View factors of photovoltaic collectors on Roof Tops

Abstract

The diffuse radiation is an important component of the global radiation affecting the output of photovoltaic (PV) collectors. This radiation depends on the view factor between the collector and sky. A simple expression for the view factor for single inclined collectors on a horizontal plane is known. However, for a photovoltaic solar field with multiple rows deployed on a horizontal or on inclined planes, the view factor is more complicated to calculate, because a collector row may obscure part of the sky for the adjacent row. More complication is added for collectors deployed on saw-tooth roofs. The present study deals with the calculation of view factors to sky for collectors deployed in multiple rows and in the presence of obscuring structures on roof tops. General and particular mathematical expressions for view factors to sky were developed for PV collectors deployed on grounds or on roof tops to determine the diffuse incident solar radiation on PV collectors, and numerical values of view factors were presented. The view factor to sky depends significantly on the inclination angle of the collector. For common deployment of collectors in multiple rows on horizontal planes, the view to sky is in the range between 0.8 and 0.9 for 30° inclination angle, whereas for 50° inclination angle, the range is between 0.6 and 0.7. The effect of the distance between collectors on the view factor is less pronounced. A wall or a fence in front of the collector may decrease significantly the view factor to sky; an increase of 1.0 to 3.0 m decreases the view to sky from 0.8 to 0.6 for 30° inclination, and from 0.7 to 0.4 for 50° inclination. The view factor to sky of vertical collectors is less than 0.5.