HCB-3 Chap 4: Solar Radiation1 Chapter 4: SOLAR RADIATION Agami Reddy (July 2016) 1.Effect of earth’s tilt and rotation about the sun 2.Basic solar angles: solar declination, latitude, hour angle 3.Derived angles: solar altitude, solar azimuth 4. Sun path diagrams and shading from adjacent objects 5.Calculation of solar time 6. Solar constant and extraterrestrial solar radiation 7. Effect of atmosphere on incoming solar radiation: attenuation, direct, diffuse and global radiation 8. ASHRAE clear sky model 9. Transposition models- radiation on flat inclined surfaces - isotropic and anistropic 10. Daily clearness index and estimation of long-term average radiation

2HCB-3 Chap 4: Solar Radiation

3 From Boyle, 2004 From Goswami et al., 2004 Time of year effect on solar radiation: -Sun not exact center of earth path (+-1.7%) -Declination causes seasonal effects Elliptical orbit (+-1.7%) Closer

HCB-3 Chap 4: Solar Radiation4 Solar Geometry- Basic Angles sin

HCB-3 Chap 4: Solar Radiation5 eography.net/funda mentals/6h.html

HCB-3 Chap 4: Solar Radiation6 -Convention: +ve in the afternoon and –ve in morning -i.e., 3 pm would be 45 degrees hour angle - and 10 am would be -30 degrees

HCB-3 Chap 4: Solar Radiation7 Mazria, 1979

HCB-3 Chap 4: Solar Radiation8 Perspective of Local Observer Equinox- equal day/night Solstice- longest day/night

HCB-3 Chap 4: Solar Radiation9 Mazria, 1979 Monthly Solar Paths

HCB-3 Chap 4: Solar Radiation10 Mazria, 1979 Time of Day Solar Paths

HCB-3 Chap 4: Solar Radiation11 Mazria, 1979 Sun’s path across the sky

Example HCB-3 Chap 4: Solar Radiation12

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HCB-3 Chap 4: Solar Radiation15 Sun paths across the sky for different latitudes and times of year 90 deg 40 deg 0 deg Effect of Earth’s Tilt and Rotation about Sun Declination of 23.5 o results in changes in day length over year and different solar paths

HCB-3 Chap 4: Solar Radiation16 Using the sun-path diagram to determine shading from adjoining objects

HCB-3 Chap 4: Solar Radiation Solar Time Calculation Definition of solar time: time of day measured from solar noon; due south (in Northern hemisphere) is zero; towards east (-) towards west (+) Difference between local standard time and solar time is described by the equation of time For locations west of Greenwich: 17 (Local) solar time = standard time + 4’(Standard meridian-Local meridian) + ET For locations east of Greenwich, this sign should be –ve. Also standard time is watch time minus 1 hr (if daylight savings is in effect)

HCB-3 Chap 4: Solar Radiation18 Equation of Time Result of elliptical orbit of earth around sun ET = 9.87sin2B – 7.53cosB – 1.5sinB where: B = 360(n-81) / 364

HCB-3 Chap 4: Solar Radiation19 Greenwich Line

HCB-3 Chap 4: Solar Radiation20 Longitudes for U.S. Time Zones UTC – coordinated universal time (same as Greenwich time)

HCB-3 Chap 4: Solar Radiation Example Phoenix, AZ L st = 105° West (Mountain) i.e., 7 hours before GMT. L loc = 112° West When is solar noon on January 1? (n=1) B = 360 ° (1-81)/364 = ° E = 9.87 sin(2B) cos(B) sin(B) → E = minutes (Local) solar time = standard time + 4’( ) + E solar time = standard time minutes orstandard time - solar time = 31.6 minutes In other words, solar time is “slower” and occurs 31.6 minutes after the standard time shows noon. The time at which solar noon occurs is therefore 12:31 21

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HCB-3 Chap 4: Solar Radiation23 From Boyle, 2004 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:

HCB-3 Chap 4: Solar Radiation24 Extra-terrestrial Solar Radiation Solar constant: radiation intensity normal to the solar rays outside the atmosphere at the mean sun-earth distance= 1367 W/m 2 Factors causing variability in extra-terrestrial solar radiation - Changes in sun-earth distance over year - Air mass (Cos thetha effect)

HCB-3 Chap 4: Solar Radiation25 Extra-terrestrial Solar Radiation At any given day of the year (n), hourly extra-terrestrial radiation normal to solar rays: Where eccentricity correction factor So on 9/10, n=253, and I 0 = x 1367 = W/m 2

HCB-3 Chap 4: Solar Radiation26 Calculating Irradiation on Collector surfaces Cos (theta) effect of solar incidence angle Concept applies to tilted-stationary and tracking collectors as well

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HCB-3 Chap 4: Solar Radiation28 From Boyle, 2004 Concept of Air Mass Solar radiation higher for lower air mass: -Latitudes close to Equator -Close to noon -In summer Concept applies to beam radiation only and relates to attenuation

HCB-3 Chap 4: Solar Radiation29 From Boyle, 2004 Effect of Atmosphere

HCB-3 Chap 4: Solar Radiation30 Components of Solar Radiation : Global, Beam (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

HCB-3 Chap 4: Solar Radiation31 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 4: Solar Radiation32 Pyranometer with shading ring- Kipp Pyranometer with thermal detector- Eppley Pyranometer with PV detector- LiCor Pyrheliometer Solar Radiation Measuring Instruments Beam Or Direct Global Diffuse Global

HCB-3 Chap 4: Solar Radiation33 ASHRAE Clear Sky Irradiance Model

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HCB-3 Chap 4: Solar Radiation38 Diurnal variation in clear sky radiation values for Phoenix, AZ during June 21 st

HCB-3 Chap 4: Solar Radiation39 Transposition Models: Hourly Radiation on Tilted Surfaces

HCB-3 Chap 4: Solar Radiation40 Solar Angles on Planes Zenith angle and azimuth of plane and incidence angle of sun on this plane Incidence angle on tilted surface:

HCB-3 Chap 4: Solar Radiation41 Hourly Radiation on Tilted Surfaces

HCB-3 Chap 4: Solar Radiation42 Three components: Global radiation = beam normal x conversion factor 1 + horizontal diffuse x view factor 2 + horizontal global x ground albedo x view factor 3 ISOTROPIC sky model

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ASHRAE Anistropic Sky Model HCB-3 Chap 4: Solar Radiation44

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HCB-3 Chap 4: Solar Radiation47 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 4: Solar Radiation48 Long-term Average Radiation The daily clearness index K T is defined as: (4.19) where H glo, hor is the daily global irradiation at the earth's surface, and H 0,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 H 0 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. Collares-Pereira and Rabl method: Just knowing one can calculate the monthly Mean daily and hourly radiation on any tilted surface

HCB-3 Chap 4: Solar Radiation49 Long-term Average Radiation Potter et al. approach: Applies only to vertical surfaces at daily time scales

HCB-3 Chap 4: Solar Radiation50 Monthly average daily radiation on vertical surfaces- Based on Potter et al. 1989

HCB-3 Chap 4: Solar Radiation51 Outcomes Understand the motion of the earth around the sun Familiarity with the basic solar angles: declination, latitude and hour angles Working knowledge of computing solar altitude and azimuth angles Working knowledge of how to compute angles of incidence on surfaces Familiarity with the sun-path diagram Working knowledge of solar time and standard time Understanding of 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 radiation on surfaces with arbitrary tilt and orientation using ASHRAE anistropic sky model Familiarity with how to determine long term radiation on vertical surfaces using the Potter approach