Irradiance & Radiation
Extraterrestrial Irradiance
This function computes the extraterrestrial irradiance outside of the earth’s atmosphere, based a Fourier series representation of the position of the sun (earthsun distance).
Inputs
Outputs
Algorithm
Reference
Bird, R., Hulstrom, R., A Simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal Surfaces, 1981
NREL SERI/TP642761
Spencer, J. W., Fourier Series Representation of the Position of the Sun, Vol. 2, 1971, p. 172.
Clearness Index
This function computes the global horizontal clearness index with respect to the extraterrestrial irradiance on the
horizontal surface.
Inputs
Outputs
Algorithm
Reference
Bird, R., Hulstrom, R., A Simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal Surfaces, 1981
NREL SERI/TP642761
Air Mass
This function empirically computes the nonpressurecorrected (sea level) and pressurecorrected (at altitude) air
masses as a function of the solar zenith angle.
Inputs
Outputs
Algorithm (Bird & Hulstrom Version)
Compute the sealevel air mass:
Algorithm (Kasten / Sandia Version)
Compute the sealevel air mass:
Algorithm (Common Pressure Correction and Filtering)
1.) Restrict the calculation of the air mass for zenith angles less than 89°
data):
Reference
Bird, R., Hulstrom, R., A Simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal Surfaces, 1981
NREL SERI/TP642761
Kasten, F. Discussions on the Relative Air Mass, Light Research Technology 25, 129.
Direct Normal Irradiance
This function computes the direct normal irradiance from the global horizontal and diffuse irradiance, if no direct normal irradiance is available.
Inputs
Outputs
Algorithm (Bird & Hulstrom Version)
Compute the direct normal irradiance only if G_{T} > G_{D} else set it to 0, as follows:
Diffuse Irradiance
PlantPredict implements three diffusedirect 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 userselectable:
Reindl
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 utilityscale 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 DiffuseDirect 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 K_{t} of 0.83 – 0.84. As a result, the threshold between segments B and C was moved from 0.78 to 0.83.
Inputs
Outputs
Algorithm
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 (f_{d}, 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 ≤ K_{t} ≤ 0.3:

 If 0.3 < K_{t} < 0.83:

 If 0.83 ≤ K_{t}:
Reference
Reindl, D. T., Beckman, W. A., Duffie, J. A., Diffuse Fraction Corrections, Solar Energy Vol. 45, No. 1, pp. 17, 1990.
Erbs Model
This routine estimates the direct normal and diffuse horizontal irradiance using the Erbs correlation.
Inputs
Outputs
Algorithm
1.) Find the piecewise correlation of the diffuse fraction f_{d} :

 If 0 ≤ K_{t} ≤ 0.22:

 2.If 0.22 < K_{t} ≤ 0.80:

 If 0.80 < K_{t}:
Reference
Erbs, et al, Estimation of the diffuse radiation fraction for hourly, daily and monthlyaverage global radiation. Solar Energy, 28:293302, 1982.
DISC Model
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.
Inputs
Outputs
Algorithm
1.) Compute the clearsky normal transmittance for all solar zenith angles.

 If K_{t } ≤ 0.60

 If K_{t } > 0.60
Please note that in Version 9 and earlier step 5 above used θ_{Z} > 87°. This caused some unrealistic spikes when using Weather File POAI with subhourly data. Beginning with Version 10 we have adjusted this condition to be θ_{Z} > 90°, which eliminated these spikes.
Reference
Maxwell, E. L., A QuasiPhysical Model for Converting Hourly Global Horizontal to Direct Normal Insolation.
Technical Report No. SERI/TR2153087, Golden, CO: Solar Energy Research Institute, 1987.
DIRINT Model
This routine determines direct normal irradiance using the DIRINT modification of the DISC model.
Inputs
Outputs
Algorithm
1.) Compute K_{T}´.
3.) Create K_{T}´ bins.
4.) Create θ_{Z} bins.
5.) Set perceptible water bin, Wbin, to 5, as this adjustment is currently not implemented in PlantPredict.
6.) Create ∆K_{T}´ bins.
7.) Perform 4D lookup of DIRINT coefficients using K_{T}´bin, θ_{Z} bins, ∆ K_{T}´ bins, and Wbin to get DIRINT_{coeff}.
8.) Calculate DIRINT direct normal irradiance.
Reference
Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, Dynamic GlobaltoDirect Irradiance Conversion Models. ASHRAE TransactionsResearch Series (1992), pp. 354369.
Maxwell, E. L., A QuasiPhysical Model for Converting Hourly Global Horizontal to Direct Normal Insolation. Technical Report No. SERI/TR2153087, Golden, CO: Solar Energy Research Institute, 1987.
Bird Sky Clear Model
This function computes the apparent shift in the solar elevation angle caused by atmospheric refraction.
Note that the output is a positive number; i.e.: near the horizon, the solar disk appears higher in the sky than its true position. The apparent elevation is the true (geometrical) elevation plus the correction factor.
Inputs
Outputs
Algorithm
The current implementation assumes default values for the following parameters:
Reference
Bird, R., Hulstrom, R., A Simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal Surfaces, 1981 NREL SERI/TP642761
Tilt Model
This function geometrically transposes the direct normal irradiance on an arbitrary tilted plane, and transposes the diffuse horizontal irradiance on the same tilted plane using a choice of userselectable tilt models: Perez or Hay.
Inputs
Outputs
Perez Algorithm (Diffuse Sky)
1.) Find the factors that account for the respective angles of incidence of circumsolar radiation on the tilted and horizontal surfaces. The circumsolar radiation is considered to be from a point source.