A Query Regarding the Calculation of Rotor Inertia for the 5MW Reference Wind Turbine in FAST v8

Wind & Water Rotor Aerodynamics
1

Hi All

I am studying the statistical properties of rotor speed for a wind turbine using FAST v8 simulations (as OpenFAST does not run smoothly on my computer, I use FAST v8 for wind turbine modeling). However, I have encountered a perplexing issue: For the 5MW reference wind turbine, how are the rotor inertia, the generator inertia relative to the high-speed shaft, and the drivetrain inertia cast to the low-speed shaft calculated in FAST v8?

  1. On pages 20-21 of Ref. 1, the following Equation 1 is provided:

    Snipaste_2024-06-20_19-43-51
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    Snipaste_2024-06-20_23-24-50
    Snipaste_2024-06-20_23-24-50946×180 72.6 KB

  2. In FAST v8, I simulated Test 18 (NREL 5 MW - Land-based wind turbine) with the following modifications:
    The flexibility of the drivetrain is ignored

    Snipaste_2024-06-20_22-49-44
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  3. Since the torsional flexibility of the drivetrain is neglected, and assuming the gearbox has no frictional losses (page 14, Ref. 1), the rotor dynamics simulation results in FAST should conform to Equation 1. Therefore, the physical quantities in the Equation 1 correspond to the simulation results in FAST.

    T_aero (in Equation 1) = RotTorq (in FAST)
    T_gen = GenTq
    N_gear = 97 [1]
    Omega = RotSpeed•2•pi/60
    t = Time

    dOmega/dt is calculated in MATLAB using the following code:

    dOmega_dt = gradient(RotSpeed•2•pi/60, Time)

  4. From the FAST v8 simulation results, the relationship between RotTorq - N_gear•GenTq and dOmega/dt is depicted in the attached figure.

    untitled_2
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    This suggests that in Equation 1,
    I_rotor + N_gear^2•I_gen = I_drivetrain = 5025•1000 (kg•m2) = 5.025•10^6 (kg•m2)

  5. However, my calculation of the moment of inertia of the three blades about the rotor axis is significantly higher, approximately 38.7•10^6 (kg•m^2), which contradicts the result in point 4. I am unsure how the value of 5.025•10^6 (kg•m^2) is derived. I am confused. I have two suspicions:The first is the value of 5.025•10^6 (kg•m^2) is obtained by multiplying the generator inertia about the high-speed shaft (534.116 kg•m^2) by N_gear^2(97^2). However, this seems to exclude the moment of inertia of the blades relative to the rotor axis.

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    The second is the value of 5.025•10^6 (kg•m^2) is given on page 36 of Ref. 2, but the same document also states, “For comparison; the rotor rotational inertia is 36.34 × 10^6 kg•m^2”. Why doesn’t FAST use this value for I_rotor?

    Please forgive me for any errors in my English writing. I hope someone can clarify my confusion, point out errors in my calculations, or identify any logical or knowledge gaps in my understanding. Thank you!

    Best regards!

    Yangyudong.Liu

[1] Jonkman, J. M. , Butterfield, S. , Musial, W. , & Scott, G. . (2009). Definition of a 5mw reference wind turbine for offshore system development. office of scientific & technical information.
[2] Lindenburg, C. , & Winkelaar, D. . (2003). Aero-elastic modelling of the dowec 6 mw pre-design in phatas.

2

Dear @Yangyudong.Liu,

Just a few comments:

  • The rotor inertia as of the NREL 5-MW baseline wind turbine as computed by ElastoDyn and reported in its summary (.ED.sum) file is 38.7 * 10^6 kg * m^2. So, I_Drivetrain from your Eq. 1 is 43.8 * 10^6 kg * m^2.
  • ElastoDyn output RotTorq is not the aerodynamic torque; rather, RotTorq is the reaction torque within the low-speed shaft, that can differ from T_Aero when the rotor is accelerating or decelerating. T_Aero is available in OpenFAST via AeroDyn v15 output RtAeroMxh. This topic has been discussed in other forum topics, e.g., see: Resistant moment of the rotor and of the electric generator.
  • I’m not sure I understand why you can’t run OpenFAST; can you clarify?

Best regards,

3

Dear @Jason.Jonkman

I apologize for the delay in responding.

Thank you for your reply, it was very helpful. I found out that one of my errors was overlooking the flexibility of the blades, which is quite embarrassing.

FAST v8 also provides the ‘RtAeroMxh’ data, and I have compared it to the sum of torques related to the rotor axis caused by aerodynamic forces in the y-direction on the blade (under the assumption of small displacements). I found that the two values are quite close.

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I will continue trying calculating the relationship between aerodynamic torque and rotor speed using structural dynamics, and analyze the statistical characteristics of rotor speed. If I find any interesting result, I will report it promptly in the forum.

Regarding your previous query, “I’m not sure I understand why you can’t run OpenFAST; can you clarify?”

Here is my response: When I attempted to install OpenFAST two years ago, I encountered errors while compiling OpenFAST using Visual Studio and was unable to resolve them due to my limited computer knowledge. Therefore, I have to use FAST v8 for my simulations. Fortunately, FAST v8 is easy to use for me and still meets the needs of my current research.

Thank you again for your reply and help.

Best regards!

Yangyudong.Liu

4

Dear @Yangyudong.Liu,

Regarding compiling OpenFAST, you may want to try again as the Visual Studio solutions have been updated over the years and many compiling-related questions have been answered on GitHub. Moreover, if you don’t want to compile yourself, NREL also provides precompiled executables of OpenFAST for Windows on the releases page: Releases · OpenFAST/openfast · GitHub.

Best regards,

5

Dear @Jason.Jonkman

Thank you for your help and advice. I will try to install openfast again to see if it works.

Best regards!

Yangyudong.Liu