Quaschning–Hanitsch › Published

Method

The direct and circumsolar light are kept when the sun, at the middle of the sunlit part of the timestep, is at or above the skyline, and removed when it is below (1). The sky light keeps the share of the sky in front of the plane that lies above the skyline, each direction weighted by the cosine of its incidence angle and of its elevation, for a uniform sky (2). The integral runs on cells of 0.25° of elevation and azimuth, with the skyline read at each cell's azimuth. A fixed plane has one factor for the year, and a tracker one per orientation. The ground-reflected light is not reduced.

The math

1. Direct light
2. Sky light

$$f_{b,i} = \begin{cases} 1 & \alpha_{m,i} \ge \alpha_{hrz}(\gamma_{m,i}) \\ 0 & \text{otherwise} \end{cases} \tag{1}$$ $$f_d = \frac{\iint_{e > \alpha_{hrz}(\gamma),\ \cos\theta > 0} \cos\theta\,\cos e\ d e\,d\gamma}{\iint_{\cos\theta > 0} \cos\theta\,\cos e\ d e\,d\gamma} \tag{2}$$

where

Symbol	Meaning	Unit
$f_{b,i}$	the fraction of the direct and circumsolar light kept at timestep $i$	—
$\alpha_{m,i}$	the sun elevation at the middle of the sunlit part of timestep $i$	degrees
$\alpha_{hrz}(\gamma)$	the skyline elevation in the direction $\gamma$	degrees
$\gamma_{m,i}$	the sun's azimuth at that instant, clockwise from north	degrees
$f_d$	the fraction of the sky light kept	—
$e, \gamma$	the elevation and azimuth of a sky direction	degrees
$\theta$	the incidence angle: between the light's direction and the perpendicular to the module plane. Of that direction	degrees

References

1. Quaschning & Hanitsch 1995, Shade calculations in photovoltaic systems, ISES Solar World Congress, Harare, https://www.volker-quaschning.de/downloads/ISES1995.pdf

API

options.far_shading_model = quaschning_hanitsch, site.use_horizon = true

Symbols follow the symbol registry.