Abstract

The effects of shape and photovoltaic cell placement on efficiency are studied for luminescent solar concentrators. The mean path length of light rays is found to be a poor measure of performance. Simple arguments based on a method of images show that the efficiency grows linearly with detector size h, saturating at hπA/λ, where A is the captation area of the collector, and λ is the attenuation length of radiation in the medium. Monte Carlo simulations confirm that efficiency is relatively independent of collector geometry.

© 1986 Optical Society of America

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References

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  1. W. A. Shurcliff, “Radiance Amplification by Multistage Fluorescence System,” J. Opt. Soc. Am. 41, 209 (1951).
    [CrossRef]
  2. W. H. Weber, J. Lambe, “Luminescent Greenhouse Collector for Solar Radiation,” Appl. Opt. 15, 2299 (1976).
    [CrossRef] [PubMed]
  3. A. M. Hermann, “Luminescent Solar Concentrators: a Review,” Sol. Energy 29, 323 (1982).
    [CrossRef]
  4. A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123, (1977).
    [CrossRef]
  5. J. M. Drake, M. L. Lesiecki, J. Sansregret, “Organic Dyes in PMMA in a Planar Luminescent Solar Collector: a Performance Evaluation,” Appl. Opt. 21, 2945 (1982).
    [CrossRef] [PubMed]
  6. J. S. Batchelder, A. H. Zewail, T. Cole, “Luminescent Solar Concentrators. 1: Theory of Operation and Techniques for Performance Evaluation,” Appl. Opt. 18, 3090 (1979).
    [CrossRef] [PubMed]
  7. E. Yablonovitch, “Thermodynamics of the Fluorescent Planar Concentrator,” J. Opt. Soc. Am. 70, 1362 (1980).
    [CrossRef]
  8. J. A. Levitt, W. H. Weber, “Materials for Luminescent Greenhouse Solar Collectors,” Appl. Opt. 16, 2684 (1977).
    [CrossRef] [PubMed]
  9. R. W. Olson, R. F. Loring, M. D. Fayer, “Luminescent Solar Concentrators and the Reabsorption Problem,” Appl. Opt. 20, 2934 (1981).
    [CrossRef] [PubMed]
  10. J. Sansregret, J. M. Drake, W. R. L. Thomas, M. L. Lesiecki, “Light Transport in Planar Luminescent Solar Concentrators: the Role of DCM Self-Absorption,” Appl. Opt. 22, 573 (1983).
    [CrossRef] [PubMed]
  11. A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).
  12. J. S. Batchelder, A. H. Zewail, T. Cole, “Luminescent Solar Concentrators. 2: Experimental and Theoretical Analysis of Their Possible Efficiencies,” Appl. Opt. 20, 3733 (1981).
    [CrossRef] [PubMed]
  13. M. L. Lesiecki, J. M. Drake, “Use of the Thermal Lens Technique to Measure the Luminescent Quantum Yields of Dyes in PMMA for Luminescent Solar Concentrators,” Appl. Opt. 21, 557 (1982).
    [CrossRef] [PubMed]
  14. K. Heidler, “Efficiency and Concentration Ratio Measurements of Fluorescent Solar Concentrators Using a Xenon Measurement System,” Appl. Opt. 20, 773 (1981).
    [CrossRef] [PubMed]
  15. K. Heidler, A. Goetzberger, V. Wittwer, Commission of the European Communities, Fourth EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Stresa, Italy, 10–14 May 1982, 682–686, EUR 8042 EN (Reidel, Dordrecht, 1982).
  16. J. Roncali, F. Garnier, “Photon-Transport Properties of Luminescent Solar Concentrators: Analysis and Optimization,” Appl. Opt. 23, 2809 (1984).
    [CrossRef] [PubMed]

1984 (1)

1983 (1)

1982 (3)

1981 (3)

1980 (1)

1979 (1)

1977 (2)

A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123, (1977).
[CrossRef]

J. A. Levitt, W. H. Weber, “Materials for Luminescent Greenhouse Solar Collectors,” Appl. Opt. 16, 2684 (1977).
[CrossRef] [PubMed]

1976 (1)

1951 (1)

Batchelder, J. S.

Cole, T.

Drake, J. M.

Fayer, M. D.

Garnier, F.

Goetzberger, A.

A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123, (1977).
[CrossRef]

K. Heidler, A. Goetzberger, V. Wittwer, Commission of the European Communities, Fourth EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Stresa, Italy, 10–14 May 1982, 682–686, EUR 8042 EN (Reidel, Dordrecht, 1982).

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

Greubel, W.

A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123, (1977).
[CrossRef]

Heidler, K.

K. Heidler, “Efficiency and Concentration Ratio Measurements of Fluorescent Solar Concentrators Using a Xenon Measurement System,” Appl. Opt. 20, 773 (1981).
[CrossRef] [PubMed]

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

K. Heidler, A. Goetzberger, V. Wittwer, Commission of the European Communities, Fourth EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Stresa, Italy, 10–14 May 1982, 682–686, EUR 8042 EN (Reidel, Dordrecht, 1982).

Hermann, A. M.

A. M. Hermann, “Luminescent Solar Concentrators: a Review,” Sol. Energy 29, 323 (1982).
[CrossRef]

Lambe, J.

Lesiecki, M. L.

Levitt, J. A.

Loring, R. F.

Olson, R. W.

Roncali, J.

Sah, R. E.

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

Sansregret, J.

Shurcliff, W. A.

Thomas, W. R. L.

Weber, W. H.

Wittwer, V.

K. Heidler, A. Goetzberger, V. Wittwer, Commission of the European Communities, Fourth EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Stresa, Italy, 10–14 May 1982, 682–686, EUR 8042 EN (Reidel, Dordrecht, 1982).

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

Yablonovitch, E.

Zastrow, A.

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

Zewail, A. H.

Appl. Opt. (10)

J. A. Levitt, W. H. Weber, “Materials for Luminescent Greenhouse Solar Collectors,” Appl. Opt. 16, 2684 (1977).
[CrossRef] [PubMed]

J. S. Batchelder, A. H. Zewail, T. Cole, “Luminescent Solar Concentrators. 1: Theory of Operation and Techniques for Performance Evaluation,” Appl. Opt. 18, 3090 (1979).
[CrossRef] [PubMed]

K. Heidler, “Efficiency and Concentration Ratio Measurements of Fluorescent Solar Concentrators Using a Xenon Measurement System,” Appl. Opt. 20, 773 (1981).
[CrossRef] [PubMed]

R. W. Olson, R. F. Loring, M. D. Fayer, “Luminescent Solar Concentrators and the Reabsorption Problem,” Appl. Opt. 20, 2934 (1981).
[CrossRef] [PubMed]

J. S. Batchelder, A. H. Zewail, T. Cole, “Luminescent Solar Concentrators. 2: Experimental and Theoretical Analysis of Their Possible Efficiencies,” Appl. Opt. 20, 3733 (1981).
[CrossRef] [PubMed]

M. L. Lesiecki, J. M. Drake, “Use of the Thermal Lens Technique to Measure the Luminescent Quantum Yields of Dyes in PMMA for Luminescent Solar Concentrators,” Appl. Opt. 21, 557 (1982).
[CrossRef] [PubMed]

J. M. Drake, M. L. Lesiecki, J. Sansregret, “Organic Dyes in PMMA in a Planar Luminescent Solar Collector: a Performance Evaluation,” Appl. Opt. 21, 2945 (1982).
[CrossRef] [PubMed]

J. Sansregret, J. M. Drake, W. R. L. Thomas, M. L. Lesiecki, “Light Transport in Planar Luminescent Solar Concentrators: the Role of DCM Self-Absorption,” Appl. Opt. 22, 573 (1983).
[CrossRef] [PubMed]

J. Roncali, F. Garnier, “Photon-Transport Properties of Luminescent Solar Concentrators: Analysis and Optimization,” Appl. Opt. 23, 2809 (1984).
[CrossRef] [PubMed]

W. H. Weber, J. Lambe, “Luminescent Greenhouse Collector for Solar Radiation,” Appl. Opt. 15, 2299 (1976).
[CrossRef] [PubMed]

Appl. Phys. (1)

A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123, (1977).
[CrossRef]

J. Opt. Soc. Am. (2)

Sol. Energy (1)

A. M. Hermann, “Luminescent Solar Concentrators: a Review,” Sol. Energy 29, 323 (1982).
[CrossRef]

Other (2)

A. Zastrow, K. Heidler, R. E. Sah, V. Wittwer, A. Goetzberger, Commission of the European Communities, Third EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Cannes, France, 27–31 Oct 1980, 413–417, EUR 7089 EN, D (Reidel, Dordrecht, 1981).

K. Heidler, A. Goetzberger, V. Wittwer, Commission of the European Communities, Fourth EC Photovoltaic Solar Energy Conference, in Proceedings, International Conference, Stresa, Italy, 10–14 May 1982, 682–686, EUR 8042 EN (Reidel, Dordrecht, 1982).

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Figures (9)

Fig. 1
Fig. 1

Rectangular collector of width a with three perfectly reflecting edges and a single absorbing edge: (a) the collector; (b) the collector with several images.

Fig. 2
Fig. 2

Rectangular collector with only a small detector strip on one edge. The rest of the perimeter is mirrored. (a) The collector; (b) the collector with several images; (c) some infinite strips laid down on top of the regular lattice without containing any absorbers.

Fig. 3
Fig. 3

Typical ray trajectories. LSC perimeter is given as a dotted line with the detector a solid line. (a) unit square with detector (h = 0.1) in lower left-hand corner and (b) irregular shape.

Fig. 4
Fig. 4

Efficiency vs l ¯ /λ for trapezoids of various shapes. The solid line E = 1 − l ¯ /λ is added for comparison.

Fig. 5
Fig. 5

Mean path length vs attenuation length for a unit square with one absorbing side. The asymptotic form l ¯ ~ 2 lnλ/π and the image solution l ¯ - 1 = λ−1 + σρ are added for comparison.

Fig. 6
Fig. 6

Efficiency vs attenuation length for the two geometries of Fig. 3.

Fig. 7
Fig. 7

Efficiencies for trapezoids of widely varying shapes: (a) E(λ) for different values of the base length a; (b) E(λ = 40) vs base length a.

Fig. 8
Fig. 8

Three of the symmetric trapezoids used for Figs. 4 and 7. The trapezoids shown here have base-to-height ratios 1.9/1.0, 1.5/1.25, and 1.1/1.66667.

Fig. 9
Fig. 9

Relative intensity distributions on the hypotenuse of a right triangle with two reflecting legs. The hypotenuse is either reflecting (flat) or absorbing (gently peaked curve). The two distributions have been scaled to unity at the midpoint of the hypotenuse.

Equations (12)

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l ¯ ( ray ) = 0 min ( r , r ) exp ( - r / λ ) d r 0 exp ( - r / λ ) d r = λ [ 1 - exp ( - r / λ ) ] .
l ¯ = λ [ 1 - exp ( - r / λ ) ] rays = λ ( 1 - E ) .
E = 1 - ( l ¯ / λ ) .
E = exp ( - 2 a y λ cos θ ) rays = 2 π 0 π 2 d θ 0 1 d y exp ( - 2 a y λ cos θ ) .
l ¯ = λ ( 1 - E ) = 2 λ π 0 1 d y 0 π 2 d θ [ 1 - exp ( - 2 a y λ cos θ ) ] .
l ¯ ~ 2 a ln ( λ ) / π .
E = 1 - l ¯ λ ~ 1 - 2 a ln λ π λ ~ 1.
E = σ ρ σ ρ + 1 / λ .
σ = 1 π - π 2 π 2 d θ h cos θ = 2 h π .
E = 1 1 + 1 λ σ ρ = 1 1 + π A λ h .
l ¯ 0 = P ( survival ) ( r + l ¯ 0 ) + P ( attenuation ) r 0 .
r 0 = λ - r 1 exp ( r / λ ) - 1 .

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