Dear Dr.Jonkman,

I’m writing in hope that you could help with an issue I’m encountering during the linearization of the NREL 5MW wind turbine. I will first outline the details of the procedure I followed for the linearization, then I will present the problems that I encountered.

-I used OpenFAST with the input file attached below to linearize the NREL 5MW Onshore turbine in Region 3 about an 18 m/s wind speed.

-In the ServoDyn input file, the following setting were used: PCMode=0; VSContrl=1; VS_RtTq=43093.55; VS_RtGnSp=VS_Rgn2K=VS_Rgn2K=999e-9.

-3 DOFs were activated: GenDOF, FlapDOF1 (first flapwise mode), and TwFADOF1 (first fore-aft mode); that is a total of 10 continuous states.

-Linearization was performed successfully at 36 azimuth steps using pitch trimming, it resulted in a steady-state pitch angle of 14.77 degrees for a nominal rotor speed of 12.1 rpm.

-The resulting linearization output files were then loaded into MATLAB by defining a FileNames cell array containing the names of the 36 files then running the GetMats_f8 script.

-The MBC transformation was performed afterwards, and the resulting LTI A,B,C,D matrices were azimuth averaged using the function mean(X,3), i.e. averaging over 3rd dimension.

-The generator azimuth state was then eliminated from the state-space model by removing the corresponding rows and columns.

-A Simulink model was then built with the state-space matrices and the response of the system was simulated for a 1 degree collective pitch angle disturbance introduced after 10s (with all other inputs set to zero).

-The response was compared to that of the non-linear OpenFAST model for the same operating conditions and disturbance, the response is attached below.

-For the linear Simulink model, the Falpwise bending moment response (attached below) was obtained by performing the inverse MBC transform on the 0,C, and S outputs of the model.

The encountered issues are the following:

-Instead of the conventional 9 inputs that the linearized OpenFAST model should expect, the output linearization files that I obtained stated that 66 inputs are expected, with input 10 through 66 all called “AD User property on blade i, node i”. The corresponding columns in the state-space matrices are however all zeros.

-After applying the MBC transform and azimuth-averaging, the columns of the A and C matrices corresponding to the generator azimuth state are not all zero as expected.

-Although the linear and non-linear models agree for the rotor speed and tower foreaft responses, they are completely different for the flapwise moment.

Attached below are all the relevant documents.

I’m sorry for the lengthy post, I wanted to make sure that everything is clear. I appreciate the help and am extremely thankful.