Theoretical Investigations on Shadow Band Correction Factors for Diffuse Radiation under Isotropic Conditions without Approximation

Abstract

The precise measurement for irradiance is important for the performance evaluations of solar systems, because both beam and diffuse radiation measurements must be known to calculate the efficiency of a solar system. One of the widely used instruments for diffuse radiation measurement is a pyranometer with a ring. Hence, investigations on shadow band correction factors are necessary. The factors are normally calculated by the expressions of Drummond and Burek et al. under isotropic conditions. However, their calculation results are approximate. While the latitude φ, the inclination angle β and the declination δ are satisfied with the condition of |−tan(φ−β)tanδ|>1, the factors cannot be calculated by their expressions. In this paper, the expressions for the factors under isotropic conditions were obtained by coordinate transformations and discussed in two different coordinate systems without approximation. Our expressions can give precise correction factors in any case and overcome the disadvantages of their expressions. While the sensor is placed horizontally, the maximum relative deviation between the results by the expression in Drummond’s paper and by our expressions is less than 2.3%. When the sensor is placed on a sloped surface, the results by the expressions in Burek’s paper and by our expressions will have considerable differences in some ranges of slope angles and latitudes. The maximum relative deviation is more than 22%.