Self-shading assumptions in pvwatts

Hello Paul,

I have read the docs to understand how self-shading is calculated in pvwatts. Here's what I think is the case for the various configuration options (note, "in front" means a "row" between the "row in question" and the sun):

1. For fixed tilt systems, the gcr is used to determine the inter-row spacing from
gcr = L/R
where L = module length (in the not-horizontal direction) and R is the inter-row spacing.  Then pvwatts does a geometric calculation of the shading by a row in front for each hour. The rows are assumed to be infinitely wide (i.e., there are no end-effects accounted for).

2. For 1-axis horizontal tracking, the modules are assumed to be butted end-to-end along the tracking axis and the gcr is L/R where R is the spacing between trackers and L is the width of modules perpendicular to the tracking axis. This is used either to calculate self-shading from a tracker in front, or the angle of incidence for zero shading in the case of backtracking. The trackers are assumed to be infinitely long (i.e. there are no end-effects accounted for).

3. For 1-axis tracking with an inclined tracking axis, the trackers are arranged in rows with some spacing (e.g., east-west rows of trackers with north-south tracking axis orientation), but the gcr is used as with horizontal trackers to calculate only the intra-row self-shading or backtracking angle, and inter-row shading is assumed to be zero.  Thus the user should input the intra-row gcr for these cases, rather than the actual gcr accounting for inter-row spacing.

4. For 2-axis tracking, self-shading is assumed to be zero and gcr has no impact on power calculations.

Therefore, for the case of inclined 1-axis or two-axis trackers, a manual shading input should be provided via the losses input, or else using an hourly adjustment array of the shading is available from some other calculation software.

Have I got it right? Of if not, can you clarify whatever I got wrong?

Thanks
Russ Jones

Hi Russ,

This looks right to me, although I'm not sure I completely follow your thinking for #3. The math for #2 and #3 is the same, only the tracking axis angle (tilt) changes. For 1-axis tracking, if the azimuth angle is 180 or zero, then the tracking axis is north-south so that the tracker rotates from east to west to follow the suns daily movement.

Best regards,
Paul.

Hi Russ,
I second Paul's answer that the math for #2 and #3 is the same, just with a different angle. The assumption for trackers (tilted or horizontal) is that all of the modules on a single tracker are in the same "plane" along the axis of rotation, meaning that there would be NO intra-row shading, only inter-row shading, which is calculated by the algorithm.
Thanks!
Janine

Hello Paul and Janine,
Since writing the original post I've done a little testing which shows my assumptions for case 3, 1-axis trackers with inclined axis of rotation, were incorrect ... but I still don't know for sure what's going on. Inclined axis 1-axis trackers have spacing in two dimensions, and by "intra-row" (within a row) I mean the spacing between trackers in the east-west direction assuming the tracker axis is north-south, and "inter-row" is the spacing between them in the north-south direction. The intra-row shading can be avoided by backtracking, whereas the inter-row spacing is analogous to the row-to-row spacing in fixed tilt arrays and shading cannot be compensated by backtracking. The problem is that pvwatts only has one gcr input.  Perhaps it uses the square root of gcr for spacing in each direction? I tried setting gcr=0.4 (a reasonable value for 1-axis horizontal) with an inclined 1-axis tracking configuration and discovered there is inter-row shading in that case (as evidenced by a lower ac generation at mid-day compared to a properly spaced fixed tilt system at the same inclination). I think that's actually good news but it still leaves the question of what is being assumed for the spacing in two distinct directions from a single user input.  The true gcr = (intra-row gcr) x (inter-row gcr), which might well be different.

Hi Russ,

For one-axis tracking with tilt > 0, PVWatts (and the Detailed PV model) basically models a single E-W row of trackers that rotate about the N-S axis. That would be appropriate for trackers installed on an incline where the tracking axis is parallel to the ground. It does not model the situation you describe, where tilted trackers are installed in a two-dimensional grid on flat ground.

Best regards,
Paul.

OK, so my original description was correct! Inter-row shading (in the north-south direction) is assumed zero, and intra-row shading (in the east-west direction) is calculated from the gcr, using the backtracking algorithm if selected.  My comment about midday shading was my error, evidently due to some other difference I had inadvertently made, but I tested it again and confirmed what you said: the mid-day output for the inclined trackers is the same as for fixed tilt at the same tilt angle, for all values of gcr.