(Solved): 1. The rated capacity, rated voltage, rated power factor and per-unit synchronous reactance of a tu ...

1. The rated capacity, rated voltage, rated power factor and per-unit synchronous reactance of a turbo-generator are $S_{\mathrm{N}}=7500\mathrm{kVA},U_{\mathrm{N}}=3150\mathrm{V},\cos {?}_{\mathrm{N}}=0.8$ (lagging), and $X_{\mathrm{c}}=1.1$. The stator winding is Y-connected, and the armature resistance and saturation are both ignored. The turbo-generator is connected to an infinite bus of the rated voltage. Scenario 1: the generator is operated with the per-unit armature current of $I_{(1)}=0.8$ and the power factor of $\cos {?}_{(1)}=0.8$ (leading). Scenario 2 : in comparison to scenario 1 , the field current is increased by $60\%$ and the output active power is constant. Scenario 3: the rated operation. (1) In scenario 1 , what are the torque angle $\left({?}_{(1)}\right)$ and the output active power $\left(P_2\right)$ ? (6 marks) (2) In scenario 2 , what are the torque angle $\left({?}_{(2)}\right)$, the armature current $\left(I_{(2)}\right)$ and the power factor $\left(\cos {?}_{(2)}\right)$ ? Is the power factor leading or lagging? ( 9 marks) (3) What is the torque angle $\left({?}_{\mathrm{N}}\right)$ in scenario 3 ? (3 marks)