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ScienceDirect Solar Energy 107 (2014) 372–379 www.elsevier.com/locate/solener
Thermal analysis of a high concentration photovoltaic/thermal system Haifei Chen, Jie Ji ⇑, Yunfeng Wang, Wei Sun, Gang Pei, Zhi Yu Department of Thermal Science and Energy Engineering, University of Science and Technology of China, #96 Jinzhai Road, Hefei City, Anhui Province, People’s Republic of China Received 16 August 2013; received in revised form 4 April 2014; accepted 28 May 2014 Available online 28 June 2014 Communicated by: Associate Editor Brian Norton
Abstract This paper presents a solar photovoltaic/thermal (PV/T) system with triple-junction solar cells. The essential components of the system are a concentrator of high concentration ratio, a PV/T module and a tracking device. Plane-mirrors array structure is applied to the concentrator, which can provide PV/T module with a uniform light intensity distribution and an adjustable concentration ratio. The PV/T module is an integration of triple-junction solar cells and a heat exchange device, where the heat from triple-junction solar cells is collected and transported for thermal applications by fluid passing through. Considering both photovoltaic and thermal conversion, the total solar utilization efficiency is greatly increased. The simulation results show that the thermal conversion efficiency of this high concentration PV/T system in hybrid operation can achieve about 52%, which is approximately in agreement with the experimental result of 48%, meanwhile the theoretical photovoltaic conversion efficiency can reach 26%. The simulation results also reveal the effect of fluid flow rate on the thermal efficiency of high concentration PV/T system, which is quite opposite to that in non-concentration PV/T system. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic/thermal; High concentration ratio; Thermal analysis; Triple-junction solar cells
1. Introduction As an effective method to alleviate energy shortage, solar photovoltaic technology has attracted numerous researchers’ attention. However, problems including low photoelectric conversion efficiency and high cost of production remain unsolved. In order to improve the efficiency of photovoltaic cells, researches have been carried out on materials and structures of solar cells. With the development of metal organic vapor phase epitaxy (MOVPE) technology, high efficiency multi-junction solar cells, such as triple-junction solar cells, show a great application potential (Olson et al., 2003; Philipps et al., 2012). Solar ⇑ Corresponding author. Tel.: +86 551 63601641; fax: +86 551 63606459. E-mail address: [email protected] (J. Ji).
http://dx.doi.org/10.1016/j.solener.2014.05.043 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
concentration systems have been developed to decrease the usage of solar cells and in turn to reduce the cost of production. Different kinds of concentration photovoltaic systems have been proposed and established (Andreev and Luque, 2007). Schuetz et al. (2012) reported a low-concentration photovoltaic system which was based on compound parabolic concentrator with a concentration ratio of 7. Wiesenfarth et al. (2012) presented a new solar cell module which was measured in a dish system showing module electrical efficiency of 22.8%. Air-cooling or passive heat sinks device is usually used in the CPV system to cool solar cells to suitable temperature range (Sun et al., 2005; Tonui and Tripanagnostopoulos, 2007). Combining the idea of PV/T system (Zondag, 2008), many researchers have attempted to develop concentration PV/T (CPV/T) systems. The efficiency of solar utilization will greatly
H. Chen et al. / Solar Energy 107 (2014) 372–379
373
Nomenclature A C D E f G h Id k L m_ M Nu Pr Q R Re rp T u x
area, m2 concentration ratio or specific heat, J/(kg K) diameter, m electric power, W friction factor, radiation flux in concentrator, W heat transfer coefficient, W/(m2 K) direct irradiance, W/m2 thermal conductivity, W/(m K) length, m mass flow, kg/s mass, kg Nusselt number, Prandtl number, power, W thermal resistance, K/W Reynolds number, ratio of cell area to aperture area, temperature, °C velocity, m/s distance, m
increase if the excess heat from solar cells in CPV system can be collected and utilized. Coventry (2005) developed a kind of photovoltaic and thermal system with a concentration ratio of 37, whose thermal efficiency was around 58% and electrical efficiency was around 11%. Kribus et al. (2006) presented a miniature concentrator PV/T system which produced about 140–180 W of electricity and 400–500 W of heat. Helmers showed an energy balance model for CPV/T system, which can give a prediction of the performance of the system, including the influence of the operating temperature and the concentration ratio (Helmers and Bett, 2012; Helmers and Kramer, 2013). In high concentration PV/T (HCPV/T) systems, very high uniformity of the radiation flux distribution and cooling technology are required, because high concentration ratio brings great heat flux density on solar cells and may result in extremely high temperature. It is known that if photovoltaic cells cannot be cooled effectively, the photovoltaic efficiency will decrease and even crystal structure of cells will be destroyed (Royne et al., 2005). When the geometric concentration ratio reaches more than 100, it calls for more expensive concentrating technologies to satisfy the demands of tracking and cooling. This paper presents a high concentration photovoltaic and thermal system, which mainly includes a concentrator, a tracking device and a PV/T module with triple-junction solar cells. To get a uniform light intensity distribution and an adjustable concentration ratio, the concentrator uses the plane-mirrors array for converging sunlight. Both numerical simulation and experiments are conducted on the analysis of the systematic characteristics of the high
Greek a b d e q g r
absorptance, temperature coefficient, K1 thickness, m emissivity, reflectance, efficiency, Stefan–Boltzman constant, W/(m2 K4)
Subscripts a air b heat exchange device e environment or electrical i insulation p triple-junction solar cells r reference w water
concentration PV/T system. The output and the thermal performance of this system under high irradiance density are studied. 2. Materials and methods 2.1. Description of the HCPV/T system Fig. 1 shows the HCPV/T system running on a rooftop, which is about 10 m2, 3 m high, and gives a concentration ratio of 450. The HCPV/T system is mainly combined by three parts: a concentrator, a PV/T module and a tracking device. The concentrator converges sunlight onto a small area of triple-junction solar cells, hence the usage of solar cells decreases and the output of electricity increases. The tracking device moves the concentrator to focus sunlight accurately onto the cells all the time throughout the day. The PV/T module is an integration of triple-junction solar cells and a heat exchange device, where solar photovoltaic and thermal conversions take place. 2.1.1. Tracking device A two-axes sun tracking device has been applied to this system. The tracking device controls the concentrator to track the sun’s azimuth angle and elevation angle by an electric turntable and a linear actuator, respectively. Suntracking accuracy got from the manufacturer is 0.2°. A programmable logic controller system including photosensitive control procedure and mechanical control program is designed to reduce the tracking error.
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the photovoltaic cells layer of PV/T module. The reflectivity of the mirrors is around 95%.
Fig. 1. Photograph of the HCPV/T system running on a rooftop.
2.1.2. Concentrator Dish concentrator is commonly used for solar high concentration system. It is mostly of continuous parabolic surface structure, which is hard to get a uniform light intensity and is prone to local overheating or “hot-spots”. And the specific cell interconnection of the receiver should also be considered to get better photoelectric conversion efficiency. Many optical analyses and designs of the CPV systems have been studied to solve this problem (Helmers et al., 2013; Kreske, 2002; Meller and Kribus, 2013). Chayet et al. (2011) presented a system using 1200 flat mirrors instead of continuous parabolic dishes. Then, in the present study, the concentrator adopts plane-mirrors array structure to get a more uniform light intensity distribution and an adjustable concentration ratio. As shown in Fig. 2, 450 flat glass mirrors of equal area reflect light on
Fig. 2. Photograph of plane-mirrors array structure.
2.1.3. PV/T module Under high irradiation conditions, temperatures of triple-junction solar cells without effective cooling will increase rapidly, and then the PV cell efficiency will decrease fast. Hence a cooling device is essential to cool and protect the cells. A PV/T module is designed in this HCPV/T system, which is composed by a photovoltaic cells layer and a heat exchange device. As shown in Fig. 3, photovoltaic cells layer uses triple-junction solar cell that consists of top cell InGaP, middle cell InGaAs and bottom cell Ge connected in series. The chip size of single triplejunction solar cell is 12 mm long and 11 mm wide. In the module, the total PV layer is 0.2 m long and 0.2 m wide. The total active cell area including gaps between cells on the layer is 0.14 m long and 0.14 m wide. It is equal to the total receiver area, on which the irradiance is focused. Positive and negative electrodes and the diodes on the layer do not receive sunlight. The whole photovoltaic cells layer consists of four identical parts. Each part has 30 pieces of triple-junction solar cells under the array of 5 6 and electrical characteristics are listed in Table 1. Triple-junction solar cells are all connected in series and every five cells are in parallel with a bypass diode that is used to prevent reverse current and protect the cells. The excess heat of triple-junction solar cells is removed by water flowing in the heat exchange device and collected for thermal applications. The heat exchange device (Fig. 4) has inlets and outlets to allow water to flow in and out and the internal fins to improve convective heat transfer. 2.2. Mathematical modeling In order to predict the performance of the HCPV/T system, a dynamical simulation model is developed. Since the solar thermal conversion take place in PV/T module,
Fig. 3. Photograph of the photovoltaic cells layer.
H. Chen et al. / Solar Energy 107 (2014) 372–379 Table 1 The electrical characteristics of each part (30 pieces of triple-junction solar cells) at different concentration ratio (AM 1.5d, 850 W/m2 and 25 °C). Parameter
Symbol
C=1
C = 500
Efficiency Open circuit voltage Short circuit voltage Maximum voltage Maximum current
g Voc Isc Vmp Imp
31.4% 75 V 12.8 mA 69 V 11.3 mA
36.6% 84 V 6.8 A 73 V 6.5 A
375
where Mp and Cp are the mass and the specific heat of triple-junction solar cells, respectively; Tp is the temperature of triple-junction solar cells. Ta is the temperature of the ambient air for convective heat exchange. Te is the temperature of surrounding environment for radiation heat exchange and it is considered equivalent to the ambient temperature in the simulation. Tb is the temperature of the heat exchange device; x is along the water flow direction. Kp and Vp are the thermal conductivity and the volume of triple-junction solar cells, respectively. And Aap = Aep = Abp = Ap. Qp is the heat absorbed by triplejunction solar cells. The convective heat transfer coefficient at the outer surface of triple-junction solar cells is given by hap ¼ 3:8ua þ 5:7
ð2Þ
where ua is the wind velocity (Kumar and Mullick, 2010). The radiative heat transfer coefficient at the outer surface of triple-junction solar cells is given by hep ¼ ep rðT 2p þ T 2e ÞðT p þ T e Þ
Fig. 4. The structure of PV/T module.
the mathematical model to simulate the heat transfer in PV/T module is established. Photovoltaic conversion and heat flux on the PV/T module are modeled as functions of concentration ratio. As shown in Fig. 5, the model can be represented by the transient energy balance equations of four nodes. The node ‘p’ is for triple-junction solar cells, the node ‘b’ for heat exchange device, the node ‘w’ for water, and the node ‘i’ for the insulation material. Heat transfer along the water flow direction (x-direction) leads to a temperature gradient, while the direction vertical to the water flow direction is not discussed here. Then the energy balance for triple-junction solar cells is: M p Cp
@T p @T p ¼ k p V p 2 þ hap Aap ðT a T p Þ þ hep Aep ðT e T p Þ @t @x ð1Þ þ hbp Abp ðT b T p Þ þ Qp
ð3Þ
where ep is the emissivity of triple-junction solar cells, and r is the Stefan–Boltzman’s constant. The conductive heat transfer coefficient at the outer surface of triple-junction solar cells is given by hbp ¼ k b =db
ð4Þ
where kb and db are the thermal conductivity and the thickness of the heat exchange device, respectively. Qp is given by Qp ¼ ap G Ep
ð5Þ
G ¼ qmirror CI d Ap
ð6Þ
where ap is the absorptance of triple-junction solar cells, qmirror is the reflectivity of the mirrors, G is radiation flux focused on the PV module, C is the concentration ratio, and Id is direct irradiance. Ep is electrical output, which is a function of temperature and irradiance. Ep ¼ rp Ggr ½1 br ðT p T r Þ
Fig. 5. Energy flow of the HCPV/T system.
ð7Þ
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where rp is packing factor, namely the ratio of photovoltaic cells area to receiver area; gr is the reference triple-junction solar cells efficiency at the reference temperature Tr; and br is a coefficient for triple-junction solar cells temperature (Chow, 2003). Both gr and br vary with the concentration ratio. The energy balance for heat exchange device is: M bCb
@T b @T b ¼ k b V b 2 þ hbp Abp ðT p T b Þ þ hib Aib ðT i T b Þ @t @x ð8Þ þ hwb Awb ðT w T b Þ
where Ti is the temperature of insulation, and Tw is the temperature of the water. hib ¼ k i =di hwb ¼ NuD
ð9Þ kw Dh
ð10Þ
Gnielinski gives the relationship that applies to a large range of Reynolds number, including the transition region (Incropera et al., 2006). NuD ¼
ðf =8ÞðReD 1000ÞPr 1 þ 12:7ðf =8Þ1=2 ðPr2=3 1Þ
ð11Þ
where Pr is the Prandtl number, f is Moody (or Darcy) friction factor, and Re is Reynolds number. The energy balance for insulation is as follows, and the boundary effects are neglected here: M iCi
dT i ¼ hib Aib ðT b T i Þ þ hia Aia ðT a T i Þ dt
ð12Þ
The energy balance for water is as follows: M wCw
@T w @T w L ¼ hwb Awb ðT b T w Þ m_ w C w @t @x
ð13Þ
where m_ w is the mass flow of water, Cw is the specific heat at the average water temperature, and L is the length along the water flow direction. The thermal output is Qw ¼ m_ w C w ðT out T in Þ
ð14Þ
where Tin and Tout are the inlet and outlet temperatures of water, respectively. The thermal efficiency of the system is given by gt ¼ Qw =G ¼ m_ w C w ðT out T in Þ=G
The thermal performance of the HCPV/T was measured under an outdoor environment. The system was set up in Guangdong Province, China, during the summer of 2012. The city is at longitude 113° and northern latitude 22°. The mass flow rate was measured with a turbine flowmeter. The wind velocity was measured with a small weather station outside, which can collect the data every minute. The air temperature, the temperature of triple-junction solar cells, the inlet and outlet temperatures of the water were measured with the T-type thermocouples. The temperature of PV cell was measured with the temperature sensor that was inset at the back face of the cell before PV module was set up. And the direct radiation was measured with a pyrheliometer (TBS-2-2). The output signals were all connected to a data logger (Agilent 34970A), which collected data every 10 s. The precision of each device is shown in Table 2. Fig. 6 shows variations of the direct irradiance, inlet temperature and ambient temperature in about half an hour during the afternoon of August 15, 2012. The direct irradiance fluctuated between 500 W/m2 and 600 W/m2. The inlet temperature of the water was 31 °C, and the ambient temperature was 34 °C. The same experimental data including the direct irradiance, the temperature of inlet water and the ambient temperature, are used for simulations. The mass flow rate is set to be 0.08 kg/s, and the relevant parameters of the system are shown in Table 3. Other data includes: ap = 0.95, ep = 0.85, qmirror = 0.92, rp = 0.83, C = 450, db = 0.01 m, L = 0.14 m, Tr = 25 °C, gr = 0.366, br = 0.002 °C1. The comparisons of simulation results and the experimental results are shown in Figs. 7 and 8. From Fig. 7, the temperatures of triple-junction solar cells are approximately the same in both the experiment and the simulation. The temperatures fluctuate between 90 °C and 100 °C due to instability of sunlight. Comparing the experiment with the simulation, difference of the outlet temperature is between 0.5 °C to 1.5 °C. Therefore, this dynamic model can primarily predict the temperature of triple-junction GaAs cells and outlet temperature of water. However, as shown in Fig. 8, the thermal efficiency in the simulation is between 49% and 52%. The thermal efficiency in hybrid operation measured in the experiment is
Table 2 List of the testing devices and the testing precisions.
ð16Þ
Device
Specification
Precision
ð17Þ
Pyrheliometer Turbine flowmeter Thermocouple Data logger
TBS-2-2 LWGY-10 Copper-constantan, T-type Agilent 34970A
63% 1% ±0.5 °C /
And the overall efficiency is go ¼ gt þ ge
3.1. Model validation
ð15Þ
The electrical efficiency is ge ¼ Ep =G
3. Results and discussions
H. Chen et al. / Solar Energy 107 (2014) 372–379
Fig. 6. Variations of inlet temperature, ambient temperature and the direct irradiance with time.
377
Fig. 8. Variations of instantaneous thermal efficiency with time.
3.2. Error analysis Table 3 Mass, specific heat and conductivity of materials.
Mass (kg) Specific heat (J kg1 K1) Conductivity (W m1 K1)
GaAs cells
Heat exchange device
Insulation
Water
According to the theory of error propagation, the experimental relative mean error (RME) during the test period is as follows:
0.16 326
0.685 903
0.019 795
0.266 4181
REg ¼
46
237
0.034
0.63
dg dðm_ w C w ðT out T in Þ=GÞ d m_ w dG 2dðT Þ ¼ ¼ þ þ g m_ w C w ðT out T in Þ=G G T out T in m_ w ð18Þ PN
RMEg ¼
1
jREg j d m_ w dG ¼ þ þ N G m_ w
P
2dðT Þ T out T in
N
¼ 19:91%
ð19Þ
Therefore, the experimental relative mean error (RME) of the thermal efficiency during the test period is 19.91%, and the error limits are shown in Fig. 8. 3.3. Simulation analysis The simulation is performed to investigate the effect of water mass flow rate and the concentration ratio on thermal and electrical performances of the HCPV/T system.
Fig. 7. Variations of the temperatures of triple-junction solar cells and the outlet water with time.
between 40% and 48%. The difference between simulation and experiment is caused by the error propagation of the experiment and simplification error of the model. The electrical efficiency mainly depends on the temperature of triple-junction solar cells and the concentration ratio. According to Eq. (16), the simulation model gives the electrical efficiency, which is about 26%. Therefore, the overall efficiency of this system can exceed 70%.
3.3.1. Effect of mass flow rate The concentration ratio is set as 500, direct irradiance is set as 550 W/m2, and the inlet temperature is set as 25 °C. From Figs. 9 and 10, it is shown that the performance of the PV/T will change rapidly, when the mass flow rate is less than 0.04 kg/s in this model. As the mass flow rate decreases from 0.04 kg/s to 0.02 kg/s, the electrical efficiency of triple-junction solar cells will drop rapidly as shown in Fig. 9 and the temperature of triple-junction solar cells will increase fast as shown in Fig. 10. If the mass flow rate is lower than 0.02 kg/s, triple-junction solar cells will be damaged because of the elevated temperature. This is chiefly because the convective heat transfer coefficient decreases with the decrease of the mass flow rate, especially when the mass flow rate is less than 0.04 kg/s, the water flow in the heat exchange device transfers from turbulent flow to laminar flow. The decrease of heat transfer results
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Fig. 9. Influence of mass flow rate on thermal, electrical and overall efficiency (C = 500).
Fig. 10. Influence of mass flow rate on temperatures of triple-junction solar cells and outlet water (C = 500).
in temperature rise of triple-junction solar cells and rapid decline of the photoelectric conversion efficiency. When the mass flow rate increases from 0.06 kg/s to 0.1 kg/s, triple-junction solar cells can be better cooled, and the system can provide expected thermal and electrical energy. In the HCPV/T system, with the increase of mass flow rate, the growth of electrical output is so great that thermal energy output decreases, although the total energy output increases, as shown in Fig. 9. This phenomenon is opposite to that in non-concentration PV/T system (C = 1) as shown in Fig. 11, where both electrical and thermal efficiency increase with the mass flow rate. Comparing Fig. 9 with Fig. 11, it is noted that high concentration makes the efficiencies change more than one order of magnitude greater. 3.3.2. Effect of the concentration ratio When the concentration ratio changes, the reference cell efficiency and the relative temperature coefficient of cell efficiency also change accordingly, which are obtained by
Fig. 11. Influence of mass flow rate on thermal and electrical efficiency (C = 1).
Fig. 12. Influence of the concentration ratio on thermal and electrical efficiency.
fitting the manufacturer’s specifications. Fig. 12 gives the effect of concentration ratio on efficiencies of the system. As the concentration ratio rises, electrical efficiency of the system increases at first and then decreases. That is because the electrical efficiency of the system increases logarithmically with the increase of irradiance. However, at high concentration ratio, the reference cell efficiency decreases and the temperature of the solar cells increases with the rise of the concentration ratio, hence the electrical efficiency of the system decreases. And it is shown that with the increase of concentration ratio, it is important to increase the mass flow rate accordingly to get a better electrical efficiency. And the electrical efficiency of this system is still more than 20%, when the concentration ratio is up to 1000. 4. Conclusions In this paper, a HCPV/T system with triple-junction solar cells is proposed, which can provide both electricity and usable heat. And a dynamical mathematical model is developed for detailed analysis of the performance of the
H. Chen et al. / Solar Energy 107 (2014) 372–379
system. A comparison between experimental results and simulation results is made, which shows that this mathematical model can give a primary prediction of the temperature of triple-junction solar cells and outlet water temperature fairly well. It shows that thermal efficiency is around 48% experimentally in hybrid operation and electrical efficiency is around 26% theoretically. Therefore, the overall efficiency of this system can exceed 70%. The simulation results indicated that the performance of this system is influenced by the concentration ratio and mass flow rate. The selection of mass flow rate should match the concentration ratio to cool the solar cells better and improve the performance of the HCPV/T system. The simulation also shows that in the hybrid operation at high concentration ratio, with the increase of the mass flow rate, not only does the overall efficiency increase, but also notably the electrical efficiency increases and the thermal efficiency decreases. The latter phenomenon is different from that in non-concentration PV/T system. Acknowledgement This work is supported by a Grant from the National High Technology Research and Development Program of China (863 Program) (No. 2013AA050403). References Andreev, V.M., Luque, A.L., 2007. Concentrator photovoltaics. Springer, Heidelberg, Germany, pp. 345. Chayet, H., Kost, O., Moran, R., Lozovsky, I., 2011. Efficient, low cost dish concentrator for a CPV based cogeneration system. In: Dimroth, F., Kurtz, S., Sala G., Bett A.W. (Eds.), 7th International Conference on Concentrating Photovoltaic Systems. Chow, T.T., 2003. Performance analysis of photovoltaic-thermal collector by explicit dynamic model. Sol. Energy 75, 143–152. Coventry, J.S., 2005. Performance of a concentrating photovoltaic/ thermal solar collector. Sol. Energy 78, 211–222.
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Helmers, H., Bett, A.W., 2012. Modeling of concentrating photovoltaic and thermal systems. Prog. Photovoltaics Res. Appl. Helmers, H., Kramer, K., 2013. Multi-linear performance model for hybrid (C) PVT solar collectors. Sol. Energy 92, 313–322. Helmers, H., Thor, W.Y., Schmidt, T., van Rooyen, D., Bett, A.W., 2013. Optical analysis of deviations in a concentrating photovoltaics central receiver system with a flux homogenizer. Appl. Opt. 52, 2974–2984. Incropera, F.P., Dewitt, D.P., Bergman, T.L., Lavine, A.S., 2006. Fundamentals of Heat and Mass Transfer. John Wily and Sons Inc., New York. Kreske, K., 2002. Optical design of a solar flux homogenizer for concentrator photovoltaics. Appl. Opt. 41, 2053–2058. Kribus, A., Kaftori, D., Mittelman, G., 2006. A miniature concentrating photovoltaic and thermal system. Energy Convers. Manage. 47, 3582– 3590. Kumar, S., Mullick, S.C., 2010. Wind heat transfer coefficient in solar collectors in outdoor conditions. Sol. Energy 84, 956–963. Meller, Y., Kribus, A., 2013. Kaleidoscope homogenizers sensitivity to shading. Sol. Energy 88, 204–214. Olson, J.M., Friedman, D.J., Kurtz, S.R., 2003. Chapter 9: HighEfficiency III-V Multijunction Solar Cells. Handbook of Photovoltaic Science and Engineering. Philipps, S.P., Guter, W., Welser, E., 2012. Present status in the development of III–V multi-junction solar cells. Next Generat. Photovoltaics, 1–21. Royne, A., Dey, C.J., Mills, D.R., 2005. Cooling of photovoltaic cells under concentrated illumination: a critical review. Sol. Energy Mater. Sol. Cells 86, 451–483. Schuetz, M.A., Shell, K.A., Brown, S.A., Reinbolt, G.S., French, R.H., Davis, R.J., 2012. Design and construction of a similar to 7x lowconcentration photovoltaic system based on compound parabolic concentrators. Ieee J. Photovoltaics 2, 382–386. Sun, J., Israeli, T., Reddy, T.A., Scoles, K., Gordon, J.M., Feuermann, D., 2005. Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators. J. Solar Energy Eng. – Trans. Asme 127, 138–145. Tonui, J.K., Tripanagnostopoulos, Y., 2007. Improved PV/T solar collectors with heat extraction by forced or natural air circulation. Renewable Energy 32, 623–637. Wiesenfarth, M., Steiner, M., Helmers, H., 2012. Front-side interconnected large area concentrator cells for compact concentrator modules. AIP Conf. Proc. Zondag, H.A., 2008. Flat-plate PV-thermal collectors and systems: a review. Renew. Sustain. Energy Rev. 12, 891–959.
ScienceDirect Solar Energy 107 (2014) 372–379 www.elsevier.com/locate/solener
Thermal analysis of a high concentration photovoltaic/thermal system Haifei Chen, Jie Ji ⇑, Yunfeng Wang, Wei Sun, Gang Pei, Zhi Yu Department of Thermal Science and Energy Engineering, University of Science and Technology of China, #96 Jinzhai Road, Hefei City, Anhui Province, People’s Republic of China Received 16 August 2013; received in revised form 4 April 2014; accepted 28 May 2014 Available online 28 June 2014 Communicated by: Associate Editor Brian Norton
Abstract This paper presents a solar photovoltaic/thermal (PV/T) system with triple-junction solar cells. The essential components of the system are a concentrator of high concentration ratio, a PV/T module and a tracking device. Plane-mirrors array structure is applied to the concentrator, which can provide PV/T module with a uniform light intensity distribution and an adjustable concentration ratio. The PV/T module is an integration of triple-junction solar cells and a heat exchange device, where the heat from triple-junction solar cells is collected and transported for thermal applications by fluid passing through. Considering both photovoltaic and thermal conversion, the total solar utilization efficiency is greatly increased. The simulation results show that the thermal conversion efficiency of this high concentration PV/T system in hybrid operation can achieve about 52%, which is approximately in agreement with the experimental result of 48%, meanwhile the theoretical photovoltaic conversion efficiency can reach 26%. The simulation results also reveal the effect of fluid flow rate on the thermal efficiency of high concentration PV/T system, which is quite opposite to that in non-concentration PV/T system. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic/thermal; High concentration ratio; Thermal analysis; Triple-junction solar cells
1. Introduction As an effective method to alleviate energy shortage, solar photovoltaic technology has attracted numerous researchers’ attention. However, problems including low photoelectric conversion efficiency and high cost of production remain unsolved. In order to improve the efficiency of photovoltaic cells, researches have been carried out on materials and structures of solar cells. With the development of metal organic vapor phase epitaxy (MOVPE) technology, high efficiency multi-junction solar cells, such as triple-junction solar cells, show a great application potential (Olson et al., 2003; Philipps et al., 2012). Solar ⇑ Corresponding author. Tel.: +86 551 63601641; fax: +86 551 63606459. E-mail address: [email protected] (J. Ji).
http://dx.doi.org/10.1016/j.solener.2014.05.043 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
concentration systems have been developed to decrease the usage of solar cells and in turn to reduce the cost of production. Different kinds of concentration photovoltaic systems have been proposed and established (Andreev and Luque, 2007). Schuetz et al. (2012) reported a low-concentration photovoltaic system which was based on compound parabolic concentrator with a concentration ratio of 7. Wiesenfarth et al. (2012) presented a new solar cell module which was measured in a dish system showing module electrical efficiency of 22.8%. Air-cooling or passive heat sinks device is usually used in the CPV system to cool solar cells to suitable temperature range (Sun et al., 2005; Tonui and Tripanagnostopoulos, 2007). Combining the idea of PV/T system (Zondag, 2008), many researchers have attempted to develop concentration PV/T (CPV/T) systems. The efficiency of solar utilization will greatly
H. Chen et al. / Solar Energy 107 (2014) 372–379
373
Nomenclature A C D E f G h Id k L m_ M Nu Pr Q R Re rp T u x
area, m2 concentration ratio or specific heat, J/(kg K) diameter, m electric power, W friction factor, radiation flux in concentrator, W heat transfer coefficient, W/(m2 K) direct irradiance, W/m2 thermal conductivity, W/(m K) length, m mass flow, kg/s mass, kg Nusselt number, Prandtl number, power, W thermal resistance, K/W Reynolds number, ratio of cell area to aperture area, temperature, °C velocity, m/s distance, m
increase if the excess heat from solar cells in CPV system can be collected and utilized. Coventry (2005) developed a kind of photovoltaic and thermal system with a concentration ratio of 37, whose thermal efficiency was around 58% and electrical efficiency was around 11%. Kribus et al. (2006) presented a miniature concentrator PV/T system which produced about 140–180 W of electricity and 400–500 W of heat. Helmers showed an energy balance model for CPV/T system, which can give a prediction of the performance of the system, including the influence of the operating temperature and the concentration ratio (Helmers and Bett, 2012; Helmers and Kramer, 2013). In high concentration PV/T (HCPV/T) systems, very high uniformity of the radiation flux distribution and cooling technology are required, because high concentration ratio brings great heat flux density on solar cells and may result in extremely high temperature. It is known that if photovoltaic cells cannot be cooled effectively, the photovoltaic efficiency will decrease and even crystal structure of cells will be destroyed (Royne et al., 2005). When the geometric concentration ratio reaches more than 100, it calls for more expensive concentrating technologies to satisfy the demands of tracking and cooling. This paper presents a high concentration photovoltaic and thermal system, which mainly includes a concentrator, a tracking device and a PV/T module with triple-junction solar cells. To get a uniform light intensity distribution and an adjustable concentration ratio, the concentrator uses the plane-mirrors array for converging sunlight. Both numerical simulation and experiments are conducted on the analysis of the systematic characteristics of the high
Greek a b d e q g r
absorptance, temperature coefficient, K1 thickness, m emissivity, reflectance, efficiency, Stefan–Boltzman constant, W/(m2 K4)
Subscripts a air b heat exchange device e environment or electrical i insulation p triple-junction solar cells r reference w water
concentration PV/T system. The output and the thermal performance of this system under high irradiance density are studied. 2. Materials and methods 2.1. Description of the HCPV/T system Fig. 1 shows the HCPV/T system running on a rooftop, which is about 10 m2, 3 m high, and gives a concentration ratio of 450. The HCPV/T system is mainly combined by three parts: a concentrator, a PV/T module and a tracking device. The concentrator converges sunlight onto a small area of triple-junction solar cells, hence the usage of solar cells decreases and the output of electricity increases. The tracking device moves the concentrator to focus sunlight accurately onto the cells all the time throughout the day. The PV/T module is an integration of triple-junction solar cells and a heat exchange device, where solar photovoltaic and thermal conversions take place. 2.1.1. Tracking device A two-axes sun tracking device has been applied to this system. The tracking device controls the concentrator to track the sun’s azimuth angle and elevation angle by an electric turntable and a linear actuator, respectively. Suntracking accuracy got from the manufacturer is 0.2°. A programmable logic controller system including photosensitive control procedure and mechanical control program is designed to reduce the tracking error.
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the photovoltaic cells layer of PV/T module. The reflectivity of the mirrors is around 95%.
Fig. 1. Photograph of the HCPV/T system running on a rooftop.
2.1.2. Concentrator Dish concentrator is commonly used for solar high concentration system. It is mostly of continuous parabolic surface structure, which is hard to get a uniform light intensity and is prone to local overheating or “hot-spots”. And the specific cell interconnection of the receiver should also be considered to get better photoelectric conversion efficiency. Many optical analyses and designs of the CPV systems have been studied to solve this problem (Helmers et al., 2013; Kreske, 2002; Meller and Kribus, 2013). Chayet et al. (2011) presented a system using 1200 flat mirrors instead of continuous parabolic dishes. Then, in the present study, the concentrator adopts plane-mirrors array structure to get a more uniform light intensity distribution and an adjustable concentration ratio. As shown in Fig. 2, 450 flat glass mirrors of equal area reflect light on
Fig. 2. Photograph of plane-mirrors array structure.
2.1.3. PV/T module Under high irradiation conditions, temperatures of triple-junction solar cells without effective cooling will increase rapidly, and then the PV cell efficiency will decrease fast. Hence a cooling device is essential to cool and protect the cells. A PV/T module is designed in this HCPV/T system, which is composed by a photovoltaic cells layer and a heat exchange device. As shown in Fig. 3, photovoltaic cells layer uses triple-junction solar cell that consists of top cell InGaP, middle cell InGaAs and bottom cell Ge connected in series. The chip size of single triplejunction solar cell is 12 mm long and 11 mm wide. In the module, the total PV layer is 0.2 m long and 0.2 m wide. The total active cell area including gaps between cells on the layer is 0.14 m long and 0.14 m wide. It is equal to the total receiver area, on which the irradiance is focused. Positive and negative electrodes and the diodes on the layer do not receive sunlight. The whole photovoltaic cells layer consists of four identical parts. Each part has 30 pieces of triple-junction solar cells under the array of 5 6 and electrical characteristics are listed in Table 1. Triple-junction solar cells are all connected in series and every five cells are in parallel with a bypass diode that is used to prevent reverse current and protect the cells. The excess heat of triple-junction solar cells is removed by water flowing in the heat exchange device and collected for thermal applications. The heat exchange device (Fig. 4) has inlets and outlets to allow water to flow in and out and the internal fins to improve convective heat transfer. 2.2. Mathematical modeling In order to predict the performance of the HCPV/T system, a dynamical simulation model is developed. Since the solar thermal conversion take place in PV/T module,
Fig. 3. Photograph of the photovoltaic cells layer.
H. Chen et al. / Solar Energy 107 (2014) 372–379 Table 1 The electrical characteristics of each part (30 pieces of triple-junction solar cells) at different concentration ratio (AM 1.5d, 850 W/m2 and 25 °C). Parameter
Symbol
C=1
C = 500
Efficiency Open circuit voltage Short circuit voltage Maximum voltage Maximum current
g Voc Isc Vmp Imp
31.4% 75 V 12.8 mA 69 V 11.3 mA
36.6% 84 V 6.8 A 73 V 6.5 A
375
where Mp and Cp are the mass and the specific heat of triple-junction solar cells, respectively; Tp is the temperature of triple-junction solar cells. Ta is the temperature of the ambient air for convective heat exchange. Te is the temperature of surrounding environment for radiation heat exchange and it is considered equivalent to the ambient temperature in the simulation. Tb is the temperature of the heat exchange device; x is along the water flow direction. Kp and Vp are the thermal conductivity and the volume of triple-junction solar cells, respectively. And Aap = Aep = Abp = Ap. Qp is the heat absorbed by triplejunction solar cells. The convective heat transfer coefficient at the outer surface of triple-junction solar cells is given by hap ¼ 3:8ua þ 5:7
ð2Þ
where ua is the wind velocity (Kumar and Mullick, 2010). The radiative heat transfer coefficient at the outer surface of triple-junction solar cells is given by hep ¼ ep rðT 2p þ T 2e ÞðT p þ T e Þ
Fig. 4. The structure of PV/T module.
the mathematical model to simulate the heat transfer in PV/T module is established. Photovoltaic conversion and heat flux on the PV/T module are modeled as functions of concentration ratio. As shown in Fig. 5, the model can be represented by the transient energy balance equations of four nodes. The node ‘p’ is for triple-junction solar cells, the node ‘b’ for heat exchange device, the node ‘w’ for water, and the node ‘i’ for the insulation material. Heat transfer along the water flow direction (x-direction) leads to a temperature gradient, while the direction vertical to the water flow direction is not discussed here. Then the energy balance for triple-junction solar cells is: M p Cp
@T p @T p ¼ k p V p 2 þ hap Aap ðT a T p Þ þ hep Aep ðT e T p Þ @t @x ð1Þ þ hbp Abp ðT b T p Þ þ Qp
ð3Þ
where ep is the emissivity of triple-junction solar cells, and r is the Stefan–Boltzman’s constant. The conductive heat transfer coefficient at the outer surface of triple-junction solar cells is given by hbp ¼ k b =db
ð4Þ
where kb and db are the thermal conductivity and the thickness of the heat exchange device, respectively. Qp is given by Qp ¼ ap G Ep
ð5Þ
G ¼ qmirror CI d Ap
ð6Þ
where ap is the absorptance of triple-junction solar cells, qmirror is the reflectivity of the mirrors, G is radiation flux focused on the PV module, C is the concentration ratio, and Id is direct irradiance. Ep is electrical output, which is a function of temperature and irradiance. Ep ¼ rp Ggr ½1 br ðT p T r Þ
Fig. 5. Energy flow of the HCPV/T system.
ð7Þ
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where rp is packing factor, namely the ratio of photovoltaic cells area to receiver area; gr is the reference triple-junction solar cells efficiency at the reference temperature Tr; and br is a coefficient for triple-junction solar cells temperature (Chow, 2003). Both gr and br vary with the concentration ratio. The energy balance for heat exchange device is: M bCb
@T b @T b ¼ k b V b 2 þ hbp Abp ðT p T b Þ þ hib Aib ðT i T b Þ @t @x ð8Þ þ hwb Awb ðT w T b Þ
where Ti is the temperature of insulation, and Tw is the temperature of the water. hib ¼ k i =di hwb ¼ NuD
ð9Þ kw Dh
ð10Þ
Gnielinski gives the relationship that applies to a large range of Reynolds number, including the transition region (Incropera et al., 2006). NuD ¼
ðf =8ÞðReD 1000ÞPr 1 þ 12:7ðf =8Þ1=2 ðPr2=3 1Þ
ð11Þ
where Pr is the Prandtl number, f is Moody (or Darcy) friction factor, and Re is Reynolds number. The energy balance for insulation is as follows, and the boundary effects are neglected here: M iCi
dT i ¼ hib Aib ðT b T i Þ þ hia Aia ðT a T i Þ dt
ð12Þ
The energy balance for water is as follows: M wCw
@T w @T w L ¼ hwb Awb ðT b T w Þ m_ w C w @t @x
ð13Þ
where m_ w is the mass flow of water, Cw is the specific heat at the average water temperature, and L is the length along the water flow direction. The thermal output is Qw ¼ m_ w C w ðT out T in Þ
ð14Þ
where Tin and Tout are the inlet and outlet temperatures of water, respectively. The thermal efficiency of the system is given by gt ¼ Qw =G ¼ m_ w C w ðT out T in Þ=G
The thermal performance of the HCPV/T was measured under an outdoor environment. The system was set up in Guangdong Province, China, during the summer of 2012. The city is at longitude 113° and northern latitude 22°. The mass flow rate was measured with a turbine flowmeter. The wind velocity was measured with a small weather station outside, which can collect the data every minute. The air temperature, the temperature of triple-junction solar cells, the inlet and outlet temperatures of the water were measured with the T-type thermocouples. The temperature of PV cell was measured with the temperature sensor that was inset at the back face of the cell before PV module was set up. And the direct radiation was measured with a pyrheliometer (TBS-2-2). The output signals were all connected to a data logger (Agilent 34970A), which collected data every 10 s. The precision of each device is shown in Table 2. Fig. 6 shows variations of the direct irradiance, inlet temperature and ambient temperature in about half an hour during the afternoon of August 15, 2012. The direct irradiance fluctuated between 500 W/m2 and 600 W/m2. The inlet temperature of the water was 31 °C, and the ambient temperature was 34 °C. The same experimental data including the direct irradiance, the temperature of inlet water and the ambient temperature, are used for simulations. The mass flow rate is set to be 0.08 kg/s, and the relevant parameters of the system are shown in Table 3. Other data includes: ap = 0.95, ep = 0.85, qmirror = 0.92, rp = 0.83, C = 450, db = 0.01 m, L = 0.14 m, Tr = 25 °C, gr = 0.366, br = 0.002 °C1. The comparisons of simulation results and the experimental results are shown in Figs. 7 and 8. From Fig. 7, the temperatures of triple-junction solar cells are approximately the same in both the experiment and the simulation. The temperatures fluctuate between 90 °C and 100 °C due to instability of sunlight. Comparing the experiment with the simulation, difference of the outlet temperature is between 0.5 °C to 1.5 °C. Therefore, this dynamic model can primarily predict the temperature of triple-junction GaAs cells and outlet temperature of water. However, as shown in Fig. 8, the thermal efficiency in the simulation is between 49% and 52%. The thermal efficiency in hybrid operation measured in the experiment is
Table 2 List of the testing devices and the testing precisions.
ð16Þ
Device
Specification
Precision
ð17Þ
Pyrheliometer Turbine flowmeter Thermocouple Data logger
TBS-2-2 LWGY-10 Copper-constantan, T-type Agilent 34970A
63% 1% ±0.5 °C /
And the overall efficiency is go ¼ gt þ ge
3.1. Model validation
ð15Þ
The electrical efficiency is ge ¼ Ep =G
3. Results and discussions
H. Chen et al. / Solar Energy 107 (2014) 372–379
Fig. 6. Variations of inlet temperature, ambient temperature and the direct irradiance with time.
377
Fig. 8. Variations of instantaneous thermal efficiency with time.
3.2. Error analysis Table 3 Mass, specific heat and conductivity of materials.
Mass (kg) Specific heat (J kg1 K1) Conductivity (W m1 K1)
GaAs cells
Heat exchange device
Insulation
Water
According to the theory of error propagation, the experimental relative mean error (RME) during the test period is as follows:
0.16 326
0.685 903
0.019 795
0.266 4181
REg ¼
46
237
0.034
0.63
dg dðm_ w C w ðT out T in Þ=GÞ d m_ w dG 2dðT Þ ¼ ¼ þ þ g m_ w C w ðT out T in Þ=G G T out T in m_ w ð18Þ PN
RMEg ¼
1
jREg j d m_ w dG ¼ þ þ N G m_ w
P
2dðT Þ T out T in
N
¼ 19:91%
ð19Þ
Therefore, the experimental relative mean error (RME) of the thermal efficiency during the test period is 19.91%, and the error limits are shown in Fig. 8. 3.3. Simulation analysis The simulation is performed to investigate the effect of water mass flow rate and the concentration ratio on thermal and electrical performances of the HCPV/T system.
Fig. 7. Variations of the temperatures of triple-junction solar cells and the outlet water with time.
between 40% and 48%. The difference between simulation and experiment is caused by the error propagation of the experiment and simplification error of the model. The electrical efficiency mainly depends on the temperature of triple-junction solar cells and the concentration ratio. According to Eq. (16), the simulation model gives the electrical efficiency, which is about 26%. Therefore, the overall efficiency of this system can exceed 70%.
3.3.1. Effect of mass flow rate The concentration ratio is set as 500, direct irradiance is set as 550 W/m2, and the inlet temperature is set as 25 °C. From Figs. 9 and 10, it is shown that the performance of the PV/T will change rapidly, when the mass flow rate is less than 0.04 kg/s in this model. As the mass flow rate decreases from 0.04 kg/s to 0.02 kg/s, the electrical efficiency of triple-junction solar cells will drop rapidly as shown in Fig. 9 and the temperature of triple-junction solar cells will increase fast as shown in Fig. 10. If the mass flow rate is lower than 0.02 kg/s, triple-junction solar cells will be damaged because of the elevated temperature. This is chiefly because the convective heat transfer coefficient decreases with the decrease of the mass flow rate, especially when the mass flow rate is less than 0.04 kg/s, the water flow in the heat exchange device transfers from turbulent flow to laminar flow. The decrease of heat transfer results
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Fig. 9. Influence of mass flow rate on thermal, electrical and overall efficiency (C = 500).
Fig. 10. Influence of mass flow rate on temperatures of triple-junction solar cells and outlet water (C = 500).
in temperature rise of triple-junction solar cells and rapid decline of the photoelectric conversion efficiency. When the mass flow rate increases from 0.06 kg/s to 0.1 kg/s, triple-junction solar cells can be better cooled, and the system can provide expected thermal and electrical energy. In the HCPV/T system, with the increase of mass flow rate, the growth of electrical output is so great that thermal energy output decreases, although the total energy output increases, as shown in Fig. 9. This phenomenon is opposite to that in non-concentration PV/T system (C = 1) as shown in Fig. 11, where both electrical and thermal efficiency increase with the mass flow rate. Comparing Fig. 9 with Fig. 11, it is noted that high concentration makes the efficiencies change more than one order of magnitude greater. 3.3.2. Effect of the concentration ratio When the concentration ratio changes, the reference cell efficiency and the relative temperature coefficient of cell efficiency also change accordingly, which are obtained by
Fig. 11. Influence of mass flow rate on thermal and electrical efficiency (C = 1).
Fig. 12. Influence of the concentration ratio on thermal and electrical efficiency.
fitting the manufacturer’s specifications. Fig. 12 gives the effect of concentration ratio on efficiencies of the system. As the concentration ratio rises, electrical efficiency of the system increases at first and then decreases. That is because the electrical efficiency of the system increases logarithmically with the increase of irradiance. However, at high concentration ratio, the reference cell efficiency decreases and the temperature of the solar cells increases with the rise of the concentration ratio, hence the electrical efficiency of the system decreases. And it is shown that with the increase of concentration ratio, it is important to increase the mass flow rate accordingly to get a better electrical efficiency. And the electrical efficiency of this system is still more than 20%, when the concentration ratio is up to 1000. 4. Conclusions In this paper, a HCPV/T system with triple-junction solar cells is proposed, which can provide both electricity and usable heat. And a dynamical mathematical model is developed for detailed analysis of the performance of the
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system. A comparison between experimental results and simulation results is made, which shows that this mathematical model can give a primary prediction of the temperature of triple-junction solar cells and outlet water temperature fairly well. It shows that thermal efficiency is around 48% experimentally in hybrid operation and electrical efficiency is around 26% theoretically. Therefore, the overall efficiency of this system can exceed 70%. The simulation results indicated that the performance of this system is influenced by the concentration ratio and mass flow rate. The selection of mass flow rate should match the concentration ratio to cool the solar cells better and improve the performance of the HCPV/T system. The simulation also shows that in the hybrid operation at high concentration ratio, with the increase of the mass flow rate, not only does the overall efficiency increase, but also notably the electrical efficiency increases and the thermal efficiency decreases. The latter phenomenon is different from that in non-concentration PV/T system. Acknowledgement This work is supported by a Grant from the National High Technology Research and Development Program of China (863 Program) (No. 2013AA050403). References Andreev, V.M., Luque, A.L., 2007. Concentrator photovoltaics. Springer, Heidelberg, Germany, pp. 345. Chayet, H., Kost, O., Moran, R., Lozovsky, I., 2011. Efficient, low cost dish concentrator for a CPV based cogeneration system. In: Dimroth, F., Kurtz, S., Sala G., Bett A.W. (Eds.), 7th International Conference on Concentrating Photovoltaic Systems. Chow, T.T., 2003. Performance analysis of photovoltaic-thermal collector by explicit dynamic model. Sol. Energy 75, 143–152. Coventry, J.S., 2005. Performance of a concentrating photovoltaic/ thermal solar collector. Sol. Energy 78, 211–222.
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