Diffuse losses with tracking systems

The diffuse (and albedo) loss evaluation for tracking systems involves several sky directions and tracker positions. Therefore, it can become very time-consuming to consider all trackers for very large or detailed scenes. To shorten the calculation time, the user can choose to evaluate diffuse shadings on a representative tracker instead.

Found in the toolbar of the 3D scene, the tool Tracker diffuse shading definition is where this alternative calculation strategy can be selected.

Calculation principles

Ideally, one would compute the whole shading table for all possible tracker orientations, and evaluating the diffuse integral over each of these shading tables.

In practice, however, PVsyst evaluates the shading factor on diffuse and albedo only for a selection of tracker orientations, thus generating an interpolation profile for the shading factor on diffuse and albedo. These are then used at the time of simulation. This calculation can nonetheless take a long time.

"Representative tracker" approximation

Originally, this was not feasible for large systems with many trackers due to the significant time needed for the elaboration of the different shading tables. Therefore, an approximation was developed that is acceptable in most cases where the trackers are uniformly arranged. In this approximation scheme, PVsyst or the user may choose one significant tracker in the middle of the system. The software then evaluates the shading factor table for this element only, using neighboring trackers and objects to cast shadings, but neglecting other shading sources. This allows a much faster diffuse shading calculation.

This approximation can be summarized as shading a representative "central tracker" with the neighboring "partial scene".

This approximation neglects the finite size of the system. Indeed, the boundary trackers (to the east or west) do not suffer from mutual shadings from one side. This may introduce an error of the order of 1/N rows, when the representative tracker and the neighbors are improperly chosen.

Tracker diffuse shading calculation modes

This window allows to select the most appropriate calculation mode for the diffuse shadings of trackers. It is available whenever trackers are defined in the 3D scene, and is found in the shading scene construction window, via Tools > Trackers diffuse shadings definition.

A mode must be selected for a each 3D tracker orientation, which can be chosen from the "Orientation" dropdown list. Different modes can be applied on different orientations, which provides greater flexibility. This orientation filter is also a solution to the problem of inhomogeneous or isolated patches of trackers, which could be shaded differently than large regular patches. It is now possible to simply define additional orientations to differentiate the different calculation modes.

Three calculation modes are now available.

• All trackers

In this case, all trackers in the orientation are considered for the diffuse shading calculation. All shading objects in the scene as well as other orientations will cast shadings. This is the most precise and recommended calculation mode, but it may become resource intensive for large or complex scenes.

• Central tracker

In this mode, among the most geometrically central trackers of the orientation, the one with the highest number of surrounding trackers casting shade on it is selected. Since this operation involves calculations, determining this tracker might take a few seconds. The chosen tracker is highlighted in green both in the window and in the scene (legend: "Shaded tracker"), while the definition window is open. The neighboring trackers, used to cast shadings on the representative tracker are highlighted in orange (legend: "Shading mask"). It should be noted that even with this approach, certain tracker configurations may still affect the accuracy of the "Central Tracker" choice. For example, if the central tracker is located at the edge of a patch of trackers, the diffuse shading might be underestimated.

• Custom tracker

Same as above, but with the possibility of manually selecting a tracker to be used as representative sample. The shading mask is defined automatically.

Tracker diffuse shading definition window

Option to include shading objects

With the calculation modes Central tracker and Custom tracker, a checkbox allows to further reduce the objects included in the calculation. If shading objects are not included, only the "mask" trackers will cast shadings on the representative tracker.

By default, shading objects are included in the mask determination, because this yields generally more accurate results.

Report

The mode used for the diffuse shadings calculation is displayed in the report, under General parameters > Near Shadings.

Previous versions and change history

• From version 8.0.15: Option to include shading objects in the representative tracker calculation modes.
• From version 8.0.8: "All trackers" is the new default mode.
• From version 8.0.0: Removed "Automatic" mode.
• From version 7.3.0: New window to select diffuse shadings calculation mode.

Incorrect calculation (up to version 6.08)

This was indeed a weakness of PVsyst in the versions before V6.08: the diffuse loss for tracking systems was not computed correctly.

For a fixed plane, the Shading factor on diffuse is computed as an integral of the actual shading factor over all space directions. This calculation is a characteristic of the PV system geometry only, it doesn't depend on the sun position nor the location, so that the shading factor is constant over the year.

For tracking systems, we applied the same method, using the usual Shading factor table calculated for different positions of the sun. But in this table the tracker orientation is adjusted for each sun's position !

We were not aware of that problem when developing the diffuse treatment for tracking.

The main effect of the errors in the old version was visible with the backtracking strategy: as by definition of backtracking the shading factor is null for any sun's direction (i.e., any element of the shading table), the integral of the shading factor was null. This is not the reality as with a tilted plane, a part of the diffuse (and the albedo) is affected by the neighbor trackers.

The new calculation gives indeed a shading factor on the diffuse, which may be of the order of 2 to 3% on the yearly system yield, depending of course of the system (especially the climate and GCR).

Now, the same arguments should apply to the non-backtracking systems: the shading factor on diffuse should depend on the instantaneous tilt. This was not apparent in the results, as with the old calculation, the existing not-null shading factor gave a not-null value for the shading factor on diffuse.

According to our first evaluations, it seems that the result with the new and the old calculations are close. This means that the "old" shading factor on diffuse represents rather well an average over the year. This should be verified with different systems, especially different climates and GCR.

This structural simulation difference between backtracking and not-backtracking systems affects of course the comparisons between both strategies, and favors the non-backtracking systems with respect to old simulations.

NB: These discrepancies are lower in very sunny climates (low diffuse fraction).