Abstract

A prototype concentrator photovoltaic (CPV) module with high solar concentration, an added low-cost solar cell, and an adjoining multi-junction solar cell is fabricated and experimentally demonstrated. In the present CPV module, the low cost solar cell captures diffuse solar radiation penetrating the concentrator lens and the multi-junction cell captures concentrated direct solar radiation. On-sun test results show that the electricity generated by a Fresnel lens-based CPV module with an additional crystalline silicon solar cell is greater than that for a conventional CPV module by a factor of 1.44 when the mean ratio of diffuse normal irradiation to global normal irradiation at the module aperture is 0.4. Several fundamental optical characteristics are presented for the present module.

© 2013 Optical Society of America

1. Introduction

Concentrator photovoltaic (CPV) modules are a promising technology for highly efficient solar energy conversion. Recently, cell conversion efficiency greater than 44.4% was achieved for a multi-junction solar cell [1] and a module efficiency of 34.9% was achieved for a CPV module [2]. Recent advances have made the cost of CPV devices competitive with flat photovoltaic (PV) modules in regions with high direct normal irradiation (DNI). In contrast, the use of CPV in regions of medium DNI is not cost effective since conventional high-concentration CPV modules cannot utilize diffuse solar radiation due to the narrow acceptance angle of the concentrator, limiting the potential market for CPV technology. On the other hand, the current drastic increase in the installation of megawatt solar power plants (which predominantly use fixed, flat PV modules) in regions of medium DNI tend to result in the lack of cheap land for further deployment. In such cases, one needs to maximize the electricity generated in a limited installation space as much as possible.

Recently, Benítez et al. [3] invented the concept of a high concentration CPV module that harvests diffuse solar radiation, which may provide one solution to the abovementioned problem, and expand the potential market for CPV modules into regions of medium DNI. Such a CPV module could also contribute to maximize solar energy conversion efficiency of a photovoltaic system as the maximum theoretical efficiency of photovoltaic conversion is achieved through the concentration of sunlight. Therefore, concentrating direct (beam) solar radiation to a high-efficiency, high-cost solar cell while simultaneously capturing diffuse solar radiation by a low cost solar cell with little or no concentration in a single module is of interest. Such a module will also be of interest when solar energy utilization is in higher demand. To date, such a CPV module has not yet been experimentally demonstrated.

In this study, we implemented this concept using a prototype Fresnel-lens-based CPV module with an additional low cost solar cell and experimentally demonstrated system performance. The improvement factor of the present module relative to a conventional CPV module is modeled and compared with experimental results. In addition, the optical characteristics of a Fresnel lens-based CPV module are illustrated by a ray-tracing simulation.

2. Optical configuration of a CPV module for harvesting diffuse solar radiation

Figure 1 shows the optical configurations of a CPV module for harvesting diffuse solar radiation through an additional low-cost cell, as described in a patent document [3]. The geometrical concentration ratio for the low-cost cell should be close to unity in order to fully capture diffuse radiation. Although other optical configurations can be conceived from this example, here we have selected a Fresnel-lens CPV module because Fresnel lenses are currently the most commonly-used type of concentrator for high-concentration CPV modules [46]. Test modules based on Fresnel lenses are easily fabricated by installing an additional low cost cell. Although the test module in this study is a single-lens module, a practical multiple-lens-array module could in principle be constructed according to the schematic shown in Fig. 2.

 

Fig. 1 Optical configuration of a high concentration CPV module harvesting diffuse solar radiation [3].

Download Full Size | PPT Slide | PDF

 

Fig. 2 Image of Fresnel-lens CPV module with additional low-cost solar cells.

Download Full Size | PPT Slide | PDF

3. Outdoor experiments

3.1 Setup

Figure 3 shows a schematic diagram and photograph of the fabricated test module. A crystalline silicon solar cell with a circular hole was installed onto a Fresnel-lens CPV module. In this configuration, incident direct solar radiation is concentrated by the Fresnel lens onto a triple-junction solar cell through the hole of the Si solar cell. Incident diffuse solar radiation through the Fresnel lens is then captured by the Si solar cell. The Si solar cell does not interrupt the concentrating rays. The Si solar cell was encapsulated by EVA without a glass cover. Placing a hole in the cell is generally not recommended but was done here in order to simplify fabrication. The four sidewalls of the test module were surrounded by high-reflection mirrors with reflectance ρ = 0.85 over the solar spectrum. This configuration ensured approximate periodic boundary conditions in the lens array module. The test module was mounted on a 2-axis solar tracker at the Nagaoka University of Technology in Japan. At 30 s intervals, the I-V curves of the Si and triple-junction solar cell were measured independently, along with the DNI and global normal irradiation (GNI) in the tracked plane. For comparison, a flat Si cell of the same type as the built-in Si cell mounted beside the test module aperture on the solar tracker was monitored.

 

Fig. 3 (a) Schematic diagram of the test module. (b) Photograph of Si solar cell and triple-junction cell. Mirrors are not shown.

Download Full Size | PPT Slide | PDF

3.2 Experimental results

Figure 4 shows a stack chart of the measured time variation of Pmax for the test module on August 22 (clear sky case) and September 18 (partially cloudy case), 2013. Here, Pmax represents the power at the maximum power point. In the figures, the potential electricity generation by the present CPV module (here after termed as “CPV+ module” to distinguish this design from conventional CPV modules) is estimated as the sum of Pmax of the triple-junction cell and the Si cell, while that of a conventional CPV module is estimated as only Pmax of the triple-junction cell. The built-in Si cell boosts electricity generation even when the triple-junction cell does not generate electricity due to the nearly zero DNI. For a clear sky, where the mean diffuse-to-total ratio γ = (GNI − DNI)/GNI = 0.18 and the mean DNI = 848 W/m2, the potential electricity generation by the CPV + module is greater than that for a conventional CPV module by a factor of 1.19. For a partially cloudy sky (γ = 0.64, DNI = 318 W/m2 on average), this factor increases up to 37.3.

 

Fig. 4 Time variation of the measured Pmax for the test module (outdoor test).

Download Full Size | PPT Slide | PDF

Figure 5 shows the relationship between the ratio defined by ISC_built-in / (ISC_ref × γ) and DNI. ISC_built-in and ISC_ref are the measured short circuit currents of the built-in Si cell and that of the reference Si cell, respectively. Thus, this ratio expresses the light intensity received by the built-in Si cell relative to that of the reference Si cell. Note that ISC_ref is corrected by a factor of γ so that (ISC_ref × γ) approximately represents the short circuit current of the reference Si cell under diffuse solar radiation exposure only. The plotted points were obtained from a 6 day experiment for ten DNI-bins ranging from 0 to 850 W/m2 with a bin size of 50 W/m2. The ratio is 0.84 when DNI is nearly zero but GNI – DNI is non-zero, i.e. the optical efficiency for incoming diffuse solar radiation to the built-in Si cell is 16% less relative to that of the reference Si cell. This reduction could be mitigated in an actual lens array module because the mirrors used in the test module result in losses from imperfect reflection. Interestingly, the ratio increases up to over 1.5 as DNI increases. This implies that a portion of the concentrated beam radiation, which is supposed to be captured by the concentrator cell, leaks onto the built-in Si cell. Further discussion accompanied by an optical simulation is presented in section 4.2.

 

Fig. 5 Relationship between short circuit current ratio of the built-in Si cell in the test module to the reference Si cell mounted on the same two-axis solar tracker. Short circuit current of the reference cell is corrected by γ.

Download Full Size | PPT Slide | PDF

4. Simulations

4.1 Fundamentals of electricity generation improvement

The experimental results indicate a significant increase in potential electricity generation using a CPV + module. This advantage primarily depends on the diffuse-to-total ratio γ, the optical efficiency, and the cell conversion efficiency of the low-cost and concentrator solar cell. Here, we derive the relationship between these factors. The module conversion efficiency of the CPV + module based on GNI is given by:

ηCPV+=ηopt_CPVηcell_CPVDNI+ηopt_PVηcell_PV(GNIDNI)GNI,
where ηopt_CPV and ηcell_CPV represent the optical efficiency of the concentrator cell component based on a DNI and the cell conversion efficiency of the concentrator cell, respectively. ηopt_PV and ηcell_PV represent the optical efficiency of the low-cost solar cell component based on GNI at the module aperture and the cell conversion efficiency of the low-cost solar cell, respectively. On the other hand, the module conversion efficiency of a conventional CPV module based on GNI is given by:
ηCPV=ηopt_CPVηcell_CPVDNIGNI.
Assuming that ηopt_CPV and ηcell_CPV in Eq. (1) are identical to those in Eq. (2), i.e. the low-cost cell component does not interfere with the concentrator cell component, we obtain the improvement factor f from:
f=ηCPV+ηCPVηCPV=ηopt_PVηcell_PVηopt_CPVηcell_CPVGNIDNIDNI.
Equation (3) is then re-written as follows:
f=γτ(1γ),
where,
τ=ηopt_CPVηcell_CPVηopt_PVηcell_PV,
γ=GNIDNIGNI.
γ is the diffuse-to-total ratio at the module aperture. τ represents the ratio of conversion efficiency of the concentrator cell to that of the low-cost solar cell in the CPV + module. Using these equations, we conducted a parametric characterization.

Figure 6 shows the characteristic curves of the improvement factor. The ratio γ depends on the atmospheric conditions at the installation site, e.g. the yearly mean value for a middle DNI region such as Tokyo (Japan) is γ ≅ 0.4, while that for a high DNI region such as Phoenix (USA) is γ ≅ 0.2. The ratio τ depends on the type of solar cell and optical system. Here, four τ values in the range 1 ≤ τ ≤ 3 were used. For larger γ, a larger improvement factor is obtained because the amount of diffuse radiation captured by the low-cost cell increases compared to that for direct radiation concentrated onto the concentrator cell. Furthermore, the larger τ results in a smaller improvement factor because the electricity generated by the low-cost cell is low compared to that generated by the concentrator cell. Figure 6 also shows statistical f values for seven γ-bins ranging from 0.2 to 0.7 with a bin size of 0.1, which were obtained from a 6 day experiment. The plotted points are consistent with the curve for τ = 1.5. For τ = 1.5, an improvement factor f of 44% is expected for an annual mean γ ≅ 0.4, whereas an f of 17% is expected for γ ≅ 0.2.

 

Fig. 6 Improvement factor vs. diffuse-to-total ratio for τ = 1.0, 1.5, 2.0, and 3.0.

Download Full Size | PPT Slide | PDF

In the Eq. (4) and Fig. 6, the amount of incident solar energy, which generally decreases as γ increases, is not considered. Here, Fig. 7 shows a simulation of the boosted electricity generation defined as ΔP = GNI (ηCPV+ηCPV). We assumed that GNI is a linear function of γ and determined by the slope and intercept of a linear fit to commercial yearly irradiation data (Meteonorm) within 20 locations including Phoenix and Tokyo. We also assumed ηopt_CPV × ηcell_CPV = 0.8 × 0.38 = 0.304 and ηopt_PV × ηcell_PV = 0.9 × 0.2 = 0.18 as a current realistic efficiency (τ = 1.69). The resulting curve shows a peak at approximately 0.4 where ΔP reaches approximately 150 kWhr/m2/year. At this peak γ, the electricity generation of the present CPV module is greater than that of a conventional CPV module by a factor of 1.4. The electricity generation is also greater than that of a tracked flat PV by factor of 1.41. Therefore, the present module is advantageous in the middle DNI regions but not in the high and low DNI regions. Obviously, the peak shifts to the right-hand side (larger γ) as τ decreases and vice versa. In terms of cost effectiveness, the present system could be feasible when the additional cost for extra solar cells is compensated by reduction in other costs, e.g., land cost.

 

Fig. 7 Simulation of the boosted generated electricity ΔP vs. the diffuse-to-total ratio.

Download Full Size | PPT Slide | PDF

4.2 Ray-tracing analysis for the effect of sunshape

In the previous section, leakage of concentrated light into the built-in Si cell was observed as in Fig. 5. The optical behavior of the beam radiation should also be characterized. In general, solar concentration is affected not only by the magnitude of DNI but also by sunshape [7], i.e. the radial distribution of incident solar energy. Here, we analyze the effect of the circumsolar ratio (CSR) on the irradiance distribution at the low-cost solar cell. CSR is the ratio of the amount of energy contained in the circumsolar aureole to the total amount of direct energy arriving from the sun [8, 9]. The angular solar intensity profile of CSR 5%, CSR 20%, and CSR 40% standardized by Neumann et al. [8] were used in ray-tracing models of the present module. The frequency of CSR for annual operation depends on the site. In sites receiving a lower annual DNI, the CSR can be observed over a broader range. Figure 8 shows the simulated local flux concentration distribution at the low-cost cell with and without tracking angle error θerror for three CSR values. For a higher CSR and larger θerror, the low-cost cell receives higher solar flux near the concentrator cell. This leakage behavior increases the energy gain at the built-in Si cell, as observed in the experiment shown in Fig. 5. This fact indicates that in the present experiment the implemented system underperforms because leaked light is converted by the low efficiency silicon cell. In addition, Fig. 8 implies that the tolerance for misalignment could be a more critical issue than CSR. The tolerance should be adequate to avoid a strong local concentration on the low cost cell, which may cause inefficient conversion efficiency and severe heat damage. Therefore, an increasing acceptance angle, in this case, would mean that either a more advanced concentrator system must be used (e.g., [4, 7]) instead of a simple Fresnel lens, or a larger triple-junction cell should be used, which would result in high efficiency and a more tolerant system. The use of a secondary optical element is a solution if the extra cost is acceptable. Adjusting the position of the low cost cell to a slightly higher level above the concentrator cell level is also one solution for mitigating a high flux concentration on the low cost cell.

 

Fig. 8 Effect of CSR on local concentration distribution for a built-in low cost cell with and without tracking angle error. The inset shows the angular solar intensity profile based on the literature [9]. The full spectrum analysis is based on AM1.5D + circumsolar standard solar spectrum and the optical properties of PMMA.

Download Full Size | PPT Slide | PDF

5. Conclusions

A high concentration CPV module for harvesting diffuse solar radiation was implemented following the concept described in the literature and experimentally demonstrated for the first time to show that a prototype module will perform mostly as expected. The present system underperformed due to the narrow acceptance angle of the concentrator. The results support the feasibility of the present concept to broaden the potential market for CPV modules in middle DNI regions, in particular when one needs to maximize solar energy conversion efficiency in a limited and expensive land area. However, since the present result is based on a single lens mini-module with one type of Fresnel lens, further studies are recommended to clarify the possible advantages in practical multiple lens array modules in long term on-sun tests. Furthermore, the aggregation of currents from both beam and diffuse irradiation must be considered. Matching the voltages in inverter, or deploying high efficiency micro DC-DC convertors into a group of cells or modules could be a solution, but further study is necessary.

References and links

1. Sharp Corporation, “Sharp develops concentrator solar cell with world's highest conversion efficiency of 44.4%,” http://sharp-world.com/corporate/news/130614.html (2013).

2. Amonix Inc, “Amonix achieves world record for PV module efficiency in test at NREL,” http://amonix.com/pressreleases/amonix-achieves-world-record-pv-module-efficiency-test-nrel (2013).

3. P. Benitez, J. C. Miñano, and R. Alvarez, “Photovoltaic concentrator with auxiliary cells collecting diffuse radiation, US patent application publication,” Pub. No.: US 2010/0126556 A1 (2010).

4. P. Benítez, 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]  

5. K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010). [CrossRef]  

6. V. D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010). [CrossRef]   [PubMed]  

7. J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011). [CrossRef]  

8. A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002). [CrossRef]  

9. D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. Sharp Corporation, “Sharp develops concentrator solar cell with world's highest conversion efficiency of 44.4%,” http://sharp-world.com/corporate/news/130614.html (2013).
  2. Amonix Inc, “Amonix achieves world record for PV module efficiency in test at NREL,” http://amonix.com/pressreleases/amonix-achieves-world-record-pv-module-efficiency-test-nrel (2013).
  3. P. Benitez, J. C. Miñano, and R. Alvarez, “Photovoltaic concentrator with auxiliary cells collecting diffuse radiation, US patent application publication,” Pub. No.: US 2010/0126556 A1 (2010).
  4. P. Benítez, 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]
  5. K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
    [CrossRef]
  6. V. D. Rumyantsev, “Solar concentrator modules with silicone-on-glass Fresnel lens panels and multijunction cells,” Opt. Express 18(S1), A17–A24 (2010).
    [CrossRef] [PubMed]
  7. J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
    [CrossRef]
  8. A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
    [CrossRef]
  9. D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
    [CrossRef]

2011 (1)

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

2010 (3)

2003 (1)

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
[CrossRef]

2002 (1)

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Araki, K.

Benítez, P.

Bett, A. W.

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

Buie, D.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
[CrossRef]

Buljan, M.

Chaves, J.

Cvetkovic, A.

Dey, C. J.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
[CrossRef]

Hernández, M.

Jaus, J.

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

Jones, S. A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Kuroda, Y.

Miñano, J. C.

Mohedano, R.

Monger, A. G.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
[CrossRef]

Neumann, A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Reinecke, H.

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

Rumyantsev, V. D.

Schmitt, G.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Weber, E. R.

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

Witzke, A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Yano, T.

Zamora, P.

Opt. Express (3)

Prog. Photovoltaics (1)

J. Jaus, A. W. Bett, H. Reinecke, and E. R. Weber, “Reflective secondary optical elements for Fresnel lens based concentrator modules,” Prog. Photovoltaics 19(5), 580–590 (2011).
[CrossRef]

Sol. Energy (1)

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003).
[CrossRef]

Trans. ASME J. Sol. Energy Eng. (1)

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” Trans. ASME J. Sol. Energy Eng. 124(2), 198–204 (2002).
[CrossRef]

Other (3)

Sharp Corporation, “Sharp develops concentrator solar cell with world's highest conversion efficiency of 44.4%,” http://sharp-world.com/corporate/news/130614.html (2013).

Amonix Inc, “Amonix achieves world record for PV module efficiency in test at NREL,” http://amonix.com/pressreleases/amonix-achieves-world-record-pv-module-efficiency-test-nrel (2013).

P. Benitez, J. C. Miñano, and R. Alvarez, “Photovoltaic concentrator with auxiliary cells collecting diffuse radiation, US patent application publication,” Pub. No.: US 2010/0126556 A1 (2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Optical configuration of a high concentration CPV module harvesting diffuse solar radiation [3].

Fig. 2
Fig. 2

Image of Fresnel-lens CPV module with additional low-cost solar cells.

Fig. 3
Fig. 3

(a) Schematic diagram of the test module. (b) Photograph of Si solar cell and triple-junction cell. Mirrors are not shown.

Fig. 4
Fig. 4

Time variation of the measured Pmax for the test module (outdoor test).

Fig. 5
Fig. 5

Relationship between short circuit current ratio of the built-in Si cell in the test module to the reference Si cell mounted on the same two-axis solar tracker. Short circuit current of the reference cell is corrected by γ.

Fig. 6
Fig. 6

Improvement factor vs. diffuse-to-total ratio for τ = 1.0, 1.5, 2.0, and 3.0.

Fig. 7
Fig. 7

Simulation of the boosted generated electricity ΔP vs. the diffuse-to-total ratio.

Fig. 8
Fig. 8

Effect of CSR on local concentration distribution for a built-in low cost cell with and without tracking angle error. The inset shows the angular solar intensity profile based on the literature [9]. The full spectrum analysis is based on AM1.5D + circumsolar standard solar spectrum and the optical properties of PMMA.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

η CPV+ = η opt_CPV η cell_CPV DNI+ η opt_PV η cell_PV (GNIDNI) GNI ,
η CPV = η opt_CPV η cell_CPV DNI GNI .
f= η CPV+ η CPV η CPV = η opt_PV η cell_PV η opt_CPV η cell_CPV GNIDNI DNI .
f= γ τ( 1γ ) ,
τ= η opt_CPV η cell_CPV η opt_PV η cell_PV ,
γ= GNIDNI GNI .

Metrics