Fundamentals of Solar Energy Use: The System of Sun and Earth

The Position of the Sun

Hochschule Bremerhaven Fundamentals of Solar Energy Use - The System of Sun and Earth - Part 2The Position of the Sun The Sun itself (by means of ist radiation) as well as the atmosphere of the earth strongly affect the energy that is reaching the surface of Earth. Obviously however, the (continuously changing) position of the Sun as observed from earth is also very important. Solar devices can be oriented very well or very badly with respect to the Sun. Thus, we must describe the position of the sun throughout a day / month / year. Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 1

The Solar Height or Altitude

The declination of Earth with respect to the solar plane does not change. Thus, the solar height/altitude Ys varies between summer and winter and depends on the geographical latitude d: Ys,max = 113.4° - ø and Ys.min = 66.6° -¢ 8= 23.4° YN Es Ys .. ... Equator S Ys=113.4°-¢ 21 June 8= - 23.4° NK Es Ys 1 Equator S 7s=66.6°-¢ 21 December One goal of planning solar devices: Avoid shadows in winter! Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 2

The Local Solar Time

The local solar time is defined according to the position of the Sun, i.e., local solar time noon is defined as when the Sun is highest in the sky. In most cases, this does not correspond to local time noon except for UTC (Coordinated Universal Time). The simple version of the (local solar) time: LST = UTC + 1h Λ 15° NORTH POLE 45° 30° 15° WEST EAST 0 60. 75. 900 15 30° 45° Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 3

Precise Calculation of Local Solar Time

A more precise calculation of the local solar time uses: . the local standard time meridian LSTM, · an equation of time EoT, and · a time correction factor TCF. LSTM = 15° AT (LT - UTC) EoT = 9.87 sin 2B - 7.53 cos B - 1.5 sin B with B = 360 365 (d - 81) 20 Equation of time (minutes) 15 10 5 0 -5 -10 -15 0 50 100 150 200 250 300 350 number of days since start of year Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 4

Local Solar Time Calculation Factors

A more precise calculation of the local solar time uses: . the local standard time meridian LSTM, · an equation of time EoT, and · a time correction factor TCF. LSTM = 15° AT (LT - UTC) EoT = 9.87 sin 2B - 7.53 cos B - 1.5 sin B with B = 360 365 (d - 81) TC = 4(A - LSTM) + EoT TC LST = LT + 60 Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 5

Calculating Sun Position

Using the LST and the TC one can calculate the position of the Sun, particularly, the solar altitude and its azimuth. 8: the declination angle Ø: the latitude w = 15°(LST - 12): the hour angle W N Y's Kas + 1 S O sin ys = sin 8 sin ø + cos & cos o cos w cos as = (sin & cos + + cos & sin @ cos w) / cos ys Homework: An equation for the declination is missing. Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 6

Sun Position Equations and Parameters

Based on these equations, which in turn are based on Earth's rotation around the Sun and around itself and the corresponding astronomical parameters, one can calculate e.g .: East South West 70 21 June 12h/ 13h Local solar time LST 60 10h 21 April a 50 9h O 15h 0 a 21 March a 40 8h 16h a 21 Feb. a 17h 30 a 0 6h 18h 20 12h 21 Dec. 11h 0 L 13h 5h 19h 10 9h 15h 0 0 0 -120 -90 -60 -30 0 30 60 90 120 Sun azimuth as See also pveducation.org for radial diagrams. Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 7

Utilizing the Known Position of the Sun

11h 14h Sun altidude y's 0 7h O 0 10h 0 13 14h OUtilizing the (Known) Position of the Sun The angular position of the Sun can be used to calculate/estimate the power produced by a tilted photovoltaic or solar device. Diffuse radiation Direct radiation Reflected radiation Ground B Pitched solar generator ß is the elevation angle. Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 8

Direct Solar Radiation Dependence

For direct solar radiation, a strong dependence on tilt and solar height can be derived. =A A Vertical Sun radiation Ys Vertical AH AH : Horizontal surface A Vertical : Surface vertical to the incidental direction AGen : Surface in generator level Sun radiation AGe = Atilt B Ys AH Solar altitude angle B : Elevation angle of the solar generator x : Complementary angle sin(Ys+B) EDirect, Device = EDirect,H sin Ys Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 9

Direct Solar Radiation Calculation

For direct solar radiation, a strong dependence on tilt and solar height can be derived. E Direct, Device = E Direct,H sin(Ys+ß) sin ys 1400 f(x) - 1300 ( z) W Direct,Device (- 1200 1100 1000 E 900 800 0 10 20 30 40 50 60 70 80 90 ₿(°) Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 10

Diffuse and Albedo Solar Radiation

For diffuse solar radiation, the calculation can be much more complicated. The isotropic assumption, however, yields: EDiffuse,Device = EDiffuse,H 1 + cos B 2 Albedo is similarly difficult to consider. However, using the isotropic assumptions one can derive: 1 - cos ß E Albedo,Device = EG 2 · ALB albedo value Material Albedo ALB Material Albedo ALB Gras (July, August) 0.25 Asphalt 0.15 Carpet 0.18 ... 0.23 Concrete, clean 0.30 Unworked fields 0.26 Concrete, weathered 0.20 Forrest 0.05 ... 0.18 Snow, fresh 0.80 ... 0.90 Moreland 0.10 ... 0.25 Snow. old 0.45 ... 0.70 Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 11

Tracked and Fixed Systems

Adjusting the elevation angle with respect to solar height is called "tracking". This can help maximizing cell or device output. However, differences are negligible if diffuse radiation dominates. 7000 6000 5000 4000 Inverter Power Output (W) 3000 26th August, 2010 2000 -tracking -fixed 1000 0 7000 6000 5000 4000 3000 18th January, 2011 2000 -+ tracking -fixed 1000 0 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 Local Time Prof. Dr. Benedikt Klobes | Fundamentals of Solar Energy Use | SS2024 12