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 the most appropriate calculation strategy can be selected.

Calculation principles

Ideally, one should compute the whole shading table for all possible tracker orientations, and evaluating the diffuse integral over each of these shading tables. In practice, PVsyst evaluates the shading factor for a choice of tracker orientations, and interpolates the shading factor at the simulation time. Even then, this calculation can take a long time. 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, we developed an approximation that is quite acceptable in most cases (especially for big homogeneous systems) where the trackers are uniformly arranged. In this approximation scheme, the program chooses one significant tracker in the middle of the system, and evaluates the shading factor table for this element only, using neighboring trackers to cast shadings, but neglecting other eventual shading sources. This allows a faster diffuse shading table calculation, while still producing shading factor evaluations for about 12 tracker positions (two-axis) or 8 (one-axis).

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

This doesn't take the finite size of the system into account, i.e., the first row (in east or west) doesn't suffer from mutual shadings. This may introduce an error of the order of 1/N rows, when the representative tracker and the neighbors are properly chosen.

Tracker diffuse shading definition window (from version 7.3.0)

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

In version 8, the former automatic mode has been removed. Three calculation modes are now possible. By default, no mode is selected when trackers are added to the system.

A mode must be selected for a each 3D tracker orientation Group, which can be chosen from the 'Orientation Group' dropdown list. Different modes can be applied depending on the orientation group, providing greater flexibility in the calculation. This orientation filter is also a solution to the problem of inhomogeneous or isolated patches of trackers, which previously contributed to reducing the accuracy of the shading factor calculation for the reference tracker. It is now possible to simply define additional orientations to differentiate the different calculation modes.

• All trackers

In this case, all trackers in the scene are considered for the diffuse shading calculation. This is the most precise and recommended calculation mode, but may become resource intensive for large or complex scenes.

• Central tracker

In this mode, among the most geometrically central trackers, 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

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

Previous versions

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's 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).