Solar utility technologies PDF

Solar utility technologies Lecture #4 Solar radiation Assoc. prof. dr. Ciril Arkar Laboratory for Sustainable Technologies in Buildings - LOTZ Chair of Thermal...

Solar utility technologies Lecture #4 Solar radiation Assoc. prof. dr. Ciril Arkar Laboratory for Sustainable Technologies in Buildings - LOTZ Chair of Thermal and Environmental Engineering UL, FS, LOTZ © Faculty of Mechanical Engineering, University of Ljubljana The Sun Solar radiation Solar radiation is considered as electromagnetic (thermal) radiation emitted by the photosphere The Sun is a spherical body consisting of very hot gases: 60% hydrogen, 35% helium +55 other elements core 40% mass and 90% energy: nuclear fusion 4 1H → 4He Sun/photosphere is considered as an optical black body - diameter ds = 1,39 109 m The radiant heat flow of the Sun is determined by the Stefan-Boltzmann law 𝑄𝑠ሶ = 𝜎 ∙ 𝐴𝑠 ∙ 𝑇𝑠4 = 𝜎 ∙ 𝜋 ∙ 𝑑𝑠2 ∙ 𝑇𝑠4 Só se coloca a A superficial de diferente Sun is isotropic radiator, the heat flux is emitted uniformly to surroundings What is the density of the radiant heat flow at the edge of the earth's atmosphere? UL, FS, LOTZ ©  Solar constant Solar constant – extra-terrestrial global irradiance The density of the Sun's radiant heat flux decreases with the square of the distance. The Earth travels in an elliptical path around the Sun. The average distance (rsz) is approximately 1,5 ∙ 1011 m. Solar constant Gex is the specific radiant heat flux of the Sun [W/m2] per unit area at the outer edge of the atmosphere on a surface perpendicular to the direction of the sun's rays. Gex normalmente sempre dado 𝑄𝑠ሶ = 𝐴𝑠𝑧 ∙ 𝐺𝑒𝑥 = 4 ∙ 𝜋 ∙ 𝑟𝑠𝑧 2 ∙ 𝐺𝑒𝑥 IMPORTANT 𝐺𝑒𝑥 = 𝑊/𝑚2 𝐺𝑒𝑥,𝑁 Abbot and Johnson (1954): 1322 W/m2, 1395 W/m2 NASA (1971): 1353 W/m2 ±1,5% WRC: 1367 W/m2 ±1% UL, FS, LOTZ © EN ISO 52010-1: 1370 W/m2 Calculation of the sun path Solar geometry - declination Declination 𝛿 is the angle between the equatorial plane and the sun's rays (the line between the center of the Sun and the Earth). Since the Earth's axis of rotation is inclined relative to the plane of its orbit around the Sun, the declination depends on the day of the year (N) and ranges from -23,45° to +23,45°. 𝛿 = −23,45 ° Quando o ano tem 365 dias 𝛿 = +23,45 ° 360 𝛿 = 23,45 ∙ 𝑠𝑖𝑛 ∙ (284 + 𝑁) 365 summer solstice spring and autumn equinox winter solstice N= 172 N=80 N= 266 N= 355 Dia mais longo do verao inicio da primavera(N=80) e inico de outono(N=266) Inicio do inverno 360 360 Quando o ano tem 366 dias (leap year) 𝛿 = 23,44 ∙ 𝑠𝑖𝑛 ∙ 𝑁 − 82,3 + 1,93 ∙ 𝑠𝑖𝑛 ∙ 𝑁 − 2,4 365,25 365,25 N current day in a leap year cycle (N=1 is January 1 of a leap year) UL, FS, LOTZ © Calculation of the sun path In EN ISO 52010-1 𝛿 = 0,33281 − 22,984 ∙ 𝑐𝑜𝑠 𝐵 − 0,3499 ∙ 𝑐𝑜𝑠 2 ∙ 𝐵 − 0,1398 ∙ 𝑐𝑜𝑠 3 ∙ 𝐵 +3,7872 ∙ 𝑠𝑖𝑛 𝐵 + 0,03205 ∙ 𝑠𝑖𝑛 2 ∙ 𝐵 + 0,07187 ∙ 𝑠𝑖𝑛 3 ∙ 𝐵 360 𝐵= ∙𝑁 365 UL, FS, LOTZ © Calculation of the sun path Solar altitude and azimuth angle The position of the Sun in the sky is described by the altitude and azimuth of the sun. Solar altitude angle 𝛼 is the angle between the sun's rays and the horizontal plane - equal to 0° at sunrise and sunset - highest at solar noon sin 𝛼 = sin 𝜑 ∙ sin 𝛿 + cos 𝜑 ∙ cos 𝛿 ∙ cos 𝜔 Sun zenith 𝜑 latitude [°] Ljubljana… 46,1°, Athens … 38°, Stockholm …59,3° Sun path W horizon 𝜔 hour angle [°] 𝜔 = 15° ∙ 𝑡𝑠 − 12 𝑡𝑠 solar time [h] S N The zenith angle z is the angle between the sun‘s ray and the zenith (highest point in the sky) UL, FS, LOTZ © E Calculation of the sun path Solar altitude and azimuth angle The position of the Sun in the sky is described by the altitude and azimuth of the sun. Solar azimuth angle 𝜙 is the angle between the projection of the sun's ray and the celestial direction of south (measured on a horizontal plane) - equals to 0° at solar noon - negative until solar noon, positive after solar noon Sun zenith cos 𝛿 ∙ sin 𝜔 sin 𝜙 = cos 𝛼 Sun path W horizon S N UL, FS, LOTZ © E Calculation of the sun path Solar altitude and azimuth angle What is the hour angle at sunrise today ? Sr=sunrise ss=sunset 𝜔𝑠𝑟 = 𝜔𝑠𝑠 Solar altitude angle 𝛼 is the angle between the sun's rays and the horizontal plane Sun zenith - equal to 0° at sunrise and sunset sin 𝛼 = sin 𝜑 ∙ sin 𝛿 + cos 𝜑 ∙ cos 𝛿 ∙ cos 𝜔 Sun path W horizon 𝜑 latitude [°] … your location cos 𝜔𝑠𝑟 = − tan 𝛿 ∙ tan 𝜑 Hour angle at sunrise (Declination,latitude) 𝜔𝑠𝑟 S N 𝑡𝑠𝑟 = 12 − 15 UL, FS, LOTZ © E Calculation of the sun path 21 de março-Equinócio(Momento em que o Sol passa do hemisfério sul para o hemisfério Norte; Mudança de estacao)N=80 Sun path diagram 21 de junho-solstício do verão (quando o sol alcança a sua posição mais alta no céu )N=172 23 de setembro-Equinócio(Momento em que o Sol passa do hemisfério Norte para o hemisfério Sul; Mudança de estacao)N=266 21 de dezembro-solstício de inverno (Quando o sol está mais baixo)N=355 … shows the apparent path of the Sun in the sky during selected days of the year - Case Ljubljana solar altitude  (°) solar time latitude 𝜑 = 46,07° longitude 𝜆 = −14,5° - at solar noon – highest in the sky and exactly due south Pontos vermelhos-Posição do sol ao longo do dia Linha Azul - Trajetoria do sol no semestre de inverno Linha azul clara-trajetoria no semestre de verao Where solar altitude angle can be 90° ? E S solar azimuth  (°) W UL, FS, LOTZ © Calculation of the sun path Actual (clock) time and solar time An analemma is a curve that shows the position of the Sun at the same clock time every day of the year. The position (azimuth) is not the same due to the elliptical path of the Earth around the Sun. The orbital speed is greatest (greatest path in one day) when the Earth is closest to the Sun (apparently equal triangles area). Equation of time describes the difference between actual and mean solar time. - teq in eq.s below is in [min], nday is the day of the year (N) from 1 to 365 or 366 Sun overtakes Sun lags behind UL, FS, LOTZ © Calculation of the sun path Sun path diagram … shows the apparent path of the Sun in the sky during selected days of the year - Case Ljubljana solar altitude  (°) solar time latitude 𝜑 = 46,07° longitude 𝜆 = +14,5° - 10. jan teq = 7 min 2,6+0,44*10=7 Significado diferença entre horário solar e o horário local The blue dots show the position of the Sun at full hour according to clock time at 12:00 clock time the 10. Jan. Sun will be in the S at 12:07 Sun will be here clock (local) time E S solar azimuth  (°) W UL, FS, LOTZ © Calculation of the sun path Actual (clock) time and solar time The difference between clock tclock and solar time ts is determined by taking into account the time shift tshift [h], which is the result of the difference between the longitude of the place and the standard meridian, which defines the time zone 𝜆0 − 𝜆 𝜆 𝑡𝑠ℎ𝑖𝑓𝑡 = = 𝑇𝑍 − 15 15 𝜆 longitude [°] LJ…+14,5°, Trebnje….+15° 𝜆0 standard meridian of time zone [°] SLO…+15° 𝑇𝑍 time zone [h] SLO…UTC+1h Teq calculado em cima pelas 𝑡𝑒𝑞 formulas 𝑡𝑠 = 𝑡𝑐𝑙𝑜𝑐𝑘 − − 𝑡𝑠ℎ𝑖𝑓𝑡 60 When does this difference matter ? -(7/60)-0.033(Estes 0,33 nao sao assim tao relevantes ) UL, FS, LOTZ ©  Calculation of the sun path solar altitude  (°) latitudes mais altas-a altitude máxima do sol durante o ano é Sun path diagram menor; Torino Isso faria com que os arcos da Case: Torino mais alto altitude solar (no eixo vertical) em altitude solar fossem mais baixos no gráfico Lj 46° +14,5° que lj Em latitudes altas, há uma variação Torino 45° +7,6° maior no caminho do sol entre as Valencia 39° 0° diferentes estações (a diferença entre verão e inverno é mais pronunciada) Alterar a longitude desloca o horário local do meio-dia solar. Por exemplo, ao mover-se para o leste, o meio- dia solar ocorre mais cedo no horário local, enquanto, ao mover-se para o oeste, ocorre mais tarde. E S solar azimuth  (°) W Valencia solar altitude  (°) solar altitude  (°) LJ E S solar azimuth  (°) W E S solar azimuth  (°) W UL, FS, LOTZ © Calculation of the sun path Sun path diagram Web tools: www , UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Solar radiation at the edge of the atmosphere 𝐺𝑒𝑥,𝑁 Extra-terrestrial solar radiation is radiation perpendicular to the direction of sun′s rays: (W/m2) 360 360 𝐺𝑒𝑥,𝑁 = 𝐺𝑒𝑥 ∙ 1 + 0,033 ∙ cos ∙ 𝑁 = 1367 ∙ 1 + 0,033 ∙ cos ∙𝑁 365 365 Hourly I and daily or monthly H solar irradiation at the edge of the atmosphere are determined for horizontal plane (index 0): (Wh/m2h, Wh/m2d, Wh/m2m) 12 𝜋 ∙ (𝜔2 − 𝜔1 ) 𝐼𝑒𝑥,𝑁,0 = ∙ 𝐺𝑒𝑥,𝑁 ∙ cos 𝜑 ∙ cos 𝛿 ∙ (sin 𝜔2 − sin 𝜔1 ) + ∙ sin 𝜑 ∙ sin 𝛿 𝜋 180 24 𝜋 ∙ 𝜔𝑠𝑠 𝐻𝑒𝑥,𝑁,0 = ∙ 𝐺𝑒𝑥,𝑁 ∙ cos 𝜑 ∙ cos 𝛿 ∙ sin 𝜔𝑠𝑠 + ∙ sin 𝜑 ∙ sin 𝛿 𝜋 180 Hex,SLO = 2,5 – 11,5 kWh/m2 per day UL, FS, LOTZ © solar azimuth  (°) Solar radiation (irradiance) and irradiation Solar radiation on horizontal surface Lambert′s cosine law: radiation intensity depends on the angle of incidence. 𝐺0 = 𝐺𝑏 ∙ 𝑐𝑜𝑠 𝑖 𝐺𝑏 𝐺0 Prove the validity of the law on the example 𝑖 of hourly solar radiation at the edge of the atmosphere : b in direction of sun‘s ray (beam) 0 on horizontal plane i incident angle UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Solar radiation on horizontal plane As solar radiation enters the Earth's atmosphere, some of it is scattered in the air, on water molecules and dust in the atmosphere. The amount of reflected, scattered and absorbed solar radiation depends on the distance traveled by the solar radiation, the level of dust particles and water vapor in the atmosphere. The intensity and radiation spectrum of solar radiation change and depend (also) on the length of the path of the sun's rays through the atmosphere. We call it the relative thickness of the atmosphere or Air mass UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Solar radiation on horizontal plane The intensity and radiation spectrum of solar radiation change and depend (also) on the length of the path of the sun's rays through the atmosphere. We call it the relative thickness of the atmosphere or Air mass 1 𝐴𝑀 = 𝛼 ≥ 10° sin 𝛼 menor de 10 graus 1 𝐴𝑀 = −1,253 sin 𝛼 + 0,15 ∙ 𝛼 + 3,885 Solar radiation on the Earth's surface can be determined with empirical expressions… 𝐺𝐴𝑀0 = 1353 𝑊/𝑚2 , 𝐺𝐴𝑀1 = 1040 𝑊/𝑚2 , 𝐺𝐴𝑀1.5 = 930 𝑊/𝑚2 , 𝐺𝐴𝑀10 = 270 𝑊/𝑚2 UL, FS, LOTZ ©  Solar radiation (irradiance) and irradiation Solar radiation on horizontal plane Global solar radiation and irradiation on horizontal plane is the sum of direct and diffuse (ir)radiation: 𝐺𝑔𝑙𝑜𝑏,0 = 𝐺𝑑𝑖𝑟,0 + 𝐺𝑑𝑖𝑓,0 𝐼𝑔𝑙𝑜𝑏,0 = 𝐼𝑑𝑖𝑟,0 + 𝐼𝑑𝑖𝑓,0 𝐻𝑔𝑙𝑜𝑏,0 = 𝐻𝑑𝑖𝑟,0 + 𝐻𝑑𝑖𝑓,0 Irradiance daily irradiation solar insolation Databases contain (several years period) average values of solar (ir)radiation on horizontal plane. The most commonly used method to determine both components of solar radiation is the (hourly or daily) clearness index method. Iex=hourly 𝐼𝑔𝑙𝑜𝑏,0 𝐻𝑔𝑙𝑜𝑏,0 extraterrestrial 𝑘𝑇 = 𝐾𝑇 = Erbs correlation: solar irradiation on a horizontal 𝐼𝑒𝑥,𝑁,0 𝐻𝑒𝑥,𝑁,0 EN ISO 52010-1 surface(slide 15) 𝐼𝑑𝑖𝑓,0 Sempre I difusa = 1 − 0,09 ∙ 𝑘 𝑇 𝑘 𝑇 ≤ 0,22 𝐼𝑔𝑙𝑜𝑏,0 𝐼𝑑𝑖𝑓,0 0,22 < 𝑘 𝑇 ≤ 0,8 = 0,9511 − 0,1604 ∙ 𝑘 𝑇 + 4,388 ∙ 𝑘 𝑇2 − 16,638 ∙ 𝑘 𝑇3 + 12,336 ∙ 𝑘 𝑇4 𝐼𝑔𝑙𝑜𝑏,0 𝑘 𝑇 > 0,8 𝐼𝑑𝑖𝑓,0 = 0,165 𝐼𝑔𝑙𝑜𝑏,0 UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Hglob,0 refere-se à irradiação solar Solar radiation on horizontal plane global acumulada ao longo de um período de tempo específico, geralmente em um Global solar radiation and irradiation on horizontal plane is the sum of direct and diffuse (ir)radiation: dia, sobre uma superfície horizontal no nível do solo. 𝐺𝑔𝑙𝑜𝑏,0 = 𝐺𝑑𝑖𝑟,0 + 𝐺𝑑𝑖𝑓,0 𝐼𝑔𝑙𝑜𝑏,0 = 𝐼𝑑𝑖𝑟,0 + 𝐼𝑑𝑖𝑓,0 𝐻𝑔𝑙𝑜𝑏,0 = 𝐻𝑑𝑖𝑟,0 + 𝐻𝑑𝑖𝑓,0 Databases contain (several years period) average values of solar radiation on horizontal plane. The most commonly used method to determine both components of solar radiation is the (hourly or daily) clearness index method. 𝐼𝑔𝑙𝑜𝑏,0 𝐻𝑔𝑙𝑜𝑏,0 Iglob=Irradiancia solar global no topo da atmosfera 𝑘𝑇 = 𝐾𝑇 = Ele representa a quantidade total de energia solar por unidade 𝐼𝑒𝑥,𝑁,0 𝐻𝑒𝑥,𝑁,0 de área recebida por um plano horizontal localizado fora da atmosfera terrestre. Gglob=radiação solar global no solo;energia solar efetivamente Liu Jordan correlation: disponível no nível do solo, após ser filtrada pela atmosfera. 𝐻𝑑𝑖𝑓,0 = 1,39 − 4,027 ∙ 𝐾𝑇 − 5,531 ∙ 𝐾𝑇2 − 3,108 ∙ 𝐾𝑇3 𝐻𝑔𝑙𝑜𝑏,0 UL, FS, LOTZ © Solar radiation (irradiance) and irradiation National database: ARSO, Annual irradiation Hourly values TMY – typical meteorological year Average daily irradiation, also for different inclination and orientation UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Database: METEONORM Output format, for different simulation tools Location selection and period (also future data) UL, FS, LOTZ © Monthly, hourly, 10 min values  Solar radiation (irradiance) and irradiation Solar instruments: Campbell-Stokes recorder Sun duration meter - heliograph Pyranometer Pyrheliometer Global solar radiation Direct solar radiation with shade – diffuse solar radiation Pyrgeometer UL, FS, LOTZ © Longwave (IR) radiation Solar radiation (irradiance) and irradiation Solar radiation on inclined and oriented surface Surface position is defined with surface inclination angle 𝛽 and surface azimuth angle 𝛾. In addition to the direct and diffuse components of solar radiation, the surface also receives reflected solar radiation. 𝐼𝑔𝑙𝑜𝑏,𝛽 = 𝐼𝑑𝑖𝑟,0 ∙ 𝑟𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓,0 ∙ 𝑟𝑑𝑖𝑓 + 𝐼𝑔𝑙𝑜𝑏,0 ∙ 𝜌𝑔𝑟 ∙ 𝑟𝑟𝑒𝑓 𝜌𝑔𝑟 ground solar reflectivity (aspfalt 0,1, grass 0,3, sand 0,4, snow 0,9) Normally we assume 0,2 r ratio of direct, diffuse, reflected hourly irradiation cos 𝑖 1+cos 𝛽 1−cos 𝛽 𝑟𝑑𝑖𝑟 = 𝑟𝑑𝑖𝑓 = 𝑟𝑟𝑒𝑓 = sin 𝛼 2 2 i solar radiation incident angle cos 𝑖 = sin 𝜑 ∙ sin 𝛿 ∙ cos 𝛽 − cos 𝜑 ∙ sin 𝛿 ∙ sin 𝛽 ∙ cos 𝛾 + cos 𝜑 ∙ cos 𝛿 ∙ cos ℎ ∙ cos 𝛽 + sin 𝜑 ∙ cos 𝛿 ∙ cos ℎ ∙ sin 𝛽 ∙ cos 𝛾 + cos 𝛿 ∙ sin ℎ ∙ sin 𝛽 ∙ sin 𝛾 UL, FS, LOTZ © Solar radiation (irradiance) and irradiation National database: ARSO, Average daily radiation, also for differently oriented and inclined surfaces Already built into engineering tools for calculation of building energy efficiency UL, FS, LOTZ © Solar radiation (irradiance) and irradiation Database: PVGIS Also solar radiation calculation for one and two axis tracking UL, FS, LOTZ © Literature S. Medved, P. Novak: Varstvo okolja in obnovljivi viri energije, UL, FS, 2000 M. Kaltschtt, W. Streicher, A. Wiese: Renewable Energy: Technology, Economics and Environment, Springer, 2007 S. Medved, S. Domjan, C. Arkar: Sustainable technologies for Nearly Zero Energy Buildings SIST EN ISO 52010-1 Video: www UL, FS, LOTZ ©