Solare Einstrahlung auf der Erde 3.2 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 Maps of horizontal surface global radiation .231 World .232 Europe .233 Germany .234 local: geliebte Saarheimat

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

Europe Maps of horizontal surface global radiation annual, March, June, September, December Angaben in [ kWh/ m2 ] für mittlere tägliche Einstrahlung / Palz-Greif 96: European Solar Radiation Atlas ,p. 322 -326

/ 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

Solarstrahlung in Deutschland 3.233 Solarstrahlung in Deutschland Angaben in [ kWh/ m2 ] für mittlere tägliche Einstrahlung

Jahresummen der Globalstrahlung Saarbrücken 1050 – 1100 [kWh/m^2/a] in Deutschland Saarbrücken 1050 – 1100 [kWh/m^2/a] Quelle: RWE-Bauhandbuch 2004, Abb.17.6

Jahressummen der Globalstrahlung auf verschieden orientierten Flächen  in [kWh/(m2a)]  Standort: Berlin , Breitengrad = 52°N Quelle: RWE-Bauhandbuch 2004, p. 17/7; Abb.17.7

Sonnenbahnen zu unterschiedlichen Jahreszeiten Standort: Berlin , Breitengrad = 52°N , Zeit: MEZ Quelle: RWE-Bauhandbuch 2004, p. 17/5; Abb.17.3

Sonnenbahndiagramm für Berlin, 52°N -90° 0° +90° Standort: Berlin , Breitengrad = 52.3°N Quelle:V. Quaschning 2003: Regenerative Energiesysteme(3.A.), Hanser Verlag München, ISBN=3-446-24983-8, Bild 2.10,p.53

In Deutschland überwiegt die diffuse Solarstrahlung Quelle: RWE-Bauhandbuch 2004, p. 17/6; Abb.17.5

Jahresummen der Globalstrahlung Mittelwerte im Superjahr 2003 Saarbrücken 1050 – 1100 [kWh/m^2/a] SB 1290 sorry, that I had to confound different sources with a different colour-scale

Regionale Solarstahlung im Saarland 3.234 Regionale Solarstahlung im Saarland Bericht über eine Messkampagne im Rahmen eines EU-Projektes Synchrone Kurzzeitmessungen (30 sec) an 15 Stationen

EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Titelblatt

of Global Solar Energy at horizontal plane over 2.5 years _1. Measuremenmts 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

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.1-1, p.7

in relation to our Institute in Saarbrücken (Station 2 at (0, 0)) 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“; Figure I.1-2, p.7

_2. Some Characteristic Patterns of global solar irradiance EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Chapter 2.2, p.42 ff

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.42

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“; p.43

Pattern 1 - Strong uniform oscillations over the whole time-period EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2.2, p.44

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 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 - 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 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 Pattern 1 - Strong uniform oscillations over the whole time-period. Far distance grid EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.4, p.47

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. EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; p.43

Pattern 2: Smooth curve with minor fluctuations all Stations EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.5, p.48

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“; p.43

Pattern 3 - Overcast Day: Smooth almost straight curve Pattern 3 - Smooth curve with low maximum EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig. III.2-.8 p.51

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 EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“;

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.

Frequency distribution and cumulated frequency of the clearness index 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. 30 sec Airmass = ca. 1.1 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. Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.2

Classification of the clearness index distribution: 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. Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Table 3.1

Bimodal Class: days with bimodal distribution 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. 30 sec Airmass = ca. 1.1 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. . Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.3

bimodal class: 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

Unimodal 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

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.

Frequency distribution and cumulated frequency of the clearness index unselected 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 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 . Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.7

Classification of the clearness index distribution: 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. Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Table 3.2, p.91

Bimodal Class: days with bimodal distribution 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. 30 sec Joint frequency distribution and cumulated frequency for days with bimodal distribution. Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.8, p.91

bimodal class: Time range: 9:00 - 15:00 UTC 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

Unimodal class: Positional parameters kt_max, kt_mean and kt_min for non-bimodal (unimodal) distributions. Time range: 9:00 - 15:00 UTC Quelle: EU-Contract JOU2-CT92-0018, Details siehe Blatt „Quelle“; Fig.III.3.10, p.92

Modellierung und Simulationsprogramme 3.24 Modellierung und Simulationsprogramme

Modellierung des Sonnenenergie Dargebotes 3.241 Modellierung des Sonnenenergie Dargebotes auf einem Excel- Kalkulationsblattt

Übersicht zum Solarangebot Sender Empfänger Kollektor bestimmt durch: 1. Normalvektor auf Fläche {Fläche, Azimut, Neigung zur Horizontalen} 2. Verschattung 3. Boden als Reflektorfläche Solarstrahlung extraterrestrisch Sonnenvektor: {I0, Azimut, Sonnenhöhe} 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.

Ermittlung der verfügbaren Solarstrahlung Sender Empfänger Solarstrahlung extraterrestrisch Input: DA$=„JJMMTT.hhmmss“ Datum + wahreOrtszeit Output: Sonnenvektor: {ok} {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} 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)

Beispiel für Berechnungskern auf einem Excel-Kalkulationsblatt Goto OriginalKalkulationsBlatt

Die Spalten, in denen die Inputs und dieGleichungen stehen