A model for the directional distribution of the diffuse sky radiance with an application to a CPC collector

The development of a new, semi-empirical model for the directional distribution of the diffuse radiance is reported. The proposed regression-type model, with the form of its base functions obtained from physical principles, is based on a combination of the purely physical reasoning approach and the purely empirical approach. Direct multiple-scattering calculations are circumvented through the use of the method of successive orders of scattering. The model is calibrated for the mean diffuse radiance estimated under all sky conditions reported in a large and comprehensive diffuse radiance data set. It is found that only a small increase in accuracy is gained by including higher orders of scattering, and this increase does not justify the complexity of the resulting model. Therefore, the single scattering approximation is recommended. The use of the model is illustrated in a typical application, in which the fraction of diffuse radiation intercepted by the receiver of a compound parabolic concentrator is computed.