Page 109 - Solutions Manual to accompany Electric Machinery Fundamentals

E  V  R I  jX I
A  A A S A
 E 7044 0    0.60   1183   25.8  A   j 6.57   1183   25.8  A 
A


E  12,930 31.2 V
A
(f) If the internal generated voltage is 12,930 V per phase, the corresponding line value would be

 12,930 V  3  22,400 V . This would require a field current of about 470 A.

4-14. During a short-circuit test, a Y-connected synchronous generator produces 100 A of short-circuit armature
current per phase at a field current of 2.5 A. At the same field current, the open-circuit line voltage is
measured to be 440 V.
(a) Calculate the saturated synchronous reactance under these conditions.
(b) If the armature resistance is 0.3 Ω per phase, and the generator supplies 60 A to a purely resistive
Y-connected load of 3 Ω per phase at this field current setting, determine the voltage regulation under
these load conditions.

SOLUTION
(a) The saturated synchronous reactance at a field current of 2.5 A can be found from the information
supplied in the problem. The open circuit line voltage at I = 2.5 A is 440 V, and the short-circuit
F
current is 100 A. Since this generator is Y-connected, the corresponding phase voltage is
V   440 V/ 3  254 V and the armature current is I  100 A . Therefore, the saturated synchronous
A
reactance is
254 V
X   2.54 
S
100 A


(b) Assume that the desired line voltage is 440 V, which means that the phase voltage V   254 0 V .


The armature current is A I 60 0 A , so the internal generated voltage is
E  A V   R I  A A jX I
S A


 E 254 0    0.30   60 0  A   j 2.54   60 0  A 
A


 E 312 29.3 V
A
This is also the phase voltage at no load conditions. The corresponding line voltage at no load conditions
would be V L ,nl   312 V  3   540 V . The voltage regulation is
V  V 540 440

VR  T ,nl T ,fl  100%   100% 22.7%

V T ,fl 440
4-15. A three-phase Y-connected synchronous generator is rated 120 MVA, 13.8 kV, 0.8-PF-lagging, and 60
Hz. Its synchronous reactance is 1.2  per phase, and its armature resistance is 0.1  per phase.
(a) What is its voltage regulation?

(b) What would the voltage and apparent power rating of this generator be if it were operated at 50
Hz with the same armature and field losses as it had at 60 Hz?

(c) What would the voltage regulation of the generator be at 50 Hz?
SOLUTION

(a) The rated armature current is

103