EE 495-695
2.1 Properties of Sunlight
Y. Baghzouz
Professor of Electrical Engineering
Electricity from the Sun
Indirect solar energy conversion (wind, ocean, hydro, fuels,…)
Direct energy conversion: solar cells (PV)
Photovoltaics - history
The first practical photovoltaic devices were

demonstrated in the 1950s.
R&D of photovoltaics received its first major boost from
the space industry in the 1960s for powering satellites.
Solar cells became an interesting scientific variation to
the rapidly expanding silicon transistor development.
It took the oil crisis in the 1970s to focus world attention
for investigating photovoltaics as a means of generating
terrestrial power.
Their application and advantage to the "remote" power
supply area was quickly recognized and prompted the
development of terrestrial photovoltaics industry.
Photovoltaics - history
Small scale applications (such as calculators and
watches) were utilized and remote power applications
began to benefit from photovoltaics.
In the 1980s, research into silicon solar cells paid off
and solar cells began to increase their efficiency.
In 1985 silicon solar cells achieved the milestone of
20% efficiency.
In the 1990s, the photovoltaic industry experienced
steady growth rates of 20%, largely promoted by the
remote power supply market.
Highest Recorded PV Cell Efficiencies
Photovoltaics - history
In the 2000s, the growth rate has been exponential!
Today solar cells are recognized as a means of
diminishing the impact of environmental damage
caused by fossil fuels.
Applications range from power stations of several
megawatts to the ubiquitous solar calculators.
A number of states have renewable portfolio
standards – where the electric utilities are requires to
produce a certain percentage of their electrical
energy they sell from renewable energy sources.
Growth of PV Installations (US)
States with Renewable Portfolio
Standards (RPS)
Properties of Light:
Visible light was viewed as a small subset of the

electromagnetic spectrum since the late 1860s.
The electromagnetic spectrum describes light as a
wave which has a particular wavelength.
Max Planck and Albert Einstein proposed that light is
made up of specific energy elements, or packets of
energy called photons (both won a Nobel prize for
physics in 1918 and 1921 for this work).
Today, quantum-mechanics explains the observation
of the wave nature of light - pictured as a "wavepacket".
Relation between speed of light c (= 3 x 108 m/sec),
wavelength λ (m), and frequency f (Hz) :
f =
c
λ
Photon Energy
A photon is characterized by either a wavelength λ (m)
or an energy E (J).
The relationship between the energy E of a photon
and the wavelength λ of a light is given by:
E=
hc
λ
where h (= 6.626 × 10-34 Joule·sec) is Planck's
constant.
Photon Energy
When dealing with photons or
electrons, a commonly used unit of
energy is the electron-volt (eV) rather
than the joule (J).
An electron-volt is the energy required
to raise an electron through 1 volt.
Thus 1 eV = 1.602 x 10-19 J.
→ A commonly used expression which
relates the energy (eV) and
wavelength (μm) of a photon:
1.24
E (eV ) =
λ ( μm)
Photon flux and power density
The photon flux Φ (# of
photons/m2sec) is defined as the
number of photons striking a unit
area per second.
The power density H (W/m2) is the
product of the photon flux and the
energy E (J) of the photon:
H = φE
For the same power density, blue
light requires fewer photons than
red light. Why?
Spectral Density and radiant power
density
The spectral irradiance F is the most common way of
characterizing a light source.
F gives the power density at a particular wavelength
(W/m2μm)
φE
H
=
F=
λ ( μm) λ ( μm)
The radiant power density is calculated by integrating
the spectral irradiance over all wavelengths emitted by
the source.
H Total = ∫ Fdλ ≈ ∑ Fi Δλi
i
Solar radiation
The sun is a hot sphere of
gas whose internal
temperatures reach over 20
million deg. K.
Nuclear fusion reaction at
the sun's core converts
hydrogen to helium.
The radiation from the inner
core is not visible since it is
absorbed by a layer of
hydrogen atoms closer to the
sun's surface.
Heat is transferred through
this layer by convection
Sun radiation
The total power emitted from the sun is composed many
wavelengths, and appears white or yellow to the human eye.
These different wavelengths can be seen by passing light
through a prism, or water droplets in the case of a rainbow.
Different wavelengths show up as different colors, but not all
the wavelengths can be seen since some are "invisible" to the
human eye.
The radiant power density at the sun’s surface Hsun = 5.961 x
107 W/m2.
Solar radiation in space
The solar irradiance on an object in space decreases
as the object moves further away from the sun.
The solar irradiance Ho on an object some distance D
from the sun is found by
2
⎛R⎞
H 0 = ⎜ ⎟ H sun
⎝D⎠
where R (= 6.955 x 108 m) is the radius of the sun.
Solar radiation intensity in
different planets
Planet
Distance D
(x 109 m)
Solar Radiation
Ho(W/m2)
Mercury
57
9228
Venus
108
2586
Earth
150
1353
Mars
227
586
Jupiter
778
50
Saturn
1426
15
Uranus
2868
4
Neptune
4497
2
Pluto
5806
1
Solar Radiation Outside the Earth’s
Atmosphere.
The actual power density varies slightly since:
the Earth-Sun distance changes as the Earth moves
in its elliptical orbit around the sun,
the sun's emitted power is not constant.
The power variation due to the elliptical orbit is about
3.4%, with the largest solar irradiance in January and
the smallest solar irradiance in July.
An equation which describes the variation through out
the year just outside the earth's atmosphere is:

⎛ 360(n − 2) ⎞
H = H o {1 + 0.033 cos⎜
⎟
⎝ 365 ⎠
where n is the day of the year
Solar Radiation at the Earth's Surface
While the solar radiation incident on the Earth's
atmosphere is relatively constant, the radiation at the
Earth's surface varies widely due to:

atmospheric effects, including absorption and
scattering;
local variations in the atmosphere, such as water
vapor, clouds, and pollution;
latitude of the location; and
the season of the year and the time of day.
The above effects have several impacts on the solar
radiation received at the Earth's surface
These changes include variations in the overall
power received, the spectral content of the light and
the angle from which light is incident on a surface.
Atmospheric Effects
Atmospheric effects have several
impacts on the solar radiation at the
Earth's surface. The major effects for
photovoltaic applications are:

a reduction in the power of the solar
radiation due to absorption, scattering
and reflection in the atmosphere;
a change in the spectral content of the
solar radiation due to greater
absorption or scattering of some
wavelengths;
the introduction of a diffuse or indirect
component into the solar radiation; and
local variations in the atmosphere
(such as water vapor, clouds and
pollution)
Absorption in the Atmosphere
As solar radiation passes through the atmosphere, gasses,
dust and aerosols (e.g., ozone, carbon dioxide, water vapor)
absorb some of the incident photons.

For example, most of the ultraviolet light below 0.3 μm is
absorbed by ozone (but not enough to completely prevent
sunburn!).
The major factor reducing the power from solar radiation is
the absorption and scattering of light due to air molecules
and dust.
This absorption process causes a power reduction,
dependant on the path length through the atmosphere.

When the sun is overhead, the absorption due to these
atmospheric elements causes a relatively uniform reduction
across the visible spectrum, so the incident light appears white.
However, for longer path lengths, higher energy (lower
wavelength) light is more effectively absorbed and scattered.
Hence in the morning and evening the sun appears much
redder and has a lower intensity than in the middle of the day.
Comparison of solar radiation outside the Earth's
atmosphere with that reaching the Earth.
Direct and Diffuse Radiation Due to
Scattering of Incident Light
Light is absorbed as it passes through the atmosphere, and

at the same time it is subject to scattering.
Scattering is caused by molecules (e.g., dust particles) in
the atmosphere. Scattering is particularly effective for short
wavelength light (i.e., blue light).
Scattered light is undirected, and so it appears to be coming
from any region of the sky. This light is called "diffuse" light.
Since diffuse light is primarily "blue" light, the light that
comes from regions of the sky other than where the sun is,
appears blue.
In the absence of scattering in the atmosphere, the sky
would appear black, and the sun would appear as a disk
light source.
On a clear day, about 10% of the total incident solar
radiation is diffuse.
Scattering of incident light
Blue light has a
wavelength similar to
the size of particles in
the atmosphere – thus
scattered.
Red light has a
wavelength that is
larger than most
particles – thus
unaffected
Effect of clouds and other local
variations in the atmosphere
The final effect of the atmosphere on incident solar radiation
is due to local variations in the atmosphere.
Depending on the type of cloud cover, the incident power
can be severely reduced.
An example of heavy cloud cover is shown below.
Air Mass
The Air Mass (AM) is the path length which light takes through the
atmosphere normalized to the shortest possible path length (i.e.,
when the sun is directly overhead).
AM quantifies the reduction in the power of light as it passes
through the atmosphere (due to absorption by air and dust). The Air
Mass is defined as:
1
y
AM ≈
=
cos θ x
where θ is the angle from the vertical (zenith angle).
Air Mass
An easy method to determine the AM is from the
shadow s of a vertical object. Air mass is the length of
the hypotenuse k divided by the object height h:
AM ≈
s +h
⎛s⎞
= 1+ ⎜ ⎟
h
⎝h⎠
2
2
hypotenuse, k
2
θ
Air Mass
The previous calculation for AM assumes that the
atmosphere is a flat horizontal layer.
Because of the curvature of the atmosphere, the air
mass is not quite equal to the atmospheric path length
when the sun is close to the horizon.
At sunrise, the angle of the sun from the vertical position
is 90° and the air mass is infinite, whereas the path
length clearly is not.
An equation which incorporates the curvature of the
earth is:
Standardized Solar Spectrum
The efficiency of a solar cell is sensitive to variations in
both the power and the spectrum of the incident light.
To facilitate an accurate comparison between solar cells
measured at different times and locations, a standard
spectrum and power density has been defined for both
radiation outside the Earth's atmosphere and at the
Earth's surface.

The standard spectrum outside the Earth's atmosphere is
called AM0, because at no stage does the light pass
through the atmosphere. It has an integrated power of
1353 W/m2. This spectrum is typically used to predict the
expected performance of cells in space.
Standardized Solar Spectrum

The standard spectrum at the Earth's surface is called
AM1.5G, (the G stands for global and includes both direct
and diffuse radiation) or AM1.5D (which includes direct
radiation only).

The intensity of AM1.5D radiation can be approximated by
reducing the AM0 spectrum by approximately 30% (due to
absorption and scattering).
The global spectrum is 10% higher than the direct
spectrum.
These calculations give approximately 970 W/m2 for
AM1.5G. However, the standard AM1.5G spectrum has
been rounded to 1kW/m2 for convenience.
Standard Solar Spectrum
(Excel file available on web)
Sunlight Intensity Calculations Based on
the Air Mass
The intensity of the direct component of sunlight
throughout each day can be determined as a function
of air mass from the experimentally determined
equation[1]:
where ID is the intensity on a plane perpendicular to the
sun's rays in units of kW/m2 and AM is the air mass.
The power term of 0.678 is an empirical fit to the
observed data, and takes into account the nonuniformities in the atmospheric layers.
[1] Meinel A.B. and Meinel M.P., "Applied Solar Energy", Addison Wesley Publishing Co., 1976
Sunlight Intensity Calculations Based on
Air Mass
Sunlight intensity increases with the height above sea
level. The spectral content of sunlight also changes
making the sky 'bluer' on high mountains. A simple
empirical fit to observed data is given by[2] :
where a = 0.14 and h is the location height above sea
level in kilometers.
Since the diffuse radiation is still about 10% of the direct
component, the global irradiance on a module
perpendicular to the sun's rays is:
[2] SPECTRAL IRRADIANCE AT DIFFERENT TERRESTRIAL ELEVATIONS", Solar Energy 13, no. 1 (1970) p43-57.
Motion of the sun
The apparent motion of the sun, caused by the rotation
of the Earth about its axis, changes the angle at which
the direct component of light will strike the Earth.
The position of the sun depends on the location of a
point on Earth (latitude and longitude), the time of day
and the time of year.
Motion of the sun
This apparent motion of the sun has a major impact on the
amount of power received by a solar collector.

When the sun's rays are perpendicular to the absorbing surface, the
power density on the surface is equal to the incident power density.
When the module is parallel to the sun's rays, the intensity of light
essentially falls to zero.
For intermediate angles, the relative power density is cos(θ) where θ
is the angle between the sun's rays and the module normal.
Solar time
Local solar time (LST) : 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 Standard Time Meridian (LSTM) is a meridian used for a
particular time zone and is similar to the Prime Meridian, which is
used for Greenwich Mean Time (GMT)..
There are 24 LSTM
spaced evenly by 15o
Solar time
Equation of Time EoT (min) is an empirical equation that corrects
for the eccentricity of the Earth's orbit and the Earth's axial tilt.
where
is in degrees and d is the number of days since the start of the year.
Solar time
The 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 above.
the factor of 4 minutes comes from the fact that the Earth
rotates 1° every 4 minutes.
The Local Solar Time (LST) can be found by using the
previous two corrections to adjust the local time (LT):
Solar time
The Hour Angle (HRA) 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
Declination angle
The declination of the sun is the angle between the
equator and a line drawn from the centre of the Earth
to the centre of the sun.
Declination angle
(Earth as reference)
Despite the fact that the Earth revolves around the sun, it is
simpler to think of the sun revolving around a stationary Earth.
This requires a coordinate transformation. Under this alternative
coordinate system, the sun moves around the Earth.
Declination angle
The declination angle can be calculated by
where d is the day of the year with Jan 1 as d = 1. A more
accurate expression is
The declination angle
is zero at the equinoxes (March 22 and Sept 22),
reaches a maximum of 23.45° on June 22,
reaches a minimum of -23.45° on December 22.
Elevation angle
The elevation (or altitude) angle is the
angular height of the sun in the sky
measured from the horizontal.

The elevation angle is 0° at sunrise and
90° when the sun is directly overhead
(which occurs for example at the equator
on the spring and fall equinoxes).
The elevation angle varies throughout the
day. It also depends on the latitude of a
particular location and the day of the year.
The zenith angle is similar to the
elevation angle, but it is measured
from the vertical rather than from the
horizontal, thus making the zenith
angle = 90° - elevation.
Maximum elevation angle
An important parameter in the design of photovoltaics
systems is the maximum elevation angle, i.e., the maximum
height of the sun in the sky at a particular time of year.
This maximum elevation angle occurs at solar noon and
depends on the latitude angle Φ and declination angle δ:
For northern hemisphere:
For southern hemisphere:
Illustration of maximum elevation angle in some
latitude in the northern hemisphere
Declination angle: δ
Latitude angle of interest: Φ
Zenith angle: ζ = Φ – δ
Elevation angle: α = 90o – ζ = 90o – Φ + δ
Variation of elevation angle
The elevation varies throughout the day according to
the following formula:
To calculate the sunrise and sunset times, the
equation for elevation is set to zero: