Exact analytical expression of the hemispherical irradiance on a sloped plane from the Perez sky

• We consider a sloped plane.
• Perez sky model approximation is reminded.
• We develop an explicit exact analytical expression of irradiance.
• Comparisons between our exact results and previous simplified results are provided.

Most of the simplified models consider that the diffuse irradiance received by a sloped plane can be split into a hemispherical part and a circumsolar part. This paper deals with the hemispherical part, as obtained by integration of the hemispherical sky radiance contribution. It is based on the Perez assumption, widely used in practice, that hemispherical sky radiance is uniform on the entire sky with the exception of a horizon band assigned to a different radiance value. Perez uses an approximate formula for the contribution of that horizon band. In this paper, an exact analytical expression of the irradiance due to the Perez horizontal band is developed and used for comparing exact and simplified values. Significant differences with the simplified Perez formula are observed. The use of our exact formula is thus advisable.