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Power Generation from Renewable Energy Sources Fall 2012 Instructor: Xiaodong Chu Email：[email protected] Office Tel.: 81696127 Flashbacks of Last Lecture • How much energy might be expected from a wind turbine in various wind regimes? 1 1 Pavg ( Av3 ) avg A(v 3 ) avg 2 2 • With the probability of wind speeds – For discrete distribution (v 3 ) avg [vi3 probabilit y(v vi )] i – For continuous probability density function (v )avg v3 f (v)dv 3 0 Flashbacks of Last Lecture • The Weibull probability density function is often used to characterize the statistics of wind speeds k v f (v ) c c k 1 v k exp c where k is called the shape parameter and c the scale parameter • 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. v 2 2v f (v) 2 exp c c Flashbacks of Last Lecture • With average wind speed estimated by an anemometer and the assumption that the wind speed distribution follows Rayleigh, the average value of the cube of wind speed can be derived as 2 0 0 (v 3 ) avg v 3 f (v)dv v 3 and v 2v exp 2 c c 3 2 dv c 4 3 (v 3 ) avg 3 6 2v v 3 1.91v 3 4 • With Rayleigh statistics, the average power in the wind P 6 1 Av 3 2 Flashbacks of Last Lecture • 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 Flashbacks of Last Lecture • Example 6.10 on page 346 of the textbook: you should master it! • Example 6.11 on page 350 of the textbook: you should master it! Wind Power Systems – Specific Wind Turbine Performance Calculations • From simple estimates of overall system efficiency associated with wind probability statistics to techniques applied to individual wind turbines based on their own specific performance characteristics • To understand how rotor blades extract energy from the wind, we start from some parameters associated with aerodynamics of wind turbines – Lift and drag forces – Angle of attack – Pitch angle Wind Power Systems – Specific Wind Turbine Performance Calculations • Lift and drag forces – Air flow over a stationary airfoil produces two forces, a lift force perpendicular to the air flow and a drag force in the direction of air flow – The air flows smoothly over both sides of the airfoil and the air flowing over the top of the airfoil has to speed up because of a greater distance to travel, which causes a slight decrease in pressure – The air pressure on top is lower than that under the airfoil, which creates the lift force perpendicular to the direction of air flow – The air moving over the airfoil also produces a drag force in the direction of the air flow, which is a loss term Wind Power Systems – Specific Wind Turbine Performance Calculations • An airfoil is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section Wind Power Systems – Specific Wind Turbine Performance Calculations • Lift and drag forces – A rotating turbine blade sees air moving toward it not only from the wind itself, but also from the relative motion of the blade as it rotates – The combination of the two is moving across the blade at the correct angle to obtain a lift force while a drag force is accompanying Wind Power Systems – Specific Wind Turbine Performance Calculations • Lift and drag forces – The lift and drag forces can be split into components parallel and perpendicular to the direction of the wind itself, and these components combined to form the net force F1 the net force F2 – The force F1 is available to do useful work whereas the force F2 must be considered in the design of the turbine blades to assure structural integrity Wind Power Systems – Specific Wind Turbine Performance Calculations • Angle of attack – It is the angle between the chord line of the turbine blade and the resulting wind direction • The chord line is the straight line connecting the leading and trailing edges of the blade – It is a dynamic angle, depending on both the speed of the blade and the speed of the wind • The blade speed at a distance r from the hub and an angular velocity ωm is rωm • A blade with twist will have a variation in angle of attack from hub to tip because of the variation of blade speed with distance from the hub Wind Power Systems – Specific Wind Turbine Performance Calculations • Angle of attack – Up to a point, increasing the angle of attack improves lift at the expense of increased drag – However, increasing the angle of attack too much can result in a phenomenon known as stall, where the air flow over the top no longer sticks to the surface and the resulting turbulence destroys lift Wind Power Systems – Specific Wind Turbine Performance Calculations • Angle of attack – The angle of attack of the wind changes much more dramatically at the root of the blade (yellow line) than at the tip of the blade (red line) as the wind changes – If the wind becomes powerful enough to make the blade stall, it will start stalling at the root of the blade Wind Power Systems – Specific Wind Turbine Performance Calculations • Pitch angle – It is the angle between the chord line of the blade and the plane of rotation • The plane of rotation is the plane in which the blade tips lie as they rotate • The blade tips actually trace out a circle which lies on the plane of rotation • Full power output would normally be obtained when the wind direction is perpendicular to the plane of rotation – When the blade is twisted, the pitch angle will change from hub to tip • In this situation, the pitch angle measured 3/4 of the distance out from the hub is selected as the reference Wind Power Systems – Specific Wind Turbine Performance Calculations • Plane of rotation Wind Power Systems – Specific Wind Turbine Performance Calculations • Pitch angle Wind Power Systems – Specific Wind Turbine Performance Calculations • The most important technical information for a specific wind turbine is the power curve, showing the relationship between wind speed and generator electrical output Wind Power Systems – Specific Wind Turbine Performance Calculations • The cut-in wind speed VC is the minimum needed to generate net power Wind Power Systems – Specific Wind Turbine Performance Calculations • When winds reach the rated wind speed VR, the generator is delivering as much power as it is designed for and above VR, there must be some way to shed some of the wind’s power or else the generator may be damaged • Three power control approaches are commonly used: stall control, pitch control and active stall control Wind Power Systems – Specific Wind Turbine Performance Calculations • Stall control – The blades are carefully designed to automatically reduce efficiency when winds are excessive – There are no moving parts, so this is referred to as passive control – The aerodynamic design of the blades, especially their twist as a function of distance from the hub, must be very carefully done so that a gradual reduction in lift occurs as the blades rotate faster Wind Power Systems – Specific Wind Turbine Performance Calculations • Pitch control – An electronic system monitors the generator output power; if it exceeds specifications, the pitch of the turbine blades is adjusted to shed some of the wind – A hydraulic system slowly rotates the blades about their axes, turning them a few degrees at a time to reduce or increase their efficiency as conditions dictate – The strategy is to reduce the blade’s angle of attack when winds are high Wind Power Systems – Specific Wind Turbine Performance Calculations • Active stall control – The blades rotate just as they do in the active, pitch-control approach – However, when winds exceed the rated wind speed, instead of reducing the angle of attack of the blades, it is increased to induce stall Wind Power Systems – Specific Wind Turbine Performance Calculations • At a wind speed VF , called the cut out or the furling wind speed, the machine must be shut down to prevent the wind turbine from danger and above VF , output power obviously is zero Wind Power Systems – Optimizing Rotor Diameter and Generator Rated Power • There are trade-offs between rotor diameter and generator size as ways to increase the energy delivered by a wind turbine – Increasing the rotor diameter, while keeping the same generator, shifts the power curve upward so that rated power is reached at a lower wind speed – Keeping the same rotor but increasing the generator size allows the power curve to continue upward to the new rated power Wind Power Systems – Optimizing Rotor Diameter and Generator Rated Power • There are trade-offs between rotor diameter and generator size as ways to increase the energy delivered by a wind turbine – Increasing the rotor diameter, while keeping the same generator, shifts the power curve upward so that rated power is reached at a lower wind speed – Keeping the same rotor but increasing the generator size allows the power curve to continue upward to the new rated power