Sky view factors of curved surfaces

Photovoltaic modules are integrated into rooftop buildings, canopies, solar carports, bus stops, greenhouses, known as Building-Integrated Photovoltaics (BIPV). Rooftops may have curved surfaces. The incident diffuse irradiation on curved surface is not uniformly distributed along the surface because the slope of the surface varies with the distance along the curvature. The non-uniform diffuse irradiation stems from the variation of the local sky view factor along the curved surface, resulting in mismatch power losses. The variation of local sky view factors of curved surfaces, in presence of obscuring structures, was not investigate in the past. The purpose of the present study is to develop a methodology for calculating the local sky view factors and the annual incident diffuse irradiation along the curvature of the surfaces. The demonstrations apply to convex and concave parabolic and elliptic surfaces, including curved surfaces obscured by flat, convex and concave nearby rooftops. The effect of an obscuring building near a curved parabolic rooftop results in a decrease of the annual incident diffuse irradiation by 9 percent for 10 m separation between the rooftop and the building. The present study may assist the designer of BIPV systems to assess the generated electric energy on curved rooftops.