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Energy Express

  • Editor: Christian Seassal
  • Vol. 21, Iss. S6 — Nov. 4, 2013
  • pp: A942–A952
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Design and testing of a uniformly solar energy TIR-R concentration lenses for HCPV systems

S. C. Shen, S. J. Chang, C. Y. Yeh, and P. C. Teng  »View Author Affiliations


Optics Express, Vol. 21, Issue S6, pp. A942-A952 (2013)
http://dx.doi.org/10.1364/OE.21.00A942


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Abstract

In this paper, total internal reflection-refraction (TIR-R) concentration (U-TIR-R-C) lens module were designed for uniformity using the energy configuration method to eliminate hot spots on the surface of solar cell and increase conversion efficiency. The design of most current solar concentrators emphasizes the high-power concentration of solar energy, however neglects the conversion inefficiency resulting from hot spots generated by uneven distributions of solar energy concentrated on solar cells. The energy configuration method proposed in this study employs the concept of ray tracing to uniformly distribute solar energy to solar cells through a U-TIR-R-C lens module. The U-TIR-R-C lens module adopted in this study possessed a 76-mm diameter, a 41-mm thickness, concentration ratio of 1134 Suns, 82.6% optical efficiency, and 94.7% uniformity. The experiments demonstrated that the U-TIR-R-C lens module reduced the core temperature of the solar cell from 108 °C to 69 °C and the overall temperature difference from 45 °C to 10 °C, and effectively relative increased the conversion efficiency by approximately 3.8%. Therefore, the U-TIR-R-C lens module designed can effectively concentrate a large area of sunlight onto a small solar cell, and the concentrated solar energy can be evenly distributed in the solar cell to achieve uniform irradiance and effectively eliminate hot spots.

© 2013 OSA

1. Introduction

The most important components of a high concentration photovoltaic (HCPV) module are the concentration lens and the solar cell. Currently, solar cells are produced from monocrystalline silicon, polycrystalline silicon, and gallium arsenide (i.e., III-V solar cells) [1

1. N. L. Panwar, S. C. Kaushik, and S. Kothari, “Role of renewable energy sources in environmental protection: A review,” Renew. Sustain. Energy Rev. 15(3), 1513–1524 (2011). [CrossRef]

]. Although contemporary monocrystalline or polycrystalline silicon solar cells are economical, their photoelectric conversion efficiencies range between 15% and 20%. By comparison, III-V solar cells possess a conversion efficiency ranging between 40% and 50% but are expensive [2

2. H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, and N. Karam, “III–V multijunction solar cells for concentrating photovoltaics,” Energy Environ. Sci. 2(2), 174–192 (2009). [CrossRef]

]. Thus, HCPV system designs contain large-area concentration lenses and small III-V solar cells, upon which a concentration of sunlight equal to hundreds and thousands of suns is irradiated, increasing the generated power.

This study adopted the energy configuration technique method to design a uniform U-TIR-R-C lens module that appropriately and evenly distributes solar energy on solar cell surfaces. This design eliminate hot spots on the surface of solar cell and increase conversion efficiency for HCPV systems.

2. Design and simulation

The design concept diagram of the U-TIR-R-C lens module is shown in Fig. 1
Fig. 1 (a) Design diagram of U-TIR-R-C lens module and (b) T-TIR-R-C lens module
. Figure 1(a) illustrates the design of the primary optical element (POE), or the TIR-R lens, and Fig. 1(b) illustrates the design of the SOE. An energy configuration technique was used in this study to design the U-TIR-R-C lens module. This technique involved simultaneously partitioning the U-TIR-R-C lens module and the solar cell surface. In other words, the light-receiving surface of the TIR-R lens was divided into n regions, and ray tracing was used to distribute incident rays to a corresponding region on the solar cell. The purpose of the SOE was to redistribute rays passing through the TIR-R lens to enable uniform distribution of solar energy on the solar cell, thereby resolving the concern of hot spots on solar cell surfaces in HCPV systems, which lowers conversion efficiency. The design of the T-TIR-R-C lens module, shown in Fig. 1(b), used only the principles of reflection and refraction in geometrical optics, which caused solar energy to focus on a single point on the solar cell. However, this design overlooked hot spot formation attributable to uneven energy distribution, which lowers conversion efficiency.

2.1 U-TIR-R-C lens module

The purpose of this study was to design an HCPV system capable of achieving a concentration ratio of 1000 Suns. The size of the triple-junction solar cells (Solapoint Corp., Taiwan) used in this study was 2 mm × 2 mm and can operate in a wide spectral range to reach a high conversion efficiency of 32%–35%. The light-receiving area of the U-TIR-R-C lens module is 40 cm2. Therefore, this study developed a U-TIR-R-C lens module that used the TIR-R lens as the POE and adjusted the path of the light lens to employ the SOE. The U-TIR-R-C lens module was designed by first analyzing the energy distribution in various regions of the solar cell surface using ray tracing. The energy configuration technique was subsequently adopted to uniformly distribute the sunlight that passed through the POE and SOE lenses onto the entire solar cell surface. To reduce the thickness of U-TIR-R-C lens module, this study employed the total internal reflection method to bend light rays. Figure 2
Fig. 2 The diagram of ray tracing paths for U-TIR-R-C lens module
is a diagram of the ray paths.

The ray tracing paths in Fig. 2 show that each light ray was reflected twice, yielding four point coordinates (S0, S1, S2, and S3) and tangent vectors for the locations of reflection. Additionally, the ray tracing technique was used to identify the relationships between angles of refraction θ2 and θ3 and the tangent vectors of the two point coordinates of reflection. In these relationships, W1, W2, and W3 are horizontal lines, point S0 is the solar light source, θ1 represents the angle of incidence, θ2 denotes the angle between the light ray reflected once and the horizontal line W2, and θ3 signifies the angle between the light ray reflected twice and the horizontal line W3. S1 and S2 are the points where the first and second reflections occurred, respectively. S3 is the location where the light ray reaches the solar cell. T1 and T2 are tangents to S1 and S2, and N1 and N2 are normal lines of S1 and S2. λ1 and λ2 denote the angle between T1 and W1 and between T2 and W1, respectively. Assume that all angles are measured according to the horizontal lines and are positive in a counterclockwise direction. The four coordinates were defined as S0 = (x0,y0), S1 = (x1,y1), S2 = (x2,y2), and S3 = (x3,y3), and the sunlight possessed an angle of incidence θ1. θ2 and θ3 represent the first and second angles of reflection, respectively.

θ2=tan1(y2y1x2x1)
(1)
θ3=tan1(y3y2x3x2)
(2)

where Eq. (1) and Eq. (2) are conversion models for angles of incidence.

The first angle of reflection is β1, the second is β2.

β1=12cos1(S0S1¯2+S1S2¯2S2S0¯22×S0S1¯×S1S2¯)
(3)
β2=12cos1(S1S2¯2+S2S3¯2S1S3¯22×S1S2¯×S2S3¯)
(4)

where Eq. (3) and Eq. (4) are conversion models for angles of reflection.

As shown in Eq. (5) and Eq. (6), the propagation path of a single light ray through a U-TIR-R-C lens module can be calculated based on the conversion models for angles of incidence, the reflection of sunlight, and λ1 and λ2, which are angles of the tangents to the reflection points.

λ1=θ1+90°β1
(5)
λ2=β2+90°θ2
(6)

where Eq. (5) and Eq. (6) are tangent conversion models.

The first ray was represented by the four parameters P1, P2, λ1, and β1, and the reflective surface profile of the first ray could be obtained using the light propagation path. As shown in Fig. 3(a)
Fig. 3 (a) The reflective surface profile of the first ray and (b) the reflective profile of the other ray. T1 represents the reflective surface of the POE and T2 represents the reflective surface of the SOE
, the other ray tracing parameters were derived from the tangent vectors of various points on the first ray. Therefore, specific spacing on Tangent T1 of the S1 reflection point were selected to determine the direction of Tangent T1′, which was then used to identify S1′, the location of the second ray. Other points were obtained by repeating this procedure, as illustrated in Fig. 3(b). After identifying the three points on the second ray, tangents to other points were identified by employing the ray path models, and the parameters of the third ray were derived using a new set of tangents. These ray tracing procedures were adopted to determine the point coordinates on the reflective surface of the U-TIR-R-C lens module. The design of the U-TIR-R-C lens module was complete after all the points were directly connected, forming a 2D profile to determine the amount of light distribution for each region of the solar cell surface, followed by the uniform distribution of light rays in each region of the lens to each region of the solar cell surface.

The energy configuration of the U-TIR-R-C lens module was established by dividing the lens into regions. The location of incidence in each region was calculated using ray tracing at the boundary of individual regions. Therefore, the light that passed through the concentration lens was not required to generate an image on the focal plane; instead, the light was collected into specific locations on the solar cell to achieve a uniform light concentration. The design of the U-TIR-R-C lens module comprised two aspects: 1) A TIR-R-C lens capable of configuring energy was installed. The central region of the lens was aspheric. Multiple total internal reflective surfaces were placed on both sides of the lens. 2) Secondary optical elements (SOE) were employed to adjust the path of light refracted by the aspheric lens and total internal reflective surfaces. These elements also uniformly distributed light onto the solar cell. Figure 4
Fig. 4 The uniform total internal reflection-refraction (TIR-R) concentration (U-TIR-R-C) lenses: (a) 3D solid models of the U-TIR-R-C lens module and (b) prototype of the U-TIR-R-C lens module
is a photograph of the designed U-TIR-R-C lens module, which possessed an overall diameter of 76 mm and a height of 41 mm. With a height and length of 2 mm each, the U-TIR-R-C lens module could concentrate 45.36 cm2 of light onto a 0.04-cm2 solar cell, for a geometric concentration ratio of 1134 Suns.

2.2 Simulation and analysis of U-TIR-R-C lens module

Before simulation, the material of the concentration lens and the source of incident light were determined. Optical-level polymethyl methacrylate (PMMA) was adopted as the concentration lens material, and the light source was the solar spectra of AM1.5D, using 1 Sun measuring 1000 W/m2 [17

17. A. Barnett, D. Kirkpatrick, and C. Honsberg, “Very high efficiency solar cells,” Proc. SPIE 6338, 63380N, 63380N-12 (2006). [CrossRef]

]. Sunlight is composed of different wavelength spectra. This study simulated the optical transmission efficiency of the U-TIR-R-C lens module for varying wavelengths. The optical efficiency of the U-TIR-R-C lens module was calculated for the PMMA material and for wavelengths between 350 and 1300 nm. A PMMA optical transmission efficiency of more than 90% was achieved between 400 and 950 nm, and between 950 and 1300 nm, the optical transmission efficiency was approximately 80%. The PMMA material one the wavelengths exhibiting optical transmission efficiency are shown in Table 1

Table1. PMMA material on the wavelength of the optical transmission efficiency

table-icon
View This Table
.

The uniformity of the U-TIR-R-C lens module was evaluated and simulated using optical software (TracePro®), which was also employed to analyze the ray paths and verify the effects of uniformity. Figure 5(a)
Fig. 5 (a) The ray tracing diagram for the U-TIR-R-C lens module; (b) a 2D irradiance distribution graph of the solar cell; (c) a 3D irradiance distribution graph of the solar cell; and (d) the 3D irradiance distribution graph of the solar cell when the sunlight was shifted 0.5°
is a ray tracing diagram for the U-TIR-R-C lens module. When concentrated by the U-TIR-R-C lens module, the sunlight uniformly irradiated on the square solar cell in equal inscribed circles, which received identical amounts of irradiance energy at each location. Figure 5(b) and 5(c) shows 2D and 3D irradiance distribution graph of the solar cell. The maximum irradiance was 1347 Suns, and the average irradiance was 937 Suns. A uniformity Eq. (7) [18

18. K. Kreske, “Optical design of a solar flux homogenizer for concentrator photovoltaics,” Appl. Opt. 41(10), 2053–2058 (2002). [CrossRef] [PubMed]

] was adopted to calculate the uniformity of the U-TIR-R-C lens module, which reached 94.72%. When the U-TIR-R-C lens module and sunlight were shifted 0.5°, the irradiance peak on the solar cell surface increased to 1554 Suns, which is within the bounds of acceptable cell performance. The uniformity of the irradiance distribution decreased from 94.72% to 82.46%, as shown in Fig. 5(d).

Uniformity=(1MaximumfluxMinmumflux2×Averageflux)×100%
(7)

The acceptance angle of the U-TIR-R-C lens module is defined as the angle of incidence when optical transmission efficiency reaches 90%. Figure 6
Fig. 6 Relationship between the angle of incidence and optical transmission efficiency for the U-TIR-R-C lens module
presents the relationship between the angle of incidence and optical transmission efficiency for the U-TIR-R-C lens module. Regarding a geometrical concentration of a maximum 1134 suns, the results show an acceptance angle of ± 1° possessing highly uniform irradiance on the triple-junction solar cell (DNI@900 W/m2, optical losses included). Figure 6 also shows the solar cell output power at various acceptance angles. The output power is more sensitive to the angle of incidence than it is to optical transmission efficiency.

3. Measurements, results, and discussion

This study assessed the optical efficiency of the U-TIR-R-C lens module, the uniformity of energy distribution, and the thermal performance of the solar cell. The 150-W solar simulator adopted for this study used a xenon lamp as the artificial light source. The spectral illumination of this simulator was converted using an optical filter into the AM 1.5G solar spectra (ranging between 300 and 1200 nm) regulated by the American Society for Testing and Materials (ASTM). The triple-junction solar cell can function in a wide spectral range (300–1200 nm), to achieve high conversion efficiency of 32%–35% at Solapoint facilities in Taiwan. When the temperature is 25 °C, the efficiency of the solar cell is 35%; when the temperature is 100 °C, the efficiency of the solar cell is 31.1%.

3.1 Optical efficiency

U-TIR-R-C lens module are produced by applying an anti-reflection (AR) coating to the lens surface, which is made from optical-level PMMA materials. Thus, with a wavelength ranging between 300 and 1200 nm, the optical transmission efficiency of the PMMA material in this lens is 93% when optical loss is not considered. However, the optical power meter readings indicated an actual optical efficiency of only 80.6% for the U-TIR-R-C lens module designed in this study. This result suggests a 12.4% optical loss caused by the following two factors: 1) Fresnel reflective losses and the geometric shape of the lens design led to optical losses of the light transmitted through media with varying refractive indices. 2) Significant optical efficiency losses may result from the round rather than pointed U-TIR-R-C lens module reflective surface caused by production processing factors. In the study, the point of the U-TIR-R-C lens module tip radius is 100 um and the draft angles of the vertical walls are 2°.

3.2 Uniform energy irradiance

3.3 Measurement of thermal performance

According to Fig. 7(a), which shows the illumination pattern measurement results, the area of a single focused light spot was 0.875 mm2; this small area provided the solar cell surface with substantial energy. Consequently, extremely high temperatures occurred in local areas, generating hot spots. To verify that U-TIR-R-C lens module can prevent the occurrence of hot spots on the surface of solar cells and increase conversion efficiency, this study constructed a sun tracker for an HCPV system with two types of TIR-R concentration lenses, as shown in Fig. 8
Fig. 8 Construction of sun tracker for an HCPV module with two types of TIR-R concentration lenses
. The sun is on-axis and direct normal irradiance (DNI) is 900 W/m2. The analysis of irradiance distribution on the triple-junction solar cell provides a uniformity of 1134 Suns (@DNI 900 W/m2). T-type thermocouples were used that possessed a wire diameter of 0.12 mm and a temperature range of −200 to 400 °C. Thermocouples were adopted to measure the temperature distribution on the solar cell surface. As shown in Fig. 9
Fig. 9 The temperature distribution on the solar cell surface with U-TIR-R lens and T-TIR-R lens
, the core temperature of the solar cell containing the T-TIR-R-C lens was 108 °C, exhibiting an overall temperature difference of 45 °C. The core temperature of the solar cell containing the U-TIR-R-C lens module was 69 °C, exhibiting an overall temperature difference of 10 °C. These results indicate that T-TIR-R-C lenses focus the irradiance on the center of solar cells, and that excessively high temperatures significantly affect the conversion efficiency of solar cells.

To measure the performance of HCPV system, a 45.36-cm2 U-TIR-R-C lens module was employed to concentrate sunlight into a 0.04-cm2 solar area at a geometric concentration ratio of 1134 Suns. The sun power ranged between 900 and 930 W/m2 during the experiment. Therefore, nearly 3.5 W was concentrated on the cell with a lens efficiency of 80.6%. Figure 10(a)
Fig. 10 (a) I/V curve and (b) P/V curve of solar cells containing U-TIR-R lens module and T-TIR-R lens module
presents the I-V curve and Fig. 10(b) shows the P-V curve derived from measurements of the solar cell. By comparing the curves to the core temperature of the solar cell, this study found that when the T-TIR-R-C lens module was used, the core temperature of the solar cell was 108 °C, the open-circuit voltage (Ioc) was 2.83 V, and the short-circuit current (Isc) was 498 mA. When the U-TIR-R-C lens module was used, the core temperature of the solar cell was 69 °C, the open-circuit voltage (Ioc) was 2.85 V, and the short-circuit current (Isc) was 523 mA. Therefore, using the solar cell containing the U-TIR-R-C lens module provided a significant increase in the open-circuit voltage and the short-circuit current. Figure 10(b) shows the P/V curves of the two cases. The U-TIR-R-C lens module possessed more power compared to the T-TIR-R-C lens module because of the solar cell’s low surface temperature. The maximum power of the HCPV with a U-TIR-R-C lens module and a T-TIR-R-C lens module was 1.12 and 1 W, respectively. The conversion efficiencies for the two cases were 34%, 31.2%. Employing the U-TIR-R-C lens module as the solar module increased the relative efficiency by approximately 3.8% compared to using the T-TIR-R-C lens module in a single solar cell. Thus, U-TIR-R-C lens module can effectively reduce hot spots on solar cell surfaces and decrease the surface temperature, thereby enhancing conversion efficiency.

4. Conclusions

The design of the proposed U-TIR-R-C lens module was based on the energy configuration technique. The proposed lens is capable of distributing solar energy onto solar cell surfaces uniformly to reduce hot spots and increase photoelectric conversion efficiency. The U-TIR-R-C lens module possessed a diameter of 76 mm and thickness of 41 mm and could concentrate 45.36 cm2 of incident light onto a 0.04-cm2 solar cell with a geometric concentration ratio of 1134 suns, optical efficiency of 80.6%, and 94.7% uniformity. As indicated by the research experiments, the U-TIR-R-C lens module substantially reduced the solar cell temperature from 108 °C to 69 °C, in addition to lowering the overall temperature difference from 45 °C to 10 °C. Furthermore, the conversion efficiency was effectively increased by 3.8%. In conclusion, the proposed U-TIR-R-C lens module can effectively concentrate large-area solar energy onto small solar cells and uniformly distribute solar energy in solar cells, thereby effectively eliminating hot spots.

Acknowledgments

The authors would like to thank National Science Council (NSC) and Research Center for Energy Technology and Strategy, National Cheng Kung University for their financial supports to the project (granted number: NSC 100-2628-E-006-019-MY3).

References and links

1.

N. L. Panwar, S. C. Kaushik, and S. Kothari, “Role of renewable energy sources in environmental protection: A review,” Renew. Sustain. Energy Rev. 15(3), 1513–1524 (2011). [CrossRef]

2.

H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, and N. Karam, “III–V multijunction solar cells for concentrating photovoltaics,” Energy Environ. Sci. 2(2), 174–192 (2009). [CrossRef]

3.

R. Leutz, A. Suzuki, A. Akisawa, and T. Kashiwagi, “Developments and designs of solar engineering Fresnel lenses”, Proceedings Symposium on Energy Engineering2, pp. 759–765, 2000.

4.

R. Leutz, A. Suzuki, A. Akisawa, and T. Kashiwagi, “Shaped nonimaging Fresnel lenses,” J. Opt. A, Pure Appl. Opt. 2(2), 112–116 (2000). [CrossRef]

5.

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011). [CrossRef]

6.

C. Sierra and A. J. Vazquez, “High solar energy concentration with a Fresnel lens,” J. Mater. Sci. 40(6), 1339–1343 (2005). [CrossRef]

7.

A. Luque and V. Andreev, Concentrator Photovoltaics (Berlin: Springer, 2007), Chap.10.

8.

K. K. Chong, S. L. Lau, T. K. Yew, and C. L. Tan, “Design and development in optics of concentrator photovoltaic system,” Renew. Sustain. Energy Rev. 19, 598–612 (2013). [CrossRef]

9.

A. Cvetkovic, M. Hernandez, and P. Benitez., “The XR nonimaging photovoltaic concentrator,” Proc. SPIE 6670, 667005.1–667005.10 (2007).

10.

O. Dross, R. Mohedano, M. Hernandez, A. Cvetkovic, J. C. Minano, and P. Benitez, “Kohler integrators embedded into illumination optics add functionality,” Proc. SPIE 7103, 71030G, 12 (2008). [CrossRef]

11.

M. Hernandez, A. Cvetkovic, P. Benitez, J. C. Miñano, W. Falicoff, Y. Sun, J. Chaves, and R. Mohedano, “CPV and illumination systems based on XR-Köhler devices,” Proc. SPIE 7785, 77850A, 77850A-11 (2010). [CrossRef]

12.

P. Benitez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express 18(S1), A25–A40 (2010). [CrossRef]

13.

P. Zamora, P. Benitez, R. Mohedano, A. Cvetkovic, J. Vilaplana, Y. L. M. Hernández, J. Chaves, and J. C. Miñano, “Experimental characterization of Fresnel-Köhler concentrators,” J. Photon. Energy 2(1), 021806 (2012). [CrossRef]

14.

W. P. Mulligan, A. Terao, S. G. Daroczi, O. Chao Pujol, M. J. Cudzinovic, P. J. Verlinden, R. M. Swanson, P. Benitez, and J. C. Minano, “A flat-plate concentrator: micro-concentrator design overview,” Photovoltaic Specialists Conference, 1495–1497 (2000). [CrossRef]

15.

M. Hernandez, P. Benitez, J. C. Minano, J. L. Alvarez, V. Diaz, and J. Alonso, “Sunlight spectrum on cell through very high concentration optic key points for high gain photovoltaic solar energy concentrators,” Proc. SPIE 5962, 298–306 (2005).

16.

K. Nishioka, Y. Ota, K. Tamura, and K. Araki, “Heat reduction of concentrator photovoltaic module using high radiation coating,” Surf. Coat. Tech. 215, 472–475 (2013). [CrossRef]

17.

A. Barnett, D. Kirkpatrick, and C. Honsberg, “Very high efficiency solar cells,” Proc. SPIE 6338, 63380N, 63380N-12 (2006). [CrossRef]

18.

K. Kreske, “Optical design of a solar flux homogenizer for concentrator photovoltaics,” Appl. Opt. 41(10), 2053–2058 (2002). [CrossRef] [PubMed]

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(150.2945) Machine vision : Illumination design

ToC Category:
Solar Concentrators

History
Original Manuscript: May 20, 2013
Revised Manuscript: July 25, 2013
Manuscript Accepted: September 10, 2013
Published: September 18, 2013

Citation
S. C. Shen, S. J. Chang, C. Y. Yeh, and P. C. Teng, "Design and testing of a uniformly solar energy TIR-R concentration lenses for HCPV systems," Opt. Express 21, A942-A952 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S6-A942


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References

  1. N. L. Panwar, S. C. Kaushik, and S. Kothari, “Role of renewable energy sources in environmental protection: A review,” Renew. Sustain. Energy Rev.15(3), 1513–1524 (2011). [CrossRef]
  2. H. Cotal, C. Fetzer, J. Boisvert, G. Kinsey, R. King, P. Hebert, H. Yoon, and N. Karam, “III–V multijunction solar cells for concentrating photovoltaics,” Energy Environ. Sci.2(2), 174–192 (2009). [CrossRef]
  3. R. Leutz, A. Suzuki, A. Akisawa, and T. Kashiwagi, “Developments and designs of solar engineering Fresnel lenses”, Proceedings Symposium on Energy Engineering2, pp. 759–765, 2000.
  4. R. Leutz, A. Suzuki, A. Akisawa, and T. Kashiwagi, “Shaped nonimaging Fresnel lenses,” J. Opt. A, Pure Appl. Opt.2(2), 112–116 (2000). [CrossRef]
  5. W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev.15(6), 2588–2606 (2011). [CrossRef]
  6. C. Sierra and A. J. Vazquez, “High solar energy concentration with a Fresnel lens,” J. Mater. Sci.40(6), 1339–1343 (2005). [CrossRef]
  7. A. Luque and V. Andreev, Concentrator Photovoltaics (Berlin: Springer, 2007), Chap.10.
  8. K. K. Chong, S. L. Lau, T. K. Yew, and C. L. Tan, “Design and development in optics of concentrator photovoltaic system,” Renew. Sustain. Energy Rev.19, 598–612 (2013). [CrossRef]
  9. A. Cvetkovic, M. Hernandez, P. Benitez, and ., “The XR nonimaging photovoltaic concentrator,” Proc. SPIE6670, 667005.1–667005.10 (2007).
  10. O. Dross, R. Mohedano, M. Hernandez, A. Cvetkovic, J. C. Minano, and P. Benitez, “Kohler integrators embedded into illumination optics add functionality,” Proc. SPIE7103, 71030G, 12 (2008). [CrossRef]
  11. M. Hernandez, A. Cvetkovic, P. Benitez, J. C. Miñano, W. Falicoff, Y. Sun, J. Chaves, and R. Mohedano, “CPV and illumination systems based on XR-Köhler devices,” Proc. SPIE7785, 77850A, 77850A-11 (2010). [CrossRef]
  12. P. Benitez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express18(S1), A25–A40 (2010). [CrossRef]
  13. P. Zamora, P. Benitez, R. Mohedano, A. Cvetkovic, J. Vilaplana, Y. L. M. Hernández, J. Chaves, and J. C. Miñano, “Experimental characterization of Fresnel-Köhler concentrators,” J. Photon. Energy2(1), 021806 (2012). [CrossRef]
  14. W. P. Mulligan, A. Terao, S. G. Daroczi, O. Chao Pujol, M. J. Cudzinovic, P. J. Verlinden, R. M. Swanson, P. Benitez, and J. C. Minano, “A flat-plate concentrator: micro-concentrator design overview,” Photovoltaic Specialists Conference, 1495–1497 (2000). [CrossRef]
  15. M. Hernandez, P. Benitez, J. C. Minano, J. L. Alvarez, V. Diaz, and J. Alonso, “Sunlight spectrum on cell through very high concentration optic key points for high gain photovoltaic solar energy concentrators,” Proc. SPIE5962, 298–306 (2005).
  16. K. Nishioka, Y. Ota, K. Tamura, and K. Araki, “Heat reduction of concentrator photovoltaic module using high radiation coating,” Surf. Coat. Tech.215, 472–475 (2013). [CrossRef]
  17. A. Barnett, D. Kirkpatrick, and C. Honsberg, “Very high efficiency solar cells,” Proc. SPIE6338, 63380N, 63380N-12 (2006). [CrossRef]
  18. K. Kreske, “Optical design of a solar flux homogenizer for concentrator photovoltaics,” Appl. Opt.41(10), 2053–2058 (2002). [CrossRef] [PubMed]

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