Abstract

Solar tracking concentrators are optical systems that collect the solar energy flux either in a line or spot using reflective or refractive surfaces. The main problem with these surfaces is their manufacturing complexity, especially at large scales. In this paper, a line-to-spot solar tracking concentrator is proposed. Its configuration allows for a low-cost solar concentrator system. It consists of a parabolic trough collector (PTC) and a two-section PMMA Fresnel lens (FL), both mounted on a two-axis solar tracker. The function of the PTC is to reflect the incoming solar radiation toward a line. Then, the FL, which is placed near the focus, transforms this line into a spot by refraction. It was found that the system can achieve a concentration ratio of 100x and concentrate an average solar irradiance of 518.857W/m2 with an average transmittance of 0.855, taking into account the effect of the chromatic aberration.

© 2015 Optical Society of America

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References

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  1. H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
    [Crossref]
  2. F. Kreith and Y. Goswami, Handbook of Energy Efficiency and Renewable Energy (CRC, 2007).
    [Crossref]
  3. J. Kreith and F. Kreider, Principles of Solar Engineering (Hemisphere Publishing Corporation, 1978).
  4. J. Duffie and W. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, Inc., 1991).
  5. R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer, 2001).
    [Crossref]
  6. Sh. Klychev, “A Method to Calculate Fresnel Lenses,” J. Appl. Sol. Energy 49(1), 36–41 (2012).
  7. W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
    [Crossref]
  8. A. Mohr, T. Roth, and S. Glunz, “BICON: High concentration PV using one-axis tracking and silicon concentrator cells,” Prog. Photovolt. 14(7), 663–674 (2006).
    [Crossref]
  9. M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
    [Crossref]
  10. T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
    [Crossref]
  11. T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
    [Crossref]
  12. E. Hecht, Optics, 4th ed., (Pearson Education, Inc., 2002).
  13. M. Polyanskiy, “Optical Constants of Plastics,” (2015). http://refractiveindex.info/?shelf=3d&book=plastics&page=pmma

2013 (2)

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

2012 (1)

Sh. Klychev, “A Method to Calculate Fresnel Lenses,” J. Appl. Sol. Energy 49(1), 36–41 (2012).

2011 (1)

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

2006 (1)

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

2002 (1)

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

1996 (1)

M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
[Crossref]

Ambrosetti, G.

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

Beckman, W.

J. Duffie and W. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, Inc., 1991).

Blieske, U.

M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
[Crossref]

Brunotte, M.

M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
[Crossref]

Cadruvi, M.

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

Cohen, G.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Cooper, T.

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

Dai, Y.

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Duffie, J.

J. Duffie and W. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, Inc., 1991).

Gee, R.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Glunz, S.

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

Goetzberger, A.

M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
[Crossref]

Goswami, Y.

F. Kreith and Y. Goswami, Handbook of Energy Efficiency and Renewable Energy (CRC, 2007).
[Crossref]

Hecht, E.

E. Hecht, Optics, 4th ed., (Pearson Education, Inc., 2002).

Kearney, D.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Klychev, Sh.

Sh. Klychev, “A Method to Calculate Fresnel Lenses,” J. Appl. Sol. Energy 49(1), 36–41 (2012).

Kreider, F.

J. Kreith and F. Kreider, Principles of Solar Engineering (Hemisphere Publishing Corporation, 1978).

Kreith, F.

F. Kreith and Y. Goswami, Handbook of Energy Efficiency and Renewable Energy (CRC, 2007).
[Crossref]

Kreith, J.

J. Kreith and F. Kreider, Principles of Solar Engineering (Hemisphere Publishing Corporation, 1978).

Leutz, R.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer, 2001).
[Crossref]

Lüpfert, E.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Mahoney, R.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Mohr, A.

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

Pedretti, A.

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

Pravettoni, M.

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

Price, H.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

Roth, T.

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

Steinfeld, A.

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

Sumathy, K.

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Suzuki, A.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer, 2001).
[Crossref]

Wang, R.

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Xie, W.

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Zarza, E.

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

J. Appl. Opt. (1)

T. Cooper, G. Ambrosetti, A. Pedretti, and A. Steinfeld, “Theory and design of line-to-point focus solar concentrators with tracking secondary optics,” J. Appl. Opt. 52(35), 8586–8616 (2013).
[Crossref]

J. Appl. Sol. Energy (1)

Sh. Klychev, “A Method to Calculate Fresnel Lenses,” J. Appl. Sol. Energy 49(1), 36–41 (2012).

J. Renew. Sustain. Energy Rev. (1)

W. Xie, Y. Dai, R. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: a review,” J. Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

J. Sol. Energy (1)

M. Brunotte, A. Goetzberger, and U. Blieske, “Two-stage concentrator permitting concentration factors up to 300X with one-axis tracking,” J. Sol. Energy 56(3), 285–300 (1996).
[Crossref]

J. Sol. Energy Eng. (1)

H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, and R. Mahoney, “Advances in Parabolic Trough Solar Power Technology,” J. Sol. Energy Eng. 124(2), 109–125 (2002).
[Crossref]

J. Sol. Energy Mater. Sol. Cells (1)

T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” J. Sol. Energy Mater. Sol. Cells 116, 238–251 (2013).
[Crossref]

Prog. Photovolt. (1)

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

Other (6)

E. Hecht, Optics, 4th ed., (Pearson Education, Inc., 2002).

M. Polyanskiy, “Optical Constants of Plastics,” (2015). http://refractiveindex.info/?shelf=3d&book=plastics&page=pmma

F. Kreith and Y. Goswami, Handbook of Energy Efficiency and Renewable Energy (CRC, 2007).
[Crossref]

J. Kreith and F. Kreider, Principles of Solar Engineering (Hemisphere Publishing Corporation, 1978).

J. Duffie and W. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, Inc., 1991).

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer, 2001).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

(a) Line-to-spot solar tracking concentrator and (b) inner/outer section of the lens

Fig. 2
Fig. 2

Sun’s rays refraction through the two-section FL

Fig. 3
Fig. 3

(a) Ray trace simulation from the PTC to the inner section of the lens and (b) refraction of the sun’s rays through the inner section (outer section not shown)

Fig. 4
Fig. 4

γ deviation of the sun’s rays through the lens thickness using (a) s = 0.001m, (b) s = 0.005m and (c) s = 0.01m

Fig. 5
Fig. 5

(a) Solar spectral irradiance using an air mass coefficient of 1.5 (AM1.5) [3]. For illustration purposes, the infrared bandwidth (from λ0 = 0.790 to λf = 1.083) accepted by the PMMA is shown (see Table 1). (b) Refractive index of PMMA as a function of the wavelength

Fig. 6
Fig. 6

(a) Line-to-spot ray-trace simulation where the incoming sun’s rays are placed near the PTC for illustration purposes. (b) Focal plane close up

Fig. 7
Fig. 7

(a–g) Solar spectrum bandwidth distribution on the spot and (h) spot image including all bandwidths. The colorbars represent the intensity of the energy in W/m2 distributed over the focal plane (see section 2.1.2 for further information)

Fig. 8
Fig. 8

Transmittance of the solar radiation irradiance over the spot’s area as a function of the (a) bandwidths and (b) full solar spectrum

Tables (4)

Tables Icon

Table 1 Ray-traced solar spectrum bandwidths

Tables Icon

Table 2 Transmittances values of every bandwidth and full solar spectrum

Tables Icon

Table 3 Average incident solar irradiance Īsun as a function of bandwidths

Tables Icon

Table 4 Spot’s solar irradiance from every bandwidth and full solar spectrum

Equations (10)

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

tan ε = R / [ n PMMA ( R 2 + f in , out 2 ) 1 / 2 f in , out ]
tan ψ i = a i / ( 2 f i )
n air sin ω = n PMMA sin η
tan γ = ( r v 2 + r w 2 ) 1 / 2 / r u
n PMMA = 1.4681 + 93.42 / ( λ 1 , 235 )
τ = τ PTC τ FL
r in = tan 2 ( η ω ) / tan 2 ( η + ω )
r in = sin 2 ( η ω ) / sin 2 ( η + ω )
τ FL = [ 1 ( r in + r in ) / 2 ] [ 1 ( r out + r out ) / 2 ]
I spot = I ¯ sun τ

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