Best plane angle, PVsyst application

Method

This is PVsyst's irradiance optimisation as two PVsyst 8.1.5 runs of a single-axis tracker field show it, one with backtracking and one without. At each sunlit timestep with a GHI of at least 14 W/m², two searches leave the tracking rule's rotation in steps of 1° (1). PVsyst kept the tracking rotation at every hour with 13 W/m² of GHI and optimised every hour with 14 W/m². The irradiance compared is the transposed irradiance less the diffuse and albedo shading of the neighbouring rows (2). Beam shading is not counted. The horizon and the IAM are not counted. Rotations carry PVsyst's sign, negative facing east on an axis toward the south. The first search steps toward lower rotations while the irradiance rises. At its first step without a gain it turns once and steps toward higher rotations from that step, up to the next step without a gain (3). The second search steps toward higher rotations while the irradiance rises (4). A step past a rotation stop lands on the stop. A search that cannot move evaluates nothing. With backtracking no step may be steeper than the tracking rule's rotation. The tracker takes the evaluated rotation with the most irradiance, the tracking rule's rotation included (5). A search may pass flat to the other side. A timestep in wind stow keeps the stow position. With the full climb of the Best plane angle search step, the rotation equals PVsyst's on 90 % of the sunlit hours with backtracking and 91 % without. Apart from the stops in the note, every rotation then lies within 1.03° of PVsyst's. With the PVsyst 8 settings it equals PVsyst's on 95.5 % and 94.3 %.

The math

1. Steps
2. Irradiance compared
3. First search
4. Second search
5. Rotation kept

$$\varphi_k = \min\left(\varphi_{max},\ \max\left(\varphi_{min},\ \varphi_{k-1} + d_k\,\Delta\right)\right),\quad \varphi_0 = \varphi_T \tag{1}$$ $$G(\varphi) = G_{POA}(\varphi) - L_{dif}(\varphi) - L_{alb}(\varphi) \tag{2}$$ $$d_k = \begin{cases} -1 & k \le k_1 \\ +1 & k_1 < k \le k_2 \end{cases},\quad k_1 = \min\{k : G(\varphi_k) \le G(\varphi_{k-1})\},\quad k_2 = \min\{k > k_1 : G(\varphi_k) \le G(\varphi_{k-1})\} \tag{3}$$ $$d_k = +1,\quad k \le k_3 = \min\{k : G(\varphi_k) \le G(\varphi_{k-1})\} \tag{4}$$ $$\varphi' = \arg\max_{\varphi \in E} G(\varphi) \tag{5}$$

where

Symbol	Meaning	Unit
$\varphi_k$	the rotation after step $k$ of a search, in PVsyst's sign	degrees
$\varphi_T$	the tracking rule's rotation	degrees
$d_k$	the direction of step $k$: $-1$ or $+1$	—
$\Delta$	the step of the searches: 1	degrees
$\varphi_{min}, \varphi_{max}$	the rotation stops	degrees
$G_{POA}(\varphi)$	the transposed plane-of-array irradiance at rotation $\varphi$	W/m²
$L_{dif}(\varphi)$	the diffuse mutual-shading loss of the rows at $\varphi$	W/m²
$L_{alb}(\varphi)$	the albedo mutual-shading loss of the rows at $\varphi$	W/m²
$k_1$	the step where the first search turns	—
$k_2$	the last step of the first search	—
$k_3$	the last step of the second search	—
$\varphi'$	the rotation the tracker takes	degrees
$E$	the evaluated rotations: $\varphi_T$ and the steps of both searches	—

Note

The first search turns on the step that failed. A step past the lower stop therefore moves the rest of that search onto the whole degrees of the stop. pvperf reproduces this. PVsyst's second search sometimes ends after one step although the next step gains. In the PVsyst 8.1.5 runs examined this happened on mornings where the second search ran alone. In a run with backtracking it happened on 277 of 4,403 sunlit hours. In the same run without backtracking it happened on 150 hours that started on the lower stop. The Best plane angle search step reproduces these stops with its PVsyst 8 settings. With the full climb the yearly effective irradiance is 0.19 % (with backtracking) and 0.16 % (without) above PVsyst's. With the PVsyst 8 settings it is 0.01 % and 0.03 % above.

References

1. PVsyst 8 help, Tracking strategies

API

array.irradiance_tracking = true, array.irradiance_tracking_method = best_angle

Symbols follow the symbol registry.