Mask-conditioned integrals

Method

The angular-response curve is integrated over every direction of a uniform sky, weighted by the cosine of the incidence angle, across the directions the row in front and the horizon leave visible (1). The ground-reflected light uses the same integral over the ground in front of the plane, with no mask (2), and the Ground IAM angle step sets the angle at which the curve is read for each ground direction. The result is one factor for the sky light and one for the ground light, constant over the year for fixed rows. For trackers both factors are computed every 5° of rotation, the sky factor with the row mask of the backtracking width and without the horizon, and read at the rotation of each timestep by linear interpolation. Fixed racks in a scene shaded by the shading-factor table or the direct projection take the mask from the scene's own shading-factor table: the sky factor is weighted by 1 minus the table's shaded fraction in each direction, and the ground factor by 1 minus its 0° row at each azimuth.

The math

1. Sky light
2. Ground-reflected light

$$F_{IAM,sky} = \frac{\int_{sky} F(\theta)\,M(\Omega)\,\cos\theta\,d\Omega}{\int_{sky} M(\Omega)\,\cos\theta\,d\Omega} \tag{1}$$ $$F_{IAM,gnd} = \frac{\int_{gnd} F(\theta)\,\cos\theta\,d\Omega}{\int_{gnd} \cos\theta\,d\Omega} \tag{2}$$

where

Symbol	Meaning	Unit
$F_{IAM,sky}$	the angular-response factor for the sky light	—
$F(\theta)$	the angular-response curve	—
$M(\Omega)$	1 minus the shaded fraction of the row for light from the sky direction $\Omega$; 0 where the horizon hides that direction	—
$\theta$	the angle between the direction $\Omega$ and the perpendicular to the module plane	degrees
$d\Omega$	an element of solid angle, taken where $\cos\theta > 0$	sr
$F_{IAM,gnd}$	the angular-response factor for the ground-reflected light	—

References

1. PVsyst 8 help, Array incidence loss (IAM)
2. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

iam.diffuse_integration = conditioned_integral

Symbols follow the symbol registry.