Basics of Solar Energy

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Basics of Solar Energy
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The Sun Earths Energy Source

• The Sun is located about 150x109 m from the Earth
  at the center of the Solar System.
• The Sun is a sphere of hot gaseous matter with
  dia of 1.39x109 m.
• 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

• The Sun generates a large amount of energy due to
  a continuous thermonuclear fusion reaction
  occurring in its interior.
• 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

• 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 Earths Energy Source

• 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 Suns
  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 L0/4pr02
• Suns surface temperature is about 5777 K.

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The Sun Earths Energy Source

• 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.

• 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 Earths Energy Source

• This process is known as the Earth energy (or
  radiation) balance.

• Earths 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

• The energy flux emitted from the Sun spreads over
  an increasing spherical surface as it moves into
  space.
• 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

• Solar radiation is energy, traveling through
  space as electromagnetic (EM) wave radiation.
• Radiation is a form of energy transfer that does
  not require mass exchange or direct contact
  between the heat exchanging bodies.
• Radiation involves the propagation of EM energy
  at the speed of light c 3x1010 cm/s.
• The speed of light c, the frequency of the EM
  waves ?, and its wavelength ? are linked through
  the following relationship c ??

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Blackbody Radiation

• A body that emits energy over all frequencies in
  a continuous manner is called a blackbody.
• Blackbody radiation is a function of temperature
  and wavelength.
• This dependence is described in Plancks law of
  radiation, which relates the EM energy flux
  emitted by a blackbody to the wavelength and the
  temperature
• E(T,?) C1 /(?5 exp(C2 /?T ) - 1 )
• Where C1 and C2 are constants ? is the
  wavelength in m, and T is the absolute
  temperature in K

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Blackbody Radiation

• 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.
• Wien law, stating the relationship between the
  wavelength corresponding to the maximum energy
  flux output by a blackbody ?max (in µm) and its
  absolute temperature T (in K) .
• ?max 2898/T

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Blackbody Radiation

• Using Wien law and the Earth and Sun average
  temperatures 288 and 5780 K, respectively we find
  that their ?max correspond to about 10 and 0.5
  µm.
• 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 sT4
• where s is referred to as the Stefan-Boltzman
  constant 5.67 x 10-8 W/m2 K4

13
Latitude

• Latitude lines run horizontally, parallel and
  equally distant from each other.
• Degrees latitude are numbered from 0 to 90
  north and south.
• Zero degrees is the equator, the imaginary line
  which divides our planet into the northern and
  southern hemispheres.
• North Pole is 90 north and South Pole and 90
  south.
• Each degree of latitude is approximately 69 miles
  (111 km) apart.

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Longitude

• 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

1. The Equator (0 deg)
2. The Antarctic Circle (66deg 33 S)
3. 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

• 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.
• Each orbit is defined by its mean distance from
  the Sun (d), by its eccentricity (e) and by its
  orientation in space.
• 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

• The rotation rate around the axis determine the
  length of the day and,
• The planets orbital rotation rate determine the
  length of its year.
• Eccentricity results in relatively small
  variations in incoming radiation, which are not
  the main reason for the seasonality.
• Obliquity (F) is the main reason for seasonality.
  If F is different from zero, the lengths of day
  and night over most of the planets surface are
  not equal but for two times during the year, the
  equinox times.

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Solar Energy and the Climate System

• The difference between the lengths of day and
  night is zero on the planets equator and changes
  poleward.
• 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.
• The times of year when the difference between the
  lengths of day and night reach their extreme
  values are called solstices.

19

• SOLAR TERMINOLOGIES
• for
• Solar Energy Calculations

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Irradiance, Irradiation

• Irradiance, G ,The rate at which the radiant
  energy is incident on a unit area surface. W/m2
• 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 earths
  surface has two components
• Direct can be focused
• Diffused gt10 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

• Radiosity, The rate at which the radiant energy
  leaves a
• surface per unit area surface by emission,
  reflection, transmission. W/m2
• 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)

• 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
• where (Rav) is the mean sun-earth distance and (R
  ) is the actual sun-earth distance depending on
  the day of the year
• Where ß 2 p 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

• 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
  earths 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 (d)
 

• 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

• 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 d

Where N is the day in the year
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Solar Declination

• For precise calculation the following equation
  could be used

where
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Solar Elevation (Sun height) Angle ( ? )

• 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
• ?s is the solar elevation angle,
• h is the hour angle of the present time ,
• d is the current sun declination and
• F is the local latitude

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Solar Time and Local Standard Time

• 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.

1. There are 360 of longitude all the way around
   the Earth.

• The Earth turns 360 in 24 hours, or at a rate of
  15 an hour.

(360 in a day24 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

• The Greenwich Time Zone, for example, is centered
  on the Prime Meridian

• This time zone is supposed to be 15 wide and
  extends from 7½ W to 7½E.

• However, the boundaries of standard time dont
  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

• The relationship between solar time and local
  standard time is required to describe the
  position of the sun in local standard time.

• 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.

• That difference depends on the exact longitude
  where solar time is calculated.

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Solar Time and Local Standard Time

• As the earth moves around the sun, solar time
  changes slightly with respect to local standard
  time.

• This is mainly related to the conservation of
  angular momentum as the earth moves around the
  sun.

• 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.

• 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

• Eqt - 14.2 sin p (n 7) / 111 for year day
  n between 1 and 106

• Eqt 4.0 sin p (n - 106) / 59) for year day n
  between 107 and 166

• Eqt - 6.5 sin p( n - 166) / 80) for year day
  n between 167 and 365

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Solar Time and Local Standard Time

• 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)

• 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.

• Typically, the hour angle is defined to be zero
  at solar noon, when the sun is highest in the sky.

h p (12 - Tsolar) / 12 , radians
Where Tsolar is the local solar time
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Solar zenith angle (?s)

• The zenith angle is the opposite angle to the sun
  height ?s.
• ?s ( 90 ?s).
• 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

• 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).
• At sea level m 1 when sun is at the zenith.
• m2 for zenith angle is 60o
• For Zenith angles from 0 to 70o at sea level
• m 1/ cos?

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Sun azimuth (aS)

• The sun azimuth (aS ) 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

• 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 (?).

• On a surface tilted (T) degrees from the
  horizontal and rotated ( ? ) 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 (? )

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Solar Radiation on Earth Surface
cos (?) sin(d)sin(?)cos(T) - sin(d)cos(?)sin(T)c
os(?)
cos(d)cos(l)cos(T)cos(h)
cos(d)sin(?)sin(T)cos(?)cos(h)
cos(d)sin(T)sin(?)sin(h)
where ? is the latitude of the location of
interest, d 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 Earths 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

1. The Equator (00)
2. The Antarctic Circle (66o 33 S)
3. 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)/(ab) 0.017, axis tilt F 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 (d), Elevation (? ) and Zenith
(?)
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