Read an Excerpt
Building Integrated Photovoltaic Thermal Systems
For Sustainable Developments
By Basant Agrawal, G. N. Tiwari The Royal Society of Chemistry
Copyright © 2011 B. Agrawal and G. N. Tiwari
All rights reserved.
ISBN: 978-1-84973-200-0
CHAPTER 1
Solar Radiation and its Availability on Earth
1.1 Introduction
The Sun flux entering the terrestrial region is nearly 1.2 × 1017 W, being absorbed by the Earth as shown in Figure 1.1. Out of this, 66.67% energy is available as the sensible amount that can be used for heating. However, we know that the Earth's surface area covered by ocean is 71% (361 × 106 km2). Also, forest covers nearly 10% of the Earth's surface or nearly 35% of the total land area. Therefore the solar flux available on the plain area of the land is nearly 2.3 × 1016 W, which can be utilized for heating or generating electricity using photovoltaic modules. If only 1/5750th part of this energy is utilized for power generation through photovoltaic systems, it is sufficient to meet the world's total electricity demand. This chapter introduces solar radiation and methodology to determine its availability on roofs and facades for utilization.
1.2 The Sun
It is considered that about 4.59 billion years ago the rapid collapse of a hydrogen molecular cloud led to the formation of a third-generation T Tauri population I star called the Sun. The surface contains nearly 92% of hydrogen (on volume basis), 7% of helium and trace quantities of other elements such as iron, nickel, oxygen, silicon, sulfur, magnesium, carbon, neon, calcium and chromium. Figure 1.2 shows the structure of the Sun. Here the Sun behaves like a fluid responsible for heat transfer by convection inside the Sun. The Sun rotates on its axis as a gaseous body in which the rotation of the equator takes about 27 days and the rotation of the polar regions take about 30 days. The Sun's radius is measured from its centre to the edge of the photosphere, which is nearly 7 × 108 m.
The energy radiated by the Sun is due to continuous fusion reactions occurring simultaneously. The most important is the one in which hydrogen molecules combine to form a helium nucleus:
H2 + H2 -> He + 25 MeV (1:1)
The energy is produced in the interior of the solar sphere, which is transferred out to the surface. The average temperature at the surface of the Sun is nearly 5777 Kelvin. The Sun provides energy in the form of sunlight and heat, which are responsible for climatic and weather changes and life on Earth.
1.3 The Earth
The Earth is the only place in the universe where life is known to exist. Scientific evidence indicates that the Earth formed 4.54 × 109 years ago and that life appeared on its surface within 109 years. It is composed mostly of 32.1% iron, 30.1% oxygen, 15.1% silicon, 13.9% magnesium, 2.9% sulfur, 1.8% nickel, 1.5% calcium, 1.4% aluminium and the remaining 1.2% as traces of the other elements. Figure 1.3 shows the structure of the Earth. The Earth behaves like a solid responsible for heat transfer through conduction inside the Earth. The average heat flow from the centre of the Earth is 0.04–0.06 W m-2. About 71% of the surface is covered with oceans and the remaining 29% consists of continents and islands.
The Earth's axis of rotation is tilted 23.451 away from the perpendicular to its orbital plane, which helps in producing seasonal variations with a period of one tropical year (365.24 solar days). The Earth's shape is very close to an oblate spheroid with an average diameter of about 12 742 km. The Earth's orbit around the Sun is an elliptical path (Figure 1.4), which causes the Earth's distance from the Sun to vary over a year. It is on average 1.495 × 1011 m from the Earth. The variation in the distance from the Sun causes the amount of solar radiation received by the Earth to vary by 6% annually.
Sunlight is the Earth's primary source of energy. The existence of blue-green algae marks the beginnings of photosynthesis. As a result of photosynthesis, the level of O2 and O3 in the atmosphere is increased. It blocks ultraviolet solar radiation coming from the Sun and make life possible on the Earth. Nearly one-third of the sunlight is reflected. This is known as Earth's albedo. The Earth receives solar energy at the rate of 5.4 × 1024 J per year.
1.4 Apparent Path of the Sun
The Sun's path refers to the apparent significant seasonal and hourly positional changes of the Sun (and length of daylight) as the Earth rotates and orbits around the Sun. The duration of sunshine is determined by the length of time when the Sun is above the horizon and varies throughout the year as the Earth–Sun geometric relationship changes.
Figure 1.5 (left) shows the Sun's path for the northern hemisphere occurring during the year. On 21st December, the sunshine duration is the shortest of the year and the Sun traces the lowest path in the southern sky, called the winter solstice. The Sun rises not exactly in the east but south of east and sets south of west. Each day after the winter solstice the Sun begins to rise closer to the east and set closer to the west until it rises exactly in the east and sets exactly in the west. On this day, about 21st March, sunshine lasts for 12 hours and is called the spring equinox.
After the spring equinox, the Sun still continues to follow a higher path through the sky with the sunshine duration growing longer. On 21st June, the sunshine duration is the longest and the Sun traces the highest path through the sky and directly above the Tropic of Cancer, called the summer solstice. This day the Sun rises not exactly in the east but north of east and sets north of west. After the summer solstice the Sun follows a lower path through the sky each day until it reaches the point where the sunshine lasts exactly 12 hours. This day is called the autumn (fall) equinox. After the this equinox, the Sun still continues to follow a lower path through the sky, with the sunshine hours growing shorter, until it reaches its lowest path at the winter solstice.
Figure 1.5 (right) shows the Sun's path for the southern hemisphere occurring in the same manner during the year. About 21st June the winter solstice occurs and on 21st December the summer solstice occurs. Note that it is incorrect to say that the summer solstice is the longest day of the year; the fact is that the day is still 24 hours long. However, it is correct to say that the number of sunshine hours is greatest.
The relative position of the Sun is a major factor in the heat gain of buildings and in the performance of solar energy systems. Accurate location-specific knowledge of the Sun's path and climatic conditions are essential for economic decisions about solar collector area, orientation, landscaping, summer shading and the cost-effective use of solar trackers.
1.5 Solar Radiation on the Earth
The radiation intensity on the surface of the Sun is approximately 6.33 × 107 W m-2. The radiation spreads out as the distance squared by the time it travels to the Earth. The radiant energy flux received per second by a surface held normal to the direction of the Sun's rays at the mean Earth–Sun distance, outside the atmosphere, is practically constant throughout the year. This is termed the solar constant and its value adopted by the World Radiation Centre is 1367 W m-2 with an uncertainty of 1%. As the Earth revolves around the Sun in an elliptic path, the extraterrestrial radiation varies as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)
where n is the nth day of the year and Isc = 1367 W m-2. Figure 1.6 shows the annual variation of radiation in the extraterrestrial region.
The Earth is in equilibrium; therefore all gains of incoming energy are approximately equal to all losses of outgoing energy. The total flux of energy entering the Earth's atmosphere is estimated at 174 × 1015 W, which is equal to the product of the solar constant and the area of the Earth's disc (1.28 × 1014 m2) as seen from the Sun. Nearly 30% of the incident solar energy is reflected back into space (20% from clouds, 6% from the atmosphere and 4% from the surface), called the albedo. The remaining 70% of the incident solar energy is absorbed by the Earth and then is re-radiated (64% by the clouds and atmosphere and 6% by the ground). Figure 1.7 shows a schematic representation of the energy exchanges between the Earth's surface, the Earth's atmosphere and outer space. Emissions of greenhouse gases, and other factors such as land-use changes, modify the balance of energy exchange between outer space and the Earth slightly but significantly.
1.6 Variation of Radiation in Extraterrestrial and Terrestrial Regions
The solar irradiance from a black body, either the Sun or the Earth, is a function of wavelength and is governed by Plank's law of radiation, which is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.3)
where Eλb represents the energy emitted per unit area per unit time per unit wavelength (µm) interval at a given wavelength, C1 = 3.74 × 10-16 m2 W and C2 = 0.0143879 mK.
While passing through the Earth's atmosphere, solar radiation is subjected to the mechanisms of atmospheric absorption and scattering. A fraction of the radiation reaching the Earth's surface is reflected back into the atmosphere and is subjected to this atmospheric phenomenon again. The remainder is absorbed by the Earth's surface. Figure 1.8 shows the position of the terrestrial and extraterrestrial regions. The atmospheric absorption is due to ozone (O3), oxygen (O2), nitrogen (N2), carbon dioxide (CO2), carbon monoxide (CO), water vapour and scattering from air molecules, dust and water droplets.
The X-rays and extreme ultraviolet radiation from the Sun are mainly absorbed in the ionosphere by nitrogen, oxygen and other atmospheric gases. Ozone and water vapour largely absorb ultraviolet (λ<0.40 mm) and infrared radiation (lambda]>2.3 µm), respectively. There is almost complete absorption of short-wave radiation (lambda]<0.29 µm) in the atmosphere. Hence, the energy in wavelength radiation below 0.29 µm and above 2.3 µm of the spectrum of solar radiation incident on the Earth's surface is negligible. Scattering by air molecules, water vapour and dust particles results in the attenuation of radiation. Figure 1.8 also shows the range of wavelength radiation emitted from the Sun, the attenuation of its amplitude during propagation from the Sun to the atmosphere and further attenuation of radiation in the atmosphere.
1.7 Terminology Associated with Solar Radiation
In order to evaluate solar radiation on photovoltaic (PV) modules, it is necessary to understand the following definitions.
1.7.1 Air Mass
This is a ratio indicating the amount of atmosphere that light must pass through before reaching an observer on the ground. The standard spectrum outside the Earth's atmosphere is called AM0 and describes solar irradiance in space. The radiation that reaches sea level at high noon in a clear sky is 1000 W m-2 and is described as AM1 (or air mass 1) radiation. The Sun is at zenith and sunlight passes through the least amount of atmosphere to reach the ground. The air mass increases as the angle between the sunlight and the zenith increases (see Figure 1.9). When the Sun is 301 above the horizon, sunlight passes through twice as much atmosphere to reach an observer on the ground, and is described as AM2 (or air mass 2.0). Thus, the relative air mass is a function of the solar elevation angle. Mathematically:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4)
where θz is the zenith angle. At noon, θz = 0; therefore the air mass = 1.
1.7.2 Diffuse Radiation
Diffuse radiation (Id) is the solar radiation scattered by the molecules or suspensoids in the atmosphere and received on the surface after a change in direction (see Figure 1.10). It is also called diffuse skylight or sky radiation and is the reason for changes in the colour of the sky. The rate at which this energy falls on a unit horizontal surface per second is called the diffuse radiation. Under a clear sky at noon it is typically 100 W m-2, but under cloudy conditions it may vary from 300 to 600 W m-2.
1.7.3 Beam or Direct Radiation
Beam radiation (Ib) is the solar irradiance measured at a given location on the Earth with a surface element perpendicular to the Sun's rays, excluding diffuse radiation (see Figure 1.10). It is also called direct radiation. Direct insolation is equal to the solar constant minus the atmospheric losses due to absorption and scattering. While the solar constant varies with the Earth–Sun distance and solar cycles, the losses depend on the air mass, cloud cover, moisture content and other impurities.
1.7.4 Total Radiation or Global Radiation
The sum of beam and diffuse radiations falling on a horizontal surface facing upwards is called the total radiation or the global radiation (symbol I).
1.7.5 Insolation
This is a term applied specifically to solar energy irradiation. The symbol H is used for insolation for a day. The symbol I is used for insolation for an hour.
1.7.6 Irradiance, Radiant Exitance and Emissive Power
These are radiometry terms for the power per unit area of electromagnetic radiation at a surface. Irradiance is the rate at which radiant energy is incident on a surface, per unit area. Radiant exitance or radiant emittance is the rate at which radiant energy leaves a surface per unit area by combined emission, reflection and transmission. Emissive power is the rate at which radiant energy leaves a surface per unit area by emission only.
1.7.7 Latitude
Latitude lines (φ) are the imaginary horizontal lines shown running east-to-west on maps that run either north or south of the equator. Technically, latitude is an angular measurement in degrees ranging from 0° at the equator to 90° at the poles (90°N or + 90° for the North Pole and 90°S or – 90° for the South Pole); see Figure 1.11. The latitude is approximately the angle between the zenith and the Sun at an equinox.
Besides the equator, four other lines of latitude are named because they play important roles in the geometrical relationship of the Earth with the Sun, namely the Arctic Circle (66°33'39"N), the Tropic of Cancer (23°26'21"N), the Tropic of Capricorn (23°26'21"S) and the Antarctic Circle (66°33'39"S).
1.7.8 Longitude
Constant longitude is represented by lines running from the north pole to the south pole of the Earth (see Figure 1.12). The line of longitude that passes through the Royal Observatory, Greenwich, in England, establishes the meaning of zero degrees of longitude, or the prime meridian. Any other longitude is identified by the east–west angle, referenced to the center of the Earth as the vertex, between the intersections with the equator of the meridian through the location in question and the prime meridian.
1.7.9 Solar Time
Universe time is the time ascertain with respect to the zero meridian. It is the same as Greenwich mean time. Standard time is the time reckoned with respect to the standard meridian of a specific time zone. It is the everyday clock time used within each one hour zone. This kind of time is not very useful in trying to locate the exact position of celestial objects.
Apparent solar time or true solar time is the time measured with respect to the Sun. It is based on the daily apparent motion of the Sun across the sky, with solar noon denoting the time the Sun crosses the local meridian. The difference between the solar time and the standard time is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5)
where Lst is the standard meridian for the local time zone, Lloc is the longitude of the location in question (in degrees west) and E is the equation of time (in minutes) which is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6)
where B = (n – 1) 360/365 and n is the day of the year (1 ≤ n ≤ 365).
(Continues...)
Excerpted from Building Integrated Photovoltaic Thermal Systems by Basant Agrawal, G. N. Tiwari. Copyright © 2011 B. Agrawal and G. N. Tiwari. Excerpted by permission of The Royal Society of Chemistry.
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