Standard Backtracking

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Summary

Standard Backtracking adjusts single-axis tracker angles to prevent row-to-row shading during morning and evening hours when sun angles are low. Designed for uniform-slope DC fields, this algorithm assumes all tracker rows share identical ground slope and spacing. PlantPredict implements the slope-aware backtracking algorithm from Anderson & Mikofski (2020), which generalizes the classical Lorenzo et al. (2011) approach to handle both horizontal and uniformly-sloped terrain.

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Inputs

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Outputs

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Detailed Description

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Ground Coverage Ratio

The ground coverage ratio characterizes array density: $$GCR = \frac{\ell}{p}$$

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Cross-Axis Slope Calculation

For non-N-S trackers or sloped terrain, the cross-axis slope ($\beta_c$) must be derived from the ground slope and tracker orientation. This follows the procedure in Anderson & Mikofski (2020). First, calculate the azimuth difference: $$\Delta\gamma = \gamma_a - \gamma_g$$ Calculate the axis tilt (slope component along the tracker axis): $$\beta_a = \arctan(\tan\beta_g \cos\Delta\gamma)$$ Calculate the tracker normal vector: $$\vec{v} = \begin{bmatrix} \sin\Delta\gamma \cos\beta_a \cos\beta_g \\ \sin\beta_a \sin\beta_g + \cos\Delta\gamma \cos\beta_a \cos\beta_g \\ -\sin\Delta\gamma \sin\beta_g \cos\beta_a \end{bmatrix}$$ Calculate the cross-axis slope: $$\beta_c = \arcsin\left(\frac{(v_x \cos\Delta\gamma - v_y \sin\Delta\gamma) \sin\beta_a + v_z \cos\beta_a}{|\vec{v}|}\right)$$ For horizontal terrain ($\beta_g = 0°$), $\beta_c = 0°$ regardless of tracker azimuth.

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Backtracking Correction

The backtracking correction angle accounts for both the true-tracking angle and the cross-axis slope: $$\theta_c = -\text{sign}(\theta_T) \cdot \arccos\left(\frac{|\cos(\theta_T - \beta_c)|}{GCR \cdot \cos(\beta_c)}\right)$$ The final backtracking angle is: $$\theta_B = \theta_T + \theta_c$$

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Backtracking Condition

Backtracking is only required when the argument to $\arccos$ is less than 1: $$\left| \frac{\cos(\theta_T - \beta_c)}{GCR \cdot \cos(\beta_c)} \right| < 1$$ When this condition is not met, no shading occurs and $\theta_B = \theta_T$.

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Horizontal Terrain

For horizontal installations ($\beta_c = 0°$), the equations simplify to: $$\theta_c = -\text{sign}(\theta_T) \cdot \arccos\left(\frac{|\cos(\theta_T)|}{GCR}\right)$$ The backtracking condition becomes $|\theta_T| > \arccos(GCR)$, which matches the classical cutoff angle from Lorenzo et al. (2011).

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Physical Interpretation

Standard Backtracking reduces the tracker rotation from the ideal sun-following position toward a more horizontal orientation that eliminates inter-row shading. The cross-axis slope term ($\beta_c$) adjusts for the effective spacing between tracker edges when viewed perpendicular to the sloped ground plane. Standard Backtracking involves a trade-off: without backtracking, arrays achieve optimal angle of incidence but suffer significant inter-row shading losses during morning and evening; with backtracking, arrays have non-optimal angle of incidence but minimal shading. The net effect typically favors backtracking for ground coverage ratios greater than 0.35. If the calculated backtracking angle equals zero, it is set to 0.001° to prevent numerical issues in angle-of-incidence and surface normal calculations. For sites with significant terrain variation where tracker rows are at different elevations, see Terrain-Aware Backtracking.

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References

• Anderson, K. & Mikofski, M. (2020). Slope-Aware Backtracking for Single-Axis Trackers. NREL Technical Report NREL/TP-5K00-76626. https://www.nrel.gov/docs/fy20osti/76626.pdf
• Lorenzo, E., Narvarte, L., & Muñoz, J. (2011). Tracking and back-tracking. Progress in Photovoltaics, 19(6), 747-753.
• Marion, B., & Dobos, A. (2013). Rotation Angle for the Optimum Tracking of One-Axis Trackers. NREL/TP-6A20-58891.