Linearization of the "NRELOffshrBsline5MW_Monopile_RF" model

Dear Jason,

thank you for your quick reply. Please find attached the excel file but I can’t attach nether *.lin file nor *.mat file (of mbc3 workspace). Do you mind if send them directly to your e-mail address?

Thank you very much,
Alessandro Giusti
MBC_v1.00.xls (253 KB)

Dear Alessandro,

I didn’t review the files you e-mailed me, but I think you are simply misinterpreting the results in the MBC_v1.00.xls (CampbellDiagram.xls) spreadsheet. Here is what I see:

Mode 1, 0.2764 Hz - 1st Tower Side-to-Side Bending
Mode 2, 0.2833 Hz - 1st Tower Fore-Aft Bending
Mode 3, 0.5229 Hz - 1st Blade Flapwise Bending (Regressive)
Mode 4, 0.6138 Hz - Drivetrain Torsion
Mode 5, 0.7505 Hz - 1st Blade Flapwise Bending (Collective)
Mode 6, 0.8980 Hz - 1st Blade Edgewise Bending (Regressive)
Mode 7, 0.9020 Hz - 1st Blade Flapwise Bending (Progressive)
Mode 8, 1.306 Hz - 1st Blade Edgewise Bending (Progressive)
Mode 9, 1.724 Hz - 2nd Blade Flapwise Bending (Regressive)
Mode 10, 2.016 Hz - 2nd Blade Flapwise Bending (Collective)
Mode 11, 2.083 Hz - 2nd Blade Flapwise Bending (Progressive)
Mode 12, 2.356 Hz - 2nd Tower Side-to-Side Bending
Mode 13, 2.403 Hz - 2nd Tower Fore-Aft Bending
Mode 14, 3.630 Hz - 1st Blade Edgewise Bending (Collective)
Mode 15, 6.092 Hz - Nacelle Yaw

See the following post for more guidance on how to interpret the full-system mode shapes resulting from application of a FAST linearization and MBC3: http://forums.nrel.gov/t/eigenanalysis-fast/362/1.

Best regards,

Hi,
I am trying to linearize the NREL Offshore Baseline 5MW Monopile RF with only 2 DOF, in such a way that the blade pitch angle and generator torque be the linearized model inputs , and the rotation of the rotor and fore aft movement of the tower be the linearized model outputs without disturbance.Also the states will be output+tower fore-aft velocity. In this case i modified the FAST input, linearization and Aerodyn files as annexed files, but after running FAST I encountered with following error:

Stack trace terminated abnormally.

NRELOffshrBsline5MW_AeroDyn.txt (2.71 KB)
NRELOffshrBsline5MW_Linear.txt (2.09 KB)
NRELOffshrBsline5MW_Monopile_RF.txt (20.5 KB)

Where are my faults?

Thanks,
Mehdi,

Dear Mehdi,

Is that the entire error message?

I don’t have all of your input files, so, I can’t reproduce your error, but from my quick glance, I didn’t notice a few problems with the input files you did provide:

  • You’ve selected VSContrl = 0 and GenModel = 2, but you haven’t set meaningful values for the Thevenin-Equivalent Induction Generator in the FAST primary input file. I’m not sure why you’ve selected the Thevenin model; normally with TrimCase = 3, you want to set constant generator torque for the operating-point determination as explained in the Linearization chapter of the FAST User’s Guide.
  • The dynamic stall model in the AeroDyn input file must be changed from BEDDOES to STEADY (to disable dynamic stall) to linearize a model.
  • This won’t be causing a problem, but you say you want blade-pitch angle and generator torque as linearized model inputs, but you haven’t selected any inputs in the linearization input file. I would have expected NInputs = 2 and CntrlInpt = 4,3.
  • This won’t be causing a problem, but you say you want the rotation of the rotor and fore-aft movement of the tower to be the linearized model outputs, but you’ve identified many more outputs than that in the OutList within the FAST primary input file.

I hope that helps.

Best regards,

Thanks Jason,

I found that error was because of
True Echo - Echo input data to “echo.out” (flag)
Statement. I changed it to False and then the mentioned error disappeared. Do you know why?
What about the determination of states? How I set the states to output+tower fore-aft velocity (Omega, X, X_dot)?

Also thanks about your notes, I implemented them in files, except your first point, i referred to FAST User’s guide as well, but I don’t know what do you mean.
Actually as i said I am trying to linearize the NREL Offshore Baseline 5MW Monopile RF with only 2 DOF, in such a way that the blade pitch angle and generator torque be the linearized model inputs , and the rotation of the rotor and fore aft movement of the tower be the linearized model outputs without disturbance.Also the states will be output+tower fore-aft velocity. I dont know how to get the linearized model with such a conditions.
The wind speed is steady 18m/s.

Help me.

Thx,
Mehdi,

Dear Mehdi,

I’m not sure what the problem is with Echo set to True, and I can’t reproduce the error without all of your input files.

Enabling the generator (GenDOF) and first tower fore-aft (TwFADOF1) degrees-of-freedom (DOFs) will result in a 4-state model with the states you want, plus the azimuth state. The azimuth state is often removed from a linearized model through post-processing, as discussed in the following forum topic: http://forums.nrel.gov/t/fast-linearized-models/249/1 (starting Sep 16, 2014).

Normally with TrimCase = 3, you want to set constant generator torque for the operating-point determination as explained in the Linearization chapter of the FAST User’s Guide. You can do this by setting the following input parameters in the FAST primary input file:

VSContrl = 1
VS_RtGnSp = 9999.9E-9
VS_RtTq = the desired constant torque; for the NREL 5-MW turbine, this is likely the rated generator torque, 43093.55 N-m
VS_Rgn2K = 9999.9E-9
VS_SlPc = 9999.9E-9

The 3rd bullet in my previous post explains how to add the blade-pitch angle and generator torque as linearized model inputs. To include the rotation of the rotor and fore-aft movement of the tower in the linearized model outputs, replace your OutList with only the following: “RotSpeed, TTDspFA, and NcIMUTVxs”. The first two items should be clear; for an explanation of NcIMUTVxs, see the following forum topic: http://forums.nrel.gov/t/tower-top-yaw-bearing-inertia-translational-velocity/278/1.

Best regards,

I linearized the model with options you said for wind speed of 18, and found the linear file as below:
This linearized model file was generated by FAST (v7.00.01a-bjj, 5-Nov-2010) on 17-Aug-2015 at 14:21:01.
The aerodynamic calculations were made by AeroDyn (v13.00.00a-bjj, 31-Mar-2010).

NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.

Some Useful Information:

Type of steady state solution found Trimmed collective blade pitch (TrimCase = 3)
Azimuth-average rotor speed, RotSpeed (rad/s) 1.26711E+00
Period of steady state solution (sec) 4.95868E+00
Iterations needed to find steady state solution 26
Displacement 2-norm of steady state solution (rad) 1.71670E-05
Velocity 2-norm of steady state solution (rad/s) 3.70742E-05
Number of equally-speced azimuth steps, NAzimStep 36
Order of linearized model, MdlOrder 1
Number of active (enabled) DOFs 2 ( 4 states)
Number of control inputs, NInputs 2
Number of input wind disturbances, NDisturbs 0
Number of output measurements 2

Order of States in Linearized State Matrices:
Row/column 1 = 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1)
Row/column 2 = Variable speed generator DOF (internal DOF index = DOF_GeAz)
Row/column 3 to 4 = First derivatives of row/column 1 to 2.

Order of Control Inputs in Linearized State Matrices:

Column 1 = electrical generator torque (N·m) 4.30936E+04 op
Column 2 = rotor collective blade pitch (rad) 2.59779E-01 op

Order of Input Wind Disturbances in Linearized State Matrices:

None selected

Order of Output Measurements in Linearized State Matrices:

Row 1 = RotSpeed (rpm)
Row 2 = NcIMUTVxs (m/sec)

Linearized Average State Matrices(after using MBC):

A18

A18 =

     0         0    1.0000         0
     0         0         0    1.0000

-3.1337 -0.0000 -0.2562 -1.2992
-0.0010 -0.0000 -0.0271 -0.2419

B18

B18 =

     0         0
     0         0

-0.0000 -9.5874
-0.0000 -1.1814

C18

C18 =

     0         0         0    9.5490
0.0000         0    1.0360         0

D18

D18 =

 0     0
 0     0

The bode diagrams


NRELOffshrBsline5MW_Linear.txt (2.1 KB)
NRELOffshrBsline5MW_Monopile_RF.txt (17.3 KB)
Is my achieved linearized model correct? If no where are my mistakes?

Regards,

Mehdi,

other related files
NRELOffshrBsline5MW_AeroDyn.txt (2.71 KB)
Steady.txt (62 Bytes)

Dear Mehdi,

Your input files look correct to me. From the resulting state-space model, it is clear that the azimuth angle of the drivetrain (variable-speed generator DOF) can be dropped as a state by simply eliminating the 2nd row and column from A, the 2nd row from B, and the 2nd column from C.

Best regards,

I manually did the following procedure for two degree of freedom monopile.


I also get the similar state space equation using FAST linearizatioin tools. Now I want to calculate the coefficients a_i, a_ii, b_i, b_ii by comparing FAST/linearization result with my own equation, but I dont know which moment of inertia do FAST uses in linearization? How is it possible to get the coefficients a_i, a_ii, b_i, b_ii with this method?

Regards

Dear Mehdi,

The FAST model is more complicated than the model you are comparing it to (even when linearizing), so you won’t be able to derive the stiffness and damping coefficients of your simpler model directly. For example, FAST uses a modal-based approach for the tower deflection rather than a rigid-body hinge model that you’re using. FAST also includes e.g. aerodynamic stiffness. It is also not possible to include a hydrodynamic moment (M_h) in the linearized model as you’ve used.

That said, you may be able to make your own assumptions about L and I_yy etc. and compare the linearized matrices FAST outputs with your model to derive most of the coefficients your model uses.

Best regards,

Dear Jason,

Are not there another ways to find fore-aft stiffness and damping of the Monopile wind turbine using FAST (or FAST linearization) in ordinary wind and wave conditions?

Regards,
Mehdi,

Dear Mehdi,

I’m sorry, but I don’t really understand your question.

Best regards,

Lets explain more.

As you know the monopile wind turbine working in specific condition shows specific attitude. How is it possible to get individual and total damping terms of aerodynamic, structrual and hydrodynamics through FAST, like what did you do for barge pitch damping ratio in fig 7-5 of your PhD dissertation ?? What about stiffness ? In this way I think I can find my coefficients a_i, a_ii, b_i, b_ii?? Or I couldnt?

Dear Mehdi,

The aerodynamic, structural, and hydrodynamic mass, stiffness, and damping are all included in the linearization output of FAST v7, when those corresponding features are enabled. (To be clear: you must disable the radiation damping from potential flow when linearizing with FAST v7, and so the radiation damping is not included in the FAST v7 linearization output, but the radiation added mass from potential flow, and the added mass and viscous damping from strip theory, are included.)

As I said in my prior post, you can derive the coefficients you seek, but you must beware that the FAST model is more complicated than your model and you must specify your own L, I_yy, etc.

Best regards,

In order to get those coefficients, I have to calculate the derivative of power and torque coefficient of rotor with respect to blade pitch angle, rotor rotational speed, wind speed.
Whats your opinion to calculate these derivatives?

Dear Mehdi,

These derivatives can all be calculated through the linearization functionality of FAST v7.

Best regards,

I amazed what is the reason of existence such differences between the thrust derivative with respect to wind speed achieved through Open-Loop and Ideal Closed Loop?
I know how you computed them, but unfortunately couldnt understand the behind theory of their such differences in results.
If it is possible help me to understand those differences.

Dear Mehdi,

The aerodynamic thrust is strongly related to the blade-pitch angle. In Open-Loop, the blade-pitch angle is not varied with the perturbations in wind speed. In Ideal Closed Loop, the blade-pitch angle is always correlated with the wind speed.

Best regards,

In order to get those coefficients, I have to calculate the derivative of rotor thrust and torque with respect to blade pitch angle, rotor rotational speed, wind speed. You said that these derivatives can all be calculated through the linearization functionality of FAST v7. Could you please tell me how is it possible using linearization functionality of FAST v7? I have read the FAST users guide but couldnt find how to calculate these derivatives.

Best regards,