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Home , Position of the Sun

Coordination for location

When planning a PV system, it is crucial to know at any given the position of the Sun in the as seen from the location of the solar system. In today's lecture we will introduce two coordinates systems that we will use to locate the sun in the sky. First the geographic and then the celestial coordinate systems.

There are several web applications that you can use for finding the path of the sun. For example, these pictures are obtained from Wolfram Alpha and you can see the view of the observer during the of winter and summer in Delft, which represents the lowest and the highest path drawn by the sun during the . Indeed, the maximum altitude of the sun which will be introduced in the next slides increases from almost 15 degrees to 61 and so also the daylight the duration becomes more than the double. Note that the sun apex during the day will have very important implication in case the PV system is embedded in a landscape with obstacles. As we shall see in the following lecture, finding the position of the Sun above a solar panel situated on the is not a trivial trigonometric problem.

Before breaking the procedure in small steps in order to solve such problem, let's learn some important terms. To begin we shall consider a panel as a surface tangent to the earth crust so it is just lying on the surface. Later on we will tilt it in order to optimize its yield. First we have to locate the panel with respect to the global position and thus we use the geographic coordinate system. This system enables to specify every location on earth with the two coordinates, and the . The latitude of a point is the angle between the equatorial plane, depicted in red in the picture and the straight line that passes through that point and the center of the earth. Points at the same latitude trace circles on the surface of earth called parallel. Thus the Pole is 90 degrees north and the is 90 degrees south and the divides the into northern and southern hemisphere. The longitude of a point is the angle between the Greenwich reference and the Meridian that passes through that point. This angle can be or east since the Greenwich Meridian determines the proper eastern and western hemispheres. Here is shown the example of Delft, which I am now, and which is located in the northern hemisphere to east of the Greenwich Meridian. This other city is Dakar and it is always in the North hemisphere, but unlike Delft, it is located to the west of the Prime Meridian.

Now that we have seen the coordinates of the earth it will be much easier to understand the celestial coordinates. Indeed, 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. It is very important to note that because of the distance of celestial objects in general and that the Sun in particular, being much larger than the radius of the earth, we can consider the observer and the center of the earth coincident. This sphere is called the and at this point is the position of the celestial object. 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 case the horizon of the observer is the grey area beneath the hemisphere and on the left hand side you can see the representation of a plane tangent to the earth, where the blue dot is the observer. Another important thing to realize is that your module now it's the observer. Therefore, the celestial sphere will have the same inclination as this plane. As we anticipated, we may neglect the translational shift of the origin of the coordinate systems from the observer to the center of the earth and thus if the PV module now it is the observer, we can always find the position of the Sun in terms of two angles. The altitude a, which is the angular elevation of the center of the solar disk above the horizontal plane. Its angular range is between the minus 90 and plus 90 degrees, where negative angles correspond to the Sun being below the horizon and in thus during night. The A capital is the angle between the line of sight projected on the horizontal plane and the north. It is counted eastward such that north has an azimuth of 0 degrees, east of 90 degrees, south of 180 degrees and finally west 270 degrees. Its angular range is thus between 0 and 360 degrees. But note that different conventions are also used by the PV community. For example, the South might correspond to zero degrees and the angles might be counted westward. To be clear, from now on we will use only the convention where a capital is equal to 0, corresponding to north. These two set of coordinates, azimuth and the altitude of the Sun with respect to the observer are very important because they are input parameters together with the date and time to calculate the solar position in the sky.

Instead of using the spherical coordinate a small and A capital, we can also use Cartesian coordinates, X, Y and Z. The principal direction which is the arrow pointing north is parallel to X, while Z axis is pointing towards the zenith. The Cartesian coordinates are connected to the spherical coordinates via this a simple trigonometric relation that expresses the Sun position of three coordinates instead of two. So let's get things together. First if we trace the path of the Sun in the celestial sphere, we obtain the of the Sun, which is represented in orange. Then we can also draw the earth coordinates in the same celestial sphere. So imagine to extend the equator of the earth to the space and this we have the so called , highlighted in blue. What you find out is that the earth and the Sun ecliptics are slanted with each other with the so called . This angle measures around 23 degrees, but it is not constant, because it has a very little variation that depends mostly on the time. Very important is the vernal that is the principal direction of the coordinate system, indicated by the sign of Aries. These obvious from the picture, the Aries lies in both the ecliptic and the equatorial planes making it a reference position. As for the geographic coordinate system, here we have two angular coordinates called the ecliptic longitude and the ecliptic latitude.

So to summarize, today we learned how to locate an observer on the Earth's crust using the latitude and longitude of the geographical coordinate system. Then we located the observer in the middle of the celestial coordinate system and defined the azimuth and altitude in order to describe objects in the sky, such as our Sun. Indeed the next step, as we will see in the following lecture, is to combine these two coordinate systems together to calculate the position of the Sun in the sky.