fix typo in section II. B "the" repeated twice in "shade projection of the row in front"

Author: mikofski

tracker-terrain-loss-part-deux.tex

@@ -130,7 +130,7 @@ \subsection{Model Simulation}
 
 The current version of SolarFarmer offers both 2D and 3D simulations. For this study, 3D simulation was used to allow trackers to follow the terrain. The 3D simulation uses a combination of two techniques to calculate shading on the trackers: a geometric solution to calculate row-to-row shading for the beam component, and a software rasterization approach that renders the scene on “hemicubes” located at the center of each module for the diffuse component. 
 
-The geometric solution uses the sun angles and position of the trackers to determine the shade projection of the the row in front to the row in back in order. The projection determines the shading extent, incident irradiance, and electrical mismatch. From these parameters,  energy output on trackers at any timestep, rotation, and terrain can be calculated. The model does not currently consider shading from arbitrary obstacles or the terrain, but for this study there were no other shading obstacles other than the trackers themselves.
+The geometric solution uses the sun angles and position of the trackers to determine the shade projection of the row in front to the row in back in order. The projection determines the shading extent, incident irradiance, and electrical mismatch. From these parameters,  energy output on trackers at any timestep, rotation, and terrain can be calculated. The model does not currently consider shading from arbitrary obstacles or the terrain, but for this study there were no other shading obstacles other than the trackers themselves.
 
 The software rasterization approach (used in the previous paper \cite{Mikofski_9300381}) is required to calculate the diffuse shading component for the trackers. Although less computationally intense than ray-tracing, the software rasterization approach is still more complex than the 2D model, so the complex calculation is simplified by binning the tracker positions at all time-steps into 10° buckets, and each time-step can then be associated with a tracker position bin. The calculation then loops over the typically twelve tracker position bins (+/-60deg tracker rotation angle) and renders the full 3D scene at a representative rotation for the bin. The shading obstacles are then projected onto pixels of each hemicube, and the results are transformed into a cache of shaded or not shaded state for each 1° azimuth and zenith bin for each hemicube. These are then transformed into a diffuse component depending on how much of the sky is visible to each hemicube. A single hemicube at the center of each module was deemed sufficient to determine diffuse sky irradiance incident in the plane of array for the entire module, as the view factor for diffuse sky varies very little on the front side of the module (around 8\% difference between top and bottom according to the 2D model \cite{Mikofski_8980572}). Also, when incorporating the diffuse component in the energy calculation, an average of the individual module diffuse sky irradiances over the site is used per time-step. Along with approximations introduced with the tracker position binning, any finer-resolution hemicube calculations would have little effect on the result.