Dear Dr. Jonkman,
Thanks for your reply and help. My problem was solved by getting the implemented file from the forum you introduced. I want to design a pitch controller but I don’t have dynamic equations of the offshore 5 MW wind turbine. I need an equation relating generator speeds (for example its second order derivative equation) to three variables pitch angle, generator and wind speed. What I mean is the equation with perturbed values of these variables. Where can I find them?
Thanks
Best Regards,
Sina
Dear Sina,
If I understand your question correctly, you want the linearized (perturbed) equations of motion of the drivetrain dependent on perturbations of the rotor-collective blade-pitch angle, generator torque, and wind speed. Such a linear form of the equations of motion can be derived from FAST using FAST’s full-system linearization functionality.
Best regards,
Dear Dr. Jonkman,
Thanks for your reply.To illustrate, I want to design a nonlinear controller for the 5 MW offshore wind turbine. I need such an equation:
but the problem is Cp that does not give me a specific equation. It seems one way is linearizing the model in this way:
My question is that since I want to design a nonlinear controller, is there any specific nonlinear equation of this model? If not, how can I linearize the model using Fast 8? Should I use a software or Matlab does it for me?
Thanks
Best Regards,
Sina
Dear Sina,
FAST itself is a nonlinear model, so, there certainly are specific nonlinear equations. But the equations are extensive (and can’t be shown in a forum post), their solutions are numerical (not analytical), and their linearization is done numerically in some areas of the model due to the complexity of the equations.
The linearization functionality of FAST v8 is built into FAST. Linear models can be generated while running FAST in Simulink or with the standalone executable. See the “Linearization” and “Linearization Files” sections of the FAST v8 ReadMe file for more information: wind.nrel.gov/nwtc/docs/README_FAST8.pdf.
Best regards,
Dear Dr. Jonkman,
Thanks a lot for your help that I need in these days to progress my research. Actually, in your document for 5 MW offshore WT, you have already given the perturbation equations and parameters (the linearized drive-train equation)! Now, I have three questions. First, what is the value of the drive-train inertia (I_Drivetrain) mentioned in (nrel.gov/docs/fy09osti/38060.pdf)?
Second, as the FAST in Simulink/Matlab does not have any actuator dynamic, I need to add a dynamic for the pitch actuator. What is the response time constant of pitch angle (actuator)? In the mentioned file for 5MW offshore, it mentions (Equivalent Blade-Pitch-Actuator Linear-Spring Constant=971,350,000N•m/rad and Equivalent Blade-Pitch-Actuator Linear-Damping Constant=206,000N•m/rad/s). I need an a dynamic equation of the pitch actuator like this:
Last but not least, how and where can I create a fault in pitch actuator in FAST/Simulink?
Thanks
Best Regards,
Sina
Dear Sina,
The total drivetrain (rotor + generator) inertia of the NREL 5-MW baseline wind turbine is documented in the following forum topic: What's the exact meaning of HubIner? - #8 by Jason.Jonkman.
The equivalent blade-pitch-actuator spring and damping constants stated result in a second-order transfer function (with a natural frequency and damping ratio) rather than the first-order form you are showing. Thus, there is no true equivalency. That said, the frequency of the second-order actuator is very high–as if the actuator does not exist. This would be equivalent to a very low value of tau_theta in your first-order transfer function.
Pitch faults are set by the override pitch maneuvers defined within the ServoDyn module.
Best regards,
Dear Dr. Jonkman,
Thank you so much for your prompt response and for clarifying the issue.
Best Regards,
Sina