PlantPredict implements three diffuse-direct decomposition models to compute the diffuse irradiance from the global horizontal irradiance if neither diffuse irradiance nor direct normal irradiance is available in the weather file. The choice of models is user-selectable:
This function computes the direct normal irradiance and the diffuse global irradiance from the global horizontal according to the Reindl correlation model, if no direct normal or diffuse irradiance is available. Three versions of the model are available in literature, as illustrated in Figure 6 :
- Function of zenith angle, clearness index, air temperature, and relative humidity (blue).
- Function of zenith angle and clearness index (red)
- Function of clearness index only (green)
A minor modification to the published algorithm was made based on one year of hourly global and diffuse measurements at a utility-scale power plant. At very high clearness indices, the discontinuity between segments B and C of the piecewise regression model is too abrupt, leading to discontinuous irradiance profiles on even clear days.
Figure 6. Reindl Diffuse-Direct Decomposition Model Compared to Measured Data
The discontinuity at Kt = 0.78 is problematic for clear sky days when there is little measured diffuse irradiance (black). An adjustment was made, as shown in Figure 7.
Figure 7. Modification of then Reindl Diffuse Correlation Model
This causes a large discontinuity in the errors of modeled DHI during these times. Based on this residual analysis it appears that the error in the Reindl model in sloped segment B is large up to a Kt of 0.83 – 0.84. As a result, the threshold between segments B and C was moved from 0.78 to 0.83.
Only versions (1) and (2) of the algorithm (as described above) are implemented, as version (3) is not necessary since ambient temperature is required in all PlantPredict weather files. If Φ is available, version (1) is used; if Φ is missing, then PlantPredict automatically defaults to version (2).
1.) Find the piecewise correlation of the diffuse fraction if air temperature and relative humidity are known (fd, first equation), or unknown (f’d, second equation). If the diffuse fraction falls out of the allowed range, clamp the result at the boundary value. Also note that these equations use the solar zenith angle, not the solar elevation angle (as defined in the Reindl paper).
- If 0 ≤ Kt ≤ 0.3:
- If 0.3 < Kt < 0.83:
- If 0.83 ≤ Kt:
Reindl, D. T., Beckman, W. A., Duffie, J. A., Diffuse Fraction Corrections, Solar Energy Vol. 45, No. 1, pp. 1-7, 1990.
This routine estimates the direct normal and diffuse horizontal irradiance using the Erbs correlation.
1.) Find the piece-wise correlation of the diffuse fraction fd :
- If 0 ≤ Kt ≤ 0.22:
- 2.If 0.22 < Kt ≤ 0.80:
- If 0.80 < Kt:
Erbs, et al, Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, 28:293-302, 1982.
This routine implements the DISC correlation function, which is not included by itself as an option in PlantPredict; however, it is used by both the DIRINT decomposition and Hay transposition models.
1.) Compute the clear-sky normal transmittance for all solar zenith angles.
- If Kt ≤ 0.60
- If Kt > 0.60
Maxwell, E. L., A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation.
Technical Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research Institute, 1987.
This routine determines direct normal irradiance using the DIRINT modification of the DISC model.
1.) Compute KT´.
3.) Create KT´ bins.
4.) Create θZ bins.
5.) Set perceptible water bin, Wbin, to 5, as this adjustment is currently not implemented in PlantPredict.
6.) Create ∆KT´ bins.
7.) Perform 4-D lookup of DIRINT coefficients using KT´bin, θZ bins, ∆ KT´ bins, and Wbin to get DIRINTcoeff.
8.) Calculate DIRINT direct normal irradiance.
Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, Dynamic Global-to-Direct Irradiance Conversion Models. ASHRAE Transactions-Research Series (1992), pp. 354-369.
Maxwell, E. L., A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation. Technical Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research Institute, 1987.