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Power Generation from Renewable Energy Sources Fall 2013 Instructor: Xiaodong Chu Email ： chuxd@sdu.edu.cn chuxd@sdu.edu.cn Office Tel.: 81696127

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Flashbacks of Last Lecture Classification of AC generators used in wind turbines – Synchronous generators Wound rotor synchronous generators (WRSG) Permanent magnet synchronous generators (PMSG) – Induction generators Squirrel cage induction generators (SCIG) Wound rotor induction generators (WRIG)

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Flashbacks of Last Lecture Wind turbine rotor speed should follow wind speed that is random in nature Limit the power in very high winds in order to avoid damage to the wind turbine For grid-connected turbines, the challenge is to accommodate variable rotor speed and fixed generator speed ControlType Pole-changing induction generators Discrete control Multiple gearboxesDiscrete control Variable-slip induction generators Limited continuous control Indirect grid connection systems Continuous control

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Flashbacks of Last Lecture Slip of an induction machine is the difference of rotating speed between magnetic field and rotor Example 6.8 on page 333 of the textbook

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Wind Power Systems – Average Power in the Wind How much energy might be expected from a wind turbine in various wind regimes? – We cannot determine the average power in the wind by substituting average wind speed – We need to find the average value of the cube of wind speed

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Wind Power Systems – Average Power in the Wind The average wind speed can be thought of as the total meters, kilometers, or miles of wind that have blown past the site, divided by the total time that it took to do so Describe the average values in probabilistic terms

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Wind Power Systems – Average Power in the Wind The average value of the cube of wind speed Describe the average values in probabilistic terms

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Wind Power Systems – Average Power in the Wind

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Probability density function (p.d.f.) of wind speed

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Wind Power Systems – Average Power in the Wind Probability that the wind is between two speeds The number of hours per year that the wind blows between any two wind speeds

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Wind Power Systems – Average Power in the Wind The average wind speed The average value of the cube of wind speed

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Wind Power Systems – Average Power in the Wind The Weibull probability density function is often used to characterize the statistics of wind speeds where k is called the shape parameter and c the scale parameter

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Wind Power Systems – Average Power in the Wind The shape parameter k of the Weibull probability density function changes the look of the p.d.f. When little detail is known about the wind regime at a site, it usually assumes k = 2, and the p.d.f. is the Rayleigh p.d.f.

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Wind Power Systems – Average Power in the Wind The impact of changing the scale parameter c for a Rayleigh p.d.f. is that larger values of c shift the curve toward higher wind speeds There is a direct relationship between the scaling parameter c and average wind speed

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Wind Power Systems – Average Power in the Wind From it can be derived and

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Wind Power Systems – Average Power in the Wind With average wind speed estimated by an anemometer and the assumption that the wind speed distribution follows Rayleigh statistics, the average value of the cube of wind speed can be derived as and With Rayleigh statistics, the average power in the wind

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Wind Power Systems – Average Power in the Wind Example 6.10 on page 346 of the textbook

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Wind Power Systems – Simple Estimates of Wind Turbine Energy How much of the energy in the wind can be captured and converted into electricity? A number of factors should be considered including the characteristics of the machine (rotor, gearbox, generator, controls), the terrain (topography, surface roughness, obstructions), and the wind regime (velocity, timing, predictability)

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Wind Power Systems – Simple Estimates of Wind Turbine Energy With the wind power density evaluated and the overall conversion efficiency into electricity obtained, we can estimate the annual energy delivered Simple estimates can be made based on wind classifications and overall efficiencies (about 30%) Example 6.11 on page 350 of the textbook

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Wind Power Systems – Simple Estimates of Wind Turbine Energy A large number of wind turbines will be installed when a good wind site is found, which is called a wind farm or a wind park How many turbines can be installed at a given site? – Wind turbines located too close together will result in upwind turbines interfering with the wind received by those located downwind – Studies of square arrays with uniform, equal spacing illustrate the degradation of performance when wind turbines are too close together

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Wind Power Systems – Simple Estimates of Wind Turbine Energy Offshore wind farms: Wind turbines sitting on flat ocean surface Near neutral atmospheric boundary layer winds High wind speed with relatively low ambient turbulence level Suffers from ‘deep array effect’ Onshore wind farms: Wind turbines sitting over complex terrains. Atmospheric stability is rarely close to near-neutral (unstable during the day time and highly stable conditions with high shear at night time) Much higher ambient turbulence level

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Wind Power Systems – Simple Estimates of Wind Turbine Energy Onshore wind farm

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Wind Power Systems – Simple Estimates of Wind Turbine Energy An array area should not be square, but rectangular with only a few long rows perpendicular to the prevailing winds, with each row having many turbines Experience has yielded some rough rules for tower spacing of such rectangular arrays – Recommended spacing is 3–5 rotor diameters separating towers within a row and 5–9 diameters between rows

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