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

http://www.ldeo.columbia.edu/edu/dees/U4735/lectures/14.html

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.324



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


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


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


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



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



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



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


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



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




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

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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.


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.


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


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


Daily 6 hours time range: 9:00 to 15.00 UTC


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


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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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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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

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