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

2. Flashbacks of Last Lecture Wind power is proportional to the cube of wind speed Factors influencing air density: temperature and pressure (altitude) Impact of tower height: mounting wind turbine on a taller tower to get higher wind speeds

3. Flashbacks of Last Lecture Examples of 6.5 and 6.6 on page 322 of the textbook

4. Wind Power Systems – Maximum Rotor Efficiency What is the constraint that limits the ability of a wind turbine to convert kinetic energy in the wind to mechanical power? The original derivation for the maximum power that a turbine can extract from the wind is formulated by Albert Betz – The analysis begins by imagining what must happen to the wind as it passes through a wind turbine – Albert Betz (25 December 1885 Schweinfurt – 16 April 1968 Göttingen), was a German physicist and a pioneer of wind turbine technologySchweinfurtGöttingenGermanphysicist wind turbine

5. Wind Power Systems – Maximum Rotor Efficiency The wind leaving the turbine has a lower velocity and its pressure is reduced, causing the air to expand downwind of the machine and forming a stream tube Why cannot the turbine extract all of the kinetic energy in the wind?

6. Wind Power Systems – Maximum Rotor Efficiency Betz showed an ideal wind turbine would slow the wind to 1/3 of its original speed The power extracted by the blades is equal to

7. Wind Power Systems – Maximum Rotor Efficiency The easiest spot to determine mass flow rate is at the plane of the rotor where we know the cross- sectional area is the swept area of the rotor

8. Wind Power Systems – Maximum Rotor Efficiency Make the assumption that the velocity of the wind through the plane of the rotor is the average of the upwind and downwind speeds, then

9. Wind Power Systems – Maximum Rotor Efficiency Define the ratio of downstream to upstream wind speed then

10. Wind Power Systems – Maximum Rotor Efficiency The rotor efficiency and What is the maximum possible rotor efficiency? (Betz efficiency or Betz’ law)

11. Wind Power Systems – Maximum Rotor Efficiency How close are modern wind turbine blades to the Betz efficiency? – They can approach 80 percent under the best operating conditions, i.e., 45 to 50 percent efficiency For a given wind speed, rotor efficiency is a function of rate at which the rotor turns – The usual way is to present rotor efficiency as a function of its tip speed ratio (TSR)

12. Wind Power Systems – Maximum Rotor Efficiency

13. Example of 6.7 on page 327 of the textbook

14. Wind Power Systems – Wind Turbine Generators The function of blades is to convert kinetic energy in the wind into rotating shaft power to spin a generator that produces electric power Grid-connected machines use ac generators including synchronous generators and asynchronous induction generators

15. Wind Power Systems – Wind Turbine Generators Synchronous generators are forced to spin at a precise rotational speed determined by the number of poles and the frequency needed for the power grid The magnetic fields are usually created on their rotors by direct current through windings around the rotor core – A rectifying circuit, i.e., exciter, is needed to convert ac from the grid into dc for the rotor – Slip rings on the rotor shaft are needed along with brushes pressing against slip rings, which adds to the maintenance

16. Wind Power Systems – Wind Turbine Generators

17. Most of current world’s wind turbines use induction generators, which do not turn at a fixed speed – As a motor, the rotor spins a little slower than the synchronous speed established by its stationary field windings and it delivers power to its rotating shaft – As a generator, the rotor spins a little faster than the synchronous speed and it delivers power to its stationary field windings The key advantage of asynchronous induction generators is that their rotors do not require the exciter, brushes, and slip rings since the magnetic field is created in the stator rather than the rotor, which means they are less complicated and less expensive

18. Wind Power Systems – Wind Turbine Generators Rotating magnetic field of an induction machine

19. Wind Power Systems – Wind Turbine Generators Rotating magnetic field of an induction machine

20. Wind Power Systems – Maximum Rotor Efficiency Slip of an induction machine