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ESCI-61
Introduction to Photovoltaic Technology
Sun Earth Relationships
Ridha Hamidi, Ph.D.
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Spring
(sun aims directly at equator)
Fall
(sun aims directly at equator) Summer
(northern hemisphere tilts toward sun)
Solar radiation
23.5 °°°° Winter
(northern hemisphere tilts away from sun)
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Earth’s Orbit
• Ecliptic Plane: the plane of Earth’s orbit around the Sun
– Perihelion: point of the Earth’s orbit when it is closest to the Sun (around Jan. 3rd) – Aphelion: point in Earth’s orbit when it is farthest from the Sun (around July 4th)
• Equatorial Plane: plane containing Earth’s equator and extending outward into space
– Earth’s axis is tilted by 23.5°(constant angle bet ween ecliptic & equatorial planes)
– This causes the seasonal variations in Earth’s climate
• Solar Declination: angle between the equatorial plane and the line joining the centers of the Sun & Earth
– Changes continuously as Earth orbits the Sun, ranging from –23.5°to +23.5°
– Apparent change as viewed from the Sun
– Visit http://www.windows.ucar.edu/ for more info
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Earth’s Orbit
• Solstices: Earth’s orbit position when solar declination is at minimum or maximum
• At any location in the Northern hemisphere, the Sun is 47°lower in the sky at solar noon on the winter solstice than at solar noon on the summer solstice
• The rate of change in declination is small, so daily change in Sun path is at minimum
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Earth’s Orbit
• Summer solstice: maximum solar declination (+23.5°), around June 21
– Northern hemisphere is at its maximum tilt toward the Sun – Days are longer than nights in the Northern hemisphere – All points south the Antarctic circle are in total darkness
– The Sun is at Zenith at solar noon at locations at 23.5°N latitude, aka Tropic of Cancer
• Winter solstice: minimum solar declination (-23.5°), around December 21
– Northern hemisphere is at its maximum tilt away from the Sun – Days are shorter than nights in the Northern hemisphere
– All points north the Arctic circle are in total darkness
– The Sun is at Zenith at solar noon at locations at 23.5°S latitude, aka Tropic of Capricorn
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Earth’s Orbit
• Equinoxes: Earth’s orbital position when solar declination is zero
– Spring Equinox: around March 21 – Fall Equinox: around September 23
• Every location on Earth has equal length days &
nights
• The Sun is at zenith at solar noon on the equator and rises and sets due East and due West,
resp., everywhere on Earth
• The rate of change in declination is large, so daily change in Sun path is at maximum
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Solar Time
• Meridian: a plane formed by a due North-South
longitude line through a location on Earth and projected out into space
• Local Meridian: meridian at the observer’s exact location
• Solar Time: timescale based on the apparent motion of the Sun crossing a local meridian
• Solar noon: the moment when the Sun crosses a local meridian and is at its highest position of the day
• Solar Day: the interval of time between sun crossings of local meridian, which is approximately 24h
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Standard Time
• Standard Meridian: a meridian located at a multiple of 15°East or West of zero longitude (Greenwich,
England), aka Prime Meridian
• Standard Time: a timescale based on the apparent motion of the Sun crossing standard meridians
• The Earth rotates 360°in approximately 24h
– Each 15°of longitude is equal to one hour of solar time – Each 1°of longitude is equal to 4mn of solar time
– Standard time zones are at one hour multiples ahead of or behind the time at the Prime Meridian, aka Greenwich Mean Time (GMT) or Universal Time (UT)
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Standard Time vs Solar Time
• Longitude Time Correction
tλ= (λlocal– λs) x 4
tλ : longitude time correction (mn) λlocal: local longitude (deg)
λs : longitude of standard meridian (deg)
• Equation of Time Correction
– Caused by eccentricities in Earth’s rotation during its orbit around the Sun – difference between actual solar noon and theoretical solar noon based on
uniform Earth motion
ts= t0 – tE + tλ
ts: Local Standard Time t0 : Solar Time
tE : Equation of Time Value tλ: Longitude Time Correction
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Solar Time Calculators
http://www.go2atp.com/resources/http_docs/pvs/index.htm
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Calculating Solar Time
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Sun Position
• Two angles are used to define the Sun’s position in the sky
– Solar Altitude: vertical angle between zero and 90°
– Solar Azimuth: horizontal angle between a
reference direction (typically due South in the Northern hemisphere) and the Sun
• varies between -180°and +180°
• Sun position to the East of due South is
represented as a positive angle, and to the West as a negative angle
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Sun Path Charts
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Sun Path Charts
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Sun Path Charts
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Array Orientation
• Array orientation is defined by two angles:
• Array Tilt: vertical angle between horizontal and the array surface
• Array Azimuth: horizontal angle between a reference direction (typically due South in the
Northern hemisphere) and the direction an array surface faces
• Incidence Angle: angle between the direction of direct radiation and a line exactly perpendicular to the array surface
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Array Tilt Angle
• Smaller tilt angles can be required by applications with high energy loads in the summer, like air-
conditioning
– Average declination during the summer is +15°, so the optimal tilt angle for the summer is (latitude - 15°)
• Larger tilt angles can be required by applications with high energy loads in the winter, like artificial lighting
– Average declination during the winter is -15°, so the optimal tilt angle for the winter is (latitude + 15°)
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Solar Radiation Data Manual
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Array Tilt Angle
• The geometry of the solar window is such that the Sun is in the sky for longer in the summer than in the winter
• Climate and atmospheric factors result in a slightly lower optimal tilt angle to maximize the annual energy production
– Summer skies are clearer than winter skies – Less air mass in the summer
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Optimal Tilt Angle
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Optimal Tilt Angle
http://www.solmetric.com/annualinsolation-us.html
