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Pushing concentration of stationary solar concentrators to the limit

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Abstract

We give the theoretical limit of concentration allowed by nonimaging optics for stationary solar concentrators after reviewing sun–earth geometry in direction cosine space. We then discuss the design principles that we follow to approach the maximum concentration along with examples including a hollow CPC trough, a dielectric CPC trough, and a 3D dielectric stationary solar concentrator which concentrates sun light four times (4x), eight hours per day year around.

©2010 Optical Society of America

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Figures (6)

Fig. 1
Fig. 1 Sun-earth geometry.
Fig. 2
Fig. 2 Sun's directions, plotted in direction cosine space on the polar plane. Black circle: unit circle; green lines: winter and summer solstices; dashed black lines: (from left to right) the first day of Jan. Feb. Mar. Apr. May, and June; vertical solid black lines: (from right to left) the first day of July, Aug. Sep. Oct. Nov. and Dec.; red lines: eight hours per day; blue lines: sunrise/sunset at a latitude of 40 degree in the north hemisphere.
Fig. 3
Fig. 3 Angular acceptance for hollow CPC troughs (yellow) and sun’s directions (green and red), plotted in direction cosine space on the polar plane.
Fig. 4
Fig. 4 Angular acceptance for a dielectric CPC trough (blue) and a hollow CPC trough (yellow) with the same acceptance angle, plotted in direction cosine space.
Fig. 5
Fig. 5 Angular acceptance for a dielectric CPC trough (blue) and a hollow CPC trough (yellow), both designed for concentrating sun light eight hours per day, and sun’s directions (green and red), plotted in direction cosine space on the polar plane.
Fig. 6
Fig. 6 Diagram of a 4x stationary dielectric concentrator.

Equations (15)

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n s = ( sin δ , cos δ sin ω , cos δ cos ω ) ,
sin δ = sin 23.45 ° cos ( 360 ° ( n + 10 ) 365.25 ) ,
ω = 360 ° 24 t ,
L 2 + M 2 sin 2 ω = 1.
L 2 cos 2 φ + M 2 = 1.
n ' 2 d x ' d y ' d L ' d M ' = n 2 d x d y d L d M ,
C = d x d y d x ' d y ' = n ' 2 n 2 d L ' d M ' d L d M .
d L d M = 2 ( δ s ' ) + sin ( 2 δ s ' ) 1.56 ,
d L d M = sin ( ω ' ) [ 2 ( δ s ' ) + sin ( 2 δ s ' ) ] ,
L 2 1 M 2 sin 2 ( θ 1 )
L 2 sin 2 ( θ 1 ) + M 2 1.
sin 2 ( θ 1 ) = sin 2 ( δ s ' ) 1 cos 2 ( δ s ' ) sin 2 ( ω ' ) .
L = n L n , M = n M n ,
L 2 sin 2 ( θ 1 ) + M 2 n 2 = 1 ,
sin 2 ( θ 1 ) = n 2 sin 2 ( δ s ' ) n 2 cos 2 ( δ s ' ) sin 2 ( ω ' ) .
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