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ME 430Fundamentals of Solar Energy Conversion

for heating and Cooling Applications

Lecture (1 of 2) Solar Energy Resource and Availability

C. Cruickshank and S. Harrison2008

The Solar Constant

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

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Variation in Extraterrestrial Solar Radiation

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

• 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.

Orientation and Tilt Angle

Sun-earth geometric relationship: motion of the earth about the sun

From “Solar Energy Engineering”, Jui Sheng Hsieh

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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

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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 thegeographical 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

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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

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Solar TimeSolar 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 TimeSolar 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 ExampleAt Madison, WI, what is the solar time corresponding to 10:30 AMcentral time on February 3?

Solar Time – LST = 4(LSM - LON) + ETIn 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 minutesSolar Time = 10:19

* This information would be provided.

Solar Radiation Definitions

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.

GG= Gdir + Gdif + Gref

From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK

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Solar Radiation

Sun’s level at midday within the course of a year in London and Berlin (latitude 52oN)

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.

From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK

Solar Spectrum

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

Solar irradiance outside atmosphere

Direct solar irradiance at sea level

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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

Monthly solar irradiation (kWh/m2 per day on a horizontal surface) around the world

The average annual global solar irradiance is significantly higher at lower than at higher latitudes.

From “Planning and Installing Solar Thermal Systems”, James & James/Earthscan, London, UK

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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

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Orientation and Tilt Angle

From “Solar Energy Engineering”, Jui Sheng Hsieh

Orientation and Tilt Angle

From “Solar Energy Engineering”, Jui Sheng Hsieh

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Orientation and Tilt Angle

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

The declination angle:

Angles are to be specified in degrees not radians!!

28423.45sin 360365

nδ +⎛ ⎞= ⎜ ⎟⎝ ⎠

Orientation and Tilt Angle

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

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:

coss DNG G θ=

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Orientation and Tilt Angle

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

Direction of Beam Radiation

From “Solar Engineering of Thermal Processes”, Duffie & Beckman

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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

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Sun Chart