An analytical solution for the solar flux density produced by a round focusing heliostat

Abstract This paper presents an analytical solution for calculation of flux density distribution on the image plane of a round spherical heliostat which is deduced from the convolution-based integration method. The two-dimensional integration for flux density calculation is converted to a one-dimensional integration and solved as a function, thereby reducing the amount of calculation and obtaining fast computation. The flux density on the receiver plane can be calculated through projection even if the distance between the heliostat and receiver is not equal to the focal length of the heliostat. The ray tracing and numerical method are applied to validate the accuracy of the analytical method which shows the analytical method can be applied to most heliostats for solar tower system with a faster calculation speed than SolTrace code, and the error source is analyzed, which is inversely proportional to the cube of the focal length f and is proportional to the biquadrate of the heliostat radius R 0 . It is proved that a radially symmetric solar flux density distribution on the image plane is produced by a round spherical heliostat, which is so far the only radially symmetric solar flux density distribution formed by the heliostat when the incident angle is not 0.