1. Chapter 4B: SOLAR IRRADIATION CALCULATION
Agami Reddy (rev- Dec 2017)
Extraterrestrial solar radiation and solar constant
Calculation of extraterrestrial irradiation
Effect of atmosphere on incoming solar radiation: attenuation, direct, diffuse and global radiation
Measuring instruments
Air mass
ASHRAE clear sky model for beam and diffuse radiation
Transposition models- radiation on flat inclined surfaces
- isotropic and anistropic models
8. Statistical correlation models- monthly mean values
- radiation on vertical surfaces
- daily diffuse from daily global
- hourly diffuse and global from daily global and diffuse
HCB-3 Chap 4B: Solar Irradiation

2. HCB-3 Chap 4B: Solar Irradiation
Extra-Terrestrial
Radiation
Effective solar
black body temp
of sun ~ 5,760 K
Notice solar spectrum
spans 100 – 3,000 nm
-Visible: (50%
of solar energy on earth)
-UV: (5%)
-Solar cells: 100-1,200
-Photochemistry:
From Boyle, 2004
HCB-3 Chap 4B: Solar Irradiation

3. Extra-terrestrial Solar Radiation
Solar constant: radiation intensity normal to the solar rays outside the atmosphere at the mean sun-earth distance
= 1367 W/m2
Factor causing variability in extra-terrestrial solar radiation
- Changes in sun-earth distance over year
HCB-3 Chap 4B: Solar Irradiation

4. Extra-terrestrial Solar Radiation
At any given day of the year (n), hourly extra-terrestrial radiation normal to solar rays:
(4.16)
where eccentricity correction factor (4.2)
So on 9/10, n=253, and I0 = x 1367 = W/m2
HCB-3 Chap 4B: Solar Irradiation

5. HCB-3 Chap 4B: Solar Irradiation
Daily Extraterrestrial Irradiation on Horizontal Surfaces
Hourly radiation on horizontal surface:
Radiation over day
on horizontal surface:
Fig. 4.10
HCB-3 Chap 4B: Solar Irradiation

6. HCB-3 Chap 4B: Solar Irradiation
Effect of Atmosphere
Figure 4.12 Solar spectrum for air mass zero (= extraterrestrial) and for air mass two, air mass being defined as 1/cos θs. The black portions indicate molecular absorption. (Absolute values of irradiance are based on an old value of solar constant and should be rescaled by 1367/1353.)
HCB-3 Chap 4B: Solar Irradiation

7. Components of Solar Radiation: Global, Direct and Diffuse
Direct solar radiation: solar radiation directly from the sun
Has a specific direction (use the solar angles presented earlier)
Magnitude: 0 to 1000 W/m^2
Is zero under overcast weather conditions or in shade
Diffuse solar radiation: solar radiation that is scattered by particle in air and other objects on earth
No specific direction
Not zero under overcast weather
condition or in shade
Fig. 4.13
HCB-3 Chap 4B: Solar Irradiation

8. Atmospheric Clearness Index
The daily clearness index KT is defined as:
(4.23)
where Hglo,hor is the daily global irradiation at the earth's surface, and H0,hor is the extraterrestrial daily irradiation on the same surface.
Thus, the clearness index includes two independent causes for the variability of terrestrial solar radiation: the local atmospheric conditions and the earth's motion which causes H0 to vary over the year.
 On heavily overcast days, may be as low as 0.05 to 0.1 while on clear days it is around 0.7 to 0.75
Monthly averages, designated by range from 0.3 for very cloudy climates such as upstate New York to 0.75 for the peak of the Sunbelt.
HCB-3 Chap 4B: Solar Irradiation

9. Radiation Availability
Three analysis trends:
(a) on-site measurements
(b) location independent correlations (lot of research done in this area in the 1970s, 80s and 90s when radiation data was limited)
(c) Satellite data: remote sensing used to create database
(software tools developed where one can use Google-earth to get preliminary cost estimates of various solar installations)
HCB-3 Chap 4B: Solar Irradiation

10. Solar Radiation Measuring Instruments
Global
Diffuse
Pyranometer with shading ring- Kipp
Pyranometer with thermal detector- Eppley
Global
Beam
Pyranometer with PV detector- LiCor
Pyrheliometer
HCB-3 Chap 4B: Solar Irradiation

11. HCB-3 Chap 4B: Solar Irradiation
Shadow ring needs adjustment every few days
HCB-3 Chap 4B: Solar Irradiation

12. Normal Incidence Pyrheliometer
acceptance angle is much larger than the solar angle of about 0.50
HCB-3 Chap 4B: Solar Irradiation

13. HCB-3 Chap 4B: Solar Irradiation
Concept of Air Mass
Concept applies to beam radiation only and relates to attenuation
m = 1/cos
Solar radiation higher for lower air mass:
Latitudes close to equator
Close to noon
In summer when sun is higher in sky
Figure 4.11 Concept of air mass
From Boyle, 2004
HCB-3 Chap 4B: Solar Irradiation

14. HCB-3 Chap 4B: Solar Irradiation
ASHRAE Clear Sky Irradiance Model
(4.20)
Eq(4.20)
(4.22)
and m is the air mass
HCB-3 Chap 4B: Solar Irradiation

15. HCB-3 Chap 4B: Solar IrradiationEq
(4.24)
(4.25)
(4.26)
(4.27)
HCB-3 Chap 4B: Solar Irradiation

16. HCB-3 Chap 4B: Solar Irradiation

17. HCB-3 Chap 4B: Solar Irradiation
4.9
4.10
HCB-3 Chap 4B: Solar Irradiation

18. HCB-3 Chap 4B: Solar Irradiation
4.21
4.26 & 4.27
4.24 & 4.259
(verify that these values are consistent with Table 4.2)
HCB-3 Chap 4B: Solar Irradiation

19. HCB-3 Chap 4B: Solar Irradiation
Fig Diurnal variation in clear sky radiation values for Phoenix, AZ during June 21st
HCB-3 Chap 4B: Solar Irradiation

20. Transposition Models: Hourly Radiation on Tilted Surfaces
Fig. 4.14
HCB-3 Chap 4B: Solar Irradiation

21. Cos (theta) effect of solar incidence angle
The cosine law states that the amount of radiation received by a surface decreases as the cosine of the incidence angle thetha
HCB-3 Chap 4B: Solar Irradiation

22. HCB-3 Chap 4B: Solar Irradiation
Isotropic Sky Model
Solar radiation from sky dome assumed uniform.
Three components:
Global radiation =
beam normal x conversion factor 1
+ horizontal diffuse x view factor Fsky
+ horizontal global x ground albedo x view factor Fgrd
HCB-3 Chap 4B: Solar Irradiation

23. HCB-3 Chap 4B: Solar Irradiation

24. ASHRAE Clear-Sky Anistropic Model
(4.34)
(4.35)
HCB-3 Chap 4B: Solar Irradiation

25. HCB-3 Chap 4B: Solar Irradiation

26. Summary: Clear day hourly solar radiation calculation
Given: location latitude, time of year, time of day, surface tilt and orientation
Calculate solar time
Calculate solar declination, hour angle, solar altitude, solar azimuth, angle of incidence
Calculate hourly extra-terrestrial solar radiation
Calculate beam radiation (normal to solar rays)
Calculate diffuse radiation on horizontal surface
Calculate beam radiation on horizontal surface
Calculate clear day solar radiation on tilted surface
HCB-3 Chap 4B: Solar Irradiation

27. Statistical Correlation Models 1/3
Mostly based on clearness index
Potter et al. approach: Applies only to vertical surfaces at daily time scales
HCB-3 Chap 4B: Solar Irradiation

28. HCB-3 Chap 4B: Solar Irradiation
Fig. 6418
HCB-3 Chap 4B: Solar Irradiation

29. HCB-3 Chap 4B: Solar Irradiation
2/3
Figure 4.16 Correlation of Collares-Pereira and Rabl (1979) for the ratio of long-term averages of daily diffuse and global solar irradiation, as a function of clearness index and sunset hour angle ωss.
HCB-3 Chap 4B: Solar Irradiation

30. HCB-3 Chap 4B: Solar Irradiation
3/3
HCB-3 Chap 4B: Solar Irradiation

31. HCB-3 Chap 4B: Solar Irradiation
Figure 4.17
Correlation between long-term averages of daily irradiation and instantaneous irradiance on a horizontal surface versus sunset hour tss: (a) for global insolation and (b) for diffuse insolation.
HCB-3 Chap 4B: Solar Irradiation

32. HCB-3 Chap 4B: Solar Irradiation
Outcomes
Understanding the concept of solar constant and its magnitude
Be able to calculate extraterrestrial irradiation- hourly and daily
Understanding effect of atmosphere and clearness index
Understanding the different components of solar radiation
Working knowledge on how to use the ASHRAE clear-sky model
Working knowledge on how to compute radiation on surfaces with arbitrary tilt and orientation using isotropic sky model
Working knowledge on how to compute clear sky radiation on surfaces with arbitrary tilt and orientation using ASHRAE anistropic sky model
Familiarity with statistical empirical correlations at monthly time scales
Working knowledge of how to determine long term radiation on vertical surfaces using the Potter approach
HCB-3 Chap 4B: Solar Irradiation