Wind turbines, such as the one shown in Figure P8.17(a), are becoming popular as a way of generating electricity. Feedback control loops are designed to control the output power of the turbine, given an input power demand. Blade-pitch control may be used as part of the control loop for a constant-speed, pitch-controlled wind turbine, as shown in Figure P8.17(b). The drivetrain, consisting of the windmill rotor, gearbox, and electric generator (see Figure P8.17(c)), is part of the control loop. The torque created by the wind drives the rotor. The windmill rotor is connected to the generator through a gearbox. The transfer function of the drivetrain is

where P_o(s) is the Laplace transform of the output power from the generator and T_R(s) is the Laplace transform of the input torque on the rotor. Substituting typical numerical values into the transfer function yields

(Anderson, 1998). Do the following for the drivetrain dynamics, making use of any computational aids at your disposal:

FIGURE P8.17

a.

b.

c.

Transcribed Image Text:

P.(s) TR(S) Ga(s) 3.92K LSSKHSSKGN²S {N*K Hss(J RS + K1ss)JGs°[Tas+ 1] + KGs) + JRs2K1ss[(JGs² + KHss) (Tels + 1) + KGs]}