Abstract

The principle of a luminescent solar concentrator is analyzed with an emphasis on the photon-transport yield. A mathematical model is developed, which takes into account the loss factors related to the photon transport in the LSC matrix. The relations obtained show that whereas the optical efficiency is still a decreasing factor with the LSC size, the concentration ratio can be optimized with regard to the geometry, the input surface, and the thickness of the LSC. The experimental analysis, carried out on two types of fluorescent PMMA, confirms the effects of these geometrical parameters on the LSC performances. A concentration ratio of 22 has been obtained experimentally with monochromatic irradiation, and a flux gain of 9.5 has also been determined in real conditions.

© 1984 Optical Society of America

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References

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  1. W. H. Weber, J. Lambe, “Luminescent Greenhouse Collector for Solar Radiation,” Appl. Opt. 15, 2299 (1976).
    [CrossRef] [PubMed]
  2. B. A. Swartz, T. Cole, A. H. Zewall, “Photon Trapping and Energy Transfer in Multiple-Dye Plastic Matrices: An Efficient Solar-Energy Concentrator,” Opt. Lett. 1, 73 (1977).
    [CrossRef] [PubMed]
  3. A. Goetzberger, W. Greubel, “Solar Energy Conversion with Fluorescent Collectors,” Appl. Phys. 14, 123 (1977).
    [CrossRef]
  4. J. A. Levitt, W. H. Weber, “Materials for Luminescent Greenhouse Solar Collectors,” Appl. Opt. 16, 2684 (1977).
    [CrossRef] [PubMed]
  5. A. Budo, I. Ketskemety, “Influence of Secondary Fluorescence on the Emission Spectra of Luminescent Solutions,” J. Chem. Phys. 25, 595 (1956).
    [CrossRef]
  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. G. Keil, “Design Principles of Fluorescence Radiation Converters,” Nucl. Instrum. Methods 87, 111 (1970).
    [CrossRef]
  8. R. W. Olson, R. F. Loring, M. D. Fayer, “Luminescent Solar Concentrators and the Reabsorption Problem,” Appl. Opt. 20, 2934 (1981).
    [CrossRef] [PubMed]
  9. R. Reisfeld, C. K. Jørgensen, “Luminescent Solar Concentrators for Energy Conversion,” Struct. Bonding Berlin 49, 15 (1982).
  10. K. Heidler, “Efficiency and Concentration Ratio Measurements of Fluorescent Solar Concentrators Using a Xenon Measurement System,” Appl. Opt. 20, 773 (1981).
    [CrossRef] [PubMed]
  11. J. M. Drake, M. L. Lesiecki, J. Sansregret, W. R. L. Thomas, “Organic Dyes in PMMA in a Planar Luminescent Solar Collector: a Performance Evaluation,” Appl. Opt. 21, 2945 (1982).
    [CrossRef] [PubMed]

1982 (2)

1981 (2)

1979 (1)

1977 (3)

1976 (1)

1970 (1)

G. Keil, “Design Principles of Fluorescence Radiation Converters,” Nucl. Instrum. Methods 87, 111 (1970).
[CrossRef]

1956 (1)

A. Budo, I. Ketskemety, “Influence of Secondary Fluorescence on the Emission Spectra of Luminescent Solutions,” J. Chem. Phys. 25, 595 (1956).
[CrossRef]

Batchelder, J. S.

Budo, A.

A. Budo, I. Ketskemety, “Influence of Secondary Fluorescence on the Emission Spectra of Luminescent Solutions,” J. Chem. Phys. 25, 595 (1956).
[CrossRef]

Cole, T.

Drake, J. M.

Fayer, M. D.

Goetzberger, A.

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

Greubel, W.

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

Heidler, K.

Jørgensen, C. K.

R. Reisfeld, C. K. Jørgensen, “Luminescent Solar Concentrators for Energy Conversion,” Struct. Bonding Berlin 49, 15 (1982).

Keil, G.

G. Keil, “Design Principles of Fluorescence Radiation Converters,” Nucl. Instrum. Methods 87, 111 (1970).
[CrossRef]

Ketskemety, I.

A. Budo, I. Ketskemety, “Influence of Secondary Fluorescence on the Emission Spectra of Luminescent Solutions,” J. Chem. Phys. 25, 595 (1956).
[CrossRef]

Lambe, J.

Lesiecki, M. L.

Levitt, J. A.

Loring, R. F.

Olson, R. W.

Reisfeld, R.

R. Reisfeld, C. K. Jørgensen, “Luminescent Solar Concentrators for Energy Conversion,” Struct. Bonding Berlin 49, 15 (1982).

Sansregret, J.

Swartz, B. A.

Thomas, W. R. L.

Weber, W. H.

Zewail, A. H.

Zewall, A. H.

Appl. Opt. (6)

Appl. Phys. (1)

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

J. Chem. Phys. (1)

A. Budo, I. Ketskemety, “Influence of Secondary Fluorescence on the Emission Spectra of Luminescent Solutions,” J. Chem. Phys. 25, 595 (1956).
[CrossRef]

Nucl. Instrum. Methods (1)

G. Keil, “Design Principles of Fluorescence Radiation Converters,” Nucl. Instrum. Methods 87, 111 (1970).
[CrossRef]

Opt. Lett. (1)

Struct. Bonding Berlin (1)

R. Reisfeld, C. K. Jørgensen, “Luminescent Solar Concentrators for Energy Conversion,” Struct. Bonding Berlin 49, 15 (1982).

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Figures (13)

Fig. 1
Fig. 1

Principle of LSC operation: 1, reflective edge; 2, photovoltaic cell.

Fig. 2
Fig. 2

Diagram of elementary processes in LSC operation. The overall optical efficiency of a LSC can be expressed as the product of the partial yields related to each elementary process.

Fig. 3
Fig. 3

Effect of self-absorption. Collection efficiency Q vs LSC width (from Ref. 6).

Fig. 4
Fig. 4

Mean propagation angle θ ¯; d = LSC thickness; h ¯ = mean elementary step; y = h ¯, projection in the LSC plane; and l ¯ = mean optical path.

Fig. 5
Fig. 5

Absorption and emission spectra of polymers A and B in CHCl3.

Fig. 6
Fig. 6

Calculated variation of the concentration ratio C(λ) with monochromatic irradiation vs captation surface S for polygons with m sides obtained from polymers A and B.

Fig. 7
Fig. 7

Experimental curves for the variation of the concentration ratio C(λ) obtained with monochromatic irradiation vs captation surface S for various LSC geometries (3, triangles; 4, squares; 5, pentagons) with polymers A and B.

Fig. 8
Fig. 8

Effect of thickness on the concentration ratio C(λ) with monochromatic light for triangular LSC (c = 10 cm): Polymer A: ○, calculated values; ◐, experimental values. Polymer B: □, calculated values; ◩, experimental values.

Fig. 9
Fig. 9

Calculated curves showing the increase of the concentration ratio obtained when thickness d is reduced to its optimal value for a triangular LSC for polymers A and B.

Fig. 10
Fig. 10

Representation of the 3-D surface showing the optimum of C corresponding to the optimum values of the captation surface Sopt and thickness dopt for an openW square with polymer A.

Fig. 11
Fig. 11

Experimental emission spectra of LSC, A and B having different optical path lengths l ¯: (1) reference spectrum, (2) 0.5 cm, (3) 8.8 cm, (4) 17.4 cm, (5) 27.3 cm, (6) A 42 cm, B 38.4 cm.

Fig. 12
Fig. 12

Experimental procedure for the measurements of concentration ratios with monochromatic irradiation. The dotted line shows the reference diode position when recording the reference signal.

Fig. 13
Fig. 13

Experimental values of the flux gain CF with xenon light vs captation surface S for polymers A and B and for various geometries: ◩ triangle, ◐ square, and ○ pentagon.

Tables (4)

Tables Icon

Table I Photon Trajectory Parameters

Tables Icon

Table II Calculated Captation Surfaces Leading to Cmax

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Table III Calculated Maximum Surfaces for Open Squares

Tables Icon

Table IV Extremum Characteristics

Equations (32)

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η pot = P out P in = C G .
L r = ( n - 1 ) 2 / ( n + 1 ) 2 .
1 - L r = 4 n / ( n + 1 ) 2 .
η abs = 1 - 10 - α d .
θ c = sin - 1 [ ( 1 / n ) ] .
L t = 1 - cos θ c = - ( 1 - 1 n 2 ) 1 / 2 ,
η trap = ( 1 - 1 n 2 ) 1 / 2 .
η conv = N / N 0 .
η trans = N / N .
η mat = 10 - m ( λ e ) l ¯ .
η self = K self × 10 - d ( λ e ) l ¯ .
η lat = r p ¯ .
η TIR = R i n i .
f = 1 cos - 1 1 n 0 cos - 1 ( 1 / n ) d x cos x = [ cos - 1 ( 1 / n ) ] lntan [ π 4 + 1 2 cos - 1 1 n ]
θ ¯ = cos - 1 ( 1 / h ) , θ ¯ = cos - 1 ( 1 / f ) ,
n i = ( l ¯ / n ) = ( l ¯ sin θ ¯ ) / d .
η trans = r p · R i [ ( l ¯ sin θ ¯ ) / d ] K self × 10 - ( m + d ) ( λ e ) l ¯ .
η o p t ( λ i ) = 0.72 · η a b s · η ϕ · r p × R i [ ( l ¯ sin θ ¯ ) / d ] K s e l f × 10 - ( m + d ) ( λ e ) l ¯ ,
C ( λ i ) = η opt ( λ i ) G .
l ¯ = γ R
A K = 0.62 , d m = 4 × 10 - 3 cm - 1 , B K = 0.76 , m d = 2.4 × 10 - 3 cm - 1 .
S = ½ m R 2 sin ( 2 π ) / m ,
s = 2 d R sin ( π / m ) ;
R ( S m 2 sin 2 π m ) 1 / 2 or R = β S ,
G = m 2 d ( S m 2 sin 2 π m ) 1 / 2 cos ( π / m )             or G = ( δ / d ) S .
η o p t ( λ i ) = 0.72 × [ 1 - 10 - α ( λ i ) d ] K × 10 - [ ( m - d ) ( λ e ) γ β S ] R i [ ( γ β S ¯ sin θ ¯ ) / d ] r p ¯ ,
C ( λ i ) = ( δ / d ) · S · η opt .
d C d S = 0 S ( C max ) = ( m d γ β ln 10 - γ sin θ ¯ d β ln R i ) - 2 .
d C d d = 0 ( 1 - 10 α d ) ( 1 + γ sin θ ¯ d · β S ln R i ) - ( α d × 10 α d ln 10 ) = 0.
K self = 0.8 ,             ( m + m ) = 10 - 3 cm - 1 ,             α abs = 20 c m - 1 , R = 0.997.
S = 9300 cm 2 ,             d = 0.076 cm ,             G opt = 320 , C 13 , η 0.05.
m = 3 , S = 43.3 , 100 , 173 cm 2 , m = 4 , S = 50 , 100 , 173 , 238 , 400 cm 2 , m = 5 , S = 50 , 100 , 173 , 238 , 400 , cm 2 .

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