Dear Cheng,
FAST is a nonlinear model; the linearization functionality only linearizes the equations of motion about a specific operating condition. What type of “nonlinear” model are you seeking? The nonlinear FAST equations of motion cannot be written out easily.
Yes, the baseline controller for the NREL 5-MW wind turbine uses a constant power torque-control law in Region 3. However, the torque is calculated by the low-pass time-filtered generator speed whereas the actual power is calculated using the unfiltered speed, so, there may be small deviations from the rated power as a result.
Best regards,
Dear Jason,
Thank you!
I designed a controller for floating wind turbine in region 3(above rated), and I made some simulation on the FAST.
I found that when I increase the wind speed. the rotor speed is increased, but the platform pitch is decreased. Is it normal? If yes, what’s the relation between the rotor speed and platform pitch? Is there any dynamic equation between the rotor speed and platform pitch in region 3?
Best regards,
Cheng
Dear Cheng,
Yes, in an active blade pitch-to-feather controller, the mean rotor thrust peaks at rated and decreases for higher wind speeds. See e.g. the following paper for more information: nrel.gov/docs/fy08osti/42589.pdf.
Best regards,
Dear Jason,
Yes, but the rotor speed is increased.
Does it mean the rotor aerodynamic torque increases, the rotor thrust force decreases?
For floating offshore wind turbines(FOWT), the control objectives are regulating power to rated value(e.g. 5MW) and regulating the platform pitch. What the meaning of regulating platform pitch? For instance, if I linearized the FAST model with a constant wind speed of 14m/s, a rotor speed of 12.1 rpm, then I got a stable state with blade pitch equals 8.6deg, platform pitch equals 1.39deg. So if wind speed changed to a 15m/s stochastic wind, does it mean we need to actuate the blade pitch to regulate the platform pitch to 1.39deg, or regulate it to 0deg?
Dear Cheng,
I would normally expect a Region 3 controller to regulate rotor speed to the rated speed. So, I would not expect the rotor speed to increase in Region 3 (except for oscillations about the rated speed). But you can always run various steady-state simulations to see how the rotor thrust varies with rotor speed, pitch angle, wind speed, etc.
I would say it is not common for the FOWT controller to regulate platform pitch. Of course, you’d likely want to design the FOWT controller so as to prevent it from exciting the platform pitch or to mitigate problematic interactions between platform pitch and power regulation.
Best regards,
Dear Jason,
Yes, the controller does not work well.
As far as I know, a lot of papers’ control objective including reducing platform pitch, the control problem of FOWT is the platform pitch motion.
I can’t understand you said it is not common for the FOWT controller to regulate platform pitch. Could you please explain to me more specific?
Best regards,
Cheng
Dear Cheng,
Yes, the FOWT controller may have on objective of adding damping (or at least not reducing damping) of the platform-pitch mode, but I would not guess it would be common to use the FOWT controller to change the target (mean) value of the platform-pitch angle. If the target (mean) value of the platform-pitch angle is not desirable for a given steady-state thrust, it would be better to redesign the platform than to attempt to correct that with FOWT control.
Best regards,
Dear Jason,
I’m not sure I understand well.
If my controller is successfully adding the damping of platform pitch. Does it mean the platform pitch acceleration is decreased?
For example, suppose that,
1.in a condition of 14m/s stochastic wind, apply a controller makes rotor speed at rated, and make the platform stable at constant value 1deg.
2in a condition of 16m/s stochastic wind, apply a controller makes rotor speed at rated, but make the platform stable at constant value 2deg.
Could I say the controller performance well? (If yes, let the platform pitch acceleration to aero can be as a control objective)
I’m really stuck in this problem, I still didn’t clear about the control objectives of FOWT, thank you for your help.
Best regards,
Cheng
Dear Cheng,
Adding damping through FOWT control should reduce the oscillations of platform pitch about the mean, not the mean value itself. Changing the mean platform-pitch angle through FOWT control is what I questioned.
Regarding your example. I would expect the mean platform-pitch angle to decrease with increasing wind speed in Region 3 due to the drop in mean rotor thrust with pitch-to-feather control. Of course the oscillations about the mean may increase with wind speed due to the increasing variation in wind speed and associated severity of sea states.
Best regards,
Dear Jason,
Yes, my example has something wrong, the platform pitch should decrease with increasing wind speed in region 3.
What I want to express is just like what you said, in different wind condition, the objective is to reduce the oscillations of platform pitch about the mean, rather than mean value itself.
Your explanation is very clear, many thanks!
So, in order to reduce the oscillation, I can design a controller that force the acceleration of platform pitch to zero.
Best regards,
Cheng
Dear Cheng,
I wouldn’t say that you could design a controller to force the acceleration of platform pitch to zero, but you could design a controller to reduce the oscillation in acceleration.
Best regards,
Dear Jason,
I have some questions concerning the FAST.
I designed a pitch controller and applied it on FAST v7 with 2 activated DOFs (GenDOF and PtfmPDOF), it works well on the SIMULINK. But when I activated ALL DOFs on FAST, the SIMULINK cannot run. The errors are as the figure following.
Could you tell me where the problem is? Thank you.
Best regards,
Cheng
Dear Cheng.Zhang,
Warnings regarding a “small angle approximation violation,” warnings regarding “supersonic blades,” a simulation crash, or very large deflections that occur in the time series near the start of a simulation are good signs of a numerical instability. Without knowing more about your simulation settings, it’s hard to know that what the problem is. But these issues have been discussed many times on this forum. I would use “Search…” in the upper-right corner to see how others have resolved similar issues in the past.
Best regards,
Dear Jason,
Thank you for your response.
Could you tell me that when activating all the DOFs in FAST, is there a big impact on the controller performance?
And, can the blade pitch angle be negative? Are there saturations on the blade pitch angle?
Best regards,
Cheng
Dear Cheng,
Yes, the structural DOFs can impact the performance of the controller.
The pitch angle can be negative, depending on definition of aerodynamic twist (the sum of the pitch + twist angles equals the angle between the chord and rotor plane). The twist is often defined such that “optimal” pitch is near zero degrees. It is common for the minimum blade-pitch angle to be saturated at the optimal pitch.
Best regards,
Dear Jason,
Recently, I met a problem about linearization.
First, I used CBP control,
and I used 2 DOFs(GenDOF, PtfmPDOF) linearized model before.
Now, I want to activate more DOFs and carry out a more precise linear model by FAST.
But, I found that when activating the DOFs on blades (e.g. FlapDOF1, EdgeDOF…), the linear model’s states on blades can not coincident with these on the FAST model.
I knew if I use IBP, I should use MBC3 to transfer the rotating states on no rotating frame, but in my case, I used CBP as the input.
So my question is, how to linearize a model from FAST with FlapDOF1 and EdgeDOF DOFs enabled while using CBP as input.
Could you tell me how to deal with this problem?
Thank you!
Best regards,
Cheng
Dear Cheng,
Yes, you can enable the blade flap and edge DOFs together with a collective-blade pitch control input. I’m not sure what problem you are running into, but in this case, the multi-blade-coordinate transformation will apply to the blade DOFs (which are in the rotating frame), but not the collective-blade control input (which is in the fixed frame).
Best regards,
Dear Jason,
Thank you for your fast reply.
I’m not sure but do you think whether it’s right like this:
Apply MBC to blade DOFs, but not the collective-blade control input. That is to say, the state space model is like this,
delta_Xdot_nr = A_nr delta_X_nr + Bdelta_u
delta_Y_nr = C_nrdelta_X _nr+ Ddelta_u
the subscript nr means use mbc3 to transfer the AvgAMat to MBC_AvgA; AvgCMat to MBC_AvgC, and mbc3 do not work on matrix B and D.
Best regards,
Cheng
Dear Cheng,
The multi-blade-coordinate (MBC) transformation applies to any states, state derivatives, inputs, or outputs that are in the rotating frame. Because you have states in the rotating frame (and hence state derivatives in the rotating frame), linear matrix B will be effected by MBC (at least by premultiplication on the left-hand side). You haven’t said what your outputs are, but if you have outputs in the rotating frame, linear matrix D will also be effected by MBC.
Best regards,
Dear Jason,
First, the outputs including rotating DOFs.
I agree that xdot and x should apply MBC, but the input u is CBP control command, it is in no rotating frame.
What I confused is how to apply MBC on state alone, and does not affect the input.
Do you think it’s right to apply MBC to get A_nr=MBC_AvgA, C_nr=MBC_AvgC and leave B = AvgBMat, D = AvgDMat?
Thank you!
Best regards,
Cheng
