Basics of Solar Energy
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Solar Energy
The Sun: Earth’s Energy Source
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The Sun is located about 150x109 m from the Earth at
the center of the Solar System.
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The Sun is a sphere of hot gaseous matter with dia of
1.39x109 m.
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The sun has an effective blackbody temperature of
5777K. The temperature in the central interior regions in
estimated at 8x106 to 40x106K.
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Solar Energy
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The Sun generates a large amount of energy due to a
continuous thermonuclear fusion reaction occurring in its
interior.
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In this interaction Hydrogen combine to form Helium and
the excess energy is released in the form of
electromagnetic radiation.
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Structure of the Sun
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Core: 0 to 0.23R, 90% energy generated.
Convective zone: zone from 0.7 to 1.0R, temperature
5000K , density 10-5 kg/m3
Sunspots: Large dark areas on sun surface.
Photosphere: upper layer of convective zone. This zone
is the source of most solar radiation.
Chromosphere: Gaseous layer, depth 10,000km, high
temperature than photosphere.
Corona: Very low density, very high temperature 106 K.
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The Sun: Earth’s Energy Source
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The total energy emitted by the Sun per unit time (Solar
luminosity) is L0 = 3.9x1026 Watts. The energy flux at the
surface of the Sun is approximately 64 x 106 W/m2 .
The average solar energy flux at the Sun’s surface, a
distance of r0 from its center, is given by the Solar
luminosity (L0) divided by the area of a sphere with a
radius r0:
I0 = L0/4πr02
Sun’s surface temperature is about 5777 K.
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The Sun: Earth’s Energy Source
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Due to the location of the Earth in the solar system , a
range of temperatures exists close to its surface makes
the Earth a habitable planet.
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This temperature range is determined through an
energy balance between the solar radiation absorbed by
the Earth and the energy the Earth sends back into
space.
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The Sun: Earth’s Energy Source
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This process is known as the Earth energy (or radiation)
balance.
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Earth’s internal source of energy, due to radioactive
decay of various elements and due to its warm core, is
much smaller (~3x10-5 times) than the amount received
from the sun.
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Solar Flux in Space
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The energy flux emitted from the Sun spreads over an
increasing spherical surface as it moves into space.
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Because the area of a sphere increases in proportion to
the square of its radius, the radiative energy flux from
the sun decreases as the inverse of the square of the
distance from the Sun.
The solar fluxes at two different distances from the Sun,
I1 and I2, relate to one another as the inverse square of
their distances from it, r1 and r2, that is:
I1/ I2 = (r2/r1)2
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Electromagnetic Energy Transfer
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Solar radiation is energy, traveling through space as
electromagnetic (EM) wave radiation.
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Radiation is a form of energy transfer that does not
require mass exchange or direct contact between the
heat exchanging bodies.
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Radiation involves the propagation of EM energy at the
speed of light
c* = 3x1010 cm/s.
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The speed of light c*, the frequency of the EM waves ν,
and its wavelength λ are linked through the following
relationship:
c* = λν
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Blackbody Radiation
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A body that emits energy over all frequencies in a
continuous manner is called a blackbody.
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Blackbody radiation is a function of temperature and
wavelength.
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This dependence is described in Planck’s law of
radiation, which relates the EM energy flux emitted by a
blackbody to the wavelength and the temperature:
E(T,λ) = C1 /(λ5[ exp(C2 /λT ) − 1] )
Where C1 and C2 are constants λ is the wavelength in m, and T is the absolute
temperature in K
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Blackbody Radiation
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Planck's law states a complex relationship between the
energy flux per unit wavelength, the wavelength, and
the temperature. From it we can derive two more
simplified relationship.
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Wien law, stating the relationship between the
wavelength corresponding to the maximum energy flux
output by a blackbody λmax (in μm) and its absolute
temperature T (in K): .
λmax = 2898/T
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Blackbody Radiation
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Using Wien law and the Earth and Sun average
temperatures 288 and 5780 K, respectively we find that
their λmax correspond to about 10 and 0.5 μm.
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Stefan-Boltzman law stating the relationship between
absolute temperature and the total energy flux emitted
by a blackbody, over the entire wavelength range Ib (in
W/m2)
Ib = σT4
where σ is referred to as the Stefan-Boltzman constant = 5.67 x 10−8 W/m2 K4
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Latitude
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Latitude lines run horizontally, parallel and equally distant
from each other.
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Degrees latitude are numbered from 0° to 90° north and
south.
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Zero degrees is the equator, the imaginary line which
divides our planet into the northern and southern
hemispheres.
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North Pole is 90° north and South Pole and 90° south.
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Each degree of latitude is approximately 69 miles (111
km) apart.
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Longitude
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Longitude lines (meridians) are vertical, converge at the
poles and are widest at the equator (about 69 miles or 111
km apart).
Zero degrees longitude is located at Greenwich, England
(0°).
The degrees continue 180° east and 180° west where
they meet and form the International Date Line in the
Pacific Ocean.
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Circles of Latitudes
i. The Equator (0 deg)
ii. The Antarctic Circle (66deg 33’ S)
iii. The Arctic Circle (66 deg 33’ N)
iv. The Tropic of Capricorn (23 deg 26’ S)
v. The Tropic of Cancer (23 deg 26’ N)
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Solar Energy and the Climate System
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The planets rotate around the Sun in elliptically shaped
orbits with the sun in one of its foci. Aphelion is the orbit
position farthest from the sun and perihelion closest.
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Each orbit is defined by its mean distance from the Sun
(d), by its eccentricity (e) and by its orientation in space.
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Each planet rotates around its axis, which in generally
inclined with the respect to the orbital plane as
measured by the obliquity angle
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Solar Energy and the Climate System
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The rotation rate around the axis determine the length of
the day and,
The planet’s orbital rotation rate determine the length of
its year.
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Eccentricity results in relatively small variations in
incoming radiation, which are not the main reason for
the seasonality.
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Obliquity (Φ) is the main reason for seasonality. If Φ is
different from zero, the lengths of day and night over
most of the planet’s surface are not equal but for two
times during the year, the equinox times.
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Solar Energy and the Climate System
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The difference between the lengths of day and night is
zero on the planet’s equator and changes poleward.
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The days are longer than the night on the hemisphere
tilting towards the Sun leading to more incoming Solar
energy than in the other hemisphere.
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The times of year when the difference between the
lengths of day and night reach their extreme values are
called solstices.
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SOLAR TERMINOLOGIES
for
Solar Energy Calculations
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Irradiance, Irradiation
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Irradiance, G ,The rate at which the radiant energy is
incident on a unit area surface. W/m2
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Irradiation ,The amount incident energy per unit area on a
surface, found by integration of irradiance over specified
time, usually an hour or day, J/m2
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Beam , Diffuse and Total Radiation
The solar radiation arriving at the earth’s surface has two components
1.
Direct: can be focused
2.
Diffused >10%: cannot be focused
(Direct / diffused) ratio : 0.9 Cloudless ,clear day
0.1 completely overcast day
The total irradiance at any surface is the
sum of the two components
Gt = Gbeam +Gdiffused
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Radiosity , Emissive Power
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Radiosity, The rate at which the radiant energy leaves a
surface per unit area surface by emission, reflection,
transmission. W/m2
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Emissive Power , The rate at which the radiant energy
leaves a surface per unit area surface by emission only
W/m2
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Extraterrestrial Radiation (Solar constant)
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Solar constant ( Io ), is the radiation incident outside the
earth's atmosphere. On average, it is 1367 W/m2. This
value varies by ±3% as the earth orbits the sun.
Io = 1367 * (Rav / R)2 W/m2
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where (Rav) is the mean sun-earth distance and (R ) is the actual sun-earth
distance depending on the day of the year
2
 R AV   1.0011  0.034221 * cos(  )  0.00128 * sin(  ) 
R
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0.000719 * cos( 2  )  0.000077 * sin( 2  )
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Where β = 2 π n / 365 and n is the day of the year. For example, January
15 is year day 15 and February 15 is year day 46.
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Solar Insolation
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The solar radiation received on a flat, horizontal surface at a
particular location on earth at a particular instant of time.
W/m2
Depend on;
Daily variation
Seasonal variation
Atmospheric clarity
latitude
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Clarity Index
The ratio of the solar radiation arriving at the earth’s
surface to extraterrestrial radiation.
The monthly average clearness index is the ratio of
monthly average daily solar radiation at the surface to
the monthly average daily extraterrestrial radiation. KT
varies from place to place – from about 0.3 for very
overcast climates to 0.8 for very sunny places.
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Solar Declination (δ)
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Solar Declination is the angle between the Sun's rays
and Earth's equatorial plane.
(Technically, it is the angle between the Earth-Sun
vector and the equatorial plane.)
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Solar Declination
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The Declination angle is 23.5° during the Northern
Summer Solstice, and –23.5° during the Southern
Summer Solstice. It is between ±23.5° the rest of the
year.
Following equations could be used for calculating solar
declination angle δ
Where N is the day in the year
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Solar Declination
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For precise calculation the following equation could
be used
where
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Solar Elevation (Sun height) Angle ( θ )
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The solar elevation angle is the elevation angle of the
sun. That is, the angle between the direction of the sun
and the (idealized) horizon.
It can be calculated, to a good approximation, using the
following formula:
Where
θs is the solar elevation angle,
h is the hour angle of the present time ,
δ is the current sun declination and
Φ is the local latitude
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Solar Time and Local Standard Time
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The system of standard time is based on two facts:
1.
The Earth completes a total rotation on its axis once
every twenty-four hours.
There are 360° of longitude all the way around the
Earth.
2.
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The Earth turns 360° in 24 hours, or at a rate of 15° an
hour.
(360° in a day÷24 hours = 15° an hour)
Each standard meridian is the center of a time zone.
Each time zone is 15° wide.
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Solar Time and Local Standard Time
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The Greenwich Time Zone, for example, is centered on
the Prime Meridian
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This time zone is supposed to be 15° wide and extends
from 7½° W to 7½°E.
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However, the boundaries of standard time don’t exactly
run along meridians. The boundaries have been
changed to fit the borders of countries and even smaller
areas.
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Solar Time and Local Standard Time
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The relationship between solar time and local standard
time is required to describe the position of the sun in
local standard time.
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Local standard time is the same in the entire time zone
whereas solar time relates to the position of the sun with
respect to the observer.
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That difference depends on the exact longitude where
solar time is calculated.
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Solar Time and Local Standard Time
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As the earth moves around the sun, solar time changes
slightly with respect to local standard time.
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This is mainly related to the conservation of angular
momentum as the earth moves around the sun.
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This time difference is called the equation of time and can
be an important factor when determining the position of the
sun for solar energy calculations.
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An approximate formula for the equation of time (Eqt) in
minutes depending upon the location of earth in its orbit
as following;
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Solar Time and Local Standard Time
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Eqt = - 14.2 sin [π (n + 7) / 111] for year day n between 1
and 106
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Eqt = 4.0 sin [π (n - 106) / 59) for year day n between
107 and 166
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Eqt = - 6.5 sin [π( n - 166) / 80) for year day n between 167
and 365
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Solar Time and Local Standard Time
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To adjust solar time for a longitude we have to add the
value resulted from the time equation and to add or
subtract the difference between the local time the clock
time for the time zone.
Tsolar = Tls + Eqt/ 60 ± (Longlocal – Longsm)/15
hours
Where Tsolar is the local solar time,
Tls is the local standard time,
Longlocal is the longitude of the observer in degrees and
Longsm is the longitude for the standard meridian for the observer's time
zone.
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Solar hour angle (h)
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Since the earth rotates approximately once every 24
hours, the hour angle changes by 15 degrees per hour
and moves through 360 degrees over the day.
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Typically, the hour angle is defined to be zero at solar
noon, when the sun is highest in the sky.
h = π * (12 - Tsolar) / 12 , radians
Where Tsolar is the local solar time
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Solar zenith angle (ωs)
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The zenith angle is the opposite angle to the sun height
θs.
ωs = ( 90° – θs).
At a sun height of 90°, the sun is at the zenith and the
zenith angle is therefore zero.
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Air Mass, m
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The ratio of the mass of atmosphere through which
beam radiation passes to the mass it would pass through
if the sun was at the zenith(directly overhead).
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At sea level m =1 when sun is at the zenith.
m=2 for zenith angle is 60o
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For Zenith angles from 0 to 70o at sea level
m = 1/ cosθ
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Sun azimuth (αS)
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The sun azimuth (αS ) is the angle, measured clockwise,
between geographical North and the point on the
horizon directly below the sun.
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Solar Radiation on Earth Surface
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The amount of direct radiation on a horizontal surface
can be calculated by multiplying the direct normal
irradiance times the cosine of the zenith angle (ω).
On a surface tilted (T) degrees from the horizontal and
rotated ( γ ) degrees from the north-south axis, the direct
component on the tilted surface is determined by
multiplying the direct normal irradiance by the following
value for the cosine of the incidence angle (θ ) ;
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Solar Radiation on Earth Surface
cos (θ) = sin(δ)sin(λ)cos(T) - sin(δ)cos(λ)sin(T)cos(γ)
+cos(δ)cos(l)cos(T)cos(h)
+cos(δ)sin(λ)sin(T)cos(γ)cos(h)
+cos(δ)sin(T)sin(γ)sin(h)
where
λ is the latitude of the location of
interest,
δ is the sun declination and
h is the hour angle .
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Thank you
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Solar Energy Flux
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Earth energy (or radiation) balance.
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The Sun: Earth’s Energy Source
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Solar Flux in Space
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Latitude and Longitude
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Latitude and Longitude
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Circles of Latitude
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Circles of Latitude
i. The Equator (00)
ii. The Antarctic Circle (66o 33’ S)
iii. The Arctic Circle (66o 33’ N)
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Circles of Latitude
The Arctic Circle (66o 33’ N)
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Circles of Latitude
iii. The Tropic of Capricorn (23o 26’ S)
iv. The Tropic of Cancer (23o 26’ N)
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Earth in Orbits
Distance from Sun d = 150x109 m,
eccentricity e = (a-b)/(a+b) = 0.017,
axis tilt Φ = 23.5°, Solar Flux (I0) = 1367 W/m2
perihelion (147 million km), aphelion (152 million km).
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Earth in Orbits
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Earth in Orbit
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Electromagnetic Energy Transfer
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Electromagnetic Energy Transfer
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Blackbody Radiation
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Solar Declination (δ), Elevation (γ )
and Zenith (ω)
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