Figure 22.8 helps to illustrate the following brief explanation of the different components of solar radiation that reach a terrestrial flat-plate PV surface
To a good approximation, the sun acts as a perfect emitter of radiation (black body) at a temperature close to 5800 K. The resulting power incident on a unit area perpendicular to the beam outside the Earth’s atmosphere, when it is 1 AU from the sun, is known as the solar constant
B0 = 1367 W/m2 (22.11)
The radiation falling on a receiver situated beyond the Earth’s atmosphere, that is, extraterrestrial radiation, consists almost exclusively of radiation travelling along a straight line from the sun. Since the intermediate space is almost devoid of material that might scatter or reflect the light, it appears virtually black, apart from the sun and faint points of light corresponding to the stars.
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Figure 22.8 Different components of solar radiation |
As the solar radiation passes through the Earth’s atmosphere, it is modified by interaction with components present there. Some of these, such as clouds, reflect radiation. Others, for example, ozone, oxygen, carbon dioxide and water vapour, have significant absorption at several specific spectral bands. Water droplets and suspended dust also cause scattering. The result of all these processes is the decomposition of the solar radiation incident on a receiver at the Earth’s surface into clearly differentiated components. Direct or beam radiation, made up of beams of light that are not reflected or scattered, reaches the surface in a straight line from the sun. Diffuse radiation, coming from the whole sky apart from the sun’s disc, is the radiation scattered towards the receiver. Albedo radiation is radiation reflected from the ground. The total radiation falling on a surface is the sum of these (direct + diffuse + albedo) and is termed global radiation.
It is intuitively obvious that the directional properties of the diffuse radiation depend to a large extent on the position, form and composition of the water vapour and dust responsible for scattering. The angular distribution of the diffuse radiation is therefore a complex function that varies with time. Diffuse radiation is essentially anisotropic. The amount of albedo radiation is greatly affected by the nature of the ground, and a wide range of features (snow, vegetation, water, etc.) occur in practice.
In the following discussion, the word radiation will be used as a general term. To distinguish between power and energy, more specific terminology will be used. Irradiance means density of power falling on a surface, and is measured in W/m2 (or similar); whereas irradiation is the density of the energy that falls on the surface over some period of time, for example, hourly irradiation or daily irradiation, and is measured in Wh/m2. Furthermore, only the symbols B0, B, D, R and G will be used, respectively, for extraterrestrial, direct, diffuse, albedo and global irradiance, whereas a first subscript, h or d, will be used to indicate hourly or daily irradiation A second subscript, m or y, will refer to monthly or yearly averaged irradiation values. Furthermore, the slope and orientation of the concerned surface are indicated among brackets. For example, Gdm(20,40) refers to the monthly mean value of the daily global irradiation incident on a surface tilted в = 20° and oriented у = 40° towards the west. For surfaces tilted towards the equator (y = 0), only the slope will be indicated. For example, B(60) refers to the value of the direct irradiance incident on a surface tilted в = 60° and oriented towards the south (in the Northern Hemisphere).
An important concept characterising the effect of atmosphere on clear days is the air mass, defined as the relative length of the direct-beam path through the atmosphere compared with a vertical path directly to sea level, which is designed as AM. For an ideal homogeneous atmosphere, simple geometrical considerations lead to
AMI = 1 /cos 9ZS (22.12)
which is generally sufficient for most engineering applications. If desired, more accurate expressions, considering second-order effects (curvature of the Earth, atmospheric pressure etc.), are available [3].
At the standard atmosphere AM1, after absorption has been accounted for, the normal irradiance is generally reduced from B0 to 1000 W/m2, which is just the value used for the standard test of PV devices (see Chapter 16). Obviously, that can be expressed as 1000 = 1367 x 0.7AM. For general AM values, a reasonable fit to observed clear days data is given by [4].
G = B0.s0 x 0.74AMa678 (22.13)
A particular example can help to clarify the use of these equations, by calculation of the sun coordinates and the global irradiance on a surface perpendicular to the sun, and also on a horizontal
surface, over two geographic positions defined by ф = 30° and ф = -30°, at 10:00 (solar time) on 14 April, being a clear day. The solution is as follows:
14 April ^ dn = 104; Є0 = 0.993; 5 = 9.04°
10 : 00h ^ ю = -30°
ф = 30° ^ cos0ZS = 0.819 ^ 0ZS = 35° ^ cos ^S = 0.508 ^ fS = -59.44°
^ AM = 1.222 ^ G = 902.4W/m2 ^ G(0) = G ■ cos 0zs = 739 W/m2
ф = -30° ^ cos0zs = 0.662 ^ 0zs = 48.54° ^ cos ^S = 0.403 ^ fS = -66.28°
^ AM = 1.510 ^ G = 846.9W/m2 ^ G(0) = G ■ cos 0zs = 561 W/m2
When solar radiation enters the Earth’s atmosphere, not only the irradiance, but also the spectral content is affected. Figure 22.9 shows the AM 1.5 spectrum, which is considered for standard test of PV devices. Figure 16.1 shows other spectra for comparison. In general, increasing air mass displaces the solar spectrum towards the red. This is why the sky becomes so nice at nightfall.
Of course, PV devices are sensitive to the spectrum, as discussed in Chapters 3, 9, 12 and 16. However, this is of little importance from the PV engineering point of view, compared with changes in total radiation incident on the PV modules. Because of that, in what follows, we will omit the detailed treatment of the spectral composition of sunlight. Additional comments will be given later on in this chapter.
