Luminescence solar concentrators act as semitransparent photovoltaic cells of interest for modern urban environments. Here, their efficiencies were analytically derived for different regular unit shapes as simple, integral-free expressions. This allowed analysis of the shape and size effect on the device performance. All regular shapes appear to have a similar efficiency as revealed by optical path distribution formulas, despite differences in the perimeter length. Rectangles of the same area feature higher efficiency due to reduced average optical path. It comes with the cost of a longer perimeter, and the relation between these two is provided. An explicit formula for the critical size of an LSC unit, above which its inner part becomes inactive, has been obtained. For square geometry with matrix absorption coefficient alpha this critical size is similar to 2.7/alpha, corresponding to 70-90 cm for common polymer materials. Obtained results can be used for treatment of individual units as well as for analysis of tiling for large areas. (C) 2020 Optical Society of America
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