Incidence angle effects on circular Gaussian flux density distributions for heliostat imaging

• Modification to HFLCAL method for accurate flux distribution applications.
• Incidence angle effects on heliostat beam quality.
• Computationally inexpensive method to determine receiver flux distribution.

Circular Gaussian distribution methods are used in certain applications to determine the flux distribution of central receiver systems. Although the method is computationally inexpensive, some assumptions bring the accuracy of the results into question. This paper addresses the confines in which acceptable accuracies are maintained. Flux distributions of an implemented HFLCAL-type model and a ray tracer are compared, and deviations of up to 20% are found in cases where both high incidence angles and high normal vector errors are present. The deviations result from the circular Gaussian distribution method not accounting for the shortening of the minor axis of the elliptical image. A modification is proposed that incorporates the effect of the incidence angle into the beam quality and tracking error terms. The modification corrects for the deviation, has negligible computational expense and is shown to be robust. In a case study of a commercial central receiver system, accuracy of the flux distribution was improved by up to 16%.