renewable energy course#04

Solar Power

Solstices

June solstice - North Pole is tilted 23.5o towards the Sun relative to the circle of illumination. All places above a latitude of 66.5oN are in 24 hours of sunlight, while locations below a latitude of 66.5oS are in darkness.

Equinoxes

Equinoxes – Earth’s axis is not tilted toward or away from the Sun and the circle of illumination cuts through the poles. Red circles are the Arctic Circle.

Equinoxes, Solstices, Aphelion, and Perihelion

Relationship of maximum Sun height to latitude for the equinox (left) and June solstice (right). The red values on the right of the globes are maximum solar altitudes at solar noon. During the equinox, the equator is the location on the Earth with a Sun angle of 90 degrees for solar noon

Solar Altitude

α = Sin-1[Sin δ Sin φ + Cos δ Cos ω Cos φ]

φ is latitude

Hour Angle

ω = 15 (ts – 12) (degrees)

ts is local solar time in hours

Declination Angleδ = Sin-1 [0.39795 Cos [0.98563 (N-173)]]

Hour Angle

Declination Angle (between the equatorial

plane and the sun-earth line)

Variation of Declination Angle

Solar Altitude Angle

Observer

Zenith Angle

Solar Spectrum and Solar Constant

1367 W/m2

Seasonal Variation of Extraterrestrial Radiation

Total Daily Extraterrestrial Solar Radiation on a Horizontal Surface

Ho,h = 86,400 Io [ωs Sin Φ Sin δ + Cos δ Cos Φ Sin ωs] / π (J/m2)

Io = Isc [1 + 0.34 cos {2πN / 365.25}] is the solar constant

Isc = 1367 Watt

ωs = cos–1[- tan(δ) tan(Φ)] is the hour angle of sunset in radians

-Ve before noon & +Ve after noon

Instantaneous Extraterrestrial Solar Radiation on a Horizontal Surface

Ioh = Io [cos δ cos Φ cos ω + sin δ sin Φ]

Photocell Response

Heliostat, Albuquerque

Designing & Fabrication of a 2-kW Parabolic Trough Solar Thermal Power Plant

Storage Requirement

Extraterrestrial Radiation on a Surface Normal to Sun

Annual cosine effect reduces solar radiation on a horizontal surface by 39% - equator, 52% - 40o latitude, 74% - 80o latitude.

Ground Level Radiation Attenuation Effect

Effect of Air Mass on Spectral Irradiance on the Ground

Air Mass = 1 for sea level normal Irradiance

Sun rise & Sun set > 30 air mass

Air mass

AM = 1/[cos θz + 0.50572 (96.07995 – θz) -1.6364]

θz = Zenith angle = 90o at sunset

Solar Radiation Attenuation Due to Air Mass

I = 1.1 x Ioh x 0.7(AM)**(0.678)

factor of 1.1 accommodates the 10% diffused radiation

Attenuation of Normal Solar Radiation Versus Azimuth Angle

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Azimuth Angle (degrees)

Air

Mas

s / S

ola

r R

adia

tio

n

Air Mass

Solar Radiation (25 W units)

Solar Radiation Measurement

Pyranometer

Normal Incidence Pyrheliometer

Global Solar Irradiance on a mostly Sunny day and a mostly Cloudy day

750 MW Imperial Valley Project of 250 kW Solar Dish Striling Engines

Linear Freznel