The recent progresses in non-imaging optics research are focused on to designs in 3D geometry. The interest in 3D designs for PVs lies in the potential capability of 3D methods to obtain practical solutions close to the optimum PV concentrator performance, defined in section 13.1.6.
Not only do 2D designs not control most of the 3D rays, but the rotational or linear symmetric devices are theoretically unable to solve some design problems due to its symmetry. For instance, linear symmetric concentrators cannot achieve isotropic illumination of cell surrounded by an optically dense medium (n > 1) [46], and rotational concentrators cannot achieve maximum concentration on a spherical receiver [47].
Designing in 3D is more difficult than in 2D, due to the greater number of rays to be controlled. For instance, while the edge rays in 2D constitute a one-parameter family of rays, they are three-parameter ones in 3D (because the dimensions increase in both the spatial and angular coordinates).
In general, the 3D design deals with the design of free-form optical surfaces (i. e. surface without rotational or linear symmetry). Note that these surfaces can presently be manufactured with optical precision (even for imaging applications) thanks to the development of multiple-axis high-accuracy diamondturning machines. Its cost is not essentially higher for mass production, because
in any mass-production replication technique it only affects the fixed cost of the master.
Some 3D design methods were developed in the past aiming to solve the bundle-coupling problem (see section 13.1.7) in 3D geometry, as extensions of two of the methods in 2D (the Flow-Line method [28,48,49] and the Poisson bracket method [50]). One device obtained with Poisson bracket method in 3D, which proved the existence of theoretically exact solutions for coupling a 3D bundle of acceptance angle a with the maximum concentration bundle (в = 90°) on a flat receiver of arbitrary contour is remarkable.
However, these methods do not lead to practical PV devices yet: some of them use inhomogeneous refractive index media and all of them use flow-line metallic mirrors. New methods are now under development, which do not have these practical limitations:
(1) A single free-form refractive or reflective surface [51-53] to solve the prescribed-irradiance problem based on the approximation of infinitesimal source. This strategy (usually called point-to-point mapping [15]) is well known for rotational optics, where its solution simply involves the integration of a nonlinear ordinary differential equation [54], but designing one free-form surface needs a nonlinear partial differential equation of the Monge-Ampere type to be solved. This design could provide, if desired, a squared aperture and sufficiently good illumination uniformity on a squared area for the real (finite radius) sun. However, the design strategy provides very small illumination angles в and, consequently, the acceptance angle seems insufficient (essentially, the suns radius), which may make it impractical.
(2) The SMS method in 3D [55,56]. With this approach, at least, two freeform surfaces are designed, transforming a selected subset of edge rays at each point of the entry aperture of the input bundle Mi into edge-rays of the output bundle Mo. It can also been applied either for bundle-coupling or for prescribed-irradianceproblems. 3D-SMS can be applied to the configuration of any of the 2D-SMS devices presented here.
These advanced techniques may be applied to PV concentrator designs in the near future. In our opinion, the 3D-SMS method has the potential of finding the first practical device approaching the optimum PV performance.
13.2 Summary
The combination of concentration and next-generation PV devices is expected to play an important role in future PV electricity generation. Due to the present high cost of the most developed next-generation approach (the tandem cells), there is a trend towards achieving practical devices working at high concentration levels.
The desired characteristics of PV concentrators (efficient, mass-producible, insensitive to errors, good illumination uniformity, capable for high concentration,
tessellatable) make their design a challenging problem for optical designers. These characteristics lead to the definition of an optimum PV concentrator performance, which can serve as the goal for the design. Approaching that goal with practical devices is still an open problem, which may not be a need for low concentration systems.
The importance of designing for a sufficient acceptance angle has highlighted one of the ignored issues in PV concentration, which may be one key feature for the future success of high-concentration next-generation systems. The acceptance angle is a measure of the allowable tolerances of the system (especially module manufacturing and installation) and, although the dependence of the system cost with the acceptance angle is uncertain at present, it may be critical. The nonlinear effects of the series connection of cells lead to a more restrictive definition for the acceptance angle other than in non-PV applications, making that the useful incidence angles are those for which the concentrator optical efficiency is high.
The problem of defining the degree of non-uniformity that can be allowed for a given cell has been discussed, specifically for front-contacted cells with low series resistance on the grid-lines. The concept of exponential concentration seems to play an important role, and the tools for the calculation of the cell efficiency, the strategies for modifying the irradiance distribution to produce the fastest approach to the optimum and the analysis of the contribution of the different concentration levels are given.
Non-imaging optics is the best framework for optical concentrator design. Classical optics (based on parabolic mirrors and Fresnel lenses) seems to be limited to obtaining high-concentration devices achieving good illumination homogeneity and sufficient acceptance angle. The non-imaging SMS design method has proven to be a versatile tool for designing concentrators that achieve high acceptance-angle concentrator products (and recently sufficiently uniform illuminations) and, at the same time, have nice practical features (simplicity, compactness). The use of the SMS techniques in 3D geometry may be a good path to follow for improving the present designs towards higher concentration levels and better illumination uniformity, keeping the tolerances at a practical level.
Acknowledgments
This work has been under the EU contract ERN6-CT2001-00548.
