Abstract

A photovoltaic concentrator is proposed that uses equatorial tracking (the rotation axis of a concentrator points to the North Star), so that the change of the sun’s altitude angle is minimized. The solar concentrator consists of a Fresnel lens (objective), a holographic optical element made on photoresist with 90% diffraction efficiency, and a field lens (making the sunlight come from different fields of view uniformly falling on the solar cell). The accuracy of the original 2-D tracking is reduced several orders over previous methods; however, it may be that only 1-D tracking is needed. A theoretical analysis and a study model have been made, and a reasonable concentration ratio has been obtained. Therefore, it can be expected that the cost will be much lower than an accurate 2-D tracking system.

© 1988 Optical Society of America

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References

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  1. Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).
  2. E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
    [CrossRef]
  3. G. C. Jain, S. Kumari, “Optimum Cost computation in Photovoltaic Systems with Concentrators,” Sol. Cells 6, 149 (1982) and references cited there.
    [CrossRef]
  4. J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).
  5. R. J. Schwartz, “Review of Silicon Solar Cells for High Concentrations,” Sol. Cells 6, 17 (1982).
    [CrossRef]
  6. S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.
  7. E. L. Burgess, B. D. Shafer, “Operational, Reliability, and Maintenance Experience with Photovoltaic Concentrator Arrays,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 360.
  8. H. Pfeiffer, “Construction and Testing of Experimental Plants Using Solar Cells and Concentrators,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 996.
  9. M. A. Green, Solar Cells (Prentice-Hall, Englewood Cliffs, NJ, 1982).
  10. Y. W. Zhang, L. Z. Cai, “Point Spread and Transfer Functions for Holographic Process,” Appl. Opt. 23, 1493 (1984).
    [CrossRef] [PubMed]
  11. Y. Ishii, K. Murata, “Flat-Field Linearized Scans with Reflection Dichromated Gelatin Holographic Gratings,” Appl. Opt. 23, 1999 (1984).
    [CrossRef] [PubMed]
  12. C. S. Ih, “Holographic Scanners with an Aspherical Auxiliary Reflector,” Proc. Soc. Photo-Opt. Instrum. Eng. 299, 169 (1981).
  13. C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus (June1981).
  14. C. J. Kramer, “Optical Scanner Using Plane Linear Diffraction Grating on a Rotating Spinner,” U.S. Patent4,289,371 (15Sept.1981).
  15. Y. W. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, 1983), Chap. 5.

1984 (2)

1983 (1)

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

1982 (4)

E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
[CrossRef]

G. C. Jain, S. Kumari, “Optimum Cost computation in Photovoltaic Systems with Concentrators,” Sol. Cells 6, 149 (1982) and references cited there.
[CrossRef]

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

R. J. Schwartz, “Review of Silicon Solar Cells for High Concentrations,” Sol. Cells 6, 17 (1982).
[CrossRef]

1981 (2)

C. S. Ih, “Holographic Scanners with an Aspherical Auxiliary Reflector,” Proc. Soc. Photo-Opt. Instrum. Eng. 299, 169 (1981).

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus (June1981).

Bose, E. C.

E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
[CrossRef]

Burgess, E. L.

E. L. Burgess, B. D. Shafer, “Operational, Reliability, and Maintenance Experience with Photovoltaic Concentrator Arrays,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 360.

Cai, L. Z.

Chang, M. J.

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

Esteve, D.

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

Follea, D.

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

Green, M. A.

M. A. Green, Solar Cells (Prentice-Hall, Englewood Cliffs, NJ, 1982).

Ih, C. S.

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

C. S. Ih, “Holographic Scanners with an Aspherical Auxiliary Reflector,” Proc. Soc. Photo-Opt. Instrum. Eng. 299, 169 (1981).

Ishii, Y.

Jain, G. C.

G. C. Jain, S. Kumari, “Optimum Cost computation in Photovoltaic Systems with Concentrators,” Sol. Cells 6, 149 (1982) and references cited there.
[CrossRef]

Kramer, C. J.

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus (June1981).

C. J. Kramer, “Optical Scanner Using Plane Linear Diffraction Grating on a Rotating Spinner,” U.S. Patent4,289,371 (15Sept.1981).

Kumari, S.

G. C. Jain, S. Kumari, “Optimum Cost computation in Photovoltaic Systems with Concentrators,” Sol. Cells 6, 149 (1982) and references cited there.
[CrossRef]

Mitsui, K.

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

Murata, K.

Oda, T.

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

Pfeiffer, H.

H. Pfeiffer, “Construction and Testing of Experimental Plants Using Solar Cells and Concentrators,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 996.

Rorry, J. P.

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

Schueler, D. G.

E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
[CrossRef]

Schwartz, R. J.

R. J. Schwartz, “Review of Silicon Solar Cells for High Concentrations,” Sol. Cells 6, 17 (1982).
[CrossRef]

Shafer, B. D.

E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
[CrossRef]

E. L. Burgess, B. D. Shafer, “Operational, Reliability, and Maintenance Experience with Photovoltaic Concentrator Arrays,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 360.

Shirabata, K.

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

Vialaret, G.

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

Yau, H. F.

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

Yoshida, S.

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

Yukinoto, Y.

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

Zhang, Y. W.

Y. W. Zhang, L. Z. Cai, “Point Spread and Transfer Functions for Holographic Process,” Appl. Opt. 23, 1493 (1984).
[CrossRef] [PubMed]

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

Y. W. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, 1983), Chap. 5.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Y. W. Zhang, C. S. Ih, H. F. Yau, M. J. Chang, “Photovoltic Concentrator Using a Dispersive Element,” J. Opt. Soc. Am. 73, A1932 (1983).

Laser Focus (1)

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus (June1981).

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

C. S. Ih, “Holographic Scanners with an Aspherical Auxiliary Reflector,” Proc. Soc. Photo-Opt. Instrum. Eng. 299, 169 (1981).

Sol. Cells (3)

E. C. Bose, B. D. Shafer, D. G. Schueler, “Economic Motivation for Photovoltaic Concentrators Technology,” Sol. Cells 6, 3 (1982) and references cited there.
[CrossRef]

G. C. Jain, S. Kumari, “Optimum Cost computation in Photovoltaic Systems with Concentrators,” Sol. Cells 6, 149 (1982) and references cited there.
[CrossRef]

R. J. Schwartz, “Review of Silicon Solar Cells for High Concentrations,” Sol. Cells 6, 17 (1982).
[CrossRef]

Sol. Energy (1)

J. P. Rorry, D. Esteve, D. Follea, G. Vialaret, “Photovoltaic Generators with Concentrators,” Sol. Energy 29, 235 (1982).

Other (6)

S. Yoshida, K. Mitsui, T. Oda, Y. Yukinoto, K. Shirabata, “High Efficiency Large Area AlGaAs/GaAs Concentrator Solar Cells,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 970.

E. L. Burgess, B. D. Shafer, “Operational, Reliability, and Maintenance Experience with Photovoltaic Concentrator Arrays,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 360.

H. Pfeiffer, “Construction and Testing of Experimental Plants Using Solar Cells and Concentrators,” in Proceedings, Third E. C. Photovoltaic Solar Energy Conference, Cannes, 27–31 Oct. 1980 (Reidel, Dordrecht, 1980), p. 996.

M. A. Green, Solar Cells (Prentice-Hall, Englewood Cliffs, NJ, 1982).

C. J. Kramer, “Optical Scanner Using Plane Linear Diffraction Grating on a Rotating Spinner,” U.S. Patent4,289,371 (15Sept.1981).

Y. W. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, 1983), Chap. 5.

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Figures (4)

Fig. 1
Fig. 1

Collector with a Fresnel lens and hologram.

Fig. 2
Fig. 2

Recording of a hologram.

Fig. 3
Fig. 3

Solar spectrum dispersed by a hologram.

Fig. 4
Fig. 4

Combination of a Fresnel lens and field lens.

Tables (1)

Tables Icon

Table II Concentration Ratios for Different Tolerances of Angle ω

Equations (44)

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( a ) a weak zero - order beam ; ( b ) a strong first - order beam ; ( c ) no or very weak higher orders .
sin φ ( 1 ) = λ 0 d - sin θ 0 ,
sin φ ( - 1 ) = λ 0 d + sin θ 0 ,
sin φ ( 2 ) = 2 λ 0 d - sin θ 0 ,
φ ( 1 ) < 90 ° , i . e . , sin φ ( 1 ) < 1 ;
φ ( - 1 ) 90 ° , i . e . , sin φ ( - 1 ) 1 ;
φ ( 2 ) 90 ° , i . e . , sin φ ( 2 ) 1.
λ 0 d - sin θ 0 < 1 ,
λ 0 d + sin θ 0 1 ,
2 λ 0 d - sin θ 0 1.
d 1.5 λ 0 .
d = 1.5 λ 0
sin θ 0 = , i . e . , θ 0 = 20 ° .
sin φ ( 1 ) = 2 λ 3 λ 0 - 1 3 < 1 ,
sin φ ( - 1 ) = 2 λ 2 λ 0 + 1 3 1 ,
sin φ ( 2 ) = 4 λ 3 λ 0 - 1 3 1.
sin θ > 2 λ 3 λ 0 - 1 ,
sin θ 1 - 2 λ 3 λ 0 ,
sin θ 4 λ 2 λ 0 - 1.
sin φ p ( 1 ) = λ p d - sin θ ,
sin φ r ( 1 ) = λ r d - sin θ ,
l p = f m sin φ p ( 1 ) = f m ( λ p d - sin θ ) ,
L p = f m cos φ p ( 1 ) = f m cos [ sin - 1 ( λ p d - sin θ ) ] ,
l r = f m sin φ r ( 1 ) = f m ( λ r d - sin θ ) ,
L r = f m cos φ r ( 1 ) = f m cos [ sin - 1 ( λ r d - sin θ ) ] .
H 1 = R 1 P 2 = [ ( l r 1 - l p 2 ) 2 + ( L p 2 - L r 1 ) 2 ] 1 / 2 = f m ( { λ r d - sin θ - λ p d + sin θ } 2 + { cos [ sin - 1 ( λ d d - sin θ ) ] - cos [ sin - 1 ( λ r d - sin θ ) ] } 2 ) 1 / 2 .
D 1 = 2 f tan ( ω + δ ) .
C = ξ η 1 η 2 cos ( ψ + δ ) cos ( ω + δ ) D 2 / H 1 D 1 ,
D 1 = 2 f tan ( 0.25 ° ) = 0.0087 f ;
D 2 = D 1 = 2 f tan ( ω + δ ) .
D 3 = D 1 p = 2 f tan ( ω + δ ) / p ,
l 1 = D 3 D f = 2 f 2 tan ( ω + δ ) / D p ,
f 1 = l 1 l 1 ( l 1 + l 1 ) = 2 F tan ( ω + δ ) f [ p + 2 F tan ( ω + δ ) ] ,
F 1 = f 1 D 1 = F [ p + 2 F tan ( ω + δ ) ] .
r 1 = ( n - 1 ) f 1 ,
b = D 1 q = 2 f tan ( ω + δ ) p q ,
X H = b n = 2 f tan ( ω + δ ) n p q .
H 2 = H 1 + H = H 1 + 2 l 1 tan φ ,
φ = sin - 1 ( m R 1 P 2 2 f )
C = ξ η 1 η 2 η 3 cos ( ψ + δ ) cos ( ω + δ ) D 2 / H 2 D 3 ,
φ = 25.04 ° H = 0.07533 f , H 2 = ( 0.08466 + 0.07533 ) f = 0.16 f .
H 3 = 2 ( f + l 1 ) tan ( ψ + δ ) .
D 3 = 2 f tan ( ω + δ ) / p .
C = ξ η 1 η 2 η 3 cos ( ψ + δ ) cos ( ω + δ ) D 2 / H 3 D 3 .

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