Solar energy and daylight on tilt planes under CIE standard skies

The CIE (International Commission on Illuminance) Standard Skies depicts the typical diffuse luminance and radiance distributions over the skydome. However, it can be challenging to interpret the luminance and radiance distribution into the irradiance and illuminance contributions on tilt planes by numerical integrations. This paper proposes a surrogate model that determines the ratio of the diffuse irradiance on an arbitrary tilt plane to that on the unobstructed horizontal plane without the complicated and time-consuming numerical integrations. The model is determined using solar altitude, sky conditions, and the angular distance of the plane (surface normal) and the sun. The proposed model is validated by measurement of the vertical illuminance and irradiance that are taken in 2004 and 2005, and the irradiance on planes of different tilt angles and azimuth directions from February to May in 2015. All measurements were in the 10-minute interval. For vertical planes, the proposed approach gives the ratio of the root mean square errors to the measurement average 1.38% to 2.04% lower than a classical model for irradiance and 3.6% to 4.6% for illuminance, when the Skies can be accurately identified. The model thus accurately interprets the luminance and radiance distributions of the CIE Standard Skies, which can be essential to a fast study for the solar energy potential as well as the thermal and daylight environments under different sky conditions.