Page 304 - Solutions Manual to accompany Electric Machinery Fundamentals

The winding factor is
k w  k p k d   947.0 0.956  0 . 905

B-4. A three-phase four-pole winding of the double-layer type is to be installed on a 48-slot stator. The pitch
of the stator windings is 5/6, and there are 10 turns per coil in the windings. All coils in each phase are
connected in series, and the three phases are connected in . The flux per pole in the machine is 0.054
Wb, and the speed of rotation of the magnetic field is 1800 r/min.
(a) What is the pitch factor of this winding?

(b) What is the distribution factor of this winding?
(c) What is the frequency of the voltage produced in this winding?
(d) What are the resulting phase and terminal voltages of this stator?

SOLUTION
(a) The pitch factor of this winding is

 150
k p  sin  sin  . 0 966
2 2
(b) The coils in each phase group of this machine cover 4 slots, and the slot pitch is 360/48 = 7.5
mechanical degrees or 15 electrical degrees. Therefore, the distribution factor is
 n 15 4  
sin sin
2
k d  2   15  . 0 958
n sin 4 sin
2 2

(c) The frequency of the voltage produces by this winding is

nP 1800 r/min 4 poles 
f  m   60 Hz
se
120 120
(d) There are 48 slots on this stator, with two coils sides in each slot. Therefore, there are 48 coils on
the machine. They are divided into 12 phase groups, so there are 4 coils per phase. There are 10 turns per
coil, so there are 40 turns per phase group. The voltage in one phase group is

E G  2N P k p k d  f e  2  turns40 0.966 0.958 0.054 Wb  Hz60  533 V

There are two phase groups per phase, connected in series (this is a 4-pole machine), so the total phase
voltage is V   2E G  1066 V . Since the machine is -connected,

V T V   1066 V

B-5. A three-phase Y-connected six-pole synchronous generator has six slots per pole on its stator winding.
The winding itself is a chorded (fractional-pitch) double-layer winding with eight turns per coil. The
distribution factor k d = 0.956, and the pitch factor k p = 0.981. The flux in the generator is 0.02 Wb per
pole, and the speed of rotation is 1200 r/min. What is the line voltage produced by this generator at these
conditions?

SOLUTION There are 6 slots per pole  6 poles = 36 slots on the stator of this machine. Therefore, there
are 36 coils on the machine, or 12 coils per phase. The electrical frequency produced by this winding is

298