Passias masking angle

Method

From a point on the collector, the row in front hides the sky below the angle to its top edge, the masking angle. Passias and Källbäck averaged that angle over the collector width in closed form, as a function of the tilt and the ground cover ratio (1). The share of the sky diffuse the row keeps is the square of the cosine of half the average angle (2), as the SAM technical reference applies it. Fixed rows use their tilt; trackers use the rotation of each timestep. It acts on the isotropic and horizon-band sky components, as the other options of this step do; the circumsolar part follows the beam. The ground cover ratio is the collector width over the pitch.

The math

1. Average masking angle
2. Sky diffuse kept

$$\bar\psi = -\frac{X}{2}\sin\beta\,\ln\left|2X\cos\beta - (X^2 + 1)\right| + (X\cos\beta - 1)\arctan\frac{X\cos\beta - 1}{X\sin\beta} + (1 - X\cos\beta)\arctan\frac{\cos\beta}{\sin\beta} + X\ln X\,\sin\beta,\qquad X = \frac{P}{W} \tag{1}$$ $$F_{sky} = \cos^2\frac{\bar\psi}{2} \tag{2}$$

where

Symbol	Meaning	Unit
$\bar\psi$	the masking angle averaged over the collector width	radians; 0 on flat rows
$X$	the inverse of the ground cover ratio, the pitch over the collector width	—
$\beta$	the tilt of the module plane from the horizontal	degrees
$P$	the row pitch, the distance between the rows	m
$W$	the collector width	m
$F_{sky}$	the fraction of the sky light the modules receive	—

References

1. Passias & Källbäck 1984, Shading effects in rows of solar cell panels, Solar Cells 11(3) 281–291
2. Gilman, DiOrio, Freeman, Janzou, Dobos & Ryberg 2018, SAM Photovoltaic Model Technical Reference Update, NREL/TP-6A20-67399
3. pvlib-python 0.16.1 source code (github.com/pvlib/pvlib-python), reference implementation: pvlib/shading.py, masking_angle_passias() and sky_diffuse_passias()

API

array.sky_masking_method = passias

Symbols follow the symbol registry.