# Variable speed generator torque control

Dear Jason,

I’m using Fast v7 and I need to do a simple generator torque control in Simulink.

My first question is: the Generator Torque (that is one of the control inputs in Simulink block) in a “resistant” torque applied to the HSS from the generator right? and this is the same value that I have to multiply to GenSpeed to obtain the GenPower?
Also, I know that the equation of motion for the drive train ( if I refer the equation to the LSS) is:

(Jrot+T^2Jgen) alpha= Taero - T* GenTq where:

T=Gearbox ratio
Taero=aerodynamic torque
alpha=angular acceleration of the rotor (LSS)

In my model I have T=1 (no Gearbox) so that: (Jrot+Jgen)alpha= Taero - GenTq
so if in the Simulink model I use “GenTq=0” as input, than I have: alpha= Taero/(Jrot+Jgen) so that if Taero=costant, alpha is costant and GenSpeed ( that is equal to RotSpeed for me because T=1) is increasing linearly.

But if I run a simulation with constant wind speed I obtain that GenSpeed increases NOT-linearly. This make me think that Taero is NOT constant for a constant wind speed, so that alpha is not constant and GenSpeed is not linear.! Am I right? Can you tell me wich is the relation between wind speed and aerodynamic torque?

thank you!

Dear Alessandro,

GenTq is the electromagnetic torque applied to the high-speed shaft from the generator; positive torque for power production and negative torque for motoring conditions. The electrical power output from the turbine is GenTq multiplied by GenSpeed multiplied by a mechnical-to-electrical efficiency loss.

Your equation is correct assuming the turbine and drivetrain are rigid (with the generator azimuth being the only degree of freedom (DOF) enabled). The equations of motion are more sophisticated when other DOFs are enabled.

In general, Taero will depend on the wind speed, rotor speed, pitch angle etc, so even with constant wind and fixed pitch, I would expect Taero and alpha to change with rotor speed. For a given rigid rotor and quasi-steady aerodynamics, the torque is based on the torque-coefficient (Cq) surface dependent on tip-speed ratio and rotor-collective blade-pitch angle.

Best regards,

Dear Jason,