Six-gaussian representation of the angular-brightness distribution for solar radiation

Abstract

The angular distribution of circumsolar radiation varies with changing atmosphere and influences the solar irradiance at the receiver of a concentrating system. In order to facilitate calculation of this irradiance, five typical sunshapes are chosen from the widest to the narrowest shape in the Lawrence Berkeley Laboratory data and are approximated by a sum of 6 gaussian distributions. An effective sunshape can then be obtained by convolution with error-cone distributions that represent a statistical description of uncertainties encountered in an optical concentrating system. Convolution of circular-normal error cones first with the sum of gaussians and then with actual sunshape indicates good agreement whenever the error-cone dispersion is greater than 0.0012. Thus the analytic convolution can replace more costly (in time and computer storage) numerical calculation. A simple prescription indicates how each of the analytic representations may be transformed to approximate sunshapes appropriate for slightly different atmospheric conditions.