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<< Click to Display Table of Contents >> Treatment of the Beam component |
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The evaluation of the beam component in the Far Shadings case is extremely simple, it is simply an "ON/OFF" treatment: at a given time the sun is over or under the horizon line for the whole system.
The simulation determines the time of the crossing of the horizon line within the simulation hour and applies this fraction of hour as loss to the beam and circumsolar components.
With near shadings, we define the Shading Factor as the shaded fraction of the PV field (visual shades) with respect to the full sensitive area, for a given position of the sun.
The geometric configuration of the shadows falling on the field, and the determination of the shading factor, are carried out in a purely geometric and analytical manner. Therefore this is an "exact" calculation, which doesn't involve any modeling or approximating hypothesis.
For a given solar position, the program first carries out a transformation of the co-ordinates of the whole system, in order to point the OZ' axis in the direction of the sun.
Next, for each sensitive element of the PV field (table like rectangle, shed, polygon, tracker), it projects each elementary surface of the surrounding 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 (table) 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 (each table).
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 is proven to be extremely complex to program 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 for 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 in terms of the resolution of the calculations of the machine, or topological criteria, etc. and the reliability of this procedure is not absolute.
In the version 5, the calculation time became prohibitive for complex systems of more than 500-1000 elements, as each sensitive element was compared to all the other ones, leading to a calculation time going with the square of the number of elements.
In the version 6, this calculation had been optimized. In a pre-evaluation phase, the program identifies the potential obstacles for each sensitive element, leading to gains in time of a factor of 10 or more.
Since version 6.40, these calculations have been greatly improved again, they can also make a better use of multi-core processors.
Use in the simulation
The shading factor is computed for the effective direction of the sun at the middle of the hourly step. The simulation may
•either use an interpolated value in the pre-calculated "Shading Factor Table" (fast option),
•or compute the full shading factor at each step (slow option).
When the circumsolar is treated separately (i.e. not included with the diffuse component), PVsyst applies the same far and linear shading factors as for the beam. However the circumsolar component will not produce shading electrical mismatch losses.