Available Solar Radiation - Part II (1)

8/10/2019 Available Solar Radiation - Part II (1)

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AVAILABLE SOLAR RADIATION

Part II

Prof. G.V. Fracastoro and Prof. M. PerinoDENERG Politecnico di TorinoC.so Duca degli Abruzzi 2410129 Torino

If not otherwise specified, figures are taken from SolarEngineering of Thermal Processes Duffie & Beckman


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DEFINITIONS - 1

Beam Radiation b (Gb): is the solar radiation received from the sun without having beenscattered by the atmosphere (beam radiation is often referred to as direct solar radiation;to avoid confusion between subscripts for direct and diffuse , we use the term beamradiation, subscript b).

Diffuse Radiation d (G d): is the solar radiation received from the sun after its direction hasbeen changed by scattering by the atmosphere (diffuse radiation is referred to, in somemeteorological literature, as sky radiation or solar sky radiation; the definition used herewill distinguish diffuse solar radiation from infrared radiation emitted by the atmosphere.Diffuse radiation, subscript d).

Total (Global) Solar Radiation (G): is the sum of beam and diffuse solar radiation on asurface (the most common measurements of solar radiation are total radiation on ahorizontal surface. When we will make reference to total solar radiation we will not use anysubscript).

G = Gb + Gd


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Irradiance, G [W/m 2]: is the rate at which radiant energy (energy flux) is incident on asurface per unit area of surface. The symbol G is used for solar irradiance, with appropriatesubscripts for beam (b), diffuse (d), or spectral radiation ( ).

Irradiation H [J/m 2, kWh/m 2]: is the incident energy per unit area on a surface, found byintegration of irradiance over a specified period (usually an hour or a day). Insolation is a

term applying specifically to solar energy irradiation. The symbol H is used for insolation fora whole day . The symbol I is sometimes used for one hourThe symbols H and I can represent beam, or total and can be on surfaces of any orientation(with their corresponding subscripts).

Subscripts on G, H, and I are as follows:

o refers to radiation above the earth's atmosphere, referred to as extraterrestrialradiation,

b and d refer, respectively, to beam and diffuse radiation;T (or ) and n refer to radiation on a tilted plane and on a plane normal to the

direction of propagation. If neither T nor n appears, the radiation is on a horizontal plane. h refers to horizontal radiation, as well

DEFINITIONS - 2


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BEAM RADIATION ON HORIZONTAL AND TILTEDSURFACE Angle scheme

G b,h G b,n

q z

n r

b

n r

G b,n

q

Sun

= tilt angle


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RATIO OF BEAM RADIATION ON TILTED SURFACE TO THATON HORIZONTAL SURFACE - 1

It is often necessary to calculate the hourly radiation on a tilted surface of a collector frommeasurements or estimates of solar radiation on a horizontal surface.

The most commonly available data are total radiation for hours or days on the horizontalsurface, whereas the need is for beam and diffuse radiation on the plane of a collector.The geometric factor Rb, the ratio of beam radiation on the tilted surface to that ona horizontal surface at any time, is given by

z z bn

bn

b

T ,bb cos

coscosGcosG

G

G R

qq

qq
http://www.pveducation.org/pvcdrom/properties-of-sunlight/solar-radiation-on-titled-surface


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RATIO OF BEAM RADIATION ON TILTED SURFACE TO THAT ONHORIZONTAL SURFACE - 2

The symbol G is used to denote rates [W/m2

], while I [J/m2

], is used for energy quantitiesintegrated over 1 hour (and H over one day).

b

T b, b G

GR

b

T b, b I

IR

When R b is calculated for hourly periods; angles are calculated at midpoint of the hour(e.g. for the assessment of R b for the hour comprised between 10 and 11 am theevaluation of the angles must be done at the time 10.30).

The optimum azimuth angle for flat-plate collectors is usually 0 in the Northernhemisphere (or 180 in the Southern hemisphere).Thus it is a common situation that = 0 (or 180 ).

http://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolation

b

T b,b H

H R
http://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolationhttp://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-fo-solar-insolation


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Solar radiation data are used in several forms and for a variety of purposes.The most detailed information available is hour-by-hour beam and diffuse solarradiation on a horizontal surface, which is used in simulations of solar processes andof heat transfer in buildings.

Daily data are often available and hourly radiation can be estimated from daily data.

Monthly total solar radiation on a horizontal surface can be used in some processdesign methods. However, as process performance is generally not linear with solarradiation, the use of averages may lead to serious errors if non linearity are not taken

into account.

SOLAR DATA AVAILABILITY


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SOLAR RADIATION MEASUREMENTS - 1

Instruments for measuring solar radiation are of two basic types: pyranometer and

pyrehliometer .A pyrehliometer (sometimes called actinometer ) is an instrument using a collimateddetector for measuring solar radiation from the sun and from a small portion of the skyaround the sun (i.e., beam radiation) at normal incidence. The instrument is mounted on a tracking mechanism. The detector is at the end of

the collimating tube, (the detector is a multijunctionthermopile). The aperture angle of theinstrument is 5.7 , so the detector receives radiation fromthe sun and from an area of the circumsolar sky two ordersof magnitude larger than that of the sun.


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A Pyranometer (or, solarimeter ) is an instrument for measuring total hemispherical solar

(beam plus diffuse) radiation, usually on a horizontal surface. If shaded from the beamradiation by a shade ring or disc, a pyranometer measures diffuse radiation.They are the most widely spread solar radiation measuring instruments.The detectors for these instruments must have a response independent of wavelength ofradiation over the solar energy spectrum, and on the angle of incidence of solar radiation.The detectors of most pyranometers are covered with one or two hemispherical glass

covers to protect them from wind, rain, smog, etc..


Solarimeter (TP)

Solarimeter (PV)


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In addition, there are instruments for measuring diffuse (or, sky) radiation, and formeasuring ground reflected radiation (albedometer).


Shadow band solarimeter(diffuse radiation measurement)

Albedometer


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The hours of bright sunshine, that is, the time in which the solar disc is visible, is of someuse in estimating long-term averages of solar radiation. Two instruments have been or arewidely used, The Campbell-Stokes sunshine recorder uses a solid glass sphere ofapproximately 10 cm diameter as a lens that produces an image of the sun on theopposite surface of the sphere.

A photoelectric sunshine recorder, which incorporates two selenium photovoltaic cells,one of which is shaded from beam radiation and one exposed to it. In the absence ofbeam radiation, the two detectors indicate (nearly) the same radiation level.

Measurement of sunshine duration

When beam radiation is incident on the

unshaded cell, the output of that cell is higherthan that of the shaded cell. The duration of acritical radiation difference detected by thetwo cells is a measure of the duration of brightsunshine.


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Solar radiation data are available in several forms. The following information aboutradiation data is important in their understanding and use: whether they are instantaneous measurements (irradiance) or values integrated oversome period of time (irradiation, usually hour or average monthly day); the time or time period of the measurements (daily, mean); whether the measurements are of beam, diffuse, or total radiation; the receiving surface orientation (horizontal, vertical S-W-E- N , sloped,..).

Most radiation data available are solar total for horizontal surfaces, and have beenmeasured with pyranometers. Most of these instruments provide radiation records as afunction of time (time profiles on hourly basis), but direct and diffuse fractions are notknown.

Two types of solar radiation data are widely available: The first is monthly average daily total radiation on a horizontal surface the second is hourly total radiation on a horizontal surface, I, for each hour for one ormore years.The data are widely available from weather services.

SOLAR RADIATION DATA

H


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Care must be taken since not all the time recorded for hourly weather data areconsistent among each other (e.g. some uses local solar time, other use local standard

clock time and can/cannot account for daylight savings time),

SOLAR RADIATION DATA


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ESTIMATION OF CLEAR-SKY RADIATION

The effects of the atmosphere in scattering and absorbing radiation are variable withtime as atmospheric conditions and air mass change.

It is useful to define a standard clear sky and calculate the hourly and dailyradiation which would be received on a horizontal surface under these standardconditions.

It is possible to estimate the beam radiation transmitted through clear atmospheres ,taking into account sun zenith angle and altitude, for a standard atmosphere.Numerous models are available, such as Hottel, or ASHRAE (Moon). In the following,the ASHRAE model will be described.


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ASHRAE Model (clear sky) irradiances

/cos z BbnG A e

q

d bnG C G

Direct (beam) normal

Diffuse horizontal (isotropic sky)

The ASHRAE model is a model of simple use, although sufficiently accurate forengineering calculations. One of the main simplifying assumptions it assumes isthe isotropic diffuse radiation.

Diffuse radiation is actually composed of three parts:

an isotropic part , received uniformly from the entire sky dome,

a circumsolar diffuse radiation, resulting from forward scattering of solarradiation and concentrated in the part of the sky around the sun,

a part referred to as horizon brightening , concentrated near the horizon andmost pronounced in clear skies.


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ASHRAE Model (clear sky) irradiances

(cos ) b d z bnG G G C Gq

1 cos2c s

F b

c g c sF 1 F

cos T bn d c s c g G G G F G F q

Total horizontal

Surface-sky and surface-ground viewfactors

Total on tilted surface

APPARENT SOLAR CONSTANT A (W/m 2)

EXTINCTION COEFFICIENT B

DIFFUSE RADIATION COEFFICIENT C


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ASHRAE model parameters during the year

Month A B C

W/m2

1 1229 0.142 0.058

2 1213 0.144 0.06

3 1185 0.156 0.071

4 1134 0.18 0.0975 1103 0.196 0.121

6 1087 0.205 0.134

7 1084 0.207 0.136

8 1106 0.201 0.122

9 1150 0.177 0.092

10 1191 0.16 0.07311 1220 0.149 0.063

12 1232 0.142 0.057


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Apparent solar constant A

1060

1080

1100

1120

1140

1160

1180

1200

1220

1240

1 2 3 4 5 6 7 8 9 10 11 12

month

A ( W / m 2 )


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Atmospheric extinction coefficient (B) and diffuseradiation coefficient (C)

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10 11 12

month

B

C


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Clear sky solar irradiance ( = 45 N)

Clear sky solar irradiance values (21 September)

Beam Normal (G bn ), Diffuse Horizontal (G dh ), Total Horizontal (G th )

0

100

200

300

400

500

600

700

800

900

1000

0.0 6.0 12.0 18.0 24.0

hour

s o l a r i r r a d i a n c e ( W / m

2 )

Gbn

Gdh Gth


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Clear sky horizontal irradiance G ( = 45 N)

0

100

200

300

400

500

600

700

800

900

1000

0.0 4.0 8.0 12.0 16.0 20.0 24.0

hour

H o r i z o n t a

l S u n i r r a

d i a n c e

( W / m 2 )

January

February

March April

May

June

July

August

Sept.

Oct.

Nov.

Dec.


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Clear sky solar irradiance on vertical surfaces(September, clear sky) ( = 45 N)

0

100

200

300

400

500

600 700

800

900

1000

0.0 6.0 12.0 18.0 24.0

S

S-E

E

N-E

N

N-W

W

S-W


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RADIATION WITH CLEAR AND CLOUDY DAYSAND HOURS

The frequency of occurrence of periods of various radiation levels, for example, of goodand bad days, is of interest to determine the fraction of diffuse radiation to totalradiation (either daily or monthly average),

To this purpose the clearness index will be introduced:

The monthly average clearness index, is the ratio of monthly average daily radiationon a horizontal surface, , to the monthly average daily extraterrestrial radiation :

TK

oHH

The data are from measurements of total solar radiation on a horizontalsurface, that is, the commonly available solarimeter (pyranometer ) measurements.Values of , (extra-atmospheric on horizontal plane) can be calculated by the methodsalready seen (eq. 15, 16 and 17)

H

oH

0 H H

K T


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Liu and Jordan (1960) found that, if for locations with a particular value of thecumulative frequency of occurrence of days with certain values of K T is plotted as afunction of K T, the resulting cumulative distribution curves are very nearly identical forlocations having the same values of , even though the locations varied widely inlatitude and elevation.On the basis of this information, they developed a set of generalized distribution curvesof KT versus f , which are functions of , the monthly clearness index:

TK

TK

TK

DISTRIBUTION OF CLEAR AND CLOUDY DAYSAND HOURS

TK In a place having =

0.5, 75% of dayshave K T < 0.7


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The usual approach is to correlate the average monthly diffuse fraction:

with the monthly average clearness index

BEAM AND DIFFUSE COMPONENTS OFRADIATION

Methods are needed to estimate the fractions of total horizontal radiation that arediffuse and beam (on hourly, daily and monthly basis).

Splitting total solar radiation on a horizontal surface into its diffuse and beamcomponents is of interest in two contexts:

methods for calculating total radiation on surfaces of other orientation from data on ahorizontal surface require separate treatments of beam and diffuse radiation.

estimates of the long time performance of most concentrating collectors must bebased on estimates of availability of beam radiation .

dK =H Hd

TK


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BEAM AND DIFFUSE COMPONENTS OFHOURLY, DAILY , MONTHLY RADIATION

Diffuse fraction of the monthly average radiation (Liu-Jordan-Klein correlation).Depends on season through the sunset hour angle, s:

(33)


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Liu-Jordan-Klein correlation for dK

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

Kt

K d

s < 81.4 s > 81.4


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RADIATION ON SLOPED SURFACESA general problem is to calculate the radiation on tilted surfaces when only total radiation

on a horizontal surface is known.A simple but sufficiently accurate model is the isotropic diffuse model (Liu & Jordanmodel) in which it is assumed that both diffuse and ground-reflected radiation areisotropic. Under this assumption, the sum of diffuse from the sky and ground-reflectedradiation on the tilted surface does not depend on orientation.

The total radiation is, then, the sum of the beam contribution calculated as H b Rb the sky diffuse contribution, equal to horizontal diffuse, H d, times the view factor

between collector surface and sky the ground diffuse contribution, equal to total horizontal, H, times the view factor

between collector surface and ground

cg g csd bbT F H F H R H H


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HT is the total radiation on a surface tilted at slope b from the horizontal plane.

Fcs =(1 + cos b )/2 is the view factor of the tilted surface (collector) to the sky.

RADIATION ON SLOPED SURFACES: DETAILS

2

1 b cos H g

Fcg =(1 - cos b )/2 is the view factor of the titled surface (collector) to the ground

if the surroundings have a diffuse reflectance of g for the total solar radiation, thereflected radiation from the surroundings on the surface will be:

http://www.pveducation.org/


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Therefore

and

AVERAGE RADIATION ON SLOPED SURFACES

Where:

is a function of (eq. 33), and values can be found in Standard UNI 10349

The ratio of the average daily beam radiation on the tilted surface to that on ahorizontal surface for the month , which is equal to is given by: bR

HH d TK

b bT HH

b

b

2

1

2

11

coscos H H

R H H

H H

R g d

bd T

b

b

2

1

2

1 cos H

cos H R H H

g d bbT

H


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Rb factor for latitude 45 N (collector facing South)

Rb factor for latitude 45 N

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

0 10 20 30 40 50 60 70 80 90

tilt angle

R b

6

5-7

4-8

3-9

2-10

1-11

12


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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 10 20 30 40 50 60 70 80 90

tilt angle

R b

6

5-7

4-8

3-9

2-10

1-11

12


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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 10 20 30 40 50 60 70 80 90

tilt angle

R b

6

5-7

4-8

3-9

2-10

1-11

12


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South surface irradiation (TO)

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12

month

D a i

l y i r r a d i a t i o n

( k W

h / m 2 )

hor 45 vert


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Azimuth effect (Torino)

Irradiation on tilted surfaces for differentazimuth values Tilt angle b = 45 Tilt angle b = 90

Global yearly value With b = 45: Esol,45 = 5420 MJ/m 2 With b = 90: E sol,90 = 3824 MJ/m 2 (70,6 %) With b = 0: Esol,0 = 4817 MJ/m 2 (89%)


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Average monthly energyTorino ( b = 45)

0.0

5.0

10.0

15.0

20.0

25.0

1 2 3 4 5 6 7 8 9 10 11 12

month

E n e r g y

( M J / m 2

d a y

South SSE/SSW SE/SW ESE/WSW E/W


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Incident energy fraction fordifferent azimuth angles ( b=45)

0.860.960.991.001.00summer

0.510.570.590.590.59 > 0 /year

0.790.880.920.961.00winter

0.320.360.370.390.41 < 0 /year

0.830.930.960.981.00year

90 60 45 30 0 azimuth


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0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90

azimuth

year winter/year winter summer/year summer


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Monthly average energyTorino ( b = 90)

0.0

5.0

10.0

15.0

20.0

25.0

1 2 3 4 5 6 7 8 9 10 11 12

month

E n e r g y

( M J / m 2

d a y )

South SSE/SSW SE/SW ESE/WSW E/W


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1.091.181.161.091.00summer

0.550.590.580.550.50summer/year

0.670.790.850.921.00winter

0.330.390.430.460.50winter/ year

0.880.981.001.011.00year

90 60 45 30 0 azimuth


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0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90

azimuth ( )

year winter/year winter summer/year summer


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Incident solar energy for different b values 0

Sun Energy variation for different tilt angle values

0.0

5.0

10.0

15.0

20.0

25.0

1

2

3

4

5

6

7

8

9

10

11

12

I n c i

d e n t s o

l a r e n e r g y

( M J / m 2

d a y )

b b 15 b 3 b 45 b 6 b 75 b 9


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Incident energy for different b values

0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90

tilt

year winter/year) summer/year)


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SUMMARY

Radiation data are available in several forms, with the most widely available being

pyranometer measurements of total (beam-plus-diffuse) radiation on horizontalsurfaces.These data are available on an hourly basis from a limited number of stations andon a daily basis for many stations.

Nevertheless, solar radiation information is needed in several different forms,

depending on the kinds of calculations that are to be done:procedures based on detailed hour-by-hour basis for long time performance of asolar process system (hourly information of solar radiation and othermeteorological measurements are needed).

procedures based on monthly average solar radiation. These are useful in

estimating long-term performance of some kinds of solar processes.

There are methods for the estimation of solar radiation information in the desiredformat from the data that are available, such as estimation of beam and diffuseradiation from total radiation, time distribution of radiation in a day, and radiationon surfaces other than horizontal.


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References for solar angles and radiation

Web: http://www.solaritaly.enea.it/CalcRggmmOrizz/Calcola1.p

hp http://re.jrc.ec.europa.eu/pvgis

Books: Duffie & Beckman, Solar Engineering of thermal processes,

Wiley & sons, 870 pp. Tiwari, Solar energy technology advances, Nova Publishers,

2006 - 138 pages Cucumo, Marinelli, Oliveti, Ingegneria solare Principi e

applicazioni, Pitagora, Bologna 1994
http://www.solaritaly.enea.it/CalcRggmmOrizz/Calcola1.phphttp://www.solaritaly.enea.it/CalcRggmmOrizz/Calcola1.phphttp://re.jrc.ec.europa.eu/pvgishttp://re.jrc.ec.europa.eu/pvgishttp://www.solaritaly.enea.it/CalcRggmmOrizz/Calcola1.phphttp://www.solaritaly.enea.it/CalcRggmmOrizz/Calcola1.php

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Available Solar Radiation - Part II (1)

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