Linearization of the "NRELOffshrBsline5MW_Monopile_RF" model

Wind & Water Computer-Aided Engineering Software Tools
1

Hi everybody,
I’m trying to linearize the 5-MW NREL offshore Baseline Model with water depth 20 m.
If the turbine is parked, I obtain (with MBC3 code) that the first two tower frequencies are about 0.28 Hz, but if the blades are rotating the first two modes have a very small frequency (almost zero), instead, the third and fourth natural frequencies are similar to the first and second ones of the parked case.
Please, see in attachment the Matlab variables after running MBC and the input files I am using.

Many thanks beforehand,
regards,

Alessandro Giusti

2

Dear Alessandro,

Your attachment didn’t show up, but as described in this forum topic: Learizing Baseline 5MW Wind Turbine with FAST, generator-DOF-induced rigid-body modes show up in MBC3 as a pair of zero-valued (or near-zero-valued) frequencies with +/- inf damping.

3

Dear Jason,

thank you for your quick reply and helpful information. Is it possible to cut these generator-DOF-induced rigid-body modes when FAST is running so that these frequencies will not appear in the results?

Many thanks,
regards,

Alessandro Giusti

4

Dear Alessandro,

Simply disable the generator DOF (GenDOF = False) and the frequencies will go away.

Best regards,

5

Dear Jason,

thank you for your quick reply, I have disabled the generator DOF but the solution does not converge. Maybe I’ve done some mistakes in the input files.
This is the error message of FAST:

The solution does not appear to converge after 3600 seconds! 

Try increasing the total run time, TMax, increasing system damping values, 
or increasing the convergence tolerances, DispTol and/or VelTol. 

The linearized system matrices were not formed. 

Aborting FAST.

This is the input file that I’ve used, could you check if there are some mistakes?

Thank you so much. Regards,

Alessandro Giusti

------- FAST INPUT FILE --------------------------------------------------------
NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.
Properties from Dutch Offshore Wind Energy Converter (DOWEC) 6MW Pre-Design (10046_009.pdf) and REpower 5M 5MW (5m_uk.pdf); Compatible with FAST v6.0.
---------------------- SIMULATION CONTROL --------------------------------------
True Echo - Echo input data to “echo.out” (flag)
1 ADAMSPrep - ADAMS preprocessor mode {1: Run FAST, 2: use FAST as a preprocessor to create an ADAMS model, 3: do both} (switch)
2 AnalMode - Analysis mode {1: Run a time-marching simulation, 2: create a periodic linearized model} (switch)
3 NumBl - Number of blades (-)
3600.00 TMax - Total run time (s)
0.0125 DT - Integration time step (s)
---------------------- TURBINE CONTROL -----------------------------------------
0 YCMode - Yaw control mode {0: none, 1: user-defined from routine UserYawCont, 2: user-defined from Simulink} (switch)
9999.9 TYCOn - Time to enable active yaw control (s) [unused when YCMode=0]
0 PCMode - Pitch control mode {0: none, 1: user-defined from routine PitchCntrl, 2: user-defined from Simulink} (switch)
0 TPCOn - Time to enable active pitch control (s) [unused when PCMode=0]
0 VSContrl - Variable-speed control mode {0: none, 1: simple VS, 2: user-defined from routine UserVSCont, 3: user-defined from Simulink} (switch)
9999.9 VS_RtGnSp - Rated generator speed for simple variable-speed generator control (HSS side) (rpm) [used only when VSContrl=1]
9999.9 VS_RtTq - Rated generator torque/constant generator torque in Region 3 for simple variable-speed generator control (HSS side) (N-m) [used only when VSContrl=1]
9999.9 VS_Rgn2K - Generator torque constant in Region 2 for simple variable-speed generator control (HSS side) (N-m/rpm^2) [used only when VSContrl=1]
9999.9 VS_SlPc - Rated generator slip percentage in Region 2 1/2 for simple variable-speed generator control (%) [used only when VSContrl=1]
2 GenModel - Generator model {1: simple, 2: Thevenin, 3: user-defined from routine UserGen} (switch) [used only when VSContrl=0]
True GenTiS-tr - Method to start the generator {T: timed using TimGenOn, F: generator speed using SpdGenOn} (flag)
True GenTiStp - Method to stop the generator {T: timed using TimGenOf, F: when generator power = 0} (flag)
9999.9 SpdGenOn - Generator speed to turn on the generator for a startup (HSS speed) (rpm) [used only when GenTiStr=False]
0.0 TimGenOn - Time to turn on the generator for a startup (s) [used only when GenTiStr=True]
9999.9 TimGenOf - Time to turn off the generator (s) [used only when GenTiStp=True]
1 HSSBrMode - HSS brake model {1: simple, 2: user-defined from routine UserHSSBr} (switch)
9999.9 THSSBrDp - Time to initiate deployment of the HSS brake (s)
9999.9 TiDynBrk - Time to initiate deployment of the dynamic generator brake [CURRENTLY IGNORED] (s)
9999.9 TTpBrDp(1) - Time to initiate deployment of tip brake 1 (s)
9999.9 TTpBrDp(2) - Time to initiate deployment of tip brake 2 (s)
9999.9 TTpBrDp(3) - Time to initiate deployment of tip brake 3 (s) [unused for 2 blades]
9999.9 TBDepISp(1) - Deployment-initiation speed for the tip brake on blade 1 (rpm)
9999.9 TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (rpm)
9999.9 TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (rpm) [unused for 2 blades]
9999.9 TYawManS - Time to start override yaw maneuver and end standard yaw control (s)
9999.9 TYawManE - Time at which override yaw maneuver reaches final yaw angle (s)
0.0 NacYawF - Final yaw angle for override yaw maneuvers (degrees)
9999.9 TPitManS(1) - Time to start override pitch maneuver for blade 1 and end standard pitch control (s)
9999.9 TPitManS(2) - Time to start override pitch maneuver for blade 2 and end standard pitch control (s)
9999.9 TPitManS(3) - Time to start override pitch maneuver for blade 3 and end standard pitch control (s) [unused for 2 blades]
9999.9 TPitManE(1) - Time at which override pitch maneuver for blade 1 reaches final pitch (s)
9999.9 TPitManE(2) - Time at which override pitch maneuver for blade 2 reaches final pitch (s)
9999.9 TPitManE(3) - Time at which override pitch maneuver for blade 3 reaches final pitch (s) [unused for 2 blades]
0.0 BlPitch(1) - Blade 1 initial pitch (degrees)
0.0 BlPitch(2) - Blade 2 initial pitch (degrees)
0.0 BlPitch(3) - Blade 3 initial pitch (degrees) [unused for 2 blades]
0.0 B1PitchF(1) - Blade 1 final pitch for pitch maneuvers (degrees)
0.0 B1PitchF(2) - Blade 2 final pitch for pitch maneuvers (degrees)
0.0 B1PitchF(3) - Blade 3 final pitch for pitch maneuvers (degrees) [unused for 2 blades]
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
9.80665 Gravity - Gravitational acceleration (m/s^2)
---------------------- FEATURE FLAGS -------------------------------------------
True FlapDOF1 - First flapwise blade mode DOF (flag)
True FlapDOF2 - Second flapwise blade mode DOF (flag)
True EdgeDOF - First edgewise blade mode DOF (flag)
False TeetDOF - Rotor-teeter DOF (flag) [unused for 3 blades]
True DrTrDOF - Drivetrain rotational-flexibility DOF (flag)
False GenDOF - Generator DOF (flag)
True YawDOF - Yaw DOF (flag)
True TwFADOF1 - First fore-aft tower bending-mode DOF (flag)
True TwFADOF2 - Second fore-aft tower bending-mode DOF (flag)
True TwSSDOF1 - First side-to-side tower bending-mode DOF (flag)
True TwSSDOF2 - Second side-to-side tower bending-mode DOF (flag)
True CompAero - Compute aerodynamic forces (flag)
False CompNoise - Compute aerodynamic noise (flag)
---------------------- INITIAL CONDITIONS --------------------------------------
0.0 OoPDefl - Initial out-of-plane blade-tip displacement (meters)
0.0 IPDefl - Initial in-plane blade-tip deflection (meters)
0.0 TeetDefl - Initial or fixed teeter angle (degrees) [unused for 3 blades]
0.0 Azimuth - Initial azimuth angle for blade 1 (degrees)
10.0 RotSpeed - Initial or fixed rotor speed (rpm)
0.0 NacYaw - Initial or fixed nacelle-yaw angle (degrees)
0.0 TTDspFA - Initial fore-aft tower-top displacement (meters)
0.0 TTDspSS - Initial side-to-side tower-top displacement (meters)
---------------------- TURBINE CONFIGURATION -----------------------------------
63.0 TipRad - The distance from the rotor apex to the blade tip (meters)
1.5 HubRad - The distance from the rotor apex to the blade root (meters)
1 PSpnElN - Number of the innermost blade element which is still part of the pitchable portion of the blade for partial-span pitch control [1 to BldNodes] [CURRENTLY IGNORED] (-)
0.0 UndSling - Undersling length [distance from teeter pin to the rotor apex] (meters) [unused for 3 blades]
0.0 HubCM - Distance from rotor apex to hub mass [positive downwind] (meters)
-5.01910 OverHang - Distance from yaw axis to rotor apex [3 blades] or teeter pin [2 blades] (meters)
1.9 NacCMxn - Downwind distance from the tower-top to the nacelle CM (meters)
0.0 NacCMyn - Lateral distance from the tower-top to the nacelle CM (meters)
1.75 NacCMzn - Vertical distance from the tower-top to the nacelle CM (meters)
87.6 TowerHt - Height of tower above ground level [onshore] or MSL [offshore] (meters)
1.96256 Twr2Shft - Vertical distance from the tower-top to the rotor shaft (meters)
0.0 TwrRBHt - Tower rigid base height (meters)
-5.0 ShftTilt - Rotor shaft tilt angle (degrees)
0.0 Delta3 - Delta-3 angle for teetering rotors (degrees) [unused for 3 blades]
-2.5 PreCone(1) - Blade 1 cone angle (degrees)
-2.5 PreCone(2) - Blade 2 cone angle (degrees)
-2.5 PreCone(3) - Blade 3 cone angle (degrees) [unused for 2 blades]
0.0 AzimB1Up - Azimuth value to use for I/O when blade 1 points up (degrees)
---------------------- MASS AND INERTIA ----------------------------------------
0.0 YawBrMass - Yaw bearing mass (kg)
240.00E3 NacMass - Nacelle mass (kg)
56.78E3 HubMass - Hub mass (kg)
0.0 TipMass(1) - Tip-brake mass, blade 1 (kg)
0.0 TipMass(2) - Tip-brake mass, blade 2 (kg)
0.0 TipMass(3) - Tip-brake mass, blade 3 (kg) [unused for 2 blades]
2607.89E3 NacYIner - Nacelle inertia about yaw axis (kg m^2)
534.116 GenIner - Generator inertia about HSS (kg m^2)
115.926E3 HubIner - Hub inertia about rotor axis [3 blades] or teeter axis [2 blades] (kg m^2)
---------------------- DRIVETRAIN ----------------------------------------------
100.0 GBoxEff - Gearbox efficiency (%)
94.4 GenEff - Generator efficiency [ignored by the Thevenin and user-defined generator models] (%)
97.0 GBRatio - Gearbox ratio (-)
False GBRevers - Gearbox reversal {T: if rotor and generator rotate in opposite directions} (flag)
28.1162E3 HSSBrTqF - Fully deployed HSS-brake torque (N-m)
0.6 HSSBrDT - Time for HSS-brake to reach full deployment once initiated (sec) [used only when HSSBrMode=1]
DynBrkFi - File containing a mech-gen-torque vs HSS-speed curve for a dynamic brake [CURRENTLY IGNORED] (quoted string)
867.637E6 DTTorSpr - Drivetrain torsional spring (N-m/rad)
6.215E6 DTTorDmp - Drivetrain torsional damper (N-m/(rad/s))
---------------------- SIMPLE INDUCTION GENERATOR ------------------------------
9999.9 SIG_SlPc - Rated generator slip percentage (%) [used only when VSContrl=0 and GenModel=1]
9999.9 SIG_SySp - Synchronous (zero-torque) generator speed (rpm) [used only when VSContrl=0 and GenModel=1]
9999.9 SIG_RtTq - Rated torque (N-m) [used only when VSContrl=0 and GenModel=1]
9999.9 SIG_PORt - Pull-out ratio (Tpullout/Trated) (-) [used only when VSContrl=0 and GenModel=1]
---------------------- THEVENIN-EQUIVALENT INDUCTION GENERATOR -----------------
9999.9 TEC_Freq - Line frequency [50 or 60] (Hz) [used only when VSContrl=0 and GenModel=2]
9998 TEC_NPol - Number of poles [even integer > 0] (-) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_SRes - Stator resistance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_RRes - Rotor resistance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_VLL - Line-to-line RMS voltage (volts) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_SLR - Stator leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_RLR - Rotor leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9 TEC_MR - Magnetizing reactance (ohms) [used only when VSContrl=0 and GenModel=2]
---------------------- PLATFORM ------------------------------------------------
2 PtfmModel - Platform model {0: none, 1: onshore, 2: fixed bottom offshore, 3: floating offshore} (switch)
“NRELOffshrBsline5MW_Platform_Monopile_RF.dat” PtfmFile - Name of file containing platform properties (quoted string) [unused when PtfmModel=0]
---------------------- TOWER ---------------------------------------------------
99 TwrNodes - Number of tower nodes used for analysis (-)
“NRELOffshrBsline5MW_Tower_Monopile_RF.dat” TwrFile - Name of file containing tower properties (quoted string)
---------------------- NACELLE-YAW ---------------------------------------------
9028.32E6 YawSpr - Nacelle-yaw spring constant (N-m/rad)
19.16E6 YawDamp - Nacelle-yaw damping constant (N-m/(rad/s))
0.0 YawNeut - Neutral yaw position–yaw spring force is zero at this yaw (degrees)
---------------------- FURLING -------------------------------------------------
False Furling - Read in additional model properties for furling turbine (flag)
FurlFile - Name of file containing furling properties (quoted string) [unused when Furling=False]
---------------------- ROTOR-TEETER --------------------------------------------
0 TeetMod - Rotor-teeter spring/damper model {0: none, 1: standard, 2: user-defined from routine UserTeet} (switch) [unused for 3 blades]
0.0 TeetDmpP - Rotor-teeter damper position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetDmp - Rotor-teeter damping constant (N-m/(rad/s)) [used only for 2 blades and when TeetMod=1]
0.0 TeetCDmp - Rotor-teeter rate-independent Coulomb-damping moment (N-m) [used only for 2 blades and when TeetMod=1]
0.0 TeetSStP - Rotor-teeter soft-stop position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetHStP - Rotor-teeter hard-stop position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetSSSp - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
0.0 TeetHSSp - Rotor-teeter hard-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
---------------------- TIP-BRAKE -----------------------------------------------
0.0 TBDrConN - Tip-brake drag constant during normal operation, CdArea (m^2)
0.0 TBDrConD - Tip-brake drag constant during fully-deployed operation, CdArea (m^2)
0.0 TpBrDT - Time for tip-brake to reach full deployment once released (sec)
---------------------- BLADE ---------------------------------------------------
“NRELOffshrBsline5MW_Blade.dat” BldFile(1) - Name of file containing properties for blade 1 (quoted string)
“NRELOffshrBsline5MW_Blade.dat” BldFile(2) - Name of file containing properties for blade 2 (quoted string)
“NRELOffshrBsline5MW_Blade.dat” BldFile(3) - Name of file containing properties for blade 3 (quoted string) [unused for 2 blades]
---------------------- AERODYN -------------------------------------------------
“NRELOffshrBsline5MW_AeroDyn.ipt” ADFile - Name of file containing AeroDyn input parameters (quoted string)
---------------------- NOISE ---------------------------------------------------
NoiseFile - Name of file containing aerodynamic noise input parameters (quoted string) [used only when CompNoise=True]
---------------------- ADAMS ---------------------------------------------------
“NRELOffshrBsline5MW_ADAMSSpecific.dat” ADAMSFile - Name of file containing ADAMS-specific input parameters (quoted string) [unused when ADAMSPrep=1]
---------------------- LINEARIZATION CONTROL -----------------------------------
“NRELOffshrBsline5MW_Linear.dat” LinFile - Name of file containing FAST linearization parameters (quoted string) [unused when AnalMode=1]
---------------------- OUTPUT --------------------------------------------------
(omitted)

6

Dear Alessandro,

I don’t see any obvious problems with your input files. (However, there are other input files of importance to the solution.)

The error message gives some suggestions on how to proceed. Have you plotted the Displacement and Velocity 2-Norms to see if there are converging such that TMax would help? Have you tried the other solutions suggested?

Best regards,

7

Hi everybody,
I linearized the offshore 5-MW NREL Baseline Model with water depth 20 m and I have postprocessed the results with mbc3.
The first tower fore-aft and side-to-side frequencies are both around 0.28 Hz. This result seems to be reasonable. However, once I copy and paste the Matlab variables into the Excel file (download/file.php?id=198) in order to properly relate the mode shapes to the natural frequencies vector, something is wrong. In fact, according to the Excel file, the second tower FA frequency would be 0.52 Hz that seems to be wrong. I would expect something smaller than 2.9 Hz (the second tower FA frequency in the onshore case is around) but much higher than 0.52 Hz. Actually in the variable NaturalFrequeciesHz there is a pair of about 2.3 Hz that could be associated with the tower second FA and SS mode shapes, as also confirmed by Figure 6 of the OC3 Report.
Furthermore I don’t understand why the natural frequencies of the blades 1, 2, 3 are so different each other.
Please, see in attachment the input files I used for this linearization. Could you please verify that the input files are correct and kindly explain how to interpret the results of mbc3 correctly?

Many thanks,
Alessandro Giusti
NRELOffshrBsline5MW_Linear.txt (2.1 KB)
5MW_Monopile.txt (20.5 KB)

8

Dear Alessandro,

I don’t see any obvious problems with your input files. (However, there are other input files of importance to the solution.)

It is difficult to identify the problem without seeing your output results. Can you attach your linearization output (*.lin) and Excel files?

Best regards,

9

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)

10

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: Eigenanalysis FAST.

Best regards,

11

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,

12

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,

13

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,

14

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: Fast Linearized Models (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: Tower-top / yaw bearing inertia translational velocity.

Best regards,

15

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

bode.jpg
bode.jpg1153×604 63.7 KB

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,

16

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

17

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,

18

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

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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

19

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,

20

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,