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Add shaded fraction (FS) calculation for true-tracking on flat terrain #1689

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@williamhobbs

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@williamhobbs
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Is your feature request related to a problem? Please describe.
It would be useful to have a shaded fraction calculation for true-tracking on flat terrain. It could be used in modeling thin film projects with (approximately) linear power loss due to self-shade.

image

Describe the solution you'd like
An implementation of equations 1-6 in Lorenzo 2011 [1], where inputs are:

  • tracker rotation angle (true-tracking, not backtracking)
  • ground coverage ratio
  • solar azimuth
  • solar elevation

And the output is shaded fraction (0-1) of each shaded row.

Describe alternatives you've considered
Custom implementations would not be difficult, but a built-in function would be nice. More robust versions that can account for non-horizontal tracker rotation axis, non-flat terrain, etc., would be nice, but are more difficult.

Additional context
Here's the description we used in a 2023 PVRW poster on the topic [2], adapted from [1]:

Calculate the ideal tracker angle,

ω = arctan(cos(θA) * sin(θel) / sin(θA))

where θel is solar elevation and θA is solar azimuth. Then calculate the shaded fraction of the array, FS, as

FS = max[0, (1-cos(ω)/GCR)]

where GCR is the row spacing divided by tracker table width.

[1] E. Lorenzo, L Narvarte, and J Muñoz. 2011. "Tracking and back-tracking". Progress in
Photovoltaics: Research and Applications 19: 747-753. https://doi.org/10.1002/pip.1085
[2] I. Azad, W. Hobbs, "Improved PV expected energy modeling with a simple self-shading model". NREL PVRW 2023. (proceedings pending)
[3] K. Anderson, W. Hobbs. "Improved CdTe PLR Estimates: Self-Shading and Spectral Mismatch". NREL PVRW, 2022. https://www.osti.gov/biblio/1846944

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