Abstract

A study is presented of solar concentrators based on total internal reflections. The concentrators are placed over photovoltaic cells. Experimental data obtained with different encapsulating materials and dependence on geometrical and physical variables are given. A theoretical model which includes the losses in the encapsulating material is proposed, giving good agreement with the experimental data. Gain factors as high as 30% have been obtained with these concentrators. The additional effect of organic dyes on absorption bands in the 350–360-nm range is also studied.

© 1983 Optical Society of America

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References

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  1. J. F. Kreider, F. Kreith, Eds., Solar Energy Handbook (McGraw-Hill, New York, 1981).
  2. A. B. Meinel, M. P. Meinel, Applied Solar Energy (Addison-Wesley, Reading, Mass., 1977).
  3. R. Winston, Sol. Energy 70, 255 (1975).
    [CrossRef]
  4. W. H. Weber, J. Lambe, Appl. Opt. 15, 2299 (1976).
    [CrossRef] [PubMed]
  5. A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
    [CrossRef]
  6. J. S. Batchelder, A. H. Zewail, T. Cole, Appl. Opt. 18, 3090 (1979).
    [CrossRef] [PubMed]
  7. A. Goetzberger, Appl. Phys. 16, 399 (1978).
    [CrossRef]
  8. F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).
  9. A. M. Hermann, Sol. Energy 29, 323 (1982).
    [CrossRef]
  10. J. M. Drake, M. L. Lesiecki, J. Sansregret, W. R. L. Thomas, Appl. Opt. 21, 2945 (1982).
    [CrossRef] [PubMed]
  11. H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
    [CrossRef]
  12. G. Smestad, P. Hamill, Appl. Phys. 21, 1298 (1982).
  13. D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
    [CrossRef]

1982

A. M. Hermann, Sol. Energy 29, 323 (1982).
[CrossRef]

G. Smestad, P. Hamill, Appl. Phys. 21, 1298 (1982).

J. M. Drake, M. L. Lesiecki, J. Sansregret, W. R. L. Thomas, Appl. Opt. 21, 2945 (1982).
[CrossRef] [PubMed]

1981

D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
[CrossRef]

1979

J. S. Batchelder, A. H. Zewail, T. Cole, Appl. Opt. 18, 3090 (1979).
[CrossRef] [PubMed]

H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
[CrossRef]

1978

A. Goetzberger, Appl. Phys. 16, 399 (1978).
[CrossRef]

1977

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

1976

1975

R. Winston, Sol. Energy 70, 255 (1975).
[CrossRef]

Batchelder, J. S.

Cole, T.

Cusso, F.

F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).

Drake, J. M.

Goetzberger, A.

A. Goetzberger, Appl. Phys. 16, 399 (1978).
[CrossRef]

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Gravisse, P.

D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
[CrossRef]

Greubel, W.

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Hamill, P.

G. Smestad, P. Hamill, Appl. Phys. 21, 1298 (1982).

Hermann, A. M.

A. M. Hermann, Sol. Energy 29, 323 (1982).
[CrossRef]

Hodgson, R. T.

H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
[CrossRef]

Hovel, H. J.

H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
[CrossRef]

Ibarra, A.

F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).

Jaque, F.

F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).

Lambe, J.

Le Poull, F.

D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
[CrossRef]

Lesiecki, M. L.

Meinel, A. B.

A. B. Meinel, M. P. Meinel, Applied Solar Energy (Addison-Wesley, Reading, Mass., 1977).

Meinel, M. P.

A. B. Meinel, M. P. Meinel, Applied Solar Energy (Addison-Wesley, Reading, Mass., 1977).

Meseguer, F.

F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).

Sansregret, J.

Sarti, D.

D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
[CrossRef]

Smestad, G.

G. Smestad, P. Hamill, Appl. Phys. 21, 1298 (1982).

Thomas, W. R. L.

Weber, W. H.

Winston, R.

R. Winston, Sol. Energy 70, 255 (1975).
[CrossRef]

Woodall, J. M.

H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
[CrossRef]

Zewail, A. H.

Appl. Opt.

Appl. Phys.

G. Smestad, P. Hamill, Appl. Phys. 21, 1298 (1982).

A. Goetzberger, Appl. Phys. 16, 399 (1978).
[CrossRef]

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Sol. Cells

D. Sarti, F. Le Poull, P. Gravisse, Sol. Cells 4, 25 (1981).
[CrossRef]

Sol. Energy

R. Winston, Sol. Energy 70, 255 (1975).
[CrossRef]

A. M. Hermann, Sol. Energy 29, 323 (1982).
[CrossRef]

Sol. Energy Mater.

H. J. Hovel, R. T. Hodgson, J. M. Woodall, Sol. Energy Mater. 2, 19 (1979).
[CrossRef]

Other

F. Cusso, A. Ibarra, F. Meseguer, F. Jaque, Proceedings, Twentieth Conference International de la C.O.M.P.L.E.S., Rabat (1981).

J. F. Kreider, F. Kreith, Eds., Solar Energy Handbook (McGraw-Hill, New York, 1981).

A. B. Meinel, M. P. Meinel, Applied Solar Energy (Addison-Wesley, Reading, Mass., 1977).

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Figures (8)

Fig. 1
Fig. 1

Experimental panel used in this work. A photovoltaic cell of diameter r is covered with a transparent material of refractive index n and thickness D. The illuminated area is controlled with masks of different radius (R/2).

Fig. 2
Fig. 2

Side view of the panel illustrating the magnitudes used in the text.

Fig. 3
Fig. 3

Experimental gain factors (points) obtained when the silicon cell is covered with different depths D of glycerin or water at several illumination areas (πR2). The theoretical lines are calculated from Eq. (9).

Fig. 4
Fig. 4

Experimental gain factor (points) against diameter R of the illuminated area for a concentrator width of 1 cm. The theoretical fitting from Eq. (1) (full line) gives a substrate reflectance Ref = 0.64.

Fig. 5
Fig. 5

Optimum depth dependence with the covering factor (cell area/panel area).

Fig. 6
Fig. 6

Gain factor I/I0 dependence on the panel refractive index. The different lines are calculated for the different absorption coefficients α ¯. The experimental points correspond to the materials used in this work: ethanol ( n = 1.31 , α ¯ = 0.07 cm 1 ); water ( n = 1.33 , α ¯ = 0.13 cm 1 ); glycerin ( n = 1.47 , α ¯ = 0.08 cm 1 ).

Fig. 7
Fig. 7

Normalized absorption (full line) and emission (dotted line) bands of different luminescent molecules compared to the solar cell response.

Fig. 8
Fig. 8

Comparison between the gain factor I/I0 obtained with pure ethanol (open symbols) or ethanol + coumarin 6 (solid symbols) at different covering factors.

Tables (1)

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Table I Mean Absorption Coefficient α ¯ ( cm 1 )

Equations (10)

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K = Δ Ω 2 π = π r 2 cos θ / ( 2 Y ) 2 2 π = r 2 cos θ 8 Y 2 ,
P = J Ref 2 π r 2 × cos θ dx 8 Y 2 ,
T 1 ( 0 ) = 4 n 1 n 2 ( n 1 + n 2 ) 2 , T 2 ( 0 ) = 4 n 2 n 3 ( n 2 + n 3 ) 2 , T 3 ( 0 ) = 4 n 1 n 3 ( n 1 + n 3 ) 2 .
α ¯ = 1 λ 2 λ 1 λ 1 λ 2 α ( λ ) d λ ,
P = J 0 T 1 T 2 exp ( α ¯ D ) [ π r 2 + Ref × x c R 2 π r 2 × cos θ exp ( 2 α ¯ Y ) 8 Y 2 d x ] = J 0 T 1 T 2 exp ( α ¯ D ) [ π r 2 + π r 2 Ref D Y c Y R exp ( 2 Y α ¯ ) Y 2 d Y ] = J 0 T 1 T 2 exp ( α ¯ D ) π r 2 ( 1 + Ref F ) ,
F = D Y c Y R [ exp ( 2 α ¯ Y ) / Y 2 ] dY = D ( Y c 1 Y R 1 + 2 α ¯ ln Y c 2 α ¯ ln Y R + ) ,
G = exp ( 2 α ¯ Y ) Ref [ 1 r 2 R 2 r 2 F ( 1 cos θ c ) ] .
P = J 0 T 1 T 2 π r 2 exp ( α ¯ D ) ( 1 + Ref F + Ref FG + Ref F G 2 + ) ,
I / I 0 = ( T 1 T 2 / T 3 ) ( 1 + F Ref / 1 G ) exp ( α ¯ D ) .
I / I 0 = ( T 1 T 2 / T 3 ) ( 1 α ¯ D ) ,

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