05 - solar radiation
TRANSCRIPT
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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