Diffuse losses with tracking systems

<< Click to Display Table of Contents >>

Navigation:  Project design > Shadings > Calculation and Model >

Diffuse losses with tracking systems

Previous pageReturn to chapter overviewNext page

The diffuse (and albedo) loss evaluation is not straightforward with tracking systems. Since the calculation involves several sky directions and tracker positions, it can become very time-consuming to consider all trackers for very large or detailed scenes.

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 some chosen 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. However this is not a problem, as for small systems the calculation is automatically performed on the full system.

Tracker diffuse shading definition window (from version 7.3.0)

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

There are several calculation modes, and by default the "Automatic" option is selected:

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

Central tracker
In this case, the tracker closest to the geometrical center of the scene is selected as representative sample for the whole scene. This 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"). Note that some arrangements of trackers invalidate the accuracy of the "central tracker" approach: if the central tracker is on the edge of a patch of trackers, the diffuse shadings will 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.

In this case PVsyst will select the best option between "All trackers" and "Central tracker", depending on the number of trackers in the scene. The threshold between both regimes can be changed in the advanced parameters ("Threshold number of tracker fields for partial scene") with a default value of 40. This is equivalent to the treatment used up to version 7.2.21 (see below).


Tracker diffuse shading definition window

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

Adjusting the partial scene cap (from version 7.2.15)

As simulated systems grow in complexity, it is not unusual to have large systems with hundreds of trackers, arranged in several patches of various shapes. Some arrangements of trackers invalidate the accuracy of the "central tracker" and "partial scene" approach: if the central tracker is on the edge of a patch of trackers, the diffuse shadings will be underestimated. The algorithm for finding relevant neighboring trackers also shows its limits in complex arrangements.

For this reason, the threshold number of trackers above which the "central tracker with partial scene" approach is applied, can be changed in the advanced parameters ("Threshold number of tracker fields for partial scene"). Increasing it from its default value of 40 to a value larger than the number of trackers in the scene is henceforth advised for systems with trackers arranged non-uniformly.

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).