and fully covered PVT-CPC systems with south facing were inclined at an angle equal to latitude (28°350 N, approx 30°). The total (It ) and diffuse radiations (Id ) were measured at the absorber plate. The beam radiation ðIb Þ was measured by the difference between total radiations and diffuse radiations. All the radiations were measured by ‘‘Solarimeter” instrument. This instrument was manufactured by Central Electronics Limited (CEL) Ltd., Sahibabad, U.P, India with 5% accuracy of overall radiation. It has a least count of 20 W/m2. Also, ambient air temperature ðT a Þ; inlet fluid temperature ðT a Þ; absorber plate temperature ðT p Þ;

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glass temperature ðT g Þ; outlet fluid temperatures ðT fo1 Þ were measured by using thermometers and thermocouples. The thermocouples used in the experiment were copper constantan thermocouples. The zeal thermometer was used to calibrate it. The experiments were conducted at constant mass flow rates of 0.10 kg/s. The observations were recorded at an interval of one hour duration. The readings were taken from 9 am to 5 pm. The instantaneous thermal efficiency ðgi Þ for both CPC system and PVT-CPC systems were calculated by the following expression:

gi ¼

_ f cf ðT fo1  T fi Þ m Aa I b

ð17Þ

The power output of the photovoltaic modules were calculated experimentally by using the values of short circuit current (Isc ) and open circuit voltage (V oc ) across the PV module. The short circuit current, open circuit voltage, load current and load voltage were noted by using the AC/DC clamp meter. The power output of the PV module of fully covered PVT-CPC system is given as:

Pm ¼ FF  Isc  V oc

ð18Þ

where FF stands for fill factor which is a constant. P m is the maximum power of the PV module. The fully covered PVT-CPC system performance has been evaluated by calculating the thermal and electrical efficiencies.

gi;exp;m ¼

Pm Aa  I b

ð19aÞ

By substituting P m from Eq. (18), the instantaneous electrical efficiency has been calculated experimentally through the expression given as:

gi;exp;m ¼

FF  Isc  V oc Aa  I b

ð19bÞ

where Aa is the aperture area and Ib is the beam radiation available on the aperture surface. 5. Exergy analysis The overall rate of exergy gain is basically the summation of rate of thermal and electrical exergy. By using the second law of thermodynamics, the overall rate of exergy gain in W is calculated as:

E_ x;ov ¼ E_ x;th þ E_ x;el

ð20Þ

Following Hepbasli [20], the thermal exergy expression of the conventional CPC system [case (A)] and fully covered PVT-CPC system [case (B)] has been given as:

  ðT þ 273Þ _ f cf ðT fo  T fi Þ  ðT a þ 273Þ ln fo E_ x;th ¼ m ðT fi þ 273Þ

ð21Þ

The electrical exergy extracted by the photovoltaic module of the fully covered PVT-CPC system is as follows:

E_ x;el ¼ gm Ib qAa

ð22Þ

6. Overall thermal energy gain The overall thermal energy gain expression from the first law of thermodynamics is as follows:

X

Q_ e;ov ¼

X

Q_ e;th þ

P _ Q e;el nP

ð23Þ

‘n0P ’ is the conversion efficiency factor of thermal power plant. It lies in the range of 0.20–0.40 and its value is 0.38 for high value coal.

7

7. Statistical analysis Following Chapra and Canale [21], a detailed statistical analysis was done to match up the experimental results with the theoretical calculated results. The correlation coefficient (r) has been calculated as:

P P P n XiY i  Xi Y i r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P P P P n X 2i  ð X i Þ2 n Y 2i  ð Y i Þ2

ð24Þ

X i is the theoretical value of ith number of observations, Y i is the experimental value of ith number of observations and n is the total number of noted observations. Root mean square percent deviation (e) has been determined from

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðei Þ2 ðeÞ ¼ n

ð25Þ

here,

ei ¼

  Xi  Y i  100 Xi

8. Results and discussion Fig. 8 shows the experiment readings of beam radiation (Ib) and ambient temperature (Ta). The experimental readings of conventional CPC and fully covered PVT-CPC systems were taken on 3rd and 4th May, 2016 at an interval of an hour. It can be seen from Fig. 8 that for both systems Ib was maximum around 1 pm. Moreover, the ambient temperature varies between 34–41 °C. The mass flow rate for [case (A)] and [case (B)] were set as 0.01 kg/s. The other design parameters of both the cases (A) and (B) are illustrated in Table 1. Tables 2 and 3 specify experimental readings of conventional CPC system and fully covered PVT-CPC system respectively. A program in Matlab 2010 was made to evaluate the theoretical results. It can be noted that both the systems (conventional CPC and fully covered PVT-CPC systems) were exposed to almost same solar radiation and ambient temperature. The hourly variation of theoretically calculated and experimental results for outlet fluid temperatures of case (A) and (B) have been presented in Fig. 9. From the figure it can be observed that the outlet fluid temperature in the case of conventional CPC system lies in the range of 42–57 °C and for fully covered PVT-CPC system there is a decrease in outlet water temperature and it lies in the range of 34.5–42.5 °C. The maximum temperatures rise attained by conventional CPC system was 16.5 °C and it was 3 °C for fully covered PVT-CPC system. This may be due to the reason that in the case of fully covered PVT-CPC system, the PV module has been mounted at the top of glass surface in the conventional CPC system. The PV module generates electrical energy. The thermal energy which is transferred to the absorber plate is the sum of indirect gain from the back of PV module to the plate and direct gain from the non packing area of the PV module. So the thermal energy in the fully covered PVT-CPC was reduced significantly as compared to the conventional CPC system. The statistical analysis was done by using Eqs. (24) and (25) and the results indicated the correlation coefficient (r = 0.99) and root mean square percent deviation (e) as (e = 2.68 and, e = 2.40) respectively. The results show a good conformity between the theoretical and the experimental results. Fig. 10 shows hourly variation of theoretically calculated and experimentally evaluated instantaneous electrical efficiency for fully covered PVT-CPC system. It can be seen from the Fig. 10 that the instantaneous electrical efficiency for fully covered PVT-CPC

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100

1000

Ib (conventional CPC system)

900

90

Ib (fully covered PVT-CPC system)

80

700

70

600

60

500

50

400

40

300

30

200

20

Ta (conventional CPC system)

100

o

Beam radiation (Ib), W/m

2

800

Ambient temperature (Ta), C

8

10

Ta (fully covered PVT-CPC system)

0

0 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hours Fig. 8. Hourly trend of beam radiation (Ib) and ambient temperature (Ta) when experiment was conducted for both conventional CPC system (3rd May, 2016) and fully covered PVT-CPC system (4th May, 2016).

Table 1 Various design parameters of conventional CPC and fully covered PVT-CPC systems. Parameters

Values

Parameters

Values

Aa Ar Lr bo b F0 Kg

1.04 m2 1 m2 1.01 m 1.03 m 0.51 m 0.9680 0.816 W/m2 K 5.7 W/m2 K 5.8 W/m2 K 9.5 W/m2 K 0.9 4.7 W/m2 K 4179 J/Kg K 0.15

Ki Kp Lg Li Lp PF c hpf

0.166 W/m K 64 W/m K 0.003 m 0.100 m 0.002 m 0.9842 100 W/m2 K 0.84 0.84 0.9 4.8 W/m2K 0.95 0:89 0.01 kg/s

hi hi1 ho

ap

U l;c cf

go

q q0 ac

U t;pa

sg

bc _f m

lated by the help of Eq. (19b). It was observed that the instantaneous electrical efficiency values have been in the range of 6– 10% as well as theoretical trend has been followed in a similar manner. The values of correlation coefficient (r) and root mean square percent deviation were noted as r = 0.99 and e = 7.52 and it indicated a fair agreement between theoretically calculated and experimentally measured values. Fig. 11 shows the thermal characteristic curve in which instantaneous thermal efficiency h i have been plotted with respect to ðT mIT a Þ : The characteristic equab

tions have been developed by linear regression analysis. Following are the characteristic equations for the instantaneous thermal efficiency for various cases: For [case (A)] conventional CPC system

gi ðin fractionÞ ¼ 0:74  3:79

  Tm  Ta Ib

ð26Þ

For [case (B)] fully covered PVT-CPC system system decreases over the period (9:00–12:00 h), even when the solar radiation increases during this period. With an increase in solar radiation the solar cell temperature also rises. At elevated temperatures, the electrical energy losses occur as there is a collision of the electrons in the depletion region of a solar cell. Therefore, the electrical efficiency (gm ) of a PV module reduces. From the Eq. (13) it can be observed that when average solar cell temperature (T c ) is increased the solar cell efficiency (gc ) decreases. The experimental instantaneous electrical efficiency (ɳm) was calcu-



gi ðin fractionÞ ¼ 0:31  5:10

Tm  Ta Ib

 ð27Þ

For PVT system (without CPC system)



gi ðin fractionÞ ¼ 0:55  4:30 where, T m ¼

h

Tm  Ta Ib

 ð28Þ

i

ðT fo þT fi Þ 2

Table 2 Hourly variation of Ta, Tfi, Tfo1, It, Id, Ib for fully covered PVT-CPC system for a typical day (4th May, 2016). S. no.

Time (hr)

Ta (°C)

Tfi (°C)

Tp (°C)

Tfo (°C)

It (W/m2)

Id (W/m2)

Ib (W/m2)

Isc (A)

Voc (V)

IL (A)

VL (V)

1 2 3 4 5 6 7 8 9

9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

34 35 36.5 39 40.5 41 39 38.5 38

33.5 34.5 36.0 38.5 40.0 40.5 39 39 38

38 44.1 49.2 50.9 53.7 54 54.2 54.9 53.1

34.5 37 38 40.0 42.5 42.5 42 40.5 40

610.90 775.60 890.50 949.00 950.00 887.53 762.00 582.10 371.00

99.00 127.67 100.50 118.00 153.00 179.00 139.00 109.00 91.00

511.90 647.93 790.00 831.00 797.00 708.53 623.00 473.10 280.00

2.2 2.3 2.4 2.4 2.5 2.4 2.3 2.2 2.1

19.25 19.09 18.73 18.56 17.43 17.23 17.36 18.12 18.40

0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2

15.72 15.69 15.48 15.39 15.73 15.56 15.43 15.33 15.23

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx Table 3 Hourly variation of Ta, Tfi, Tfo1, It, Id, Ib for conventional CPC system for a typical day (3rd May,2016). S. no.

Time (hr)

Ta (°C)

Tfi (°C)

Tfo (°C)

It (W/m2)

Id (W/m2)

Ib (W/m2)

1 2 3 4 5 6 7 8 9

9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

34 35.5 37 39 40 41 38.5 38 38

33 34 36 38 40 41.5 39 38.5 38

42 46 52 54.5 56 57 52.8 46.6 45

608.84 776.25 888.40 948.32 950.82 886.51 761.39 580.81 371.43

98 125 100 115 150 175 136 100 85

510.84 651.25 788.40 833.32 800.82 711.51 625.39 480.80 286.43

9

The values of gain factor and loss term for different systems have been given in Table 4. The instantaneous thermal efficiency of conventional CPC system was more as compared to the fully covered PVT-CPC system and PVT system (without CPC system) owing to maximum gain factor and minimum loss term. The Fig. 12 shows the hourly trend of theoretically calculated and experimentally evaluated absorber plate temperature, Tp (°C) for fully covered PVT-CPC system. It can be noted from the above figure that the absorber plate temperature varied in the range of 38– 55 °C which was higher than the outlet fluid temperature. The losses were also less as the fluid (water in this case) flows below the plate. The small increase in absorber plate temperature over the period (12.00–17.00) when the solar radiation decreases over

60

o

Outlet fluid temperature Tfo1, C

50

40

30

20

Theoretical [ e = 2.68, r = 0.99 ] [case(A)] rd Experimental, 3 May 2016, New Delhi [case(A)] Theoretical [ e = 2.40, r= 0.99 ] [case(B)] th Experimental, 4 May 2016, New Delhi [case(B)]

10 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hour Fig. 9. Hourly variation of theoretically calculated and experimentally evaluated outlet fluid temperature Tfo1, °C for conventional CPC system and fully covered PVT-CPC system.

Instantaneous electrical efficiency (ηm ), %

10 9

Fully covered PVT-CPC system

8 7 6 5 4

e=7.52 ; r = 0.99

3 2

Theoretical th Experimental (4 May 2016, New Delhi)

1 0 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hour Fig. 10. Hourly trend of theoretically calculated and experimentally evaluated instantaneous electrical efficiency for fully covered PVT-CPC system.

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

Instantaneous thermal efficiency ηi, in fraction

1.0

Conventional CPC system Fully covered PVT-CPC system PVT system (without CPC)

0.8

0.6

0.4

0.2

0.0 0.005

0.010

0.015

0.020 o

0.025

0.030

2

(Tm-Ta)/Ib, Cm /W Fig. 11. Thermal characteristic curve for conventional CPC system, fully covered PVT-CPC system and PVT system (without CPC).

Table 4 Values of gain factor and loss coefficient for different systems. System

Gain factor

Loss term

Conventional CPC system [case (A)] PVT-CPC system PVT-CPC system [case (B)] PVT system (without CPC system)

0.74 0.31 0.55

3.79 5.10 4.30

this period was due to the (i) lower value of solar radiation available and (ii) reduced top loss coefficient. The values of correlation coefficient and the root mean square percent deviation were

r = 0.99 and e = 3.15 which showed a good agreement between theoretically calculated and experimentally evaluated values. The Fig. 13 shows the monthly variation of thermal exergy gain, overall exergy gain as well as an overall thermal energy gain in kW h for cases (A) and (B). The output daily thermal exergy has been calculated by using Eq. (21). Further, the output exergy for every month has been calculated by multiplying type of days (a– d) with daily thermal exergy output and adding them altogether. Similarly, the monthly overall exergy gain and monthly overall thermal energy output has been evaluated by the help of Eqs. (20) and (23). The maximum and minimum overall thermal energy

60

o

Absorber plate temperture, C

50

40

30

Theoretical th Experimental (4 May, 2016) r = 0.99 e = 3.15

20

Fully covered PVT-CPC system 10

0 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hour Fig. 12. Hourly trend of theoretically calculated and experimentally evaluated absorber plate temperature, Tp (°C) for fully covered PVT-CPC system.

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D. Atheaya et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

140

Overall exergy gain, kWh

120

thermal exergy gain of conventional CPC system, [case (A)] overall exergy gain of fully covered PVT-CPC water system, [case (B)] overall thermal energy gain of fully covered PVT-CPC system, [case (B)]

100 80 60 40 20 0 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month of year Fig. 13. Monthly variation of thermal exergy gain, overall exergy gain and overall thermal energy gain for [case (A)] and [case (B)].

gain of fully covered PVT-CPC system was in the April and February month. Also from the figures it can be seen that the thermal exergy gain of conventional CPC system [case (A)] was maximum for the summer month of April and minimum in the winter month of December. Also, it can be observed from the Fig. 13 that overall exergy gain was highest in the month of May due to high solar radiation values.

 U t;pa ¼

F r1 ¼

1 Lg 1 þ þ hi K g ho

1

 þ

In this research paper, a conventional CPC system [case (A)] and a fully covered PVT-CPC system [case (B) have been set up and the theoretical modeling has been done to analyze the systems. An experimental investigation was conducted on both the systems. The following conclusions have been drawn from the experimental validation of conventional CPC system and fully covered PVT-CPC system. (i) The validation results indicate a close match between theoretical values and experimental values. (ii) In case of end user priority only for thermal energy generation, the conventional CPC system is the best. (iii) The fully covered PVT-CPC system is preferred where electricity generation along with relatively low outlet temperature is the end user’s priority. In addition, it was also noted that overall maximum thermal energy gain (from Fig. 13) was found to be 118 kW h for the month of April.

1

  0  _ f cf m F U l;c Ar 1  exp _ f cf U l;c Ar m

Constants for Eqs. (5) and (9) are

ðasÞ2;eff ¼ qap s3g ð1  bC Þ

9. Conclusions

Li 1 þ K i hi1

PF 1 ¼

U t;cp U t;cp þ U t;ca

U L1 ¼

U t;ca  U t;cp ðU t;ca þ U t;cp Þ

Aa ; Ar

ðasÞ1;eff ¼ qðaC bC s2g  gm Þ

Aa Ar

ðasÞm;eff ¼ ðasÞ2;eff þ PF 1 ðasÞ1;eff   Aa ¼ ðasÞ2;eff þ PF 1  qðaC bC s2g  gm Þ Ar PF 2 ¼

hpf ; F 0 hpf þ U L1

U l;m ¼

U L1  hpf F 0 hpf þ U L1

ðasÞm;eff ¼ ðasÞ2;eff þ PF 1  ðasÞ1;eff

References Appendix A The expression for various constants used in Eqs. (1) and (2) are

ðasÞc;eff ¼ qap sg U l;c ¼

Aa Ar

hpf  U t;pa ðF 0  hpf Þ þ U t;pa

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