## NREL 5MW Torque vs GenSpeed Curve Points

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Jon.Martinez
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### NREL 5MW Torque vs GenSpeed Curve Points

Dear Dr. Jonkman,

I am applying the Torque vs GenSpeed Curve in the Torque Control Loop inside Simulink for simulating the NREL 5MW wind turbine with FAST v8 (v8.16.00a-bjj, 27-Jul-2016).

I have defined the curve with a MATLAB Function block, basing on the information given in the "Definition of a 5-MW Reference Wind Turbine for Offshore System Development" document (https://www.nrel.gov/docs/fy09osti/38060.pdf) in pages 19-20.

Nevetherless, I have some doubts about some of the points defining the curve, which I would like to clarify. I know this issue has been trated previously, but I was not able to understand fully. I attach an image of the curve for referring to the specific points which I would like to define.

TorqueCurve.png (70.68 KiB) Viewed 1919 times

As I understand, the transitional generator speed between Regions 2 1/2 and 3 is the 99% of the rated, therefore:

wGen_A = wGenRated * 0.99 = 1173.7 * 0.99 = 1161.963 rpm

From that point, until the cut off wind speed (in Region 3), the power is held constant, and therefore as I understand, in point A we have already reached the rated power (5MW).

Taking that consideration into account, my calculations for the torque in that point give the following result:

torque_A(Nm) = GenPwrRatedMec(W) / wGen_A(rad/s) = (GenPwrNom(W) / GenEff) / wGen_A(rad/s) = 5e6 / 0.944 / (1161.963 * pi / 30) = 43528.84 Nm

Therefore, the torque obtained in point A is higher than the rated torque (43093.55Nm), which is reached later, with the rated wind speed.

As for point B, I calculated it as the crossing point of curve from Region 2 (quadratic region curve) and curve from Region 2 1/2.

In order to define the curve from Region 2 1/2, I applied that the slip percentage of 10% means that point C is at 90% of wGenRated, therefore being:

wGen_C = 0.9 * wGenRated = 0.9 * 1173.7 = 1056.33 rpm

And after calculating the cross point, the result is the following:

wGen_C = 1136.498 rpm
torque_C = 33035.165 Nm

Are these calculations alright?

Jon Martínez Rico

Jason.Jonkman
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### Re: NREL 5MW Torque vs GenSpeed Curve Points

Dear Jon,

Just a couple corrections:
• The synchronous speed for Region 2.5 (point C) should be calculated as wGen_C = wGen_A/(1+0.1) = 1056.33 rpm
• The transition between Regions 2 and 2.5 (point B) should be wGen_B = 1136.498 rpm, torque_B = 33035 Nm
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

Jon.Martinez
Posts: 5
Joined: Thu Jul 18, 2019 2:03 am
Organization: Tekniker
Location: Spain

### Re: NREL 5MW Torque vs GenSpeed Curve Points

Dear Jason,

For your corrections, I see that even if I calculated wGen_C in a different way, the result is the same.
As for the second correction, I made a mistake, and wrote letter C instead of B, but my results were also the same

Thank you and best regards,

Jon Martínez Rico