Skip to content

The Hay transposition model

Model

The Hay or Hay-Davies transposition model1 applies different transformations to the different irradiance components.

The beam component follows a purely geometrical transformation (no model, no intrinsic error):

\[ \mathsf{BeamInc} = \mathsf{BeamHor}\, \frac{\cos \mathsf{AngInc} }{\sin \mathsf{HSol}}\,. \]

The diffuse component is supposed to be decomposed into an isotropic distribution and a circumsolar contribution proportional to \(K_b\):

\[ \begin{align*} \mathsf{DiffInc} &= \mathsf{DiffHor}\,(1-K_b) (1 + \cos \theta) / 2 \,,\\ \mathsf{CircInc} &= \mathsf{DiffHor}\,K_b\,\frac{\cos \mathsf{AngInc}} {\sin \mathsf{HSol}}\,. \end{align*} \]

The albedo component is the irradiance reflected by the ground "seen" by the plane:

\[ \mathsf{AlbInc} = \rho\; \mathsf{GlobHor}\,(1 - \cos \theta) / 2\,. \]

where
\(\theta\) = Plane tilt
\(\mathsf{HSol}\) = Sun height on horizontal plane
\(\mathsf{AngInc}\) = Incidence angle
\(K_b\) = Clearness index of beam \(= \mathsf{BeamHor} / \textsf{EHI}\)
EHI = Extraterrestrial irradiance projected in horizontal plane
\(\rho\) = Albedo coefficient (usual value 0.2)

Warning

With the old transposition methodology (replaced by a new default since PVsyst 7),

\[ \mathsf{DiffInc} = \mathsf{DiffHor}\left[(1-K_b) (1 + \cos \theta) / 2 + \,K_b\,\frac{\cos \mathsf{AngInc}} {\sin \mathsf{HSol}}\right] \,,\enspace\mathsf{CircInc} = 0\,. \]

This difference had consequences in particular for shadings and IAM losses.

Cutoff for low sun heights

PVsyst applies a cutoff for low sun heights \(\mathsf{HSol} < 2°\). In such a case:

\[ \mathsf{BeamInc} = 0\,,\enspace\mathsf{CircInc} = 0\,. \]

  1. John E. Hay and J. A. Davies. Calculations of the solar radiation incident on an inclined surface. In John E. Hay and K. Won Thorne, editors, Proceedings: First Canadian Solar Radiation Data Workshop. Ottawa, Canada : Supply and Services Canada, 1980. URL: https://archive.org/details/proceedingsfirst00cana/mode/2up. ↩