The Sun as an Energy Resource
The sun is the source of the life on our planet Earth and, directly or
indirectly, is the fuel for most renewable systems. Photovoltaic and solar
thermal systems, as well as solar thermal power stations, convert solar
irradiation directly into useable energy. Continuing our Fundamentals
series, Volker Quaschning gives an overview of the solar energy resource.
The sun is made up of about 80% hydrogen, 20% helium and only 0.1% other elements.
Its radiant power comes from nuclear fusion processes, during which the sun loses
4.3 million tonnes of mass each second. This mass is converted into radiant energy.
Each square metre of the sun’s surface emits a radiant power of 63.1 MW, which
means that just a fifth of a square kilometre of the sun’s surface emits an
amount of energy equal to the global primary energy demand on earth.
Fortunately, only a small part of this energy reaches the earth’s surface. Solar
irradiance decreases with the square of the distance to the sun. Since the distance
of the earth to the sun changes during the year, solar irradiance outside the earth’s
atmosphere also varies between 1325 W/m˛ and 1420 W/m˛. The annual mean solar
irradiance is known as the solar constant and is 1367±2 W/m˛. On Mars, which is
further from the sun than Earth, solar irradiance is below 600 W/m˛ – a factor to
be considered when designing PV-powered satellites for the Mars orbit. Only a surface that is
perpendicular to the incoming sun’s rays receives this level of irradiance.
Outside the atmosphere, and therefore not subject to its influence, solar irradiance
has only a direct component – all solar radiation is virtually parallel. This irradiance
is also called direct normal or beam irradiance Ebeam.
Under these conditions, a
surface that is oriented parallel to the sun’s rays receives no irradiance. (The specific
direct solar irradiance Edir that reaches an inclined surface is lower depending on
the cosine of the angle of incidence q:
Edir = Ebeam·cos q.)
Irradiance, Irradiation and Illuminance
Various different terms are used when dealing with solar radiation. However,
these terms are often used incorrectly, even by some solar specialists.
The total specific radiant power, or radiant flux, per area that reaches a
Spectrum AM 0 (extraterrestrial) Spectrum AM 1.5 (terrestrial)
receiver surface is called irradiance. Irradiance is measured in W/m˛ and has
the symbol E. When integrating the irradiance over a certain time period it
becomes solar irradiation. Irradiation is measured in either J/m˛ or Wh/m˛, and
represented by the symbol H. For daylighting purposes, only the
visible part of the sunlight is considered. The analogous quantity to the irradiance
for visible light is the illuminance. This uses the unit lm/m˛ (lumen/m˛) or lx (lux).
It is the surface temperature of the sun that mainly characterizes the solar
spectrum. This spectrum defines the corresponding spectral irradiance for all
wavelengths of sunlight. Visible light, with wavelengths between 0.4 µm and
0.75 µm, has a 46% share of the spectrum, infrared light 47%, and
ultraviolet light only 7% (see Figure 1). The earth’s atmosphere reduces the
irradiance that reaches the earth’s surface. Ozone, water vapour and carbon dioxide
absorb radiation with certain wavelengths as it passes through the atmosphere. The
significant reduction in mainly the ultraviolet and infrared parts of the
spectrum is a result of this absorption.
FIGURE 1. Extraterrestrial and terrestrial spectrum of sunlight
Direct and Diffuse Irradiance
Other atmospheric particles reflect or scatter sunlight. Only a part of the
extraterrestrial beam irradiance reaches the earth’s surface directly (see Figure 2).
The scattered part of the irradiance has no direction. Only direct irradiance can be
used for concentrating solar systems, but non-concentrating systems can also use
the scattered, or diffuse irradiance. The so-called global irradiance Eg on a
horizontal surface on earth consists of the direct Edir and diffuse irradiance
Edif. On a tilted plane, there is another irradiance component
Eref, which is that component reflected from the ground.
The average ground reflection is about 20% of the global irradiance. Hence, the
irradiance Etilt on the tilted plane consists of three components,
Etilt = Edir + Edif + Eref.
A surface perpendicular to the incoming direct sunlight usually gets the highest
possible irradiance. Normally, it is below 1000 W/m˛; higher values are only
possible in particular situations, such as if snow or clouds reflect sunlight onto the
FIGURE 2. Sunlight passing through the atmosphere
If the sun is perpendicular to the earth’s surface, sunlight only has to pass through
the air mass (AM) of the atmosphere once. Therefore, this state is called AM 1. In all
other cases, the route of the solar radiation through the atmosphere is longer.
This way depends on the sun’s height. AM 2 indicates that the path of the
sunlight through the atmosphere is twice AM 1. This is the case if the sun is 30°
above the horizon (gS = 30°). In general, the
definition of the air mass is AM = 1/sin(gS).
Figure 3 shows the variation of the air mass during the year for Berlin and Cairo
at solar noon – that is, the time during a day with the highest sun elevation, which
depends on longitude, latitude and date. It is obvious that in Cairo the air mass is
always lower than in Berlin.
FIGURE 3. Position of the sun and AM values at solar noon for various days in Berlin, Germany and Cairo, Egypt
Position of the Sun
The optimum tilt angle for solar systems depends on the position of the sun. Two
angles define this position:
1. Sun height, height angle, solar altitude angle or elevation gS
This is the angle between a line that points from the site towards the centre of the
sun, and the horizon (see Figure 4). The zenith angle is the opposite angle to the
sun height (90° – gS).
At a sun height of 90°, the sun is at the zenith and the zenith
angle is therefore zero.
2. 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 (at the end of a line running from the centre of the sun to the horizon).
(Another definition is sometimes used, whereby the definition of the sun height
remains the same but the sun azimuth is counted as zero when the sun is in the
South and measured anticlockwise.Sometimes the symbols of azimuth and
sun height are also interchanged.)
The calculation of the position of the sun is rather complicated. It is mainly
influenced by the earth’s orbit around the sun and the rotation of the earth. If the
sun’s height is very low, the visible position of the sun varies from the real position due
to refraction of sunlight in the atmosphere. However, some algorithms have been
developed to calculate the position of the sun with accuracies better than 0.1°. (A
free on-line tool to estimate the position of the sun with three different algorithms can
be found at
FIGURE 4. Definition of the angles for the description of the position of the sun
Optimal Solar System Orientation
Figure 5 visualizes the sun angles, azimuth and tilt angle to define the position of a
tilted surface. The angle of incidence q depends on all these angles.
As mentioned above, the maximum irradiance can usually be obtained by a surface that
is perpendicular to the sun. Since the position of the sun changes during the day
and year, only a two-axis tracked surface gets the maximum irradiation. The
annual irradiation can be more than 30% higher than on a non-tracked surface, while for a
one-axis tracked surface the irradiation gain will be in the range of 20%. Near the
equator, the optimal orientation of a non-tracked surface is nearly horizontal. In the
Northern Hemisphere, it should be tilted towards the south, and in the southern
hemisphere, towards the north. The optimal tilt angle increases with higher
latitudes, and is higher in winter than in summer.
FIGURE 5. Angles to define the position of the sun and the orientation of a tilted plane
Outside the atmosphere, the annual solar irradiation is about 12,000 kWh/m˛ (8760 h
at 1367 W/m˛). At every site on the earth, half of the year is night, with no sunshine.
The atmosphere reduces the irradiance at least by 25%. Clouds and dust cause a
further reduction. The best sites on earth, in extreme desert areas, receive an
annual solar irradiation which can be more than 2500 kWh/m˛. On the other hand,
there are cloudy sites at high latitudes with an annual irradiation far below 1000
kWh/m˛. On-site measurements are the only way to estimate the solar potential for
solar systems. Different types of sensors exist to measure the solar irradiance.
A pyranometer measures the global irradiance. Different designs offer different
levels of accuracy (see photographs). Low-cost pyranometers use silicon
sensors with a small photovoltaic cell that generates an electrical current that is
nearly proportional to the solar irradiance. However, these sensors measure only part
of the solar spectrum – they cannot sense infrared light. The annual accuracy of
these sensors is limited because the spectrum changes with the air mass.
In the ideal case error margins be of the order of 5%.
More precise pyranometers use a black receiver plate that is mounted below
a double glass dome. This plate heats up depending on the incoming irradiance. A
thermocouple converts the heat difference between the plate and its surroundings
into a voltage signal that is proportional to the irradiance. These sensors can obtain
annual error margins of less than 3%.
To measure the direct normal or beam irradiance, the sensor is mounted inside
the end of an absorber tube (this tube keeps the diffuse irradiance away). This
so-called pyrheliometer has to be mounted on a two-axis tracker that follows the sun
very accurately. If a shading ball, or shading ring, permanently shades a
pyranometer, it measures the diffuse irradiance since direct irradiance is kept
However, careful maintenance of all sensors is necessary in order to obtain
high levels of accuracy. Dust on the sensors, inaccurate trackers or dirt can
reduce the measurement quality significantly. In the worst case,
measurements can be totally useless!
Sensors for solar irradiance measurements
Pyranometer with thermal sensor for global irradiance measurements (left top)
Two-axis tracked pyrheliometer for direct normal irradiance measurements (left bottom)
Pyranometer with shading ball for diffuse irradiance measurements (right)
Meteorological satellites can also provide irradiance data. Half-hourly meteorological
images are compared with clear sky pictures. The result is a cloud index for the
whole satellite image. Finally, models that consider the position of the sun, water
vapour and aerosols provide the reduction of the extraterrestrial irradiance on the way
through the atmosphere. The annual accuracy of satellite measurements
compared with ground measurements is not bad, and can exceed 5%.
Solar Irradiance Data Sources
Since the variation of annual irradiations from year to year can be well over 20%, a
measurement period should cover at least 7–10 years. Carrying out a measurement
campaign over such a long time period is unlikely to be possible before planning and
installing a solar system, so irradiance data can be taken from existing
databases. Local irradiance maps or atlases offer information on annual or
monthly irradiance. In many cases, local weather services can provide very
detailed data. However, this data is rarely available free. The Meteonorm software
(www.meteotest.ch) includes the largest
commercially available database of irradiance data with some thousands of
sites around the world. Some internet databases offer free irradiance data, while
the US National Renewable Energy Laboratory provides 239 free hourly data
sets of the US
The World Radiation Data Centre
NASA surface meteorology resource website
offer additional global irradiance data.
Finally, the European projects S@tel-light
(www.satellight.com) and SoDa
exhaustive data for Europe.
With irradiance data that describe the availability of the fuel for solar systems the
planning and prediction of the energy yield of solar systems is possible. These
aspects will be discussed in later articles in this series.