A 500-kW, 2400-V, four-pole, 60-Hz induction machine has the following equivalent-circuit parameters in ohms per phase Y referred to the stator: R₁ = 0.122 R₂ = 0.317 X₁ = 1.364 X₂ = 1.32 X_m = 45.8. It achieves rated shaft output at a slip of 3.35 percent with an efficiency of 94.0 percent. The machine is to be used as a generator, driven by a wind turbine. It will be connected to a distribution system which can be represented by a 2400-V infinite bus.

a. From the given data calculate the total rotational and core losses at rated load.

b. With the wind turbine driving the induction machine at a slip of -3.2 percent, calculate

(i) The electric power output in kW,

(ii) The efficiency (electric power output per shaft input power) in percent and

(iii) The power factor measured at the machine terminals.

c. The actual distribution system to which the generator is connected has an effective impedance of 0.18 + j0.41 Ω/phase. For a slip of -3.2 percent, calculate the electric power as measured

(i) At the infinite bus and

(ii) At the machine terminals.