Page 107 - Solutions Manual to accompany Electric Machinery Fundamentals

S 12.5 MVA
I  I    1735 A
A L
3 T 3  V V 4160

The power factor is 0.80 lagging, so I  1735 36.87 A . Therefore,
A
E  V  R I  jX I
A  A A S A
 E 2402 0    0.03  1735  36.87  A   j 1.1   1735   36.87  A 
A


 E 3888 22.6 V
A
4-12. Suppose that you were an engineer planning a new electric co-generation facility for a plant with excess
process steam. You have a choice of either two 10 MW turbine-generators or a single 20 MW turbine
generator. What would be the advantages and disadvantages of each choice?
SOLUTION A single 20 MW generator will probably be cheaper and more efficient than two 10 MW
generators, but if the 20 MW generator goes down all 20 MW of generation would be lost at once. If two
10 MW generators are chosen, one of them could go down for maintenance and some power could still be
generated.

4-13. A 25-MVA, 12.2-kV, 0.9-PF-lagging, three-phase, two-pole, Y-connected, 60-Hz synchronous generator
was tested by the open-circuit test, and its air-gap voltage was extrapolated with the following results:

Open-circuit test
Field current, A 275 320 365 380 475 570
Line voltage, kV 12.2 13.0 13.8 14.1 15.2 16.0
Extrapolated air-gap voltage, kV 13.3 15.4 17.5 18.3 22.8 27.4
The short-circuit test was then performed with the following results:

Short-circuit test
Field current, A 275 320 365 380 475 570
Armature current, A 890 1040 1190 1240 1550 1885

The armature resistance is 0.6  per phase.
(a) Find the unsaturated synchronous reactance of this generator in ohms per phase and in per-unit.
(b) Find the approximate saturated synchronous reactance X S at a field current of 380 A. Express
the answer both in ohms per phase and in per-unit.
(c) Find the approximate saturated synchronous reactance at a field current of 475 A. Express the
answer both in ohms per phase and in per-unit.
(d) Find the short-circuit ratio for this generator.

(e) What is the internal generated voltage of this generator at rated conditions?
(f) What field current is required to achieve rated voltage at rated load?

SOLUTION
(a) The unsaturated synchronous reactance of this generator is the same at any field current, so we will
look at it at a field current of 380 A. The extrapolated air-gap voltage at this point is 18.3 kV, and the
short-circuit current is 1240 A. Since this generator is Y-connected, the phase voltage is
V   18.3 kV/ 3 10,566 V and the armature current is I  1240 A . Therefore, the unsaturated

A
synchronous reactance is

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