0. ECE 333 Renewable Energy Systems
Lecture 10: Wind Power Systems
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign

1. Announcements Read Chapter 7 Quiz today on HW 4
HW 5 is posted on the website; there will be no quiz on this material, but it certainly may be included in the exams
First exam is March 5 (during class); closed book, closed notes; you may bring in standard calculators and one 8.5 by 11 inch handwritten note sheet
In ECEB 3017 and 3002

2. Variable-Slip Induction Generators
Purposely add variable resistance to the rotor
External adjustable resistors - this can mean using a wound rotor with slip rings and brushes which requires more maintenance
Mount resistors and control electronics on the rotor and use an optical fiber link to send the rotor a signal for how much resistance to provide

3. Effect of Rotor Resistance on Induction Machine Power-Speed Curves
Left plot shows the torque-power curve from slip of -1 to 1 with external resistance = 0.05; right plot is with external resistance set to 0.99 pu.

4. Variable Slip Example: Vestas V80 1.8 MW
The Vestas V MW turbine is an example in which an induction generator is operated with variable rotor resistance (opti-slip).
Adjusting the rotor resistance changes the torque-speed curve
Operates between 9 and 19 rpm
Source: Vestas V80 brochure

5. Induction Machine Circuit
I, S into the machine (motor convention)
Rs = stator resistance (small)
Xls = stator leakage flux
Xm = magnetizing reactance, Xm >> Xls
Xlr = inductance of rotor referred to stator
Rr/s = represents energy transfer between electrical and mechanical side

6. Induction Motor Thevenin Equiv.
Find VTH and ZTH looking into the left
VTH = VOC
If Rs = 0, expression simplifies:

7. Induction Motor Thevenin Equiv.
Short circuit Va to find ZTH
If Rs = 0, expression simplifies:
Call this XTH

8. Simplified Circuit
Assuming Rs = 0 simplifies the induction machine equivalent circuit and obtains this circuit which is easy to analyze
We can rewrite Rr/s as in which the first term represents the rotor losses (heating) and the second term represents the mechanical power transfer

9. Equivalent Circuit Example
Find the input power.
2 pole, 60 Hz machine
Rs = 0 Ω
Xls = 0.5 Ω
Xm = 50 Ω
Xlr = 0.5 Ω
Rr = 0.1 Ω
Slip = 0.05
VLN = 5000° V
Step 1: Calculate the equivalent circuit parameters

10. Equivalent Circuit Example
Step 2: Draw the circuit
Step 3: Analyze the equivalent circuit
equivalent circuit

11. Motor Starting Now let s=1 (standstill)
Looks like a load to the system
A lot of reactive power is being transferred!
Ever notice that the lights dim when your air conditioner comes on?

12. Calculating Torque-Speed Curve
If you continue this analysis for different values of s, and plot the results, you’ll get the torque speed curve: torque * speed = power
What if s = 0? (synchronous)
Like a jet flying at the same speed as another jet – there is no relative motion
Rotor can’t see the stator field go by, so Rr looks infinite and I is zero (open circuit)

13. Induction Generator Example
Now let s = (a generator)
The negative resistance means that power is being transferred from the wind turbine to the grid
A generator producing P but absorbing Q!

14. Reactive Power Support
Wind turbine generators can produce real power but consume reactive power
This is especially a problem with Types 1 and 2 wind turbines which are induction machines, like this model
Capacitors or other power factor correction devices are needed
Types 3 and 4 can provide reactive support, details beyond the scope of this class

15. Induction Generator Rotor Losses
What about rotor losses?
This means before getting out to the stator and producing the 100 kW, there are 5 kW being lost in the rotor.
That means what was actually captured from the wind was 105 kW, but 5 was lost!
Rr = 0.1

16. Doubly-Fed Induction Generators
Another common approach is to use what is called a doubly-fed induction generator in which there is an electrical connection between the rotor and supply electrical system using an ac-ac converter
This allows operation over a wide-range of speed, for example 30% with the GE 1.5 MW and 3.6 MW machines
Called Type 3 wind turbines

17. GE 1.5 MW DFIG Example
GE 1.5 MW turbines were the best selling wind turbines in the US in 2011
Source: GE Brochure/manual

18. Indirect Grid Connection Systems
Wind turbine is allowed to spin at any speed
Variable frequency AC from the generator goes through a rectifier (AC-DC) and an inverter (DC-AC) to 60 Hz for grid-connection
Good for handling rapidly changing windspeeds

19. Wind Turbine Gearboxes
A significant portion of the weight in the nacelle is due to the gearbox
Needed to change the slow blade shaft speed into the higher speed needed for the electric machine
Gearboxes require periodic maintenance (e.g., change the oil), and have also be a common source of wind turbine failure
Some wind turbine designs are now getting rid of the gearbox by using electric generators with many pole pairs (direct-drive systems)

20. Average Power in the Wind
How much energy can we expect from a wind turbine?
To figure out average power in the wind, we need to know the average value of the cube of velocity:
This is why we can’t use average wind speed vavg to find the average power in the wind

21. Average Windspeed vi = wind speed (mph)
The fraction of total hours at vi is also the probability that v = vi

22. Average Windspeed
This is the average wind speed in probabilistic terms
Average value of v3 is found the same way:

23. Example Windspeed Site Data

24. Wind Probability Density Functions
Windspeed probability density function (pdf): between 0 and 1, area under the curve is equal to 1

25. Windspeed p.d.f. f(v) = wind speed pdf
Probability that wind is between two wind speeds:
# of hours/year that the wind is between two wind speeds:

26. Average Windspeed using p.d.f.
This is similar to earlier summation, but now we have a continuous function instead of discrete function
Same for the average of (v3)
discrete
continuous
discrete
continuous

27. Weibull p.d.f.
Starting point for characterizing statistics of wind speeds
k = shape parameter
c = scale parameter
Keep in mind actual data is key. The idea of introducing the Weibull pdf is to see if we can get a an equation that approximates the characteristics of actual wind site data

28. Weibull p.d.f.
k=2 looks reasonable for wind
Weibull p.d.f. for c = 8

29. Where did the Weibull PDF Come From
Invented by Waloddi Weibull in 1937, and presented in hallmark American paper in 1951
Weibull's claim was that it fit data for a wide range of problems, ranging from strength of steel to the height of adult males
Initially greeted with skepticism – it seemed too good to be true, but further testing has shown its value
Widely used since it allows a complete pdf response to be approximated from a small set of samples
But this approximation is not going to work well for every data set!!
Reference: