Question

QUIESTION 1
A three-phase synchronous generator is connected to an infinite bus. The infinite bus voltage and the generated voltage are o 1.0 pu ∠0 and o 1.0pu ∠42.84 , respectively. The synchronous reactance is 0.85 pu and resistances are neglected. a) Compute power angle (δ), armature current (Is), power factor (pf), real power (P), and reactive power (Q). Draw the phasor diagram. b) If the prime mover torque is kept constant at a value corresponding to P=0.8 pu, compute the required value of the generated voltage (E2) for the unity power factor condition (and constant power, P=0.8 pu). What is the new value of power angle (δ2)? Solution: δ= 42.84o , Is = 0.86pu ∠21.44o , pf=0.93, P=0.8 ph, Q= -0.314pu, δ2 = 34.2o , E2= 1.21pu

QUESTION 2
Two “three-phase Y-connected synchronous generators” have per phase generated voltages of o 1 E = 120 V∠10 and o 2 E = 120 V∠20 under no load, and resistance of X j5 Ω / phase 1 = and X j8 Ω / phase 2 = . They are connected in parallel to a load impedance of XL = 4 + j3 Ω / phase . Compute: a) Per phase terminal voltage Vt (both magnitude and phase angle). b) Armature currents for each generator ( a1 a2 I and I ). c) Power supplied by each generator (P1 and P2 ). d) The total output power (Pout ). Solution: Vt= 82 V ∠-5.94o , Ia1 = 9.36 A ∠-51.17o , Ia2 = 7.31 A ∠-32.06o , P1 = 1621 W, P2 = 1614.5 W, Pout = 3236 W.

Answer 1