# Linearized model

Hello all,
I am going to compare the open loop response of linear and nonlinear model, but their results were different! I assumed just generator speed as the DOF for the NREL 5MW wind turbine and linearized the model, the linearization parameters are set as followed:

---------------------- FAST LINEARIZATION CONTROL FILE -------------------------
NREL 5.0 MW offshore baseline linearization input properties.
---------------------- PERIODIC STEADY STATE SOLUTION --------------------------
True CalcStdy - Calculate periodic steady state condition {False: linearize about initial conditions} (flag)
2 TrimCase - Trim case {1: find nacelle yaw, 2: find generator torque, 3: find collective blade pitch} (switch) [used only when CalcStdy=True and GenDOF=True]
0.01 DispTol - Convergence tolerance for the 2-norm of displacements in the periodic steady state calculation (rad ) [used only when CalcStdy=True]
0.01 VelTol - Convergence tolerance for the 2-norm of velocities in the periodic steady state calculation (rad/s) [used only when CalcStdy=True]
---------------------- MODEL LINEARIZATION -------------------------------------
36 NAzimStep - Number of equally-spaced azimuth steps in periodic linearized model (-)
1 MdlOrder - Order of output linearized model {1: 1st order A, B, Bd, C, D, Dd; 2: 2nd order M, C, K, F, Fd, VelC, DspC, D, Dd} (switch)
---------------------- INPUTS AND DISTURBANCES ---------------------------------
1 NInputs - Number of control inputs [0 (none) or 1 to 4+NumBl] (-)
3 CntrlInpt - List of control inputs [1 to NInputs] {1: nacelle yaw angle, 2: nacelle yaw rate, 3: generator torque, 4: collective blade pitch, 5: individual pitch of blade 1, 6: individual pitch of blade 2, 7: individual pitch of blade 3 [unavailable for 2-bladed turbines]} (-) [unused if NInputs=0]
1 NDisturbs - Number of wind disturbances [0 (none) or 1 to 7] (-)
2 Disturbnc - List of input wind disturbances [1 to NDisturbs] {1: horizontal hub-height wind speed, 2: horizontal wind direction, 3: vertical wind speed, 4: horizontal wind shear, 5: vertical power law wind shear, 6: linear vertical wind shear, 7: horizontal hub-height wind gust} (-) [unused if NDisturbs=0]

The input to this model is generator torque of 10000Nm and the disturbance is v=8 m/s. I did the simulation for both linearized and nonlinear model but the results were different and the steady state generator speed for nonlinear model was arouund 1400 rpm and for linearized one was around 2000 rpm. (All the simulation were done by MATLAB simulink)
The generator speed response for linearized and nonlinear model and also simulation box for linearized model are attached.
Thank you so much

Hi,
I could figured it out. My mistake was that the input to the linearized model should be the deviation from the equilibrium point, but I was wrongly inputting the absolute values of wind speed and generator torque.
Does anyone know the difference between different values of VSContrl when we are linearizing the wind turbine model?
Thank you
Omid

Dear Omid,