PVsyst 8 settings

Method

The field's shading-factor table is formed with every tracker at each of 7 rotations evenly spread between the rotation limits (1). At each rotation the diffuse and albedo factors are the table's integrals (page step.near_shading.pvsyst_table, equations 4 and 5). The diffuse angular-response factor is the curve integrated over the sky, weighted by 1 minus the table's shaded fraction in each direction, in steps of 1° (2). The ground-reflected factor is the same integral over the ground with the table's 0° row (3). A timestep reads each factor at its rotation from a cubic between the two nearest rotations (4). The cubic's second derivative at each rotation is the second difference of the 7 values, and at the two limits that of the next rotation (5). At the flat rotation the plane sees no ground. Its albedo shading factor is the mean of those at the two rotations beside it (6), and its ground-reflected angular-response factor is 1. The tables also read each tracker's far neighbours (7). These are the tables whose centre lies within 25 collector widths across the axis and that reach to within 25 collector widths of the tracker's ends. At 60° of rotation the shadow of a tracker's top edge at a sun height of 2°, the table's lowest row, runs 25 collector widths on level ground. The projection at each timestep of the direct projection option keeps the neighbours across.

The math

1. Tracker rotations
2. Diffuse angular-response factor at a rotation
3. Ground-reflected angular-response factor at a rotation
4. Factor at a timestep
5. Second derivatives
6. Albedo shading factor at the flat rotation
7. Far neighbours

$$\rho_k = \rho_{min} + k\,h,\qquad h = \frac{\rho_{max} - \rho_{min}}{6},\qquad k = 0, \dots, 6 \tag{1}$$ $$F_{IAM,sky,k} = \frac{\int_{sky} F(\theta)\,\bigl(1 - F_{sh,k}(e, \gamma)\bigr)\cos\theta\,d\Omega}{\int_{sky} \bigl(1 - F_{sh,k}(e, \gamma)\bigr)\cos\theta\,d\Omega} \tag{2}$$ $$F_{IAM,gnd,k} = \frac{\int_{gnd} F(\theta_{rd})\,\bigl(1 - F_{sh,k}(0, \gamma)\bigr)\cos\theta\,d\Omega}{\int_{gnd} \bigl(1 - F_{sh,k}(0, \gamma)\bigr)\cos\theta\,d\Omega} \tag{3}$$ $$y(\rho) = (1 - t_\rho)\,y_k + t_\rho\,y_{k+1} + \left[\left((1 - t_\rho)^3 - (1 - t_\rho)\right) M_k + (t_\rho^3 - t_\rho)\,M_{k+1}\right]\frac{h^2}{6},\qquad t_\rho = \frac{\rho - \rho_k}{h} \tag{4}$$ $$M_k = \frac{y_{k+1} - 2\,y_k + y_{k-1}}{h^2}\ \ (k = 1, \dots, 5),\qquad M_0 = M_1,\qquad M_6 = M_5 \tag{5}$$ $$f_{gnd,3} = \tfrac{1}{2}\bigl(f_{gnd,2} + f_{gnd,4}\bigr)\quad \text{where the plane at } \rho_3 \text{ is flat} \tag{6}$$ $$\lvert d_\perp \rvert \le 25\,W,\qquad \lvert d_\parallel \rvert - \tfrac{1}{2}(L_t + L_n) \le 25\,W \tag{7}$$

where

Symbol	Meaning	Unit
$\rho_k$	the rotation $k$ of the tabulation	degrees
$\rho_{min},\ \rho_{max}$	the rotation limits, Racking tab	degrees
$h$	the step between two rotations	degrees
$F_{IAM,sky,k}$	the angular-response factor for the sky light at rotation $\rho_k$	—
$F(\theta)$	the incidence-angle modifier: the accepted fraction of light at the incidence angle	—
$F_{sh,k}(e, \gamma)$	the shaded fraction of the field's table with every tracker at $\rho_k$, at elevation $e$ and azimuth $\gamma$	—
$\theta$	the incidence angle: between the light's direction and the perpendicular to the module plane. Of the direction $\Omega$	degrees
$d\Omega$	an element of solid angle, taken where $\cos\theta > 0$	sr
$F_{IAM,gnd,k}$	the angular-response factor for the ground-reflected light at rotation $\rho_k$	—
$\theta_{rd}$	the angle at which the Ground IAM angle step reads the curve for the ground direction	degrees
$y(\rho)$	the tabulated factor at rotation $\rho$. The diffuse or albedo shading factor, or an angular-response factor	—
$y_k$	the tabulated factor at rotation $\rho_k$	—
$\rho$	the tracker rotation about its axis. At the timestep, between $\rho_k$ and $\rho_{k+1}$	degrees
$t_\rho$	the position of $\rho$ between $\rho_k$ and $\rho_{k+1}$, from 0 to 1	—
$M_k$	the second derivative of the factor at rotation $\rho_k$, per degree squared	—
$f_{gnd,k}$	the albedo shading factor at rotation $\rho_k$	—
$d_\perp$	the distance across the tracker's axis from its centre to the centre of the other table	m
$d_\parallel$	the distance along the axis between the two centres	m
$L_t,\ L_n$	the lengths of the tracker and of the other table	m
$W$	the collector width along the slope	m

References

1. PVsyst 8 help, Diffuse losses with tracking systems
2. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

array.scene_tracker_tables = pvsyst_8

Symbols follow the symbol registry.