Page 278 - Solutions Manual to accompany Electric Machinery Fundamentals

(c) The generator will now be differentially compounded.
8-30. A three-phase synchronous machine is mechanically connected to a shunt dc machine, forming a motor-
generator set, as shown in Figure P8-11. The dc machine is connected to a dc power system supplying a
constant 240 V, and the ac machine is connected to a 480-V 60-Hz infinite bus.

The dc machine has four poles and is rated at 50 kW and 240 V. It has a per-unit armature resistance of
0.03. The ac machine has four poles and is Y-connected. It is rated at 50 kVA, 480 V, and 0.8 PF, and its
saturated synchronous reactance is 3.0  per phase.

All losses except the dc machine’s armature resistance may be neglected in this problem. Assume that the
magnetization curves of both machines are linear.
(a) Initially, the ac machine is supplying 50 kVA at 0.8 PF lagging to the ac power system.
1. How much power is being supplied to the dc motor from the dc power system?

2. How large is the internal generated voltage E of the dc machine?
A
3. How large is the internal generated voltage E A of the ac machine?
(b) The field current in the ac machine is now increased by 5 percent. What effect does this change have
on the real power supplied by the motor-generator set? On the reactive power supplied by the motor-
generator set? Calculate the real and reactive power supplied or consumed by the ac machine under
these conditions. Sketch the ac machine’s phasor diagram before and after the change in field current.
(c) Starting from the conditions in part (b), the field current in the dc machine is now decreased by 1
percent. What effect does this change have on the real power supplied by the motor-generator set?
On the reactive power supplied by the motor-generator set? Calculate the real and reactive power
supplied or consumed by the ac machine under these conditions. Sketch the ac machine’s phasor
diagram before and after the change in the dc machine’s field current.
(d) From the above results, answer the following questions:
1. How can the real power flow through an ac-dc motor-generator set be controlled?

2. How can the reactive power supplied or consumed by the ac machine be controlled without
affecting the real power flow?

SOLUTION
(a) The power supplied by the ac machine to the ac power system is

P  AC S  cos   50 kVA 0.8    40 kW

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