Solar engineering

The Sun

The sun is a spherical body filled with hot gas and atoms of hydrogen are converted into helium by nuclear fusion, reaching an internal temperature of about 20 million Kelvin. The radiation from its inner core cannot be seen as it is absorbed by the layer of hydrogen ions at the surface.

Fig.1: The Sun [1]

The power that is emitted from the sun composes of different wavelengths which are of high and low-energy photons and can be seen only through a prism. An equilibrium is established when incoming radiation from the sun and that from the Earth surface meet. The presence of the atmosphere maintains the Earth’s temperature and when the level of carbon-dioxide is high, the outgoing radiation starts getting absorbed hence causing global warming

Fig.2: Solar radiation [2]

The Electromagnetic Spectrum

Sunlight forms part of the electromagnetic spectrum and visible light is only a small subset. Light is made of an energy quantum, i.e. light is a wave, as proposed by Planck and later in 1921, Einstein won the Nobel Prize for demonstrating that light is a packet of energy particles, known as photons.

Fig.3: The electromagnetic spectrum [1]

The energy of a photon, E is given by:

where h is the Planck’s constant, c is the speed of light and λ is the wavelength of the light (µm).

h = 6.626 x 10-34 Js

c = 2.998 x 108 m/s

The inverse relationship between photon energy and wavelength implies that for light having high energy photon (blue light), the wavelength is small. The contrary is also true. When energy of particles namely photons and electrons are calculated, the most commonly used unit is the electron-volt (eV) instead of joule (J). One electron-volt is defined as the energy required to raise an electron through one volt. Thus, the energy of a proton is 1.602 × 10-19 J. The photon flux is defined as the number of photons per second per unit area [1].

Solar irradiance

Solar irradiance is defined as the amount of solar energy falling on the Earth’s surface per unit area and per unit time. The sun radiates energy at a rate of 3.85 x 1026 W. Just outside the earth’s atmosphere, solar energy is received, assuming normal incidence at a rate of 1336 W/m2.

Fig.4: Solar energy input to the Earth [3]

The mean distance between the Earth and the Sun is 150 x 106 km. The solar irradiance on an object some distance D from the sun is found by dividing the total power emitted from the sun by the surface area over which the sunlight falls. The total solar radiation emitted by the sun is given by Eradiated, energy radiated by the sun multiplied by the surface area of the sun (4πR2Sun) where Rsun is the radius of the sun. The surface area over which the power from the sun falls will be 4πD2, where D is the distance of the object from the sun. Therefore, the solar radiation intensity, H0 in (W/m2), incident on an object is:

where HSun is the power density at the Sun’s surface in W/m2

HSun = 64 x 106 W/m2 and RSun = 695 x 106 m.

Fig.5: Illustrating the equation for calculating radiation intensity at a body’s surface [1]

Since the speed of light is 3 x 108 m/s, light reaches the earth’s surface in approximately 8 minutes. The solar constant (in W/m2) can be calculated from the sun’s power out by applying the inverse square law. The solar constant is the energy per square meter per day at the outer edge of the atmosphere. The amount that reaches the earth’s surface is less because some is absorbed and some is reflected.

The radiation reaching the earth's surface is given in three different ways:

  1. Global horizontal irradiance (GHI) is the total amount of shortwave radiation received on a horizontal surface.
  2. Direct normal irradiance (DNI) is the portion of GHI that comes in a straight line from the sun.
  3. Diffuse horizontal irradiance (DHI) is that portion of radiation that arrives at the surface from indirect paths.

Atmospheric effects

Atmospheric effects have several impacts on the solar radiation at the Earth's surface. The major effects for photovoltaic applications are:

  1. A reduction in the power of the solar radiation due to absorption, scattering and reflection in the atmosphere;
  2. A change in the spectral content of the solar radiation due to greater absorption or scattering of some wavelengths;
  3. The introduction of a diffuse or indirect component into the solar radiation; and
  4. The local variations in the atmosphere (such as water vapour, clouds and pollution) which have additional effects on the incident power, spectrum and directionality.

Peak sun hours

The solar insolation that a particular location would receive if the sun were shining at its maximum value for a certain number of hours is known as the peak sun hour (PSH). Since the peak solar radiation is 1 kW/m2, the number of peak sun hours is numerically identical to the average daily solar insolation. For example, a location that receives 7.5 kWh/m2 per day can be said to have received 7.5 hours of sun per day at 1 kW/m2 [6].

Fig.6: Peak sun hours [1]

Air mass

The air mass (AM) is the path length which light takes through the atmosphere normalized to the shortest possible path length (that is, when the sun is directly overhead). The Air Mass quantifies the reduction in the power of light as it passes through the atmosphere and is absorbed by air and dust.

where θ is the angle between DHI at solar noon and at one other time of the day.

Motion of the Sun

A sunpath diagram is essential in determining the Sun’s position and the Sun’s elevation as well as any shading phenomena associated with solar panels. It is represented by the:

  1. solar elevation
  2. azimuth angles from sunrise to sunset

Fig.7: Motion of the Sun [3]

Solar elevation

Solar elevation, α(n,t) is the angle between a line collinear with the sun’s rays and the horizontal plane. It varies throughout the day. It also depends on the latitude of a particular location and the day of the year. An important parameter in the design of photovoltaics systems is the maximum elevation angle, that is, the maximum height of the sun in the sky at a particular time of year.

where

L is the latitude of the region.

δs(n) is the solar declination.

hs(t) is the hour angle.

t is the time.

n is the day number with 1st January as day 1.

Fig.8: Elevation and zenith angles [1]

Azimuth angle

Solar azimuth angle, γ(n,t), is the angle between a due south line and the projection of the site to sun line on the horizontal plane. The azimuth angle is like a compass direction with North = 0°and South = 180°.

Fig.9: Azimuth angle [1]

Solar declination

The declination of the sun, δs(n) is the angle between the equator and a line drawn from the center of the Earth to the center of the sun. Declination north of equator is positive and south of equator is negative.

The solar elevation data is critical as this will determine the spaces between two strings of panel. It is directly proportional to the distance between two strings. For a smaller solar elevation angle, the ground coverage ratio (GCR) is higher and this is not desirable. So, depending on the tilt angle also, the appropriate GCR can be met.

Extraterrestrial radiation

The sky clearance index, KT gives the ratio of GHI to extraterrestrial irradiation, G0(n). The higher the index, the lower is the cloud coverage. The extraterrestrial irradiation is measured in kWh/m2 and is given by G0(n) as:

where I0 is the solar constant (1354 W/m2) and ωs(n) is the sunset hour angle which is given by:


References:

[1] “PVEducation.” [Online]. Available: https://www.pveducation.org/pvcdrom.

[2] S. Blumberg, “NASA Looks to Eclipse to Understand Earth’s Energy,” 2017, [Online]. Available: http://www.nasa.gov/feature/goddard/2017/nasa-looks-to-the-solar-eclipse-to-help-understand-the-earth-s-energy-system.

[3] “Four decades and counting: New NASA instrument continues measuring solar energy input to Earth – Climate Change: Vital Signs of the Planet.” [Online]. Available: https://climate.nasa.gov/news/2659/four-decades-and-counting-new-nasa-instrument-continues-measuring-solar-energy-input-to-earth/.