• Outline

– Properties of radiation: Summary of equations, terms, concepts – Solar Spectrum – Terrestrial Solar Radiation: Effects of atmosphere, angular dependence of radiation, variation of solar radiation – Calculation of Solar Radiation: • Estimate of intensity of solar radiation • Angular Dependence – Solar Noon calculations – Time-based calculations – Solar Radiation Data Sets Caution: Watch your units!!! Make sure you pay attention to radians, degrees. Also pay attention to details - which hemisphere, difference between solar noon and local time, etc.

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Solar Radiation

• Goals

– Calculate power density, photon flux, photon energy, photon wavelength & relationships between them. – Calculate properties of arbitrary light source given its spectral irradiance – Calculate properties of black body radiation: Max temperature, total power. – Convert local time to solar time – Determine angles of incident sunlight, both at solar noon and as a function of time. – Determine light normal to a surface, at solar noon and at an arbitrary time

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Properties of Radiation

Summary of equations & concepts: • Wave/energy relationship: Electromagnetic Spectrum

• •

Common units of energy: electron-V (eV)

1 eV = 1.602x10-19 J

Power density (H, W/m²) and monochromatic photon flux (Φ, photons/sec·m²): – Power density (in W/m²) is photon flux (# photons/m²·sec) multiplied by energy per photon.

hc 1.24 ⎛W ⎞ H⎜ 2 ⎟ = Φ × ( J ) = qΦ λ λ (µm ) ⎝m ⎠

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Spectral Irradiance

• • • Spectral irradiance, F, is standard way to specify the properties of a light source Gives the power density at a particular wavelength. W 1 Units are m ² µm . The W/m² refers to the power density at a given wavelength, the µm refers to the wavelength at which the power density is specified. The spectral irradiance of xenon (green), halogen (blue) and mercury (red) light bulbs (left axis) are compared to the spectral irradiance from the sun (purple, which corresponds to the right axis).

⎛W ⎞ ∞ H⎜ ⎟ = ∫ F (λ )dλ m² ⎠ 0 ⎝ = ∑ Fi (λ )∆λ i =1 N

continuous spectral irradiance Discrete spectral irradiance, N is # points in F(λ)

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Black Body Radiation

• Blackbody: emits based on its temperature; absorbs all light incident on it. • Spectral Irradiance for black body: – Depend on temperature of blackbody source – ↑T -» ↑ power density, shifts spectrum more to blue

• Power density for blackbody:

H = σT 4

• Wavelength at peak spectral irradiance:

λp ( µm ) =

2900 T

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Solar Radiation

• Sun approximates a black body at ~6000K, radiating with a power density of Hsun ≈ 73MW/m². • Total power emitted is 4πR2sun , where the radius of the sun, Rsun = 6.96 ×105 km. • Power density at a distance D from sun if given by: 2 ⎛ W ⎞ Rsun H⎜ ⎟ = 2 × Hsun ⎝ m² ⎠ D

ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2008 C. Honsberg

Terrestrial Radiation

• Earth’s atmosphere has several impacts on radiation:

– Scattering of ~10% of light causes this light to hit earth’s surface at a wide range of angles and coming from anywhere in the sky. It is most effective for higher energy photons. • Direct light is the light from the sun which reaches the earth without scattering. • Diffuse light is scattered by the atmosphere. – Absorption in the atmosphere changes both the power density and the spectral distribution of terrestrial solar spectrum. • Ozone absorbs at high photon energies. • Water vapor, CO2, absorb in infra-red. – Clouds, other local variation in atmosphere introduce variability (both...