An analytical flux density distribution model with a closed-form expression for a flat heliostat

Predicting the flux density distribution on the receiver surface is of significance for designing and deploying a central receiver system. In this paper, an analytical model with a closed-form expression is presented to accurately describe the flux density distribution that a flat heliostat reflects on the receiver plane. The flux spot is modeled as a two dimensional convolution between a uniform light flux density distribution over the heliostat effective reflection surface and a two dimensional quasi-Cauchy kernel. The convolution is solved analytically as a closed-form expression. The proposed model takes into account the sunlight direction, sun shape, heliostat position, size, orientation, slope error, and shadowing and blocking effects, etc. Extensive experiments and comparisons were conducted, and it shows that the proposed model is more accurate than the prevalent elliptical Gaussian model, in terms of total power and flux density distribution. Due to its closed-form expression, the proposed model can also be efficiently evaluated on a contemporary graphics processing unit to predict the flux spot of a heliostat within 2.8 ms. Thus this model has promising potential in the practical optimization applications.