How is the Shading Loss on diffuse calculated, with tracking systems ?

[André Mermoud]

The diffuse (and albedo) loss evaluation is not straightforward with tracking systems.

Calculation up to version 6.08

This was indeed a weakness of PVsyst in the versions before V6.09: 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 characteristics 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 !

I was not aware of that problem when developing the diffuse treatment for tracking.

Calculation from version 6.10

The right calculation implies computing the whole shading table for each tracker position, and evaluate the diffuse integral over each of these tables (in practice: evaluate the shading factor for some chosen tracker's orientations, and interpolate the shading factor at the simulation time).

This was not feasible with the "standard" calculation" due to the significant time for the elaboration of the shading table.

Therefore we developed an approximation, which should be quite acceptable in most cases (especially for big systems). The program chooses one significant tracker in the middle of the system, and evaluates the shading factor table for this element only, using the neighbor trackers, but neglecting other eventual shading sources. This allows a fast table calculation, and produces shading factor evaluations for about 12 tracker positions (two-axis) or 8 (one-axis).

This doesn't take the "finite" size of the system into account, i.e. the first row (in east or west) doesn't suffer of mutual shading; this may introduce an error of the order of 1/N rows.

Consequences

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 - 3% or even more, 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.

However 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 without backtracking are close to each other. 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 by respect to old simulations.

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

You can see some comments on our forum Additional Shading Losses in V6.1.

See also How to explain the high loss values on diffuse with (back)tracking systems ?