Solar Energy

Heliostats!!!

Solar Radiations & its Measurements

Different Sources of Energy Solar Energy Wind Energy Biomass and Biogas Ocean Thermal Energy Conversion Tidal Energy Wave Energy Geothermal Energy

Solar Constant Solar Constant ISC : Rate of arrival of solar energy at the top of the earth’s atmosphere. It is the energy received in unit time over a unit surface area perpendicular to the direction of solar radiations at the mean distance of earth from the sun. Some of the data related to solar constant are: Diameter of sun – 1.39X106Km Diameter of earth – 1.27X104Km Mean distance between sun and earth – 1.5X108Km Angle subtended on earth by the sun – 32minutes

Solar Constant The solar radiations are almost parallel to each other and perpendicular to earth. The solar constant can be given as: 1.353kW/m2 Or 116.5 langleys / hour (1 langley = 1 cal/cm2) Or 429.2 btu / ft2 / hour The distance between earth and sun is min. during summers and max. during winters of northern hemisphere. The change in distance changes the solar constant.

Solar Constant The change in solar constant can be approximated by the following equation: where I is solar radiation n is the number of days

Solar Constant

Solar Constant Classification of Solar Energy on earth: Sr No. Type of Radiation Percent of Total Radiation Wavelength Approx Energy (W/m2) Approximate percentage of total energy 1 Ultraviolet 8% - 10% <0.39μm 95 7% 2 Visible Light 40% - 46% 0.39μm – 0.78μm 640 47.3% 3 Infra Red 46% - 50% >0.78μm 618 45.7%

Variation in Solar Radiations Radiations obtained on earth’s surface are classified as: Beam and Diffuse radiations Part of radiations are reflected back due to clouds. Radiations entering earth’s atmosphere are partly absorbed by the molecules in the air. Ultraviolet radiations are absorbed by oxygen and ozone whereas the infrared radiations are absorbed by water vapour and CO2. A part of the radiations are scattered by droplets and dust particles. Solar radiations that are not absorbed or scattered, reach the earth’s surface and are called as “direct radiation” or Beam radiation. Radiations reaching earth’s surface after reflection and scattering by the atmosphere are called as “Diffuse” radiations. The radiation reaching earth's surface varies due to: atmospheric elements which cause absorption and scattering; local variations in atmosphere, such as water vapour, clouds, and pollution; latitude of the location; and season of the year and time of the day.

Variation in Solar Radiations

Variation in Solar Radiations The total radiation reaching earth’s surface is also termed as ‘insolation’ at that point. Insolation is defined as the total solar radiation energy received on a horizontal surface of unit area (e.g. 1 m2) on the ground in unit time (e.g., 1 day) The insolation changes from location to location also due to altitude of the sun in the sky. If the sun’s altitude is lower it will have to pass through greater thickness of atmosphere. This will cause more absorption and scattering of the solar radiations. Insolation will be is less if the sun has lower altitude and vice versa. On a clear cloudless day, about 10 – 20% of insolation is diffuse radiation and 80 – 90% is beam radiations. While on a cloudy day the diffuse radiations may increase up to 100%.

Air Mass Air Mass is the path of radiation through the atmosphere considering the vertical path at sea level as unity. It is denoted by ‘m’ or ‘AM’. It is the ratio of path of the solar radiations through earth’s atmosphere to the length of path when the sun is vertically over head. The different values of air mass for various positions of sun in the sky are: m=1 when sun is over head m=2 when sun is at an angle of 60° m=sec (θz) when m>3 m=0 just above earth’s atmosphere.

Air Mass

Solar Radiation Geometry Inclination Angle (altitude)(α): The angle between the sun’s rays and its projection on a horizontal surface is known as inclination angle. Zenith Angle (θz): It is the angle between the sun’s rays and the perpendicular to the horizontal plane. Solar Azimuth Angle (γs): It is the angle on the horizontal plane between the line south and the projection of the sun’s rays on the horizontal plane. It is taken positive when measured from south towards west.

Solar Radiation Geometry Angle of Incidence (θi): It is the angle between the sun’s ray incident on plane surface (collector) and normal to that surface. Angle of incidence can be expressed as: cosθi =(cosφ cosβ + sinφ sinβ cosγ) cosδ cosω + cosδ sinω sinβ sinγ + sinδ (sinφ cosβ - cosφ sinβ cosγ) Special Case: For a surface facing south, γ=0 cosθi =cos(φ-β)cosδ cosω + sinδ sin(φ-β) For a horizontal surface β=0, θi= θz cosθz =cosφ cosδ cosω + sinδ sinφ For vertical surface facing due south, γ=0, β=90° cosθi =-sinδ cosφ + cosδ cosω sinφ

Solar Radiation Geometry Angle of Latitude (φ): The angle of latitude of a location on the earth’s surface is the angle made by a radial line joining the given location to the centre of the earth with its projection on the equator plane. The angle of latitude is positive for northern hemisphere and negative for southern hemisphere. Slope (Tilt Angle)(β): It is the angle between the inclined plane surface (collector), under consideration and the horizontal. It is taken to be positive for the surface sloping towards south.

Solar Radiation Geometry Hour Angle (ω): The hour angle at any moment is the angle through which the earth must turn to bring the meridian of the observer directly in line with the sun’s rays. One hour corresponds to 15° of rotation. At solar noon when the sun’s rays are in line with local meridian, the hour angle is zero. It is negative in before noon i.e., before 12pm and positive in after noon i.e, after 12pm. Eg: at 6hrs it is -90° and at 18hrs it is +90°. The formula for the hour angle is: ω=[Solar Time – 12]*15°

Solar Radiation Geometry Declination(δ) angle: It is defined as the angular displacement of the sun from the plane of the earth’s equator. It is positive when measured above equatorial plane in the northern hemisphere. The formula for declination angle is: δ=23.45 * sin degrees where n is the day of the year.

Solar Radiation Geometry Surface Azimuth Angle (γ): It is the angle in the horizontal plane, between the line due south and the horizontal projection of normal to the inclined plane surface (collector). It is taken positive when measured from south towards west.

Local Solar Time The time based on the position of sun with respect to a particular location is called as local solar time. It is also called as local apparent time. Solar time is measured with reference to zenith position of sun during solar noon. At this time the sun crosses over the observer’s meridian & is at the highest position in the sky at solar noon. The solar time at a location can be calculated from standard time in a clock by applying two corrections. The first correction is due to the difference in longitude between a particular location and the meridian on which the standard time of the clock is based. For difference of every degree in longitude a correction of 4 minutes is done. The second correction is due to small perturbations in earth’s orbit and rate of rotation. This correction is called as the equation of time correction.

Local Solar Time The equation of time correction is based on experimental observations and plotted as shown in figure below.

Local Solar Time Local solar time (LST) = standard time + 4 (standard time longitude – longitude of location) + (equation of time correction) where equation of time correction is given as: 9.87sin2A – 7.53cosA – 1.5sinA (unit - min) where A = (360/364) (n-81) where n  day of the year, starting from 1st January. While calculating local solar time, ‘+’ sign is used if the standard meridian of the country lies in the western hemisphere with respect to the prime meridian. While ‘-‘ sign is used for countries in eastern hemisphere. Equation of time correction is also called equation of time. The solar day, is the duration between two consecutive solar noons. It is not exactly of 24 hours throughout the year.

Numericals