Abstract

We give the theoretical limit of concentration allowed by nonimaging optics for stationary solar concentrators after reviewing sun–earth geometry in direction cosine space. We then discuss the design principles that we follow to approach the maximum concentration along with examples including a hollow CPC trough, a dielectric CPC trough, and a 3D dielectric stationary solar concentrator which concentrates sun light four times (4x), eight hours per day year around.

©2010 Optical Society of America

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References

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  • Publication
  1. R. Winston, “Light Collection within the Framework of Geometrical Optics,” J. Opt. Soc. Am. 60(2), 245 (1970).
    [Crossref]
  2. R. Winston, “Principles of solar concentrators of a novel design,” Sol. Energy 16(2), 89–95 (1974).
    [Crossref]
  3. R. Winston, J. C. Miñano, and P. Benítez with contributions by Narkis Shatz and John C. Bortz, Nonimaging Optics, (Elsevier Academic Press, Burlington, MA 2005).
  4. A. Rabl, Active Solar Collectors and Their Applications, (Oxford University Press, New York, New York, 1985), Chap. 2.
  5. R. Winston, “Dielectric compound parabolic concentrators,” Appl. Opt. 15(2), 291–292 (1976).
    [Crossref] [PubMed]
  6. R. Winston, “Development of the Compound Parabolic Concentrator (CPC),” Proc. Soc. Photo Opt. Instrum. Eng. 68, 136–144 (1975).
  7. E. Lorenzo, “Energy Collected and Delivered by PV Modules,” in Handbook of Photovoltaic Science and Engineering, A. Luque and S. Hegedus eds. (Wiley, Chichester, West Sussex, 2003), Chap. 20.
  8. R. S. Scharlack, “All-dielectric compound parabolic concentrator,” Appl. Opt. 16(10), 2601–2602 (1977).
    [Crossref] [PubMed]
  9. W. T. Welford, and R. Winston, High Collection Nonimaging Optics, (Academic Press, New York and London, 1989).
  10. H. Hinterberger and R. Winston, “An Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37(8), 1094 (1966).
    [Crossref]
  11. E. Yablonovitch and G. D. Cody, “Enhancement in Textured Optical Sheets for Solar Cells,” IEEE Transactions on Electron Devices,” Vol. ED 29(2), 300 (1982).

1982 (1)

E. Yablonovitch and G. D. Cody, “Enhancement in Textured Optical Sheets for Solar Cells,” IEEE Transactions on Electron Devices,” Vol. ED 29(2), 300 (1982).

1977 (1)

1976 (1)

1975 (1)

R. Winston, “Development of the Compound Parabolic Concentrator (CPC),” Proc. Soc. Photo Opt. Instrum. Eng. 68, 136–144 (1975).

1974 (1)

R. Winston, “Principles of solar concentrators of a novel design,” Sol. Energy 16(2), 89–95 (1974).
[Crossref]

1970 (1)

1966 (1)

H. Hinterberger and R. Winston, “An Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37(8), 1094 (1966).
[Crossref]

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Enhancement in Textured Optical Sheets for Solar Cells,” IEEE Transactions on Electron Devices,” Vol. ED 29(2), 300 (1982).

Hinterberger, H.

H. Hinterberger and R. Winston, “An Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37(8), 1094 (1966).
[Crossref]

Scharlack, R. S.

Winston, R.

R. Winston, “Dielectric compound parabolic concentrators,” Appl. Opt. 15(2), 291–292 (1976).
[Crossref] [PubMed]

R. Winston, “Development of the Compound Parabolic Concentrator (CPC),” Proc. Soc. Photo Opt. Instrum. Eng. 68, 136–144 (1975).

R. Winston, “Principles of solar concentrators of a novel design,” Sol. Energy 16(2), 89–95 (1974).
[Crossref]

R. Winston, “Light Collection within the Framework of Geometrical Optics,” J. Opt. Soc. Am. 60(2), 245 (1970).
[Crossref]

H. Hinterberger and R. Winston, “An Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37(8), 1094 (1966).
[Crossref]

Yablonovitch, E.

E. Yablonovitch and G. D. Cody, “Enhancement in Textured Optical Sheets for Solar Cells,” IEEE Transactions on Electron Devices,” Vol. ED 29(2), 300 (1982).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Proc. Soc. Photo Opt. Instrum. Eng. (1)

R. Winston, “Development of the Compound Parabolic Concentrator (CPC),” Proc. Soc. Photo Opt. Instrum. Eng. 68, 136–144 (1975).

Rev. Sci. Instrum. (1)

H. Hinterberger and R. Winston, “An Efficient Light Coupler for Threshold Cerenkov Counters,” Rev. Sci. Instrum. 37(8), 1094 (1966).
[Crossref]

Sol. Energy (1)

R. Winston, “Principles of solar concentrators of a novel design,” Sol. Energy 16(2), 89–95 (1974).
[Crossref]

Vol. ED (1)

E. Yablonovitch and G. D. Cody, “Enhancement in Textured Optical Sheets for Solar Cells,” IEEE Transactions on Electron Devices,” Vol. ED 29(2), 300 (1982).

Other (4)

R. Winston, J. C. Miñano, and P. Benítez with contributions by Narkis Shatz and John C. Bortz, Nonimaging Optics, (Elsevier Academic Press, Burlington, MA 2005).

A. Rabl, Active Solar Collectors and Their Applications, (Oxford University Press, New York, New York, 1985), Chap. 2.

E. Lorenzo, “Energy Collected and Delivered by PV Modules,” in Handbook of Photovoltaic Science and Engineering, A. Luque and S. Hegedus eds. (Wiley, Chichester, West Sussex, 2003), Chap. 20.

W. T. Welford, and R. Winston, High Collection Nonimaging Optics, (Academic Press, New York and London, 1989).

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Figures (6)
Fig. 1
Fig. 1 Sun-earth geometry.

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Fig. 2
Fig. 2 Sun's directions, plotted in direction cosine space on the polar plane. Black circle: unit circle; green lines: winter and summer solstices; dashed black lines: (from left to right) the first day of Jan. Feb. Mar. Apr. May, and June; vertical solid black lines: (from right to left) the first day of July, Aug. Sep. Oct. Nov. and Dec.; red lines: eight hours per day; blue lines: sunrise/sunset at a latitude of 40 degree in the north hemisphere.

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Fig. 3
Fig. 3 Angular acceptance for hollow CPC troughs (yellow) and sun’s directions (green and red), plotted in direction cosine space on the polar plane.

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Fig. 4
Fig. 4 Angular acceptance for a dielectric CPC trough (blue) and a hollow CPC trough (yellow) with the same acceptance angle, plotted in direction cosine space.

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Fig. 5
Fig. 5 Angular acceptance for a dielectric CPC trough (blue) and a hollow CPC trough (yellow), both designed for concentrating sun light eight hours per day, and sun’s directions (green and red), plotted in direction cosine space on the polar plane.

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Fig. 6
Fig. 6 Diagram of a 4x stationary dielectric concentrator.

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Equations (15)

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n s = ( sin δ , cos δ sin ω , cos δ cos ω ) ,
sin δ = − sin 23.45 ° cos ( 360 ° ( n + 10 ) 365.25 ) ,
ω = 360 ° 24 t ,
L 2 + M 2 sin 2 ω = 1.
L 2 cos 2 φ + M 2 = 1.
n ' 2 d x ' d y ' d L ' d M ' = n 2 d x d y d L d M ,
C = ∫ d x d y ∫ d x ' d y ' = n ' 2 n 2 ∫ d L ' d M ' ∫ d L d M .
∫ d L d M = 2 ( δ s ' ) + sin ( 2 δ s ' ) ≈ 1.56 ,
∫ d L d M = sin ( ω ' ) [ 2 ( δ s ' ) + sin ( 2 δ s ' ) ] ,
L 2 1 − M 2 ≤ sin 2 ( θ 1 )
L 2 sin 2 ( θ 1 ) + M 2 ≤ 1.
sin 2 ( θ 1 ) = sin 2 ( δ s ' ) 1 − cos 2 ( δ s ' ) sin 2 ( ω ' ) .
L = n L n ,   M = n M n ,
L 2 sin 2 ( θ 1 ) + M 2 n 2 = 1 ,
sin 2 ( θ 1 ) = n 2 sin 2 ( δ s ' ) n 2 − cos 2 ( δ s ' ) sin 2 ( ω ' ) .

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