ME 430
Fundamentals of Solar Energy Conversion
for heating and Cooling Applications
Lecture (1 of 2)
Solar Energy Resource and Availability
C. Cruickshank and S. Harrison
2008
The Solar Constant
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
1
Variation in Extraterrestrial Solar Radiation
• Due to variation in the radiation emitted by the sun (less than
1% variation)
• Due to variation of the earth-sun distance (up to 3% variation)
For engineering purposes, in view of uncertainties and
variability of atmospheric transmission, the energy emitted by
the sun can be considered to be fixed.
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
Orientation and Tilt Angle
Sun-earth geometric relationship: motion of the earth about the sun
From “Solar Energy Engineering”, Jui Sheng Hsieh
2
Orientation and Tilt Angle
Sun-earth geometric relationship: location of artic and antarctic circles
and the tropics
From “Solar Energy Engineering”, Jui Sheng Hsieh
Solar Energy Availability in Canada
Annual Mean Daily Global Solar Radiation and Variability of Solar
Radiation Incident on a Horizontal Surface
Source: http://www.nrcan.ca
3
Solar Energy Availability in Canada
Annual Mean Daily Global Radiation, Incident on Inclined Surfaces of
90o and 60o with a South Orientation
Source: http://www.nrcan.ca
Solar Energy Availability
The sun’s path at different times of the year at central European latitude (London, Berlin)
The amount of solar energy available on the earth depends on the
geographical latitude and the time of day and year at a given location.
Because of the inclination of the earth’s axis, the sun reaches high solar
altitudes in the summer than in the winter.
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
4
Solar Energy Availability
From “Solar Energy Engineering”, Jui Sheng Hsieh
Solar Energy Availability
Daily courses and daily totals for irradiation in London
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
5
Solar Time
Solar time ≠ Local Clock Time
Solar time is used in all of the sun-angle relationships. It is
based on the apparent angular motion of the sun across the
sky with solar noon the time that the sun crosses the
meridian of the observer.
Apply 2 corrections:
-difference in longitude between observer’s meridian and
the meridian on which local standard time is based on
(4 mins to transverse 1o)
- equation of time – account for perturbations in the earth’s
rotation which affect the time the sun crosses the
observer’s meridian
Solar Time
Solar time is calculated from:
Solar Time – LST = 4(LSM - LON) + ET
where:
• LST is the local standard time
• LSM is the local standard meridian
• LON is the local longitude
• ET is the equation of time given by:
ET= 229.2*(0.000075 + 0.001868 cos(B) – 0.032077 sin(B)
- 0.014615 cos(2B) – 0.04089 sin(2B))
Where B = (n-1)*(360/365), n = day of the year
All equations use degrees not radians!
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Solar Time Example
At Madison, WI, what is the solar time corresponding to 10:30 AM
central time on February 3?
Solar Time – LST = 4(LSM - LON) + ET
In this case:
• LST is the local standard time (10:30)
• LSM is the local standard meridian (90o W) *
• LON is the local longitude (89.4o W) *
• ET is the equation of time given by:
ET= 229.2*(0.000075 + 0.001868 cos(B) – 0.032077 sin(B)
- 0.014615 cos(2B) – 0.04089 sin(2B))
Where B = (n-1)*(360/365), n = 34 therefore B = 32.55
Thus ET = -13.5 minutes
Solar Time – 10:30 = 4(90 – 89.4) + (-13.5) = -11 minutes
Solar Time = 10:19
* This information would be provided.
Solar Radiation Definitions
GG= Gdir + Gdif + Gref
Global solar irradiance
and its components
The radiation from the sun that meets the earth without any change in
direction is called direct or beam radiation, Gdir.
The radiation from the sun after its direction has been changed by
scattering in the atmosphere is called diffuse radiation, Gdif.
The radiation from the sun after it is reflected on the ground is called the
ground reflected radiation, Gref.
The sum of the beam, diffuse and reflected solar radiation on a surface
is called the global solar irradiance, GG.
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
7
Solar Radiation
Sun’s level at
midday within the
course of a year in
London and Berlin
(latitude 52oN)
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
The air mass factor (AM) is a measure of the length of the
path of the sunlight through the earth’s atmosphere in terms
of one atmosphere thickness.
Solar Spectrum
Solar irradiance outside atmosphere
Direct solar irradiance at sea level
Sun spectrum AM 0 in space and AM 1.5 on the earth with
a sun elevation of 41.8o
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
8
Solar Radiation
Global solar irradiance and its components with different
sky conditions
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
Solar Radiation
The average annual global solar irradiance is
significantly higher at lower than at higher latitudes.
Monthly solar irradiation (kWh/m2 per day on a horizontal
surface) around the world
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
9
Solar Radiation
Monthly sum of global solar irradiance (diffuse and
direct) for Miami, USA.
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
Orientation and Tilt Angle
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
10
Orientation and Tilt Angle
From “Solar Energy Engineering”, Jui Sheng Hsieh
Orientation and Tilt Angle
From “Solar Energy Engineering”, Jui Sheng Hsieh
11
Orientation and Tilt Angle
The declination angle:
284 + n ⎞
⎛
δ = 23.45sin ⎜ 360
⎟
365 ⎠
⎝
Angles are to be
specified in degrees not
radians!!
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
Orientation and Tilt Angle
The intensity of the beam
radiation on a tilted surface or
horizontal surface, Gs, is
equivalent to the direct normal
beam radiation, GDN, multiplied
by the cosine of the angle of
incidence of beam radiation on
the surface:
Gs = GDN cos θ
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
12
Orientation and Tilt Angle
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
Direction of Beam Radiation
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
13
Effects of Receiving Surface Orientation
From “Solar Engineering of Thermal Processes”, Duffie & Beckman
Sun Chart
Solar altitude diagram with example silhouettes of
objects (for a latitude of about 50o)
From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK
14
Sun Chart
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