0195136047.pdf

12.2 emf PRODUCED BY WINDINGS 521

Instant 1 Instant 1

ωm ωm

Instant 2 Instant 2

(a) (b)

ωm ωm

Figure 12.2.5(a)Slip-ring action.(b)Commutator action connections.

The instantaneous electric power associated with the speed voltage should be equal to the
instantaneous mechanical power associated with the electromagnetic torqueTe, the direction of
power flow being determined by whether the machine is operating as a motor or a generator,

Teωm=EaIa (12.2.17)

whereIais the armature current (dc). With the aid of Equation (12.2.15), it follows that

Te=KaφIa (12.2.18)

which is created by the interaction of the magnetic fields of stator and rotor. If the machine is acting
as a generator, this torque opposes rotation; if the machine is acting as a motor, the electromagnetic
torque acts in the direction of the rotation.
In a conventional dc machine, the brush axis is fixed relative to the stator. If, however, there
is continuous relative motion between poles and brushes, the voltage at the brushes will in fact
be alternating. This principle is made use of in ac commutator machines.

EXAMPLE 12.2.1

A two-pole, three-phase, 60-Hz, wye-connected, round-rotor synchronous generator hasNa= 12
turns per phase in each armature phase winding and flux per pole of 0.8 Wb. Find the rms induced
voltage in each phase and the terminal line-to-line rms voltage.

Solution

Emax= 2 πf Naφ= 2 π× 60 × 12 × 0. 8 =3619 V

Erms= 3619 /

√

2 = 2559 .5V

VT= 2559. 5

√

3 =4433 V line-to-line rms