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Transcript of Solare Einstrahlung auf der Erde 3.2 3.21 The revolution of the earth around the sun 3.22 Solare...
Solare Einstrahlung auf der Erde3.2
3.21 The revolution of the earth around the sun 3.22 Solare Einstrahlung .221 Wo steht die Sonne .222 Streuung und Absorption der Solarstrahlung (Rayleigh, Angström,Linke) .223 Diffuse und direkte Solarstrahlung (Liu Jordan,Reindl,Perez) [.224 Verschattung und Bodenreflektion]
3.23 Maps of horizontal surface global radiation Welt, Europa, Deutschland, Saarheimat
3.24 Simulationsprogramme .251 Excelblatt: Modellierung des Sonnenenergie - Dargebotes
.252 kommerzielle Simulationsprogramme (hübsch, vermutlich korrekt, aber undurchsichtig und für Außergewöhnliches nicht zu gebrauchen)
Maps of horizontal surface global radiation
3.23
.231 World
.232 Europe
.233 Germany
.234 local: geliebte Saarheimat
3.231 World
World Map of mean global Solar Irradiance
BezugsQuelle: University of Columbia, http://www.ldeo.columbia.edu/edu/dees/U4735/lectures/14.html Prof. Pitman:Energy:lecture14
annual, March, June, September, December
Angaben in [ kWh/ m2 ] für mittlere tägliche Einstrahlung
/ Palz-Greif 96: European Solar Radiation Atlas ,p. 322 -326
Europe
Maps of horizontal surface global radiation
3.232 Europe
/ Palz-Greif 96: European Solar Radiation Atlas ,p. 322
/ Palz-Greif 96: European Solar Radiation Atlas ,p. 323
/ Palz-Greif 96: European Solar Radiation Atlas,p.324
/ Palz-Greif 96: European Solar Radiation Atlas ,p. 325
/ Palz-Greif 96: European Solar Radiation Atlas ,p. 326
Angaben in [ kWh/ m2 ] für mittlere tägliche Einstrahlung
Solarstrahlung in Deutschland
3.233
Jahresummen der Globalstrahlungin Deutschland
Quelle: RWE-Bauhandbuch 2004, Abb.17.6
Saarbrücken 1050 – 1100 [kWh/m^2/a]
Quelle: RWE-Bauhandbuch 2004, p. 17/7; Abb.17.7 Standort: Berlin , Breitengrad = 52°N
Jahressummen der Globalstrahlung auf verschieden orientierten Flächen
in [kWh/(m2a)]
Sonnenbahnen zu unterschiedlichen Jahreszeiten
Quelle: RWE-Bauhandbuch 2004, p. 17/5; Abb.17.3
Standort: Berlin , Breitengrad = 52°N , Zeit: MEZ
Quelle:V. Quaschning 2003: Regenerative Energiesysteme(3.A.), Hanser Verlag München, ISBN=3-446-24983-8, Bild 2.10,p.53
Standort: Berlin , Breitengrad = 52.3°N
Sonnenbahndiagramm für Berlin, 52°N
0° +90°-90°
In Deutschland überwiegt die diffuse Solarstrahlung
Quelle: RWE-Bauhandbuch 2004, p. 17/6; Abb.17.5
Saarbrücken 1050 – 1100 [kWh/m^2/a]
SB 1290
Jahresummen der Globalstrahlung Mittelwerte im Superjahr 2003
sorry, that I had to confound different sources with a different colour-scale
Regionale Solarstahlung im Saarland
Bericht über eine Messkampagne im Rahmen eines EU-Projektes
Synchrone Kurzzeitmessungen (30 sec) an 15 Stationen
3.234
Quelle:
Staatliches Institut für Gesundheit und Umwelt
(SIGU)
Direktor: Dr. rer. nat. Gerhard Luther
66117 Saarbrücken
FINAL REPORT
01.04.1996
Authors: Dr. rer. nat. Gerhard Luther Dipl.-Phys. Frank Schirra Supported by: Commission of the European Communities Contract-No.: JOU2-CT92-0018
CONSEQUENCES OF DECENTRALISED PV ON
LOCAL NETWORK MANAGEMENT
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Titelblatt
Short Time Measurement (30 sec)
of Global Solar Energy at horizontal plane
over 2.5 years
at 15 stations in the Region of Saarbrücken,
Germany
_1. Measuremenmts
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Figure I.1-1, p.7
Relative Coordinates of Measuring Stations
-15
-10
-5
0
5
10
15
20
-35 -30 -25 -20 -15 -10 -5 0 5 10 15
East [km]
9
111
15
1013
8
6
North [km]12
2
Relative coordinates of all measuring stations in relation to our Institute in Saarbrücken (Station 2 at (0, 0)). Coordinates of station 2: Longitude= 6°58’ ; Latitude=49° 14’
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Figure I.1-2, p.7
Relative Coordinates of Stations in the Near Grid
-1,6
-1,4
-1,2
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
East [km]
North [km]
2
6
5
3
4
E
7
Figure I.1-2: Relative coordinates of measuring stations in the near distance-grid in relation to our Institute in Saarbrücken (Station 2 at (0, 0))
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Chapter 2.2, p.42 ff
_2. Some Characteristic Patterns of global solar irradiance
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; p.42
Inspection of our solar radiation atlas gives rise to 8 main radiation patterns.
In all diagrams, we confine ourselfs to the following time-range:
Days: 931001 – 950930
Time: 08:30 - 15:10 fixed UTC-time (but slightly varying local solar time)
In the following slides we give only some examples
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; p.43
Pattern 1 : Percentage of days: 52%
Strong uniform oscillations over the whole time range under consideration.
In the mean, the difference between minimum and maximum amplitudes is 200 W/m2.
Less pronounced oscillations occur at the margins of the time range.
This is characterstic for a day with blue sky, compact clouds drifting uniformly over the region.
The time intervall between successive minima or maxima varies between 10 and 50 minutes.
Seasonal dependence: During summer days the maximum of the curve is located mainly above 600 W/m2,
On the other days it is clearly below.
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2.2, p.44
Global Radiation in the Region of Saarbrücken at 950621
0
200
400
600
800
1000
1200
1400
21,36 21,41 21,46 21,51 21,56 21,61 21,66
solar day
W/m
2̂
max
mean
min
0
Pattern 1 - Strong uniform oscillations over the whole time-period
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.2a, p.45
Pattern 1 - Strong uniform oscillations over the whole time-period
Pattern 1 - Same as fig. III.2-2, but moving averages over 2.5 min and 5 min included
Global Radiation in the Region of Saarbrücken at 950621
0
200
400
600
800
1000
1200
1400
21,30 21,35 21,40 21,45 21,50 21,55 21,60 21,65 21,70
solar day
W/m
2̂
max
mean
min
5 ma
10 ma
0
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.3, p.46
Pattern 1 - Strong uniform oscillations over the whole time-period. Near distance grid
Pattern 1 - Strong uniform oscillations over the whole time-period for stations in the near distance-grid
Global Radiation in the Region of Saarbrücken at 950621Near Stations: 2,3,4,5,6,7,14
0
200
400
600
800
1000
1200
1400
21,36 21,41 21,46 21,51 21,56 21,61 21,66
solar day
W/m
2̂
max
mean
min
0
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.4, p.47
Pattern 1 - Strong uniform oscillations over the whole time-period. Far distance grid
Global Radiation in the Region of Saarbrücken at 950621Far Stations: 1,6,8,9,10,11,12,13,15
0
200
400
600
800
1000
1200
1400
21,36 21,41 21,46 21,51 21,56 21,61 21,66
solar day
W/m
2̂
max
mean
min
0
Figure III.2-4: Pattern 1 - Strong uniform oscillations over the whole time-period for stations in the far-distance grid
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; p.43
Pattern 2 : Percentage of days: 5%
Clear Day: Smooth parabolic curve with at most only minor disturbances.
The maximum of the curve is located above 600 W/m2 ,
with only a few exceptions mainly during winter days.
This is characterstic for a clear day with no clouds.
Even the regional maximum and minimum do not show strong fluctuations, -indeed, a very sunny summer-day.
Seasonal dependence: During summer days the maximum of the curve is located mainly above 600 W/m2,
On the other days it is clearly below.
Pattern 2: Smooth curve with minor fluctuations all Stations
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.5, p.48
Global Radiation in the Region of Saarbrücken at 950810
0
200
400
600
800
1000
1200
10,36 10,41 10,46 10,51 10,56 10,61 10,66
solar day
W/m
2̂ max
mean
min
0
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; p.43
Pattern 3 : Percentage of days: 12%
Overcast Day: Smooth almost straight curve
The maximum of the radiation does rarely exceed 100 W/m2.
This pattern mainly occurs during the cold season and seems to indicate a uniform cloud coverage in the region of observation.
The cloud-coverage does not seem to have remarkable gaps
and is more or less of uniform thickness.
Seasonal dependence: Most of the days showing such a pattern belong to the time between October and March.
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.8 p.51
Pattern 3 - Overcast Day: Smooth almost straight curve
Pattern 3 - Smooth curve with low maximum
Global Radiation in the Region of Saarbrücken at 950531
0
200
400
600
800
1000
1200
1400
31,36 31,41 31,46 31,51 31,56 31,61 31,66
solar day
W/m
2̂
max
mean
min
0
Die anderen Klassen sind mehr oder weniger Kombinationen der vorgenannten
EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“;
The Bimodal Structure of the Regional Solar Energy
Daily "snapshots“, taken from 12.30 to 12.40 UTC
during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
0
2
4
6
8
10
12
14
40
160
280
400
520
640
760
880
100
0
11
20
Clearness Index [Promille]
Fre
qu
ency
[%
]
0
10
20
30
40
50
60
70
80
90
100
Cum
ula
ted F
requen
cy [
%]
unselected
Frequency distribution and cumulated frequency of the clearness index, measured simultaneously at the 9 stations of the far-distance grid in 30 second time intervals for an airmass of am=1.1 . The daily "snapshots" are taken from 12.30 to 12.40 UTC during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
Frequency distribution and cumulated frequency of the clearness index
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.2
Daily "snapshots“, taken from 12.30 to 12.40 UTC
during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
Airmass = ca. 1.1
30 sec
Classification of the clearness index distribution:
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Table 3.1
Daily "snapshots“, taken from 12.30 to 12.40 UTC during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
Table III.3-1: Classification of the distributions of kt in 234 daily 10 minute intervals with am = 1.1 .
Class subclass kt_ mean span kt_min kt_max frequency
PL low < 0.2 6%
PR high < 0.2 10%
Unimodal PL_broad > 0.2 < 0.6 12%
PR_broad > 0.2 > 0.4 3% 31%
Bimodal BM < 0.4 > 0.6 69%
Kt values kt only for the distributions belonging to the bimodal class of table 1 (with kt_maximum < 600 [promille] and kt_minimum < 400 [promille] (160 snapshots out of the 234 represented in Fig III.3.2. .
Bimodal Class: days with bimodal distribution
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.3
Daily "snapshots“, taken from 12.30 to 12.40 UTC
during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
Airmass = ca. 1.1
0
2
4
6
8
10
12
40 120
200
280
360
440
520
600
680
760
840
920
1000
1080
1160
Clearness-Index [Promille]
Fre
quen
cy [
%]
0
10
20
30
40
50
60
70
80
90
100
Cum
ulat
ed F
requ
ency
[%
]
Class "BIMODAL"
Max > 600; Min < 400
30 sec
Positional parameters: Maximum, Mean, Minimum
0
200
400
600
800
1000
1200
1 21 41 61 81 101 121 141Days
Cle
arne
ss I
ndex
[pr
omil
le]
MaxMeanMin
bimodal
Max > 600; Min < 400
Positional parameters kt_max, kt_mean and kt_min of the distributions of clearness index belonging to the bimodal class. The days are sorted for ascending kt_mean.
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.4
bimodal class:
Positional parameters kt_max, kt_mean and kt_min of the distributions of clearness index belonging to the unimodal class. In each subclass (c.f. Table III.3-1) the days are sorted for ascending kt_mean.
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.5
Positional parameters
0
100
200
300
400
500
600
700
800
900
1000
1 11 21 31 41 51 61 71Days
Clea
rnes
s Ind
ex [P
rom
ille]
Max
Mean
Min
PL
PL_broad
PR
PR_broad
Unimodal class:
Daily 6 hours time range:from 9:00 to 15.00 UTC
during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
0
2
4
6
8
10
12
40 160
280
400
520
640
760
880
1000
1120
Clearness-Index [Promille]
Fre
quen
cy [
%]
0
10
20
30
40
50
60
70
80
90
100
Cu
mu
late
d F
req
uen
cy [
%]
Frequency distribution and cumulated frequency of the clearness index for the time-range 9:00 - 15:00 UTC (this and the following diagrams). All 234 days are taken into account .
Frequency distribution and cumulated frequency of the clearness index
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.7
Daily 6 hours time range: 9:00 to 15.00 UTC
during all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
30 sec
unselected
Classification of the clearness index distribution:
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Table 3.2, p.91
Daily 6 hours time range: from 9:00 to 15.00 UTC in all 234 days between 15.5 and 31.7. in 1993, 1994 and 1995.
Table III.3-2: Classification of the distributions of kt in 234 daily 6 hour intervals (9:00 - 15:00 UTC)
Class subclass kt_ mean span kt_min kt_max frequency
PL low 0%
PR high < 0.2 1.7%
Unimodal PL_broad > 0.2 < 0.65 4.7%
PR_broad > 0.2 > 0.4 2.5% 9%
Bimodal BM < 0.4 > 0.65 91%
Bimodal Class: days with bimodal distribution
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.8, p.91
Daily 6 hours time range: 9:00 to 15.00 UTC
during “bimodal” days between 15.5 and 31.7. in 1993, 1994 and 1995.
Joint Frequency for Bimodal Days
0
2
4
6
8
10
12
40 160
280
400
520
640
760
880
1000
1120
Clearness Index [Promille]
Fre
qu
ency
[%
]
0
10
20
30
40
50
60
70
80
90
100
Cu
mu
late
d F
req
uen
cy [
%]Max > 650; Min < 400
30 sec
Joint frequency distribution and cumulated frequency for days with bimodal distribution.
Positional parameters kt_max, kt_mean and kt_min of the distributions of clearness index belonging to the bimodal class. The days are sorted for ascending kt_mean.
Time range: 9:00 - 15:00 UTC
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.9
bimodal class:
Positional parameters: Maximum, Mean, Minimum
0
200
400
600
800
1000
1200
1 21 41 61 81 101 121 141 161 181 201days
ktMax
Mw
Min
bimodal
Max > 650; Min < 400
Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.10, p.92
Unimodal class:
Positional parameters
0
100
200
300
400
500
600
700
800
900
1000
1 3 5 7 9 11 13 15 17 19 21days
ktMax
Mw
Min
PRPL_broad PR_broad
Positional parameters kt_max, kt_mean and kt_min for non-bimodal (unimodal) distributions. Time range: 9:00 - 15:00 UTC
Modellierung und Simulationsprogramme
3.24
Modellierung des Sonnenenergie Dargebotes
auf einem Excel- Kalkulationsblattt
3.241
Kollektor bestimmt durch:
1. Normalvektor auf Fläche {Fläche, Azimut, Neigung zur Horizontalen}
2. Verschattung
3. Boden als Reflektorfläche
Übersicht zum Solarangebot
Transmission durch Atmosphäre: Streuung, Absorption
Output:1 . Direkte Strahlung, Diffuse Streustrahlung G = I + D , D ist nicht isotrop !
2 . Frequenzfilter spektrale Transmission
unterschiedlich für I und D.
Sender Empfänger
Solarstrahlung extraterrestrisch
Sonnenvektor: {I0, Azimut, Sonnenhöhe}
Kollektor bestimmt durch: 1. Normalvektor auf Fläche {ok} {Fläche, Azimut, Neigung zur Horizontalen}
2. Verschattung {etwas aufwendig, aber ok}
3. Boden als Reflektorfläche {schwierig}
Ermittlung der verfügbaren Solarstrahlung
Transmission durch Atmosphäre:
Messwert meist nur: Globalstrahlung G(0)
(1) aus statistischer Korrelation: D(0) {Liu-Jordan + Nachfolger, Reindl-Duffi-Beckman 89}
(2) aus Modell : Transponieren auf Kollektorebene: D(Kollektor) {Peretz Modell} I(Kollektor) {trivial, geometrisch}
G(Kollektor) = D(Kollektor) + I(Kollektor)
Sender Empfänger
Solarstrahlung extraterrestrisch Input: DA$=„JJMMTT.hhmmss“ Datum + wahreOrtszeitOutput: Sonnenvektor: {ok} {I0, Azimut, Sonnenhöhe}
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1 2 3 4 5 6 7 8 9 10 11 12 13
Strahlung auf geneigter EbeneVersion:2005__0617,09,07
0. Input Data
horizontale Globalstrahlung:aktuelle Werte G_0= 372,1 [W/m^2] kt= 0,50
Referenzwerte für Korrelation: (Stundenmittel oder Äquivalente wie z.B. temporal-regionales Gleitmittel)
Referenz-kt kt_Ref= 0,6000 G_0_ref= 446,543kT-Wert als Input für G-D Korrelation, z.B. temporal-regionales GleitmittelMittel
Sonnenvektor: I0_et_normal 1328,35 [W/m^2]
Datum.Zeit DAZ= 990601.154030 solarer Azimut AZI 84,66 [°] Süd=0, West=+90
UTC-Zeit! Azi_arc= 1,477655 84,66 [°]extraterrestrisch_horizontalI0_0= 744,238 [W/m^2] Sonnenhöhe 0,594715 34,07
Zenitdistanz Z_arc= 0,976081 55,93
airmass am= 1,741KollektorFläche
Neigungswinkel betaKol= 30,00 [°] Solare Inzidenz auf Kollekt. Teta_i_arc= 0,45 25,93 [°]FlächenNormale AziKol= 84,663 [°] Nord=+-180, West=+90 0,45 test
Standort: Latitude= 49,2 Longitude= 7 Altitude= nn
nach Standortänderung muss RESET gemacht werden,
1. Reindl-Korrelation (diffuser Anteil auf horzontaler Ebene)
Diffuse Strahlung_horizontal_Referenz: Direkte Strahlung_horizontal:
Stundenwerte: D_0_ref = 200,84 [W/m^2] I_0_ref= 245,70 [W/m^2]
aktuelle Werte D_0= 200,84 [W/m^2] I_0= 171,28 [W/m^2]
2. Perez Modell (diffuse Strahlung auf geneigter Ebene)/Perez_PISMS90_SE44-5p271/, zitiert in /Quaschning 2003,Tabelle 2.10p57/
Ergebnis: D_Kol= 237,40 [W/m^2] I_Kol= 274,9(Gl.(9) in /PISMS90, p.281/) G_Kol= 512,3 (Gl.(9) in /PISMS90, p.281/)
Perez-parameter: kappa_P= 1,041 Brightening coefficients:
eps_P= 1,7734 a_P= 0,899 F1_P= 0,329274delta_P= 0,2632 b_P= 0,560 F2_P= 0,055329
eps_cat= 4
Beispiel für Berechnungskern
auf einem Excel-Kalkulationsblatt
Goto OriginalKalkulationsBlatt
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0. Input Data Spalte 3horizontale Globalstrahlung:aktuelle WerteG_0= 350 [W/m^2]
Referenzwerte für Korrelation. (Stundenmittel oder Äquivalente wie z.B. temporal-regionales Gleitmittel)
Referenz-kt kt_Ref= 0.6kT-Wert als Input für G-D Korrelation, z.B. temporal-regionales GleitmittelMittel
Sonnenvektor:
Datum.Zeit DAZ= 990601.154030
UTC-Zeit! extraterrestrisch_horizontalI0_0= =I0_et(DAZ) [W/m^2]
airmass am= =airmass(DAZ)
KollektorFlächen NeigungswinkelbetaKol= 30 [°]
Ausrichtung:AzimutAziKol= =Azi_arc*180/PI() [°] Nord=+-180, West=+90
Standort: Latitude= 49.2
1. Reindl-Korrelation (diffuser Anteil auf horzontaler Ebene)
Diffuse Strahlung_horizontal_Referenz: Stundenwerte:D_0_ref = =Dh_0_Reindl(DAZ, kt_Ref) [W/m^2]
aktuelle WerteD_0= =MIN(D_0_ref,G_0) [W/m^2]
2. Perez Modell (diffuse Strahlung auf geneigter Ebene)
/Perez_PISMS90_SE44-5p271/, zitiert in /Quaschning 2003,Tabelle 2.10p57/
Ergebnis: D_Kol= =D_0*((1-F1_P)*(1+COS(betaKol*PI()/180))/2 +F1_P*a_P/b_P+F2_P*SIN(betaKol*PI()/180)) [W/m^2]
(Gl.(9) in /PISMS90, p.281/) I_Kol=
Perez-parameter:kappa_P= 1.041eps_P= =((D_0+I_0/COS(Z_arc))/D_0 +kappa_P*Z_arc^3)/(1+kappa_P*Z_arc^3)delta_P= =am*D_0/(I0_0/COS(Z_arc))eps_cat= =eps_Bin(eps_P)
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23 24
Spalte 10
kt= =G_0/I0_0
G_0_ref= =kt_Ref*I0_0
I0_et_normal =I0_et_normal(DAZ)
AZI =Azi(DAZ)
Azi_arc= =Azi(DAZ)*PI()/180Sonnenhöhe =SolHoehe(DAZ)*PI()/180
Z_arc= =PI()/180*(90-SolHoehe(DAZ))
Teta_i_arc= =EinfallsWinkel(DAZ, AziKol, betaKol)*PI()/180 =teta_gen(DAZ, AziKol, betaKol)*PI()/180
Altitude=
Direkte Strahlung_horizontal:
I_0_ref= =kt_Ref*I0_0-D_0_ref
I_0= =G_0-D_0
I_Kol= =I_0*COS(Teta_i_arc)/COS(Z_arc)
G_Kol= =D_Kol+I_Kol
Brightening coefficients: F1_P= =F1_Perez(eps_P,delta_P,Z_arc)F2_P= =F2_Perez(eps_P,delta_P,Z_arc)
a_P= =MAX(0,COS(Teta_i_arc))b_P= =MAX(0.087,COS(Z_arc))
Die Spalten, in denen die Inputs und dieGleichungen stehen