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ESCI-61
Introduction to Photovoltaic Technology
Sun Earth Relationships
Ridha Hamidi, Ph.D.
Spring
(sun aims directly
at equator)
Winter
(northern hemisphere 23.5 °
tilts away from sun)
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Solar
radiation
Summer
(northern hemisphere
tilts toward sun)
Fall
(sun aims directly at equator)
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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
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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
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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 : Local Standard Time
t0 : Solar Time
tE : Equation of Time Value
tλ : Longitude Time Correction
ts = t0 – tE + tλ
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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 airconditioning
– 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
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