Abstract

The application of a kaleidoscope as a flux homogenizer to a concentrating photovoltaics system with a central receiver is investigated. The optical setup of a primary dish-type concentrator, a secondary homogenizer optics, and a photovoltaic receiver is simulated using ray tracing. The influence of various deviations from the ideal—namely sunshape (circumsolar radiation), shading, tracking error, and shape of the primary optical concentrator—on the performance of the homogenizer is analyzed quantitatively using the optical efficiency and the normalized standard deviation as a measure of inhomogeneity. Flux distributions for different progressively increasing deviations are discussed qualitatively. Experimental validation of the simulation is presented. It is demonstrated that the performance of the homogenizer is not particularly sensitive to sunshape. If sufficient length is provided, the homogenizer effectively compensates for tracking error, misalignment, and shape deviations of the primary concentrator. Yet despite the presence of the homogenizer, shading due to the holder of the receiver significantly affects the flux distribution at the receiver.

© 2013 Optical Society of America

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  4. S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.
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2013 (1)

Y. Meller and A. Kribus, “Kaleidoscope homogenizers sensitivity to shading,” Solar Energy 88, 204–214 (2013).
[CrossRef]

2010 (1)

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

2008 (1)

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

2005 (1)

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

2003 (1)

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Solar Energy 74, 113–122 (2003).
[CrossRef]

2002 (2)

K. Kreske, “Optical design of a solar flux homogenizer for concentrator photovoltaics,” Appl. Opt. 41, 2053–2058 (2002).
[CrossRef]

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

1999 (1)

1997 (1)

H. Ries, J. M. Gordon, and M. Lasken, “High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs,” Solar Energy 60, 11–16 (1997).
[CrossRef]

1975 (1)

D. G. Burkhard and D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Solar Energy 17, 221–227 (1975).
[CrossRef]

1963 (2)

M. M. Chen, J. B. Berkowitz-Mattuck, and P. E. Glaser, “The use of a kaleidoscope to obtain uniform flux over a large area in a solar or arc imaging furnace,” Appl. Opt. 2, 265–271 (1963).
[CrossRef]

P. E. Glaser, M. M. Chen, and J. Berkowitz-Mattuck, “The flux redistributor: an optical element for achieving flux uniformity,” Solar Energy 7, 12–17 (1963).
[CrossRef]

Agert, C.

H. Helmers, A. W. Bett, J. Parisi, and C. Agert, “Modeling of concentrating photovoltaic and thermal systems,” Prog. Photovoltaics (2012).
[CrossRef]

Akisawa, A.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Araki, K.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Beckman, W. A.

J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 3rd ed. (Wiley, 2006).

Berkowitz-Mattuck, J.

P. E. Glaser, M. M. Chen, and J. Berkowitz-Mattuck, “The flux redistributor: an optical element for achieving flux uniformity,” Solar Energy 7, 12–17 (1963).
[CrossRef]

Berkowitz-Mattuck, J. B.

Bett, A. W.

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

A. W. Bett and H. Lerchenmüller, “The FLATCON system from concentrix solar,” in Concentrator Photovoltaics, A. Luque and V. Andreev, eds., Vol. 130 (Springer, 2007), pp. 301–319.

H. Helmers, A. W. Bett, J. Parisi, and C. Agert, “Modeling of concentrating photovoltaic and thermal systems,” Prog. Photovoltaics (2012).
[CrossRef]

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Bingham, C.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Biryukov, S.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Bokobza, D.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Boos, A.

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

Bothe, T.

A. Heimsath, W. Platzer, T. Bothe, and W. Li, “Characterization of optical components for linear Fresnel collectors by fringe reflection method,” in Proceedings of 14th Solar Power And Chemical Energy Systems Conference, Las Vegas, Nevada, 4–7 March 2008.

Bronner, W.

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

Buie, D.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Solar Energy 74, 113–122 (2003).
[CrossRef]

P. Schramek, D. R. Mills, D. Buie, and A. G. Imenes, “A new approach to achieve uniform illumination of the receiver of a concentrating solar collector,” in Proceedings of Eurosun2004 (ISES, 2004), pp. 308–317.

Burgess, A. E.

Burkhard, D. G.

D. G. Burkhard and D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Solar Energy 17, 221–227 (1975).
[CrossRef]

Cervantes, R.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Chayet, H.

H. Chayet, O. Kost, R. Moran, and I. Lozovsky, “Efficient, low cost dish concentrator for a CPV based cogeneration system,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 249–252.

Chen, M. M.

M. M. Chen, J. B. Berkowitz-Mattuck, and P. E. Glaser, “The use of a kaleidoscope to obtain uniform flux over a large area in a solar or arc imaging furnace,” Appl. Opt. 2, 265–271 (1963).
[CrossRef]

P. E. Glaser, M. M. Chen, and J. Berkowitz-Mattuck, “The flux redistributor: an optical element for achieving flux uniformity,” Solar Energy 7, 12–17 (1963).
[CrossRef]

Chiappori, E.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Chong, J. Y.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Conley, G.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Dey, C. J.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Solar Energy 74, 113–122 (2003).
[CrossRef]

Dimroth, F.

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Duffie, J. A.

J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 3rd ed. (Wiley, 2006).

Egami, T.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Ekins-Daukes, N. J.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Faiman, D.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Flitsanov, Y.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Fork, D.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Glaser, P. E.

M. M. Chen, J. B. Berkowitz-Mattuck, and P. E. Glaser, “The use of a kaleidoscope to obtain uniform flux over a large area in a solar or arc imaging furnace,” Appl. Opt. 2, 265–271 (1963).
[CrossRef]

P. E. Glaser, M. M. Chen, and J. Berkowitz-Mattuck, “The flux redistributor: an optical element for achieving flux uniformity,” Solar Energy 7, 12–17 (1963).
[CrossRef]

Gordon, J.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Gordon, J. M.

H. Ries, J. M. Gordon, and M. Lasken, “High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs,” Solar Energy 60, 11–16 (1997).
[CrossRef]

Guter, W.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Heimsath, A.

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

A. Heimsath, W. Platzer, T. Bothe, and W. Li, “Characterization of optical components for linear Fresnel collectors by fringe reflection method,” in Proceedings of 14th Solar Power And Chemical Energy Systems Conference, Las Vegas, Nevada, 4–7 March 2008.

Helmers, H.

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

H. Helmers, A. W. Bett, J. Parisi, and C. Agert, “Modeling of concentrating photovoltaic and thermal systems,” Prog. Photovoltaics (2012).
[CrossRef]

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Hiramatsu, M.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Horne, S.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Imenes, A. G.

P. Schramek, D. R. Mills, D. Buie, and A. G. Imenes, “A new approach to achieve uniform illumination of the receiver of a concentrating solar collector,” in Proceedings of Eurosun2004 (ISES, 2004), pp. 308–317.

Jetter, F.

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

Jones, S. A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

Kabalo, S.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Kemmoku, Y.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Kinsey, G. S.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Kost, O.

H. Chayet, O. Kost, R. Moran, and I. Lozovsky, “Efficient, low cost dish concentrator for a CPV based cogeneration system,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 249–252.

Kreske, K.

Kribus, A.

Y. Meller and A. Kribus, “Kaleidoscope homogenizers sensitivity to shading,” Solar Energy 88, 204–214 (2013).
[CrossRef]

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Kubera, T.

R. Löckenhoff, T. Kubera, and K. D. Rasch, “Water cooled TJ dense array modules for parabolic dishes in Proceedings of 6th International Conference on Concentrator Photovoltaic Systems,” Vol. 1277 (AIP, 2010), pp. 43–46.

Lasich, J. B.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Lasken, M.

H. Ries, J. M. Gordon, and M. Lasken, “High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs,” Solar Energy 60, 11–16 (1997).
[CrossRef]

Laurent, O.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Lee, H. S.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Lerchenmüller, H.

A. W. Bett and H. Lerchenmüller, “The FLATCON system from concentrix solar,” in Concentrator Photovoltaics, A. Luque and V. Andreev, eds., Vol. 130 (Springer, 2007), pp. 301–319.

Lewandowski, A.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Li, W.

A. Heimsath, W. Platzer, T. Bothe, and W. Li, “Characterization of optical components for linear Fresnel collectors by fringe reflection method,” in Proceedings of 14th Solar Power And Chemical Energy Systems Conference, Las Vegas, Nevada, 4–7 March 2008.

Löckenhoff, R.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

R. Löckenhoff, T. Kubera, and K. D. Rasch, “Water cooled TJ dense array modules for parabolic dishes in Proceedings of 6th International Conference on Concentrator Photovoltaic Systems,” Vol. 1277 (AIP, 2010), pp. 43–46.

Lozovsky, I.

H. Chayet, O. Kost, R. Moran, and I. Lozovsky, “Efficient, low cost dish concentrator for a CPV based cogeneration system,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 249–252.

Luque-Heredia, I.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Meada, P.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Meller, Y.

Y. Meller and A. Kribus, “Kaleidoscope homogenizers sensitivity to shading,” Solar Energy 88, 204–214 (2013).
[CrossRef]

Melnichak, V.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Mills, D. R.

P. Schramek, D. R. Mills, D. Buie, and A. G. Imenes, “A new approach to achieve uniform illumination of the receiver of a concentrating solar collector,” in Proceedings of Eurosun2004 (ISES, 2004), pp. 308–317.

Miyazaki, Y.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Monger, A. G.

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Solar Energy 74, 113–122 (2003).
[CrossRef]

Moran, R.

H. Chayet, O. Kost, R. Moran, and I. Lozovsky, “Efficient, low cost dish concentrator for a CPV based cogeneration system,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 249–252.

Neumann, A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

Ohm, A.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Oliva, E.

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Parisi, J.

H. Helmers, A. W. Bett, J. Parisi, and C. Agert, “Modeling of concentrating photovoltaic and thermal systems,” Prog. Photovoltaics (2012).
[CrossRef]

Philipps, S. P.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Platzer, W.

A. Heimsath, W. Platzer, T. Bothe, and W. Li, “Characterization of optical components for linear Fresnel collectors by fringe reflection method,” in Proceedings of 14th Solar Power And Chemical Energy Systems Conference, Las Vegas, Nevada, 4–7 March 2008.

Polonsky, G.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Quéméré, G.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

Rasch, K. D.

R. Löckenhoff, T. Kubera, and K. D. Rasch, “Water cooled TJ dense array modules for parabolic dishes in Proceedings of 6th International Conference on Concentrator Photovoltaic Systems,” Vol. 1277 (AIP, 2010), pp. 43–46.

Ries, H.

H. Ries, J. M. Gordon, and M. Lasken, “High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs,” Solar Energy 60, 11–16 (1997).
[CrossRef]

Rose, A.

A. Rose, Vision: Human and Electronic (Plenum, 1973).

Schmitt, G.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

Schöne, J.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Schrader, E.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Schramek, P.

P. Schramek, D. R. Mills, D. Buie, and A. G. Imenes, “A new approach to achieve uniform illumination of the receiver of a concentrating solar collector,” in Proceedings of Eurosun2004 (ISES, 2004), pp. 308–317.

Shealy, D. L.

D. G. Burkhard and D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Solar Energy 17, 221–227 (1975).
[CrossRef]

Shelef, G.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Sherif, R. A.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Siefer, G.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

Steiner, M.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Uozumi, H.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Verlinden, P. J.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

Welser, E.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

Wiesenfarth, M.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

Wilde, J.

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

Witzke, A.

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

Yamaguchi, M.

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Zimmermann, T.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

Appl. Opt. (2)

IEEE Trans. Electron Devices (1)

H. Helmers, E. Oliva, W. Bronner, F. Dimroth, and A. W. Bett, “Processing techniques for monolithic interconnection of solar cells at wafer level,” IEEE Trans. Electron Devices 57, 3355–3360 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Sol. Energy Eng. (1)

A. Neumann, A. Witzke, S. A. Jones, and G. Schmitt, “Representative terrestrial solar brightness profiles,” J. Sol. Energy Eng. 124, 198–204 (2002).
[CrossRef]

Prog. Photovoltaics (2)

R. Löckenhoff, F. Dimroth, E. Oliva, A. Ohm, J. Wilde, D. Faiman, S. Biryukov, V. Melnichak, S. Kabalo, D. Bokobza, and A. W. Bett, “Development, characterisation and 1000 suns outdoor tests of GaAs monolithic interconnected module (MIM) receivers,” Prog. Photovoltaics 16, 101–112 (2008).

K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, and M. Yamaguchi, “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovoltaics 13, 513–527 (2005).

Solar Energy (5)

Y. Meller and A. Kribus, “Kaleidoscope homogenizers sensitivity to shading,” Solar Energy 88, 204–214 (2013).
[CrossRef]

D. G. Burkhard and D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Solar Energy 17, 221–227 (1975).
[CrossRef]

D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Solar Energy 74, 113–122 (2003).
[CrossRef]

P. E. Glaser, M. M. Chen, and J. Berkowitz-Mattuck, “The flux redistributor: an optical element for achieving flux uniformity,” Solar Energy 7, 12–17 (1963).
[CrossRef]

H. Ries, J. M. Gordon, and M. Lasken, “High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs,” Solar Energy 60, 11–16 (1997).
[CrossRef]

Other (16)

A. Heimsath, W. Platzer, T. Bothe, and W. Li, “Characterization of optical components for linear Fresnel collectors by fringe reflection method,” in Proceedings of 14th Solar Power And Chemical Energy Systems Conference, Las Vegas, Nevada, 4–7 March 2008.

J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 3rd ed. (Wiley, 2006).

A. Rose, Vision: Human and Electronic (Plenum, 1973).

H. Chayet, O. Kost, R. Moran, and I. Lozovsky, “Efficient, low cost dish concentrator for a CPV based cogeneration system,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 249–252.

S. P. Philipps, W. Guter, E. Welser, J. Schöne, M. Steiner, F. Dimroth, and A. W. Bett, “Present status in the development of III-V multi-junction solar cells,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 1–21.

I. Luque-Heredia, G. Quéméré, R. Cervantes, O. Laurent, E. Chiappori, and J. Y. Chong, “The sun tracker in concentrator photovoltaics,” in Next Generation of Photovoltaics, A. B. Cristóbal López, A. Martí Vega, and A. Luque López, eds. (Springer, 2012), Vol. 165, pp. 61–93.

H. Helmers, A. Boos, F. Jetter, A. Heimsath, M. Wiesenfarth, and A. W. Bett, “Outdoor test setup for concentrating photovoltaic and thermal (CPVT) systems,” in Proceedings of 7th International Conference on Concentrator Photovoltaic Systems (AIP, 2011), Vol. 1407, pp. 175–179.

“Glass in building—determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors,” ISO 9050:2003(E).

“Standard tables for reference solar spectral irradiances: direct normal and hemispherical on 37° tilted surface,” ASTM G173-03 (2008).

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A Solid 500 Sun Compound Concentrator PV Design,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 694–697.

A. W. Bett and H. Lerchenmüller, “The FLATCON system from concentrix solar,” in Concentrator Photovoltaics, A. Luque and V. Andreev, eds., Vol. 130 (Springer, 2007), pp. 301–319.

P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceedings of 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597.

R. Löckenhoff, T. Kubera, and K. D. Rasch, “Water cooled TJ dense array modules for parabolic dishes in Proceedings of 6th International Conference on Concentrator Photovoltaic Systems,” Vol. 1277 (AIP, 2010), pp. 43–46.

M. Wiesenfarth, M. Steiner, H. Helmers, G. Siefer, E. Oliva, F. Dimroth, G. Shelef, G. Polonsky, Y. Flitsanov, A. Kribus, and A. W. Bett, “Front-side interconnected large area concentrator cells for compact concentrator modules,” in Proceedings of 8th International Conference on Concentrator Photovoltaic Systems (AIP, 2012), Vol. 1477, pp. 204–207.

H. Helmers, A. W. Bett, J. Parisi, and C. Agert, “Modeling of concentrating photovoltaic and thermal systems,” Prog. Photovoltaics (2012).
[CrossRef]

P. Schramek, D. R. Mills, D. Buie, and A. G. Imenes, “A new approach to achieve uniform illumination of the receiver of a concentrating solar collector,” in Proceedings of Eurosun2004 (ISES, 2004), pp. 308–317.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic illustration of the investigated flux homogenizer based on a kaleidoscope.

Fig. 2.
Fig. 2.

Picture of the dense array receiver, which consists of four MIMs separated by 1 mm wide gaps. The vertical black stripes are the individual solar cell segments, which are separated by metalized interconnection trenches. The MIMs are interconnected by wire bonds. In total, the receiver consists of two parallel strings of 46 solar cells each.

Fig. 3.
Fig. 3.

Flowchart of the ray-tracing simulation environment. See text for definition of the symbols.

Fig. 4.
Fig. 4.

Illustration of the simulated optical efficiency as a function of the length L of the homogenizer. Symbols denote simulation results. The lines represent linear fits to illustrate trends. The upper graph shows the optical efficiency ηopt for the ideal scenario (No. 1). In the lower graph, the additional losses Δηopt due to introduction of deviations are shown (in %abs) for scenarios No. 2 through No. 6 (see legend). Note that the scales differ. The introduction of CSR (Nos. 2 and 3) and tracking (No. 5 compared to No. 4) have practically no influence on ηopt, and shading (No. 4) is merely negligible (<0.2% at 300 mm). The realistic shape (No. 6) leads to a small reduction of 0.8% at 300 mm.

Fig. 5.
Fig. 5.

Influence of the length L of the homogenizer on the homogeneity of the flux distribution across the receiver for the different investigated scenarios. On the ordinate, the normalized standard deviation σn is shown. Symbols denote simulation results. For all scenarios, an oscillatory decrease, which levels off with increasing length, is observed.

Fig. 6.
Fig. 6.

Simulated flux distributions for scenarios No. 1 through No. 6 (except No. 2). In the left column, the flux distributions at the entrance of the homogenizer, i.e., at the focal spot of the primary concentrator, are shown. In the center and right columns, the flux distributions at the end of the homogenizer are shown for homogenizer lengths of 50 and 150 mm, respectively. The intensity scales are normalized to the average of the respective distributions. Note the zoomed-in x and y scales for the focal spot in the left column, compared with the center and right columns, in which the distributions across the entire receiver are shown. Shading (No. 4) influences the flux distribution across the receiver most significantly; see the text for a detailed discussion.

Fig. 7.
Fig. 7.

I–V characteristics of the photovoltaic receiver with homogenizer in perpendicular and parallel orientations (diamonds and triangles, respectively). For comparison, the I–V curve measured indoors under homogeneous illumination at a flash sun simulator under 360 suns is shown (solid black line).

Fig. 8.
Fig. 8.

View into the mounted homogenizer (in the perpendicular orientation) overlaid with five schematic measurement positions (a)–(e), where each indicates where the focal spot enters the homogenizer. The picture also illustrates the concept of the kaleidoscope: the vertical mirrors show reflections of the MIM receiver in the center. The small gaps between the vertical mirror facets result from manufacturing tolerances.

Fig. 9.
Fig. 9.

I–V characteristics of the photovoltaic receiver in five different positions (a)–(e) (symbols, compare Fig. 8). For comparison, the I–V curve measured indoors under homogeneous illumination at a flash sun simulator under 360 suns is shown (solid black line). The agreement of the I–V curves indicates the tolerance against inaccurate positioning and tracking error.

Tables (2)

Tables Icon

Table 1. Overview of Investigated Scenarios with Progressive Introduction of Deviations from the Ideal

Tables Icon

Table 2. Measured Data and System Parameters for Thermal Efficiency Measurement

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ηopt2nd=Pout2ndPout1st,
σn=1G1N1i=1N(GiG)2,
ηth=PthrecPin1st=m˙cp(ToutTin)DNIAtotal,
ηopt=AeffAtotalηopt1stηopt2nd(1Rrec),
ηopt2nd=m˙cp(ToutTin)DNIAeffηopt1st(1Rrec).
C=ISCISC1x=Prec/Arec1000W/m2.
Prec=DNIAtotalAeffAtotalηopt1stηopt2nd.
ηopt2nd=ISCISC1x1000W/m2DNIArecAeffηopt1st.

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