Basics of Solar Energy

The Sun: Earth’s Energy Source The Sun is located about 150x109 m from the Earth at the center of the Solar System. The Sun is a sphere of hot gaseous matter with dia of 1.39x109 m. The sun has an effective blackbody temperature of 5777K. The temperature in the central interior regions in estimated at 8x106 to 40x106K.

Solar Energy The Sun generates a large amount of energy due to a continuous thermonuclear fusion reaction occurring in its interior. In this interaction Hydrogen combine to form Helium and the excess energy is released in the form of electromagnetic radiation.

Structure of the Sun Core: 0 to 0.23R, 90% energy generated. Convective zone: zone from 0.7 to 1.0R, temperature 5000K , density 10-5 kg/m3 Sunspots: Large dark areas on sun surface. Photosphere: upper layer of convective zone. This zone is the source of most solar radiation. Chromosphere: Gaseous layer, depth 10,000km, high temperature than photosphere. Corona: Very low density, very high temperature 106 K.

The Sun: Earth’s Energy Source The total energy emitted by the Sun per unit time (Solar luminosity) is L0 = 3.9x1026 Watts. The energy flux at the surface of the Sun is approximately 64 x 106 W/m2 . The average solar energy flux at the Sun’s surface, a distance of r0 from its center, is given by the Solar luminosity (L0) divided by the area of a sphere with a radius r0: I0 = L0/4πr02 Sun’s surface temperature is about 5777 K.

The Sun: Earth’s Energy Source Due to the location of the Earth in the solar system , a range of temperatures exists close to its surface makes the Earth a habitable planet. This temperature range is determined through an energy balance between the solar radiation absorbed by the Earth and the energy the Earth sends back into space.

The Sun: Earth’s Energy Source This process is known as the Earth energy (or radiation) balance. Earth’s internal source of energy, due to radioactive decay of various elements and due to its warm core, is much smaller (~3x10-5 times) than the amount received from the sun.

Solar Flux in Space The energy flux emitted from the Sun spreads over an increasing spherical surface as it moves into space. Because the area of a sphere increases in proportion to the square of its radius, the radiative energy flux from the sun decreases as the inverse of the square of the distance from the Sun. The solar fluxes at two different distances from the Sun, I1 and I2, relate to one another as the inverse square of their distances from it, r1 and r2, that is: I1/ I2 = (r2/r1)2

Electromagnetic Energy Transfer Solar radiation is energy, traveling through space as electromagnetic (EM) wave radiation. Radiation is a form of energy transfer that does not require mass exchange or direct contact between the heat exchanging bodies. Radiation involves the propagation of EM energy at the speed of light c* = 3x1010 cm/s. The speed of light c*, the frequency of the EM waves ν, and its wavelength λ are linked through the following relationship: c* = λν

E(T,λ) = C1 /(λ5[ exp(C2 /λT ) − 1] ) Blackbody Radiation A body that emits energy over all frequencies in a continuous manner is called a blackbody. Blackbody radiation is a function of temperature and wavelength. This dependence is described in Planck’s law of radiation, which relates the EM energy flux emitted by a blackbody to the wavelength and the temperature: E(T,λ) = C1 /(λ5[ exp(C2 /λT ) − 1] ) Where C1 and C2 are constants λ is the wavelength in m, and T is the absolute temperature in K

Blackbody Radiation Planck's law states a complex relationship between the energy flux per unit wavelength, the wavelength, and the temperature. From it we can derive two more simplified relationship. Wien law, stating the relationship between the wavelength corresponding to the maximum energy flux output by a blackbody λmax (in μm) and its absolute temperature T (in K): . λmax = 2898/T

Blackbody Radiation Using Wien law and the Earth and Sun average temperatures 288 and 5780 K, respectively we find that their λmax correspond to about 10 and 0.5 μm. Stefan-Boltzman law stating the relationship between absolute temperature and the total energy flux emitted by a blackbody, over the entire wavelength range Ib (in W/m2) Ib = σT4 where σ is referred to as the Stefan-Boltzman constant = 5.67 x 10−8 W/m2 K4

Latitude Latitude lines run horizontally, parallel and equally distant from each other. Degrees latitude are numbered from 0° to 90° north and south. Zero degrees is the equator, the imaginary line which divides our planet into the northern and southern hemispheres. North Pole is 90° north and South Pole and 90° south. Each degree of latitude is approximately 69 miles (111 km) apart.

Longitude Longitude lines (meridians) are vertical, converge at the poles and are widest at the equator (about 69 miles or 111 km apart). Zero degrees longitude is located at Greenwich, England (0°). The degrees continue 180° east and 180° west where they meet and form the International Date Line in the Pacific Ocean.

Circles of Latitudes The Equator (0 deg) The Antarctic Circle (66deg 33’ S) The Arctic Circle (66 deg 33’ N) iv. The Tropic of Capricorn (23 deg 26’ S) v. The Tropic of Cancer (23 deg 26’ N)

Solar Energy and the Climate System The planets rotate around the Sun in elliptically shaped orbits with the sun in one of its foci. Aphelion is the orbit position farthest from the sun and perihelion closest. Each orbit is defined by its mean distance from the Sun (d), by its eccentricity (e) and by its orientation in space. Each planet rotates around its axis, which in generally inclined with the respect to the orbital plane as measured by the obliquity angle

Solar Energy and the Climate System The rotation rate around the axis determine the length of the day and, The planet’s orbital rotation rate determine the length of its year. Eccentricity results in relatively small variations in incoming radiation, which are not the main reason for the seasonality. Obliquity (Φ) is the main reason for seasonality. If Φ is different from zero, the lengths of day and night over most of the planet’s surface are not equal but for two times during the year, the equinox times.

Solar Energy and the Climate System The difference between the lengths of day and night is zero on the planet’s equator and changes poleward. The days are longer than the night on the hemisphere tilting towards the Sun leading to more incoming Solar energy than in the other hemisphere. The times of year when the difference between the lengths of day and night reach their extreme values are called solstices.

SOLAR TERMINOLOGIES for Solar Energy Calculations

Irradiance, Irradiation Irradiance, G ,The rate at which the radiant energy is incident on a unit area surface. W/m2 Irradiation ,The amount incident energy per unit area on a surface, found by integration of irradiance over specified time, usually an hour or day, J/m2

Beam , Diffuse and Total Radiation The solar radiation arriving at the earth’s surface has two components Direct: can be focused Diffused >10%: cannot be focused (Direct / diffused) ratio : 0.9 Cloudless ,clear day 0.1 completely overcast day The total irradiance at any surface is the sum of the two components Gt = Gbeam +Gdiffused

Radiosity , Emissive Power Radiosity, The rate at which the radiant energy leaves a surface per unit area surface by emission, reflection, transmission. W/m2 Emissive Power , The rate at which the radiant energy leaves a surface per unit area surface by emission only W/m2

Extraterrestrial Radiation (Solar constant) Solar constant ( Io ), is the radiation incident outside the earth's atmosphere. On average, it is 1367 W/m2. This value varies by ±3% as the earth orbits the sun. Io = 1367 * (Rav / R)2 W/m2 where (Rav) is the mean sun-earth distance and (R ) is the actual sun-earth distance depending on the day of the year Where β = 2 π n / 365 and n is the day of the year. For example, January 15 is year day 15 and February 15 is year day 46.

Solar Insolation The solar radiation received on a flat, horizontal surface at a particular location on earth at a particular instant of time. W/m2 Depend on; Daily variation Seasonal variation Atmospheric clarity latitude

Clarity Index The ratio of the solar radiation arriving at the earth’s surface to extraterrestrial radiation. The monthly average clearness index is the ratio of monthly average daily solar radiation at the surface to the monthly average daily extraterrestrial radiation. KT varies from place to place – from about 0.3 for very overcast climates to 0.8 for very sunny places.

Solar Declination (δ)   Solar Declination is the angle between the Sun's rays and Earth's equatorial plane. (Technically, it is the angle between the Earth-Sun vector and the equatorial plane.)

Solar Declination The Declination angle is 23.5° during the Northern Summer Solstice, and –23.5° during the Southern Summer Solstice. It is between ±23.5° the rest of the year. Following equations could be used for calculating solar declination angle δ Where N is the day in the year

Solar Declination For precise calculation the following equation could be used where

Solar Elevation (Sun height) Angle ( θ ) The solar elevation angle is the elevation angle of the sun. That is, the angle between the direction of the sun and the (idealized) horizon. It can be calculated, to a good approximation, using the following formula: Where θs is the solar elevation angle, h is the hour angle of the present time , δ is the current sun declination and Φ is the local latitude

Solar Time and Local Standard Time The system of standard time is based on two facts: The Earth completes a total rotation on its axis once every twenty-four hours. There are 360° of longitude all the way around the Earth. The Earth turns 360° in 24 hours, or at a rate of 15° an hour. (360° in a day÷24 hours = 15° an hour) Each standard meridian is the center of a time zone. Each time zone is 15° wide.

Solar Time and Local Standard Time The Greenwich Time Zone, for example, is centered on the Prime Meridian This time zone is supposed to be 15° wide and extends from 7½° W to 7½°E. However, the boundaries of standard time don’t exactly run along meridians. The boundaries have been changed to fit the borders of countries and even smaller areas.

Solar Time and Local Standard Time The relationship between solar time and local standard time is required to describe the position of the sun in local standard time. Local standard time is the same in the entire time zone whereas solar time relates to the position of the sun with respect to the observer. That difference depends on the exact longitude where solar time is calculated.

Solar Time and Local Standard Time As the earth moves around the sun, solar time changes slightly with respect to local standard time. This is mainly related to the conservation of angular momentum as the earth moves around the sun. This time difference is called the equation of time and can be an important factor when determining the position of the sun for solar energy calculations. An approximate formula for the equation of time (Eqt) in minutes depending upon the location of earth in its orbit as following;

Solar Time and Local Standard Time Eqt = - 14.2 sin [π (n + 7) / 111] for year day n between 1 and 106 Eqt = 4.0 sin [π (n - 106) / 59) for year day n between 107 and 166 Eqt = - 6.5 sin [π( n - 166) / 80) for year day n between 167 and 365

Tsolar = Tls + Eqt/ 60 ± (Longlocal – Longsm)/15 hours Solar Time and Local Standard Time To adjust solar time for a longitude we have to add the value resulted from the time equation and to add or subtract the difference between the local time the clock time for the time zone. Tsolar = Tls + Eqt/ 60 ± (Longlocal – Longsm)/15 hours Where Tsolar is the local solar time, Tls is the local standard time, Longlocal is the longitude of the observer in degrees and Longsm is the longitude for the standard meridian for the observer's time zone.

h = π * (12 - Tsolar) / 12 , radians Solar hour angle (h) Since the earth rotates approximately once every 24 hours, the hour angle changes by 15 degrees per hour and moves through 360 degrees over the day. Typically, the hour angle is defined to be zero at solar noon, when the sun is highest in the sky. h = π * (12 - Tsolar) / 12 , radians Where Tsolar is the local solar time

Solar zenith angle (ωs) The zenith angle is the opposite angle to the sun height θs. ωs = ( 90° – θs). At a sun height of 90°, the sun is at the zenith and the zenith angle is therefore zero.

Air Mass, m The ratio of the mass of atmosphere through which beam radiation passes to the mass it would pass through if the sun was at the zenith(directly overhead). At sea level m =1 when sun is at the zenith. m=2 for zenith angle is 60o For Zenith angles from 0 to 70o at sea level m = 1/ cosθ

Sun azimuth (αS) The sun azimuth (αS ) is the angle, measured clockwise, between geographical North and the point on the horizon directly below the sun.

Solar Radiation on Earth Surface The amount of direct radiation on a horizontal surface can be calculated by multiplying the direct normal irradiance times the cosine of the zenith angle (ω). On a surface tilted (T) degrees from the horizontal and rotated ( γ ) degrees from the north-south axis, the direct component on the tilted surface is determined by multiplying the direct normal irradiance by the following value for the cosine of the incidence angle (θ ) ;

Solar Radiation on Earth Surface cos (θ) = sin(δ)sin(λ)cos(T) - sin(δ)cos(λ)sin(T)cos(γ) +cos(δ)cos(l)cos(T)cos(h) +cos(δ)sin(λ)sin(T)cos(γ)cos(h) +cos(δ)sin(T)sin(γ)sin(h) where λ is the latitude of the location of interest, δ is the sun declination and h is the hour angle .

Thank you

Solar Energy Flux

Earth energy (or radiation) balance.

The Sun: Earth’s Energy Source

Solar Flux in Space

Latitude and Longitude

Latitude and Longitude

Circles of Latitude

Circles of Latitude The Equator (00) The Antarctic Circle (66o 33’ S) The Arctic Circle (66o 33’ N)

Circles of Latitude The Arctic Circle (66o 33’ N)

Circles of Latitude iii. The Tropic of Capricorn (23o 26’ S) iv. The Tropic of Cancer (23o 26’ N)

Earth in Orbits Distance from Sun d = 150x109 m, eccentricity e = (a-b)/(a+b) = 0.017, axis tilt Φ = 23.5°, Solar Flux (I0) = 1367 W/m2 perihelion (147 million km), aphelion (152 million km).

Earth in Orbits

Earth in Orbit

Electromagnetic Energy Transfer

Electromagnetic Energy Transfer

Blackbody Radiation

Solar Declination (δ), Elevation (γ ) and Zenith (ω)