Abstract

Two-stage photovoltaic concentrators with Fresnel lenses as primaries and dielectric totally internally reflecting nonimaging concentrators as secondaries are discussed. The general design principles of such two-stage systems are given. Their optical properties are studied and analyzed in detail using computer ray trace procedures. It is found that the two-stage concentrator offers not only a higher concentration or increased acceptance angle, but also a more uniform flux distribution on the photovoltaic cell than the point focusing Fresnel lens alone. Experimental measurements with a two-stage prototype module are presented and compared to the analytical predictions.

© 1987 Optical Society of America

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References

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  1. R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, American Solar Energy Society Annual Meeting, Boulder, CO (1986), p. 417.
  2. X. Ning, R. Winston, J. O’Gallagher, “Dielectric Totally Internally Reflecting Concentrators,” Appl. Opt. 26, 300 (1987).
    [CrossRef] [PubMed]
  3. W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).
  4. J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic Systems,” in Proceedings, American Solar Energy Society Annual Meeting, Minneapolis (1983), p. 941.
  5. G. Nixon, “Cast Acrylic Fresnel Lens Solar Concentrator,” in Proceedings, ERDA Conference on Concentrating Solar Collectors, Atlanta, GA (1977), pp. 5–33.
  6. L. W. James, “Fresnel Optics for Solar Concentration on Photovoltaic Cells,” in Proceedings, IEEE Photovoltaic Thirteenth Special ConferenceWashington, DC (1978), p. 673.
  7. R. W. Sanderson, D. T. O’Donnell, C. E. Backus, “The Effects of Nonuniform Illumination and Temperature Profiles on Silicon Solar Cells Under Concentrated Sunlight,” in Proceedings, IEEE Photovoltaic Fourteenth Special Conference, San Diego (1980), p. 431.

1987 (1)

Backus, C. E.

R. W. Sanderson, D. T. O’Donnell, C. E. Backus, “The Effects of Nonuniform Illumination and Temperature Profiles on Silicon Solar Cells Under Concentrated Sunlight,” in Proceedings, IEEE Photovoltaic Fourteenth Special Conference, San Diego (1980), p. 431.

James, L. W.

L. W. James, “Fresnel Optics for Solar Concentration on Photovoltaic Cells,” in Proceedings, IEEE Photovoltaic Thirteenth Special ConferenceWashington, DC (1978), p. 673.

Ning, X.

X. Ning, R. Winston, J. O’Gallagher, “Dielectric Totally Internally Reflecting Concentrators,” Appl. Opt. 26, 300 (1987).
[CrossRef] [PubMed]

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, American Solar Energy Society Annual Meeting, Boulder, CO (1986), p. 417.

Nixon, G.

G. Nixon, “Cast Acrylic Fresnel Lens Solar Concentrator,” in Proceedings, ERDA Conference on Concentrating Solar Collectors, Atlanta, GA (1977), pp. 5–33.

O’Donnell, D. T.

R. W. Sanderson, D. T. O’Donnell, C. E. Backus, “The Effects of Nonuniform Illumination and Temperature Profiles on Silicon Solar Cells Under Concentrated Sunlight,” in Proceedings, IEEE Photovoltaic Fourteenth Special Conference, San Diego (1980), p. 431.

O’Gallagher, J.

X. Ning, R. Winston, J. O’Gallagher, “Dielectric Totally Internally Reflecting Concentrators,” Appl. Opt. 26, 300 (1987).
[CrossRef] [PubMed]

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic Systems,” in Proceedings, American Solar Energy Society Annual Meeting, Minneapolis (1983), p. 941.

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, American Solar Energy Society Annual Meeting, Boulder, CO (1986), p. 417.

Sanderson, R. W.

R. W. Sanderson, D. T. O’Donnell, C. E. Backus, “The Effects of Nonuniform Illumination and Temperature Profiles on Silicon Solar Cells Under Concentrated Sunlight,” in Proceedings, IEEE Photovoltaic Fourteenth Special Conference, San Diego (1980), p. 431.

Welford, W. T.

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Winston, R.

X. Ning, R. Winston, J. O’Gallagher, “Dielectric Totally Internally Reflecting Concentrators,” Appl. Opt. 26, 300 (1987).
[CrossRef] [PubMed]

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic Systems,” in Proceedings, American Solar Energy Society Annual Meeting, Minneapolis (1983), p. 941.

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, American Solar Energy Society Annual Meeting, Boulder, CO (1986), p. 417.

Appl. Opt. (1)

Other (6)

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic Systems,” in Proceedings, American Solar Energy Society Annual Meeting, Minneapolis (1983), p. 941.

G. Nixon, “Cast Acrylic Fresnel Lens Solar Concentrator,” in Proceedings, ERDA Conference on Concentrating Solar Collectors, Atlanta, GA (1977), pp. 5–33.

L. W. James, “Fresnel Optics for Solar Concentration on Photovoltaic Cells,” in Proceedings, IEEE Photovoltaic Thirteenth Special ConferenceWashington, DC (1978), p. 673.

R. W. Sanderson, D. T. O’Donnell, C. E. Backus, “The Effects of Nonuniform Illumination and Temperature Profiles on Silicon Solar Cells Under Concentrated Sunlight,” in Proceedings, IEEE Photovoltaic Fourteenth Special Conference, San Diego (1980), p. 431.

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, American Solar Energy Society Annual Meeting, Boulder, CO (1986), p. 417.

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Figures (13)

Fig. 1
Fig. 1

Two-stage concentrator, where the primary is a Fresnel lens and the secondary is a DTIRC with refractive index n. The secondary plane coincides with the focal plane of the primary Fresnel lens.

Fig. 2
Fig. 2

Angular acceptance curves for a two-stage design with concentration of 200× at the 22-cm primary–secondary spacing, and for the primary lens alone at the 22-cm lens–receiving plane spacing.

Fig. 3
Fig. 3

Angular acceptance curves for a two-stage design with concentration of 1220× at the 22-cm primary–secondary spacing, and for the primary lens alone at the 22-cm lens–receiving plane spacing.

Fig. 4
Fig. 4

Typical ray picture for the 220× design based on simulation results. The primary is not shown. The angle of incidence is 3°.

Fig. 5
Fig. 5

Acceptance at normal incidence vs the primary–secondary spacing for the 200× two-stage concentrator and vs the lens–receiving spacing for the primary lens alone.

Fig. 6
Fig. 6

Acceptance at normal incidence vs the primary–secondary spacing for the 1220× two-stage concentrator and vs the lens–receiving spacing for the primary lens alone.

Fig. 7
Fig. 7

Flux distribution profiles for the primary lens alone at various lens–receiving separations. The maximum peak of the profile is normalized to a constant. The circle represents the receiving area boundary (solar cell).

Fig. 8
Fig. 8

Flux distribution profiles for the two-stage at various primary–secondary separations. The maximum peak of the profile is normalized to a constant. The circle represents the receiving area boundary (solar cell).

Fig. 9
Fig. 9

Variances vs the lens–cell spacing for the lens alone and vs the primary–secondary spacing for the two-stage concentrator. The distribution profile is digitized into 390 bins and the average number of rays per bin is normalized to one.

Fig. 10
Fig. 10

Comparisons of the measured angular acceptance curves with the ray tracing predictions for the 200× two-stage concentrator and the primary lens alone. The measured data were adjusted for the physical losses incurred in the secondary.

Fig. 11
Fig. 11

Acceptance at normal incidence vs the primary–secondary spacing for the 200× two-stage concentrator and vs the lens–receiving spacing for the primary lens alone. The measured data were adjusted for the physical losses incurred in the secondary.

Fig. 12
Fig. 12

Measured fill factors and open circuit voltages vs the lens–cell spacing for the primary lens alone.

Fig. 13
Fig. 13

Measured fill factors and open circuit voltages vs the primary–secondary spacing for the 200× two-stage concentrator.

Tables (1)

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Table I Design Parameters of a 200× and a 1220× Two-Stage Concentrator

Equations (3)

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θ c = tan - 1 ( D + L 2 F ) ,
ϕ max = π 2 - θ c .
F ( θ ) = I 2 ( θ ) C g I 0 ,

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