Baseline Blade Pitch Controller - Torque in Region 3

Dear all,
I have been working on the blade-pitch and generator-torque controller lately. Initially, the generator torque in region 3 was determined so that the generator power was constant [1]. Then, further studies on the floating system suggested to use a constant torque in region 3, for stability reasons [2].

My question is: shouldn’t the equations for the blade-pitch controller change according to the new generator-torque law in region 3?

For example, in [1] at page 21, formula (7.6), it is said that “because the generator-torque controller maintains constant generator power in Region 3, the generator torque in Region 3 is inversely proportional to the generator speed”. However, with the new characteristic in region 3 this does not hold anymore.

Could you give me any help about this matter?

[1] Jonkman et al., “Definition of a 5-MW Reference Wind Turbine for Offshore System Development”, 2009
[2] Jonkman et al., “Definition of the Floating System for Phase IV of OC3”, 2010

Best regards

I solved it.

Re-writing the equations and assuming constant generator torque i.e. T_gen = P_0/Omega_0, the negative damping term -P_0/Omega_0^2 that appears in (7.11) of [1] cancels out; since int the NREL paper that term was neglected, then the integral and proportional gains comes out to be exactly the same as before.

Sorry for posting on the forum before thinking a little bit more on it.

Best regards,