Calculation of Rotor Rotational Dynamics in FAST

Wind & Water Rotor Aerodynamics
1

Hi,

I have a question concerning the calculation of the rotor rotational dynamics in FAST.

I am simulating a reduced-order, dynamic wind turbine model (as described in Bianchi: Wind Turbine Control Systems) where I implemented the rotor torque and thrust calculations via look-up tables of the Cq- and Ct-coefficients extracted from the NREL 5MW reference turbine.

For the sake of comparison, I also implemented a full BEM-calculation (including the usual corrections) in the dynamic simulation, which yielded almost the same results. Running a closed-loop simulation using turbulent wind as input, the deviations in the aerodynamic rotor torque around the mean value are quite high and therefore also in the rotor rotational speed.

By contrast, running a simulation with FAST (using the same pitch controller), rotor torque and the rotor speed are much more concentrated around the mean value with less deviations. These deviations between FAST and my simulation can also be observed when only the rotor rotational degree of freedom is switched on.

My question is: How is the rotor rotational speed calculated in FAST?

Other than the aerodynamic rotor torque, are there additional terms in FAST that lead to an averaging effect and how are they calculated?

For a stiff drivetrain model, I would assume the differential equation to be

d/dt om_rotor = (M_A – M_g)/(J_r + J_g)

(om_rotor: rotor rotational speed, M_A: aerodynamic torque, M_g: generator torque, J_r, J_g: rotor and generator inertias).

Am I missing something here?

2

Dear Matthias,

I answered a similar question in the following forum post: Resistant moment of the rotor and of the electric generator. The equation you state in your post is equivalent to the equation under point (1) in the link.

I hope that helps.

Best regards,

3

Dear Jason,

thank you for your answer.

I discovered that the reason for the deviations is the way I use the turbulent wind input. For my simulation of the reduced-order model, I use a hub-height *.hh wind file generated from TurbSim as wind input, whereas in FAST I used the full field *.bts file. When I use the hub-height wind file in FAST, the agreement to the reduced-order model is good.

This brings me to another question: Why are there such pronounced differences when using the hub-height respectively the full-field turbulent wind data as input for FAST/Aerodyn? Does the full-field turbulent simulation lead to an averaging effect compared to simulations using the hub-height wind files?

Best regards

4

Dear Matthias,

Basically, “yes.” The hub-height-formatted files store wind that is uniform across the rotor disk (perhaps with shear) whereas the full-field-formatted files store wind that varies spatially across the rotor disk (the latter being more realisitc). See Figure 17 in the TurbSim User’s Guide for a clear picture of the differnces.

Best regards,

5

Dear Jason,

ok, thank you, that’s what I thought.

Best regards