Table of shading factor
The shading factor is a complex calculation which spends too much time to be performed during simulation at each time step. Therefore the program builds a table in sun's height (10° steps) and azimuth (20° steps). The simulation can then interpolate in this table.
Shading factor computation details
The geometric configuration of the shadow falling on the field, and the determination of the shading factor, are carried out in a purely geometric and analytical manner.
For a given solar position, the programme first carries out a transformation of the co-ordinates of the whole system, so as to point the OZ' axis in the direction of the sun.
Next, for each sensitive element of the PV field (sheds, rectangles, polygons), it projects each elementary surface of the system on the plane of the field being considered. The intersection of the field element with the positive projections (i.e. in front of the plane) of each element is then calculated. The reunion of these elementary shadows forms a polygon representing the global shading on the field element under consideration. The shading loss factor is the ratio of the area of the shadow polygon, to that of the sensitive element. This process is repeated for each sensitive field element (for example each shed).
The greatest difficulty with this procedure resides in the calculation of reunions and intersections of polygons in the plane, in the general case. This operation has proved to be extremely complex to programme using polygons defined by their summits. The difficulties mainly appear when the summits or the segments are overlapping or very close, as it is the case in most of the object constructions, when each summit is a part of several elementary surfaces in the 3D space. Topological decisions depend on the proximity of points in space. It is therefore necessary to define distance criteria as functions of the resolution of the calculations of the machine, or topological criteria, etc. and the reliability of this procedure is not absolute.
Thus, in some cases, the result may be erroneous. Often, the programme finds it out on its own, and again begins the calculation with a slightly different solar position (trials with modifications of 1° in height or azimuth).
If it fails again , the shading factor is calculated in a completely different manner: the PV field is partitioned in about 2000 points, and the shading is calculated for each point. Although this method is an approximation, it always leads to a reliable result.
Nevertheless some calculations may sometimes stay erroneous (the program doesn't detect the error by itself); but in practice, this error has usually very little influence on the global simulation over one year.
During the elaboration of the shading table, the points (sun's positions) situated behind the plane of the PV field appear in blue.