Isotropic integral of the row shading factor

Method

The fraction of the sky light the rows leave is the integral of the row shading factor over every direction of a uniform sky, weighted by the cosine of the incidence angle. For fixed rows the integral has a closed form in the ratio of the collector width to the pitch. For trackers it is evaluated at every timestep at the tracker's rotation.

The math

$$F_{sky} = 1 - \frac{\mathcal{I}_{sky}}{1+\cos\beta},\qquad \mathcal{I}_{sky} = \frac{W + b_{top}}{W_{tot}}\left(\cos\beta - \cos(\beta+\psi_0)\right) - \frac{P}{W_{tot}}\left(1-\cos\psi_0\right),\qquad \tan\psi_0 = \frac{(W + b_{top})\sin\beta}{P - (W + b_{top})\cos\beta} \tag{1}$$

where

Symbol	Meaning	Unit
$F_{sky}$	the fraction of the sky light the modules receive	—
$\mathcal{I}_{sky}$	the integral of the shading factor over the sky	—
$\beta$	the tilt of the module plane from the horizontal	degrees
$W$	the collector width	m
$b_{top}$	the inactive band at the top edge	m
$W_{tot}$	the total row width including the bands	m
$\psi_0$	the profile angle at which the front row just clears the top of the collector; 90° when the denominator is 0 or less	degrees
$P$	the row pitch, the distance between the rows	m

References

1. PVsyst 8 help, Unlimited sheds
2. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

array.sky_masking_method = isotropic_integral

Symbols follow the symbol registry.