Abstract

For reflective cylindrical concentrators the acceptance function, as determined in the meridian plane, remains constant for more oblique planes of incidence. However, if the reflective surface has a linear corrugated structure, it is possible to increase the acceptance in the meridian plane at the expense of reduced acceptance at a more oblique incidence. A ray-tracing study has been performed on the optical properties of troughlike compound parabolic concentrators (CPC’s) with linear corrugated reflectors. Calculations of angular acceptance for a modified CPC with concentration C = 2× is presented. A possible application of this new concentrator is as a secondary concentrator for tracking parabolic troughs.

© 1998 Optical Society of America

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References

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  1. A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985).
  2. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).
  3. A. Rabl, “Comparison of solar energy concentrators,” Sol. Energy 18, 93–111 (1976).
    [CrossRef]
  4. B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
    [CrossRef]
  5. M. Rönnelid, B. Karlsson, J. M. Gordon, “The impact of high latitudes on the optical design of solar systems,” in Proceedings of the EuroSun ’96, A. Goetzberger, J. Luther, eds. (DGS-Sonnenenergie Verlags-GmbH, München, 1996), pp. 341–345.
  6. B. Perers, B. Johansson, “Parabolic trough collectors for the Swedish climate. Measurement, evaluation and cost analysis (Linjärparaboliska solfångare för svenskt klimat. Mätning, utvärdering och kostnadsanalys),” Report Studsvik/ED-90/12 (Studsvik AB, Nyköping, Sweden, 1990) (in Swedish).
  7. S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).
  8. M. Rönnelid, B. Perers, B. Karlsson, “Optical properties of nonimaging concentrators with corrugated reflectors,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, V. Wittwer, C. G. Granquist, C. M. Lampert, eds., Proc. SPIE2255, 595–602 (1994).
    [CrossRef]

1995

S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).

1994

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

1976

A. Rabl, “Comparison of solar energy concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

Bergkvist, M.

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

Bowden, S.

S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).

Gordon, J. M.

M. Rönnelid, B. Karlsson, J. M. Gordon, “The impact of high latitudes on the optical design of solar systems,” in Proceedings of the EuroSun ’96, A. Goetzberger, J. Luther, eds. (DGS-Sonnenenergie Verlags-GmbH, München, 1996), pp. 341–345.

Green, M. A.

S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).

Johansson, B.

B. Perers, B. Johansson, “Parabolic trough collectors for the Swedish climate. Measurement, evaluation and cost analysis (Linjärparaboliska solfångare för svenskt klimat. Mätning, utvärdering och kostnadsanalys),” Report Studsvik/ED-90/12 (Studsvik AB, Nyköping, Sweden, 1990) (in Swedish).

Karlsson, B.

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

M. Rönnelid, B. Perers, B. Karlsson, “Optical properties of nonimaging concentrators with corrugated reflectors,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, V. Wittwer, C. G. Granquist, C. M. Lampert, eds., Proc. SPIE2255, 595–602 (1994).
[CrossRef]

M. Rönnelid, B. Karlsson, J. M. Gordon, “The impact of high latitudes on the optical design of solar systems,” in Proceedings of the EuroSun ’96, A. Goetzberger, J. Luther, eds. (DGS-Sonnenenergie Verlags-GmbH, München, 1996), pp. 341–345.

Perers, B.

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

M. Rönnelid, B. Perers, B. Karlsson, “Optical properties of nonimaging concentrators with corrugated reflectors,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, V. Wittwer, C. G. Granquist, C. M. Lampert, eds., Proc. SPIE2255, 595–602 (1994).
[CrossRef]

B. Perers, B. Johansson, “Parabolic trough collectors for the Swedish climate. Measurement, evaluation and cost analysis (Linjärparaboliska solfångare för svenskt klimat. Mätning, utvärdering och kostnadsanalys),” Report Studsvik/ED-90/12 (Studsvik AB, Nyköping, Sweden, 1990) (in Swedish).

Rabl, A.

A. Rabl, “Comparison of solar energy concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985).

Rönnelid, M.

M. Rönnelid, B. Karlsson, J. M. Gordon, “The impact of high latitudes on the optical design of solar systems,” in Proceedings of the EuroSun ’96, A. Goetzberger, J. Luther, eds. (DGS-Sonnenenergie Verlags-GmbH, München, 1996), pp. 341–345.

M. Rönnelid, B. Perers, B. Karlsson, “Optical properties of nonimaging concentrators with corrugated reflectors,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, V. Wittwer, C. G. Granquist, C. M. Lampert, eds., Proc. SPIE2255, 595–602 (1994).
[CrossRef]

Welford, W. T.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

Wenham, S. R.

S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).

Winston, R.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

Prog. Photovoltaics

S. Bowden, S. R. Wenham, M. A. Green, “Application of static concentrators to photovoltaic roof tiles,” Prog. Photovoltaics 3, 413–423 (1995).

Sol. Energy

A. Rabl, “Comparison of solar energy concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

Other

M. Rönnelid, B. Karlsson, J. M. Gordon, “The impact of high latitudes on the optical design of solar systems,” in Proceedings of the EuroSun ’96, A. Goetzberger, J. Luther, eds. (DGS-Sonnenenergie Verlags-GmbH, München, 1996), pp. 341–345.

B. Perers, B. Johansson, “Parabolic trough collectors for the Swedish climate. Measurement, evaluation and cost analysis (Linjärparaboliska solfångare för svenskt klimat. Mätning, utvärdering och kostnadsanalys),” Report Studsvik/ED-90/12 (Studsvik AB, Nyköping, Sweden, 1990) (in Swedish).

M. Rönnelid, B. Perers, B. Karlsson, “Optical properties of nonimaging concentrators with corrugated reflectors,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, V. Wittwer, C. G. Granquist, C. M. Lampert, eds., Proc. SPIE2255, 595–602 (1994).
[CrossRef]

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985).

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

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Figures (6)

Fig. 1
Fig. 1

Incident radiation onto a linear concentrator characterized by two projected incidence angles, θ and θ.

Fig. 2
Fig. 2

Acceptance of radiation, incident in the meridian plane: a, CPC with smooth reflectors; b, c-CPC with corrugated reflectors. θ a , Acceptance half-angle defined by Eq. (2); θ a(mr), largest angle of acceptance for meridian rays.

Fig. 3
Fig. 3

Definition of corrugation angle β for the reflectors.

Fig. 4
Fig. 4

Reflection in the corrugated reflector for radiation incident in the meridian plane. If the corrugation angle β exceeds 30°, multiple reflection of the ray in the local corrugation valley can occur. One corrugation valley seen from the upper (or lower) edge of the reflector with the beam impinging in the meridian plane is seen.

Fig. 5
Fig. 5

Acceptance functions for untruncated c-CPC’s with C = 2× and different corrugated reflectors: a, β = 0° (smooth reflector); b, β = 10°; c, β = 30°; d, β = 50°. The numbers show the fraction of rays that reach the exit aperture from different angles of incidence on the entry aperture.

Fig. 6
Fig. 6

Distribution of extraterrestrial irradiation at the Equator versus projected incidence angles relative to zenith. θ and θ are defined in the text. The numbers are irradiation in units of kW h yr-1, square deg-1.

Equations (5)

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F θ = F θ = 1   for   θ θ a , F θ = F θ = 0   for   θ > θ a ,
C ideal , 2 - D = 1 / sin θ a
C ideal , 3 - D = 1 / sin 2 θ a .
F 0 ,   θ 1 / C     θ   large .
θ = arctan tan 2   θ + tan 2   θ 1 / 2 .

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