Abstract
Curved structures are used in buildings and may be integrated with photovoltaic modules. Self-shading occurs on non-flat (curved) surface collectors resulting in a non-uniform distribution of the direct beam and the diffuse incident solar radiation along the curvature the surface. The present study uses analytical expressions for calculating and analyzing the incident solar radiation on a general parabolic concave surface. Concave surfaces facing north, south and east/west are considered, and numerical values for the annual incident irradiations (in kWh) are demonstrated for two locations: 32° N (Tel Aviv, Israel) and 52.2° N (Lindenberg, Germany). The numerical results show that the difference in the incident global irradiation for the different surface orientations is not very wide. At 32° N, the irradiation difference between the south and north-oriented surface is about 15 percent, and between the south and east surface orientation it is about 9.6 percent. For latitude 52.2° N, the global irradiation difference between the south and north-oriented surface is about 16 percent, and between the south and east orientation it is about 3 percent.
Highlights
Curved structures with concave and convex surfaces are used in buildings and may be integrated with photovoltaic (PV) modules to generate electrical power
The present paper develops analytical expressions for calculating the selfshading areas, direct beam, diffuse and global incident radiation on a parabolic concave PV collector that is applicable to BIPV
Concave structures have elegant curvatures that enhance the aesthetics of the building and at the same time may be covered with flexible PV modules to generate electricity
Summary
Curved structures with concave and convex surfaces are used in buildings and may be integrated with photovoltaic (PV) modules (known as BIPV) to generate electrical power. Reference [1] deals mainly with self-shading on a catenary surface deployed on a Martian surface, and some results of solar radiation are presented. References [4,5,6,7,8] do not deal with self-shading, an important effect to consider in solar radiation calculation on curved surfaces, which affects the electrical energy generated by the PV modules. The present paper develops analytical expressions for calculating the selfshading areas, direct beam, diffuse and global incident radiation on a (smooth) parabolic concave PV collector that is applicable to BIPV. The calculation shows that the south-oriented surface receives the highest irradiation, is the east surface and last is the north surface; the difference in the irradiation is not very big and is about 15 percent between the south and north-oriented parabolic surfaces
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