The problem about Linearization result under parking situation

Dear Bonnie.Jonkman
I am now doing linearization analysis of 10MW turbine and I have some problems in the analysis.
(1) According to the manual, when turbine is parking the linearization result (. Lin file) can be processed and analyzed by CCE. M in matlab. At this time, I found that for every degree of freedom of blade, such as 1st flapwise bending mode, I would get three results, such as three different avgdampungratio results. So, whether these three data represent the linearization results of three different blades or the results of three different modes as MBC’s result.
(2) I found that in papers, when the turbine is shut down, there is only one Damping ratio value for a degree of freedom. Then which one of the three results under the same degree of freedom obtained through CCE. M processing should be used.

Thank you

JiYuan.Men

Dear JiYuan.Men,

Post-processing of the FAST linearization analysis results in coupled modes of the full wind turbine system, i.e., how the blades couple with the drivetrain, and support structure (depending on which degrees of freedom (DOFs) are enabled). The blades may couple with the drivetrain and support structure differently depending on the orientation of the rotor (azimuth angle). An “N” DOF system will result in “N” modes.

If all DOFs except the blade DOFs are disabled and gravity set zero, I would expect that each mode would show up in sets of three for a three-bladed rotor because there would be no coupling between the blades; otherwise, I would expect some differences in modes, natural frequencies, and damping.

Best regards,

Dear Bonnie.Jonkman
Thank you for your reply. According to your explanation, can I understand that three results under the same degree of freedom are caused by different positions of three blades. However, in some articles (also used FAST), there is only one result under a degree of freedom (i.e. flapwise bending mode) in parking state, which makes me a little confused.

Thank you

JiYuan. Men

Dear JiYuan.Men,

If there is only one value reported for a given blade mode, either the value is reported for an isolated blade (not coupled to the rest of the turbine), or the values for the three blades are nearly identical.

Best regards,

Dear Bonnie.Jonkman

JiYuan.Men

Dear Bonnie.Jonkman
Recently, I was dealing with the linearization results of 10MW turbine under parking condition. I find that the results of blades and tower get by cce.m, for example AvgDampedFrequency, AvgDampingRatio and so on, were same as the result get from mbc3.m. (the value of AvgDampedFrequency was equal to the MBC_DampedFrequency). So I have some question:
(1) Whether the three results of same blade degree of freedom get by cce.m represent the result of cone, sine and cosine just like results get form mbc3.m ?
(2) If the first suppose is right. How can I get the result of real blades which is based on blade coordinate system .

Thank you

JiYuan.Men

Dear JiYuan.Men,

For a parked or idling (not rotating) wind turbine, the eigenvalues (natural frequencies and damping) will not depend on whether the multi-blade coordinate (MBC) transformation has been applied nor whether the results are azimuth averaged before performing the eigenanalysis.

(1) cce does not apply the MBC transformation. The DOFs will be in terms of individual blades if you have not previously applied the MBC transformation or in terms of collective, sine, and cosine if you’ve applied the MBC transformation before running cce.
(2) To get the results in terms of individual blades, then don’t apply the MBC transformation. The FAST linearization output is in terms of individual blades, so, don’t apply the MBC transformation if that is what you want.

Best regards,

Dear Jason.Jonkman
Thank you for your help! But I still have some problem. The picture I upload was the 1st edge response of three blades under parking condition with the steady wind speed at 55m/s and the vertical incidence angle was 30 degree. It shows that the response of three blades was divergence. I did 40 times linearization during 200s-210s and used cce.m to get the Damping result and the result shown in the table I uploaded. Then I find that only the Damping Ratio of Blade 2 was negative and it seems that the eigenvalue result was not match with the time response. If the outputs of cce.m was in terms of individual blades why the Damping ration of other two blades was Positive?

Thank you

JiYuan.Men

Dear JiYuan.Men,

My guess is the operating point you are linearizing about is not identical to the condition you have in the time domain (e.g., it may be difficult to set the operating point with the three blades displaced identically with the mean of the time-domain response in the linearization area). Nevertheless, your linearization is showing a negative damping, and your response is showing an instability, so, there is at least some level of consistency between the linearized and time-domain solutions.

Best regards,

Dear Jason.Jonkman
Thank you very much for solving my question again. So How the FAST calculate the Operation point of every DOFs?

Thank you

JiYuan.Men

Dear JiYuan,

I’m not sure which version of FAST you are using. In FAST v7, you could linearize about initial conditions or calculate an operating point via a trim calculation. In FAST v8 and OpenFAST, you can linearize at any point in time. We are working to add a trim calculation in OpenFAST, which we hope to release soon. How have you defined the operating point?

Best regards,

Dear Jason.Jonkman

Sorry for not responding in time and thank you very much for your reply, which makes me find that I misunderstand the definition of operation point at before. From your reply, I understand operation point like this：In Open Fast, the Operation Points of different DOFs refers to the response values corresponding to the time point performing the linearization. For example, if the linearization is performed at 500s, the Operation Point of ED 1st Flapwise of Blade 1 is the response value of 1st flap at 500s. If my understanding is correct, I have the following questions:
(1) The A matrix get by linearization contains the equivalent damping C. Is this the average value of the equivalent damping obtained at each mesh of the blade?
(2) I have learned that the linearization result of Open Fast is expanded to the first derivative term. Considering that the oscillation of amplitude of motion response and load response is dramatically when blade flutter, whether this linearization of FAST can meet the accuracy？Is this the reason why there is a difference between the damping ratio get by linearization and the time history response？

Thank you

JiYuan.Men

Dear JiYuan.Men,

I’m not sure I fully understand your questions, but I’ll try to answer them:

Regarding (1), the A matrix does not contain any “averages”, unless you’ve time-averaged or azimuth-averaged it by post-processing multiple instances of the matrix. The A matrix describes in linear form how the state derivatives are related to the states. For a standard linear second-order system of the form:

Mqdd + Cqd + K*q = 0

with the first-order state:

dx = { dq, dqd }^T

then the first-order form is:

dxd = A*dx

with:

A = [ 0, I; -[M^1]*K, -[M^-1]*C ]

Here “d” after the variable represents the first time derivative (and “dd” represents the second time derivative) and the “d” before the variable represents a perturbation about an operating point, e.g., q = q_op + dq.

Regarding (2), the linear system can only capture linear effects. For flutter, it is presumed you are using BeamDyn (to capture the blade-torsion DOF), the linear system can identify that negative damping of flutter is present, but the linear system cannot well predict the nonlinear limit-state response after flutter. This is generally OK because you want to identify flutter so as to change the design or controller to eliminate flutter, rather than see if the system can survive flutter.

Best regards,

Dear Dr. Jason Jonkman

Sorry to bother you!
I’m using FAST to do the linearization analysis to calculate the eigenfrequency of each Dof, and the reference wind turbine is NREL 5-MW Onshore WT. This is the first time that I used FASTV8 to do the linearization analysis. During the analysis, I faced so many problems which are showed below:

1. I’m using test 18 to do the analysis. When I enabled the linearization module in .fst file, they can output Test18.01.lin file and Test 18.02.lin files. I have donwloaded the MBC toolbox, and there is an example test which called test01.lin. The content of test18.01.lin and test01.lin file are quite different.
2. I used the test18.01.lin to do post-process to get the eigenvalue of each dof by using MBC and It worked finally. I checked the output results after running cce.m program,I get the average natural frequency results as shown below. However, I don’t know what each data represents. Can you help me?

Sorry to bother you again! I would be appericate if you can help me!

Best regard
Lixian Zhang

Dear Lixian,

Regarding 1), the 01, 02,etc. in the linearization output file names; these refer to the LinTimes you’ve set in the FAST primary input file (01 is LinTimes(1), 02 is LinTimes(2), etc.). If the rotor is stationary, you should only need to linearize once (NLinTimes = 1). If the rotor is spinning, I would normally recommend linearizing a number of times around a full azimuth rotation, e.g., NLinTimes = 36 with a linearization every 10-degrees of azimuth rotation (where LinTimes would depend on the rotor speed).

Regarding 2), there are several topics on this forum where the interpretation of the FAST linearization output is explained, e.g. see: http://forums.nrel.gov/t/campbell-diagram-mbc3-output-relation/687/9.

Best regards,

Dear Dr.Jason