0195136047.pdf

PROBLEMS 545

ωm

θm

Stator

magnetic axis

Rotor

magnetic axis

Figure P12.2.1Rotating machine with uniform air

gap.

(iv) Obtain the time functions of the line-to-

line voltages.

12.2.5A wye-connected, three-phase, 50-Hz, six-pole

synchronous alternator develops a voltage of

1000 V rms between the lines when the rotor dc

field current is 3 A. If this alternator is to generate

60-Hz voltages, find the new synchronous speed,

and calculate the new terminal voltage for the

same field current.

12.2.6Determine the synchronous speed in revolutions

per minute and the useful torque in newton-

meters of a 200-hp, 60-Hz, six-pole synchronous

motor operating at its rated full load (1 hp∼= 746

W).

12.2.7From a three-phase, 60-Hz system, through a

motor–generator set consisting of two directly

coupled synchronous machines, electric power

is supplied to a three-phase, 50-Hz system.

(a) Determine the minimum number of poles for

the motor.

(b) Determine the minimum number of poles for

the generator.

(c) With the number of poles decided, find the

speed in r/min at which the motor–generator

set will operate.

*12.2.8Two coupled synchronous machines are used as
a motor–generator set to link a 25-Hz system to
a 60-Hz system. Find the three highest speeds at
which this linkage would be possible.

12.2.9A 10-turn square coil of side 200 mm is mounted

on a cylinder 200 mm in diameter. If the cylinder

rotates at 1800 r/min in a uniform 1.2-T field,

determine the maximum value of the voltage

induced in the coil.

12.3.10A four-pole dc machine with 728 active conduc-

tors and 30 mWb flux per pole runs at 1800 r/min.

(a) If the armature winding is lap wound, find

the voltage induced in the armature, given

that the number of parallel paths is equal to

the number of poles for lap windings.

(b) If the armature is wave wound, calculate the

voltage induced in the armature, given that

the number of parallel paths is equal to 2 for

wave windings.

(c) If the lap-wound armature is designed to

carry a maximum line current of 100 A, com-

pute the maximum electromagnetic power

and torque developed by the machine.

(d) If the armature were to be reconnected as

wave wound, while limiting per-path current

to the same maximum as in part (c), will

either the maximum developed power or the

torque be changed from that obtained in part

(c)?

12.2.11A four-pole, lap-wound armature has 144 slots

with two coil sides per slot, each coil having

two turns. If the flux per pole is 20 mWb and

the armature rotates at 720 r/min, calculate the