Abstract

Sunlight concentration is essential to reach high temperatures of a working fluid in solar-thermal applications and to reduce the cost of photovoltaic (PV) electricity generation systems. Commonly, sunlight concentration is realized by parabolic or cylindrical reflectors, which do not provide uniform concentration on the receiver finite surface. Uniform concentration of sunlight is favored especially for the PV conversion applications since it not only enhances the conversion efficiency of sunlight but also reduces the thermal variations along the receiving PV cell, which can be a performance and life-span limiting factor. In this paper a reflector profile that uniformly infiltrates the concentrated sunlight into the receiving unit is attempted. The new design accounts for all factors that contribute to the nonuniform concentration, like the reflector curvature, which spatially reflects the sunlight nonuniformly, and the angular dependency of both the reflector reflectivity and the sunlight transmission through the PV cell.

© 2014 Optical Society of America

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References

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  1. H. Pfeiffer and M. Bihler, “The effects of non-uniform illumination of solar cells with concentrated light,” Sol. Cells 5, 293–299 (1982).
    [CrossRef]
  2. H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
    [CrossRef]
  3. H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
    [CrossRef]
  4. N. Sellami and T. K. Mallick, “Optical characterisation and optimisation of a static window integrated concentrating photovoltaic system,” Sol. Energy 91, 273–282 (2013).
    [CrossRef]
  5. J. J. O’Gallagher and R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays,” Proc. SPIE 4446, 60–64 (2001).
    [CrossRef]
  6. D. G. Jenkings, “High-uniformity solar concentrators for photovoltaic systems,” Proc. SPIE 4446, 52–59 (2001).
    [CrossRef]
  7. A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16, 81–87 (1996).
    [CrossRef]
  8. H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
    [CrossRef]

2013

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

N. Sellami and T. K. Mallick, “Optical characterisation and optimisation of a static window integrated concentrating photovoltaic system,” Sol. Energy 91, 273–282 (2013).
[CrossRef]

2012

H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
[CrossRef]

2001

J. J. O’Gallagher and R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays,” Proc. SPIE 4446, 60–64 (2001).
[CrossRef]

D. G. Jenkings, “High-uniformity solar concentrators for photovoltaic systems,” Proc. SPIE 4446, 52–59 (2001).
[CrossRef]

1997

H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
[CrossRef]

1996

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16, 81–87 (1996).
[CrossRef]

1982

H. Pfeiffer and M. Bihler, “The effects of non-uniform illumination of solar cells with concentrated light,” Sol. Cells 5, 293–299 (1982).
[CrossRef]

Akbarzadeh, A.

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16, 81–87 (1996).
[CrossRef]

Baig, H.

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
[CrossRef]

Bihler, M.

H. Pfeiffer and M. Bihler, “The effects of non-uniform illumination of solar cells with concentrated light,” Sol. Cells 5, 293–299 (1982).
[CrossRef]

Gordon, J. M.

H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
[CrossRef]

Heasman, K. C.

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
[CrossRef]

Jenkings, D. G.

D. G. Jenkings, “High-uniformity solar concentrators for photovoltaic systems,” Proc. SPIE 4446, 52–59 (2001).
[CrossRef]

Laxen, M.

H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
[CrossRef]

Mallick, T. K.

N. Sellami and T. K. Mallick, “Optical characterisation and optimisation of a static window integrated concentrating photovoltaic system,” Sol. Energy 91, 273–282 (2013).
[CrossRef]

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
[CrossRef]

O’Gallagher, J. J.

J. J. O’Gallagher and R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays,” Proc. SPIE 4446, 60–64 (2001).
[CrossRef]

Pfeiffer, H.

H. Pfeiffer and M. Bihler, “The effects of non-uniform illumination of solar cells with concentrated light,” Sol. Cells 5, 293–299 (1982).
[CrossRef]

Ries, H.

H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
[CrossRef]

Sarmah, N.

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

Sellami, N.

N. Sellami and T. K. Mallick, “Optical characterisation and optimisation of a static window integrated concentrating photovoltaic system,” Sol. Energy 91, 273–282 (2013).
[CrossRef]

Wadowski, T.

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16, 81–87 (1996).
[CrossRef]

Winston, R.

J. J. O’Gallagher and R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays,” Proc. SPIE 4446, 60–64 (2001).
[CrossRef]

Appl. Therm. Eng.

A. Akbarzadeh and T. Wadowski, “Heat pipe-based cooling systems for photovoltaic cells under concentrated solar radiation,” Appl. Therm. Eng. 16, 81–87 (1996).
[CrossRef]

Proc. SPIE

J. J. O’Gallagher and R. Winston, “Nonimaging solar concentrator with near-uniform irradiance for photovoltaic arrays,” Proc. SPIE 4446, 60–64 (2001).
[CrossRef]

D. G. Jenkings, “High-uniformity solar concentrators for photovoltaic systems,” Proc. SPIE 4446, 52–59 (2001).
[CrossRef]

Renew. Sust. Energ. Rev.

H. Baig, K. C. Heasman, and T. K. Mallick, “Non-uniform illumination in concentrating solar cells,” Renew. Sust. Energ. Rev. 16, 5890–5909 (2012).
[CrossRef]

Sol. Cells

H. Pfeiffer and M. Bihler, “The effects of non-uniform illumination of solar cells with concentrated light,” Sol. Cells 5, 293–299 (1982).
[CrossRef]

Sol. Energy

N. Sellami and T. K. Mallick, “Optical characterisation and optimisation of a static window integrated concentrating photovoltaic system,” Sol. Energy 91, 273–282 (2013).
[CrossRef]

H. Ries, J. M. Gordon, and M. Laxen, “High-flux photovoltaic solar concentrators with kaleidoscope based optical designs,” Sol. Energy 60, 11–16 (1997).
[CrossRef]

Sol. Energy Mater. Sol. Cells

H. Baig, N. Sarmah, K. C. Heasman, and T. K. Mallick, “Numerical modelling and experimental validation of a low concentrating photovoltaic system,” Sol. Energy Mater. Sol. Cells 113, 201–219 (2013).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Ray tracing of sunlight concentration and infiltration into a vertical PV cell receiver. (b) Ray tracing of sunlight incident at the starting point (xo,yo) of the reflector.

Fig. 2.
Fig. 2.

(a) 100 cm wide stainless steel reflector surface profile with uniform sunlight infiltration into silicon PV cell receiver (left scale) and the reflector profile difference when the angular dependences are ignored with R=0.613 and T=0.6515 (right scale) (C=40, xo=10, yo=10cm). (b) Effect of reflection and transmittance angular dependencies on the sunlight infiltration into the PV silicon cell with R=0.613 and T=0.6515 for the case when angular dependencies are not accounted (C=40, xo=10, yo=10cm). (c) Corresponding stainless steel reflectivity and transmittance through the silicon PV cell receiver (C=40, xo=10, yo=10cm). (d) Effect of sunlight divergence (±0.26°) on the sunlight infiltration into the PV silicon cell (C=40, xo=10, yo=10cm).

Fig. 3.
Fig. 3.

(a) Surface profiles of a 100 cm wide stainless steel reflector at three different relative positions of the receiver with respect to the reflector: yo=10cm, yo=40, and yo=70 (C=40, xo=10). (b) Corresponding reflectivity along the stainless steel reflector with the three different relative positions of the receiver with respect to the reflector: yo=10cm, yo=40, and yo=70 (C=40, xo=10). (c) Corresponding transmittance through the PV silicon receiver with the three different relative positions of the receiver with respect to the reflector: yo=10cm, yo=40, and yo=70 (C=40, xo=10). (d) Corresponding sunlight infiltration into the PV silicon receiver with the three different relative positions of the receiver with respect to the reflector: yo=10cm, yo=40, and yo=70 (C=40, xo=10).

Fig. 4.
Fig. 4.

(a) Surface profiles of a 100 cm wide stainless steel reflector with three different concentration ratios: C=40, C=200, and C=1000 (xo=10, yo=10). (b) Corresponding sunlight infiltration into the PV silicon receiver with the three different concentration ratios: C=40, C=200, and C=1000. (xo=10, yo=10).

Equations (28)

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tan(2θ)=2tan(θ)1tan2(θ)=2y1y2,
tan(2θ)=xhy,
y=tan(θ).
h(x,y)=y+x(1y22y).
R(θ)=12[|sin(θϕ)sin(θ+ϕ)|2+|tan(θϕ)tan(θ+ϕ)|2],
sin(θ)=N1sin(ϕ).
T(α)=112[|sin(αβ)sin(α+β)|2+|tan(αβ)tan(α+β)|2],
sin(α)=N2sin(β).
C=(1R(θ)T(α))dxdh.
dhdx=y+(1y22y)+xddx(1y22y),
dhdx=(y2+1)(yxy)2y2.
R(θ)=12[|1tan(ϕ)tan(θ)1+tan(ϕ)tan(θ)|2(1+|1tan(θ)tan(ϕ)1+tan(θ)tan(ϕ)|2)].
tan(ϕ)=y(N121)y2+N12.
R(y)=12[|(N121)y2+N121(N121)y2+N12+1|2(1+|(N121)y2+N12y2(N121)y2+N12+y2|2)].
T(α)=112[|1tan(β)tan(α)1+tan(β)tan(α)|2(1+|1tan(α)tan(β)1+tan(α)tan(β)|2)].
tan(α)=1tan(2θ)=1y22y.
tan(β)=1y2N22(1+y2)2(1y2)2.
T(y)=112[|N22(1+y2)2(1y2)22yN22(1+y2)2(1y2)2+2y|2(1+|2yN22(1+y2)2(1y2)2(1y2)22yN22(1+y2)2(1y2)2+(1y2)2|2)].
y=y(y2+1)R(y)T(y)C2y2x(y2+1)R(y)T(y)C.
g=y,
dgdx=f(x,g)=g(g2+1)R(g)T(g)C2g2x(g2+1)R(g)T(g)C,
xoyo=tan(2θ)=2g(xo)1g(xo)2.
g(xo)=go=yo2+xo2+yoxo.
gi+1=gi+Δxf(xi+0.5,gi+0.5),
xi+0.5=xi+Δx2,
gi+0.5=gi+Δx2f(xi,gi),
f(xi,gi)=gi(gi2+1)R(gi)T(gi)C2gi2xi(gi2+1)R(gi)T(gi)C,
hi=yi+yi+12,Ci=Δx[Ii+Ii+12(yi+1yi)],

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