On the comparison of parabolical and cylindrical primary mirrors for linear Fresnel solar concentrators

The design of a linear Fresnel concentrator is challenging. One task related to the curvature design of the primary mirrors is the selection of a bent shape: parabolic or cylindrical. This article presents a new and general approach to comparing both shapes. It is based on the root mean square measure of local slope deviations as an overall metric to represent how much a cylindrical mirror deviates from the parabolical one. The presented results show the influence of the design parameters and indicate that for reasonable geometric relations of current commercial linear Fresnel collectors, maximum values of overall slope deviations are lower than 0.7 mrad – more than ten times lower than the size of optical errors of the state-of-the-art mirror panels. Moreover, the main hypothesis is that parabolical and cylindrical primary mirrors would perform similarly when the root mean square slope deviation is low or negligible compared to other sources of beam spread that compose the effective source (e.g., sunshape, specular error, contour error, tracking error). Thus, literature data of reported cases of equivalence were analyzed in terms of worst-case scenarios of the proposed metric to validate this hypothesis, and the results of this analysis corroborate it.