05 - solar radiation

8/9/2019 05 - Solar Radiation

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Solar Radiation

Interaction with the athmosphere

Direct and diffuse radiation

Geometry of direct solar radiation

Solar diagrams and determination of shades

Incident energy by radiation per day

Influence of clouds through clarity parameter

Calculation of contribution to solar pannels

Wavelength of Radiatoin

• Radiation can be addressed as a propagation of photons or an electromagnetic wave with associated wavelength.

• The wavelength where radiation intensity is maximum is inverse to the absolute temperature of the emitter.

• Solar radiation therefore has small wavelength while radiation from ambient and surfaces has larger.

• The human eye is most sensible at 0.55 μm where solar intensity is

(300 K) the peak is at ~ 10 μm

• The emissivity is the energy emitted compared with that of a black body

• The incident radiation is absorbed α, reflected ρ and transmitted τ.

Incropera


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Spectral properties• The different wave length is important because the properties of surfaces may change considerably with wavelength:

– Glass transmits most solar radiation and absorb ambient radiation

– The absorption coefficient for solar radiation αs can be significativelly different from the emissivity ε for the ambient temperature

– The reflectivity of the surfaces for solar radiation is also called albedo.

Extraterrestrial Solar Radiation

• Radiation is directional but due to the large distance from the sun, solar radiation may be considered in a single direction.

• The intensity outside the athmosphere changes during the year due to the elliptic earth trajectory and is given aproximately by:

365

3360cos901367

nG

n is the day in the year and

the cos argument is in degrees

• Due to the variation of the earth velocity in the trajectory the (True)Apparent Solar Time is corrected adding to time the Equivalent Time:

The time correction is smaller than 15 min.

)]sin(24.089 –)cos(21.4615 –

)sin(3.2077 –)cos(0.1868

..

365360sin Duffie‐Beckman


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Latitude and Longitude• The AST is a function of the longitude of the place:

– LST – Local standard time (In Summer the time is one advanced one hour)

– – ‐

)1(60/º15 Summer inh ET SM ON LST AST

‐

for the time zone considered (In Portugal = Greenwich; Azores: 15oW)

– e.g. In Lisbon on 30th Sept. solar noon is at: 13h26m (see calculation)

Hour = 12 + 1 ‐ (‐9o8’20”‐0) – 10/60

• The latitude defines the position of a location in angle from the equator line. The combination of latitude and declination δ

e nes e ang e o nc ence o so ar ra a on. • Declination in degrees is:

365

284360sin45.23

no

Interaction with the athmosphere

• Depending on the latitude and time of the day solar radiation has a different length to cross through the athmosphere.

• At solar noon the sun altitude α is hi her with a value in Lisbon of 75o in 21st June (δ=23,45o) and 28o in 21st December.

• In the athmosphere radiation is:

• Absorbed by gases decreasing the intensity.• Scattered by particulates dispersing in all

directions forming a diffuse part.

Rogério DuarteIncropera


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Direct and diffuse radiation• For a clear sky, ASHRAE defines the direct beam Gb and the

diffuse Gd radiation by:

sinexp B AGb bd CGG

• where the constants A, B and C have representative values on the 21st each month as presented in the following table:

Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

decl. (º) -20 -10.8 0 11.6 20 23.45 20.6 12.3 0 -10.5 -19.8 -23.45

G (W/m2) 1416 1404 1383 1360 1339 1330 1328 1343 1364 1386 1408 1417

mB 0.142 0.144 0.156 0.18 0.196 0.205 0.207 0.201 0.177 0.16 0.149 0.142

C 0.058 0.06 0.071 0.097 0.121 0.134 0.136 0.122 0.092 0.073 0.063 0.057

These values were defined for an average situation in USA at sea level.

There are also tables for specific locations.

In 2009 edition there is a further detailed model with parameters for USA.

Information for Portugal• The information that is regularly registered is the solar

radiation intensity in an horizontal surface Gh (Why hor. ?)

• Clarity index defined from 0 to 1 with 1 for clear sky.(


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Radiation observations (Mainland)

i l

Gh – Horizontal solar radiation energy (Wh/m2 day).

Kt – Clarity Index – Characterizes the level of sky clarity

Tg – Average gas temperature (oC)

Azores and Madeira

have also studies to

be included later.

an ev ar br ai un ul go e u ov ez

Gh 1638 2653 3844 5455 6640 7260 7838 6762 4939 3205 2087 1414Bragança Kt 0.416 0.492 0.515 0.578 0.610 0.632 0.703 0.680 0.607 0.531 0.484 0.406

Tg 2.5 5 7.5 10 12.5 15 20 20 15 12 5 4Gh 1806 2741 3974 5780 6668 7332 7526 6613 4956 3384 2184 1701

Porto Kt 0.445 0.498 0.526 0.609 0.611 0.638 0.675 0.663 0.603 0.551 0.492 0.472Tg 8 10 12.5 14 15 18 20 20 17.5 15 12.5 10Gh 2022 2970 4095 5480 6212 6534 6872 6244 4829 3557 2428 2027

Coimbra Kt 0.480 0.526 0.534 0.574 0.569 0.569 0.615 0.623 0.581 0.567 0.531 0.541Tg 9 10 12.5 15 15 18 20 20 20 15 12.5 10Gh

Lisboa Kt 0.490 0.540 0.553 0.611 0.626 0.660 0.709 0.700 0.639 0.584 0.529 0.505Tg 9 11 13 15 17 20 22.5 22.5 20 1.5 15 10Gh 1988 2949 4022 5610 6655 7322 7816 6867 5101 3558 2358 1879

Évora Kt 0.443 0.500 0.511 0.580 0.607 0.638 0.699 0.679 0.602 0.546 0.486 0.466Tg 9 10 12.5 14 17.5 20 24 24 21 17.5 12.5 9Gh 2402 3362 4560 6198 7329 7895 7979 7094 5713 4038 2731 2244

Faro Kt 0.505 0.547 0.566 0.634 0.667 0.689 0.714 0.697 0.662 0.600 0.535 0.522Tg 12.5 12.5 13 15.5 17.5 21 23 23 22.5 20 15 12.5

Direct solar radiation geometry

• While diffuse radiation may be considered uniform from all directions in an horizontal plane, direct radiation has a single

direction that can be well characterised by angles.

Figure from Renewable Energy using the same nomenclature


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List of relevant angles• Latitude L and longitude λ

• o ar a t tu e α eam an or zonta pro ect on

• Solar azimuth as (horizontal projection and south)

• Surface azimuth aw (hor. projection of normal and S)

• Surface inclination β (surface and horizontal)

• Incidence an le i normal to surface and sun beam

• Solar hour (hs) (Solar hour negative at sun rise and zero at noon to be similar to azimuth referential)

24

36012 AST hs

Solar Geometry

• Solar height can be related to latitude, declination and solar hour. That is for a given place and time.

• From this equation the sun rise/sun set time can be obtained (from the condition α=0):

•

sss h L L coscoscossinsin)sin(

Ltgtghh ssSS sSR coscos

• The sun position is represented in two types of sun trajectory diagrams: Circular and planar.

cossincos)sin( sss ha


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Circular sun diagram(Sun trajectory seen from top)

Depends on

latitude

José Luis Alexandre, FEUP

Calculations in diagram

• For shadows the angles can be represented as

a function of profile Azimute

00

N

ang e γ an az mu asAltitude

90

20

40

60

80 EW

270

21 Jun

21 Jul/Mai

21 Ago/Abr

21 Set/Mar

21 Out/Fev

sa

tgtg

cos

180S

HorasDias ou

declinações

ov an

21 Dez

8h

10h


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Planar solar diagramSun trajectory seen

the observer

Altitude

Hor a

Dia

21 Jun

21 Jul/Mai

21 Ago/Abr

21 Set/Mar

asAzimute

Horas

21 Out/Fev

21 Nov/Jan

21 Dez

90º Este 180º Sul 270º Oeste

Solar Diagrams

Circular Sun diagram (Sun

tra ector seen from to

Plane Sun diagram (Sun

trajectory seen in a circle

around the observer)


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Radiation incident in surfaces• The radiation incident in a surface is the sum of

– Direct radiation that depends on the direct intensity and on

– Diffuse radiation that is coming from all directions.

– Reflected radiation from the ground, depends on albedo

– Radiation from other surfaces in the view field of the surface.

The last is usually neglected when temperatures are similar and

the diffuse/reflected contributions depend on the view factor

• The geometrical characteristics of the surface are defined by the angle with the horizontal plane (β) and

the azimuth (aw)

Incident direct radiation• Can be calculated from the cosine of the incidence angle i:

cossinsincoscoscos ws aai

expresse ere as a unc on o so ar a u e an az mu

• This can also be represented as a function of latitude, declination, solar time and surface azimuth:

sws

w

hah L

a L Li

sinsinsincoscoscoscoscos

cossincossincossinsincos

• For a vertical surface (β=90o) facing south (aw=0) then:sw

Lh Li s cossincossincoscos


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Relation with horizontal radiation• From the horizontal radiation the direct solar beam

contribution can be calculated sind hb GGG • The direct radiation incident in a surface can thus be

calculated from:

• Although instant values can be defined it is usual to define an average value as the clarity is also an average value.

•

sincoscos iGGiGG d hbbs

south can be expressed as:

ssss

ssSS sSS b

Laa L

Laa L R

sinsin180/sincoscos

sinsin180/sincoscos

and are represented in diagrams for diferent values of L‐β ( φ‐β )

Graphical representation of Rb.

• These values are monthly averaged values for the Rb factor.• There are graphs for other orientations including vertical surfaces


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Total radiation in surfaces• The radiation incident in a surface is the sum of the

direct, diffuse and reflected components.

• The diffuse and reflected components depend on the view factor of the sky and the ground taken as

respectively: (1+cosβ)/2 and (1‐cosβ)/2.

2

cos1

2

cos1

r d bd hrsdsbss GG RGGGGGG

2

cos1

2

cos11

ground

h

d b

h

d hs

G

G R

G

GGG

Ratio defined from Clarity Index

AlbedoGround reflectivity

of solar radiation

Albedo or Ground Reflectance


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Information in RCCTE• For calculation of heat loads through the windows and

opaque surface over‐heating the heat flux in (kWh/m2) is given as a function of orientation for summer (122 days).

The heat flux is also given for

a vertical surface facing south

during the heating period.

Energia solar média incidente numa superfície vertical

orientada a sul na estação de aquecimento Gsul (kWh/m2 mês)

Regiões I1 I2 I3

Continente 108 93 90

Açores 70 50 50

Madeira 100 80 80

R C C T E

C a l c u l a

t i o n i

S h a d o

05 - solar radiation

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