Abstract

In this work we analyze a two-stage concentrator in which the first stage is reflective and the second stage considers the first one as a Lambertian source in order to obtain the highest possible gain. We determine the profile and the position of this first stage, which happens to be a parabola, and we calculate the value of the gain as a function of the acceptance angle and the focal length of the first stage.

© 1980 Optical Society of America

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References

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  1. A. Rabl, R. Winston, Appl. Opt. 15, 2880 (1976);R. Winston, U.S. Patent3,957,031 (1976).
    [CrossRef] [PubMed]
  2. W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978), pp. 20–25.
  3. A. Luque et al., in Proceedings, Photovoltaic Solar Energy Conference (D. Reidel, Dordrecht, Holland, 1978), pp. 269–277.
    [CrossRef]
  4. A. Luque, Spanish Patent453,575 (1976);U.S. Patent4,169,738 (1979).
  5. A. Luque et al., in Proceedings, COMPLES Conference, Milan, Cassa di Risparmio Calabria e Lucania, Comples Italian Session, Roma, 1980; in press.
  6. Ref. 2, p. 135.
  7. R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
    [CrossRef]
  8. A. Luque et al., in Proceedings, ISES Silver Jubilee Congress, K. W. Böer, B. H. Glenn, Eds. (Pergamon, New York, 1979), Vol. 3, pp. 1813–1817.
  9. R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
    [CrossRef]

1978 (1)

1976 (1)

1975 (1)

R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
[CrossRef]

Hinterberger, H.

R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
[CrossRef]

Luque, A.

A. Luque et al., in Proceedings, Photovoltaic Solar Energy Conference (D. Reidel, Dordrecht, Holland, 1978), pp. 269–277.
[CrossRef]

A. Luque, Spanish Patent453,575 (1976);U.S. Patent4,169,738 (1979).

A. Luque et al., in Proceedings, ISES Silver Jubilee Congress, K. W. Böer, B. H. Glenn, Eds. (Pergamon, New York, 1979), Vol. 3, pp. 1813–1817.

A. Luque et al., in Proceedings, COMPLES Conference, Milan, Cassa di Risparmio Calabria e Lucania, Comples Italian Session, Roma, 1980; in press.

Rabl, A.

Welford, W. T.

R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
[CrossRef]

W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978), pp. 20–25.

Winston, R.

R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
[CrossRef]

A. Rabl, R. Winston, Appl. Opt. 15, 2880 (1976);R. Winston, U.S. Patent3,957,031 (1976).
[CrossRef] [PubMed]

R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
[CrossRef]

W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978), pp. 20–25.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Sol. Energy (1)

R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
[CrossRef]

Other (6)

A. Luque et al., in Proceedings, ISES Silver Jubilee Congress, K. W. Böer, B. H. Glenn, Eds. (Pergamon, New York, 1979), Vol. 3, pp. 1813–1817.

W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978), pp. 20–25.

A. Luque et al., in Proceedings, Photovoltaic Solar Energy Conference (D. Reidel, Dordrecht, Holland, 1978), pp. 269–277.
[CrossRef]

A. Luque, Spanish Patent453,575 (1976);U.S. Patent4,169,738 (1979).

A. Luque et al., in Proceedings, COMPLES Conference, Milan, Cassa di Risparmio Calabria e Lucania, Comples Italian Session, Roma, 1980; in press.

Ref. 2, p. 135.

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Figures (5)

Fig. 1
Fig. 1

Quasi-optimum pseudo-Lambertian reflecting concentrator for bifacial solar cells.

Fig. 2
Fig. 2

Diagram of the position of the reflector of the first stage (points AA′) with respect to the entry aperture OO′ of the second stage. Only reflectors inside the shadowed contour can give high gain concentrators. The hyperbolas of equietendue are also represented by dotted lines. The outline of the reflector with the biggest gain is A 3 A 4

Fig. 3
Fig. 3

Gain of the concentrator as a function of position ω of point A 2 (see Fig. 2). The parameters are the orientation α of the first stage and the acceptance angle 2θ.

Fig. 4
Fig. 4

Approximate value to within ±1% for semiacceptance angles smaller than 10° of that of the structure's output GTH/GTHOPT and exact value of the gain of the first stage (multiplied by the sine of the semiacceptance angle) as a function of the first stage.

Fig. 5
Fig. 5

Gain GTH as a function of entry aperture D (normalized to the focal length) with the semiangle of acceptance as the parameter.

Equations (31)

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E 2 = 2 P ,
E 2 = 2 nW ,
E 2 = 4 nW ,
E 2 = ( A O A O ) ( AO A O ) = 2 a 2 a .
G TH = D / P = 2 D / E 2 ,
G PHM = n G TH ,
G PHB = 2 n G TH ,
G 1 = D / 2 c ,
E 2 = DS ( D ) sin 2 θ ( D 2 / 4 ) ( 1 cos 2 θ ) ,
E 1 = D sin 2 θ ( D 2 / 4 ) ( 1 cos 2 θ ) .
η = G TH G THI = E 1 E 2 = 1 ( D / 4 ) tan θ S ( D ) ( D / 4 ) tan θ
G THI = 2 D E 1 = 1 sin θ cos θ ( 1 ( D / 4 ) tan θ ) .
G 1 = D / 2 c = ( 1 D 2 + 9 16 + 3 32 D 2 + 1 256 D 4 ) 1 / 2 / sin 2 θ .
ρ = c 2 a 2 a + c cos ω .
ρ = 2 c sin 2 θ sin ( ω + 2 θ ) ,
ρ = 2 r 1 + cos ( ω α ) ,
r = c sin 2 θ sin ( ω + 2 θ ) [ 1 + cos ( ω α ) ] .
a = ( r 2 + 4 c 2 4 rc cos α ) 1 / 2 r 2 .
a = ( ρ 2 + 4 e 2 4 ρ c cos ω ) 1 / 2 ρ 2 .
D = ρ sin ( ω α ) .
r m = 2 c sin 2 θ sin ( α + 2 θ ) ,
x 2 + y 2 2 x x 0 y = 0 ,
x 2 = 4 y ,
x 0 = 3 8 D + 1 32 D 3 .
A 4 O = 1
A 3 O = 1 + ( D 2 / 4 ) .
O O = ( 1 + 4 x 0 2 ) sin 2 2 θ = 2 c .
A 4 O = cos 2 θ 2 x 0 sin 2 θ .
A 3 O = ( 1 + D 2 / 4 ) cos 2 θ + [ ( 1 + D 2 / 4 ) 2 + ( 1 + 4 x 0 ) 2 ] 1 / 2 sin 2 θ .
E 2 = ( O A 3 O A 3 ) + ( O A 4 O A 4 ) ,
S ( D ) = ( 3 4 + D 2 16 ) + ( 1 16 + D 2 32 + D 4 256 ) 1 / 2 .

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