Design methods

The design of solar concentrators has different drivers respect to imaging optical elements. Indeed, the design goal here is to maximize the flux density, i. e. the irradiance, at the receiver. Different methods can be implemented to achieve this result (Winston et al., 2005); one of the most commons is the edge ray method. This is based on the assumption that the edge rays in the phase space, i. e. with higher incidence angle at the entrance boundaries of the concentrator, correspond at the extreme rays, in term of positions as well as angles, at the receiver too; the rays between the edge rays are collected to the receiver as well, supposing smoothing and optical active surfaces in continuous media for the concentrator. The first example of non-imaging concentrator obtained with this technique is the compound parabolic concentrator (CPC), as shown in fig. (3); a bundle of parallel rays with an angle respect to the CPC’s axis of symmetry (which is the max angle of divergence for the collected rays), is focused onto a point at the exit area by the reflection on a parabolic surface; this point is on the edge of the exit of the concentrator. All the rays entering with lower angle of incidence are collected at the exit surface. This kind of concentrator allows for the maximal theoretical level of concentration for a linear collector, and it’s almost ideal for the 3D case, with a surface obtained by revolution.

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Fig. 3. Scheme of the edge ray method applied to a compound parabolic concentrator (CPC); the dotted arrows represents the incoming rays

Other methods have been developed since the 70’s till today (flow line method, Tailored Edge Ray, Poisson bracket method, Simultaneous Multiple Surface, Point-source Differential Equation method) both analytical as well as numerical.

The design of solar concentrators must take into account many different aspects other than the geometrical optical efficiency and concentration levels; indeed, the physical optical properties former reported have to be considered, in order to achieve an effective high

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optical efficiency. Moreover, the concentrators should be as much compact as possible, deliver a suitable irradiance distribution at the receiver, allowing for cheap assembling and good thermal management of the system components. All these variables have enlarged the space of possible configurations for CPV optics and there is indeed a wide spectrum of real applications. Currently, most of them are based on Fresnel lenses for the primary optics; the Fresnel lenses are particular kind of lenses for which the dielectric transparent volume material is reduced at the minimum, as shown in fig.(4a), in order to reduce the mass, so the weight, as well as the light absorbance. Other solutions use the reflection of the light instead of the refraction to concentrate the light; the classical parabolic reflectors are used as well as more complex configuration in the form of cassegrain designs, as in fig. (4c); this optical design based on two reflections has the aim to achieve a compact structure, with the light focus behind the primary concentrator. The cassegrain structure is normally employed in telescopes, for the magnification of the far field objects, and, in its basic design for imaging optics, use a parabolic mirror reflecting toward a hyperbolic mirrored surface.

The CPV optical systems are often composed of a primary concentrator with a secondary optical element (SOE); these secondary elements are usually joint to the photovoltaic cells and are employed to improve the concentration factor and the angular acceptance. Moreover, they are often used to increase the light uniformity on the receiver through multiple reflections with kaleidoscopic effect (Ries et al, 1997; Chen et al, 1963); in this latter case, to allow for good optical efficiency, the reflections must be associated to negligible losses. An optical phenomena used to achieve this result is the total internal reflection (TIR) effect; this is obtainable through the channeling of the light into transparent dielectric means shaped to allow the striking of the rays on their surfaces only with an angle lower than the limit angle &c (8); this angle is a direct consequence of the Snell law, when the SOE is made of a material with dielectric index m, placed in a mean of dielectric index n2. It works like a light pipe.

&c = Arcsin( ~~) (8)

The shape of the secondary optics is directly related to the primary concentrator, because it works on the already deflected bundle of rays. So, a number of different designs for these components can be found. However, the most popular can be classified in few groups, like domed shapes, CPCs, truncated pyramids or cones (Victoria et al., 2009). Other original configurations can be found, depending on the requirements of every CPV manufacturer.

Concentrated light beams

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Fig. 5. Examples of geometries for simple secondary concentrators

Currently, powerful modern raytrace-based analysis tools for optics design are available; the majority of these software employ the Monte-Carlo method to solve the coupled integral differential equations used to calculate the illuminance distribution in 3D models (Dutton & Shao, 2010).

These software tools often allow for the accounting of physical parameters too, delivering very realistic estimations for optical performances.

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Fig. 6. Cassegrain type optics for solar concentration arranged in modules by Solfocus Inc. (www. solfocus. com)

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