## Cp-TSR curve in a VS-FP stall regulated small turbine

Discuss the theory and modeling of rotor aerodynamics.

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Alvaro.Olcoz
Posts: 22
Joined: Thu Nov 15, 2018 5:46 pm
Location: Navarra

### Cp-TSR curve in a VS-FP stall regulated small turbine

Dear all,
I feel a bit confused about the shape and meaning of the typical Cp-TSR curve in a turbine with the following characteristics:
- 10 kW generator rated power
- Fixed Pitch and Variable Speed ( range from U= 2m/s to 6 m/s)
- Stall power regulation
- Cut-in and cut-out velocities are 2 and 18 m/s respectively.
The turbine will work at design TSR (6 in this case) within 2 and 6 m/s of wind velocity. Then, rotational speed will remain constant, and as wind velocity increases, angles of attack at blade sections will increase and lead to stall power regulation. When this happens, TSR decreases from optimun.
My concerns are the followings:
1) As we have seen, the TSR operation range goes from 6 (within a wind velocity range) to below 6. So, do we really need the right part of a typical turbine Cp-TSR figure (attachment 1)? Will the WT ever work at those points ?
2) In the variable speed region, as wind velocity increases so does the rotational speed and thus, the TSR remains constant (and equal to 6, in this case). The problem is that even if TSR is equal in this range, Re numbers at blade sections are higher near 6 m/s of wind speed than near 2, and it happens that for low wind speed wind turbine, glide ratio is higher with higher Re numbers (attachment 2). This leads to a subtle increase in Cp when wind velocity increases within 2 and 6 m/s (attachment 3) and, in other words, to several different Cp values for the same TSR=TSRopt.
It makes me think about using a third axis for the plot (Cp-lambda-omega), for example.
I hope I have explained myself clearly.
Thank you very much in advance.
Alvaro Olcoz
Attachments
Attachment 3
example.png (25.14 KiB) Viewed 3456 times
Attachment 2
at2.PNG (9.41 KiB) Viewed 3456 times
Attachment 1
at1.PNG (7.38 KiB) Viewed 3456 times

Jason.Jonkman
Posts: 5723
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

### Re: Cp-TSR curve in a VS-FP stall regulated small turbine

Dear Alvaro,

1) A wind turbine may operate at a TSR higher than optimal at low wind speeds when it produces power because one often limits the variable-speed range to avoid resonances; in this case, the controller may have the rotor spin faster at low wind/rotor speeds than it would for optimal power.

2) I agree. The impact of the Reynolds number likely depends on the airfoil (some airfoils are more Reynolds number sensitive than others). We discussed this recently in a related forum topic: viewtopic.php?f=13&t=2165&p=12153.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Alvaro.Olcoz
Posts: 22
Joined: Thu Nov 15, 2018 5:46 pm
Location: Navarra

### Re: Cp-TSR curve in a VS-FP stall regulated small turbine

Dear Jason,
I would like to thank you for your always rapid and helpful replies.
Alvaro Olcoz