1/71 AES-LECTURE 1. Solar energy. solar radiation definitions incident solar energy

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1 1/71 AES-LECTURE 1 Solar energy solar radiation definitions incident solar energy

2 Sun 2/71 closest star centre of our planetary system solar system

3 Sun 3/71 diameter km 109 x larger than Earth weight 2 x kg x greater than Earth 99,86 % weight of the solar system consists of: 70 % hydrogen H, 28 % helium He, 2 % other elements

4 Sun 4/71 origin of solar energy in nuclear reactions nuclear fusion takes place inside the Sun at high temperatures 10 6 K and pressures Mpa, atoms are ionised synthesis of hydrogen nuclei (H) helium nuclei (He) 564 x 10 9 kg/s Hydrogen transforms to 560 x 10 9 kg/s Helium mass difference 4 x 10 9 kg/s is radiated in the form of energy E = m.c 2 radiative power: 3,6 x W specific radiated power (density): 6 x 10 7 W/m 2

5 Sun 5/71 core (to 23 % radius) temperature 10 6 K, X-ray radiation 90 % of Sun s energy generated radiative zone (from 23 to 70 % radius) temperature falls down to K radiative energy transfer (fotons) convective zone (from 70 to 100 % radius) lower density, convective energy transfer photosphere (visible surface of Sun) temperature 5800 K, solar radiation

6 Spectral density of radiative flux 6/71 Sun radiates as perfect black body with surface temperature 5800 K spectral density of radiative solar flux (Planck s law) E č (, T ) 2 hc 5 2 e hc kt 1 1 [W/m 2.mm] h = 6,6256 x J.s k = 1,3805 x J/K c = 2,9979 x 10 8 m/s T Planck s constant Boltzmann s constant light velocity in vacuum thermodynamic surface temperature [K]

7 Planck s law 7/71

8 density of radiative flux [W/(m 2.nm)] Spectral density of radiative flux 8/71 UV VIS NIR UV: ultraviolet radiation 0,2 to 0,4 mm (> 0,32 mm) UVA / UVB / UVC (< 0,28 mm) VIS: visible radiation 0,40 to 0,75 mm NIR: near infrared radiation 0,75 to 5 mm black body 5800 K wavelength [nm]

9 density of radiative flux [W/(m 2.nm)] Solar energy irradiated 9/71 UV VIS NIR 9 % 41 % 50 % black body 5800 K wavelength [nm]

10 density of radiative flux [W/(m 2.nm)] Wien s law 10/71 maximum of radiative flux seeking the extreme of Planck s function E č (, T ) 0 max T 2898 [mm.k] 5800 K: max = 0,5 mm 373 K: max = 7,8 mm Wien s displacement law black body 5800 K wavelength [nm]

11 Propagation of solar energy 11/71 Sun Earth power spreads to larger area with increasing distance from Sun 0,5 x 10-9 of the irradiated Sun s power is incident on Earth radiative flux 1,7 x W solar beams considered as parallel (32 )

12 Earth rotates around Sun... 12/71 eliptic orbit (almost circular), Sun in one of focuses Sun Earth

13 Radiative flux density out of atmosphere 13/71 solar radiative flux incident on area unit perpendicular to direction of propagation changes during the year, variable distance Sun-Earth (eliptic orbit) change of distance 1,7 %, change of flux 3,3 % value for mean distance Sun-Earth solar constant G sc = 1367 W/m 2 (value from WRC, 1 %) original measurements Ch. Abbot in mountains 1322 W/m 2, today satellites Merkur: 9040 W/m 2... Neptun: 1,5 W/m 2

14 Radiative flux density out of atmosphere 14/ G on G sc 360n 1 0,033cos 365 G on [W/m 2 ] dny v roce day in the year

15 Solar radiation passing the atmosphere 15/71 solar radiation enters the atmosphere (no definite boundary, exosphere continuosly fading to interplanetary space) ionosphere (60 km) atmospheric gases O 2, N 2 absorb x-ray and ultraviolet radiation, becoming ionised ozonosphere (20 to 30 km) ozon O 3 absorbs rest of harmfull ultraviolet radiation (UVC) troposphere (lowest layer, clouds) water vapor, CO 2, dust, water droplets absorb infrared radiation

16 density of radiative flux [W/(m 2.nm)] Solar radiation passing the atmosphere 16/71 AM0: spectrum outside atm. AM1: perpendicular pass AM1,5: spectrum at 48 AM2: spectrum at 60 outside atmosphere sea level wavelength [nm] solar radiation: 0,3 to 3 mm

17 Annual balance of energy flows 17/71 reflection from atmosphere 34 % absorption in atmosphere 19 % incident and absorbed by Earth surface 47 % absorbed at surface emitted back 14 % energy of environment evaporation (oceans) 23 % water energy convection, winds 10 % wind energy biologic reactions, photosynthesis 0,1 % energy of biomass

18 Solar geometry - angles 18/71 surface slope b surface azimuth g latitude f

19 Solar geometry - angles 19/71 (time, date) (time angle t ) (declination d ) Sun altitude h Sun azimuth g s

20 Solar geometry - angles 20/71 surface slope b surface azimuth g latitude f time, date time angle t declination d Sun altitude h Sun azimuth g s incidence angle q

21 Surface position 21/71 latitude f convention: north (+), south (-) angle between plane of equator and a line connecting Earth centre and given place on Earth surface

22 Surface position 22/71 high difference between north and south in one country Norway: 57 to 71 Sweden: 55 to 68

23 Surface orientation 23/71 slope angle b convention: horizontal 0, vertical 90 angle between horizontal plane and surface plane surface azimuth g convention: east (-), west (+), south (0 ) angle between projection of surface normal and local meridian (south) b S g

24 Declination (tilt of Earth axis) 24/71 declination d december (solstice) 23. september 0 (equinox) march (equinox) 21. june (solstice)

25 Declination d 25/71 tilt angle of Earth s axis due to precession movement during rotation angle between the line (connecting centres of Earth and Sun) and equator plane latitude of place on Earth where in given day in the noon the Sun is in zenith

26 Calculation of declination d 26/71 calender date DD.MM. DD 29,7 ) d 23,45 sin 0,98 MM 109 number of the day in the year n d 284 n 23,45 sin

27 Calculation of declination d 27/71 30 declination [ ] ,45 solstice 10 deklinace [ ] equinox solstice , pořadí dne v roce order of the day in a year

28 time (hour) angle t 28/71 angle of virtual translation of Sun above local meridians due to Earth rotation, related to solar noon Earth is rotating around its axis (360 ) once for 24 hours translation motion of Sun by 15 over 1 hour time angle is calculated from solar time ST ST ) t convention: before noon (-), after noon (+)

29 Solar time ST 29/71 each timezone has a time related to local (standard) meridian timezones of 1 h ~ meridians of 15 CET: local standard time at meridian 15 east longitude solar time: daily time defined from virtual translation of Sun observer at reference meridian: local time = solar time observer out of reference meridian: local time solar time shift up to 30 minutes

30 Solar time ST 30/71 15 example: Prague 14,4 12:02 Brno 16,6 11:53 Košice 21,2 11:35 longitude solar noon

31 Sun altitude h 31/71 angle between line connecting surface--sun and horizontal sin h sind sinf cos d cos f cost latitude f time angle t complement angle to 90 : zenith angle q z declination d qz 90 h

32 Air mass 32/71?

33 Air mass 33/71 ratio between mass of atmosphere passed by solar radiation to mass, which would be passed if Sun is in zenith AM 1 cosq z 1 sinh AM = 0 outside atmosphere AM = 1 zenith h = 90 AM = 1,5 q z = 48 h = 42 AM = 2 q z = 60 h = 30

34 density of radiative flux [W/(m 2.nm)] Change of spectrum with air mass 34/71 h = 90 AM = 1,00 h = 70 AM = 1,06 h = 50 AM = 1,31 h = 30 AM = 2,00 h = 10 AM = 5,76 wavelength [nm]

35 35/71 h = 3 AM=21

36 Time of sunrise and sunset 36/71 sunrise / sunset: altitude angle = 0 sinh sind sinf cosd cosf cost 0 time angle of sunrise / sunset t 1,2 f tgd ) arccos tg theoretical period of sunshine = time between sunrise and sunset t t t 1,

37 37/71 Azimuth of Sun g s angle between projection of line connecting surface-sun and local meridian (south) convention: measured from south east (-), west (+) Sun sing s cos d sint cos h

38 Altitude and azimuth of Sun 38/ june 23. september 21. march 22. december W N S E source: solarpraxis

39 Altitude and azimuth of Sun 39/71 source: solarpraxis

40 Incidence angle 40/71 angle between line connecting surface-sun and surface normal cosq sin h cos b cos h sin b cos g g ) s surface slope b Sun surface azimuth g Sun altitude h surface normal Sun azimuth g s

41 Example for February 20 th 10:00 41/71 collector plane: latitude f = 50 slope b = 45 azimuth g = +15 declination d 23,45 sin 0,98DD 29,7 MM 109) 0, , ) 11. d 23,45 sin 7

42 Example for February 20 th 10:00 42/71 time angle 10 12) t Sun altitude h arcsin 23 sin h sind sinf cos d cos f cost sin( 11.7) sin50 cos( 11.7) cos 50 cos( 30) ) Sun azimuth sing s cos d sint cos h g s cos( 11.7) arcsin sin( 30) cos23

43 Example for February 20 th 10:00 43/71 incidence angle q arccos sin23 cos 45 cos 23 sin45 cos ) ) 44 time angle of sunrise / sunset cosq sin h cos b cos h sin b cos tg50 ( 11.7) ) 75. t1,2 arccos tg 8 t 1,2 g g ) s f tgd ) arccos tg time of sunrise t 1 t1, :54 BUT...

44 Deviation of solar time 44/71 due to nonuniform rotation of Earth... deviation cca 14 minutes to be added

45 Solar radiation - definitions 45/71 solar irradiance G [W/m 2 ] - radiative power incident at area unit, density of solar radiative flux solar irradiation H [kwh/m 2, J/m 2 ] density of radiative energy, integral of flux density per time period, e.g. hour, day,... H t 2 t 1 G. dt

46 Solar radiation - definitions 46/71 direct solar radiation (index b, beam) without scattering in atmosphere angle dependent, significant intensity in one direction diffuse solar radiation (index d, diffuse) scattered in atmosphere all-directions, isotropic: identical intesity in all direction reflected solar radiation (index r, reflected) reflection from terrain, buildings usual surfaces reflect diffusively considered together with diffuse radiation

47 Solar radiation - definitions 47/71 reflection from air molecules, dust particles, ice crystals reflected radiation reflection from terrain direct radiation diffuse radiation source: solarpraxis

48 Solar radiation passing the atmosphere 48/71 direct normal solar irradiance (on surface perpendicular to direction of propagation) after passing atmosphere G bn G bn G on Z G on exp Z normal solar irradiance above atmosphere attenuation factor 9, ,0015(1 2 0,5 sinh (0,003 sin h) 0, L v h Sun altitude [ ] L v 10 4 elevation above sea-level [m] ) [W/m 2 ] ε factor depends on the height of the Sun above the horizon and the elevation above m. sea l.

49 Attenuation factor Z 49/71 how many times the clear atmosphere should be optically thicker, to have the same transmissivity as the real polluted atmosphere polluted means also water vapor not only dust, emissions, etc. gives attenuation of solar flux when passing the real atmosphere Z lng lng 0n 0n lng lng bn b0 G 0n normal solar irradiance above atmosphere G bn direct normal solar irradiance after passing atmosphere G b0 direct irradiance after passing completely clear atmosphere (with Z = 1)

50 Attenuation factor 50/71 Month mountains Average monthly values for Z for locations with different environment country side cities industrial I. 1,5 2,1 3,1 4,1 II. 1,6 2,2 3,2 4,3 III. 1,8 2,5 3,5 4,7 IV. 1,9 2,9 4,0 5,3 V. 2,0 3,2 4,2 5,5 VI. 2,3 3,4 4,3 5,7 VII. 2,3 3,5 4,4 5,8 VIII. 2,3 3,3 4,3 5,7 IX. 2,1 2,9 4,0 5,3 X. 1,8 2,6 3,6 4,9 XI. 1,6 2,3 3,3 4,5 XII. 1,5 2,2 3,1 4,2 simplified: mountains Z = 2 countryside Z = 3 cities Z = 4 industrial Z > 5 annual average 1,9 2,75 3,75 5,0

51 Solar irradiance on general surface 51/71 total solar irradiance on generally sloped and oriented surface G T G bt G dt G rt [W/m 2 ] direct irradiance diffuse irradiance from sky diffuse reflected irradiance diffuse character

52 Solar irradiance on general surface 52/71 direct sky dome diffuse G bt G dt G rt horizon reflected

53 Solar irradiance on general surface 53/71 direct solar irradiance on given surface cosq GbT Gbn cosq Gb Gb sinh cosq cosq direct normal Incidence / sun altitude Incidence / zenith angle z [W/m 2 ] sky diffuse solar irradiance on given surface G 1 cos b 2 dt G d [W/m 2 ] reflected diffuse solar irradiance on given surface G rt g 1 cosb 2 G G ) b d [W/m 2 ]

54 Terrain reflectance (albedo) 54/71 ratio between reflected and incident solar irradiance for calculations considered g = 0,20 usual surfaces 0,10 to 0,15 snow 0,70 to 0,90 Earth albedo (planet) 0,30 (average)

55 Solar irradiance on horizontal plane 55/71 direct solar irradiance on horizontal plane G b G bn sinh [W/m 2 ] direct normal sun altitude diffuse solar irradiance on horizontal plane G d G G ) sinh 0,33 on bn [W/m 2 ] simplified model: 1/3 of solar radiatin lost in atmosphere comes to horizontal plane (sin h) as a diffuse isotropic radiation

56 Example for February 20 th 10:00 56/71 angles: Sun altitude h = 23.0 Sun azimuth g s = incident angle q = 44.0 from the date and time solar constant 1367 W/m 2 attenuation factor Z = 4 altitude 200 m local parameters

57 Example for February 20 th 10:00 57/71 extraterrestrial normal solar irradiance G on ,033cos 1396 W/m 365 ε factor depends on the height of the Sun above the horizon and the elevation AMSL G on [W/m 2 ] dny v roce 2 2 0,5 sin23 (0,003 sin 23) 0, , ,0015( ) direct normal irradiance (after passing atmosphere) G bn G on exp Z exp W/m

58 Example for February 20 th 10:00 58/71 direct solar irradiance on horizontal plane G b G bn sin h 593sin W/m diffuse solar irradiance on horizontal plane G d 0,33 0,33 Gon Gbn ) sin ) sin W/m

59 Example for February 20 th 10:00 59/71 direct solar irradiance on given surface G bt G bn cosq 593 cos W/m sky diffuse solar irradiance on given surface 1 cos b G dt G 2 d 1 cos W/m reflected diffuse solar irradiance on given surface G rt 1 cos b g 2 1 cos G G ) b d ) 10 W/m

60 Example for February 20 th 10:00 60/71 G T = G bt + G dt + G rt = = 524 W/m 2... for given time and date... for clear sky (no clouds)

61 Solar irradiation on general surface 61/71 theoretical daily solar irradiation, integration of irradiance on a plane from sunrise t 1 to sunset t 2 H T, day, th t 2 t 1 G T dt [kwh/(m 2.day)] mean daily solar irradiance G T, m H T, day, th t t [W/m 2 ] H T,day,th time t t

62 Influence of slope 62/71 H T,den,teor [kwh/m 2.den] H T,den,teor [kwh/m 2.den] month měsíc měsíc month azimuth 0 (south) azimuth 45 (SW, SE) optimum slope: summer winter annual 35-45

63 Solar irradiation on general surface 63/71 diffuse daily solar irradiation, integration of diffuse solar irradiance on a plane from sunrise t 1 to sunset t 2 H T, day, dif t 2 t 1 G dt dt [kwh/(m 2.day)] H T,day,th H T,day.dif G T,m } tabelled in literature for given: slopes, azimuths, locations (attenuation factors)

64 Real duration of sunshine 64/71 duration of direct solar radiation > 120 W/m 2 t t s s, i i [h] meteo-institute (CZ) presents the values for 22 locations relative period of sunshine 120 W/m 2 t s t r t t [-]

65 Real duration of sunshine 65/71 Month Real duration of suhshine ts [h] Praha České Budějovice Hradec Králové Brno I II III IV V VI VII VIII IX X XI XII S

66 Real duration of sunshine in CZ 66/ h/year

67 Real duration of sunshine in Europe 67/71 < 1200 h > 2500 h

68 Total irradiation on given plane 68/71 daily solar irradiation t r ) HT, day dif H T, day t r HT, day, th 1, [kwh/(m 2.day)] monthly solar irradiation H T, mon nht, day [kwh/(m 2.mon)] annual solar irradiation XII I H T, year HT, mon [kwh/(m 2.year)]

69 Annual solar irradiation in CZ 69/71 MJ/m 2 slope 30 to 45, south orientation: 1000 to 1200 kwh/m 2 slope 90, south orientation: 750 to 900 kwh/m 2

70 15-60 slope Optimum slope for Central Europe? 70/71 southeast - southwest kwh/m 2.a azimuth east south west

71 Optimum slope worldwide? 71/71 Optimum slope = latitude + ( ) Example: Sydney latitude = - 33 a) North orientation Optimum slope 33 + ( ) = ca 40 b) North west orientation Optimum slope lower ca 20-30

72 Solar energy: typical values 72/71 solar irradiance G (power) clear sky 800 to 1000 W/m 2 semibright 400 to 700 W/m 2 overcast 100 to 300 W/m 2 solar irradiation H (energy) winter spring, autumn summer 3 kwh/(m 2.day) 5 kwh/(m 2.day) 8 kwh/(m 2.day)