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T system based on unsteady-state thermal model
Solar Energy 177 (2019) 427–439
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Design and performance study on a large-scale hybrid CPV/T system based on unsteady-state thermal model
T
⁎
Zexin Wanga, Jinjia Weia,b, , Gaoming Zhanga, Huling Xiec, Muhammad Khalidb a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shanxi 710049, China c Sichuan Energy Internet Research Institute, Tsinghua University, Chengdu, Sichuan 610213, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Large-scale CPV/T system South-north tracking Steady-state thermal model Unsteady-state thermal model
A hybrid CPV/T unit designed in this work concentrates solar radiation by a compound parabolic concentrator (CPC) and converts solar energy into electrical and thermal energy by a PV/T module. The CPC eliminating multiple reflections of solar radiation is defined as the ‘EMR-CPC’ in our previous work, which improves photoelectric and thermal conversion efficiencies. Two similar CPV/T units were tested with two-axis tracking device and south-north single-axis tracking device respectively, and the average photoelectric conversion efficiencies were 13% and 12%. A large-scale south-north tracking hybrid CPV/T system with sunlight collecting area of 810 m2 was built to explore practical application of this CPV/T unit. The whole-day thermal efficiency and total thermal output of the large-scale hybrid CPV/T system were 55% and 1,730,039 kJ respectively on April 14, 2017. The steady-state and unsteady-state thermal models of the hybrid CPV/T system were established and the energy loss was analyzed. The calculated whole-day comprehensive thermal efficiencies of the unsteadystate thermal model and the steady-state thermal model were 55.3% and 55.0% respectively, which were close to the measurement 55.8%. However, the steady-state thermal model failed to accurately predict the whole-day thermal efficiency variation of the system. In comparison, the unsteady-state thermal model accurately predicts instantaneous thermal efficiency of the system varying with meteorological conditions and its total daily heat output.
1. Introduction As the most widely used photoelectric conversion device in the world, crystalline silicon photovoltaic (PV) cells play an important role in global energy supply recently. To improve photoelectric conversion efficiency of PV cells, researchers designed different PV systems to tap the potential of the existing PV by using a concentrator to increase the solar energy density on PV cell surface. Early in 1976, the American national laboratory developed a concentrated photovoltaic (CPV) system which concentrated light by Fresnel lens cluster (Luque and Andreev, 2007). However, with the increase in solar energy density on PV cell surface, working temperature of PV cells increases, reducing photoelectric conversion efficiency and service life of PV cells. Thus, to reduce temperature of PV cells and recover thermal energy of PV cells efficiently becomes a hot spot in the PV field, giving rise to the advent of the concentrated photovoltaic/thermal (CPV/T) system. According to the study of Hasan and Sumathy. (2010), the total efficiency of a CPV/T
⁎
system can reach 60% to 80%. As is known, the CPV/T systems are classified into CPV/T systems with high concentration ratios and those with low concentration ratios (2–10) (Baig et al., 2012). Conventional crystalline silicon photovoltaic cells are used in CPV/T systems with low concentration ratios, while the compound parabolic concentrators (CPCs) are relatively common concentrators with low concentration ratios. Compared with highly-concentrated CPV/T systems in which costs of concentrator manufacturing and the accurate tracking system are relatively high and scattered light can’t be adopted, the CPV/T systems with low concentration ratios are more promising for their commercialization. Othman et al. (2005) designed a dual-channel PV/T with a radiator fan for an air collector system using the CPC to collect solar radiation and established a one-dimensional steady-state heat transfer model for thermal efficiency analysis. Nilsson, J. et al. (2007) long term evaluation of an asymmetric CPC PV-thermal hybrid built for high latitudes (lat 55.7o), and calculated the output of this system by MINSUN simulation program. Bernardo et al. (2011) propose a complete methodology which can characterize, simulate and evaluate CPV/
Corresponding author at: State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. E-mail address: [email protected] (J. Wei).
https://doi.org/10.1016/j.solener.2018.11.043 Received 10 July 2018; Received in revised form 15 November 2018; Accepted 17 November 2018 0038-092X/ © 2018 Published by Elsevier Ltd.
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L1′
Nomenclature
As C Cw Cg Cs Ce cos θ Dc Dd Dw Fend Fw f GTSI GDNI GSDI Gt′ Gm
Gms
H1 H2 h sa h sky h sw
Im kw L
aperture area of PV/T module, m2 geometric concentration ratio of EMR-CPC specific heat capacity of water, J/(kg K) specific heat capacity of PV glass, J/(kg K) specific heat capacity of PV cell, J/(kg K) specific heat capacity of heat exchanger, J/(kg K) Cosine loss coefficient length of PV cells, (m) distance between the best concentration plane and the outlet plane, (m) equivalent diameter of water flow (cooling channel) edge loss factor water flow rate, L/h Darcy drag coefficient, total solar radiation intensity, W/m2 direct solar radiation intensity, W/m2 diffuse solar radiation intensity, W/m2 total radiation intensity of south-north tracking hybrid CPV/T system, W/m2 the intensity of solar radiation collected by the concentrator, W/m2 the intensity of solar radiation absorbed by PV/T component (module), W/m2 height of the CPV/T unit, (m) maximum height of east-west tracking CPV/T system, (m) convective heat transfer coefficient, W/(m2 K) radiative heat transfer coefficient, W/(m2 K) coefficient of heat transfer between PV cells and water, W/ (m2 K) maximum operating current, A thermal conductivity of water, W/(m2 K) total length of the direction of the tracking axis, (m)
l Ms Mw Mg Me Nu Prw Qoutput Re Tout Tin Ts Te Tγ Ta Tsky Um u(ηt ) u(ηe ) α β δ εs γ ηa ηe ηm ηg ηt ηγ ρ Φ
length of the tilted single-axis east-west tracking CPV/T system, (m) length of aluminum alloy rectangular channel, (m) mass of PV cells, kg mass of water in heat exchanger (cooling channel), kg mass of PV glass, kg mass of heat exchanger, kg Nusselt number Prandtl number thermal power output, W Reynolds number outlet water temperature, °C inlet water temperature, °C temperature of PV cells, °C temperature of heat exchanger, °C reference temperature, °C temperature of environment, °C sky temperature, °C maximum operating voltage, V maximum uncertainty of thermal efficiency maximum uncertainty of electrical efficiency solar elevation angle, ° solar azimuth, ° angle of installation for east-west tracking system, ° emissivity of PV cell, – acceptance half angle of EMR-CPC, ° total efficiency electrical efficiency reflectivity of reflector mirror transmittance of solar PV glass thermal efficiency solar cells efficiency at the reference temperature solar radiation absorptivity of solar cell power, W
HP system achieved an averaged COP of 4.8, with an output electrical efficiency of 17.5%, 1.36 times higher than that of the LCPV system. Hangweirer et al. (2015) designed a linear Fresnel concentrator mirror module and used in a CPV/T system, the electrical efficiency of the CPV/T system was 6.2%, and thermal efficiency was 61.2%. The thermal efficiency and electrical efficiency of the trough concentrator CPV/T system were 58% and 11% respectively, and the total energy conversion efficiency was 69% Coventry. (2005). Kong et al. (2013) developed a linear Fresnel coupling CPV/T system and tested the output performance of this CPV/T system in different weather conditions. In sunny weather conditions, the electrical efficiency was 9.86%, and the thermal efficiency was 63%. Li et al. (2011) compared the optimum concentration ratios of different photovoltaic cells in the trough concentrator system and found out that the optimal concentration ratio of crystalline silicon cells was 4.23 times. Milad et al. (2017) devised a novel CPV/T system, and its daily average electrical and thermal efficiencies could reach 4.83% and 46.16% respectively. Karathanassis et al. (2017) adopted parabolic trough as the concentrator, coupled an efficient heat exchanger and developed a CPV/T system. The CPV/T prototype has an overall efficiency approximate to 50% (44% thermal and 6% electrical efficiencies). At present, the CPV/T system is still in development as a single experiment system. Many scholars tried to optimize the condenser and the heat exchanger to improve the electrical efficiency and thermal efficiency of the system, but these systems are still far from practical application. So it is very important to develop an efficient low-cost CPV/T system that can be used on a large scale. In this work, we have designed and developed a large-scale hybrid CPV/T system by using the CPV/T unit of one new type truncated CPC (Compound Parabolic
T hybrid systems. And they exemplified in a particular case study. The measurements show that, there is margin of improvement for the studied this CPV/T system. Chaabane et al. (2013) tested the performance of a non-symmetrical CPC concentrator with PV and PV/T. The experimental results showed that the CPV/T system has higher power output and electrical efficiency than the CPV system. Brogren et al. (2001) discussed the concentration ratios CPC-PV/T system adopting water for heat exchange and proposed a set of methods based on the overall efficiency of the optical data calculation model of the CPC-PV/T system. Baig et al. (2014) designed a three-dimensional Cross Compound Parabolic Concentrator (3-DCCPC) with a geometric concentrating ratio of 3.6, and the maximum output power of the concentrated PV was 2.67 times as much as the non-concentrated PV. They also studied the effect of uneven concentrated light spot on photoelectric efficiency of the system. Tripathi and Tiwari. (2017) designed and fabricated a fully covered CPC-PVT system, and they considered two cases, case (i): fixed position and case (ii): manual maximum power point tracking technique. The results show that the annual net thermal energy and exergy, obtained by case (ii), were 1.25 and 1.19 times higher than for case (i). Proell, M. et al. (2017) constructed real-size CPC PV/T collector prototype. The thermal efficiency and electrical efficiency of this CPC PV/T system were 34% and 9%. In addition to CPC, the coupling PV/T systems with the trough concentrator and the linear Fresnel concentrator are also commonly studied. Karathanassis et al. (2013) used two different microchannel heat sink suitable for the cooling of a linear parabolic trough Concentrating Photovoltaic/Thermal (CPVT) system. Xu et al. (2011) constructed a novel low-concentrating CPV/T integrated heat pump system with a parabolic concentrator. Experimental results showed that the LCPV/T428
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predict the variation curve of the whole-day thermal efficiency of the system.
Concentrator), tested and analyzed its electrical and thermal performance. These are key steps for commercial application of the CPV/T system. This new type truncated CPC in the system has been defined as EMR (Eliminating Multiple Reflections) CPC for the sake of distinction, and Eliminating Multiple Reflections of solar radiation is the truncation method of CPC for designing EMR-CPC. In fact, the truncation principle of this new type truncated CPC has been previously studied and ‘EMRCPC’ has been defined before by our group Xie et al. (2016). This EMRCPC has higher optical efficiency than common CPCs due to its characteristic of eliminating multiple reflections of solar radiation. The uniformity and optical efficiency of EMR-CPC were higher than full CPC. Besides, the material consumption and height of EMR-CPC are about one-half less than that of full CPC, which reduced the manufacture and maintenance costs substantially. EMR-CPC is the CPC after truncated with acceptance half angle of 10.6°, which means it is more dependent on the solar tracking system than full CPC. We adopted different tracking methods to couple them with the CPV/T units and compared the electrical efficiencies of the CPV/T units with two-axis tracking and single-axis south-north tracking methods. We found that except for cosine loss, the single-axis southnorth tracking has no other influence on the electrical efficiency of the CPV/T unit. Under overall consideration of the construction cost and application field of CPV/T systems with four different kinds of tracking methods, the single-axis south-north tracking method was chosen for large-scale hybrid CPV/T system. Based on the work above, we designed and established a large-scale south-north tracking hybrid CPV/T system with the sunlight collecting area of 810 m2 for large-scale commercialization application. The measuring results showed the performance of the large-scale south-north tracking hybrid CPV/T system was better than expected. And the series connection between multiple CPV/T units in the large-scale CPV/T system had lower mismatch loss and ohm loss. To study the thermal performance of the large-scale CPV/T system, steady-state and unsteady-state thermal models were established respectively. Steady-state thermal model is widely used to analyze the thermal performance of the CPV/T and PV/T systems, and it can predict the thermal performance accurately when the solar radiation is stable. However, there usually is cosine loss in single-axis tracking CPV/T systems. The intensity of solar radiation which can be used by singleaxis tracking CPV/T systems is continuously changed, therefore the steady-state thermal model cannot predict the thermal output of singleaxis tracking solar systems well. So, we established an unsteady-state thermal model to analyze the energy loss of hybrid CPV/T system, which can predict the thermal output of the single-axis tracking CPV/T system accurately. The unsteady-state thermal model is more advanced than the steady-state thermal model because the former considers impacts of temperature variations of the PV cell, PV glass, heat exchanger and heat transfer media in the system on thermal output performance of the system. Therefore, the unsteady-state thermal model can accurately
2. Description of hybrid CPV/T systems Two hybrid CPV/T systems were set up in Xi’an, Shaanxi Province, China, at 114° east longitude and 34° north latitude. Those systems were configured with different types of sun tracking devices, two-axis tracking and south-north tracking. The two-axis tracking hybrid CPV/T system composed of 12 CPV/T units was used for testing and improving design of the CPV/T units. Accordingly, the large-scale south-north tracking hybrid CPV/T system with 810 CPV/T units was constructed to explore the possibility for practical application. 2.1. CPV/T unit Flat-plate photovoltaic-thermal (PV/T) collectors and CPC eliminating multiple reflections of solar radiation (EMR-CPC) are the main parts of the CPV/T unit. The structure of PV/T module is shown in Fig. 1. Ten156mm × 156 mm polycrystalline PV cells manufactured by JA SOLAR Corporation were cut into twenty 156 mm × 78 mm cells by laser light and then the cells were connected in series. In the concentration case, the operating current increases greatly since it is proportional to the solar radiation, which increases the ohm loss greatly. Reducing the area of single cell made the maximum operating current of the 156 mm × 78 mm solar cells was about one-half less than that of the 156 mm × 156 mm solar cells, and the maximum operating voltage was doubled. This approach greatly reduces the ohm loss of the CPV/T unit. Next, those cells were laminated onto an aluminum alloy rectangular channel heat exchanger in which water is used as the coolant. Compared with the method of attaching PV cells to the heat exchanger with thermal conductive silicone, the lamination method can make more even and closer contact between the heat exchanger and the PV cells, and effectively improve the heat transfer coefficient between the PV cells and heat exchanger. To a large extent, it avoids occurrence of heat exchange failure between local PV cells and heat exchangers, thus ensures safe operation of the system and greatly increases the service life of PV/T module. The geometric concentration ratio of EMR-CPC is 4×, and EMR-CPC is coupled by symmetrical parabolic reflectors. The back-silvered reflector mirrors can provide reflectivity as high as 0.94. The design method of EMR-CPC has been reported Xie et al. (2016). The optical efficiency of EMR-CPC can be expressed as follows respectively:
ηEMR = [(C - 1) ηm GDNI + GDNI + GSDI ]/ Gm
(1)
Gm = CGDNI + CGSDI
(2)
where ηm is reflectivity of the reflector mirror, GDNI is direct solar
Fig. 1. (A) The cross sectional view of PV/T unit and (B) Diagram of water flow in PV/T unit. 429
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ηt = Qoutput / As (CGDNI + CGSDI ) = Fw Cw (Tout − Tin )/ As (CGDNI + CGSDI )
radiation intensity, GSDI is diffuse solar radiation intensity, Gm is the intensity of solar radiation which can be used by EMR-CPC, and C is geometric concentration ratio of EMR-CPC, and C = 4 . The top surface of PV/T is installed on the best concentration plane of EMR-CPC to form CPV/T unit which is shown in Fig. 2. It is noted that the best concentration plane is not the outlet plane of the EMRCPC, and it is parallel to and lower from the outlet plane. According to the edge-ray principle, a large proportion of solar radiation must be concentrated on the edge of the outlet aperture of EMR-CPC and then the uniformity of solar radiation on outlet aperture is certainly bad, so it is not a good strategy to install the PV/T on outlet aperture. On the best concentration plane, the nonuniformity of the concentrated solar flux distribution is the smallest Xie et al. (2016). The distance between the best concentration plane and the outlet plane can be given by:
D b = Do ·tan γ
(5) where ηt is the thermal efficiency of hybrid CPV/T system. Qoutput is the thermal power output of hybrid CPV/T system. Where Fw is water flow rate. Cw is specific heat capacity of water. Tout and Tin are outlet water temperature and inlet water temperature respectively. The total efficiency is obtained by:
ηa = ηt + ηe
Though the two-axis tracking CPV/T system has high output performance, it cannot be applied on a large-scale due to many deficiencies. One reason is the high cost, and another reason is the large height which requires higher steel strength to resist wind and snow, and higher steel strength means greater mass, so it is difficult to be installed on the roof. As discussed above, for the large-scale application of CPV/T systems, the two-axis tracking mode is not suitable, so the single-axis tracking mode can be considered. For linear concentrators like CPCs, common single-axis tracking modes include three types: single-axis south-north tracking, flat single-axis east-west tracking and tilted single-axis east-west tracking modes. As for the titled single-axis eastwest tracking mode, the maximum height of the CPV/T system can be calculated by:
(3)
where Do is the width of outlet plane, Do = DB = Dc = 156 mm , where D b is the width of best concentration plane of EMR-CPC, and Dc is the width of PV cells, γ is the acceptance half angle of EMR-CPC. 2.2. Two-axis tracking hybrid CPV/T system With high half acceptance angle of EMR-CPC and low geometric concentration ratio, this CPV/T unit doesn’t need a high-precision solar tracking device. So we adopted a more mature two-axis tracking device with a single chip. The system consists of 12 CPV/T units in series arranged in six rows as shown in Fig. 3A. Fig. 3B is the schematic diagram of the system. The measurement points assigned are far more abundant than those shown in Fig. 4, which helps to understand the performance parameters of the system. The electrical efficiency can be obtained by:
ηe = Im Um/ As (CGDNI + CGSDI )
(6)
H2 = (L′1 + H1)·cos δ
(7)
where δ is the angle of installation for tilted single-axis east-west tracking CPV/T system. H1 is the height of the CPV/T unit. L′1 is the length of the tilted single-axis east-west tracking CPV/T system. Assuming that L′1 is 6 m and H1 is 0.9 m, the maximum height of the tilted single-axis east-west tracking CPV/T system in Xi’an (34°N) can reach as high as 5.3 m. As we can see, it is not safe and reliable to install the tilted single-axis east-west tracking CPV/T system on the roof. The system is not easy to maintain either. If the length of CPV/T system decreases, more tracking devices have to be used, which means the cost increases. Thus the tilted single-axis east-west tracking mode is not suitable for the large scale application of CPV/T systems. And for the single-axis south-north tracking and flat single-axis east-
(4)
where Im is maximum operating current, Um is maximum operating voltage, and As is Aperture area of PV/T module. The thermal efficiency is obtained by:
Fig. 2. Schematic of CPV/T unit. 430
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Fig. 3. (A) Photograph of two-axes tracking hybrid CPV/T system (B) Schematic diagram of the system.
2.3. Large-scale south-north tracking hybrid CPV/T system
west tracking modes, the edge loss and cosine loss will be introduced. The edge loss can be eliminated by expand the length of the concentrator, but the cosine loss is inevitable. The maximum cosine loss coefficient of these two tracking modes are cos 42° and cos 56° respectively. For the flat single-axis east-west tracking mode, the maximum cosine loss coefficient arises on winter solstice. In winter, the demand for thermal energy is significantly large but the efficiency of the flat single-axis east-west tracking CPV/T system is low due to large cosine loss, and thus low output cannot match the large demand for thermal energy, which means the flat single-axis east-west tracking mode has a very large difference of thermal energy output between summer and winter and is not suitable for the large scale application of CPV/T systems either. Finally, for the single-axis south-north tracking mode, the maximum cosine loss coefficient arises on summer solstice. In summer, the demand for thermal energy is not as large as that in winter, so the effect of the decrease in efficiency due to cosine loss on the thermal energy supply to the user terminal is not obvious. In conclusion, the single-axis south-north tracking mode is the most suitable tracking strategy for the large-scale application of CPV/T systems.
Based on the CPV/T unit, we designed a new-type south-north tracking hybrid CPV/T system which has its construction cost, maximum installation height and unit mass far lower than those of the twoaxis tracking hybrid CPV/T system with the same peak output power (see Table 1), so the former is more suitable for large scale utilization. Fig. 4A is the design drawing of the south-north tracking hybrid CPV/T system, and we built one small-scale south-north tracking hybrid CPV/T system based on this design. The photograph of this small-scale system is shown in Fig. 4B, and Fig. 4C is the schematic diagram. The small-scale CPV/T system consists of 6 CPV/T units in series, which are arranged in two rows. This CPV/T system is used to verify the feasibility and reliability of the south-north tracking hybrid CPV/T. Based on the small-scale CPV/T system, we established the largescale south-north tracking hybrid CPV/T system. The large-scale system consists of 810 CPV/T units arranged in eighteen different rectangular arrays in series. These eighteen arrays include six 7 × 6 arrays, seven 8 × 8 arrays and five 2 × 11 arrays placed at the top of two buildings. The aerial photograph of the large-scale system is shown in Fig. 5A. Fig. 5B is the schematic diagram of a part of the large-scale system consisting of four 7 × 6 arrays. 431
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Fig. 4. (A) photograph of the small-scale system; (B) Schematic diagram of small-scale syst.
total radiation intensity of the south-north tracking hybrid CPV/T system can be expressed as follows:
The incident surface of the south-north tracking hybrid CPV/T system is not perpendicular to the direction of the direct solar radiation, and we assume that the incident angle, that is, the angle between the incident ray and the normal line of the incident surface is θ . Thus cos θ is the cosine loss coefficient of direct solar radiation, while the intensity of diffuse solar radiation is consistent in all directions. Therefore, the
Gt′ = GDNI cos θ + GSDI where cos θ is given by: 432
(8)
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Table 1 maximum installation height and unit mass of different tracking mode.
Two-axis tracking hybrid CPV/T system South-north tracking hybrid CPV/T system
Maximum installation height (m)
Unit mass (kg)
3.2 1.7
171 55
Fig. 5. (A) Aerial photograph of the large-scale system; (B) Schematic diagram of a part of the large-scale system. 433
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cos θ =
(cos α cos β )2 + sin2 α (cos α cos β )2 + (cos α sin β )2 + sin2 α
With the variation in solar azimuth angle, the cosine loss appears in the south-north tracking CPV/T unit, so that its output power is gradually lower than that of the two-axis tracking unit. At the same time, with the change of the direct radiation incidence angle, the energy distribution on the optimal concentration plane changes, and its uniformity decreases. Therefore, the electrical efficiency and fill factor of the south-north tracking CPV/T unit are lower than those of the twoaxis tracking unit. However, the electrical efficiency of these two units reaches to the lowest at noon, because higher solar radiation intensity enlarges the maximum operating current of CPV/T units, resulting in larger ohm loss at noon. Fig. 7 shows the electrical efficiency and electrical power output of large-scale south-north tracking hybrid CPV/T system and the solar radiation intensity affected by the cosine effect. From Fig. 7, we can see that the large-scale south-north tracking hybrid CPV/T system and CPV/T unit 2# have similar electrical characteristics, while the electrical efficiency of the large-scale CPV/T system is lower than that of CPV/T unit 2# due to slight mismatch between multiple CPV/T units in series. Generally, large-scale photovoltaic systems have different degrees of mismatch. The electrical efficiency of the large-scale CPV/T system is between 12.2% and 13.2%, with the highest electrical power output of 91.8 kW.
(9)
where α is solar elevation angle, and β is solar azimuth angle. When β = 0 , cos θ = 1. The south-north tracking hybrid CPV/T system has no cosine loss at this time. Gt′ can be directly measured when the pyranometer is mounted parallel to the incident plane of the south-north tracking hybrid CPV/T system. The south-north tracking hybrid CPV/T system also has the edge loss effect, and the edge loss factor is defined as Fend :
Fend = 1 −
H tan θ L
(10)
where L is the total length of the EMR-CPC, and H relates to the structure of the concentrator, mainly affected by the height of EMRCPC. We calculated the length of the concentrator, made it longer than PV/T module, and thus avoided the edge loss effect on the system completely. 3. Results and discussion 3.1. Uncertainty analysis
3.3. Thermal analysis of hybrid CPV/T system
The uncertainty analysis of variables is based on the method of Kline et al. (1953). The accuracy grades of main instruments are shown in Table2. The maximum uncertainty of thermal efficiency of the system is given by:
u(ηt ) =
u (Fw )2 + u (T )2 + u (G )2
Assuming that the thermal resistance of thermal insulation material was infinite, the thermal loss from insulation material of the PV/T module would not be considered. The analysis on the transmission and transformation of solar radiation in the CPV/T system is shown in Fig. 8. Gm is the solar radiation intensity concentrated by EMR-CPC, which can be figured out by Eq. (2). Some concentrated solar radiation passes through the solar PV glass and illuminates on the surface of PV/T, whilst some is absorbed and reflected by the glass. Assuming the transmittance of solar PV glass is ηg , the absorptivity of solar cell is ρ and n is the number of times that sunlight reflects between PV cell and PV glass. The solar radiation intensity absorbed by the PV/T module Gms can be expressed as (Gueymard, 2004):
(11)
where u (Fw ) , u (T ) and u (G ) are the maximum uncertainty of flow meter, thermocouple and pyranometer respectively. The maximum uncertainty of electrical efficiency of the system is given by:
u(ηe ) =
u (IV )2 + u (G )2
(12)
where u (IV ) is the maximum uncertainty of IV curve tester. According to Eqs. (11) and (12), the maximum uncertainties of thermal efficiency and electrical efficiency are 3.5% and 3.16% respectively.
∞
Gms = Gm ηEMR ρηg
∑
[(1 − ρ)(1 − ηg )]n =
n= 0
Gρηg 1 − (1 − ρ)(1 − ηg )
(13)
As is the aperture area of PV/T, and the heat exchange area of aluminium alloy rectangular channel is expressed as Ah , Ah = As . With part of As Gms (the solar radiation power absorbed by the PV/T module) converted to electrical power, the rest is the thermal energyQ , which can be obtained by:
3.2. Electrical performance of CPV/T systems with different tracking modes Two CPV/T units were studied with almost the same configuration but different tracking modes. The CPV/T unit 1# used two-axis tracking device to track the sun, while the CPV/T unit 2# used the south-north tracking device. The tested results showed that the average electrical efficiency of two-axis tracking CPV/T unit was 13%, while the southnorth tracking CPV/T unit was 12.5%. Fig. 6(A) displays the IV and PV characteristic curves of the two CPV/T units above at noon, and Fig. 6(B) shows the variations with time in their electrical efficiency and electrical power output by simultaneous determination. As shown in the Fig. 6(B), the electrical performances of the two CPV/T units are almost the same at noon (12:34 local time), because of inexistence of cosine loss in the south-north tracking CPV/T unit.
(14)
Q = As Gms - Es where Es is the electrical power output.
Es = As ηe Gm = As ηγ [1 − β (Ts − Tγ )] Gms
(15)
where ηγ represents the solar cell efficiency at the reference temperature Tγ , and Ts represents the temperature of solar cells. With the transfer of thermal energy from PV cells to the aluminum alloy rectangular channel and then into water in the heat exchanger,
Table 2 Accuracy grades of main instruments. Name
Accuracy grade
units
Institute for metrology
Flow meter Thermocouple Radiation meter for solar ray IV curve tester
0.6% 1.7% 3% 1%
L/h °C W/m2 W
Shaanxi Institute of Metrology Science Shaanxi Institute of Metrology Science National Institute of Metrology, China Shaanxi Institute of Metrology Science
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Fig. 6. (A) IV and PV curves of the two units (B) Variationsin electrical efficiency and electrical power output of the two units.
where Ms and Mg are the mass of PV cells and Solar PV glass, Cs and Cg are their specific heat.
the temperature of the solar PV glass, PV cells and aluminum alloy rectangular channel changes. With the decrease of the above-mentioned temperature, energy released by the three parts of PV/T is transferred to water flow to increase water temperature. When the variation in solar radiation intensity is too small to be ignored, the water flow is constant, which means the temperatures of the above three parts are unchanged. In this case, the CPV/T system was in steady state. The approximation here represents that the temperature of Solar PV glass and PV cells is always consistent and can be considered as a whole. Φ1 represents the thermal power of PV cells and Solar PV glass, and Φ2 indicates the thermal power of aluminum alloy rectangular channel, and can be expressed respectively as
Φ1 = (Ms Cs + Mg Cg )
∂Ts ∂t
Φ2 = Me Ce
∂Te ∂t
(17)
where Me and Ce are the mass and specific heat of aluminum alloy rectangular channel. Likewise, in unsteady state, the average temperature of water in the heat exchanger changes as well, directly affecting the thermal output of the system, and the thermal power of water can be expressed as.
Φ3 = Mw Cw
∂Tw ∂t
(18)
where Mw , Cw and Tw are respectively the mass, specific heat and temperature of water in the heat exchanger. At the same time, there are radiation heat loss and convection heat loss on the outer surface of PV/T.
(16) 435
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Fig. 7. (A) Electrical efficiency of large-scale south-north tracking hybrid CPV/T system on April 14, 2017. (B) Electrical power output of large-scale south-north tracking hybrid CPV/T system on April 14, 2017.
Fig. 8. Energy flow diagram of the CPV/T system.
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Fig. 9. (A) Measured and simulated thermal efficiency of large-scale south-north tracking hybrid CPV/T system on April 14, 2017. (B) Measured and simulated thermal output of large-scale south-north tracking hybrid CPV/T system on April 14, 2017.
h sky is the radiating heat transfer coefficient, Tsky is the sky temperature, and εs is the emissivity of PV cells. The energy balance for CPV/T system can be expressed as:
Table 3 Whole-day comprehensive thermal efficiency of scale system.
Whole-day comprehensive thermal efficiency (%) Whole-day total thermal output (kJ)
Measured
Unsteady state
Steady state
55.8%
55.3%
55.0%
1730039.13 kJ
1714907.03 kJ
1704641.70 kJ
Q = Φ1 + Φ2 + Φ3 + Φ4 + Φ5 + Qoutput Q = (Ms Cs + Mg Cg ) + Mw Cw
(19)
h sa = 2.8 + 3.0uw
(20)
where, h sa is the convective heat transfer coefficient of the outer surface of PV/T, Ta is environment temperature, and uw is environmental wind velocity. Radiation heat loss can be expressed as follow:
Φ5 = h se As (Ts − Tsky )
(21)
2 h sky = σεs (Ts + Tsky )(Ts2 + Tsky )
(22)
+ Me Ce
∂T h ∂t
+ h sa As (Ts − Ta ) + h sky As (Ts − Tsky ) + MW in Cw
∂Tw L ∂x
(23)
where MW in is the water flow rate, and L is the total length of heat exchanger. Eq. (23) can calculate the thermal efficiency of the CPV/T system under unsteady condition. However, when the CPV/T system is in stable state, it shows:
Convection heat loss can be expressed as:
Φ4 = h sa As (Ts − Ta )
∂Tw ∂t
∂Ts ∂t
Φ1 = Φ2 = Φ3 = 0
Q = h sa As (Ts − Ta ) + h sky As (Ts − Tsky ) + MW in Cw
∂Tw L ∂x
(24)
Thus Eq. (24) is the steady thermal model for the CPV/T system. Under steady state, we can get the following relations according to the law of energy conservation. 437
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Q − Φ4 − Φ5 = h sw As (Ts − Tw )
(25)
measured one than that calculated by steady thermal model. This is because Xi’an was under a favorable meteorological condition, a clear day free of changeable weather like cloud or rain, during the operation on April 14, 2017, which ensured a relatively completed system operation cycle. Both the endothermic process of the system components at the start-up of the CPV/T system in the early morning, and exothermic process of the system components in the late afternoon with gradual decrease in solar irradiance and increase in cosine loss are relatively completed, during which the heat absorbed and released offsets with each other, and the total daily heat output of the system is close to that of the steady-state thermal model. However, in case that the weather changes from sunny to cloudy or from sunny to rainy and snowy during operation of the CPV/T system, the operation may suddenly break off, thus causing an incomplete exothermic process of the system components. Moreover, the steady-state thermal model doesn’t consider the endothermic process of the components at the start-up of the system, so the predicted values are higher than the actual ones. Yet the unsteady-state thermal model can always accurately predict the thermal output performance of the system during one operational cycle (one day). Therefore, in case that certain meteorological data are obtained, the annual thermal output performance of the system can be predicted by unsteady-state thermal model.
where h sw is the heat transfer coefficient between PV cells and water in the heat exchanger, which can be given by:
h sw = Nu
kw Dw
(26)
where k w is thermal conductivity of water, Dw is equivalent diameter of the flow channel, Nu is Nusselt number. For forced convective heat transfer of turbulence flow in aluminum alloy rectangular channel, Nusselt number can be given by:
Nu =
(f/8)(Re−1000)Prw D ⎡1 + ( w )⎤ l ⎦ 1 + 1.27 f/8 (Pr 2/3 w − 1) ⎣
(27)
where Re is Reynolds number, Prw is Prandtl number, f is Darcy drag coefficient, l is the length of aluminum alloy rectangular channel. Through Eq. (25) and Eq. (26), the difference of temperatures between PV cells and water in the heat exchanger can be calculated under different stable conditions. Fig. 9 shows the measured and simulated thermal efficiencies and thermal outputs of the large-scale south-north tracking hybrid CPV/T system on April 14, 2017, and the simulated results are calculated by unsteady and steady thermal models respectively. From Fig. 9, we can see that the simulation result calculated by unsteady thermal model coincides with the measured one. When the large-scale system operated initially, the thermal efficiency is low because part of solar radiation is absorbed and stored by PV cells, PV glass and heat exchanger, which reduces the temperature rise of water. When the rising rate of the temperature gradually decreases, thermal efficiency of the system continues to increase until the solar irradiance became almost stable. In the afternoon, the solar irradiance gradually decreases, and the thermal efficiency of the system increases because the above-mentioned three parts release heat to water while their temperatures decrease. The thermal efficiency curve shows that the simulated thermal output is slightly less than the measured one as the time goes, because the temperature change of some smaller devices in the large-scale system is not accounted for. The steady thermal model curve and the measured curve show different trends. In the morning and afternoon, the steady heat model curve shows lower system efficiency, while it is in good agreement with the measured one as the irradiance is relatively stable. Due to the higher environmental temperature at noon, the calculated heat loss is lower. While the environmental temperature in the morning and afternoon is lower than that at noon, the calculated heat loss is still larger. During the operation of system, the output power and solar radiation intensity per second can be obtained by measurement. Meanwhile, the thermal output power of the system can be calculated by the steady and unsteady thermal models. The whole-day comprehensive thermal efficiency of the large-scale system (work 6 h) can be obtained:
4. Conclusion The electrical and thermal output performance of two hybrid CPV/T units and then a large-scale hybrid CPV/T system was investigated at different time in one day. The result showed that the electrical efficiency of both two-axis tracking and south-north tracking CPV/T unit can reach 13%, which indicates that the effect of tracking mode on the electrical efficiency of the system was not obvious. Except for noon, the south-north tracking CPV/T unit, due to cosine loss, had lower electrical output power than the double-axis tracking CPV/T unit. The large-scale south-north tracking CPV/T system had slightly lower electrical efficiency than the south-north tracking CPV/T unit, due to the slight mismatch of multiple CPV/T units in series. Therefore, the CPV/T unit can be easily extended to different scale utilization without obvious electrical efficiency change, which is a strong basis for popularization and application of the CPV/T system. To study the thermal output performance of the large-scale CPV/T system, the unsteady-state thermal model and the steady-state thermal model was established. The steady-state thermal model can’t predict the thermal performance for the cases of rapid increase or decrease of solar radiation in the morning or afternoon due to thermal inertia of PV/T unit. In addition, the unsteady-state thermal model was adopted in the calculation, according to which the whole-day comprehensive thermal efficiency of the system is 55.3%, close to the measurement value 55.8%.Unlike the steady-state thermal model, unsteady-state thermal model can accurately predict the whole-day thermal efficiency variation of the system, and thus is of broader application value than steadystate thermal model.
Q
η=
21600 Qoutput i ∑Qoutput output i = Qoutput1
G
21600 As × ∑Gm Gm i m i = Gm 1
× 100\%
Acknowledgments
(28)
where Qoutput i is the system’s thermal output power at every moment by actual measurement or by model calculation, Gm i is the meteorological data at every moment by actual measurement. And Gm i can be given by:
Gm i = CGDNI i + CGSDI i
The present work is supported by the Key Research Project of Shaanxi Province (No. 2017ZDXM-GY-017), the Fundamental Research Funds for the Central Universities (No. cxtd2017004) and Yulin Science and Technology Project (NO. 2017KJJH-03).
(29)
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Design and performance study on a large-scale hybrid CPV/T system based on unsteady-state thermal model
T
⁎
Zexin Wanga, Jinjia Weia,b, , Gaoming Zhanga, Huling Xiec, Muhammad Khalidb a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shanxi 710049, China c Sichuan Energy Internet Research Institute, Tsinghua University, Chengdu, Sichuan 610213, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Large-scale CPV/T system South-north tracking Steady-state thermal model Unsteady-state thermal model
A hybrid CPV/T unit designed in this work concentrates solar radiation by a compound parabolic concentrator (CPC) and converts solar energy into electrical and thermal energy by a PV/T module. The CPC eliminating multiple reflections of solar radiation is defined as the ‘EMR-CPC’ in our previous work, which improves photoelectric and thermal conversion efficiencies. Two similar CPV/T units were tested with two-axis tracking device and south-north single-axis tracking device respectively, and the average photoelectric conversion efficiencies were 13% and 12%. A large-scale south-north tracking hybrid CPV/T system with sunlight collecting area of 810 m2 was built to explore practical application of this CPV/T unit. The whole-day thermal efficiency and total thermal output of the large-scale hybrid CPV/T system were 55% and 1,730,039 kJ respectively on April 14, 2017. The steady-state and unsteady-state thermal models of the hybrid CPV/T system were established and the energy loss was analyzed. The calculated whole-day comprehensive thermal efficiencies of the unsteadystate thermal model and the steady-state thermal model were 55.3% and 55.0% respectively, which were close to the measurement 55.8%. However, the steady-state thermal model failed to accurately predict the whole-day thermal efficiency variation of the system. In comparison, the unsteady-state thermal model accurately predicts instantaneous thermal efficiency of the system varying with meteorological conditions and its total daily heat output.
1. Introduction As the most widely used photoelectric conversion device in the world, crystalline silicon photovoltaic (PV) cells play an important role in global energy supply recently. To improve photoelectric conversion efficiency of PV cells, researchers designed different PV systems to tap the potential of the existing PV by using a concentrator to increase the solar energy density on PV cell surface. Early in 1976, the American national laboratory developed a concentrated photovoltaic (CPV) system which concentrated light by Fresnel lens cluster (Luque and Andreev, 2007). However, with the increase in solar energy density on PV cell surface, working temperature of PV cells increases, reducing photoelectric conversion efficiency and service life of PV cells. Thus, to reduce temperature of PV cells and recover thermal energy of PV cells efficiently becomes a hot spot in the PV field, giving rise to the advent of the concentrated photovoltaic/thermal (CPV/T) system. According to the study of Hasan and Sumathy. (2010), the total efficiency of a CPV/T
⁎
system can reach 60% to 80%. As is known, the CPV/T systems are classified into CPV/T systems with high concentration ratios and those with low concentration ratios (2–10) (Baig et al., 2012). Conventional crystalline silicon photovoltaic cells are used in CPV/T systems with low concentration ratios, while the compound parabolic concentrators (CPCs) are relatively common concentrators with low concentration ratios. Compared with highly-concentrated CPV/T systems in which costs of concentrator manufacturing and the accurate tracking system are relatively high and scattered light can’t be adopted, the CPV/T systems with low concentration ratios are more promising for their commercialization. Othman et al. (2005) designed a dual-channel PV/T with a radiator fan for an air collector system using the CPC to collect solar radiation and established a one-dimensional steady-state heat transfer model for thermal efficiency analysis. Nilsson, J. et al. (2007) long term evaluation of an asymmetric CPC PV-thermal hybrid built for high latitudes (lat 55.7o), and calculated the output of this system by MINSUN simulation program. Bernardo et al. (2011) propose a complete methodology which can characterize, simulate and evaluate CPV/
Corresponding author at: State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. E-mail address: [email protected] (J. Wei).
https://doi.org/10.1016/j.solener.2018.11.043 Received 10 July 2018; Received in revised form 15 November 2018; Accepted 17 November 2018 0038-092X/ © 2018 Published by Elsevier Ltd.
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L1′
Nomenclature
As C Cw Cg Cs Ce cos θ Dc Dd Dw Fend Fw f GTSI GDNI GSDI Gt′ Gm
Gms
H1 H2 h sa h sky h sw
Im kw L
aperture area of PV/T module, m2 geometric concentration ratio of EMR-CPC specific heat capacity of water, J/(kg K) specific heat capacity of PV glass, J/(kg K) specific heat capacity of PV cell, J/(kg K) specific heat capacity of heat exchanger, J/(kg K) Cosine loss coefficient length of PV cells, (m) distance between the best concentration plane and the outlet plane, (m) equivalent diameter of water flow (cooling channel) edge loss factor water flow rate, L/h Darcy drag coefficient, total solar radiation intensity, W/m2 direct solar radiation intensity, W/m2 diffuse solar radiation intensity, W/m2 total radiation intensity of south-north tracking hybrid CPV/T system, W/m2 the intensity of solar radiation collected by the concentrator, W/m2 the intensity of solar radiation absorbed by PV/T component (module), W/m2 height of the CPV/T unit, (m) maximum height of east-west tracking CPV/T system, (m) convective heat transfer coefficient, W/(m2 K) radiative heat transfer coefficient, W/(m2 K) coefficient of heat transfer between PV cells and water, W/ (m2 K) maximum operating current, A thermal conductivity of water, W/(m2 K) total length of the direction of the tracking axis, (m)
l Ms Mw Mg Me Nu Prw Qoutput Re Tout Tin Ts Te Tγ Ta Tsky Um u(ηt ) u(ηe ) α β δ εs γ ηa ηe ηm ηg ηt ηγ ρ Φ
length of the tilted single-axis east-west tracking CPV/T system, (m) length of aluminum alloy rectangular channel, (m) mass of PV cells, kg mass of water in heat exchanger (cooling channel), kg mass of PV glass, kg mass of heat exchanger, kg Nusselt number Prandtl number thermal power output, W Reynolds number outlet water temperature, °C inlet water temperature, °C temperature of PV cells, °C temperature of heat exchanger, °C reference temperature, °C temperature of environment, °C sky temperature, °C maximum operating voltage, V maximum uncertainty of thermal efficiency maximum uncertainty of electrical efficiency solar elevation angle, ° solar azimuth, ° angle of installation for east-west tracking system, ° emissivity of PV cell, – acceptance half angle of EMR-CPC, ° total efficiency electrical efficiency reflectivity of reflector mirror transmittance of solar PV glass thermal efficiency solar cells efficiency at the reference temperature solar radiation absorptivity of solar cell power, W
HP system achieved an averaged COP of 4.8, with an output electrical efficiency of 17.5%, 1.36 times higher than that of the LCPV system. Hangweirer et al. (2015) designed a linear Fresnel concentrator mirror module and used in a CPV/T system, the electrical efficiency of the CPV/T system was 6.2%, and thermal efficiency was 61.2%. The thermal efficiency and electrical efficiency of the trough concentrator CPV/T system were 58% and 11% respectively, and the total energy conversion efficiency was 69% Coventry. (2005). Kong et al. (2013) developed a linear Fresnel coupling CPV/T system and tested the output performance of this CPV/T system in different weather conditions. In sunny weather conditions, the electrical efficiency was 9.86%, and the thermal efficiency was 63%. Li et al. (2011) compared the optimum concentration ratios of different photovoltaic cells in the trough concentrator system and found out that the optimal concentration ratio of crystalline silicon cells was 4.23 times. Milad et al. (2017) devised a novel CPV/T system, and its daily average electrical and thermal efficiencies could reach 4.83% and 46.16% respectively. Karathanassis et al. (2017) adopted parabolic trough as the concentrator, coupled an efficient heat exchanger and developed a CPV/T system. The CPV/T prototype has an overall efficiency approximate to 50% (44% thermal and 6% electrical efficiencies). At present, the CPV/T system is still in development as a single experiment system. Many scholars tried to optimize the condenser and the heat exchanger to improve the electrical efficiency and thermal efficiency of the system, but these systems are still far from practical application. So it is very important to develop an efficient low-cost CPV/T system that can be used on a large scale. In this work, we have designed and developed a large-scale hybrid CPV/T system by using the CPV/T unit of one new type truncated CPC (Compound Parabolic
T hybrid systems. And they exemplified in a particular case study. The measurements show that, there is margin of improvement for the studied this CPV/T system. Chaabane et al. (2013) tested the performance of a non-symmetrical CPC concentrator with PV and PV/T. The experimental results showed that the CPV/T system has higher power output and electrical efficiency than the CPV system. Brogren et al. (2001) discussed the concentration ratios CPC-PV/T system adopting water for heat exchange and proposed a set of methods based on the overall efficiency of the optical data calculation model of the CPC-PV/T system. Baig et al. (2014) designed a three-dimensional Cross Compound Parabolic Concentrator (3-DCCPC) with a geometric concentrating ratio of 3.6, and the maximum output power of the concentrated PV was 2.67 times as much as the non-concentrated PV. They also studied the effect of uneven concentrated light spot on photoelectric efficiency of the system. Tripathi and Tiwari. (2017) designed and fabricated a fully covered CPC-PVT system, and they considered two cases, case (i): fixed position and case (ii): manual maximum power point tracking technique. The results show that the annual net thermal energy and exergy, obtained by case (ii), were 1.25 and 1.19 times higher than for case (i). Proell, M. et al. (2017) constructed real-size CPC PV/T collector prototype. The thermal efficiency and electrical efficiency of this CPC PV/T system were 34% and 9%. In addition to CPC, the coupling PV/T systems with the trough concentrator and the linear Fresnel concentrator are also commonly studied. Karathanassis et al. (2013) used two different microchannel heat sink suitable for the cooling of a linear parabolic trough Concentrating Photovoltaic/Thermal (CPVT) system. Xu et al. (2011) constructed a novel low-concentrating CPV/T integrated heat pump system with a parabolic concentrator. Experimental results showed that the LCPV/T428
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predict the variation curve of the whole-day thermal efficiency of the system.
Concentrator), tested and analyzed its electrical and thermal performance. These are key steps for commercial application of the CPV/T system. This new type truncated CPC in the system has been defined as EMR (Eliminating Multiple Reflections) CPC for the sake of distinction, and Eliminating Multiple Reflections of solar radiation is the truncation method of CPC for designing EMR-CPC. In fact, the truncation principle of this new type truncated CPC has been previously studied and ‘EMRCPC’ has been defined before by our group Xie et al. (2016). This EMRCPC has higher optical efficiency than common CPCs due to its characteristic of eliminating multiple reflections of solar radiation. The uniformity and optical efficiency of EMR-CPC were higher than full CPC. Besides, the material consumption and height of EMR-CPC are about one-half less than that of full CPC, which reduced the manufacture and maintenance costs substantially. EMR-CPC is the CPC after truncated with acceptance half angle of 10.6°, which means it is more dependent on the solar tracking system than full CPC. We adopted different tracking methods to couple them with the CPV/T units and compared the electrical efficiencies of the CPV/T units with two-axis tracking and single-axis south-north tracking methods. We found that except for cosine loss, the single-axis southnorth tracking has no other influence on the electrical efficiency of the CPV/T unit. Under overall consideration of the construction cost and application field of CPV/T systems with four different kinds of tracking methods, the single-axis south-north tracking method was chosen for large-scale hybrid CPV/T system. Based on the work above, we designed and established a large-scale south-north tracking hybrid CPV/T system with the sunlight collecting area of 810 m2 for large-scale commercialization application. The measuring results showed the performance of the large-scale south-north tracking hybrid CPV/T system was better than expected. And the series connection between multiple CPV/T units in the large-scale CPV/T system had lower mismatch loss and ohm loss. To study the thermal performance of the large-scale CPV/T system, steady-state and unsteady-state thermal models were established respectively. Steady-state thermal model is widely used to analyze the thermal performance of the CPV/T and PV/T systems, and it can predict the thermal performance accurately when the solar radiation is stable. However, there usually is cosine loss in single-axis tracking CPV/T systems. The intensity of solar radiation which can be used by singleaxis tracking CPV/T systems is continuously changed, therefore the steady-state thermal model cannot predict the thermal output of singleaxis tracking solar systems well. So, we established an unsteady-state thermal model to analyze the energy loss of hybrid CPV/T system, which can predict the thermal output of the single-axis tracking CPV/T system accurately. The unsteady-state thermal model is more advanced than the steady-state thermal model because the former considers impacts of temperature variations of the PV cell, PV glass, heat exchanger and heat transfer media in the system on thermal output performance of the system. Therefore, the unsteady-state thermal model can accurately
2. Description of hybrid CPV/T systems Two hybrid CPV/T systems were set up in Xi’an, Shaanxi Province, China, at 114° east longitude and 34° north latitude. Those systems were configured with different types of sun tracking devices, two-axis tracking and south-north tracking. The two-axis tracking hybrid CPV/T system composed of 12 CPV/T units was used for testing and improving design of the CPV/T units. Accordingly, the large-scale south-north tracking hybrid CPV/T system with 810 CPV/T units was constructed to explore the possibility for practical application. 2.1. CPV/T unit Flat-plate photovoltaic-thermal (PV/T) collectors and CPC eliminating multiple reflections of solar radiation (EMR-CPC) are the main parts of the CPV/T unit. The structure of PV/T module is shown in Fig. 1. Ten156mm × 156 mm polycrystalline PV cells manufactured by JA SOLAR Corporation were cut into twenty 156 mm × 78 mm cells by laser light and then the cells were connected in series. In the concentration case, the operating current increases greatly since it is proportional to the solar radiation, which increases the ohm loss greatly. Reducing the area of single cell made the maximum operating current of the 156 mm × 78 mm solar cells was about one-half less than that of the 156 mm × 156 mm solar cells, and the maximum operating voltage was doubled. This approach greatly reduces the ohm loss of the CPV/T unit. Next, those cells were laminated onto an aluminum alloy rectangular channel heat exchanger in which water is used as the coolant. Compared with the method of attaching PV cells to the heat exchanger with thermal conductive silicone, the lamination method can make more even and closer contact between the heat exchanger and the PV cells, and effectively improve the heat transfer coefficient between the PV cells and heat exchanger. To a large extent, it avoids occurrence of heat exchange failure between local PV cells and heat exchangers, thus ensures safe operation of the system and greatly increases the service life of PV/T module. The geometric concentration ratio of EMR-CPC is 4×, and EMR-CPC is coupled by symmetrical parabolic reflectors. The back-silvered reflector mirrors can provide reflectivity as high as 0.94. The design method of EMR-CPC has been reported Xie et al. (2016). The optical efficiency of EMR-CPC can be expressed as follows respectively:
ηEMR = [(C - 1) ηm GDNI + GDNI + GSDI ]/ Gm
(1)
Gm = CGDNI + CGSDI
(2)
where ηm is reflectivity of the reflector mirror, GDNI is direct solar
Fig. 1. (A) The cross sectional view of PV/T unit and (B) Diagram of water flow in PV/T unit. 429
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ηt = Qoutput / As (CGDNI + CGSDI ) = Fw Cw (Tout − Tin )/ As (CGDNI + CGSDI )
radiation intensity, GSDI is diffuse solar radiation intensity, Gm is the intensity of solar radiation which can be used by EMR-CPC, and C is geometric concentration ratio of EMR-CPC, and C = 4 . The top surface of PV/T is installed on the best concentration plane of EMR-CPC to form CPV/T unit which is shown in Fig. 2. It is noted that the best concentration plane is not the outlet plane of the EMRCPC, and it is parallel to and lower from the outlet plane. According to the edge-ray principle, a large proportion of solar radiation must be concentrated on the edge of the outlet aperture of EMR-CPC and then the uniformity of solar radiation on outlet aperture is certainly bad, so it is not a good strategy to install the PV/T on outlet aperture. On the best concentration plane, the nonuniformity of the concentrated solar flux distribution is the smallest Xie et al. (2016). The distance between the best concentration plane and the outlet plane can be given by:
D b = Do ·tan γ
(5) where ηt is the thermal efficiency of hybrid CPV/T system. Qoutput is the thermal power output of hybrid CPV/T system. Where Fw is water flow rate. Cw is specific heat capacity of water. Tout and Tin are outlet water temperature and inlet water temperature respectively. The total efficiency is obtained by:
ηa = ηt + ηe
Though the two-axis tracking CPV/T system has high output performance, it cannot be applied on a large-scale due to many deficiencies. One reason is the high cost, and another reason is the large height which requires higher steel strength to resist wind and snow, and higher steel strength means greater mass, so it is difficult to be installed on the roof. As discussed above, for the large-scale application of CPV/T systems, the two-axis tracking mode is not suitable, so the single-axis tracking mode can be considered. For linear concentrators like CPCs, common single-axis tracking modes include three types: single-axis south-north tracking, flat single-axis east-west tracking and tilted single-axis east-west tracking modes. As for the titled single-axis eastwest tracking mode, the maximum height of the CPV/T system can be calculated by:
(3)
where Do is the width of outlet plane, Do = DB = Dc = 156 mm , where D b is the width of best concentration plane of EMR-CPC, and Dc is the width of PV cells, γ is the acceptance half angle of EMR-CPC. 2.2. Two-axis tracking hybrid CPV/T system With high half acceptance angle of EMR-CPC and low geometric concentration ratio, this CPV/T unit doesn’t need a high-precision solar tracking device. So we adopted a more mature two-axis tracking device with a single chip. The system consists of 12 CPV/T units in series arranged in six rows as shown in Fig. 3A. Fig. 3B is the schematic diagram of the system. The measurement points assigned are far more abundant than those shown in Fig. 4, which helps to understand the performance parameters of the system. The electrical efficiency can be obtained by:
ηe = Im Um/ As (CGDNI + CGSDI )
(6)
H2 = (L′1 + H1)·cos δ
(7)
where δ is the angle of installation for tilted single-axis east-west tracking CPV/T system. H1 is the height of the CPV/T unit. L′1 is the length of the tilted single-axis east-west tracking CPV/T system. Assuming that L′1 is 6 m and H1 is 0.9 m, the maximum height of the tilted single-axis east-west tracking CPV/T system in Xi’an (34°N) can reach as high as 5.3 m. As we can see, it is not safe and reliable to install the tilted single-axis east-west tracking CPV/T system on the roof. The system is not easy to maintain either. If the length of CPV/T system decreases, more tracking devices have to be used, which means the cost increases. Thus the tilted single-axis east-west tracking mode is not suitable for the large scale application of CPV/T systems. And for the single-axis south-north tracking and flat single-axis east-
(4)
where Im is maximum operating current, Um is maximum operating voltage, and As is Aperture area of PV/T module. The thermal efficiency is obtained by:
Fig. 2. Schematic of CPV/T unit. 430
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Fig. 3. (A) Photograph of two-axes tracking hybrid CPV/T system (B) Schematic diagram of the system.
2.3. Large-scale south-north tracking hybrid CPV/T system
west tracking modes, the edge loss and cosine loss will be introduced. The edge loss can be eliminated by expand the length of the concentrator, but the cosine loss is inevitable. The maximum cosine loss coefficient of these two tracking modes are cos 42° and cos 56° respectively. For the flat single-axis east-west tracking mode, the maximum cosine loss coefficient arises on winter solstice. In winter, the demand for thermal energy is significantly large but the efficiency of the flat single-axis east-west tracking CPV/T system is low due to large cosine loss, and thus low output cannot match the large demand for thermal energy, which means the flat single-axis east-west tracking mode has a very large difference of thermal energy output between summer and winter and is not suitable for the large scale application of CPV/T systems either. Finally, for the single-axis south-north tracking mode, the maximum cosine loss coefficient arises on summer solstice. In summer, the demand for thermal energy is not as large as that in winter, so the effect of the decrease in efficiency due to cosine loss on the thermal energy supply to the user terminal is not obvious. In conclusion, the single-axis south-north tracking mode is the most suitable tracking strategy for the large-scale application of CPV/T systems.
Based on the CPV/T unit, we designed a new-type south-north tracking hybrid CPV/T system which has its construction cost, maximum installation height and unit mass far lower than those of the twoaxis tracking hybrid CPV/T system with the same peak output power (see Table 1), so the former is more suitable for large scale utilization. Fig. 4A is the design drawing of the south-north tracking hybrid CPV/T system, and we built one small-scale south-north tracking hybrid CPV/T system based on this design. The photograph of this small-scale system is shown in Fig. 4B, and Fig. 4C is the schematic diagram. The small-scale CPV/T system consists of 6 CPV/T units in series, which are arranged in two rows. This CPV/T system is used to verify the feasibility and reliability of the south-north tracking hybrid CPV/T. Based on the small-scale CPV/T system, we established the largescale south-north tracking hybrid CPV/T system. The large-scale system consists of 810 CPV/T units arranged in eighteen different rectangular arrays in series. These eighteen arrays include six 7 × 6 arrays, seven 8 × 8 arrays and five 2 × 11 arrays placed at the top of two buildings. The aerial photograph of the large-scale system is shown in Fig. 5A. Fig. 5B is the schematic diagram of a part of the large-scale system consisting of four 7 × 6 arrays. 431
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Fig. 4. (A) photograph of the small-scale system; (B) Schematic diagram of small-scale syst.
total radiation intensity of the south-north tracking hybrid CPV/T system can be expressed as follows:
The incident surface of the south-north tracking hybrid CPV/T system is not perpendicular to the direction of the direct solar radiation, and we assume that the incident angle, that is, the angle between the incident ray and the normal line of the incident surface is θ . Thus cos θ is the cosine loss coefficient of direct solar radiation, while the intensity of diffuse solar radiation is consistent in all directions. Therefore, the
Gt′ = GDNI cos θ + GSDI where cos θ is given by: 432
(8)
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Table 1 maximum installation height and unit mass of different tracking mode.
Two-axis tracking hybrid CPV/T system South-north tracking hybrid CPV/T system
Maximum installation height (m)
Unit mass (kg)
3.2 1.7
171 55
Fig. 5. (A) Aerial photograph of the large-scale system; (B) Schematic diagram of a part of the large-scale system. 433
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cos θ =
(cos α cos β )2 + sin2 α (cos α cos β )2 + (cos α sin β )2 + sin2 α
With the variation in solar azimuth angle, the cosine loss appears in the south-north tracking CPV/T unit, so that its output power is gradually lower than that of the two-axis tracking unit. At the same time, with the change of the direct radiation incidence angle, the energy distribution on the optimal concentration plane changes, and its uniformity decreases. Therefore, the electrical efficiency and fill factor of the south-north tracking CPV/T unit are lower than those of the twoaxis tracking unit. However, the electrical efficiency of these two units reaches to the lowest at noon, because higher solar radiation intensity enlarges the maximum operating current of CPV/T units, resulting in larger ohm loss at noon. Fig. 7 shows the electrical efficiency and electrical power output of large-scale south-north tracking hybrid CPV/T system and the solar radiation intensity affected by the cosine effect. From Fig. 7, we can see that the large-scale south-north tracking hybrid CPV/T system and CPV/T unit 2# have similar electrical characteristics, while the electrical efficiency of the large-scale CPV/T system is lower than that of CPV/T unit 2# due to slight mismatch between multiple CPV/T units in series. Generally, large-scale photovoltaic systems have different degrees of mismatch. The electrical efficiency of the large-scale CPV/T system is between 12.2% and 13.2%, with the highest electrical power output of 91.8 kW.
(9)
where α is solar elevation angle, and β is solar azimuth angle. When β = 0 , cos θ = 1. The south-north tracking hybrid CPV/T system has no cosine loss at this time. Gt′ can be directly measured when the pyranometer is mounted parallel to the incident plane of the south-north tracking hybrid CPV/T system. The south-north tracking hybrid CPV/T system also has the edge loss effect, and the edge loss factor is defined as Fend :
Fend = 1 −
H tan θ L
(10)
where L is the total length of the EMR-CPC, and H relates to the structure of the concentrator, mainly affected by the height of EMRCPC. We calculated the length of the concentrator, made it longer than PV/T module, and thus avoided the edge loss effect on the system completely. 3. Results and discussion 3.1. Uncertainty analysis
3.3. Thermal analysis of hybrid CPV/T system
The uncertainty analysis of variables is based on the method of Kline et al. (1953). The accuracy grades of main instruments are shown in Table2. The maximum uncertainty of thermal efficiency of the system is given by:
u(ηt ) =
u (Fw )2 + u (T )2 + u (G )2
Assuming that the thermal resistance of thermal insulation material was infinite, the thermal loss from insulation material of the PV/T module would not be considered. The analysis on the transmission and transformation of solar radiation in the CPV/T system is shown in Fig. 8. Gm is the solar radiation intensity concentrated by EMR-CPC, which can be figured out by Eq. (2). Some concentrated solar radiation passes through the solar PV glass and illuminates on the surface of PV/T, whilst some is absorbed and reflected by the glass. Assuming the transmittance of solar PV glass is ηg , the absorptivity of solar cell is ρ and n is the number of times that sunlight reflects between PV cell and PV glass. The solar radiation intensity absorbed by the PV/T module Gms can be expressed as (Gueymard, 2004):
(11)
where u (Fw ) , u (T ) and u (G ) are the maximum uncertainty of flow meter, thermocouple and pyranometer respectively. The maximum uncertainty of electrical efficiency of the system is given by:
u(ηe ) =
u (IV )2 + u (G )2
(12)
where u (IV ) is the maximum uncertainty of IV curve tester. According to Eqs. (11) and (12), the maximum uncertainties of thermal efficiency and electrical efficiency are 3.5% and 3.16% respectively.
∞
Gms = Gm ηEMR ρηg
∑
[(1 − ρ)(1 − ηg )]n =
n= 0
Gρηg 1 − (1 − ρ)(1 − ηg )
(13)
As is the aperture area of PV/T, and the heat exchange area of aluminium alloy rectangular channel is expressed as Ah , Ah = As . With part of As Gms (the solar radiation power absorbed by the PV/T module) converted to electrical power, the rest is the thermal energyQ , which can be obtained by:
3.2. Electrical performance of CPV/T systems with different tracking modes Two CPV/T units were studied with almost the same configuration but different tracking modes. The CPV/T unit 1# used two-axis tracking device to track the sun, while the CPV/T unit 2# used the south-north tracking device. The tested results showed that the average electrical efficiency of two-axis tracking CPV/T unit was 13%, while the southnorth tracking CPV/T unit was 12.5%. Fig. 6(A) displays the IV and PV characteristic curves of the two CPV/T units above at noon, and Fig. 6(B) shows the variations with time in their electrical efficiency and electrical power output by simultaneous determination. As shown in the Fig. 6(B), the electrical performances of the two CPV/T units are almost the same at noon (12:34 local time), because of inexistence of cosine loss in the south-north tracking CPV/T unit.
(14)
Q = As Gms - Es where Es is the electrical power output.
Es = As ηe Gm = As ηγ [1 − β (Ts − Tγ )] Gms
(15)
where ηγ represents the solar cell efficiency at the reference temperature Tγ , and Ts represents the temperature of solar cells. With the transfer of thermal energy from PV cells to the aluminum alloy rectangular channel and then into water in the heat exchanger,
Table 2 Accuracy grades of main instruments. Name
Accuracy grade
units
Institute for metrology
Flow meter Thermocouple Radiation meter for solar ray IV curve tester
0.6% 1.7% 3% 1%
L/h °C W/m2 W
Shaanxi Institute of Metrology Science Shaanxi Institute of Metrology Science National Institute of Metrology, China Shaanxi Institute of Metrology Science
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Fig. 6. (A) IV and PV curves of the two units (B) Variationsin electrical efficiency and electrical power output of the two units.
where Ms and Mg are the mass of PV cells and Solar PV glass, Cs and Cg are their specific heat.
the temperature of the solar PV glass, PV cells and aluminum alloy rectangular channel changes. With the decrease of the above-mentioned temperature, energy released by the three parts of PV/T is transferred to water flow to increase water temperature. When the variation in solar radiation intensity is too small to be ignored, the water flow is constant, which means the temperatures of the above three parts are unchanged. In this case, the CPV/T system was in steady state. The approximation here represents that the temperature of Solar PV glass and PV cells is always consistent and can be considered as a whole. Φ1 represents the thermal power of PV cells and Solar PV glass, and Φ2 indicates the thermal power of aluminum alloy rectangular channel, and can be expressed respectively as
Φ1 = (Ms Cs + Mg Cg )
∂Ts ∂t
Φ2 = Me Ce
∂Te ∂t
(17)
where Me and Ce are the mass and specific heat of aluminum alloy rectangular channel. Likewise, in unsteady state, the average temperature of water in the heat exchanger changes as well, directly affecting the thermal output of the system, and the thermal power of water can be expressed as.
Φ3 = Mw Cw
∂Tw ∂t
(18)
where Mw , Cw and Tw are respectively the mass, specific heat and temperature of water in the heat exchanger. At the same time, there are radiation heat loss and convection heat loss on the outer surface of PV/T.
(16) 435
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Fig. 7. (A) Electrical efficiency of large-scale south-north tracking hybrid CPV/T system on April 14, 2017. (B) Electrical power output of large-scale south-north tracking hybrid CPV/T system on April 14, 2017.
Fig. 8. Energy flow diagram of the CPV/T system.
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Fig. 9. (A) Measured and simulated thermal efficiency of large-scale south-north tracking hybrid CPV/T system on April 14, 2017. (B) Measured and simulated thermal output of large-scale south-north tracking hybrid CPV/T system on April 14, 2017.
h sky is the radiating heat transfer coefficient, Tsky is the sky temperature, and εs is the emissivity of PV cells. The energy balance for CPV/T system can be expressed as:
Table 3 Whole-day comprehensive thermal efficiency of scale system.
Whole-day comprehensive thermal efficiency (%) Whole-day total thermal output (kJ)
Measured
Unsteady state
Steady state
55.8%
55.3%
55.0%
1730039.13 kJ
1714907.03 kJ
1704641.70 kJ
Q = Φ1 + Φ2 + Φ3 + Φ4 + Φ5 + Qoutput Q = (Ms Cs + Mg Cg ) + Mw Cw
(19)
h sa = 2.8 + 3.0uw
(20)
where, h sa is the convective heat transfer coefficient of the outer surface of PV/T, Ta is environment temperature, and uw is environmental wind velocity. Radiation heat loss can be expressed as follow:
Φ5 = h se As (Ts − Tsky )
(21)
2 h sky = σεs (Ts + Tsky )(Ts2 + Tsky )
(22)
+ Me Ce
∂T h ∂t
+ h sa As (Ts − Ta ) + h sky As (Ts − Tsky ) + MW in Cw
∂Tw L ∂x
(23)
where MW in is the water flow rate, and L is the total length of heat exchanger. Eq. (23) can calculate the thermal efficiency of the CPV/T system under unsteady condition. However, when the CPV/T system is in stable state, it shows:
Convection heat loss can be expressed as:
Φ4 = h sa As (Ts − Ta )
∂Tw ∂t
∂Ts ∂t
Φ1 = Φ2 = Φ3 = 0
Q = h sa As (Ts − Ta ) + h sky As (Ts − Tsky ) + MW in Cw
∂Tw L ∂x
(24)
Thus Eq. (24) is the steady thermal model for the CPV/T system. Under steady state, we can get the following relations according to the law of energy conservation. 437
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Q − Φ4 − Φ5 = h sw As (Ts − Tw )
(25)
measured one than that calculated by steady thermal model. This is because Xi’an was under a favorable meteorological condition, a clear day free of changeable weather like cloud or rain, during the operation on April 14, 2017, which ensured a relatively completed system operation cycle. Both the endothermic process of the system components at the start-up of the CPV/T system in the early morning, and exothermic process of the system components in the late afternoon with gradual decrease in solar irradiance and increase in cosine loss are relatively completed, during which the heat absorbed and released offsets with each other, and the total daily heat output of the system is close to that of the steady-state thermal model. However, in case that the weather changes from sunny to cloudy or from sunny to rainy and snowy during operation of the CPV/T system, the operation may suddenly break off, thus causing an incomplete exothermic process of the system components. Moreover, the steady-state thermal model doesn’t consider the endothermic process of the components at the start-up of the system, so the predicted values are higher than the actual ones. Yet the unsteady-state thermal model can always accurately predict the thermal output performance of the system during one operational cycle (one day). Therefore, in case that certain meteorological data are obtained, the annual thermal output performance of the system can be predicted by unsteady-state thermal model.
where h sw is the heat transfer coefficient between PV cells and water in the heat exchanger, which can be given by:
h sw = Nu
kw Dw
(26)
where k w is thermal conductivity of water, Dw is equivalent diameter of the flow channel, Nu is Nusselt number. For forced convective heat transfer of turbulence flow in aluminum alloy rectangular channel, Nusselt number can be given by:
Nu =
(f/8)(Re−1000)Prw D ⎡1 + ( w )⎤ l ⎦ 1 + 1.27 f/8 (Pr 2/3 w − 1) ⎣
(27)
where Re is Reynolds number, Prw is Prandtl number, f is Darcy drag coefficient, l is the length of aluminum alloy rectangular channel. Through Eq. (25) and Eq. (26), the difference of temperatures between PV cells and water in the heat exchanger can be calculated under different stable conditions. Fig. 9 shows the measured and simulated thermal efficiencies and thermal outputs of the large-scale south-north tracking hybrid CPV/T system on April 14, 2017, and the simulated results are calculated by unsteady and steady thermal models respectively. From Fig. 9, we can see that the simulation result calculated by unsteady thermal model coincides with the measured one. When the large-scale system operated initially, the thermal efficiency is low because part of solar radiation is absorbed and stored by PV cells, PV glass and heat exchanger, which reduces the temperature rise of water. When the rising rate of the temperature gradually decreases, thermal efficiency of the system continues to increase until the solar irradiance became almost stable. In the afternoon, the solar irradiance gradually decreases, and the thermal efficiency of the system increases because the above-mentioned three parts release heat to water while their temperatures decrease. The thermal efficiency curve shows that the simulated thermal output is slightly less than the measured one as the time goes, because the temperature change of some smaller devices in the large-scale system is not accounted for. The steady thermal model curve and the measured curve show different trends. In the morning and afternoon, the steady heat model curve shows lower system efficiency, while it is in good agreement with the measured one as the irradiance is relatively stable. Due to the higher environmental temperature at noon, the calculated heat loss is lower. While the environmental temperature in the morning and afternoon is lower than that at noon, the calculated heat loss is still larger. During the operation of system, the output power and solar radiation intensity per second can be obtained by measurement. Meanwhile, the thermal output power of the system can be calculated by the steady and unsteady thermal models. The whole-day comprehensive thermal efficiency of the large-scale system (work 6 h) can be obtained:
4. Conclusion The electrical and thermal output performance of two hybrid CPV/T units and then a large-scale hybrid CPV/T system was investigated at different time in one day. The result showed that the electrical efficiency of both two-axis tracking and south-north tracking CPV/T unit can reach 13%, which indicates that the effect of tracking mode on the electrical efficiency of the system was not obvious. Except for noon, the south-north tracking CPV/T unit, due to cosine loss, had lower electrical output power than the double-axis tracking CPV/T unit. The large-scale south-north tracking CPV/T system had slightly lower electrical efficiency than the south-north tracking CPV/T unit, due to the slight mismatch of multiple CPV/T units in series. Therefore, the CPV/T unit can be easily extended to different scale utilization without obvious electrical efficiency change, which is a strong basis for popularization and application of the CPV/T system. To study the thermal output performance of the large-scale CPV/T system, the unsteady-state thermal model and the steady-state thermal model was established. The steady-state thermal model can’t predict the thermal performance for the cases of rapid increase or decrease of solar radiation in the morning or afternoon due to thermal inertia of PV/T unit. In addition, the unsteady-state thermal model was adopted in the calculation, according to which the whole-day comprehensive thermal efficiency of the system is 55.3%, close to the measurement value 55.8%.Unlike the steady-state thermal model, unsteady-state thermal model can accurately predict the whole-day thermal efficiency variation of the system, and thus is of broader application value than steadystate thermal model.
Q
η=
21600 Qoutput i ∑Qoutput output i = Qoutput1
G
21600 As × ∑Gm Gm i m i = Gm 1
× 100\%
Acknowledgments
(28)
where Qoutput i is the system’s thermal output power at every moment by actual measurement or by model calculation, Gm i is the meteorological data at every moment by actual measurement. And Gm i can be given by:
Gm i = CGDNI i + CGSDI i
The present work is supported by the Key Research Project of Shaanxi Province (No. 2017ZDXM-GY-017), the Fundamental Research Funds for the Central Universities (No. cxtd2017004) and Yulin Science and Technology Project (NO. 2017KJJH-03).
(29)
References
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