Simplified Calculational Procedure for Determining the Amount of Intercepted Sunlight in an Imaging Solar Concentrator

Abstract

In imaging solar concentrators, the solar radiation incident on a receiver surface depends upon both the overall concentrator shape and the angular distribution of light rays (sunshape) that reach the receiver. Calculation of the amount of sunlight incident on the receiver usually requires sophisticated computer programs. A simplified calculational procedure is presented to solve this problem for both one and two-dimensional concentrators, with the results presented in graphical form. The procedure first determines the amount of sunshape broadening resulting from optical scattering caused by reflector or glazing materials, surface slope errors, or other “mechanical” factors such as tracking errors or vibrations. These optical effects are combined into an effective error cone which is convoluted with measured sunshapes in order to obtain effective, broadened sunshapes. Broadened sunshapes for a variety of effective error-cone distributions are calculated and presented. It is found that when the root-mean-square (RMS) width of the effective error cone is greater than approximately two times the RMS width of the incident sunshape, the broadened sunshape can be adequately described by a circular normal distribution. A specific example is included which illustrates the calculational procedure discussed in the paper.