Angle of Incidence

The angle of incidence ($$AOI$$) between the Sun’s rays and the PV array can be determined as:

$$AOI=\cos^{-1}[\cos\left(\Theta_z\right)\cos\left(\theta_T\right)+\sin\left(\theta_Z\right)\sin\left(\sin\theta_T\right)\cos\left(\theta_A-\theta_{A},_{array}\right)]$$

where $$\theta_A$$ and $$\theta_Z$$ are the solar azimuth and zenith angles, respectively.  $$\theta_T$$ and $$\theta_{A},_{array}$$ are the tilt and azimuth angles of the array, respectively.

Azimuth angle convention is defined as degrees east of north (e.g. North = 0, East = 90, West = 270).  Array azimuth is defined as the horizontal normal vector from the array surface.  An array facing south has an array azimuth of 180 deg.  Array tilt is defined as the angle from horizontal.

Content contributed by Sandia National Laboratories