Validation of Linear System

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Jason.Jonkman
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Re: Validation of Linear System

Dear Syed,

Above rated wind speed, I would expect the power, torque, and thrust to drop with an increase in blade-pitch angle. The drop in torque should lead to drop in rotor speed.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Syed.Muzaher
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Location: Germany

Re: Validation of Linear System

Dear Jason,
Thank you for answering my previous questions.

I agree to what you have said. But Ideally both the linear and nonlinear systems should behave somewhat similar.

I want to validate my linear system with nonlinear system.
For this reason, when i see the behavior of nonlinear system. Whether i apply step in wind speed or blade pitch angle, the torque is constant. To achieve this the nonlinear system only make adjustments in rotor speed and generator speed.

But for the linear system when i apply the unit step wind in the input, the torque increases and linear system make adjustments accordingly in rotor speed and generator speed. vice versa if i apply the unit step in blade pitch angle.

so the question in my mind is that why the systems are behaving differently in this regard i.e. for nonlinear case torque is constant as i am applying constant torque to the system. but the linear system's torque is changing after applying unit step in blade pitch or wind speed, Ideally i am apply constant torque for the linear system as well, why is this so?

can you shed some light on the issue? or correct me if i am wrong.

Best regards
Syed Shah
Best regards
Syed Shah

Jason.Jonkman
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Location: Boulder, CO
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Re: Validation of Linear System

Dear Syed,

I agree that the linear and nonlinear system should have similar behavior for small perturbations about the operating point for models that are set up the same. Do you have the same torque control model enabled for your linear and nonlinear system? I would have to see the behavior you are describing to better understand what is happening and why you are not seeing the behavior you expect.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Syed.Muzaher
Posts: 51
Joined: Mon Aug 28, 2017 4:17 pm
Location: Germany

Re: Validation of Linear System

Dear Jason,

Please see the attachment for the comparison of above mentioned outputs.

For linearization, i have enabled "simple variable-speed torque control" in which I define rated generator torque and rated generator speed.

As far as the torque control model is concerned, I have tried 2 torque control models, but the problem discussed before is still there.

1: Same torque control model is enabled for both - linear and nonlinear - systems. (simple variable-speed torque control)

2: For linearization, i have enabled "simple variable-speed torque control" and for nonlinear system, i have enabled "user-defined variable-speed control mode from Simulink" in which i apply the rated generator torque to the nonlinear system.

In my opinion, (perhaps) FAST has implemented some sort of closed-loop control during the linearization procedure due to which the generator torque is dependent on generator speed. I have looked at the averaged system of matrices before and after applying MBC transform and verified that the generator torque output in the C matrix depends on the generator speed state alone. How to solve this issue?

Best regards
Syed Shah
Attachments
Comparison of SrvD GenTq ED RotSpeed ED GenSpeed.zip
Best regards
Syed Shah

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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Re: Validation of Linear System

Dear Syed,

• Your attachment only shows the case where the nonlinear system has constant torque from (2). What does the nonlinear solution look like when it has the simple variable-speed torque control from (1)?
• What are you settings for the simple variable-speed torque control i.e. what are VS_RtGnSp, VS_RtTq, VS_Rgn2K, and VS_SlPc?
• No, FAST has not implemented a closed-loop control during the linearization procedure. Actually, the simple variable-speed torque controller is a very simple algebraic equation relating the generator torque to the generator speed, so, what you describe regarding the linearized C matrix is what I would expect in this case.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Syed.Muzaher
Posts: 51
Joined: Mon Aug 28, 2017 4:17 pm
Location: Germany

Re: Validation of Linear System

Dear Jason,

Following are the answer to you questions.

• Please see the attachment for the nonlinear solution when simple variable-speed torque control is enabled ( from (1))
• Settings for the simple variable-speed torque control:
VS_RtGnSp = 480
VS_RtTq = 200000
VS_Rgn2K = 0.2
VS_SlPc = 1

With Regards
Syed Shah
Attachments
Comparison of SrvD GenTq ED RotSpeed ED GenSpeed_simple variable-speed torque control.zip
1: simple variable-speed torque control
Best regards
Syed Shah

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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Re: Validation of Linear System

Dear Syed,

Ah, now I see what is going on. You've linearized the simple variable-speed torque controller at the most nonlinear part of the curve i.e. at the "knee" of the curve transitioning between Regions 2.5 and 3. The linear model will not compare well to the nonlinear model at this point because the linear model cannot handle the nonlinearities of the "knee".

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Syed.Muzaher
Posts: 51
Joined: Mon Aug 28, 2017 4:17 pm
Location: Germany

Re: Validation of Linear System

Dear Jason,

so what you are suggesting me is that i should wait a little more before applying linearization? How to avoid nonlinearities of the "knee"? I want to do linearization in region 3.

With Regards
Syed Shah
Best regards
Syed Shah

Jason.Jonkman
Posts: 4005
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Validation of Linear System

Dear Syed,

It is common to linearize in Region 3 with a constant torque i.e. change VS_RtGnSp to be a bit below the actual rated generator speed such that when you linearize the change in generator torque with speed is zero. In this case, the linear model should match well to your case (2), but not your case (1). It will not be possible for your linear model to match case (1) because of the strong nonlinearities involved in case (1).

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Syed.Muzaher
Posts: 51
Joined: Mon Aug 28, 2017 4:17 pm
Location: Germany

Re: Validation of Linear System

Dear Jason,

Thank you for you help. i solved the issue with your advice.

With Regards
Syed Shah
Best regards
Syed Shah