1) A 12 KV, 60 MVA, 0.85 lagging PF, 60 Hz, 4-Pole, delta connected synchronous generator has a
reactance of 2 Ohms, and its armature resistance is 0.1 Ohms, its mechanical losses are 1 MW
and its core losses are 1.5 MW.
a) What is the mechanical speed of the prime mover in this machine?
$f_e = \frac{120f}{p} = \frac{60 \times 120}{4} = 1800M$
b) What is the internal voltage ($E_A$) of this machine under rated conditions?
$60 = \sqrt{3} (12 \times 10^3) I_L \implies I_L = 2886.75A \quad cos(\alpha_{ss}) = 0.9$
$I_L = 2886.75 \angle 31.78^\circ, V_t = E_A - jX_s I_A \quad V_t = V_t - 12kV$
$\implies 12k = E_A - j(2)(2886.75 \angle -31.75^\circ) \implies 12k + j(2)(2886.75 \angle -31.75^\circ) = E_A$
$\implies E_A = 4921.51 + j3038.016 \implies 5785.7 \angle -31.43^\circ$
c) Draw the phasor diagram under the above listed conditions?
d) What is the Voltage regulation of this SG at 0.9 lagging?
$12k = 8 \quad V_L = 2886.75 \times 0.9 \quad VR = 1.5V$
e) What is the efficiency of this SG under full load conditions, 0.9 lagging?
$P_{in} = \sqrt{3} (12k)(2886.75) = 60M$
$P_{cu} + P_{core} + P_{losses} = 60M - P_{out} + 1M$
$P_{cu}$