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T system with static miniature solar concentrator
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ScienceDirect Solar Energy 120 (2015) 565–574 www.elsevier.com/locate/solener
Numerical and experimental study on a PV/T system with static miniature solar concentrator Guiqiang Li a, Gang Pei a,⇑, Jie Ji a,⇑, Ming Yang a, Yuehong Su b, Ning Xu a a
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 96 Jinzhai Road, Hefei City 230026, China b Institute of Sustainable Energy Technology, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 16 January 2015; received in revised form 14 July 2015; accepted 31 July 2015
Communicated by: Associate Editor Yanjun Dai
Abstract A photovoltaic/thermal (PV/T) system with static miniature solar concentrators can be integrated with building in the similar way to the flat plat PV/T system, however it can not only save lots of the PV materials, but also to some extent obtain a lower heat loss when the temperature is the same as that in the flat plate PV/T system. In this paper, a mathematical model was made to indicate the performances of the static miniature solar concentrating PV/T system. Experiments were also conducted to validate the results of the simulation. A comparison between the simulation and experiment demonstrated that the model was able to obtain the satisfactory simulation outcome to match the experiment outcome. Results showed that the absolute value of the deviation between simulation and experiment on PV electrical efficiencies were about 0.015 and 0.0065 on March 31st and May 13th, and the temperature curves of simulation and experiment were also consistent. In addition, the electrical and thermal performances on four days in different seasons were also simulated and the linear regression analysis on the thermal performance of this solar concentrating PV/T system was expressed to compare with the flat plate PV/T system, which indicated that the static miniature solar concentrating PV/T system has the lower heat loss coefficient and could further expand the use scope of solar energy in buildings. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Static solar concentrator; PV/T; Miniature; Mathematical model
1. Introduction Building integrated photovoltaic/thermal (BIPV/T) or building attached photovoltaic/thermal (BAPV/T) systems are fastly becoming a feature of the building for saving energy, which can provide a promising solution to the electrical and thermal demand for the building (Chow et al., 2007a). In addition, BIPV/T or BAPV/T systems can also reduce the heating and the cooling loads for buildings in comparison with the conventional building envelope
⇑
Corresponding authors. Tel./fax: +86 551 63607367. E-mail address: [email protected] (G. Pei).
http://dx.doi.org/10.1016/j.solener.2015.07.046 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
elements (Chow et al., 2007a; Zogou and Stapountzis, 2011). In these systems, the PV/T usually was fixed onto the existing building envelope (such as the PV/T panels installed over the roof or the wall) or used as a part of the building envelope. Several investigations on BIPV/T or BAPV/T systems have been carried out previously. The most common types of BIPV/T or BAPV/T systems are based on the air and water taking the heat away from the PV cells. Tripanagnostopoulos (2012) performed an extensive study on water cooling PV/T systems and their integration with buildings. Ji et al. (2011) and Chow et al. (2009) also studied the water cooling BIPV/T in Hefei and Hong Kong, China
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Nomenclature cross sectional area of the pipe (m2) cross sectional area of the tank (m2) temperature coefficient capacity (J/(kg K)) thickness (m) diameter of copper pipe (m) irradiance (W/m2) diffuse irradiance (W/m2) direct irradiance (W/m2) total irradiance (W/m2) photovoltaic power (W) convection heat-transfer coefficient between the pipe and the water (W/(m2 K)) hlen,c convective heat-transfer coefficients between the front glazing and the top surface (W/(m2 K)) hlen,r radiant coefficients between the front glazing and the top surface (W/(m2 K)) hsky radiant coefficients between the front glazing and surroundings (W/(m2 K)) hw convective heat-transfer coefficients between the front glazing and surroundings W/(m2 K) k thermal conductivity (W/(m K)) m_ mass flow rate (kg/s) NuD Nusselt number P perimeter (m) u_ 1 total volume flowing rate of the water (m3/s) u_ w volume flowing rate of the water in the pipe (m3/s) ReD Reynolds number Rlen thermal resistance per unit between the top and bottom surface of the lens-walled CPC (K/W) Rlen,bottom-pv thermal resistance between the bottom surface of the lens-walled CPC and PV (K/W)
A1 A2 Br c d Dpipe G Gdif Gdir H Epv hf
respectively. Chow et al. (2007b) also presented an air cooling BIPV/T system integrated with the window of an office building. Tingting and Andreas (2014) conducted a study on the BIPV/T system with glazed air collector and multiple inlets. Vats and Tiwari (2012) took the performance evaluation of a building integrated semitransparent PV/T system in comparison with a building integrated opaque PV/T system. In addition, many researchers also paid the attention on the PV conversion efficiency (Ghani et al., 2012) or energy and exergy analysis (Kanchan and Tiwari, 2012). However, the heat source temperature obtained by common BIPV/T or BAPV/T is limited which is difficult to meet the current higher temperature requirement of other solar applications such as the absorption and adsorption refrigeration for buildings. Therefore, researchers paid more attention towards the solar concentrating PV/T system because the solar concentrating PV/T can avoid
Rpipe-back thermal resistance between the pipe and back (K/W) T temperature (K) Ti inlet temperature (K) T a average air temperature (K) Vw wind speed (m/s) Wback width of the top aperture of the back (m) Wlen width of the top aperture of the lens-walled CPC (m) Subscripts air air g front glazing len lens-walled CPC len,bottom bottom of lens-walled CPC tank water tank pipe copper pipe pv photovoltaic Greek symbols a absorptivity e emissivity gdif optical efficiency of diffuse irradiance gdir optical efficiency direct irradiance gpv PV electrical efficiency gth system thermal efficiency l dynamic viscosity (kg/(s m)) q density (kg/m3) cg reflectance r Stefan–Boltzmann constant s transmittance
the above mentioned disadvantage. Moreover, the concentrating PV/T can save lots of PV/T materials than the common flat plate PV/T and further decrease the cost. Renno and Petito (2013), Renno (2014) designed and optimized a concentrating PV/T (CPV/T) system for the domestic electricity, heating and cooling application. Vivar et al. (2012) designed a hybrid CPV–T micro-concentrator system. The average electrical efficiency and thermal efficiency were found to be 8% and 50% respectively. Kostic et al. (2010), Coventry (2005) and Kribus et al. (2006) also made the researches on the performances of the CPV/T systems. However, the common CPV or CPV/T systems always need the tracking systems and many operation components, which are difficult to integrate with buildings. Besides, the large scale solar concentrators on the outsider of the building can also cause the esthetic problem of buildings. Therefore, the miniature static solar concentrators should be a good choice to overcome these problems
G. Li et al. / Solar Energy 120 (2015) 565–574
above. Based on the initial study of the solar concentrator modules, the improved lens-walled compound parabolic concentrators (CPC) has been found to have a larger half acceptance angle and more uniform flux distribution than the mirror CPC (Guiqiang et al., 2013; Guiqiang et al., 2014a, 2014b). Considering the influence of the physical dimension, the solar concentrating PV/T system adopted the miniature lens-walled CPC as a static solar concentrator to make it suitable for the building integration. In this paper, the dynamic model of this static solar concentrating PV/T system was set up and the comparison between the simulation and experiment was carried out. The PV and thermal performances were analyzed to reveal the validity of the model. In addition, the common flat plate PV/T system and the static miniature solar concentrating PV/T system were compared to illustrate the advantage of the higher temperature obtained from static miniature solar concentrating PV/T system, which is advantageous for building integrated with solar energy application.
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strings were connected in series and laminated together on one copper square tube. The size of each PV is 15.6 cm * 1.0 cm.), and the sketch of a single miniature lens-walled CPC–PV/T was shown in Fig. 1(b). The PV was inserted within the encapsulated materials, which included the transparent TPT (tedlar-polyestertedlar) and the EVA (ethylene–vinyl acetate) layers on the top as well as the EVA and TPT layers underneath. TPT is known as a good electrical insulator and EVA was an adhesive material. A layer of thermal insulation was put further below the cooling square pipe. The structure of the miniature lens-walled CPC was shown in Fig. 1(c). The total internal reflection could occur on the outside surface of the lens-walled structure as a result of the existence of the air gap, as shown in Fig. 1 (c). This would reduce the optical losses of the lenswalled CPC and further increased the optical efficiency. The lens-walled CPC was made of PMMA (polymethylmethacrylate). The top aperture width and bottom width are 2.4 cm and 1.0 cm, and the height of the lens-walled CPC is 2.6 cm.
2. Structure of static solar concentrating PV/T system 3. Mathematical model This static solar concentrating PV/T system can be installed in the form of modules in a similar way to a common flat plate PV/T system since the static solar concentrator consisted of several two-dimensional miniature lens-walled CPCs in parallel. Therefore, the static solar concentrating PV/T system is suitable for the building fac¸ade integration. Fig. 1(a) showed one way to install it on the building roof. Based on the design of the miniature lens-walled CPC and the PV/T technology (Four PV (crystalline silicon)
3.1. Thermal analysis In this study, a mathematical model was developed for the static miniature solar concentrating PV/T system. For the single static miniature solar concentrating PV/T, the width was only 2.4 cm, and the length was much larger than the width. In order to simplify calculation, some assumptions have been made in the model, which are listed below:
Fig. 1. Schematic diagram of static solar concentrating PV/T system.
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The temperature distribution of the front glazing and the back plate are considered to be uniform. The temperatures on each surface of the lens-walled CPC are uniform. The heat capacity of the adhesive layer (EVA and TPT) has been neglected. Heat conduction in the width direction has been neglected. Considering the effects of the PV coverage ratio on the absorptivity, the equivalent absorptivity for the absorber is used in the system simulation.
surface of the lens-walled CPC and PV. W len is the width of the top aperture of the lens-walled CPC. For PV cell, the energy balance equation can be expressed as:
For the front glazing, the heat-balance equation is given as follows:
gpv ¼
d g qg cg
@T g ¼ hsky ðT sky T g Þþhw ðT air T g Þ @t þhlen;r ðT len;top T g Þþhlen;c ðT len;top T g ÞþGag ð1Þ
where hsky and hw are the radiant and the convective heattransfer coefficients, respectively, between the front glazing and surroundings; hlen;r and hlen;c are the radiant convective heat-transfer coefficients and the thermal resistance between the front glazing and the top surface of the lens-walled CPC; T sky is the sky temperature, the value is expressed below (Duffie and Beckman, 1991): T sky ¼ 0:0552T 1:5 air
d pv qpv cpv
@T pv T pv T len;bottom T pv T pipe ¼ þ @t Rlen;bottompv Rpvpipe sg apv ðGdir gdir þ Gdif gdif Þ þ Epv
ð8Þ
where apv is the absorptivity of PV. gpv is the instantaneous PV electrical efficiency, which can be expressed by: Epv ðGdir gdir þ Gdif gdif Þsg
ð9aÞ
It can also be expressed as follow: gpv ¼ sg gr ð1 Br ðT pv T r ÞÞ
ð9bÞ
where gr is the reference cell efficiency at the reference operating temperature, Tr = 298.15 K; Br is the temperature coefficient, and Br = 0.004 K1. gdir = 0.82, gdif = 0.5 (Guiqiang et al., 2014a, 2014b). For the square pipe, @T pipe 1 T pipe T pv T pipe T back ¼ þ þðT pipe T f Þhf P pipe qp cp d p Rpvpipe @t Rpipeback
ð2Þ
ð10Þ
The convective and the radiant heat-transfer coefficients between the front glazing and surroundings are given as below (Suresh and Mullick, 2010):
where hf is the convection heat-transfer coefficient between the pipe and the water. P pipe is the perimeter of the pipe. For the back panel: @T b 1 T pipe T back ¼ qb cb þ ðT back T air Þhw W back ð11Þ d b Rpipeback @t
hw ¼ 6:5 þ 3:3V w
ð3Þ
hsky ¼ eg rðT 2sky þ T 2g ÞðT sky þ T g Þ
ð4Þ
The radiant heat-transfer coefficients between the front glazing and the top surface of the lens-walled CPC are given as follows hlen;r ¼
rðT 2g þ T 2len;top ÞðT g þ T len;top Þ 1 eg
1 þ elen 1
ag ¼ 1 s g c g
ð5Þ ð6Þ
where ag , sg and cg are the absorptivity of the glass, the transmittance and the reflectance of the front glazing respectively. For the lens-walled CPC, the thermal balance equations of the top and bottom surfaces are expressed as: T len;top T len;bottom þ ðT len;top T g Þðhlen;r þ hlen;c ÞW len ¼ 0 Rlen ð7aÞ T len;bottom T len;top T len;bottom T pv þ ¼0 Rlen Rlen;bottompv
ð7bÞ
where Rlen is the thermal resistance per unit between the top and bottom surfaces of the lens-walled CPC, Rlen;bottompv is the thermal resistance per unit length between the bottom
For the cooling water in the each pipe, A1 qw cw
@T f @T f ¼ u_ w q cw þ ðT pipe T f Þhf P pipe @t @x w
ð12Þ
where u_ w is the volume flowing rate of the water. A is the cross sectional area of the pipe. For the water tank: qw cw A2
@T tan k T air T tan k @T tan k ¼ 1 qw cw þ u_ 1 d @t @x þ hw P tan k kP tan k
ð13Þ
where u_ 1 is the total volume flowing rate of the water of the system. A2 is the cross sectional area of the tank. The heating capacity obtained by the water in the tank can be expressed as follows: Q_th ¼ mw
tank cw
dT ; dt
ð14Þ
where T is the average water temperature in the tank, °C. The system thermal efficiency gth is calculated by R t2 Q_th dt t ; ð15Þ gth ¼ 1R t2 Ac t1 Gdt
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3.2. Discretization of equations In order to solve this problem, the static solar concentrating PV/T collector can be integrated by many single miniature lens-walled CPC–PV/T in parallel. Each miniature lens-walled CPC–PV/T can be divided into small segments, as shown in Fig. 2. The water in the pipe are classified from i = 1 to i = m. Using the finite difference method (time step Dt = 1 s and space step Dx1 = 0.05 m), the mathematical model of this miniature solar concentrating PV/T can be discretized. For the front glazing, T 1g T 0g ¼ hsky ðT sky T 1g Þ þ hw ðT air T 1g Þ Dt þ hlen;r ðT len;top T 1g Þ þ hlen;c ðT len;top T 1g Þ þ Gag
Fig. 3. Differential grid partition of water in the tank.
d g qg cg
ð16Þ
For the PV cell, d pv qpv cpv
T 1pv T 0pv T 1pv T len;bottom T 1pv T pipe ¼ þ Dt Rlen;bottompv Rpvpipe sg apv ðGdir gdir þ Gdif gdif Þ þ Epv
ð17Þ
For the square pipe, d p qp cp
T 1pipe T 0pipe T 1pipe T pv T 1pipe T back ¼ þ Dt Rpvpipe Rpipeback þ ðT 1pipe T f Þhf P pipe
ð18Þ
For the cooling water in the pipe, A1 qw cw
T 1f ðiÞ T 0f ðiÞ ¼ ðT pipe T 1f ðiÞÞhf P pipe Dt T 1f ði 1Þ T 1f ðiÞ þ u_ w qw cw Dx1
3.3. Parameters verification It is difficult to calculate many parameters according to the general formulas due to the special structure of the miniature solar concentrator. In order to attain the approximate values of the parameters, the CFD simulation was introduced to analyze the parameter values based on the experimental data. Fig. 4 shows the temperature distribution of the cross section on 10:00 AM (May 13th). The boundary conditions are the temperatures of PV (323.1 K), lens-walled CPC (320.0 K) and the front glass (315.9 K). From the series of the CFD simulations, the parameter values at the different time can be obtained. From Fig. 5, it can be seen that Rlen (the thermal resistance between the top and bottom surface of the lens-walled CPC) and hlen;c (the thermal resistance between the front glazing and the top surface of the lens-walled CPC) were all nearly stable, and the values of them were 0.065 K/W and 0.091 W/ (m2 K) respectively for the single static solar concentrator.
ð19Þ
For the water in the storage tank, the differential segments are shown in Fig. 3. In addition, the upwind scheme is used in the discretization, and the water tank are classified from j = 1 to j = n, shown in Fig. 3 (space step Dx2 = 0.15 m). The equation can be expressed as: T air T 1tan k ðjÞ T 1tan k ðj 1Þ T 1tan k ðjÞ _ þ u qw cw 1 1 d Dx2 þ kP tan hw P tan k k ¼ qw cw A2
T 1tan k ðjÞ T 0tan k ðjÞ Dt
Fig. 2. Differential grid partition of water in the pipe.
ð20Þ
Fig. 4. Temperature distribution of the cross section on 10:00 AM based on CFD.
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From Eq. (21),
Thermal resistance
0.09
ReD ¼
0.08
0.06
between the top and bottom surfaces of the lens-walled structure between the top surface of the lens-walled structure and the front glazing
0.04 0.03 0.02
ð23Þ
The ReD can be calculated based on the experimental data. Here the ReD 2300, Hence the flow is laminar. With the assumption of fully developed conditions, the appropriate heat transfer correlation is NuD = 4.36 and hf can be obtained. In the solution procedure, the instantaneous boundary conditions can be obtained from the experimental data, including solar radiation, ambient temperature, and mass flow rate etc. The initial water temperature in the simulation is set to be equal to the initial water temperature in the tank.
0.07
0.05
4m_ pDpipe l
8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 5. Related parameter values during the test.
4. Experimental setup and error analysis For the convective heat-transfer coefficient between the pipe and water hf , it can be obtained by Incropera et al. (2007) hf ¼
NuD k f Dpipe
ð21Þ
P pipe p
ð22Þ
Dpipe ¼
A schematic diagram of the test platform of the static solar concentrating PV/T system was presented in Fig. 6. A mini-pump was used to circulate water between the water tank and the solar collector, and the power of the pump was about 1.5 W. The flow rate was approximately kept up to 0.03 m3/h. The electrical output has adopted the maximum power point tracking technology (MPPT) using a controlling device, and a battery was used as the energy storage device. The storage capacity of the
Fig. 6. Schematic diagram of the test platform.
G. Li et al. / Solar Energy 120 (2015) 565–574
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Table 1 Specification of the test components. Test equipment
Specification
Production site
Quantity
Position
Ultrasonic flowmeter
TUF-2000P
1
Main pipe line
Thermocouple
0.2 mm copperconstantan TBQ-2 TBS-2-2
Shanghai Juguan Industry Automation Device Ltd. Homemade
7
Jinzhou, China (Sun Co.) Jinzhou, China (Sun Co.)
1 1
PV surface; top surface of the concentrator; storage tank; front glazing; back plate et Near experimental rig with the same tilted angle Near experimental rig
Jinzhou, China (Sun Co.)
1
Near experimental rig
Pyranometer Normal incidence pyranometer Ambient monitor
JZH-1
Others: Data Acquisition Instrument: Agilent 34970A(USA), test computer, electrical wires, etc.
800
T (%)
G (%)
gpv (%)
gth (%)
RME
0.063
2.0
4.2
21.2
700
Solar radiation Wm -2
Variable
Mar.31st
Direct radiation on the titled surface Diffuse radiation on the titled surfac Ambient temperature
34 32 30 28
600
26 24
500
22
400
20
300
18
200
16 14
100
Ambient temperature oC
900
Table 2 The experimental RME of the variables.
12 10
8: 00 8: 30 9: 00 9: 3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0
Time
(a) 50
1000 th
45
May 13
Solar radiation Wm-2
800
40
700
35
600 500
30
400
Direct radiation on the titled surface Diffuse radiation on the titled surfac Ambient temperature
300 200
25 20
Ambient temperature oC
900
15
100
10
8: 00 8: 30 9: 00 9: 30 10 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0
Fig. 7. Photo of miniature solar concentrating PV/T system.
Time
water-storage tank was 20L. Three thermocouples were arranged vertically and symmetrically in the tank to test the water temperature in the storage tank. The solar collector consisted by 18 miniature static concentrators and the length of each miniature static solar concentrator was 0.8 m. The PV coverage ratio was approximately 0.76. One thermocouple was attached on the surface of PV to test the PV temperature. The ambient temperature and wind speed etc. were tested by ambient monitor. The components of the test equipment are shown in Table 1. According to the theory of error propagation, the relative error (RE) of the dependent variable y can be calculated as follows (Gang et al., 2012):
(b) Fig. 8. Ament parameters during the test.
RE ¼
dy @f dx1 @f dx2 @f dxn ¼ þ þ þ y @x1 y @x2 y @xn y
y ¼ f ðx1 ; x2 xn Þ
ð24Þ ð25Þ
where xi, (i = 1,. . .,n) is the variable of the dependent variable y. of/@x is the error transferring coefficient of the variables. The experimental relative mean error (RME) during the test period can be expressed as:
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G. Li et al. / Solar Energy 120 (2015) 565–574 Mar. 31st
Mar. 31st
0.14
55
0.13 0.12
50
0.11 0.10
Water temperature oC
PV Efficiency
Simulation Experiment
0.09 0.08
Experiment Simulation
0.07 0.06 0.05
45 40 35 30 25
0.04 20
0.03
15 07:12
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.02
08:24
09:36
10:48
Time
14:24
15:36
13:12
14:24
15:36
May 13th
May 13th
70
0.105 0.100
Simulation Experiment
60
Water temperature oC
0.095
PV Efficiency
13:12
(a)
(a) 0.110
12:00
Time
0.090 0.085 0.080
Experiment Simulation
0.075 0.070
50
40
30
0.065 0.060 --
20 07:12
08
:0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.055
08:24
09:36
10:48
12:00
Time
Time
(b)
(b)
Fig. 10. Water temperature during the test. Fig. 9. PV efficiency during the test.
PN RME ¼
jREj N
1
ð26Þ
According to the Eqs. (22)–(24), the RMEs of all variables were calculated and the results were given in Table 2. 5. Result and analysis The static solar concentrating PV/T system was installed on the rooftop in Hefei (31°530 N,N,117°150 E). The orientation of the system was facing south at a 32° tilt angle. The photo of the system was shown in Fig. 7. The size parameters in the simulation and experiment were consistent. The experiment commenced at 8:00 and concluded at 15:30. The experiment outcome on two day (Mar. 31st and May 13th) was introduced in detail to compare the simulation outcome. The ambient parameters on the two days during our test are shown in Fig. 8. The average ambient temperatures on the two days were 16.9 °C and 32.7 °C. The proportion of the direct and diffuse solar radiation
on Mar. 31st was close to each other, and the direct solar radiation occupied the major proportion in the total solar radiation on May 13th. The PV efficiency comparison between the simulation and experiment was indicated in Fig. 9. The absolute values of the deviation between simulation and experiment were about 0.015 on Mar. 31st and 0.0065 on May 13th respectively, therefore the simulation and experimental values were relatively consistent. The slight fluctuation of experimental curve was caused by some dynamic factors, such as flux distribution uniformity on the PV surface, which is the main reason that the experimental values were slight lower than the simulative values at the same time. Besides of these, it can be seen that in the concentrating PV/T system, the PV efficiency is lower than the standard efficiency. Taking the each PV cell efficiency on May 13th for example, the overall value is about 9.3%, which is obviously lower than the standard PV efficiency of 12.5%. One reason is that the high temperature in the solar concentrating PV/T system can reduce the PV efficiency and the other
G. Li et al. / Solar Energy 120 (2015) 565–574
Similar to the water temperature, the thermal efficiencies of the miniature solar concentrating PV/T system in the simulation and the experiment were also consistent, as shown in Fig. 11. The maximum instantaneous thermal efficiencies of the miniature solar concentrating PV/T system on the two days were approximately 45.0% and 50.0% respectively.
Mar.13th
0.6
Thermal efficiency
0.5 0.4 0.3 0.2
Experiment Simulation
6. Discussion
0.1
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.0
Time
(a) May 13th 0.6 0.5
Thermal efficiency
573
0.4 0.3
gth ¼ a U
Experiment Simulation
0.2
Based on the mathematical model verified by the experiment, the solar concentrating PV/T performance on different ambient conditions can be simulated to indicate the PV efficiency and thermal efficiency. Table 3 shows the performances on different days in four seasons. It is clearly that with lower ambient temperature, the system has a lower final water temperature and a lower thermal efficiency, but the PV efficiencies are kept above 9%. Considering that efficiency of the water system is affected by solar radiation, ambient temperature, initial temperature and mass of the water in the system obviously, an evaluation method of the water system’s performance is defined as the equation as follow:
0.1
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.0
Time
(b)
T i T a H
where T a is the daily average ambient temperature. In this equation a is daily average thermal efficiency when initial temperature of the water equals daily average ambient temperature, U is a heat loss coefficient during the energycollecting period. The specific outcome of the linear regression analysis of this solar concentrating PV/T system is expressed,
Fig. 11. Thermal efficiency during the test.
gth ¼ 0:340 0:101 reason is the effect of the non-uniform solar radiation distribution on PV, which can also significantly alter the temperature distribution of the solar cell, causing hot spots in some regions of the solar cell. The initial water temperatures in the simulation on the two days can be obtained from the experiment data (Fig. 10) that were 17.9 °C and 26.6 °C respectively. Taking the data on May 13th for example, the final temperatures of the water in the tank in the simulation and experiment were 70.1 °C and 69.8 °C. The temperature curves of simulation and experiment were consistent and the maximum temperature difference was approximately 0.5 °C.
ð27Þ
T i T a H
ð28Þ
Referring to Chow et al. (2007a), the thermal efficiencies of the flat plate PV/T solar collectors can be expressed as respectively: gth ¼ 0:389 0:153
T i T a H
ð29Þ
It is clear that the miniature static solar concentrating PV/T system has a lower a than the flat plate PV/T system, which means that the flat plate PV/T system has a higher thermal efficiency when the water temperature is low within a certain range. However, the heat loss coefficient of the miniature static solar concentrating PV/T system is lower
Table 3 Performances on different days in four seasons. Date
Total solar radiation/MJ
Initial water temperature/°C
Average ambient temperature/°C
Final water temperature/°C
Thermal efficiency
PV efficiency
Mar.14th Jun.15th Sep.24th Dec.19th
16.38 14.87 17.55 17.55
10.0 25 20.0 5.0
15.0 30.2 26.9 2.1
43.6 55.9 56.9 36.0
36.3 36.7 37.2 31.2
10.1 9.7 9.5 10.6
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than that of the flat plate PV/T. Thus, since the miniature static solar concentrating PV/T system has a smaller absorber, it has less thermal loss than flat plat PV/T system, and when the water temperature is higher, the thermal efficiency of the miniature static solar concentrating PV/T system is higher than that of the flat plate PV/T system. The further researches on improving the optical performance, heat exchange structure and heat absorption material etc. would be done, which could further increase the performance for the miniature static solar concentrating PV/T system. 7. Conclusion The static miniature solar concentrating PV/T system can be integrated with buildings, and provide the electricity and heat for energy supply. It is different from the common CPV or CPV/T since the static miniature solar concentrating PV/T system dose not need the tracking system, so it has many advantages. In this paper, a mathematical model was developed to predict the performances of the static miniature solar concentrating PV/T system. Experiments were also conducted to validate the results obtained from the simulation. Results showed that the absolute value of the deviation between simulation and experiment on PV electrical efficiency were about 0.015 on Mar. 31st and 0.0065 on May 13th respectively, and the temperature curves of simulation and experiment were also consistent. Therefore, the model was able to obtain satisfactory simulation outcome. In addition, the performances on different days in four seasons were performed to indicate the PV and thermal efficiencies. The specific outcome of the linear regression analysis of this solar concentrating PV/T system was expressed. The result showed that the flat plate PV/T system has a higher thermal efficiency when the water temperature was low within a certain range, but the static miniature solar concentrating PV/T system has a lower heat loss coefficient, which indicated that the system could be applied in the higher temperature application. Acknowledgments The study was sponsored by the National Science Foundation of China (Grant Nos. 51178442, 51408578), National High Technology Research and Development Program of China (863 Program) (No. 2013AA050403), Anhui Provincial Natural Science Foundation (1508085QE96), DongGuan Innovative Research Team Program (No. 2014607101008), the Fundamental Research Funds for the Central Universities and China Postdoctoral Science Foundation (2014M550350, 2015T80665). References Renno, Carlo, 2014. Optimization of a concentrating PV/T (CPV/T) system used for a domestic application. Appl. Therm. Eng. 67, 396–408.
Chow, T.T., Chan, A.L.S., Fong, K.F., Lin, Z., He, W., Ji, J., 2009. Annual performance of building-integrated photovoltaic/water heating system for warm climate application. Appl. Energy 86, 689–696. Chow, T.T., He, W., Ji, J., 2007a. An experimental study of facadeintegrated photovoltaic/water-heating system. Appl. Therm. Eng. 27 (1), 37–45. Chow, T.T., Fong, K.F., He, W., Lin, Z., Chan, A.L.S., 2007b. Performance evaluation of a PV ventilated window applying to office building of Hong Kong. Energy Build. 39, 643–650. Coventry, J.S., 2005. Performance of a concentrating photovoltaic/ thermal solar collector. Solar Energy 78, 211–222. Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Processes, 2nd ed. John Wiley & Sons, New York. Gang, Pei, Guiqiang, Li, Xi, Zou, Jie, Ji, Yuehong, Su, 2012. Experimental study and exergetic analysis of a CPC-type solar water heater system using higher-temperature circulation in winter. Solar Energy 86 (5), 1280–1286. Ghani, F., Duke, M., Carson, J.K., 2012. Estimation of photovoltaic conversion efficiency of a building integrated photovoltaic/thermal (BIPV/T) collector array using an artificial neural network. Solar Energy 86, 3378–3387. Guiqiang, Li, Gang, Pei, Ming, Yang, Jie, Ji, Yuehong, Su, 2014a. Optical evaluation of a novel static incorporated compound parabolic concentrator with photovoltaic/thermal system and preliminary experiment. Energy Convers. Manage. 85, 204–211. Guiqiang, Li, Gang, Pei, Yuehong, Su, Jie, Ji, Riffat, Saffa B., 2013. Experiment and simulation study on the flux distribution of lenswalled compound parabolic concentrator compared with mirror compound parabolic concentrator. Energy 58, 398–403. Guiqiang, Li, Gang, Pei, Yuehong, Su, Yunyun, Wang, Jie, Ji, 2014b. Design and investigation of a novel lens-walled compound parabolic concentrator with air gap. Appl. Energy 125, 21–27. Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S., 2007. Fundamentals of heat and mass transfer, 6th ed. John Wiley & Sons, New York. Jie, Ji, Luo, Chenglong, Chow, Tin-Tai, Sun, Wei, He, Wei, 2011. Thermal characteristics of a building-integrated dual-function solar collector in water heating mode with natural circulation. Energy 36, 566–574. Kanchan, Vats, Tiwari, G.N., 2012. Energy and exergy analysis of a building integrated semitransparent PV/T (BISPVT) system. Appl. Energy 96, 409–416. Kostic, Lj.T., Pavlovic, T.M., Pavlovic, Z.T., 2010. Optimal design of orientation of PV/T collector with reflectors. Appl. Energy 87, 3023–3029. Kribus, A., Kaftori, D., Mittelman, G., Hirshfeld, A., Flitsanov, Y., Dayan, A., 2006. A miniature concentrating photovoltaic and thermal system. Energy Convers. Manage. 47, 3582–3590. Renno, C., Petito, F., 2013. Design and modeling of a concentrating PV/T (CPV/T) system for a domestic application. Energy Build. 62, 392–402. Suresh, Kumar, Mullick, S.C., 2010. Wind heat transfer coefficient in solar collectors in outdoor conditions. Solar Energy 84 (6), 956–963. Tingting, Yang, Andreas, K. Athienitis, 2014. A study of design options for a building integrated photovoltaic/thermal (BIPV/T) system with glazed air collector and multiple inlets. Solar Energy 104, 82–92. Tripanagnostopoulos, Y., 2012. Photovoltaic/thermal solar collectors. In: Sayigh, A. (Ed.), . In: Comprehensive Renewable Energy, vol. 3. Elsevier, Oxford, pp. 255–300. Vats, K., Tiwari, G.N., 2012. Performance evaluation of a building integrated semitransparent PV/T system for roof and fac¸ade. Energy Build. 45, 211–218. Vivar, M., Everett, V., Fuentes, M., Blakers, A., Tanner, A., Le Lievre, P., Greaves, M., 2012. Initial field performance of a hybrid CPV–T microconcentrator system. Progress Photovolt.: Res. Appl. http://dx. doi.org/10.1002/pip.2229. Zogou, Olympia, Stapountzis, Herricos, 2011. Energy analysis of an improved concept of integrated PV panels in an office building in central Greece. Appl. Energy 88, 853–866.
ScienceDirect Solar Energy 120 (2015) 565–574 www.elsevier.com/locate/solener
Numerical and experimental study on a PV/T system with static miniature solar concentrator Guiqiang Li a, Gang Pei a,⇑, Jie Ji a,⇑, Ming Yang a, Yuehong Su b, Ning Xu a a
Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 96 Jinzhai Road, Hefei City 230026, China b Institute of Sustainable Energy Technology, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 16 January 2015; received in revised form 14 July 2015; accepted 31 July 2015
Communicated by: Associate Editor Yanjun Dai
Abstract A photovoltaic/thermal (PV/T) system with static miniature solar concentrators can be integrated with building in the similar way to the flat plat PV/T system, however it can not only save lots of the PV materials, but also to some extent obtain a lower heat loss when the temperature is the same as that in the flat plate PV/T system. In this paper, a mathematical model was made to indicate the performances of the static miniature solar concentrating PV/T system. Experiments were also conducted to validate the results of the simulation. A comparison between the simulation and experiment demonstrated that the model was able to obtain the satisfactory simulation outcome to match the experiment outcome. Results showed that the absolute value of the deviation between simulation and experiment on PV electrical efficiencies were about 0.015 and 0.0065 on March 31st and May 13th, and the temperature curves of simulation and experiment were also consistent. In addition, the electrical and thermal performances on four days in different seasons were also simulated and the linear regression analysis on the thermal performance of this solar concentrating PV/T system was expressed to compare with the flat plate PV/T system, which indicated that the static miniature solar concentrating PV/T system has the lower heat loss coefficient and could further expand the use scope of solar energy in buildings. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Static solar concentrator; PV/T; Miniature; Mathematical model
1. Introduction Building integrated photovoltaic/thermal (BIPV/T) or building attached photovoltaic/thermal (BAPV/T) systems are fastly becoming a feature of the building for saving energy, which can provide a promising solution to the electrical and thermal demand for the building (Chow et al., 2007a). In addition, BIPV/T or BAPV/T systems can also reduce the heating and the cooling loads for buildings in comparison with the conventional building envelope
⇑
Corresponding authors. Tel./fax: +86 551 63607367. E-mail address: [email protected] (G. Pei).
http://dx.doi.org/10.1016/j.solener.2015.07.046 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
elements (Chow et al., 2007a; Zogou and Stapountzis, 2011). In these systems, the PV/T usually was fixed onto the existing building envelope (such as the PV/T panels installed over the roof or the wall) or used as a part of the building envelope. Several investigations on BIPV/T or BAPV/T systems have been carried out previously. The most common types of BIPV/T or BAPV/T systems are based on the air and water taking the heat away from the PV cells. Tripanagnostopoulos (2012) performed an extensive study on water cooling PV/T systems and their integration with buildings. Ji et al. (2011) and Chow et al. (2009) also studied the water cooling BIPV/T in Hefei and Hong Kong, China
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Nomenclature cross sectional area of the pipe (m2) cross sectional area of the tank (m2) temperature coefficient capacity (J/(kg K)) thickness (m) diameter of copper pipe (m) irradiance (W/m2) diffuse irradiance (W/m2) direct irradiance (W/m2) total irradiance (W/m2) photovoltaic power (W) convection heat-transfer coefficient between the pipe and the water (W/(m2 K)) hlen,c convective heat-transfer coefficients between the front glazing and the top surface (W/(m2 K)) hlen,r radiant coefficients between the front glazing and the top surface (W/(m2 K)) hsky radiant coefficients between the front glazing and surroundings (W/(m2 K)) hw convective heat-transfer coefficients between the front glazing and surroundings W/(m2 K) k thermal conductivity (W/(m K)) m_ mass flow rate (kg/s) NuD Nusselt number P perimeter (m) u_ 1 total volume flowing rate of the water (m3/s) u_ w volume flowing rate of the water in the pipe (m3/s) ReD Reynolds number Rlen thermal resistance per unit between the top and bottom surface of the lens-walled CPC (K/W) Rlen,bottom-pv thermal resistance between the bottom surface of the lens-walled CPC and PV (K/W)
A1 A2 Br c d Dpipe G Gdif Gdir H Epv hf
respectively. Chow et al. (2007b) also presented an air cooling BIPV/T system integrated with the window of an office building. Tingting and Andreas (2014) conducted a study on the BIPV/T system with glazed air collector and multiple inlets. Vats and Tiwari (2012) took the performance evaluation of a building integrated semitransparent PV/T system in comparison with a building integrated opaque PV/T system. In addition, many researchers also paid the attention on the PV conversion efficiency (Ghani et al., 2012) or energy and exergy analysis (Kanchan and Tiwari, 2012). However, the heat source temperature obtained by common BIPV/T or BAPV/T is limited which is difficult to meet the current higher temperature requirement of other solar applications such as the absorption and adsorption refrigeration for buildings. Therefore, researchers paid more attention towards the solar concentrating PV/T system because the solar concentrating PV/T can avoid
Rpipe-back thermal resistance between the pipe and back (K/W) T temperature (K) Ti inlet temperature (K) T a average air temperature (K) Vw wind speed (m/s) Wback width of the top aperture of the back (m) Wlen width of the top aperture of the lens-walled CPC (m) Subscripts air air g front glazing len lens-walled CPC len,bottom bottom of lens-walled CPC tank water tank pipe copper pipe pv photovoltaic Greek symbols a absorptivity e emissivity gdif optical efficiency of diffuse irradiance gdir optical efficiency direct irradiance gpv PV electrical efficiency gth system thermal efficiency l dynamic viscosity (kg/(s m)) q density (kg/m3) cg reflectance r Stefan–Boltzmann constant s transmittance
the above mentioned disadvantage. Moreover, the concentrating PV/T can save lots of PV/T materials than the common flat plate PV/T and further decrease the cost. Renno and Petito (2013), Renno (2014) designed and optimized a concentrating PV/T (CPV/T) system for the domestic electricity, heating and cooling application. Vivar et al. (2012) designed a hybrid CPV–T micro-concentrator system. The average electrical efficiency and thermal efficiency were found to be 8% and 50% respectively. Kostic et al. (2010), Coventry (2005) and Kribus et al. (2006) also made the researches on the performances of the CPV/T systems. However, the common CPV or CPV/T systems always need the tracking systems and many operation components, which are difficult to integrate with buildings. Besides, the large scale solar concentrators on the outsider of the building can also cause the esthetic problem of buildings. Therefore, the miniature static solar concentrators should be a good choice to overcome these problems
G. Li et al. / Solar Energy 120 (2015) 565–574
above. Based on the initial study of the solar concentrator modules, the improved lens-walled compound parabolic concentrators (CPC) has been found to have a larger half acceptance angle and more uniform flux distribution than the mirror CPC (Guiqiang et al., 2013; Guiqiang et al., 2014a, 2014b). Considering the influence of the physical dimension, the solar concentrating PV/T system adopted the miniature lens-walled CPC as a static solar concentrator to make it suitable for the building integration. In this paper, the dynamic model of this static solar concentrating PV/T system was set up and the comparison between the simulation and experiment was carried out. The PV and thermal performances were analyzed to reveal the validity of the model. In addition, the common flat plate PV/T system and the static miniature solar concentrating PV/T system were compared to illustrate the advantage of the higher temperature obtained from static miniature solar concentrating PV/T system, which is advantageous for building integrated with solar energy application.
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strings were connected in series and laminated together on one copper square tube. The size of each PV is 15.6 cm * 1.0 cm.), and the sketch of a single miniature lens-walled CPC–PV/T was shown in Fig. 1(b). The PV was inserted within the encapsulated materials, which included the transparent TPT (tedlar-polyestertedlar) and the EVA (ethylene–vinyl acetate) layers on the top as well as the EVA and TPT layers underneath. TPT is known as a good electrical insulator and EVA was an adhesive material. A layer of thermal insulation was put further below the cooling square pipe. The structure of the miniature lens-walled CPC was shown in Fig. 1(c). The total internal reflection could occur on the outside surface of the lens-walled structure as a result of the existence of the air gap, as shown in Fig. 1 (c). This would reduce the optical losses of the lenswalled CPC and further increased the optical efficiency. The lens-walled CPC was made of PMMA (polymethylmethacrylate). The top aperture width and bottom width are 2.4 cm and 1.0 cm, and the height of the lens-walled CPC is 2.6 cm.
2. Structure of static solar concentrating PV/T system 3. Mathematical model This static solar concentrating PV/T system can be installed in the form of modules in a similar way to a common flat plate PV/T system since the static solar concentrator consisted of several two-dimensional miniature lens-walled CPCs in parallel. Therefore, the static solar concentrating PV/T system is suitable for the building fac¸ade integration. Fig. 1(a) showed one way to install it on the building roof. Based on the design of the miniature lens-walled CPC and the PV/T technology (Four PV (crystalline silicon)
3.1. Thermal analysis In this study, a mathematical model was developed for the static miniature solar concentrating PV/T system. For the single static miniature solar concentrating PV/T, the width was only 2.4 cm, and the length was much larger than the width. In order to simplify calculation, some assumptions have been made in the model, which are listed below:
Fig. 1. Schematic diagram of static solar concentrating PV/T system.
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The temperature distribution of the front glazing and the back plate are considered to be uniform. The temperatures on each surface of the lens-walled CPC are uniform. The heat capacity of the adhesive layer (EVA and TPT) has been neglected. Heat conduction in the width direction has been neglected. Considering the effects of the PV coverage ratio on the absorptivity, the equivalent absorptivity for the absorber is used in the system simulation.
surface of the lens-walled CPC and PV. W len is the width of the top aperture of the lens-walled CPC. For PV cell, the energy balance equation can be expressed as:
For the front glazing, the heat-balance equation is given as follows:
gpv ¼
d g qg cg
@T g ¼ hsky ðT sky T g Þþhw ðT air T g Þ @t þhlen;r ðT len;top T g Þþhlen;c ðT len;top T g ÞþGag ð1Þ
where hsky and hw are the radiant and the convective heattransfer coefficients, respectively, between the front glazing and surroundings; hlen;r and hlen;c are the radiant convective heat-transfer coefficients and the thermal resistance between the front glazing and the top surface of the lens-walled CPC; T sky is the sky temperature, the value is expressed below (Duffie and Beckman, 1991): T sky ¼ 0:0552T 1:5 air
d pv qpv cpv
@T pv T pv T len;bottom T pv T pipe ¼ þ @t Rlen;bottompv Rpvpipe sg apv ðGdir gdir þ Gdif gdif Þ þ Epv
ð8Þ
where apv is the absorptivity of PV. gpv is the instantaneous PV electrical efficiency, which can be expressed by: Epv ðGdir gdir þ Gdif gdif Þsg
ð9aÞ
It can also be expressed as follow: gpv ¼ sg gr ð1 Br ðT pv T r ÞÞ
ð9bÞ
where gr is the reference cell efficiency at the reference operating temperature, Tr = 298.15 K; Br is the temperature coefficient, and Br = 0.004 K1. gdir = 0.82, gdif = 0.5 (Guiqiang et al., 2014a, 2014b). For the square pipe, @T pipe 1 T pipe T pv T pipe T back ¼ þ þðT pipe T f Þhf P pipe qp cp d p Rpvpipe @t Rpipeback
ð2Þ
ð10Þ
The convective and the radiant heat-transfer coefficients between the front glazing and surroundings are given as below (Suresh and Mullick, 2010):
where hf is the convection heat-transfer coefficient between the pipe and the water. P pipe is the perimeter of the pipe. For the back panel: @T b 1 T pipe T back ¼ qb cb þ ðT back T air Þhw W back ð11Þ d b Rpipeback @t
hw ¼ 6:5 þ 3:3V w
ð3Þ
hsky ¼ eg rðT 2sky þ T 2g ÞðT sky þ T g Þ
ð4Þ
The radiant heat-transfer coefficients between the front glazing and the top surface of the lens-walled CPC are given as follows hlen;r ¼
rðT 2g þ T 2len;top ÞðT g þ T len;top Þ 1 eg
1 þ elen 1
ag ¼ 1 s g c g
ð5Þ ð6Þ
where ag , sg and cg are the absorptivity of the glass, the transmittance and the reflectance of the front glazing respectively. For the lens-walled CPC, the thermal balance equations of the top and bottom surfaces are expressed as: T len;top T len;bottom þ ðT len;top T g Þðhlen;r þ hlen;c ÞW len ¼ 0 Rlen ð7aÞ T len;bottom T len;top T len;bottom T pv þ ¼0 Rlen Rlen;bottompv
ð7bÞ
where Rlen is the thermal resistance per unit between the top and bottom surfaces of the lens-walled CPC, Rlen;bottompv is the thermal resistance per unit length between the bottom
For the cooling water in the each pipe, A1 qw cw
@T f @T f ¼ u_ w q cw þ ðT pipe T f Þhf P pipe @t @x w
ð12Þ
where u_ w is the volume flowing rate of the water. A is the cross sectional area of the pipe. For the water tank: qw cw A2
@T tan k T air T tan k @T tan k ¼ 1 qw cw þ u_ 1 d @t @x þ hw P tan k kP tan k
ð13Þ
where u_ 1 is the total volume flowing rate of the water of the system. A2 is the cross sectional area of the tank. The heating capacity obtained by the water in the tank can be expressed as follows: Q_th ¼ mw
tank cw
dT ; dt
ð14Þ
where T is the average water temperature in the tank, °C. The system thermal efficiency gth is calculated by R t2 Q_th dt t ; ð15Þ gth ¼ 1R t2 Ac t1 Gdt
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3.2. Discretization of equations In order to solve this problem, the static solar concentrating PV/T collector can be integrated by many single miniature lens-walled CPC–PV/T in parallel. Each miniature lens-walled CPC–PV/T can be divided into small segments, as shown in Fig. 2. The water in the pipe are classified from i = 1 to i = m. Using the finite difference method (time step Dt = 1 s and space step Dx1 = 0.05 m), the mathematical model of this miniature solar concentrating PV/T can be discretized. For the front glazing, T 1g T 0g ¼ hsky ðT sky T 1g Þ þ hw ðT air T 1g Þ Dt þ hlen;r ðT len;top T 1g Þ þ hlen;c ðT len;top T 1g Þ þ Gag
Fig. 3. Differential grid partition of water in the tank.
d g qg cg
ð16Þ
For the PV cell, d pv qpv cpv
T 1pv T 0pv T 1pv T len;bottom T 1pv T pipe ¼ þ Dt Rlen;bottompv Rpvpipe sg apv ðGdir gdir þ Gdif gdif Þ þ Epv
ð17Þ
For the square pipe, d p qp cp
T 1pipe T 0pipe T 1pipe T pv T 1pipe T back ¼ þ Dt Rpvpipe Rpipeback þ ðT 1pipe T f Þhf P pipe
ð18Þ
For the cooling water in the pipe, A1 qw cw
T 1f ðiÞ T 0f ðiÞ ¼ ðT pipe T 1f ðiÞÞhf P pipe Dt T 1f ði 1Þ T 1f ðiÞ þ u_ w qw cw Dx1
3.3. Parameters verification It is difficult to calculate many parameters according to the general formulas due to the special structure of the miniature solar concentrator. In order to attain the approximate values of the parameters, the CFD simulation was introduced to analyze the parameter values based on the experimental data. Fig. 4 shows the temperature distribution of the cross section on 10:00 AM (May 13th). The boundary conditions are the temperatures of PV (323.1 K), lens-walled CPC (320.0 K) and the front glass (315.9 K). From the series of the CFD simulations, the parameter values at the different time can be obtained. From Fig. 5, it can be seen that Rlen (the thermal resistance between the top and bottom surface of the lens-walled CPC) and hlen;c (the thermal resistance between the front glazing and the top surface of the lens-walled CPC) were all nearly stable, and the values of them were 0.065 K/W and 0.091 W/ (m2 K) respectively for the single static solar concentrator.
ð19Þ
For the water in the storage tank, the differential segments are shown in Fig. 3. In addition, the upwind scheme is used in the discretization, and the water tank are classified from j = 1 to j = n, shown in Fig. 3 (space step Dx2 = 0.15 m). The equation can be expressed as: T air T 1tan k ðjÞ T 1tan k ðj 1Þ T 1tan k ðjÞ _ þ u qw cw 1 1 d Dx2 þ kP tan hw P tan k k ¼ qw cw A2
T 1tan k ðjÞ T 0tan k ðjÞ Dt
Fig. 2. Differential grid partition of water in the pipe.
ð20Þ
Fig. 4. Temperature distribution of the cross section on 10:00 AM based on CFD.
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From Eq. (21),
Thermal resistance
0.09
ReD ¼
0.08
0.06
between the top and bottom surfaces of the lens-walled structure between the top surface of the lens-walled structure and the front glazing
0.04 0.03 0.02
ð23Þ
The ReD can be calculated based on the experimental data. Here the ReD 2300, Hence the flow is laminar. With the assumption of fully developed conditions, the appropriate heat transfer correlation is NuD = 4.36 and hf can be obtained. In the solution procedure, the instantaneous boundary conditions can be obtained from the experimental data, including solar radiation, ambient temperature, and mass flow rate etc. The initial water temperature in the simulation is set to be equal to the initial water temperature in the tank.
0.07
0.05
4m_ pDpipe l
8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time Fig. 5. Related parameter values during the test.
4. Experimental setup and error analysis For the convective heat-transfer coefficient between the pipe and water hf , it can be obtained by Incropera et al. (2007) hf ¼
NuD k f Dpipe
ð21Þ
P pipe p
ð22Þ
Dpipe ¼
A schematic diagram of the test platform of the static solar concentrating PV/T system was presented in Fig. 6. A mini-pump was used to circulate water between the water tank and the solar collector, and the power of the pump was about 1.5 W. The flow rate was approximately kept up to 0.03 m3/h. The electrical output has adopted the maximum power point tracking technology (MPPT) using a controlling device, and a battery was used as the energy storage device. The storage capacity of the
Fig. 6. Schematic diagram of the test platform.
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Table 1 Specification of the test components. Test equipment
Specification
Production site
Quantity
Position
Ultrasonic flowmeter
TUF-2000P
1
Main pipe line
Thermocouple
0.2 mm copperconstantan TBQ-2 TBS-2-2
Shanghai Juguan Industry Automation Device Ltd. Homemade
7
Jinzhou, China (Sun Co.) Jinzhou, China (Sun Co.)
1 1
PV surface; top surface of the concentrator; storage tank; front glazing; back plate et Near experimental rig with the same tilted angle Near experimental rig
Jinzhou, China (Sun Co.)
1
Near experimental rig
Pyranometer Normal incidence pyranometer Ambient monitor
JZH-1
Others: Data Acquisition Instrument: Agilent 34970A(USA), test computer, electrical wires, etc.
800
T (%)
G (%)
gpv (%)
gth (%)
RME
0.063
2.0
4.2
21.2
700
Solar radiation Wm -2
Variable
Mar.31st
Direct radiation on the titled surface Diffuse radiation on the titled surfac Ambient temperature
34 32 30 28
600
26 24
500
22
400
20
300
18
200
16 14
100
Ambient temperature oC
900
Table 2 The experimental RME of the variables.
12 10
8: 00 8: 30 9: 00 9: 3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0
Time
(a) 50
1000 th
45
May 13
Solar radiation Wm-2
800
40
700
35
600 500
30
400
Direct radiation on the titled surface Diffuse radiation on the titled surfac Ambient temperature
300 200
25 20
Ambient temperature oC
900
15
100
10
8: 00 8: 30 9: 00 9: 30 10 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0
Fig. 7. Photo of miniature solar concentrating PV/T system.
Time
water-storage tank was 20L. Three thermocouples were arranged vertically and symmetrically in the tank to test the water temperature in the storage tank. The solar collector consisted by 18 miniature static concentrators and the length of each miniature static solar concentrator was 0.8 m. The PV coverage ratio was approximately 0.76. One thermocouple was attached on the surface of PV to test the PV temperature. The ambient temperature and wind speed etc. were tested by ambient monitor. The components of the test equipment are shown in Table 1. According to the theory of error propagation, the relative error (RE) of the dependent variable y can be calculated as follows (Gang et al., 2012):
(b) Fig. 8. Ament parameters during the test.
RE ¼
dy @f dx1 @f dx2 @f dxn ¼ þ þ þ y @x1 y @x2 y @xn y
y ¼ f ðx1 ; x2 xn Þ
ð24Þ ð25Þ
where xi, (i = 1,. . .,n) is the variable of the dependent variable y. of/@x is the error transferring coefficient of the variables. The experimental relative mean error (RME) during the test period can be expressed as:
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G. Li et al. / Solar Energy 120 (2015) 565–574 Mar. 31st
Mar. 31st
0.14
55
0.13 0.12
50
0.11 0.10
Water temperature oC
PV Efficiency
Simulation Experiment
0.09 0.08
Experiment Simulation
0.07 0.06 0.05
45 40 35 30 25
0.04 20
0.03
15 07:12
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.02
08:24
09:36
10:48
Time
14:24
15:36
13:12
14:24
15:36
May 13th
May 13th
70
0.105 0.100
Simulation Experiment
60
Water temperature oC
0.095
PV Efficiency
13:12
(a)
(a) 0.110
12:00
Time
0.090 0.085 0.080
Experiment Simulation
0.075 0.070
50
40
30
0.065 0.060 --
20 07:12
08
:0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.055
08:24
09:36
10:48
12:00
Time
Time
(b)
(b)
Fig. 10. Water temperature during the test. Fig. 9. PV efficiency during the test.
PN RME ¼
jREj N
1
ð26Þ
According to the Eqs. (22)–(24), the RMEs of all variables were calculated and the results were given in Table 2. 5. Result and analysis The static solar concentrating PV/T system was installed on the rooftop in Hefei (31°530 N,N,117°150 E). The orientation of the system was facing south at a 32° tilt angle. The photo of the system was shown in Fig. 7. The size parameters in the simulation and experiment were consistent. The experiment commenced at 8:00 and concluded at 15:30. The experiment outcome on two day (Mar. 31st and May 13th) was introduced in detail to compare the simulation outcome. The ambient parameters on the two days during our test are shown in Fig. 8. The average ambient temperatures on the two days were 16.9 °C and 32.7 °C. The proportion of the direct and diffuse solar radiation
on Mar. 31st was close to each other, and the direct solar radiation occupied the major proportion in the total solar radiation on May 13th. The PV efficiency comparison between the simulation and experiment was indicated in Fig. 9. The absolute values of the deviation between simulation and experiment were about 0.015 on Mar. 31st and 0.0065 on May 13th respectively, therefore the simulation and experimental values were relatively consistent. The slight fluctuation of experimental curve was caused by some dynamic factors, such as flux distribution uniformity on the PV surface, which is the main reason that the experimental values were slight lower than the simulative values at the same time. Besides of these, it can be seen that in the concentrating PV/T system, the PV efficiency is lower than the standard efficiency. Taking the each PV cell efficiency on May 13th for example, the overall value is about 9.3%, which is obviously lower than the standard PV efficiency of 12.5%. One reason is that the high temperature in the solar concentrating PV/T system can reduce the PV efficiency and the other
G. Li et al. / Solar Energy 120 (2015) 565–574
Similar to the water temperature, the thermal efficiencies of the miniature solar concentrating PV/T system in the simulation and the experiment were also consistent, as shown in Fig. 11. The maximum instantaneous thermal efficiencies of the miniature solar concentrating PV/T system on the two days were approximately 45.0% and 50.0% respectively.
Mar.13th
0.6
Thermal efficiency
0.5 0.4 0.3 0.2
Experiment Simulation
6. Discussion
0.1
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.0
Time
(a) May 13th 0.6 0.5
Thermal efficiency
573
0.4 0.3
gth ¼ a U
Experiment Simulation
0.2
Based on the mathematical model verified by the experiment, the solar concentrating PV/T performance on different ambient conditions can be simulated to indicate the PV efficiency and thermal efficiency. Table 3 shows the performances on different days in four seasons. It is clearly that with lower ambient temperature, the system has a lower final water temperature and a lower thermal efficiency, but the PV efficiencies are kept above 9%. Considering that efficiency of the water system is affected by solar radiation, ambient temperature, initial temperature and mass of the water in the system obviously, an evaluation method of the water system’s performance is defined as the equation as follow:
0.1
--
08 :0 08 0 :3 09 0 :0 09 0 :3 10 0 :0 10 0 :3 11 0 :0 11 0 :3 12 0 :0 12 0 :3 13 0 :0 13 0 :3 14 0 :0 14 0 :3 15 0 :0 15 0 :3 0
0.0
Time
(b)
T i T a H
where T a is the daily average ambient temperature. In this equation a is daily average thermal efficiency when initial temperature of the water equals daily average ambient temperature, U is a heat loss coefficient during the energycollecting period. The specific outcome of the linear regression analysis of this solar concentrating PV/T system is expressed,
Fig. 11. Thermal efficiency during the test.
gth ¼ 0:340 0:101 reason is the effect of the non-uniform solar radiation distribution on PV, which can also significantly alter the temperature distribution of the solar cell, causing hot spots in some regions of the solar cell. The initial water temperatures in the simulation on the two days can be obtained from the experiment data (Fig. 10) that were 17.9 °C and 26.6 °C respectively. Taking the data on May 13th for example, the final temperatures of the water in the tank in the simulation and experiment were 70.1 °C and 69.8 °C. The temperature curves of simulation and experiment were consistent and the maximum temperature difference was approximately 0.5 °C.
ð27Þ
T i T a H
ð28Þ
Referring to Chow et al. (2007a), the thermal efficiencies of the flat plate PV/T solar collectors can be expressed as respectively: gth ¼ 0:389 0:153
T i T a H
ð29Þ
It is clear that the miniature static solar concentrating PV/T system has a lower a than the flat plate PV/T system, which means that the flat plate PV/T system has a higher thermal efficiency when the water temperature is low within a certain range. However, the heat loss coefficient of the miniature static solar concentrating PV/T system is lower
Table 3 Performances on different days in four seasons. Date
Total solar radiation/MJ
Initial water temperature/°C
Average ambient temperature/°C
Final water temperature/°C
Thermal efficiency
PV efficiency
Mar.14th Jun.15th Sep.24th Dec.19th
16.38 14.87 17.55 17.55
10.0 25 20.0 5.0
15.0 30.2 26.9 2.1
43.6 55.9 56.9 36.0
36.3 36.7 37.2 31.2
10.1 9.7 9.5 10.6
574
G. Li et al. / Solar Energy 120 (2015) 565–574
than that of the flat plate PV/T. Thus, since the miniature static solar concentrating PV/T system has a smaller absorber, it has less thermal loss than flat plat PV/T system, and when the water temperature is higher, the thermal efficiency of the miniature static solar concentrating PV/T system is higher than that of the flat plate PV/T system. The further researches on improving the optical performance, heat exchange structure and heat absorption material etc. would be done, which could further increase the performance for the miniature static solar concentrating PV/T system. 7. Conclusion The static miniature solar concentrating PV/T system can be integrated with buildings, and provide the electricity and heat for energy supply. It is different from the common CPV or CPV/T since the static miniature solar concentrating PV/T system dose not need the tracking system, so it has many advantages. In this paper, a mathematical model was developed to predict the performances of the static miniature solar concentrating PV/T system. Experiments were also conducted to validate the results obtained from the simulation. Results showed that the absolute value of the deviation between simulation and experiment on PV electrical efficiency were about 0.015 on Mar. 31st and 0.0065 on May 13th respectively, and the temperature curves of simulation and experiment were also consistent. Therefore, the model was able to obtain satisfactory simulation outcome. In addition, the performances on different days in four seasons were performed to indicate the PV and thermal efficiencies. The specific outcome of the linear regression analysis of this solar concentrating PV/T system was expressed. The result showed that the flat plate PV/T system has a higher thermal efficiency when the water temperature was low within a certain range, but the static miniature solar concentrating PV/T system has a lower heat loss coefficient, which indicated that the system could be applied in the higher temperature application. Acknowledgments The study was sponsored by the National Science Foundation of China (Grant Nos. 51178442, 51408578), National High Technology Research and Development Program of China (863 Program) (No. 2013AA050403), Anhui Provincial Natural Science Foundation (1508085QE96), DongGuan Innovative Research Team Program (No. 2014607101008), the Fundamental Research Funds for the Central Universities and China Postdoctoral Science Foundation (2014M550350, 2015T80665). References Renno, Carlo, 2014. Optimization of a concentrating PV/T (CPV/T) system used for a domestic application. Appl. Therm. Eng. 67, 396–408.
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