of fully covered concentrated photovoltaic thermal (PVT) water collector

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Instantaneous efficiency and water collector ... lized for water heating in hot water systems, swimming pools as ... tion of electricity and hot water production.
Solar Energy 146 (2017) 180–190

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Solar Energy journal homepage: www.elsevier.com/locate/solener

Annual performance evaluation (energy and exergy) of fully covered concentrated photovoltaic thermal (PVT) water collector: An experimental validation Rohit Tripathi ⇑, G.N. Tiwari Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

a r t i c l e

i n f o

Article history: Received 12 December 2016 Received in revised form 17 February 2017 Accepted 21 February 2017

Keywords: PVT Compound parabolic concentrator Instantaneous efficiency and water collector

a b s t r a c t In the present communication, an experimental set up of single unit of fully covered concentrated photovoltaic thermal (CPVT) collector is designed and fabricated to achieve thermal as well as electrical gain. This system is installed at the rooftop of the building of Centre for energy studies, IIT Delhi, India. Here, semitransparent PV module is used to cover the collector. The monthly observations are taken in clear sky day condition for (September 2015 to August 2016). Two cases are considered on the basis of receiver rotation according to sun movement, to study the annual behaviour of present system, case (i): fixed position and case (ii): manual maximum power point tracking technique (M-MPPT). The manual tracking is adopted for 3 times/day in a 3 h interval (09.00–12.00–15.00 h). Consecutive days are selected for taking observation for both cases (i-ii) in each month throughout the year. The validation has been found to be fair agreement between theoretical and experimental results by calculating correlation coefficient (r) and error (e). It was found that case (ii) is dominating for overall thermal energy as well as exergy gain. The annual net thermal energy and exergy, obtained by case (ii), were 1.25 and 1.19 times higher than for case (i). Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, solar energy has been strongly promoted as a viable energy source. One of the simply available and most direct applications of solar energy is the convergence of solar radiation into heat and electrical power. Solar radiation can be widely utilized for water heating in hot water systems, swimming pools as well as solar fluids for power generation by steam turbine. Solar water heating systems consists of mainly two parts: solar collector and storage tank. Solar collector collects solar radiation from sun and converts this radiation into heat by using a fluid: water and electrical power. Solar heating system can either be active or passive but active systems are found common in use. Active systems can work with pump or motor to circulate the fluid from collector to storage tank. Wolf (1976) and Kern and Russel (1978) have identified the basic theoretical concepts of PVT collector. Solar collector are known as PVT collector which consists PV cells or panel and thermal absorber. PVT collectors further identified mainly in concentrated PVT and flat plate PVT collector (Coventy, 2005; Rosell et al., 2005). Many scientists and researchers reported the different ⇑ Corresponding author. E-mail address: [email protected] (R. Tripathi). http://dx.doi.org/10.1016/j.solener.2017.02.041 0038-092X/Ó 2017 Elsevier Ltd. All rights reserved.

types of configuration of PVT collector in recent studies (Charalambous et al., 2007; Zondag, 2008; Chow, 2010; Ibrahim et al., 2011). Number of studies for PVT collector have been accomplished on a fluid: water (Tripanagnostopoulos et al., 2002; Zondag et al., 2003; Chow et al., 2006) and air (Sopian et al., 1996; Hegazy, 2000; Tiwari and Sodha, 2006). On overall exergy efficiency point of view, the best electricity performance obtained for unglazed PVT collectors (Fraisse et al., 2007; Chow et al., 2009). Chow et al. (2009) validated the overall energy and exergy analysis of PVT collector by experimental study. It is concluded that overall exergy efficiency of water-cooled unglazed PVT collector was usually higher than for a glazed PVT collector. Tiwari et al. (2009) have presented the overall energy and exergy evaluation of a PVT collector. It is identified that the overall exergy and thermal efficiency has found maximum at the hot water withdrawal flow rate of 0.006 kg/s. Fudholi et al. (2014) have evaluated the energy of a PVT water collector with 500–800 W/m2 solar radiation range. It has observed that 68.4% overall efficiency of PVT water collector has obtained at flow rate 0.041 kg/s and 800 W/m2 solar radiation. Bouraiou et al. (2015) investigated the performance of PV module which installed in desert, to analyze the impact of climatic parameters. The experimental results validated by theoretical results to consider parameters like Imax, Vmax, Voc, Pmax, Isc.

R. Tripathi, G.N. Tiwari / Solar Energy 146 (2017) 180–190

181

Nomenclature

ac

m_ f

sg

Cf b0 Lr La Lrc ; Lrm Lac ; Lam

gc gm

b bo Arm Arc Aam Aac Lg Kg Ib ðtÞ Ta Li Ki ðasÞeff F0 Tc Tp Lp Kp Tfi Tf Tfom

go

absorptivity of the solar cell mass flow rate of water (kg/s) transmissivity of the glass specific heat of water (J/kg K) temperature coefficient of efficiency (K1) total length of receiver area (m) total length of aperture area (m) length of receiver covered by glass or PV module (m) length of aperture covered by glass or PV module (m) solar cell efficiency PV module efficiency breath of receiver (m) breath of aperture (m) area of receiver covered by PV module (m2) area of receiver covered by glass (m2) area of aperture covered by PV module (m2) area of aperture covered by glass (m2) thickness of glass cover (m) thermal conductivity of glass (W/m K) beam radiation (W/m2) ambient temperature (°C) thickness of insulation (m) thermal conductivity of insulation (W/m K) product of effective absorptivity and transmittivity collector efficiency factor solar cell temperature (°C) absorption plate temperature (°C) thickness of absorption plate (m) thermal conductivity of absorption plate (W/m K) inlet water temperature (°C) water temperature (°C) outlet water temperature at the end of PV module (°C) efficiency at standard test condition

Tan et al. (2014) reported the characteristics parameters of the PV cell for concentrating and non -concentrating solar radiation respectively, tested experimentally. The experimental study of the two-stage photovoltaic thermal system was established with a 1.8 m2 mirror PVT stage and a 15 m2 mirror heating stage and 1.8 m2 mirror PVT stage and 30 m2 mirror heating stage. Kunnemeyer et al. (2014) and Li et al. (2015) carried the performance of a V-trough photovoltaic thermal concentrator and concluded that better electrical output could be achieved. Mohsenzadeh and Hosseini (2015) proposed a PVT with a combination of a booster diffuse reflector and vacuum tube for generation of electricity and hot water production. A silicon monocrystalline PV module was used to appropriate reflectors in order to increase insolation in conjunction with a closed loop cooling facility to efficient extract the PV panel’s heat. Tripathi et al. (2016a, 2016b, 2016c, 2016e, 2016f) and Tripathi and Tiwari (2016) proposed thermal modelling and the temperature dependent electrical efficiency for partially covered N number of PVT-compound parabolic concentrator connected in series. The annual overall energy and exergy have evaluated for N-PVT-CPC collector connected in series by considering all type of whether condition (a-d type) and compared with the output of N-CPC, NPVT and N-FPC-CPC for New Delhi, India. Daily overall energy and exergy have been evaluated for partially covered N-PVT-CPC collector at constant collection temperature mode. Atheaya et al. (2016) validated the energy and exergy fully covered PVT-CPC collector. They proposed two cases: case (i): convectional compound parabolic concentrator collector and case (ii): fully covered NPVT-CPC collector.

Tfoc TfomN TfoN 0

hi ho hi Utc;a Utc;p hpf Utp;a UL;m UL;c PF1 PF2 PF3 PFc b

outlet water temperature at the end of portion covered by glass (°C) outlet water temperature at the end of Nth PV module (°C) outlet water temperature at the end of Nth PVT-CPC water collector (°C) heat transfer coefficient from bottom of PVT to ambient (W/m2 K) heat transfer coefficient from top of PVT to ambient (W/ m2 K) heat transfer coefficient for space between the glazing and absorption plate (W/m K) overall heat transfer coefficient from cell to ambient (W/m2 K) overall heat transfer coefficient from cell to plate(W/ m2 K) heat transfer coefficient from blackened plate to water (W/m2 K) overall heat transfer coefficient from plate to ambient (W/m2 K) overall heat transfer coefficient from module to ambient (W/m2 K) overall heat transfer coefficient from glassing to ambient (W/m2 K) penalty factor due to the glass covers of module penalty factor due to plate below the module penalty factor due to the absorption plate for the glazed portion penalty factor due to the glass covers for the glazed portion packing factor of the module

In present communication, the comparative study for manual tracking and non-tracking (fixed) process has been performed experimentally for fully covered PVT-CPC water collector, at clear day condition, New Delhi, India. 2. System description Atheaya et al. (2016) have presented a set-up of PVT-CPC water collector with withdrawn of water in open loop. Further, they considered two cases namely: case (a): conventional CPC collector and case (b): fully covered PVT-CPC collector. Here, only fully covered (semitransparent PV module) concentrated PVT collector has been considered by having two cases as case (i): fixed (Non-MPPT) fully covered concentrated PVT collector and case (ii): manual maximum power point tracking (M-MPPT) fully covered concentrated PVT collector. An experimental setup was installed at the roof top of the building of Centre for energy studies, IIT Delhi. It was inclined at 28.37° of latitude for New Delhi, for maximum output throughout the year. This experiment was done for no water withdrawn. The outlet water from the collector the water tank and it was a closed loop system procedure with forced mode, for higher storage water temperature. 2.1. Fixed concentrated PVT collector [case (i)] A schematic diagram of fix fully covered PVT-CPC collector has been shown in Fig. 1. A semitransparent PV module which area has 0.52 m2 (102 cm  52 cm) was fix just above the tube-in-plate col-

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Tfo PVC water tank

Insulated water pipes Floating valve

Cast iron tank stand

Tout,tank=Tfi DC motor

Tfo

PV module

Insulator Stand Inlet, Tfi Fig. 1. Experimental setup for fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector in forced mode.

lector in insulated aluminum channel box. It was mounted on an iron frame whose legs are permanently fixed on the floor. The tube in plate is made of copper with black chrome painted to increase absorptivity factor which was placed below the semitransparent PV module. The internal diagram of collector has been shown in Fig. 2. The glass wool (insulator) was also set below the tube in plate to reduce the bottom thermal losses. It has one inlet, known as Tfi and one outlet known as Tfo. The reflectors or CPC are made of stainless steel for high reflectivity factor. These CPC were installed on the aluminum channel box with supporting of three mild steel trips through bolts. A PVP water tank was placed on iron stand at height to the system due to proper water circulation. Water capacity of the tank is 25 L which has a floating valve to regulate the flow of water or to make constant flow rate. The tank outlet is considered as system inlet (Tfi) and the outlet of system (Tfo) as inlet to the water tank except very first hour to the operation. It is just a close loop system and no withdrawn water from tank. The experimental setup of present system has been shown in Figs. 3a and 3b [case (i)] and Fig. 4b [case (ii)].

(a) Fully covered PVT-CPC water collector is supposed in quasi steady state. (b) Ohmic losses in semitransparent PV modules are neglected. (c) Heat capacity of insulation, absorber and PV cell materials, etc. are neglected. (d) There is no temperature gradient across thickness of PV module, insulation and glass materials. (e) Heat conduction is one directional only. 3.1. Energy balance equation for semitransparent (glass to glass) PV module

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

ð1Þ

From Eq. (1), one can find solar cell temperature (T c ) as follows:

Tc ¼

ðasÞ1;eff Ib þ U tc;a T a þ U tc;p T p U tc;a þ U tc;p

ð2Þ

3.2. Energy balance for absorber tube in plate below the PV module 2.2. Manual-MPPT concentrated PVT collector [case (ii)] The procedure of manual MPPT of PVT-CPC collector has been shown in Fig. 4a. Here, collector configuration is same as previous case (i). But the observation was taken as three angles in one day with different timings. First observation was taken with collector to solar radiation angle, was kept 45° in 09.00–11.00 h, second was on 90° in 12.00–14.00 h and third was on 135° in 15.00– 16.00 h. The observation could be taken in 17.00 h but shadow of other systems, who were already installed on roof top, was fallen on the collector. MPPT technology is applied to enhance the input solar energy which produces the maximum overall energy or exergy. The experimental set up of manual MPPT PVT-CPC collector has been shown in Fig. 4b (see Table 1).

qap s2g ð1  bc ÞIb Aa þ U t;cp ðT c  T p ÞAr ¼ F 0 hpf ðT p  T f ÞAr þ U t;pa ðT p  T f ÞAr

ð3Þ

From Eqs. (2) and (3), one can get an expression for as

Tp ¼

½ðasÞ2;eff þ PF 1 ðasÞ1;eff Ib þ U L2 T a þ F 0 hpf T f ðU L2 þ F 0 hpf Þ

ð4Þ

Expressions for ðasÞ2;eff ; ðasÞ1;eff , PF 1 ; U L2 ; hpf ; U tp;a ; U tc;a and U tc;p have been available in Appendix A. 3.3. Energy balance for flowing water as fluid below the absorber plate

_ f cf m

dT f dx ¼ F 0 hpf ðT p  T f Þbdx dx

3. Thermal modelling

from Eqs. (2) and (4), Eq. (5) can be rewritten as follows:

Certain assumptions have been taken to write the basic energy balance equations for proposed systems.

_ f cf m

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

ð5Þ

ð6Þ

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Sun

Absorber

Air gap Solar cell

Thermal

Water tubes

Fig. 2. Internal diagram for collector of fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector.

Fig. 3a. Actual photograph of experiment set up (front view) for fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector in forced mode [case (i)].

Further, Eq. (6) has been solved with the help of Eqs. (2) and (4). The solution of the above equation can be achieved by using initial condition i.e. (T f jx¼0 ¼ T fi ) as

 Tf ¼

PF 2 ðasÞm;eff Ib þ Ta U L;m



 1  exp

0

bF U L;m x _ f cf m



 þ T fi exp

0

bF U L;m x _ f cf m

 ð7Þ

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Fig. 3b. Actual photograph of experiment set up (side and top view) for fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector in forced mode [case (i)].

12.00 to 14.00 hr

Fig. 4a. Diagram (front view) of manner of experiment for manual MPPT for fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector [case (ii)] (from 09.00 h -12.00 h-15.00 h).

Fig. 4b. Actual photograph of experiment set up (front view) for fully covered photovoltaic thermal-compound parabolic concentrator (PVT-CPC) collector in forced mode [case (ii)] (right to left - at 09.00 h [1] -12.00 h [2]-15.00 h [3]).

And the outlet temperature of fully covered PVT-CPC collector has been evaluated Tf = Tfo1 at x = Lr       0 0 PF 2 ðasÞm;eff Ib bF U L;m Lr bF U L;m Lr Tf0 ¼ þ T a 1  exp þ T fi exp _ f cf _ f cf U L;m m m



PF 2 ðasÞm;eff Ib þ Ta U L;m



 1  exp

Ar F 0 U L;m _ f cf m



 þ T fi exp

Ar F 0 U L;m _ f cf m

Q_ uthe ¼ m_ f cf ðT fo  T fi Þ

ð9Þ

and put the value of Tfo from Eq. (8) in Eq. (9). One can get the expression as following

Or Tf 0 ¼

The rate of useful thermal energy gain from fully PVT-CPC water collector has been calculated by following equation, with help of Eq. (8).

 ð8Þ

Q_ uthe ¼ Ar F rm ½Ib PF 2 ðasÞm;eff  U L;m ðT fi  T a Þ

ð10Þ

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R. Tripathi, G.N. Tiwari / Solar Energy 146 (2017) 180–190 Table 1 Values of design parameters of fully covered PVT-CPC collector [case (i) and case (ii)]. Ar ¼ 1 m2 Arm ¼ 0:25 m2 Arc ¼ 0:75 m2 Aa ¼ 2 m2 Aam ¼ 0:5 m2 Aac ¼ 1:5 m2 cf ¼ 4179 J/kg K for water m_ f = 0.01 kg/s F rm ¼ 0:8110 m2 K g ¼ 0:816 W/m °C Lg ¼ 0:003 m K i ¼ 0:166 W/m °C Li ¼ 0:100 m K p ¼ 6 W/m °C Lp ¼ 0:002 m U L1 ¼ 3:47 W/m2 °C U L;m ¼ 7:87 W/m2 °C U tc;a ¼ 9:17 W/m2 °C U Lc ¼ 4:7 W/m2 °C

U tc;p ¼ 5:58 W/m2 °C U tp;a ¼ 4:8 W/m2 °C PF 1 ¼ 0:3782 PF 2 ¼ 0:9512 PF c ¼ 0:9842 hpf ¼ 100 W/m2 hi ¼ 5:7 W/m2

For getting T f (average fluid temperature) the above Eq. (7) has been integrated as following

1 T f ¼ Lr

Z

Lr

T f dx 0

And

0

hi ¼ 5:8 W/m2 ho ¼ 9:5 W/m2 q = 0.84 sg ¼ 0:95 ac ¼ 0:9 bc ¼ 0:89 ap ¼ 0:8 F 0 ¼ 0:9680 F rc ¼ 0:8693 m2 FF ¼ 0:8 go ¼ 0:15 Tube diameter = 0.0125 m

T f ¼ Ib

       PF 2 ðasÞm;eff Ar F rm Ar F rm Ar F rm 1 þ T þ T 1  a fi U l;m F0 F0 F0

where Ar F rm ¼

_ f cf m U L;m

ð18Þ

h  0 i F U L;m Ar . 1  exp _ c m f f

By substituting the average fluid temperature in Eqs. (4) and (2) to obtain the average plate temperature (T p ) and solar cell temperature (T c ) respectively. The analytical expression for the temperature dependent electrical efficiency of solar cells of PVT-CPC water collectors has been evaluated by following expression

gc ¼ g0 ½1  b0 ðT c  T 0 Þ And, the rate of thermal exergy from fully covered PVT-CPC water collector has been obtained following expression as

ðT fo þ 273Þ E_ xth ¼ m_ f cf ðT fo  T fi Þ  m_ f cf ðT a þ 273Þln ðT fi þ 273Þ

ð11Þ

where m_ f = mass flow rate of water, cf = specific heat of water, T fi = inlet water temperature and Ta = ambient air temperature. The instantaneous thermal efficiency for both cases have been calculated by following expression

gith ¼

Q_ uthe I b  Aa

ð12Þ

In Eq. (10), if Tfi = (Tw in tank) for every hour. Then the rate of useful thermal energy for PVT-CPC collector as following

Q_ u;the ¼ Ar F rm ½Ib PF 2 ðasÞm;eff  U L;m ðT w  T a Þ

ð13Þ

A small part of thermal energy available from hot water from outlet of fully covered PVT-CPC collector increases the temperature of water inside the tank and some thermal energy was lost to the ambient. The energy balance for the storage water tank without withdrawn of water is given as following:

dT w Q_ u;the ¼ Mw C w þ ðUAÞtank ðT w  T a Þ dt

ð14Þ

To simplify the above Equation, one can rewrite the expression as

dT w þ aT w ¼ f ðtÞ dt where a¼

f ðtÞ ¼ Mw1C w ½F rm PF 2 ðasÞm;eff Ib þ ðF rm U L;m þ ðUAÞtank Þ

ð15Þ and

ðF rm U L;m þðUAÞtank Þ . Mw C w

The solution of Eq. (15) with initial condition t = 0, Tw = Two as follows

Tw ¼

f ðtÞ ð1  eat Þ þ T wo eat a

ð16Þ

From Eqs. (16)–(18), one can obtain the expression for water temperature in storage tank as following     Ar F rm Ib PF 2 ðasÞm;eff ððAr F rm U L;m þ ðUAÞtank ÞtÞ þ T a 1  exp Tw ¼ Mw C w ðAr F rm U L;m þ ðUAÞtank Þ   ððAr F rm U L;m þ ðUAÞtank ÞtÞ þ T fi exp ð17Þ Mw C w

ð19Þ

where g0 is efficiency at standard test condition, T c is the average solar cell temperature of PVT-CPC water collector and b0 is temperature coefficient of solar cell efficiency. The above Eq. (19) can further be rewritten following as:  n  o 3 3 2 2 2 33 qsg ac bc AAar þ UL2UþFtc;p0 hpf ðasÞ2;eff þPF 1 qac sg bc AAar þ 7 6 6I 6 77 6 n  oi

57 6 6 b 4 U tc;p F 0 hpf PF 2 h 77 7 6 Aa 6 6 77 6 1 ArFF0rm 7 _ ðU þF 0 h Þ ðasÞ2;eff þ PF 1 qac sg bc Ar 6 1 6 77 7 6 U l;m L2 pf 6 6 77 7 g0 6 1b T h i 0 77 0 6U tc;p þU tc;a 6 0



7 6 U F h U U tc;p tc;p L2 pf Ar F rm 6 6 77 7 6 U þ þ 1 þT 0 0 0 a tc;a U L2 þF hpf ðU L2 þF hpf Þ F 6 6 77 7 6 4 4 55 5 4 h i U tc;p F 0 hpf Ar F rm þT fi ðU þF 0 h Þ L2 pf h  n  o  ii gc ¼ h 0 g 0 b0 I b qsg bc AAar þ ðU UþFtc;p0 h Þ PF 1 qsg bc AAar þ U UðUtc;p FþFhpf0 h Þ PF 2 qsg bc 1 Ar FF0Rm 1 ðU tc;a þU tc;p Þ 2

L2

pf

L;m

L2

pf

ð20Þ

Now, from Eq. (20), the temperature dependent electrical efficiency of PV modules of PVT-CPC collector is following as

gm ¼ sg bc gc

ð21Þ

And, with the help of Eq. (21), the rate of useful electrical gain from PVT-CPC collector has been solved by following equation

Q_ xele ¼ qAa Ib gm

ð22Þ

But,

Q_ xele;net ¼ Q_ xele  Pw

ð23Þ

where Pw = power consumed by motor. The power consumed by the DC motor or pump Pw has been determined by the following expression (Mishra and Tiwari, 2013).

Pw ¼

_ f gH m

gw

ð24Þ

_ f = flow rate in kg/s, g = acceleration for gravity in m/s2, where m H = head height of tube in plate in meters (m) and gw = motor efficiency in percentage. The rate of overall thermal energy of fully covered PVT-CPC collector can be obtained from following expression. Overall thermal energy = thermal energy + thermal equivalent of electrical energy.

Q_ xele;net Q_ ov erall;the ¼ Q_ uthe þ 0:38

ð25Þ

Exergy of fully covered PVT-CPC water collector system will be calculated based on second law of thermodynamics. With the help of Eqs. (11) and (23), an overall exergy can be obtained as follows

E_ xu ¼ E_ xth þ Q_ xele;net

ð26Þ

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Table 2 Least count of measuring instruments used in experimental study. S. No.

Measuring parameters

Instruments

Least count (units)

1. 2. 3. 4. 5. 6. 7. 8.

Solar intensity Ambient air temperature Water outlet temperature Tank’s water temperature Solar module temperature Wind velocity Open circuit voltage Short circuit current

Solar meter Thermometer Thermometer Thermometer Thermometer Anemometer Clamp meter Clamp meter

20 (W/m2) 1.0 (°C) 1.0 (°C) 1.0 (°C) 1.0 (°C) 0.1 (m/s) 0.1 (v) 0.1 (A)

3.4. Experimental details The experimental set up was installed on the roof top of Centre for energy studies, Indian Institute of Technology Delhi, New Delhi, India. It was inclined at latitude angle of New Delhi (28°350 ). The observation have been noted down in clear sky day condition only (type ‘a’). The hourly observation was taken from 9.00 h to 16.00 h in a day for both cases in forced mode (closed loop) and it was consecutive day’s observation for cases (i-ii). Following parameters values were noted during experiments.          

Ambient air temperature (Ta) Solar beam intensity, (Ib) Inlet fluid (water) temperature, (Tfi) Mass flow rate, (mf) Outlet fluid (water) temperature, (Tfo) Solar cell temperature or module temperature, (TC) Short circuit current, (ISC) Open circuit voltage, (VOC) Load voltage, (VL) Load current (IL)

The solar radiation was measured by ‘Solar meter’ only. The ambient temperature, solar cell temperature, inlet and outlet temperature of fluid and water temperature were measured by thermometers. The experiment was observed at constant flow rate of water which is 0.01 kg/s throughout the observations. Open circuit voltage, short circuit current, load voltage and load current (load: DC motor) were measured by clamp meter. The least count of measuring instruments has been given in Table 2.

Fig. 5a. Hourly variation of beam radiation for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

Fig. 5b. Hourly variation of ambient air temperature for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

The power output of the photovoltaic modules were calculated experimentally by using the value of short circuit current (Isc) and open voltage (Voc) across the PV module. The output power of PV module of fully covered PVT-CPC collector is given as following:

Pm ¼ FF  Isc  V oc

ð27Þ

where FF is fill factor (FF = 0.55). Pm is the maximum power of the module. Then, the instantaneous electrical efficiency has been evaluated by following expression.

giele ¼

Pm I b Aa

Or

giele ¼

FF  Isc  V oc I b Aa

ð28Þ

where Aa is the aperture area.

Fig. 6. Hourly variation of outlet water temperature from the collector for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

R. Tripathi, G.N. Tiwari / Solar Energy 146 (2017) 180–190

Fig. 7. Hourly variation of water temperature in the tank for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

Fig. 8. Hourly variation of solar cell temperature for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

187

Fig. 10a. Hourly variation of experimental instantaneous thermal efficiency for cases (i-ii) for clear sky condition in month of September.

Fig. 10b. Hourly variation of experimental instantaneous electrical efficiency for cases (i-ii) for clear sky condition in month of September.

4. Statistical analysis Following Chapra and Canale (2006), a detailed statistical analysis was done to validate 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 ffi r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 P P 2ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n X i  ð X i Þ n Y 2i  ð Y i Þ2

ð29Þ

where Xi is the theoretical value of the ith number of observation, Yi is the experimental value of ith number of observation and n is the total number of noted observations. Root mean square percent deviation (e) has been determined from following expression

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðei Þ2 e¼ n Fig. 9. Hourly variation of temperature dependent electrical efficiency of PV module for theoretical and experimental for cases (i-ii) for clear sky condition in month of September.

where ei ¼



X i Y i Xi

ð30Þ

 100.

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Fig. 11. Monthly variation of beam radiation for theoretical and experimental for cases (i-ii) for clear sky condition in a year.

Fig. 12a. Monthly variation of experimental electrical gain for cases (i-ii) for clear sky condition in a year.

Fig. 12b. Monthly variation of experimental overall thermal energy gain for cases (i-ii) for clear sky condition in a year.

Fig. 12c. Monthly variation of experimental overall exergy for cases (i-ii) for clear sky condition in a year.

5. Methodology In order to validate the outlet fluid temperature, water temperature in storage tank, solar cell temperature, instantaneous thermal and electrical efficiency, electrical efficiency of PV module, an overall thermal energy and exergy for fully covered PVT-CPC water collector, following methodology has been adopted: The observations have been taken in hourly basis for ambient air temperature, inlet fluid temperature, outlet fluid temperature, solar cell temperature and water temperature in storage tank. After getting temperatures, electrical efficiency of PV module, the thermal energy and exergy, overall thermal energy and exergy were calculated by Eqs. (10), (11), (23), (25) and (26).

6. Results and discussion The first observation has been taken in clear sky day from 09.00 h to 16.00 h on 21 and 22 September 2015 at New Delhi,

India for case (i) and case (ii), respectively. One clear day from each month has been selected for taking observations for both cases. The observations have been continued till August 2016 for one year. The hourly variation of beam radiation and ambient air temperature of theoretical and experimental values has been shown in Figs. 5a and 5b. Here, it is seen that the beam radiation is higher for case (ii) than case (i) due to manual maximum power point tracking technique. Hourly variation of outlet water temperature (Tfo) from the collector, water temperature in the tank (Tw) and solar cell temperature (Tc) have been shown for theoretical and experimental values for cases (i-ii) in Figs. 6–8. It is clear to see in the figure that the maximum outlet temperature has been obtained at 14.00 h and it is found higher for case (ii) than case (i), due to higher input beam radiation. The water temperature in tank has been increased gradually hour by hour and reached maximum at last hour, due to

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hpf U L2 hpf U tp;a ; U L;c ¼ 0 ; F 0 hpf þ U L2 F hpf þ U tp;a

closed loop system. The solar cell temperature has been found maximum at 12.00 h due to maximum beam radiation is available at this hour. The obtained values for case (ii) have been found higher than for case (i). The ‘r’ and ‘e’ values have been shown in respective figures (Figs. 5a, 5b, 6–9) and a fair agreements have been obtained in theoretical and experimental output values. The hourly variation of temperature dependent electrical efficiency of PV module of PVT-CPC collector has been shown in Fig. 9. The electrical efficiency decreases with increases in solar cell temperature, due to thermal losses occur at higher temperature. The minimum efficiency (gm) has been obtained at 12.00 h for both cases and lower for case (ii) than case (i). The hourly variation of experimental instantaneous thermal and electrical efficiency of fully covered PVT-CPC collector for both cases have been shown in Figs. 10a and 10b. The experimental instantaneous thermal efficiency (gith) has been obtained higher for case (ii) and instantaneous electrical efficiency (giele) found to be higher for case (i), due to lower input radiation. Monthly variation of input beam radiation (kW/m2) of theoretical and experimental for both cases have been shown in Fig. 11. The maximum beam radiation has been obtained as 255.78 kW/m2 for case (ii), due to MPPT technique. Maximum monthly gain has been obtained in month of September due large number of clear days. The monthly variation of electrical gain, overall thermal energy and exergy have been shown in Figs. 12a, 12b and 12c. The electrical gain, overall thermal energy and exergy have been obtained maximum as 19.60 kW h, 150.40 kW h and 20.85 kW h respectively, for case (ii) Fig. 12c.

U L;m ¼

7. Conclusions

  ðAF R U L Þ1 ; Kk ¼ 1  _ f cf m

Certain conclusions have been made on the basis of the present analysis:  The validation of theoretical and experimental values indicate fair agreement for output parameters (Figs. 5–9).  The instantaneous thermal and electrical efficiency of case (ii) are maximum for fully covered PVT-CPC collector (Figs. 10a and 10b).  Case (ii) of fully covered PVT-CPC collector has been chosen best for thermal as well as electrical output gain for annual basis by increasing input beam radiation through manual MPPT technique (Figs. 11, 12a, 12b, 12c).

Appendix A Following terms are used in thermal modelling and numerical computation for PVT-CPC collectors system:

 U tc;a ¼

1 Lg þ ho K g

1

 ;

U tc;p ¼

1 Lg þ hi K g

1 ;

ho ¼ 5:7 þ 3:8V; W=m2 K; V ¼ 1 m=s; hi ¼ 5:7 W=m2 K; 

U tp;a

1 1 ¼ þ U tc;a U tc;p

1

"

1 1 Li þ 0þ þ hi hpf K i

0

hi ¼ 2:8 þ 3V 0 ; W=m2 K; V 0 ¼ 1 m=s; U L1 ¼

U tc;p U tc;a ; U L2 ¼ U L1 þ U tp;a ; U tc;p þ U tc;a

#1 ;

PF 1 ¼

hpf U tc;p ; PF 2 ¼ 0 ; U tc;p þ U tc;a F hpf þ U L2

PF c ¼

hpf ; F 0 hpf þ U tp;a

ðasÞ1;eff ¼ ðac  gc Þsg bc

Aam Aam ; ðasÞ2;eff ¼ ap s2g ð1  bÞ ; Arm Arm

h i ðasÞm;eff ¼ ðasÞ1;eff þ PF 1 ðasÞ1;eff ;

ðasÞc;eff ¼ PF c ap sg

Aac ; Arc

Arm ¼ bLrm ; Aam ¼ bo Lam ; Ac F Rc ¼

  0  _ f cf m F U L;c Ac ; 1  exp _ f cf U L;c m

Am F Rm ¼

  0  _ f cf m F U L;m Am ; 1  exp _ f cf U L;m m

   Ac F Rc U L;c ðAF R ðasÞÞ1 ¼ Ac F Rc ðasÞc;eff þ PF 2 ðasÞm;eff Am F Rm 1  ; _ f cf m    Ac F Rc U L;c ; ðAF R U L Þ1 ¼ Ac F Rc U L;c þ Am F Rm U L;m 1  _ f cf m

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