18.1
18
Location issues
In Chapter 5 we discussed solar radiation on Earth. There, we introduced the AM1.5
spectrum, which is used to evaluate the performance of solar cells and modules in
laboratories and industry. The AM1.5 spectrum represents the solar irradiance if the centre
of the solar disc is at an angle of 41.8° above the horizon.
Of course the Sun is not always at this position; the position is dependent on the time
of the day and the year, and also on the location on Earth. In this chapter we will discuss
how to calculate the position of the Sun at every location on Earth at an arbitrary time and
date. Furthermore we will discuss scattering of sunlight when it traverses the atmosphere
and how this influences the direct and diffuse spectra. We will also discuss the influence
of the mounting angle and position of a PV module on the irradiance at the module.
The position of the Sun
When planning a PV system it is crucial to know the position of the Sun in the sky at the
location of the solar system at a given time. In this section we explain how this position
can be calculated.
Since celestial objects like the Sun, the Moon and the stars are very far away from the
Earth it is convenient to describe their motion projected on a sphere with arbitrary radius
and concentric to the Earth. This sphere is called the celestial sphere. The position of
every celestial object thus can be parameterized by two angles. For photovoltaic
applications it is most convenient to use the horizontal coordinate system, where the
horizon of the observer constitutes the fundamental plane. In this coordinate system, the
position of the Sun is expressed by two angles that are illustrated in Figure 18.1. The
altitude a is the angular elevation of the centre of the solar disc above the horizontal plane.
Its angular range a ϵ [−90°, 90°], where negative angles correspond to the object being
below the horizon and thus not visible. The azimuth A is the angle between the line of
sight projected on the horizontal plane and due North. It is counted eastward, such that A =
0°, 90°, 180°, 270° correspond to due North, East, South and West, respectively. Its
angular range is A ∈ [0°, 360°]. In a different convention also used by the PV community,
18
Location issues
In Chapter 5 we discussed solar radiation on Earth. There, we introduced the AM1.5
spectrum, which is used to evaluate the performance of solar cells and modules in
laboratories and industry. The AM1.5 spectrum represents the solar irradiance if the centre
of the solar disc is at an angle of 41.8° above the horizon.
Of course the Sun is not always at this position; the position is dependent on the time
of the day and the year, and also on the location on Earth. In this chapter we will discuss
how to calculate the position of the Sun at every location on Earth at an arbitrary time and
date. Furthermore we will discuss scattering of sunlight when it traverses the atmosphere
and how this influences the direct and diffuse spectra. We will also discuss the influence
of the mounting angle and position of a PV module on the irradiance at the module.
The position of the Sun
When planning a PV system it is crucial to know the position of the Sun in the sky at the
location of the solar system at a given time. In this section we explain how this position
can be calculated.
Since celestial objects like the Sun, the Moon and the stars are very far away from the
Earth it is convenient to describe their motion projected on a sphere with arbitrary radius
and concentric to the Earth. This sphere is called the celestial sphere. The position of
every celestial object thus can be parameterized by two angles. For photovoltaic
applications it is most convenient to use the horizontal coordinate system, where the
horizon of the observer constitutes the fundamental plane. In this coordinate system, the
position of the Sun is expressed by two angles that are illustrated in Figure 18.1. The
altitude a is the angular elevation of the centre of the solar disc above the horizontal plane.
Its angular range a ϵ [−90°, 90°], where negative angles correspond to the object being
below the horizon and thus not visible. The azimuth A is the angle between the line of
sight projected on the horizontal plane and due North. It is counted eastward, such that A =
0°, 90°, 180°, 270° correspond to due North, East, South and West, respectively. Its
angular range is A ∈ [0°, 360°]. In a different convention also used by the PV community,