final version submitted to pvsc

tracker-terrain-loss-part-deux.tex

@@ -28,7 +28,7 @@
 \maketitle
 
 \begin{abstract}
-Trackers on variable terrain can incur electric mismatch losses from row-to-row shading even with backtracking. Tracker terrain loss is the difference between the performance of trackers on horizontal ground and that on variable terrain. SolarFarmer was used to study tracker terrain loss by simulating the Hopewell Friends Solar power plant, which has an average 4\% southwest slope. The results yielded a tracker terrain loss of \textasciitilde2\% with standard backtracking. By subdividing the site from one to three layouts, the tracker terrain loss decreased \textasciitilde0.5\%. The 1-hour versus 5-minute input data did not significantly affect the tracker terrain loss, but using slope-aware backtracking completely recovered the 2\% loss. This study is a continuation of a previous study that prompted improvements in SolarFarmer's 3-dimensional tracker shading algorithm. The results of this study demonstrate that SolarFarmer can now be used to calculate tracker terrain loss. A comparison of the SolarFarmer results with a separate uneven terrain model developed by DNV using PVsyst produced similar results.
+Trackers on variable terrain can incur electric mismatch losses from row-to-row shading even with backtracking. Tracker terrain loss is the difference between the performance of trackers on horizontal ground and that on variable terrain. SolarFarmer was used to study tracker terrain loss by simulating the Hopewell Friends Solar power plant, which has an average 4\% southwest slope. The results yielded a tracker terrain loss of -2\% with standard backtracking and but slope-aware backtracking completely recovered the 2\% loss. By subdividing the site from one to three layouts, the tracker terrain loss decreased 0.5\%. The 1-hour versus 5-minute input data did not significantly affect the tracker terrain loss. This study is a continuation of a previous study that prompted improvements in SolarFarmer's 3-dimensional tracker shading algorithm. The results of this study demonstrate that SolarFarmer can now be used to calculate tracker terrain loss. A comparison of the SolarFarmer results with a separate uneven terrain model developed by DNV using PVsyst produced similar results.
 \end{abstract}
 
 \begin{IEEEkeywords}
@@ -42,7 +42,7 @@ \section{Introduction}
 
 Evaluating tracker terrain loss is important for estimating system energy production. Most solar energy simulation models currently available in the industry are limited to modeling standard backtracking on horizontal ground or with only north-south (N-S) tracker axis tilt. Also notable is that various custom backtracking algorithms exist in the industry. Slope-aware backtracking is only one type of non-standard backtracking. Different algorithms reduce shade loss on terrain in different ways, leading to varying tracker terrain losses. 
 
-To study tracker terrain loss in detail, SolarFarmer \cite{Mikofski_8547323} was used to perform full 3-dimensional (3D) modeling of shade and irradiance on the trackers, which can be in any position on any terrain. The model calculates full sub-module electrical mismatch to determine the performance of the PV system at each time step. This study is a continuation from last year \cite{Mikofski_9300381} which concluded that the prior methods used in SolarFarmer were too coarse to resolve row-to-row shade for trackers during backtracking. Therefore, over the past year, a new hybrid 3D geometric shade algorithm was implemented in SolarFarmer to calculate the row-to-row shade on trackers at each time step exactly without approximations. This paper presents the results of the new SolarFarmer methods applied to the same tracker simulations from last year, which included 1) dividing the array into layouts of varying granularity and 2) placing the trackers "in-plane" and "following terrain". In addition, this year's study expands the results with 3) standard and slope-aware backtracking algorithms and 4) 5-minute and 1-hour input data resolution, to explore whether these factors have an impact on tracker terrain losses. Lastly, the SolarFarmer results were compared to a separate tracker terrain loss model developed by DNV using PVsyst. 
+To study tracker terrain loss in detail, SolarFarmer \cite{Mikofski_8547323} was used to perform full 3-dimensional (3D) modeling of shade and irradiance on the trackers, which can be in any position on any terrain. The model calculates full sub-module electrical mismatch to determine the performance of the PV system at each time step. This study is a continuation from last year \cite{Mikofski_9300381} which concluded that the prior methods used in SolarFarmer were too coarse to resolve row-to-row shade for trackers during backtracking. Therefore, over the past year, a new hybrid 3D geometric shade algorithm was implemented in SolarFarmer to calculate the row-to-row shade on trackers at each time step. This paper presents the results of the new SolarFarmer methods applied to the same tracker simulations from last year, which included 1) dividing the array into layouts of varying granularity and 2) placing the trackers "in-plane" and "following terrain". In addition, this year's study expands the results with 3) standard and slope-aware backtracking algorithms and 4) 5-minute and 1-hour input data resolution, to explore whether these factors have an impact on tracker terrain losses. Lastly, the SolarFarmer results were compared to a separate tracker terrain loss model developed by DNV using PVsyst. 
 
 \section{Methods}
 
@@ -63,7 +63,7 @@ \subsection{Site Characteristics}
 \begin{center}
 \begin{tabular}{|c|c|c|c|}
 \hline
-\textbf{Aisle} & \textbf{\textit{Maximum}}& \textbf{\textit{Average}}& \textbf{\textit{Direction}} \\
+\textbf{Aisle} & \textbf{\textit{Maximum \%}}& \textbf{\textit{Average \%}}& \textbf{\textit{Direction}} \\
 \hline
 1& 7.81& 6.22& west \\
 \hline
@@ -91,7 +91,7 @@ \subsection{Site Characteristics}
 \begin{center}
 \begin{tabular}{|c|c|c|c|}
 \hline
-\textbf{Row} & \textbf{\textit{Maximum}}& \textbf{\textit{Average}}& \textbf{\textit{Direction}} \\
+\textbf{Row} & \textbf{\textit{Maximum \%}}& \textbf{\textit{Average \%}}& \textbf{\textit{Direction}} \\
 \hline
 1&  1.76&  1.11& south \\
 \hline
@@ -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 results in sufficient accuracy to determine shade, incident irradiance, and electrical mismatch, and therefore determines the resulting energy output on trackers at any arbitrary timestep, rotation, and terrain. 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 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.
 
@@ -386,7 +386,7 @@ \subsection{Uneven Terrain DNV Shade Loss Model}
 \end{table}
 
 \section{Conclusions}
-The Hopewell Friends Solar power plant was simulated with SolarFarmer to calculate tracker terrain loss. This site has variable terrain and an average 4\% southwest slope. The study examined tracker terrain loss using different time intervals, tracker placement, array subdivisions, and backtracking algorithms. With standard backtracking, the tracker terrain loss from SolarFarmer was -1.7-2.4\% when compared to horizontal across array subdivisions and tracker placement models. Dividing the site into more layouts led to tracker terrain losses approximately 0.5\% lower than a single layout. The simulations were repeated with 5-minute and 1-hour input data, but the tracker terrain loss change was marginal. The simulations were also repeated with slope-aware backtracking, which indicated that the tracker terrain loss for this particular site was predominantly caused by the E-W slope and therefore recoverable with slope-aware backtracking. The site has a south-facing tilt which contributes an energy gain. The slope-aware follows terrain had tracker terrain losses of -0.4\% to +0.4\%. The SolarFarmer results were also compared with an independent DNV terrain shade loss model. The DNV model yielded -2.1\% net terrain impact from standard backtracking and +0.7\% for compared to horizontal, results which are similar to SolarFarmer. This site had a mostly southwest slope and further work is needed to study tracker terrain losses at more sites, especially those with more complex terrain. In addition, field data of custom backtracking is currently limited in the industry and should be examined to determine how it compares with simulations.
+The Hopewell Friends Solar power plant was simulated with SolarFarmer to calculate tracker terrain loss. This site has variable terrain and an average 4\% southwest slope. The study examined tracker terrain loss using different time intervals, tracker placement, array subdivisions, and backtracking algorithms. With standard backtracking, the tracker terrain loss from SolarFarmer was -1.7-2.4\% when compared to horizontal across array subdivisions and tracker placement models. Dividing the site into more layouts led to tracker terrain losses approximately 0.5\% lower than a single layout. The simulations were repeated with 5-minute and 1-hour input data, but the tracker terrain loss change was marginal. The simulations were also repeated with slope-aware backtracking, which indicated that the tracker terrain loss for this particular site was predominantly caused by the E-W slope and therefore recoverable with slope-aware backtracking. The site has a south-facing tilt which contributes an energy gain. The slope-aware follows terrain had tracker terrain losses of -0.4\% to +0.4\%. The SolarFarmer results were also compared with an independent DNV terrain shade loss model. The DNV model yielded -2.1\% net terrain impact from standard backtracking and +0.7\% compared to horizontal, results which are similar to SolarFarmer. This site had a mostly southwest slope and further work is needed to study tracker terrain losses at more sites, especially those with more complex terrain. In addition, field data of custom backtracking is currently limited in the industry and should be examined to determine how it compares with simulations.
 
 \section*{Acknowledgment}