Terrain-aware backtracking

Method

Each tracker of a scene computes its own rotation. The true-tracking rotation comes from the tracker's axis (1). When the tracker's axis azimuth and axis tilt both lie within 0.05° of its orientation group's, the group's axis is used. For each neighbour, the slope of the line between the two axes (2) gives the shade test (3) and the backtracking rotation of the pair (4). The tracker takes the candidate with the most correction (5). Each neighbour on either side is evaluated at the lowest and the highest height difference along the stretch the two trackers share, and at the height difference where the neighbour lies on the sun's line when it falls between them. The shade test covers both directions, so the tracker neither receives shade nor casts it. A side with no neighbour adds no candidate: a tracker at the edge of the field still turns back so that its shadow misses the neighbour on its other side, and a tracker with no neighbour at all tracks the sun. On each side the method takes the nearest 8 tables whose centres lie within 10 of the tracker's collector widths across the axis and that overlap the tracker along it. Fixed racks among them add no candidate. The rotation stops of the Racking tab apply afterwards, then wind stow, then irradiance-optimised tracking. The widths are the backtracking widths of the Backtracking width step. Terrain-aware backtracking needs a scene with trackers and near shading by direct projection, which projects each tracker and each neighbour at its own rotation, or off. The plane-of-array irradiance of an orientation group is the module-weighted mean of its trackers' own transpositions, each tracker on its own axis at its own rotation. The rest of the group's calculation, the incidence angle included, uses the mean of their rotations.

The math

1. True tracking
2. Slope between the axes
3. Shade test
4. Backtracking rotation of the pair
5. Rotation

$$\rho_T = \operatorname{atan2}\!\left(\cos e \sin(\gamma_s - A_{ax}),\ \cos e \sin\tau \cos(\gamma_s - A_{ax}) + \sin e \cos\tau\right) \tag{1}$$ $$\beta_c = -\arctan\frac{\Delta z}{x_n} \tag{2}$$ $$x_c = \frac{|\cos(\rho_T - \beta_c)|}{\text{GCR}_n \cos\beta_c},\qquad \text{GCR}_n = \frac{(W + W_n)/2}{|x_n|} \tag{3}$$ $$\rho_c = \begin{cases} -\operatorname{sign}(\rho_T)\arccos x_c & x_c < 1 \\ 0 & x_c \ge 1 \end{cases},\qquad \rho_B = \rho_T + \rho_c \tag{4}$$ $$\rho = \arg\min_{c \in C} \operatorname{sign}(\rho_T)\,c,\qquad C = \{\rho_T\} \cup \{\rho_B(n, \Delta z) : n,\ \Delta z \in \{\Delta z_{min}, \Delta z_{max}, \Delta z^*\}\} \tag{5}$$

where

Symbol	Meaning	Unit
$\rho_T$	the true-tracking rotation	degrees
$e$	the sun elevation	degrees
$\gamma_s$	the sun azimuth, clockwise from north	degrees
$A_{ax}$	the axis azimuth of the tracker	degrees
$\tau$	the axis tilt of the tracker	degrees
$\beta_c$	the slope angle of the line from the tracker's axis to the neighbour's	degrees
$x_n$	the neighbour's signed distance across the axis, positive on the side $A_{ax} + 90°$	scene units
$\Delta z$	the height of the neighbour's axis above the tracker's, square to the tracker's axis	scene units
$x_c$	the shade test: the pair shades at true tracking when it is below 1	—
$\text{GCR}_n$	the ground cover ratio of the pair	—
$W$	the tracker's backtracking width	scene units
$W_n$	the neighbour's backtracking width	scene units
$\rho_c$	the backtracking correction	degrees
$\rho_B$	the backtracking rotation of the pair	degrees
$\rho$	the rotation the tracker takes, before the rotation stops	degrees
$C$	the candidates: true tracking and each neighbour's pair rotation	—
$\Delta z_{min}, \Delta z_{max}$	the lowest and highest height of the neighbour's axis along the shared stretch	scene units
$\Delta z^*$	the height of the neighbour's axis at which it lies on the sun's line, $x_n \cos\rho_T / \sin\rho_T$, used when it falls between $\Delta z_{min}$ and $\Delta z_{max}$	scene units

References

1. Anderson & Mikofski 2020, Slope-Aware Backtracking for Single-Axis Trackers, NREL/TP-5K00-76626

API

array.backtracking_angle = terrain_aware

Symbols follow the symbol registry.