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Transposition model

Transposition is the calculation of incident irradiance on a tilted plane from horizontal irradiance data.

PVsyst offers two transposition models:

Hay or Hay-Davies model1, a classic and robust model which gives good results even when the knowledge of the diffuse irradiation is not perfect,

Perez model, is a more sophisticated model requiring good (well measured) horizontal data (cf Perez, Ineichen et al.2).

Transposition is calculated separately for each irradiance component:

  • The beam component involves a purely geometrical transformation (cosine effect), which doesn't involve any physical assumption.

  • The diffuse component is treated differently in the two models:

    In the Hay model, the diffuse irradiance is divided into an isotropic contribution, and a "circumsolar" part, which is proportional to the diffuse component. Through transposition, the isotropic part is reduced according to the solid angle "seen" by the collector plane (i.e: the fraction \((1 + \cos \theta) / 2\), where \(\theta\) is the tilt angle). The circumsolar part is transposed geometrically as the beam component. The specificity of the Hay model is the determination of the circumsolar fraction, which is chosen as the Clearness index Ktb of the beam component.

    The Perez model introduces the "horizon band" as a third diffuse component. It divides the sky into sectors, and parametrizes the magnitude of the circumsolar and the horizon band components according to correlations established on the basis of data of several dozens of measurement sites, distributed all over the world. A geometrical transformation is then performed on each component.

  • The albedo component is evaluated in the same manner in both models, as a given fraction (the "albedo coefficient") of the global, weighted by the spherical wedge defined between the horizontal and the tilted plane extension (i.e. the half sphere complement of the "seen" sky hemisphere), which is the fraction (1-cosi)/2 of the half-sphere.

Accuracy and Validations

The transposition models are highly dependent on the diffuse component, usually evaluated using a model (Liu-Jordan3, DirInt4, or Erbs5 correlation) which is not very well assessed.

Using measured diffuse component significantly improves transposition accuracy.

During early validations of the software, we tested both models with data from each site. Comparison of mean bias errors (MBE) shows systematic differences of 1.8-2.2% depending on Swiss sites, while RMSE standard deviations are comparable in all cases. This indicates that the Perez model, which is more complex and particularly sensitive to accurate diffuse irradiation determination, is often not justified in PVsyst except when measured hourly weather data is available.

Therefore, up to version 5, PVsyst used the Hay model by default.

However, recent work by Pierre Ineichen (P. Ineichen, 20116) concluded that the Perez model is slightly better (in terms of RMSD) in all cases, even with synthetic data. Therefore, from version 6, the Perez model is the default. However, the Perez model typically yields yearly averages higher than the Hay model, ranging from 0% to 2% depending on climate and plane orientation.

By the way you can always choose the model to be used in PVsyst (main menu: option Preferences > Preferences).

You can also choose if the model that has been used will be mentioned in the simulation report.

Two different uses of the circumsolar irradiance in the Simulation

Up to PVsyst V6.7.9, circumsolar irradiance was always combined with isotropic diffuse irradiance for shading and IAM calculations. From V6.8.0, a new treatment was introduced that handles circumsolar irradiance separately. This new transposition required explicit user activation. Since PVsyst V7.0, the new transposition is the default.

The switch between transposition algorithms is done either globally (which determines the default for new Projects) in Preferences -> Physical models, or at the project level in Project settings -> Design conditions.

The updated handling of the circumsolar irradiance changes slightly the linear shading losses and the IAM losses. It leads to a more precise simulation, especially for large tilts, namely vertical bifacial PV systems.

  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. ↩

  2. R. Perez, P.Ineichen, R. Seals, J. Michalsky, and R. Stewart. Modeling daylight availability and irradiance componentfrom direct and global irradiance. Solar Energy, 44(5):271–289, 1990. ↩

  3. Benjamin Y.H. Liu and Richard C. Jordan. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy, 4(3):1–19, July 1960. doi:10.1016/0038-092x(60)90062-1. ↩

  4. Richard Perez, Pierre Ineichen, E. L. Maxwell, R. D. Seals, and A. Zelenka. Dynamic global-to-direct irradiance conversion models. ASHRAE Transactions, 98:354–369, 01 1992. ↩

  5. D.G. Erbs, S.A. Klein, and J.A. Duffie. Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, 28(4):293–302, 1982. doi:10.1016/0038-092x(82)90302-4. ↩

  6. Pierre Ineichen. Global irradiance on tilted and oriented planes: model validations. Technical Report, Université de Genève, Institut des sciences de l'environnement, 2011. URL: https://archive-ouverte.unige.ch/unige:23519. ↩