Chapter II Summary of literature review in the fields of solar energy and related
2.1 Solar energy and its availability
2.1.1 Solar radiation
The Sun is an “inexhaustible” source of energy that is produced in the process of nuclear fusion of gases (mainly hydrogen into helium), similarly to what occurs in other stars life cycles. The radiation from the sun can be approximated to that of a blackbody with an effective temperature of about 5777 K (Duffie, et al., 2006), which irradiates energy with a given spectral distribution, according to Planck’s law. The major portion of this irradiated energy lies between 250 and 3000 nm. Of this, a significant portion is the visible spectrum (380 nm to 780 nm) with a share of about 48% of the total irradiated energy. The other big share belongs to the infrared region (>780 nm) with 45.6% of the sun irradiated energy (Duffie, et al., 2006). Figure 3, shows the solar energy spectral distribution.
Figure 3 – Spectral energy distribution of solar radiation (for sun effective blackbody temperature of 5525K). Source: R.Rohde (http://www.globalwarmingart.com)
The solar radiation that hits the earth’s upper atmosphere is called extraterrestrial radiation and fits nearly the Planck’s blackbody law. The extraterrestrial solar radiation may vary due to many reasons, including sun spot activity (by ±1.5%), the earth’s orbital eccentricity that varies the earth-sun distance (by ±3.3%) (Duffie, et al., 2006).
The solar constant (Gsc) expresses the extraterrestrial energy received from the sun per unit time outside the atmosphere, per unit area of a surface normal to the radiation, at mean sun-earth distance (1.49x1011m).
Gsc = 1367 W/m2 (2.1.1.1)
To account for variations of extraterrestrial radiation due to variations of the earth- sun distance a variable magnitude of the energy expressed in terms of the solar constant is represented by Gon:
Gon = Gsc'1 ) 0.033cos01 2013 4 (2.1.1.2) or more accurately:
Gon=Gsc"1.000110 ) 0.03422178 9 ) 0.0012808;<9 ) 0.00071978 29 ) 0.0000778;< 29#(2.1.1.2.1) Where d is the day of the year (from 1 to 365), and B the fractional year, expressed
as: B = (d-1) 01013 (2.1.1.2.2)
When the radiation from the sun passes through the earth’s atmosphere, it is partly scattered and/or selectively absorbed by atmospheric gases (mainly by O3, O2, H2O, CO2), dust and other substances present in the atmosphere (Brogren, 2004)5. The solar radiation that hits the earth’s surface is reduced by about 30% (Brogren, 2004). This means also that the amount of solar radiation that reaches the earth’s surface is affected by the zenith angle (see Figure 4 and Figure 6) since the greater the zenith angle the larger the atmospheric gap that it has to cross. This factor is expressed in terms of the air mass (AM), the ratio of the path length of the radiation through the atmosphere, given a zenith angle θz:
?"A@
B# (2.1.1.3)
where m is the air mass number. The minimum m (=1) is when θz is null, when the beam radiation is incident on the zenith line at equatorial latitudes, and it grows progressively with latitude.
The path length L (see Figure 4) corresponds to m=1 (θz=0) while Lz corresponds to m=1/cos(θz) for any θz > 0. The given formula (2.1.1.3) is a good approximation only for zenith angles between 0 and 700 at sea level . For angles near 900, and to account for effects of the earth curvature and the altitude (h), the expression below by Kasten and Young (1989) (as cited by Duffie, et al. 2006), is more accurate:
? CD.DDDEEFGHI
JKL MNO .33P"Q1.RS MN#CE.TUG (2.1.1.3.1)
where h is the altitude of the observer and θz the zenith angle.
5 As also reported by JPL (Jet Propulsion Laboratory, 1998)
The amount of solar radiation that passes the top atmosphere layers may be further influenced by atmospheric conditions such as clouds, fog, rain, snow, etc.
In the end, besides all the obstacles described above, the solar radiation that is available in a certain geographic location, is intermittent6 due to the earth’s rotational movement. This is not quite a disadvantage, since the rotation guarantees a periodic distribution of the available sun energy to all the earth’s regions affected only by the latitude and the day of the year. The selective absorption of some wave lengths (mainly the ultraviolet region) preventing them from reaching the biosphere7 is also beneficial because they could otherwise cause serious health and long term irreversible ecosystem problems. Example: the ozone’s depletion (a global climate change problem) allows high energy radiation (which is dangerous to live species) to enter the biosphere.
2.1.1.1 Types of solar radiation
The total solar radiation that hits the earth’s surface classified in two types: beam and diffuse radiations:
• Beam or direct radiation: Is the one that hits the earth’s surface without having been formerly deviated due to scattering, denoted as Ib;
• Diffuse radiation: the one that reaches the earth’s surface after being scattered, denoted by Id;
• The total or global radiation: is the sum of the beam and diffuse radiations, denoted as It.
6 Intermittent: it is available during the day and also affected by cloudy conditions.
7 Biosphere is the Earth’s region comprising the living organisms and their habitats. This is a shared space which includes: a part of the atmosphere (the air zone of the lower layer), a part of the hydrosphere (waters) and a part of the lithosphere (solid earth).
Figure 4 - Zenith angle and Air Mass
L
Earth’s atmosphere
Earth’s surface Zenith line (normal to the earth’s surface)
θz Sun
Top of atmosphere
Lz
2.1.1.2 Solar radiation detection and measurement
There are various types of photodetectors for detecting and measuring light, with different spectral responsivities. These include photodiodes, photoresistors, thermopiles, CCDs, solar cells, etc. For measuring the components of solar radiation (beam, diffuse or global as well as other related quantities), there are special instruments (built from elementary photodetectors) classified as radiometers or sun photometers. The key instruments are the pyrheliometer (sun photometer) for measuring beam, and the pyranometer (radiometer) for measuring either global or diffuse radiations (Duffie, et al., 2006) (Brooks, 2006).
2.1.1.3 Available clear sky solar radiation
The direct radiation (Ib) incident on a surface (say, a two axis tracking collector) with known latitude and time of day can be estimated through the equation of Hu and White as cited by Alata (Alata, et al., 2005):
VW? XYZ[ \. ]^\._]` (2.1.1.4)
where Gon is the solar constant (as in eq.2.1.1.2 and 2.1.1.2.1) and m (as in eq.2.1.1.3 and 2.1.1.3.1) is the air mass number. This magnitude is important when evaluating the efficiency of the tracking and concentrating systems for clear sky conditions.
2.1.2 Solar Radiation Geometry with Respect to Earth and Collector Surface