Abstract

In this study, an evolutionary algorithm (EA), which consists of genetic and immune algorithms, is introduced to design the optical geometry of a nonimaging Fresnel lens; this lens generates the uniform flux concentration required for a photovoltaic cell. Herein, a design procedure that incorporates a ray-tracing technique in the EA is described, and the validity of the design is demonstrated. The results show that the EA automatically generated a unique geometry of the Fresnel lens; the use of this geometry resulted in better uniform flux concentration with high optical efficiency.

© 2010 OSA

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  1. A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
    [CrossRef]
  2. A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
    [CrossRef]
  3. G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON®,” Prog. Photovolt. Res. Appl. 13(7), 627–634 (2005).
    [CrossRef]
  4. M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
    [CrossRef]
  5. A. W. Bett, C. Baur, F. Dimroth, G. Lange, M. Meusel, S. van Riesen, G. Siefer, V. M. Andreev, V. D. Rumyantsev, and N. A. Sadchikov, “FLATCONTM-modules: technology and characterization,” in Proceedings of IEEE Conference on WCPEC-3, (IEEE, 2003), pp. 634−637.
  6. D. R. Reid and G. S. Smith, “Design and optimization of Fresnel zone plates using a genetic algorithm and a full electromagnetic simulator,” Microw. Opt. Technol. Lett. 51(9), 2223–2227 (2009).
    [CrossRef]
  7. W. G. Chen, C. M. Uang, and C. H. Jou, “Optimal design of an irregular Fresnel lens for multiple light sources using a three-layered Hierarchical Genetic Algorithm,” Opt. Express 15(16), 9918–9935 (2007).
    [CrossRef] [PubMed]
  8. W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006).
    [CrossRef]
  9. N. Yamada, and T. Ogawa, “Optimization method of concentrating optics by using evolutionary algorithm,” presented at the Second International Workshop on Concentrating Photovoltaic Optics and Power Darmstadt (2009), http://www.concentrating-pv.org/papers.html .
  10. L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000).
    [CrossRef]
  11. R. Leutz, and A. Suzki, Nonimaging Fresnel Lenses Design and Performance of Solar Concentrators (Springer Verlag, 2001).
  12. R. Winston, J. Miano, and P. Bentez, Nonimaging Optics (Academic Press, 2005)
  13. M. Victoria, C. Domínguez, I. Antón, and G. Sala, “Comparative analysis of different secondary optical elements for aspheric primary lenses,” Opt. Express 17(8), 6487–6492 (2009).
    [CrossRef] [PubMed]

2009

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

D. R. Reid and G. S. Smith, “Design and optimization of Fresnel zone plates using a genetic algorithm and a full electromagnetic simulator,” Microw. Opt. Technol. Lett. 51(9), 2223–2227 (2009).
[CrossRef]

M. Victoria, C. Domínguez, I. Antón, and G. Sala, “Comparative analysis of different secondary optical elements for aspheric primary lenses,” Opt. Express 17(8), 6487–6492 (2009).
[CrossRef] [PubMed]

2007

2006

M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
[CrossRef]

W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006).
[CrossRef]

A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
[CrossRef]

2005

G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON®,” Prog. Photovolt. Res. Appl. 13(7), 627–634 (2005).
[CrossRef]

2000

L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000).
[CrossRef]

Antón, I.

Antonini, A.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Araki, K.

M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
[CrossRef]

Armani, M.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Baggio, N.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Butturi, M. A.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Chen, W.

W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006).
[CrossRef]

Chen, W. G.

Di Benedetto, P.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Dimroth, F.

G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON®,” Prog. Photovolt. Res. Appl. 13(7), 627–634 (2005).
[CrossRef]

Domínguez, C.

Glunz, S. W.

A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
[CrossRef]

Jiao, L.

L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000).
[CrossRef]

Jou, C. H.

Milan, E.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Mohr, A.

A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
[CrossRef]

Parretta, A.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Peharz, G.

G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON®,” Prog. Photovolt. Res. Appl. 13(7), 627–634 (2005).
[CrossRef]

Reid, D. R.

D. R. Reid and G. S. Smith, “Design and optimization of Fresnel zone plates using a genetic algorithm and a full electromagnetic simulator,” Microw. Opt. Technol. Lett. 51(9), 2223–2227 (2009).
[CrossRef]

Roth, T.

A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
[CrossRef]

Sala, G.

Smith, G. S.

D. R. Reid and G. S. Smith, “Design and optimization of Fresnel zone plates using a genetic algorithm and a full electromagnetic simulator,” Microw. Opt. Technol. Lett. 51(9), 2223–2227 (2009).
[CrossRef]

Stefancich, M.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Takamoto, T.

M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
[CrossRef]

Uang, C.

W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006).
[CrossRef]

Uang, C. M.

Uderzo, D.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

Victoria, M.

Wang, L.

L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000).
[CrossRef]

Yamaguchi, M.

M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
[CrossRef]

Zurru, P.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000).
[CrossRef]

Microw. Opt. Technol. Lett.

D. R. Reid and G. S. Smith, “Design and optimization of Fresnel zone plates using a genetic algorithm and a full electromagnetic simulator,” Microw. Opt. Technol. Lett. 51(9), 2223–2227 (2009).
[CrossRef]

Opt. Eng.

W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006).
[CrossRef]

Opt. Express

Prog. Photovolt. Res. Appl.

A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, and N. Baggio, “Rondine® PV concentrators: field results and developments,” Prog. Photovolt. Res. Appl. 17(7), 451–459 (2009).
[CrossRef]

A. Mohr, T. Roth, and S. W. Glunz, “BICON: high concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. Res. Appl. 14(7), 663–674 (2006).
[CrossRef]

G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON®,” Prog. Photovolt. Res. Appl. 13(7), 627–634 (2005).
[CrossRef]

Sol. Energy Mater. Sol. Cells

M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells 90(18–19), 3068–3077 (2006).
[CrossRef]

Other

A. W. Bett, C. Baur, F. Dimroth, G. Lange, M. Meusel, S. van Riesen, G. Siefer, V. M. Andreev, V. D. Rumyantsev, and N. A. Sadchikov, “FLATCONTM-modules: technology and characterization,” in Proceedings of IEEE Conference on WCPEC-3, (IEEE, 2003), pp. 634−637.

N. Yamada, and T. Ogawa, “Optimization method of concentrating optics by using evolutionary algorithm,” presented at the Second International Workshop on Concentrating Photovoltaic Optics and Power Darmstadt (2009), http://www.concentrating-pv.org/papers.html .

R. Leutz, and A. Suzki, Nonimaging Fresnel Lenses Design and Performance of Solar Concentrators (Springer Verlag, 2001).

R. Winston, J. Miano, and P. Bentez, Nonimaging Optics (Academic Press, 2005)

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Figures (7)

Fig. 1
Fig. 1

Flow chart of EA optimization for design of optical geometry of solar concentrator.

Fig. 2
Fig. 2

Model of nonimaging Fresnel lens: Half of the lens geometry is omitted because of symmetry.

Fig. 3
Fig. 3

Genetic manipulations, namely, (a) crossover and (b) mutation, which generate new geometries.

Fig. 4
Fig. 4

Evaluation index E vs. generation (iteration) step for F = 0.3. E is a nondimensional value. E = 0.60 for the conventional Fresnel lens. E = 0.75 for the EA-generated Fresnel lens at the 100th generation. The ideal value of E is 1.0.

Fig. 5
Fig. 5

Energy distribution on PV cell surface of (a) conventional Fresnel lens, (b) EA-generated Fresnel lens at the 100th generation for F = 0.3, and (c) EA-generated Fresnel lens at the 100th generation for F = 0.5. λ = 0.40 μm (blue), λ = 0.80 μm (green), and λ = 1.20 μm (red); the average of these three wavelengths is shown in black. The corresponding optical efficiency is (a) η = 84.0%, (b) η = 82.7%, and (c) η = 77.4%.

Fig. 7
Fig. 7

Optical efficiency - uniformity trade-off by tuning F value 0.1 - 0.9. Result for a wider incident angle θin = ± 0.5° is additionally plotted.

Fig. 6
Fig. 6

Geometry of nonimaging Fresnel lens. (a) Conventional Fresnel lens, (b) EA-generated Fresnel lens at the 100th generation for F = 0.3, and (c) EA-generated Fresnel lens at the 100th generation for F = 0.5. The y-scale is reduced to 1/10th of the original scale.

Tables (1)

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Table 1 Specifications of Nonimaging Fresnel Lens

Equations (1)

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E = η F D = I t I i n c i d e n t F 1 I i n c i d e n t i = 1 N | I t N I i | ,

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