The harvesting and conversion of solar radiation by concentrating photovoltaic (CPV) technologies depends explicitly on the quality and quantity of the solar resource that is available, as well as the optical and electrical properties of the photovoltaic technology. This chapter will address the quantitative and qualitative aspects of the solar resource, the direct solar radiation, and briefly, more qualitative discussions of the interaction of the resource with the photovoltaic technologies and system design issues. More quantitative discussion of the latter will be addressed in detail in subsequent chapters.
1.1.1 Orbital and Geometrical Considerations
The Earth orbits a typical star, the sun, which provides energy in the form of optical and thermal radiation that enables and supports life on our planet. A reference for most of the numerical data presented in this section is Allen's Astrophysical Quantities [1].
The sun has a diameter (ds) of 1 390 000 km (840 000 miles). At the surface of the sun (at radius Rs = 695 000 km from the center) the power flux density emitted is about 6.33 × 107 Wm−2. The Earth's orbit about the sun is an ellipse with an eccentricity of 0.0167. Closest approach of the Earth to the sun (perihelion) occurs on about January 2 or 3, and the furthest distance (aphelion) occurs on about July 4 or 5. The Earth's perihelion, Rp, and aphelion, Ra, distances are about 147.5 million km and 152.6 million km, respectively. That is, the Earth-Sun distance varies from −1.4% to +2.0% of the average Earth-Sun distance, or a range of 3.4% during the year. The average distance (Ro) between the sun and Earth is 1 Astronomical Unit (AU) of 149 597 870.7 km (92 955 807.273 miles).
Using simple geometry, the apparent angular diameter of the solar disk in degrees at 1 AU is arctangent (ds/Ro) = arctangent (1.390/149.59787) = 0.532° or 9.28 mrad. The apparent diameter of the solar disk changes by 3.4% as the sun moves from aphelion (arctan (ds/Ra) = 0.521 = 0.91 mrad) to perihelion (arctan (ds/Rp) = 0.539° = 0.94 mrad). In the absence of an atmosphere, because the solar disk subtends a solid angle of about 0.5°, an observer on the Earth's surface will observe that the rays of sunlight falling on a plane surface with the surface normal (perpendicular) pointed at the center of the solar disk fill a solid angle of the same dimensions. The solar radiation filling the 0.5° cone of rays falling on a surface which is normal (i.e., perpendicular) to the axis of the cone constitute the direct normal radiation, or direct beam irradiance, also called direct normal irradiance, or DNI. Note than in the presence a clear, cloudless atmosphere, the actual solid angle of the DNI over short periods of time will vary slightly, both in time and physical extent. These tiny variations are due to the effects of turbulence and variations in density of the atmosphere as the direct beam radiation propagates through the atmosphere. The magnitude of these effects is demonstrated by the ‘twinkling’ of starlight from much more distant and more truly point-source-like stars.
As the sun moves in elevation from the horizon at sunrise, to higher in the sky at noon, to the horizon at sunset, the elevation angle, e, of the solar disk, or angle from the horizon to the center of the disk, is constantly changing. Thus the path length through the atmosphere for the photons (defined as the air mass, m) also changes from long to shorter to longer as the sun moves from sunrise to noon to sunset. The geometrical air mass, m, is defined as approximately m = 1/sin(e). The complement of the solar elevation angle is the solar zenith angle, z, the angle between the local vertical and the center of the solar disk, thus m is also defined approximately as m = 1/cos(z).
For a surface or collector to capture the DNI, the normal or perpendicular to the surface must point to the center of the solar disk throughout the day. This will keep the incidence angle (the angle between the DNI beam and the surface normal, θ) of the DNI beam near zero, and requires a mechanism to track the elevation and azimuth of the sun throughout the day. The accuracy of the mechanical system in performing the tracking function is an important aspect of the design of systems for intercepting and concentrating, or focusing the direct beam radiation.
For a stationary horizontal surface the incident angle of the direct beam will vary from 90° at sunrise to the (less than 90°, depending on the latitude of the site) solar elevation angle at noon to 90...
