## Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry |

Optics Express, Vol. 18, Issue S2, pp. A126-A132 (2010)

http://dx.doi.org/10.1364/OE.18.00A126

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### 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

## 1. Introduction

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. Evolutionary algorithm

## 3. Optimization of nonimaging Fresnel lens by EA

### 3.1 Model and method

*w*. The total number of geometries is 200. GA manipulations start from the center segment of the Fresnel lens to the outer segment one by one. Each segment consists of three vertices (vertex 1, 2, and 3 as shown in Fig. 3). To keep curve and slope continuity, outer side vertex 3 of the previous segment was directly used as center side vertex 1 of the next segment. In addition, interval between center side and outer side vertices of each segment was kept to be the prism width

*w*. Middle vertex 2 of each segment was kept within vertex 1 and 3 in the

*y*-direction. Vertical range allowed to all vertices was ± 0.1 mm from

*y*= 0 level.

### 3.2 Evaluation index

*E*used in the present optimization can be represented as follows:where

*I*is total incident energy over Fresnel lens aperture.

_{incident}*I*and

_{t}*I*denote the total energy over the PV cell surface and the energy at each finite element of the PV cell surface, respectively.

_{i}*I*and

_{t}*I*are summation for the three representative refractive indices. The PV cell surface is equally divided into 100 finite elements, i.e.,

_{i}*N*= 100.

*F*, which denotes the weighting factor, is primary set to 0.3 and 0.5; for verification of the effect of the weighting value on the optical performance of the geometry,

*F*is varied in the range 0.1 - 0.9. The first term of Eq. (1) is the optical efficiency, and

*D*of the second term represents the degree of nonuniformity of flux concentration on the PV cell surface. Therefore, the value of index

*E*will increase as the uniformity and optical efficiency increase. Although

*D*was defined as normalized sum of absolute deviation from an average energy, one can use variance instead of

*D*because final result may not be much affected, whereas speed of evolution may be affected in some cases.

## 4. Results

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]

*E*and the generation (iteration) step for

*F*= 0.3 is shown in Fig. 4 . The calculation was terminated at the 100th generation. The value of

*E*for the EA-generated Fresnel lens before the first generation is same as that for the conventional Fresnel lens (

*E*= 0.60). As expected, the value of

*E*increased with the generation step and became

*E*= 0.75 at the 100th generation.

## 5. Conclusion

## Acknowledgments

## References and links

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 |

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. |

3. | G. Peharz and F. Dimroth, “Energy payback time of the high-concentration PV system FLATCON |

4. | M. Yamaguchi, T. Takamoto, and K. Araki, “Super high-efficiency multi-junction and concentrator solar cells,” Sol. Energy Mater. Sol. Cells |

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, “FLATCON |

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. |

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 |

8. | W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. |

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. |

11. | R. Leutz, and A. Suzki, |

12. | R. Winston, J. Miano, and P. Bentez, |

13. | M. Victoria, C. Domínguez, I. Antón, and G. Sala, “Comparative analysis of different secondary optical elements for aspheric primary lenses,” Opt. Express |

**OCIS Codes**

(220.1770) Optical design and fabrication : Concentrators

(350.6050) Other areas of optics : Solar energy

(220.4298) Optical design and fabrication : Nonimaging optics

**ToC Category:**

Solar Concentrators

**History**

Original Manuscript: March 25, 2010

Revised Manuscript: May 14, 2010

Manuscript Accepted: May 16, 2010

Published: May 19, 2010

**Citation**

N. Yamada and T. Nishikawa, "Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry," Opt. Express **18**, A126-A132 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S2-A126

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### References

- 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]
- 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]
- 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.
- 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]
- 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]
- W. Chen and C. Uang, “Better reading light system with light-emitting diodes using optimized Fresnel lens,” Opt. Eng. 45(6), 063001 (2006). [CrossRef]
- 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 .
- L. Jiao and L. Wang, “A novel genetic algorithm based on immunity,” IEEE Trans. Syst. Man Cybern. 30(5), 552–561 (2000). [CrossRef]
- 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)
- 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]

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