Computation of Kp and Ki for baseline controller of 5 MW turbine

Wind & Water Controls
1

Dear Jonkman,
I got a problem in the evaluation of the parameters for the baseline control.
the parameters used are:
drivetrain inertia (Irot): 38,759,228 kgm2;
nominal rotor speed (w0): 12.1 RPM or 1.2671 rad/s (last value used in formula);
natural control frequency (wn): 0.6 rad/s;
damping (csi) : 0.7;
pitch sensitivity at 0 degrees (S0): 28.24*10^6 watt/rad;

when I try to use the formula:
Kp=2Irot wn* csi* w0/S0 = 1.4608;
Ki=Irot/wn^2* w0/S0 = 0.6261;
my values don’t match the values reported in: “Definition of a 5-MW Reference Wind Turbine for Offshore System Development” showing that:
Kp=0.01882681;
Ki=0.008068634;
and 1.4608/0.0188=0.6261/0.008= 77.6.
I can’t figure out why there is a difference between the numbers.
Can you explain me how Kp and Ki are computed in the paper?
thank you in advance
best regards
Massimo Sirigu

2

Dear Massimo Sirigu,

I see a few issues:

  • The drivetrain inertia should be the sum of the rotor inertia and generator inertia; you are only using the rotor inertia. You should add to this 534.116*97^2, where 97 is the gearbox ratio.
  • The gains are calculated relative to the high-speed shaft, and so, need to be divided by the gearbox ratio (97).
  • The gains use the linear fit to the pitch sensitivity, so, S0 = 25.52*10^6 watt/rad.

Best regards,