Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Thermodynamic efficiency of solar concentrators

Narkis Shatz, John Bortz, and Roland Winston

Open Access Open Access

Abstract

The optical thermodynamic efficiency is a comprehensive metric that takes into account all loss mechanisms associated with transferring flux from the source to the target phase space, which may include losses due to inadequate design, non-ideal materials, fabrication errors, and less than maximal concentration. We discuss consequences of Fermat’s principle of geometrical optics and review étendue dilution and optical loss mechanisms associated with nonimaging concentrators. We develop an expression for the optical thermodynamic efficiency which combines the first and second laws of thermodynamics. As such, this metric is a gold standard for evaluating the performance of nonimaging concentrators. We provide examples illustrating the use of this new metric for concentrating photovoltaic systems for solar power applications, and in particular show how skewness mismatch limits the attainable optical thermodynamic efficiency.

©2010 Optical Society of America

Full Article  |  PDF Article
More Like This
Aplanatic optics for solar concentration

Jeffrey M. Gordon
Opt. Express 18(S1) A41-A52 (2010)

Pushing concentration of stationary solar concentrators to the limit

Roland Winston and Weiya Zhang
Opt. Express 18(S1) A64-A72 (2010)

Line-focus solar concentration 10 times higher than the 2D thermodynamic limit

Håkon J. D. Johnsen, Juan C. Miñano, and Jan Torgersen
Opt. Express 30(14) 24362-24374 (2022)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)
Fig. 1
Fig. 1 Refractive solar concentrator with 40-mm-diameter entrance aperture and 6-mm-square solar cell.

Download Full Size | PDF

Fig. 2
Fig. 2 Flux-transfer efficiency as a function of the source’s angular half width for refractive concentrator (solid line) and hypothetical ideal concentrator (dashed line).

Download Full Size | PDF

Fig. 3
Fig. 3 Boundaries of direction-cosine regions corresponding to source (red line) and target (blue line) for second example. The unit circle is depicted as a dashed black line. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θ trg = 60°.

Download Full Size | PDF

Fig. 4
Fig. 4 Source and target translational skewness distributions for the second example. The source has unit area and the target étendue equals that of the source. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θ trg = 60°.

Download Full Size | PDF

Fig. 5
Fig. 5 Source and target translational skewness distributions for the second example. The source has unit area and the target area has been adjusted to the smallest value that allows the target’s skewness distribution to completely enclose the source’s skewness distribution. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θ trg = 60°.

Download Full Size | PDF

Fig. 6
Fig. 6 Upper limit on optical thermodynamic efficiency as a function of daily operation time for the second example. The maximum allowed incidence angle on the target is θ trg = 60°.

Download Full Size | PDF

Equations (28)

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

C A P ≡ C g sin ( α ) ,
C A P i d e a l = n t r g n s r c sin ( θ t r g m a x ) ,
S = k ⋅ log E + Thermal term,
η s y s t e m * = η o p t i c s * ⋅ η c e l l s * ,
L s r c a v e = Φ s r c ε s r c .
Φ t r g m a x = L s r c a v e ε t r g .
Φ t r g m a x = Φ s r c ε t r g ε s r c .
η o p t i c s * ≡ Φ t r g Φ s r c ,  for  ε t r g ≤ ε s r c .
η o p t i c s * ≡ Φ t r g Φ t r g m a x ,  for  ε s r c < ε t r g .
η o p t i c s * = Φ t r g Φ s r c ⋅ ε s r c ε t r g ,  for  ε s r c < ε t r g .
η o p t i c s * = η o p t i c s min ( 1 , ε s r c ε t r g ) ,
η o p t i c s ≡ Φ t r g Φ s r c
ε s r c = π A s r c sin 2 ( θ s r c ) = 29.99 mm 2 sr
ε t r g = π A t r g = 113.10 mm 2 sr,
η o p t i c s = 60.48 % .
η o p t i c s * = 16.04 % .
| k y | ≤ sin ( θ y )
| k z | ≤ sin [ θ z ( T ) ] 1 − k y 2 ,
θ y = θ e a r t h + θ s u n
θ z ( T ) = T 12 hr ⋅ 90 ° + θ s u n ,
k y 2 + k z 2 ≤ sin 2 ( θ t r g ) ,
ε s r c ( T ) = 2 A s r c sin [ θ z ( T ) ] [ sin ( θ y ) cos ( θ y ) + θ y ] ,
ε t r g = π A t r g sin 2 ( θ t r g ) ,
d ε s r c ( S z ) d S z = [ 2 A s r c sin ( θ y ) ,    for  | S z | ≤ sin [ θ z ( T ) ] cos ( θ y ) 2 A s r c 1 − S z 2 sin 2 [ θ z ( T ) ] ,      for  sin [ θ z ( T ) ] cos ( θ y ) < | S z | ≤ sin [ θ z ( T ) ] 0 ,      for  sin [ θ z ( T ) ] < | S z | ,
d ε t r g ( S z ) d S z = [ 2 A t r g sin 2 ( θ t r g ) − S z 2 ,    for  | S z | ≤ sin ( θ t r g ) 0 ,    for  sin ( θ t r g ) < | S z | .
d ε s r c d S z ( sin [ θ z ( T ) ] cos ( θ y ) ) = d ε t r g d S z ( sin [ θ z ( T ) ] cos ( θ y ) ) ,
A t r g , r e q = A s r c sin ( θ y ) sin 2 ( θ t r g ) − sin 2 [ θ z ( T ) ] cos 2 ( θ y ) ,
T ≤ θ t r g − θ s u n 90 ° ⋅ 12 hr .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use