Motion of the Sun. View Comments

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1 Login 2017 Survey to Improve Photovoltaic Education Christiana Honsberg and Stuart Bowden View Comments Instructions 1. Introduction 2. Properties of Sunlight 2.1. Basics of Light Properties of Light Energy of Photon Photon Flux Spectral Irradiance Radiant Power Density 2.2. Blackbody Radiation Blackbody Radiation 2.3. Solar Radiation The Sun Solar Radiation in Space Solar Radiation Outside the Earth's Atmosphere 2.4. Terrestrial Solar Radiation Solar Radiation at the Earth's Surface Atmospheric Effects Air Mass Motion of the Sun Solar Time Declination Angle Elevation Angle Azimuth Angle The Sun's Position Sun Position Calculator Sun's Position to High Accuracy Solar Radiation on a Tilted Surface Arbitrary Orientation and Tilt Calculation of Solar Insolation 2.5. Solar Radiation Data Measurement of Solar Radiation Analysis of Solar Irradiance Data Sets Typical Meteorological Year Data (TMY) Making Use of TMY Data Average Solar Radiation Isoflux Contour Plots Sunshine Hour Data Cloud Cover Data Chapter 2 Quiz 3. PN Junction 4. Solar Cell Operation 5. Design of Silicon Cells 6. Manufacturing Si Cells 7. Modules and Arrays 8. Characterization 9. Material Properties 11. Appendices Korean Version List of: Like 3.1K people like this. Sign Up to see what your friends like. Motion of the Sun Air Mass Solar Time The apparent motion of the sun, caused by the rotation of the Earth about its axis, changes the angle at which the direct component of light will strike the Earth. From a fixed location on Earth, the sun appears to move throughout the sky. The position of the sun depends on the location of a point on Earth, the time of day and the time of year. This apparent motion of the sun is shown in the figure below. Path of the sun in the southern hemisphere. This apparent motion of the sun has a major impact on the amount of power received by a solar collector. When the sun's rays are perpendicular to the absorbing surface, the power density on the surface is equal to the incident power density. However, as the angle between the sun and the absorbing surface changes, the intensity on the surface is reduced. When the module is parallel to the sun's rays (and the angle to the module normal = 90 ) the intensity of light essentially falls to zero. For intermediate angles, the relative power density is cos(θ) where θ is the angle between the sun's rays and the module normal. Click on the picture to adjust the module tilt and see the effect on the light intensity. In this picture, the module is being titled, but the same effects occur as the angle of the incident solar radiation changes. The angle between the sun and a fixed location on Earth depends on the particular location (the longitude of the location), the time of year and the time of day. In addition, the time at which the sun rises and sets depends on the longitude of the location. Therefore, complete modeling of the sun's Drag the slider to examine the impact of changing the angle between the absorbing surface and the angle to a fixed position on Earth requires the latitude, incident light. longitude, day of the year, and time of day. This is discussed in the following pages. Air Mass Solar Time Log in or register to post comments Reader comments and discussion of this page Español

2 Login 2017 Survey to Improve Photovoltaic Education Christiana Honsberg and Stuart Bowden View Comments Instructions 1. Introduction 2. Properties of Sunlight 2.1. Basics of Light Properties of Light Energy of Photon Photon Flux Spectral Irradiance Radiant Power Density 2.2. Blackbody Radiation Blackbody Radiation 2.3. Solar Radiation The Sun Solar Radiation in Space Solar Radiation Outside the Earth's Atmosphere 2.4. Terrestrial Solar Radiation Solar Radiation at the Earth's Surface Atmospheric Effects Air Mass Motion of the Sun Solar Time Declination Angle Elevation Angle Azimuth Angle The Sun's Position Sun Position Calculator Sun's Position to High Accuracy Solar Radiation on a Tilted Surface Arbitrary Orientation and Tilt Calculation of Solar Insolation 2.5. Solar Radiation Data Measurement of Solar Radiation Analysis of Solar Irradiance Data Sets Typical Meteorological Year Data (TMY) Making Use of TMY Data Average Solar Radiation Isoflux Contour Plots Sunshine Hour Data Cloud Cover Data Chapter 2 Quiz 3. PN Junction 4. Solar Cell Operation 5. Design of Silicon Cells 6. Manufacturing Si Cells 7. Modules and Arrays 8. Characterization 9. Material Properties 11. Appendices Korean Version List of: Azimuth Angle Elevation Angle The Sun's Position The azimuth angle is the compass direction from which the sunlight is coming. At solar noon, the sun is always directly south in the northern hemisphere and directly north in the southern hemisphere. The azimuth angle varies throughout the day as shown in the animation below. At the equinoxes, the sun rises directly east and sets directly west regardless of the latitude, thus making the azimuth angles 90 at sunrise and 270 at sunset. In general however, the azimuth angle varies with the latitude and time of year and the full equations to calculate the sun's position throughout the day are given on the following page. The azimuth angle is like a compass direction with North = 0 and South = 180. Other authors use a variety of slightly different definitions (i.e., angles of ± 180 and South = 0 ). Like 3.1K people like this. Sign Up to see what your friends like. The azimuth is calculated from the above parameters: where α is the elevation The above equation only gives the correct azimuth in the solar morning so that: Azimuth = Azi, for LST <12 or HRA < 0 Azimuth = 360 Azi, for LST > 12 or HRA >0 [ + ] Feedback

3 Azimuth = 360 Azi, for LST > 12 or HRA >0 Elevation Angle The Sun's Position Log in or register to post comments Reader comments and discussion of this page Español

4 Login 2017 Survey to Improve Photovoltaic Education Christiana Honsberg and Stuart Bowden View Comments Instructions 1. Introduction 2. Properties of Sunlight 2.1. Basics of Light Properties of Light Energy of Photon Photon Flux Spectral Irradiance Radiant Power Density 2.2. Blackbody Radiation Blackbody Radiation 2.3. Solar Radiation The Sun Solar Radiation in Space Solar Radiation Outside the Earth's Atmosphere 2.4. Terrestrial Solar Radiation Solar Radiation at the Earth's Surface Atmospheric Effects Air Mass Motion of the Sun Solar Time Declination Angle Elevation Angle Azimuth Angle The Sun's Position Sun Position Calculator Sun's Position to High Accuracy Solar Radiation on a Tilted Surface Arbitrary Orientation and Tilt Calculation of Solar Insolation 2.5. Solar Radiation Data Measurement of Solar Radiation Analysis of Solar Irradiance Data Sets Typical Meteorological Year Data (TMY) Making Use of TMY Data Average Solar Radiation Isoflux Contour Plots Sunshine Hour Data Cloud Cover Data Chapter 2 Quiz 3. PN Junction 4. Solar Cell Operation 5. Design of Silicon Cells 6. Manufacturing Si Cells 7. Modules and Arrays 8. Characterization 9. Material Properties 11. Appendices Korean Version List of: Elevation Angle Declination Angle Azimuth Angle The elevation angle (used interchangeably with altitude angle) is the angular height of the sun in the sky measured from the horizontal. Confusingly, both altitude and elevation are also used to describe the height in meters above sea level. The elevation is 0 at sunrise and 90 when the sun is directly overhead (which occurs for example at the equator on the spring and fall equinoxes). The elevation angle varies throughout the day. It also depends on the latitude of a particular location and the day of the year. An important parameter in the design of photovoltaic systems is the maximum elevation angle, that is, the maximum height of the sun in the sky at a particular time of year. This maximum elevation angle occurs at solar noon and depends on the latitude and declination angle as shown in the figure below. Like 3.1K people like this. Sign Up to see what your friends like. [ + ] Feedback The maximum elevation angle at solar noon (α) is a function of latitude and the declination angle (δ).

5 From the previous figure, a formula for the elevation angle at solar noon can be determined according to the formula: When the equation above gives a number greater than 90 then substract the result from 180. It means the sun at solar noon is coming from the south as is typical the northern hemisphere. where: φ is the latitude of the location of interest (+ve for the northern hemisphere and ve for the southern hemisphere). δ is the declination angle, which depends on the day of the year. At the Tropic of Cancer on summer solstice, the sun is directly overhead and the elevation angle is 90. In summer at latitudes between the equator and the Tropic of Cancer, the elevation angle at solar noon is greater than 90, implying that the sunlight is coming from the north rather than from the south as in most of the northern hemisphere. Similarly, at latitudes between the equator and the Tropic of Capricorn, during some periods of the year, sunlight is incident from the south, rather than from the north. While the maximum elevation angle is used even in very simple PV system design, more accurate PV system simulation requires the knowledge of how the elevation angle varies throughout the day. These equations are given in the following page. The elevation, α, can be found using the following formula: where HRA is the hour angle Zenith Angle The zenith angle is the angle between the sun and the vertical. The zenith angle is similar to the elevation angle but it is measured from the vertical rather than from the horizontal, thus making the zenith angle = 90 elevation. Sunrise and Sunset To calculate the sunrise and sunset time the elevation is set to zero and the elevation equation above is rearranged to give: and sunset: these equations can be simplified as:

6 Login 2017 Survey to Improve Photovoltaic Education Christiana Honsberg and Stuart Bowden View Comments Instructions 1. Introduction 2. Properties of Sunlight 2.1. Basics of Light Properties of Light Energy of Photon Photon Flux Spectral Irradiance Radiant Power Density 2.2. Blackbody Radiation Blackbody Radiation 2.3. Solar Radiation The Sun Solar Radiation in Space Solar Radiation Outside the Earth's Atmosphere 2.4. Terrestrial Solar Radiation Solar Radiation at the Earth's Surface Atmospheric Effects Air Mass Motion of the Sun Solar Time Declination Angle Elevation Angle Azimuth Angle The Sun's Position Sun Position Calculator Sun's Position to High Accuracy Solar Radiation on a Tilted Surface Arbitrary Orientation and Tilt Calculation of Solar Insolation 2.5. Solar Radiation Data Measurement of Solar Radiation Analysis of Solar Irradiance Data Sets Typical Meteorological Year Data (TMY) Making Use of TMY Data Average Solar Radiation Isoflux Contour Plots Sunshine Hour Data Cloud Cover Data Chapter 2 Quiz 3. PN Junction 4. Solar Cell Operation 5. Design of Silicon Cells 6. Manufacturing Si Cells 7. Modules and Arrays 8. Characterization 9. Material Properties 11. Appendices Korean Version List of: Sun's Position to High Accuracy Solar Radiation on a Tilted Surface Arbitrary Orientation and Tilt The power incident on a PV module depends not only on the power contained in the sunlight, but also on the angle between the module and the sun. When the absorbing surface and the sunlight are perpendicular to each other, the power density on the surface is equal to that of the sunlight (in other words, the power density will always be at its maximum when the PV module is perpendicular to the sun). However, as the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight. The amount of solar radiation incident on a tilted module surface is the component of the incident solar radiation which is perpendicular to the module surface. The following figure shows how to calculate the radiation incident on a tilted surface (S module ) given either the solar radiation measured on horizontal surface (S horiz ) or the solar radiation measured perpendicular to the sun (S incident ). Tilting the module to the incoming light reduces the module output. Like 3.1K people like this. Sign Up to see what your friends like. The animation shows the calculation of the various insolations. In each case the length of the vector gives the relative intensity of the radiation. The equations relating S module, S horiz and S incident are: [ + ] Feedback

7 where α is the elevation angle; and β is the tilt angle of the module measured from the horizontal. The elevation angle has been previously given as: where φ is the latitude; and δ is the declination angle previously given as: where d is the day of the year. Note that from simple math (284+d) is equivalent to (d 81) which was used before. Two equations are used interchangeably in literature. From these equations a relationship between S module and S horiz can be determined as: The following active equations show the calculation of the incident and horizontal solar radiation and that on the module. Enter only one of S module, S horiz and S incident and the program will calculate the others. Components of Radiation on Tilted Surface Calculator Array Tilt, β = degrees. Latitude, φ = degrees. Hemisphere: North South Day Number, d = Declination, δ= Sun Angle, α = degrees degrees. S horiz = S incident = S module = S module = S incident = S horiz = S module = S horiz = S incident = The tilt angle has a major impact on the solar radiation incident on a surface. For a fixed tilt angle, the maximum power over the course of a year is obtained when the tilt angle is equal to the latitude of the location. However, steeper tilt angles are optimized for large winter loads, while lower title angles use a greater fraction of light in the summer. The simulation below calculates the maximum number of solar insolation as a function of latitude and module angle.

8 Latitude: 41 North Array Tilt: 23 The effect of latitude and module tilt on the solar radiation received through out the year in W.h.m 2.day 1 without cloud. On the x axis, day is the number of days since January 1. The Module Power is the solar radiation striking a tilted module. The module tilt angle is measured from the horizontal. The Incident Power is the solar radiation perpendicular to the sun's rays and is what would be received by a module that perfectly tracks the sun. Power on Horizontal is the solar radiation striking the ground and is what would be received for a module lying flat on the ground. These values should be regarded as maximum possible values at the particular location as they do not include the effects of cloud cover. The module is assumed to be facing south in the northern hemisphere and north in the southern hemisphere. For some angles, the light is incident from the rear of the module and in these cases the module power drops to 0. As can be seen from the above animation, for a module tilt of 0, the Module Power and Power on Horizontal are equal since the module is lying flat on the ground. At a module tilt of 80, the module is almost vertical. The Module Power is less than the Incident Power except when the module is perpendicular to the sun's rays and the values are equal. The module is orientated to the equator so it faces north in the Southern Hemisphere and south in the Northern Hemisphere. As module moves from the Northern to Southern Hemisphere (latitude = 0 ), the module is turned to face in the opposite direction and so the Module Power curve flips. When the light is incident from the rear of the module the Module Power drops to zero. Try setting the latitude to your location and then varying the module tilt to see the effect on the amount of power received throughout the year. Sun's Position to High Accuracy Arbitrary Orientation and Tilt Log in or register to post comments Reader comments and discussion of this page Español

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