Power Generation from Renewable Energy Sources Fall 2013 Instructor: Xiaodong Chu ： Office Tel.:

Flashbacks of Last Lecture The probability that the wind is less than some specified wind speed V is given by which is called the cumulative distribution function The cumulative distribution function for Weibull statistics and for Rayleigh statistics

Flashbacks of Last Lecture The probability that the wind is greater than a certain value For Weibull statistics For Rayleigh statistics

Flashbacks of Last Lecture One of the most important characteristics of any electrical power system is its rated power; that is, how many kW it can produce on a continuous, full-power basis The capacity factor CF is a convenient, dimensionless quantity between 0 and 1 that connects rated power to energy delivered Estimate CF and use it to estimate energy delivered

The Solar Resource Before we can talk about solar power, we need to talk about the sun – Need to know how much sunlight is available – Can predict where the sun is at any time Insolation : incident solar radiation Want to determine the average daily insolation at a site Want to be able to choose effective locations and panel tilts of solar panels

The sun – 1.4 million km in diameter – 3.8 x MW of radiated electromagnetic energy Black bodies – Both a perfect emitter and a perfect absorber – Perfect emitter – radiates more energy per unit of surface area than a real object of the same temperature – Perfect absorber – absorbs all radiation, none is reflected The Solar Resource – The Solar Spectrum

Plank’s law – wavelengths emitted by a blackbody depend on temperature λ = wavelength (μm) E λ = emissive power per unit area of black body (W/m 2 - μm ) T = absolute temperature (K)

The Solar Resource – The Solar Spectrum Visible light has a wavelength of between 0.4 and 0.7 μm, with ultraviolet values immediately shorter, and infrared immediately longer

The Solar Resource – The Solar Spectrum The earth as a black body Area under curve is the total radiant power emitted

The Solar Resource – The Solar Spectrum Total radiant power emitted is given by the Stefan –Boltzman law of radiation E = total blackbody emission rate (W) σ = Stefan-Boltzmann constant = 5.67x10 -8 W/m 2 -K 4 T = absolute temperature (K) A = surface area of blackbody (m 2 )

The Solar Resource – The Solar Spectrum The wavelength at which the emissive power per unit area reaches its maximum point T = absolute temperature (K) λ = wavelength (μm) λ max =0.5 μm for the sun, T = 5800 K λ max = 10.1 μm for the earth (as a blackbody), T = 288 K

The Solar Resource – The Solar Spectrum Masters, Figure 7.2

Sun photosphere “AM” means “air mass” Intensity Extraterestrial sunlight (AM0) Sunlight at sea level at 40°N Latitude at noon (AM1.5) The Solar Resource – The Solar Spectrum

Air mass ratio of 1 (“AM1”) means sun is directly overhead AM0 means no atmosphere AM1.5 is assumed average at the earth’s surface As sunlight passes through the atmosphere, less energy arrives at the earth’s surface

The Solar Resource – The Solar Spectrum m increases as the sun appears lower in the sky Notice there is a large loss towards the end for higher m, which is why the sun appears reddish at sun rise and sun set

The Solar Resource – The Earth’s Orbit For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging

The Earth’s orbit is not circularecliptic

The Solar Resource – Altitude Angle of the Sun at Solar Noon Solar declination δ – the angle formed between the plane of the equator and the line from the center of the sun to the center of the earth δ varies between +/ ˚ Assuming a sinusoidal relationship, a 365 day year, and n=81 is the spring equinox, the approximation of δ for any day n can be found from

The Solar Resource – Altitude Angle of the Sun at Solar Noon

Predict where the sun will be in the sky at any time Pick the best tilt angles for photovoltaic (PV) panels Solar declination

The Solar Resource – Altitude Angle of the Sun at Solar Noon Solar noon – sun is directly over the local line of longitude Rule for the Northern Hemisphere - a south facing collector tilted at an angle equal to the local latitude During solar noon, the sun’s rays are perpendicular to the collector face

The Solar Resource – Altitude Angle of the Sun at Solar Noon Altitude angle at solar noon β N – angle between the sun and the local horizon Zenith – perpendicular axis at a site