Losses in a three-dimensional compound parabolic concentrator as a second stage of a solar concentrator

In this article, the losses due to reflection properties in a three-dimensional compound parabolic concentrator (3-D C.P.C.) are calculated and the effect of these losses on the concentration is analyzed. The 3-D C.P.C. is used as a second stage in two configurations of a two-stage concentrator: (a) a parabolic dish as a first stage, and (b) a Cassegrainian as a first stage. The nonplanar rays play an important role in 3-D C.P.C. losses. Thus, a ray-tracing procedure is needed to evaluate the losses. In this study, a rigorous three-dimensional ray tracing program was specially developed. The reflection losses and their effect on the concentration were determined from the reflection distribution derived by the developed ray-tracing program. As a result, the reflection losses were approximated by a simple empirical linear model useful in practical ranges of the 3-D C.P.C. acceptance angles and reflectivities. This model facilitates design and system optimization by analytical methods without resorting to a ray-tracing procedure. The approach presented in this article may be used to compare the performance of the two-system configurations, taking into account the 3-D C.P.C. losses.