Verify FAST v8 linearization result

Wind & Water Computer-Aided Engineering Software Tools
1

Dear Jason,

I am trying to verify the linearization results of FAST v8, considering 2 DOF (generator DOF and shaft DOF) for the NREL 5MW turbine. According to the internal DOF variables defined in FAST, I write the system linear model and compare with the results given by FAST. Some entities in the system matrix do not match (highlighted in red). The results are attached. For example, dTt/dwr should be zero, which is the derivative of aerodynamic torque with respect to generator speed, and also the last two entities in the last row of A matrix. I would really appreciate if you can let me know where is wrong.

Thanks,
Xiao

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model.png

2

Dear Xiao,

A couple comments:

  • What is the source of your model.png image? I’m not sure I follow all of the nomenclature, nor why the (3,3) term would be zero – the generator acceleration could be impacted by the aerodynamic or generator torque.
  • The accuracy of the linear model depends on many things, e.g. which model features are enabled, the quality of the state-state solution, whether you’ve linearized at a number of azimuth steps, applied MBC/azimuth averaging, etc. I’d have to understand more about what you are doing to comment on your results.

Best regards,

3

Hi Jason,

Thanks a lot for your reply.

  1. It is just the two-mass shaft model that I rewrite in terms of the state variables defined in FAST ( DOF_GeAz is the generator angle and DOF_DrTr is the twist angle at the LSS side). I consider only the 2 DOFs for the beginning, and simulate under a steady wind speed condition. In this model, the aerodynamic torque can be linearized as Tt=Tt0+dTt/dwt*(delta_wt)+dTt/dV*(delta_Vwind), so I think (3,3) should be zero from Jg*dwr/dt=Tsh-Te, which should only involve theat_tw and w_tw due to Tsh (shaft torque). I attach a figure on how the system model is obtained.

  2. I did not apply MBC since the states related to blades are not included. I guess the issues might be that all the inputs are included in the linearization process. Should I choose the inputs like in FAST V7?

Thanks,
Xiao
explain.png

4

Dear Xiao,

Just a couple comments:

  • OK, I think I’m starting understand your nomenclature and equations. But keep in mind that Te (electrical generator torque) may depend on the generator speed, omega_r (depending on how you are linearizing) and Tt (the aerodynamic torque) is likely generator speed dependent; so, the derivatives of these w.r.t. rotor speed will involve terms associated with the generator speed and torsion rate. And Tsh (the shaft torque) can be written in terms of ktheta_tw and comega_tw.
  • I agree that you don’t need MBC since you don’t have states in the rotating frame. But you’ll still need to choose what generator torque model is being applied, how the aerodynamics are linearized, and find a steady-state solution. If you have any flow skew or shear, it may help to linearize at multiple azimuth steps and azimuth average as well.

Best regards,

5

Hi Jason,

Finally, I get what is the problem by reading FAST 7 manual again. I ignore to set the variable-speed control by giving small values for slip, torque constant and rated speed. Now the results match the theoretical derivation.

Thanks a lot for your help!
Regards,
Xiao