Higher Kp & Ki values used for pitch control of 5MW turbine

Wind & Water Controls
1

Hello everyone,

This is a seemingly long post, but that’s just because it’s spaced out very well. So just go through it and skip the last part in the curly braces if you want to.
In the 5MW technical report, ([url]http://www.nrel.gov/docs/fy09osti/38060.pdf[/url]), page 25 of the document (page 36 in the file) the Kp and Ki values , the proportional and integral gains respectively are derived as follows:

Kp=2IωζΩ/(N*(-∂P/∂θ))

Ki=(Iω Ω^2)/(N*(-∂P/∂θ))

It’s also told that the following recommended values are used: ω=0.6 rad/s & ζ=0.7 {Natural frequency and damping ratio}
The other values:
Ω=12.1 rpm = 1.267109037 rad/s {rated rotor rpm}
N=97 {gear ratio}
∂P/∂θ at θ=0 degrees is 28.24E06 watt/rad
I_drivetrain= I = 43784724.94 kg-m^2 (calculated value)

If we substitute this value of I and all the other listed values, we get

Ki=7.29E-03 whereas Ki in the report obtained substituting the same values is Ki(θ = 0º) = 8.068634E03 (I_drivetrain is never explicitly calculated or mentioned though)

Similarly Kp is a different value (again lower than the value obtained in the report, the I_drivetrain value that I calculated seems to be lower than what the report uses?).

Where am I going wrong? I’ve checked the I-rotor value several times (including hand calculation of I_rotor using parallel axis theorem since I_blade are given w.r.t. root)

{I’ve already stated this in one of my other posts, but it’s relevant here too: Kp & Ki values calculated in the report are rounded off but interchanged in the simple control loop of the labview sample code, is this a mistake?}
:question:

{Note: these are the calculations to obtain I_drivetrain:
I = NNI_generator + I_rotor (where I is the moment of inertia of the drive train)…b[/b] {This is again given in the report}

In the FAST summary file, the I_rotor is generated for the 5MW turbine as :38759227.492 kg-m^2 (approx 3.9E07)
The I_generator is : 534.116 kg-m^2. Hence NNI_generator= 5025497.444 kg-m^2

So I from (1) above is: I_drivetrain=I= 43784724.94 kg-m^2}

Can someone please help me out here?

Regards

2

Dear Harimanjunathan,

The value you report for I_Drivetrain is correct; however the NREL 5-MW specifications report gives a value of K_I(θ=0) = 0.008068634 (not 8.068634E03), which is close to the number you calculated. The difference in the two numbers comes from the fact that the report calculates K_I(θ=0º) using the best-fit line of ∂P/∂θ (whereby ∂P/∂θ(θ=0º) = -25.52E+6 watt/rad) whereas you used the actual value of ∂P/∂θ(θ=0º) from Table 7-1 (whereby ∂P/∂θ(θ=0º) = -28.24E+6 watt/rad).

Please note that the equation you’ve written in your post for Kp is correct, but the equation for Ki is incorrect – ω should be squared and Ω shouldn’t. Regardless, it looks like you’ve applied the correct equation in your mathematical results.

I hope that helps.

3

Dear Jason,
That solves the problem.Great! And yes, the formula and the Ki value in question have typos (I meant to type 8.068634E-03). Thanks for your time.