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Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry

N. Yamada and T. Nishikawa

Open Access Open Access

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 Optical Society of America

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Figures (7)
Fig. 1
Fig. 1 Flow chart of EA optimization for design of optical geometry of solar concentrator.

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Fig. 2
Fig. 2 Model of nonimaging Fresnel lens: Half of the lens geometry is omitted because of symmetry.

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Fig. 3
Fig. 3 Genetic manipulations, namely, (a) crossover and (b) mutation, which generate new geometries.

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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.

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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%.

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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.

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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.

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Tables (1)

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Table 1 Specifications of Nonimaging Fresnel Lens

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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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