A three phase, 690V, star connected, 50Hz, four-pole wound-rotor induction generator is used for a new model wind turbine. It operates at a nominal speed of 1570 rpm when the rotor windings are short-circuited whilst generating rated power. It has the following parameters
per phase (all quantities referred to the stator):

Rs = 0.2 Ω ,Rr = 0.13 Ω ,Xs = Xr = 0.45 Ω ,Xm = 36 Ω

(a) Derive the Thevenin equivalent circuit parameters (Vth, Rth & Xth) for this machine.
(b) Find the value of slip at which maximum torque is developed.
(c) Find the maximum torque developed when motoring and generating.
(d) How much stator referred „external? resistance per phase should be connected in the rotor
circuit such that maximum torque in generation mode occurs at a speed of 2,000 rpm