SUN RADIATION

SUN RADIATION
MAGISTER TEKNIK ELEKTRO

PROPERTIES OF LIGHT
Sunlight is a form of
"electromagnetic radiation" and the
visible light that we see is a small subset
of the electromagnetic spectrum shown
at the right.
Light as a wave stated in the early 1800s
Planck:
total energy of light is made up of
indistinguishable energy elements, or a
quanta of energy.
Einstein, distinguished the values of these
quantum energy elements.
MAGISTER TEKNIK ELEKTRO

Light may be viewed as consisting of "packets" or particles of energy,
called photons.
wave-particle wave particle duality
Key characteristics of the incident solar energy :
the spectral content of the incident light
the radiant power density from the sun;
the angle at which the incident solar radiation strikes a
photovoltaic module;
the radiant energy from the sun throughout a year or day for
a particular surface.
MAGISTER TEKNIK ELEKTRO

SUN
The sun is a hot sphere of gas whose internal temperatures
reach over 20 million degrees kelvin due to nuclear fusion
reactions at the sun's core which convert hydrogen to helium.
The total power emitted by the sun is calculated by multiplying
the emitted power density by the surface area of the sun which
gives 9.5 x 1025 W
Only a fraction of the total power emitted by the sun impinges on
an object in space which is some distance from the sun. The
solar irradiance (H0 in W/m2) is the power density incident on an
object due to illumination from the sun.
MAGISTER TEKNIK ELEKTRO

The solar radiation intensity, H 0 in (W/m 2 ), incident on an object is:
H
0 =
R
2
sun
H
2 sun
D
where:
H sun is the power density at the sun's surface (in W/m 2 ) as determined by
Stefan-Boltzmann's blackbody equation;
R sun is the radius of the sun in meters as shown in the figure below; and
D is the distance from the sun in meters as shown in the figure below.
MAGISTER TEKNIK ELEKTRO

The table below gives standardised values for the radiation at
each of the planets.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Distance
(x 10 9 m)
57
108
150
227
778
1426
2868
4497
5806
MAGISTER TEKNIK ELEKTRO
Solar Constant
(W/m 2 )
9228
2586
1353
586
50
15
4
2
1

SOLAR RADIATION OUTSIDE THE EARTH
MAGISTER TEKNIK ELEKTRO
The solar radiation outside the
earth's atmosphere is calculated
using the radiant power density
(H sun ) at the sun's surface (5.961 x
107 W/m2), the radius of the sun
(R sun ), and the distance between the
earth and the sun. The calculated
solar irradiance at the Earth's
atmosphere is about 1.36 kW/m2.
The actual power density varies slightly since the Earth-Sun
distance changes as the Earth moves in its elliptical orbit around
the sun, and because the sun's emitted power is not constant.
The power variation due to the elliptical orbit is about 3.4%,

An equation describe the variation through out the year just outside the
earth atmosphere:
H
H
const
=
1
+
0.
033
cos(
360
( n
365
where:
H is the radiant power density outside the Earth's atmosphere (in W/m2);
H const is the value of the solar constant, 1.353 kW/m2; and
n is the day of the year.
−
2)
MAGISTER TEKNIK ELEKTRO
)

SOLAR RADIATION ON THE EARTH’S EARTH S SURFACE
The radiation at the Earth's surface varies widely due to:
oatmospheric effects, including absorption and scattering;
olocal variations in the atmosphere, such as water vapour, clouds,
and pollution;
olatitude of the location; and
othe season of the year and the time of day.
The amount of energy reaching the surface of the Earth every hour is
greater than the amount of energy used by the Earth's population
over an entire year.
MAGISTER TEKNIK ELEKTRO

ATMOSPHERIC EFFECTS
The major effects for photovoltaic applications
are:
a reduction in the power of solar radiation due
to absorption, scattering, reflection in the
atmosphere
a change in the spectral content of the solar
radiation due to greater absorption or scattering
of some wavelengths
local variation in the atmosphere (water vapour,
clouds and pollution) which have additional effect
on the incident power, spectrum and directional
MAGISTER TEKNIK ELEKTRO

EFFECT OF AIR MASS
The Air Mass quantifies the reduction in the power of light as it
passes through the atmosphere and is absorbed by air and dust.
The Air Mass is defined as:
AM
=
1
cos( θ )
where θ is the angle from
the vertical (zenith angle).
When the sun is directly
overhead, the Air Mass is 1.
MAGISTER TEKNIK ELEKTRO

An easy method to determine the air
mass is from the shadow of a vertical pole
AM
=
⎛ s ⎞
1 + ⎜ ⎟
⎝ h ⎠
assuming the atmosphere is flat layer
2
MAGISTER TEKNIK ELEKTRO

SOLAR TIME
LOCAL SOLAR TIME (LST) & LOCAL TIME (LT)
Twelve noon local solar time (LST) is defined as when the sun is highest
in the sky.
Local time (LT) usually varies from LST because of the eccentricity of the
Earth's orbit, and because of human adjustments such as time zones and
daylight saving.
LOCAL STANDART TIME MERIDIAN (LSTM)
The Local Standard Time Meridian
(LSTM) is a reference meridian used
for a particular time zone and is
similar to the Prime Meridian, which is
used for Greenwich Mean Time.
MAGISTER TEKNIK ELEKTRO
The LSTM is calculated by:
LSTM = . Δ
15 0
TGMT
where ∆T GMT is the difference of the Local Time (LT) from Greenwich
Mean Time (GMT) in hours. 15°= 360°/24 hours

EQUATION OF TIME
The equation of time (EoT) (in minutes) is an empirical equation that
corrects for the eccentricity of the Earth's orbit and the Earth's axial
tilt.
EoT = 9. 87sin(
2B)
− 7.
53COS(
B)
−1.
5sin(
B)
where
360
B = ( d − 81)
365
The time correction EoT is plotted
in degrees and d is the number of
days since the start of the year
MAGISTER TEKNIK ELEKTRO

TIME CORRECTION FACTOR
TC = 4(
LSTM − Longitude)
+
EoT
The net Time Correction Factor (in minutes) accounts for the variation of
the Local Solar Time (LST) within a given time zone due to the longitude
variations within the time zone and also incorporates the EoT
The factor of 4 minutes comes from the fact that the Earth rotates
1° every 4 minutes
LOCAL SOLAR TIME LST= LT + TC
HOUR ANGLE (HRA)
HRA= 15 0 (LST – 12)
The Hour Angle converts the local solar time (LST) into the
number of degrees which the sun moves across the sky. By
definition, the Hour Angle is 0° at solar noon. Since the Earth
rotates 15° per hour, each hour away from solar noon corresponds
to an angular motion of the sun in the sky of 15°. In the morning
the hour angle is negative, in the afternoon the hour angle is
positive.
MAGISTER TEKNIK ELEKTRO

Latitude of interest ϕ
Equator
Axis parallel to
the sunlight
ELEVATION ANGLE
Earth
δ
ϕ
δ
North
zenith angle
The elevation angle can be calculate as:
α
MAGISTER TEKNIK ELEKTRO
The zenith angle is the angle
between the sun and the vertical.
zenith = 90° -elevation.
ζ=ϕ-δ
Elevation angle
sin 1 −
[ sin δ sin φ + cos cos( HRA)
]
Elevation =
δ

ELEVATION ANGLE
To calculate the sunrise and sunset time the equation for elevation is
set to zero and the elevation equation
1 −1⎡
sinφ
sin γ ⎤ TC
Sunrise = 12 − cos
−
0 ⎢ ⎥
15 ⎣cosφ
cosδ
⎦ 60
1 −1⎡
sinφ
sinδ
⎤ TC
Sunrise = 12 + cos
−
0 ⎢ ⎥
15 ⎣cosφ
cosδ
⎦ 60
MAGISTER TEKNIK ELEKTRO

AZIMUTH ANGLE
The azimuth angle is the compass direction from which the sunlight is
coming
Azimuth
=
−
cos 1
⎡sinδ cosφ
− cosγ
sinφ
cos( HRA)
⎢
⎣
cosα
MAGISTER TEKNIK ELEKTRO
⎤
⎥
⎦

SOLAR RADIATION ON TILTED SURFACE
The power incident on a PV module depends on:
•the power contained in the sunlight
•the angle between the module and the sun.
The power density will always be at its maximum when the PV module is
perpendicular to the sun
However, as the angle between the sun and a fixed surface is continually
changing, the power density on a fixed PV module is less than that of the
incident sunlight.
MAGISTER TEKNIK ELEKTRO
continued

The figure shows how to calculate the radiation incident on a
titled surface (S module ) given either the solar radiation measured
on horizontal surface (S horiz ) or the solar radiation measured
perpendicular to the sun (S incident ).
The equations:
S horizontal = S incident sinα
S module = S incident sin (α + β)
where
α is the elevation angle (α = 90-ϕ+∂ ) latitude + declination angle
β is the tilt angle of the module measured from
the horizontal.
Therefore:
S
module
S
= horizontal
sinα
MAGISTER TEKNIK ELEKTRO
sin( α + β )
0 ⎡360
⎤
δ = 23.
45 sin⎢
( 284 + d)
⎥
⎣365
⎦

USING VECTOR TO CALCULATE SOLAR DIRECTION
As the number of tilts and orientations become more complicated it is
often easier to convert the solar directions of azimuth and elevation to
vectors.
S module = S incident cosγ = S incident S.N
MAGISTER TEKNIK ELEKTRO