Abstract

A novel approach for the design of refractive lenses is presented, where the lens is mounted on a stationary aperture and the Sun is tracked by a moving solar cell. The purpose of this work is to design a quasi-stationary concentrator by replacing the two-axis tracking of the Sun with internal motion of the miniaturized solar cell inside the module. Families of lenses are designed with a variation of the simultaneous multiple surface technique in which the sawtooth genetic algorithm is implemented to optimize the geometric variables of the optic in order to produce high fluxes for a range of incidence angles. Finally, we show examples of the technique for lenses with 60° and 30° acceptance half-angles, with low to medium attainable concentrations.

© 2010 Optical Society of America

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References

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    [CrossRef]

2010

2009

2006

A. Luque, G. Sala, and I. Luque-Heredia, “Photovoltaic concentration at the onset of its commercial deployment,” Prog. Photovoltaics 14, 413–428 (2006).
[CrossRef]

C. Koumousis and V. K. Katsaras, “A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance,” IEEE Trans. Evol. Computat. 10, 19–28 (2006).
[CrossRef]

2005

2004

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

2000

1996

R. P. Friedman, J. M. Gordon, and H. Ries, “Compact high-flux two-stage solar collectors based on tailored edge-ray concentrators,” Solar Energy 56, 607–615 (1996).
[CrossRef]

1995

1994

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4, 65–85 (1994).
[CrossRef]

1992

Benitez, P.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Benítez, P.

Blen, J.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Chaves, J.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

J. Chaves, Introduction to Nonimaging Optics (CRC, 2008).
[CrossRef]

Dross, O.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Falicoff, W.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Feuermann, D.

Friedman, R. P.

R. P. Friedman, J. M. Gordon, and H. Ries, “Compact high-flux two-stage solar collectors based on tailored edge-ray concentrators,” Solar Energy 56, 607–615 (1996).
[CrossRef]

Goldberg, D. E.

B. L. Miller and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

D. E. Goldberg, “Sizing populations for serial and parallel genetic algorithms,” in “Proceedings of the 3rd International Conference on Genetic Algorithms,” (Morgan Kaufmann, 1989), pp. 70–79.

González, J. C.

Gordon, J. M.

Hernandez, M.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

Infante, J.

Katsaras, V. K.

C. Koumousis and V. K. Katsaras, “A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance,” IEEE Trans. Evol. Computat. 10, 19–28 (2006).
[CrossRef]

Koumousis, C.

C. Koumousis and V. K. Katsaras, “A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance,” IEEE Trans. Evol. Computat. 10, 19–28 (2006).
[CrossRef]

Lin, W.

Luneburg, R. K.

R. K. Luneburg and H. Mendlowitz, Mathematical Theory of Optics (Academic, 1965), Vol. 18.

Luque, A.

A. Luque, G. Sala, and I. Luque-Heredia, “Photovoltaic concentration at the onset of its commercial deployment,” Prog. Photovoltaics 14, 413–428 (2006).
[CrossRef]

Luque-Heredia, I.

A. Luque, G. Sala, and I. Luque-Heredia, “Photovoltaic concentration at the onset of its commercial deployment,” Prog. Photovoltaics 14, 413–428 (2006).
[CrossRef]

Mendlowitz, H.

R. K. Luneburg and H. Mendlowitz, Mathematical Theory of Optics (Academic, 1965), Vol. 18.

Miller, B. L.

B. L. Miller and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

Miñano, J. C.

Mohedano, R.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Muñoz, F.

Ostroumov, N.

Ries, H.

R. P. Friedman, J. M. Gordon, and H. Ries, “Compact high-flux two-stage solar collectors based on tailored edge-ray concentrators,” Solar Energy 56, 607–615 (1996).
[CrossRef]

Sala, G.

A. Luque, G. Sala, and I. Luque-Heredia, “Photovoltaic concentration at the onset of its commercial deployment,” Prog. Photovoltaics 14, 413–428 (2006).
[CrossRef]

Santamaría, A.

Whitley, D.

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4, 65–85 (1994).
[CrossRef]

Winston, R.

Zhang, W.

Appl. Opt.

Complex Syst.

B. L. Miller and D. E. Goldberg, “Genetic algorithms, tournament selection, and the effects of noise,” Complex Syst. 9, 193–212 (1995).

IEEE Trans. Evol. Computat.

C. Koumousis and V. K. Katsaras, “A saw-tooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance,” IEEE Trans. Evol. Computat. 10, 19–28 (2006).
[CrossRef]

Opt. Eng

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng 43, 1489–1502 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Prog. Photovoltaics

A. Luque, G. Sala, and I. Luque-Heredia, “Photovoltaic concentration at the onset of its commercial deployment,” Prog. Photovoltaics 14, 413–428 (2006).
[CrossRef]

Solar Energy

R. P. Friedman, J. M. Gordon, and H. Ries, “Compact high-flux two-stage solar collectors based on tailored edge-ray concentrators,” Solar Energy 56, 607–615 (1996).
[CrossRef]

Stat. Comput.

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4, 65–85 (1994).
[CrossRef]

Other

R. Winston, P. Benítez, and J. C. Miñano, Nonimaging Optics (Elsevier, 2005).

A.L.Luque López and V.M.Andreev, eds., Concentrator Photovoltaics, Vol. 130 of Springer Series in Optical Sciences (Springer, 2007).
[CrossRef]

D. E. Goldberg, “Sizing populations for serial and parallel genetic algorithms,” in “Proceedings of the 3rd International Conference on Genetic Algorithms,” (Morgan Kaufmann, 1989), pp. 70–79.

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

R. K. Luneburg and H. Mendlowitz, Mathematical Theory of Optics (Academic, 1965), Vol. 18.

J. Chaves, Introduction to Nonimaging Optics (CRC, 2008).
[CrossRef]

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Figures (22)

Fig. 1
Fig. 1

Initialization of the SMS technique. The acceptance angle, lens aperture MN, initial receiver R1R2, and the receiver’s étendue are defined.

Fig. 2
Fig. 2

Cartesian oval P1P2 is created after launching rays from θ max to θ max .

Fig. 3
Fig. 3

Focal points are modified across P1R2 and P2R1.

Fig. 4
Fig. 4

With R 2 new as the new focal point, Cartesian oval S2 is created.

Fig. 5
Fig. 5

Cartesian oval S3 is created after choosing R 1 new and launching rays from R 1 new to the light source.

Fig. 6
Fig. 6

Rays from the light source focus on R 2 new , determining Cartesian oval S4.

Fig. 7
Fig. 7

Starting points of lower surface of the lens, P1a, P1b and P 1 a .

Fig. 8
Fig. 8

Impact of initializing parameters on lens design for θ i = 0 ° . Different points P1a and P1b that lie on the hyperbola yield different NAs and different attainable concentrations.

Fig. 9
Fig. 9

Comparison between two optimized lenses with different thicknesses.

Fig. 10
Fig. 10

Flowchart of the optimization process. The process begins with the initialization of the working scene. The GA chooses the modified receiver points and the produced lens is characterized by a ray tracer. The process is continued until the optimum design is found.

Fig. 11
Fig. 11

Left, an example of an SMS refractive lens with acceptance half-angle 60 ° ( C init = 0.78 and NA = 0.15 ). The dashed line shows the initializing receiver R1R2. Right, illustration of the required trajectory of the solar cell for high collection efficiency.

Fig. 12
Fig. 12

Left, second SMS example for a different initializing receiver plane R1R2 ( C init = 1.04 and NA = 0.35 ). Right, the receiver trajectory for high collection efficiency shows a shorter of focal length due to the smaller initializing receiver R1R2.

Fig. 13
Fig. 13

Concentration for different incidence angles. The results refer to lenses with inititializing parameters C init = 0.78 and C init = 1.04 .

Fig. 14
Fig. 14

Maximum concentration as a function of the initializing receiver.

Fig. 15
Fig. 15

Efficiency plots for lenses with different NAs for SMS lenses with acceptance angle 60 ° with varying C init .

Fig. 16
Fig. 16

SMS refractive lens with 30 ° acceptance angle ( C init = 1.04 and NA = 0.36 ), the required cell trajectory and the corresponding concentration per incidence angle.

Fig. 17
Fig. 17

Overview of SMS tilted lenses.

Fig. 18
Fig. 18

Off-axis performance for displacements on the x axis for SMS lens with 30 ° acceptance angle, C init = 1.04 , and NA = 0.36 .

Fig. 19
Fig. 19

Off-axis performance for displacements in the y axis; C init = 1.04 and NA = 0.36 .

Fig. 20
Fig. 20

Chromatic aberration for SMS lens with C init = 1.04 and NA = 0.36 .

Fig. 21
Fig. 21

Three-dimensional ray tracing with collimated and monochromatic light for rotationally symmetric refractive SMS lens with 60 ° acceptance angle ( C init = 0.78 and NA = 0.15 ). The lens exhibits good behavior only for small incidence angles, but astigmatism has detrimental effects in high incidence angles.

Fig. 22
Fig. 22

Three-dimensional ray tracing with collimated and monochromatic light for rotationally symmetric refractive SMS lens with 30 ° acceptance angle, C init = 1.04 , and NA = 0.36 .

Equations (4)

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U = 2 * [ N , M ] * sin ( θ max ) ,
F = max { R 1 new , R 2 new } { C ( R 1 new , R 2 new , η ) η = 0.95 } .
C max , 2 D = n out sin θ out n in sin θ in
C max , 3 D = [ C max , 2 D ] 2

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