Question about the generator torque- and pitch controller

Wind & Water Computer-Aided Engineering Software Tools
1

Dear Jason,

currently I do my project work with the FAST Simulink Interface. The task is to design a generator torque- and a collective pitch controller for the NREL5MW Reference Wind turbine in Simulink.

In the Definition of the 5MW- Reference Wind Turbine there is no value for the transitional generator speed between region 2 and 2 1/2. In the Source Code for the Control System DLL you calculated the transitional generator speed between region 2 an 2 1/2 with the following equation:
VS_TrGnSp = ( VS_Slope25 - SQRT( VS_Slope25*( VS_Slope25 - 4.0VS_Rgn2KVS_SySp ) ) )/( 2.0*VS_Rgn2K )
Please can you explain where this equation comes from?

After implementing the generator torque controller in Simulink, it works fine. The most problems I have with the collective pitch controller.
When I use the Kp (Kp=0.01882681 s) and the Ki (Ki=0.008068634) values from the Definition of the 5MW- Reference Wind the pitch controller begins to oscillate.
The plot shows the oscillating pitch controller for a constant wind (WindVxi=11.4m/s) and a inetial rotor speed of 12.1 rpm.
I don’t know why, because I didn’t change the masses or inertia for the NREL5MW Windturbine.
So the Kp and the Ki values and the pitch sensitivity dP/d(theta) should be the same.

Thanks for your help,
Lars
untitled.png

2

Dear Lars,

That equation comes from solving for the point where the curve for the Region 2 control law (k*omega^2) intersects the curve for the Region 2.5 control law (linear). I’m sure you can rederive it with a bit of algebra.

I’m not sure why your Simulink model shows a different response. Here are a couple questions:
*Have you implemented the low-pass filter on the generator speed?
*Are you using the correct units for blade pitch (the gains you report assume blade pitch is in radians, not degrees)?

Best regards,

3

Dear Jason,

thank you for your fast reply. I have implemented the low- pass filter, which is described in the Defintion NREL5MW reference.
The incoming speed error for the pitch controller is in rad/s and I hope this is right.
These are the used values for the pitch controller, which I have defined in the Simsetup file.

%Pitch
PC_RefSpd = 122.9096; % (rad/s) Reference HSS speed for pitch
PC_MaxPit = pi/2; % (rad) Maximum pitch limit
PC_MinPit = 0; % (rad) Minimum pitch limit
PC_MaxRat = 8pi/180; % (rad) Maximum pitch rate limit (for NREL5MW wind turbine is the Maximum pitch rate limit equal to the minimum pitch rate)
PC_GainS = 6pi/180; % (rad) Is the blade- pitch angle at which the sensitivity has doubled
PC_KP = 0.01882681; % - Proportional Gain
PC_KI = 0.008068634; % (s) Integration Gain

Mabye there is a mistake in the units.
regards,
Lars

Pitch.png
Pitch.png834×236 3.54 KB

4

Dear Lars,

I don’t see any obvious problems with your Simulink model. (Please note the units of PC_KP should be “s” and units of PC_KI should be “-” – you have these switched in your comments, but these are comments, so, won’t effect the solution.)

I don’t know where the problem is. I suggest you debug what your Simulink model is giving you versus what the DLL is computing in a very step-by-step process to identify the difference(s).

Best regards,

5

Dear Jason,

I found the problem for the oszillating pitch controller. You defined two conditions for Region 3 of the generator torque controller.
The first condition is that the filtered rotor speed is bigger than 1161.963 rpm and the second condition is that the pitch is bigger than 1°.
At first I neglected the second condition. The result was a oszillating pitch.
After implementing the second condition in the generator torque controller the pitch controller works without oszillation.

My last question regarding the pitch controller design. I compared your pitch controller
design with the design technique which is explained in the technical report “Advanced Control Design for Wind Turbines”.
In the technical report they calculated K_I and K_P for the CART wind turbine over the following equations (In the technical report equation 3.10):

K_I = (-omega^2*(1-B*K_D))/B

K _P= -A/B-(2Deltaomega(1-B*K_D))/B

The values for A and B they got from a linearization.

When I do the lineariziation for the NREL5MW reference wind turbine with a constant wind of 11.4 m/s and only one DOF (GenDOF)
I get the following values for A and B:

A=-3.823E-01 and B=-3.278E-01.

The values for K_I and K_P is calculted over equation 3.10 to:
K_I = 1.0982
and
K_P = 1.396
I used for omega 0.6 , delta 0.7 and K_D=0.

This is the linearization input file:

---------------------- 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)
3 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]
0.0001 DispTol - Convergence tolerance for the 2-norm of displacements in the periodic steady state calculation (rad ) [used only when CalcStdy=True]
0.001 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] (-)
4 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] (-)
1 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]

Is there a mistake in the linearization file or is this technique not applicable for the calculation of the K_I and K_P values for the NREL5MW reference wind turbine?

Thanks for your help and regards
Lars

6

Dear Lars,

I’m glad to hear that you fixed the problem with your Simulink model.

I think you are getting different gains between those published for the NREL 5-MW turbine and those derived following the procedure described in the “Advanced Control Design for Wind Turbines” technical report for two reasons:

*The NREL 5-MW control gains are based on generator speed error whereas the “Advanced Control Design for Wind Turbines” technical report is based on rotor speed error. This leads to a factor of the gearbox ratio (97:1 for the NREL 5-MW turbine) between the gains using the two methods. With this factor, your results are within about 20% of the published values for the NREL 5-MW turbine.
*The remaining differences are likely the result of the fact that the gains for the NREL 5-MW turbine were derived using a customized version of FAST that employed a frozen wake assumption during linearization, which is described more in the following forum topic: Gain Scheduling.

I hope that helps.

Best regards,

7

Dear Jason,

thanks for your fast reply. Now I can finish the controller design in Simulink :slight_smile:.

Best regards,

Lars