DOCSLIB.ORG

Coordination for Sun Location When Planning a PV System, It Is Crucial To

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Coordination for Sun Location When Planning a PV System, It Is Crucial To Coordination for Sun location When planning a PV system, it is crucial to know at any given time the position of the Sun in the sky as seen from the location of the solar system. In today's lecture we will introduce two coordinates systems that we will use to locate the sun in the sky. First the geographic and then the celestial coordinate systems. There are several web applications that you can use for finding the path of the sun. For example, these pictures are obtained from Wolfram Alpha and you can see the zenith view of the observer during the solstice of winter and summer in Delft, which represents the lowest and the highest path drawn by the sun during the year. Indeed, the maximum altitude of the sun which will be introduced in the next slides increases from almost 15 degrees to 61 and so also the daylight the duration becomes more than the double. Note that the sun apex during the day will have very important implication in case the PV system is embedded in a landscape with obstacles. As we shall see in the following lecture, finding the position of the Sun above a solar panel situated on the earth is not a trivial trigonometric problem. Before breaking the procedure in small steps in order to solve such problem, let's learn some important terms. To begin we shall consider a panel as a surface tangent to the earth crust so it is just lying on the surface. Later on we will tilt it in order to optimize its yield. First we have to locate the panel with respect to the global position and thus we use the geographic coordinate system. This system enables to specify every location on earth with the two coordinates, latitude and the longitude. The latitude of a point is the angle between the equatorial plane, depicted in red in the picture and the straight line that passes through that point and the center of the earth. Points at the same latitude trace circles on the surface of earth called parallel. Thus the North Pole is 90 degrees north and the South Pole is 90 degrees south and the equator divides the globe into northern and southern hemisphere. The longitude of a point is the angle between the Greenwich reference Meridian and the Meridian that passes through that point. This angle can be west or east since the Greenwich Meridian determines the proper eastern and western hemispheres. Here is shown the example of Delft, which I am now, and which is located in the northern hemisphere to east of the Greenwich Meridian. This other city is Dakar and it is always in the North hemisphere, but unlike Delft, it is located to the west of the Prime Meridian. Now that we have seen the coordinates of the earth it will be much easier to understand the celestial coordinates. Indeed, since celestial objects like the Sun the moon and the stars are very far away from the earth, it is convenient to describe their motion projected on a sphere with arbitrary radius and concentric to the earth. It is very important to note that because of the distance of celestial objects in general and that the Sun in particular, being much larger than the radius of the earth, we can consider the observer and the center of the earth coincident. This sphere is called the celestial sphere and at this point is the position of the celestial object. For photovoltaic applications it is most convenient to use the horizontal coordinate system, where the horizon of the observer constitutes the fundamental plane. In this case the horizon of the observer is the grey area beneath the hemisphere and on the left hand side you can see the representation of a plane tangent to the earth, where the blue dot is the observer. Another important thing to realize is that your module now it's the observer. Therefore, the celestial sphere will have the same inclination as this plane. As we anticipated, we may neglect the translational shift of the origin of the coordinate systems from the observer to the center of the earth and thus if the PV module now it is the observer, we can always find the position of the Sun in terms of two angles. The altitude a, which is the angular elevation of the center of the solar disk above the horizontal plane. Its angular range is between the minus 90 and plus 90 degrees, where negative angles correspond to the Sun being below the horizon and in thus during night. The azimuth A capital is the angle between the line of sight projected on the horizontal plane and the north. It is counted eastward such that north has an azimuth of 0 degrees, east of 90 degrees, south of 180 degrees and finally west 270 degrees. Its angular range is thus between 0 and 360 degrees. But note that different conventions are also used by the PV community. For example, the South might correspond to zero degrees and the angles might be counted westward. To be clear, from now on we will use only the convention where a capital is equal to 0, corresponding to north. These two set of coordinates, azimuth and the altitude of the Sun with respect to the observer are very important because they are input parameters together with the date and time to calculate the solar position in the sky. Instead of using the spherical coordinate a small and A capital, we can also use Cartesian coordinates, X, Y and Z. The principal direction which is the arrow pointing north is parallel to X, while Z axis is pointing towards the zenith. The Cartesian coordinates are connected to the spherical coordinates via this a simple trigonometric relation that expresses the Sun position of three coordinates instead of two. So let's get things together. First if we trace the path of the Sun in the celestial sphere, we obtain the ecliptic of the Sun, which is represented in orange. Then we can also draw the earth coordinates in the same celestial sphere. So imagine to extend the equator of the earth to the space and this we have the so called celestial equator, highlighted in blue. What you find out is that the earth and the Sun ecliptics are slanted with each other with the so called axial tilt. This angle measures around 23 degrees, but it is not constant, because it has a very little variation that depends mostly on the time. Very important is the vernal equinox that is the principal direction of the coordinate system, indicated by the sign of Aries. These obvious from the picture, the Aries lies in both the ecliptic and the equatorial planes making it a reference position. As for the geographic coordinate system, here we have two angular coordinates called the ecliptic longitude and the ecliptic latitude. So to summarize, today we learned how to locate an observer on the Earth's crust using the latitude and longitude of the geographical coordinate system. Then we located the observer in the middle of the celestial coordinate system and defined the azimuth and altitude in order to describe objects in the sky, such as our Sun. Indeed the next step, as we will see in the following lecture, is to combine these two coordinate systems together to calculate the position of the Sun in the sky. .
Load more

Recommended publications
  • Planet Positions: 1 Planet Positions
    Planet Positions: 1 Planet Positions As the planets orbit the Sun, they move around the celestial sphere, staying close to the plane of the ecliptic. As seen from the Earth, the angle between the Sun and a planet -- called the elongation -- constantly changes. We can identify a few special configurations of the planets -- those positions where the elongation is particularly noteworthy. The inferior planets -- those which orbit closer INFERIOR PLANETS to the Sun than Earth does -- have configurations as shown: SC At both superior conjunction (SC) and inferior conjunction (IC), the planet is in line with the Earth and Sun and has an elongation of 0°. At greatest elongation, the planet reaches its IC maximum separation from the Sun, a value GEE GWE dependent on the size of the planet's orbit. At greatest eastern elongation (GEE), the planet lies east of the Sun and trails it across the sky, while at greatest western elongation (GWE), the planet lies west of the Sun, leading it across the sky. Best viewing for inferior planets is generally at greatest elongation, when the planet is as far from SUPERIOR PLANETS the Sun as it can get and thus in the darkest sky possible. C The superior planets -- those orbiting outside of Earth's orbit -- have configurations as shown: A planet at conjunction (C) is lined up with the Sun and has an elongation of 0°, while a planet at opposition (O) lies in the opposite direction from the Sun, at an elongation of 180°. EQ WQ Planets at quadrature have elongations of 90°.
    [Show full text]
  • Sun Tool Options
    Sun Study Tools Sophomore Architecture Studio: Lighting Lecture 1: • Introduction to Daylight (part 1) • Survey of the Color Spectrum • Making Light • Controlling Light Lecture 2: • Daylight (part 2) • Design Tools to study Solar Design • Architectural Applications Lecture 3: • Light in Architecture • Lighting Design Strategies Sun Tool Options 1. Paper and Pencil 2. Build a Model 3. Use a Computer The first step to any of these options is to define…. Where is the site? 1 2 Sun Study Tools North Latitude and Longitude South Longitude Latitude Longitude Sun Study Tools North America Latitude 3 United States e ud tit La Sun Study Tools New York 72w 44n 42n Site Location The site location is specified by a latitude l and a longitude L. Latitudes and longitudes may be found in any standard atlas or almanac. Chart shows the latitudes and longitudes of some North American cities. Conventions used in expressing latitudes are: Positive = northern hemisphere Negative = southern hemisphere Conventions used in expressing longitudes are: Positive = west of prime meridian (Greenwich, United Kingdom) Latitude and Longitude of Some North American Cities Negative = east of prime meridian 4 Sun Study Tools Solar Path Suns Position The position of the sun is specified by the solar altitude and solar azimuth and is a function of site latitude, solar time, and solar declination. 5 Sun Study Tools Suns Position The rotation of the earth about its axis, as well as its revolution about the sun, produces an apparent motion of the sun with respect to any point on the altitude earth's surface. The position of the sun with respect to such a point is expressed in terms of two angles: azimuth The sun's position in terms of solar altitude (a ) and azimuth (a ) solar azimuth, which is the t s with respect to the cardinal points of the compass.
    [Show full text]
  • Equatorial and Cartesian Coordinates • Consider the Unit Sphere (“Unit”: I.E
    Coordinate Transforms Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. declination the distance from the center of the (δ) sphere to its surface is r = 1) • Then the equatorial coordinates Equator can be transformed into Cartesian coordinates: right ascension (α) – x = cos(α) cos(δ) – y = sin(α) cos(δ) z x – z = sin(δ) y • It can be much easier to use Cartesian coordinates for some manipulations of geometry in the sky Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. the distance y x = Rcosα from the center of the y = Rsinα α R sphere to its surface is r = 1) x Right • Then the equatorial Ascension (α) coordinates can be transformed into Cartesian coordinates: declination (δ) – x = cos(α)cos(δ) z r = 1 – y = sin(α)cos(δ) δ R = rcosδ R – z = sin(δ) z = rsinδ Precession • Because the Earth is not a perfect sphere, it wobbles as it spins around its axis • This effect is known as precession • The equatorial coordinate system relies on the idea that the Earth rotates such that only Right Ascension, and not declination, is a time-dependent coordinate The effects of Precession • Currently, the star Polaris is the North Star (it lies roughly above the Earth’s North Pole at δ = 90oN) • But, over the course of about 26,000 years a variety of different points in the sky will truly be at δ = 90oN • The declination coordinate is time-dependent albeit on very long timescales • A precise astronomical coordinate system must account for this effect Equatorial coordinates and equinoxes • To account
    [Show full text]
  • Lecture 6: Where Is the Sun?
    4.430 Daylighting Massachusetts Institute of Technology Christoph Reinhart Department of Architecture 4.430 Where is the sun? Building Technology Program Goals for This Week Where is the sun? Designing Static Shading Systems MIT 4.430 Daylighting, Instructor C Reinhart 1 1 MISC Meeting on group projects Reduce HDR image size via pfilt –x 800 –y 550 filne_name_large.pic > filename_small>.pic Note: pfilt is a Radiance program. You can find further info on pfilt by googeling: “pfilt Radiance” MIT 4.430 Daylighting, Instructor C Reinhart 2 2 Daylight Factor Hand Calculation Mean Daylight Factor according to Lynes Reinhart & LoVerso, Lighting Research & Technology (2010) Move into the building, design the facade openings, room dimensions and depth of the daylit area. Determine the required glazing area using the Lynes formula. A glazing = required glazing area A total = overall interior surface area (not floor area!) R mean = area-weighted mean surface reflectance vis = visual transmittance of glazing units = sun angle 3 ‘Validation’ of Daylight Factor Formula Reinhart & LoVerso, Lighting Research & Technology (2010) Graph of mean daylighting factor according to Lynes formula v. Radiance removed due to copyright restrictions. Source: Figure 5 in Reinhart, C. F., and V. R. M. LoVerso. "A Rules of Thumb Based Design Sequence for Diffuse Daylight." Lighting Research and Technology 42, no. 1 (2010): 7-32. Comparison to Radiance simulations for 2304 spaces. Quality control for simulations. LEED 2.2 Glazing Factor Formula Graph of mean daylighting factor according to LEED 2.2 v. Radiance removed due to copyright restrictions. Source: Figure 11 in Reinhart, C. F., and V.
    [Show full text]
  • Using the SFA Star Charts and Understanding the Equatorial Coordinate System
    Using the SFA Star Charts and Understanding the Equatorial Coordinate System SFA Star Charts created by Dan Bruton of Stephen F. Austin State University Notes written by Don Carona of Texas A&M University Last Updated: August 17, 2020 The SFA Star Charts are four separate charts. Chart 1 is for the north celestial region and chart 4 is for the south celestial region. These notes refer to the equatorial charts, which are charts 2 & 3 combined to form one long chart. The star charts are based on the Equatorial Coordinate System, which consists of right ascension (RA), declination (DEC) and hour angle (HA). From the northern hemisphere, the equatorial charts can be used when facing south, east or west. At the bottom of the chart, you’ll notice a series of twenty-four numbers followed by the letter “h”, representing “hours”. These hour marks are right ascension (RA), which is the equivalent of celestial longitude. The same point on the 360 degree celestial sphere passes overhead every 24 hours, making each hour of right ascension equal to 1/24th of a circle, or 15 degrees. Each degree of sky, therefore, moves past a stationary point in four minutes. Each hour of right ascension moves past a stationary point in one hour. Every tick mark between the hour marks on the equatorial charts is equal to 5 minutes. Right ascension is noted in ( h ) hours, ( m ) minutes, and ( s ) seconds. The bright star, Antares, in the constellation Scorpius. is located at RA 16h 29m 30s. At the left and right edges of the chart, you will find numbers marked in degrees (°) and being either positive (+) or negative(-).
    [Show full text]
  • NOAA Technical Memorandum ERL ARL-94
    NOAA Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERIS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOAA 'Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERlS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOTICE The Environmental Research Laboratories do not approve, recommend, or endorse any proprietary product or proprietary material mentioned in this publication. No reference shall be made to the Environmental Research Laboratories or to this publication furnished by the Environmental Research Laboratories in any advertising or sales promotion which would indicate or imply that the Environmental Research Laboratories approve, recommend, or endorse any proprietary product or proprietary material mentioned herein, or which has as its purpose an intent to cause directly or indirectly the advertised product to be used or purchased because of this Environmental Research Laboratories publication. Abstract A system of FORTRAN language computer programs is presented which have the ability to locate the sun at arbitrary times. On demand, the programs will return the distance and direction to the sun, either as seen by an observer at an arbitrary location on the Earth, or in a stan- dard astronomic coordinate system. For one century before or after the year 1960, the program is expected to have an accuracy of 30 seconds 5 of arc (2 seconds of time) in angular position, and 7 10 A.U. in distance. A non-standard algorithm is used which minimizes the number of trigonometric evaluations involved in the computations. 1 The NOAA Solar Ephemeris Program Albion D. Taylor National Oceanic and Atmospheric Administration Air Resources Laboratories Silver Spring, MD January 1981 Contents 1 Introduction 3 2 Use of the Solar Ephemeris Subroutines 3 3 Astronomical Terminology and Coordinate Systems 5 4 Computation Methods for the NOAA Solar Ephemeris 11 5 References 16 A Program Listings 17 A.1 SOLEFM .
    [Show full text]
  • Solar Time, Angles, and Irradiance Calculator
    Solar Time, Angles, and Irradiance Calculator: User Manual Circular 674 Thomas Jenkins and Gabriel Bolivar-Mendoza1 Cooperative Extension Service • Engineering New Mexico Resource Network College of Agricultural, Consumer and Environmental Sciences • College of Engineering OVERVIEW in their allowable values. For example, the “Hr” cell in This user manual and accompanying Microsoft Excel the Time sheet (Figure 3) will only accept entries be- spreadsheet (http://aces.nmsu.edu/pubs/_circulars/ tween 0 and 23. If you enter a value outside this range, CR674/CR674.xlsm) are intended to be used as a guide an error message will be displayed and you must re-enter for calculating solar time, angles, and irradiation, and to a valid value in this cell before continuing. aid in feasibility and implementation decisions for solar Some cells may also have a “drop-down” menu associ- energy projects. The spreadsheet is designed to allow ated with them. A drop-down menu will list the cell’s you to enter a variety of values such as system location valid entries and allow you to just click on a menu entry. (i.e., latitude and longitude angles), date, local time, A cell’s menu can be accessed by placing the cursor on panel tilt angle, etc. By entering different values, you the cell and clicking on it. A note and a drop-down can investigate a variety of scenarios before making final menu tab are displayed to the right of the cell. When implementation decisions. this tab is clicked, the drop-down menu displays the There are NO expressed or implied guarantees with valid entries for this cell.
    [Show full text]
  • RISING and SETTING of the SUN the Position at Which the Sun Appears Above the Horizon Changes a Little Every Day
    TEACHER RESOURCE STARDOME OBSERVATORY & PLANETARIUM FACTS, RESOURCES AND ACTIVITIES ON... RISING AND SETTING OF THE SUN The position at which the Sun appears above the horizon changes a little every day. In winter, the Sun rises north of east (and sets north TO NORTH of west). The day it rises in its northern-most position EAST is the winter solstice. TO SOUTH In summer, the Sun rises south of east (and sets south of west). The day it rises in its southern-most position is the summer solstice. The two days of the year the Sun is directly between these northern and southern points are the equinoxes—one in March and one in September (autumn and spring). WINTER SOLSTICE EQUINOXES The calendars of some cultures, including Māori, are SUMMER partly based on this cycle of annual ‘Sun movement’. SOLSTICE The Māori year starts at the time of the winter solstice and some iwi say the stars of Matariki appear in the sky to call for the Sun to return to the south after it has been in the north. RISING POSITION OF THE SUN THROUGHOUT THE YEAR SETTING POSITION OF THE SUN THROUGHOUT THE YEAR Sunrise position Sunset position Sunrise azimuth relative to due east Sunset azimuth (a compass bearing relative to due west Date (a negative number is left/ Date (a compass bearing (a negative number is left/ measured clockwise from north of east; a positive measured clockwise from due north; E is 90°) south of west; a positive number is right/south of due north; W is 270°) number is right/north of east; E is 0) west; W is 0) 22 January 116° +26 22 January 244° -26
    [Show full text]
  • Solar Geometry
    Chapter 6: SOLAR GEOMETRY Full credit for this chapter to Prof. Leonard Bachman of the University of Houston “SOLAR GEOMETRY AS A DETERMINING FACTOR OF HEAT GAIN, SHADING AND THE POTENTIAL OF DAYLIGHT PENETRATION...” "Declination" refers to the tilt of the earth's axis measured from perpendicular to the sun's rays. This angle is 0 degrees at the spring and autumn equinox. Maximum declination is reached at the summer (23.45 deg.) and winter (-23.45 deg. ) solstice. "Air Mass" is the effective thickness of the atmospheric path of sunlight relative to the shortest possible path. An air mass of 2.0, for example, is twice as long (thick) as the direct path. When the sun travels through higher air masses , less solar energy reaches the surface of the earth. This is a primary cause of seasonal weather. Beyond an air mass of 5.0, little sun will be received. Air Mass = 1 / sin(solar altitude angle) "Equation of Time” (EOT) is a variable that adjusts for the ellipicity of the earth's orbit and non-uniform solar time. "Solar Noon” occurs when the sun is at its mid point and highest angle of its daily path across the sky. The position of the sun relative to the horizon at this time is called "True South'. "Magnetic Deviation” accounts for the difference between magnetic north and true north. This varies with location. "Solar Time” is the measure of time which a sundial would read at any particular location. This is different from "clock' or "standard' time due mostly to conventions of time zones and Daylight Savings.
    [Show full text]
  • Solar Geometry
    Solar Geometry — A Look into the Path of the Sun When designing any type of system that relies on solar radiation, it is important to take into consideration the seasonal and hourly changes in position of the sun. This has a direct influence on the incident angle of sunlight, so it is valuable to incorporate a system that can adjust to the position of the sun. It is also helpful to consider the position of the sun when deciding the placement of a structure’s windows. The position of the sun can be described by two different angles. The first angle is the solar azimuth (denoted by α, alpha), which is defined as the clockwise angle between the sun and the cardinal direction of true north. It is measured up to the horizontal projection of the sun’s position onto the Earth’s surface (see Figure 1). The second angle is the solar altitude or elevation (denoted by Φ, phi), indicating the angle of the sun’s position from the horizontal (see Figure 1). The angle of incidence is not a measure of the sun’s position, but rather a measure of the amount of radiation incident on a vertical surface. The angle of incidence is related to the solar altitude as follows: Together, the two angles provide useful information about the orientation of incoming sunlight on an object or structure. Knowing this, solar collectors and other devices should be installed so they are within 20° of either side of perpendicular to the sun. By incorporating a system that adjusts to the incident angle of the sun, we can further control the angle incident on the surface of the collector.
    [Show full text]
  • Which Way Is North?
    Which Way is North? GRADE LEVEL 3rd -5th; Content Standards for 3rd and 5th SUBJECTS Earth & Space Science, Interpreting Data DURATION Preparation: 5 minutes Activity: 40 minutes (total over one day) SETTING Classroom Objectives In this activity students will: 1. Observe how the position of the sun in the sky changes during the course of the day 2. Discover the cardinal directions by tracking the motion of the sun Materials One large sheet of white paper (such as easel paper) One pencil width wooden dowel or similar, 12-15 inches long A ball of clay Permanent marker Weights or adhesive tape to hold the paper in position Scientific Terms for Students axis: the center around which something rotates cardinal direction: one of the four principal compass points: north, south, east and west equinox: the two times in the year (spring and fall) when day and night are of equal length gnomon: a vertical shaft or column used for determining the altitude of the sun by measuring the length of its shadow cast at noon; also, the part of a sundial that casts the shadow local noon: the time when the sun crosses an imaginary north-south circle in the sky north celestial pole: The point in the sky aligned with the earth’s axis, about which all the stars seen from the northern hemisphere rotate north star: The closest star in the sky to the north celestial pole (currently Polaris) rotation: a single complete turn solstice: the times in the year when the sun reaches its highest (summer) or lowest (winter) altitude in the sky above the horizon at local noon Background for Educators Teacher and Youth Education, 2015 1 Which Way is North? Many people know how to determine the cardinal directions by finding Polaris, the North Star, in the night sky.
    [Show full text]
  • Terrestrial Position from Celestial Observations
    The linked image cannot be displayed. The file may have been moved, renamed, or deleted. Verify that the link points to the correct file and location. .NC STATE UNIVERSITY . PY 124: Terrestrial Position from Celestial Observations Robert A. Egler Senior Lecturer in Astronomy Member Royal Institute of Navigation The linked image cannot be displayed. The file may have been moved, renamed, or deleted. Verify that the link points to the correct file and location. Determining Your Position The determination of your position on the Earth by measuring the position of celestial objects is known as celestial navigation . The topic of celestial navigation is very large, and we will only scratch the surface here. Special note: Actual, accurate, celestial navigation requires attention to many more details than presented here. In real life, mistakes in navigation may result in your death or the destruction of your vessel . This page discusses the very fundamentals from an astronomy viewpoint, but if you are actually going to rely on navigation in real life, sailing perhaps, you should take navigation courses, to include piloting, GPS and radio navigation, and celestial navigation. Some excellent navigation courses (but not celestial) are available at modest charge taught by the US Coast Guard Auxiliary (go to www.cgaux.org for more information.) Longitude At any moment there is one spot on the Earth where the sun is directly overhead. This spot, called the subsolar point , moves around the Earth in one solar day, 24 hours, thus the subsolar point moves 15 o of longitude for each hour of the day (360 o / 24 h).
    [Show full text]