The concentration ratio theoretically is around 46,000. But most of the existing technologies have a very low concentration ratio.
The maximum concentration for a point-cocus concentrator (2-axis tracking) is 1/sin^2(x) and for a line-focus (1-axis tracking) is 1/sin(x). x is the view angle of the sun, which is 0.27 deg. approx. The former gives 46,000 and the second about 200. These maxima come from the conservation of the etendue (or lagrange invariant) in an optical system.
Hi, if you are referring to CPV, the concentration ratio is usually limited by the optics but instead the solar cell used. If using a silicon solar cell, designs usually stay under 100X otherwise recombination within the solar cell gets too high. In the III-V devices (GaAs based), this can go higher and something like 500X might be more common. Hope this helps, regards, Bryce
Thank you for the answer sir, but here the concentration ratio i am talking is for a parabolic dish which are used in power plants. Please help me in that knowing why cannot we achieve much high CR of 46,000. What are the difficulties involved in it ?
Hi Chaitanya,
The equation provided by Himanshu is true for 2D/linear concentrators (such as the trough) in air, and gives the maximum concentration which is ~210. For parabolic dishes though, the geometry is 3D and the equation that governs the maximum theoretical limit would be n/sin^2 x (which for the refractive index of air n~1 and the same acceptance half-angle will result in ~45000).
If you want to know more about this I would recommend a couple of textbooks on nonimaging optics from R. Winston or O'Gallagher. that also include experimental demonstrations towards this limit and the difficulties involved.
Regards, Georgios
In a nutshell, parabolic troughs use 1-axis tracking, which is only an approximate way to concentrate the sun. A truly effective concentration requires 2-axis tracking, which is precisely what used in CPV systems, with concentration ratios now larger than 1000X in commercial systems.
The maximum concentration for a point-cocus concentrator (2-axis tracking) is 1/sin^2(x) and for a line-focus (1-axis tracking) is 1/sin(x). x is the view angle of the sun, which is 0.27 deg. approx. The former gives 46,000 and the second about 200. These maxima come from the conservation of the etendue (or lagrange invariant) in an optical system.
The posts above cover the optical limitations to concentration very well. The limit you cite might be related to what the light is being focussed on - stronger concentration gives higher temperatures and both photovoltaics and solar thermal have maximum sensible operating temperatures. To answer this we would need to know if you have been looking at concentration onto a solar cell, onto a fluid for solar thermal power generation, etc.
Chaitanja, interesting question, this paper will also assist.
http://www.psi.ch/lst/BooksEN/Solar_Thermochemical_Process_Technology.pdf
and you will find this patent interesting as well:
http://www.google.com/patents/US5005958
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