0195136047.pdf

16.1 POWER SEMICONDUCTOR-CONTROLLED DRIVES 777

With rotor resistance control,

T=

3

ωS

[

V 12 (R′a/S)

(

R 1 +R′b+Ra′/S

) 2

+(Xl 1 +Xl′ 2 )^2

]

WithR′b=(π^2 / 9 − 1 )Ra′= 0. 0966 R′a, and slip=( 1200 − 1000 )/ 1200 = 0 .167, we obtain

1. 5 × 70. 6 =

3

125. 7

[

2542 (Ra′/ 0. 167 )

(

0. 5 + 0. 0966 R′a+Ra′/ 0. 167

) 2

+ 42

]

Thus,Ra′^2 − 2. 18 R′a+ 0. 44 =0, orR′a= 0 .225, or 1.955. The value of 0.225 being less than

R′ 2 is not feasible; thereforeRa′= 1. 955 .

From Equation (16.1.53),Reff=(Ra′−R′ 2 )/(turns ratio)^2 =( 1. 955 − 0. 5 )/ 252 = 0. 233 .

From Equations (16.1.52) and (16.1.51), we calculate

( 1 −δ)=

2 Reff−Rd

R

=

2 × 0. 233 − 0. 22

1

= 0. 446 ,orδ= 0. 554

Instead of wasting the slip power in the rotor circuit resistance, as was suggested by Scherbius,
we can feed it back to the ac mains by using a scheme known as astatic Scherbius drive.The slip
power can be converted to mechanical power (with the aid of an auxiliary motor mounted on the
induction-motor shaft), which supplements the main motor power, thereby delivering the same
power to the load at different speeds, as in the Kramer drive.

Solid-State Control of Synchronous Motors

The speed of a synchronous motor can be controlled by changing its supply frequency. With
variable-frequency control, two modes of operation are possible: true synchronous mode, em-
ployed with voltage source inverters, in which the supply frequency is controlled from an
independent oscillator; and self-controlled mode, in which the armature supply frequency is
changed proportionally so that the armature field always rotates at the same speed as the rotor. The
true synchronous mode is used only in multiple synchronous-reluctance and permanent-magnet
motor drives, in applications such as paper mills, textile mills, and fiber-spinning mills, because
of the problems associated with hunting and stability. Variable-speed synchronous-motor drives,
commonly operated in the self-controlled mode, are superior to or competitive with induction-
motor or dc-motor variable-speed drives.
Drives fed from a load-commutated current-source inverter or a cycloconverter find applica-
tions in high-speed high-power drives such as compressors, conveyors, traction, steel mills, and
ship propulsion. The drives fed from a line-commutated cycloconverter are used in low-speed
gearless drives for mine hoists and ball mills in cement production. Self-controlled permanent-
magnet synchronous-motor drives are replacing the dc-motor drives in servo applications.
Self-control can be applied to all variable-frequency converters, whether they are voltage-
source inverters, current-source inverters, current-controlled PWM inverters, or cycloconverters.
Rotor position sensors, i.e., rotor position encoders with optical or magnetic sensors, or armature
terminal voltage sensors, are used for speed tracking. In the optical rotor position encoder shown
in Figure 16.1.25 for a four-pole synchronous machine, the semiconductor switches are fired at
a frequency proportional to the motor speed. A circular disk, with two slotsS′andS′′on an
inner radius and a large number of slots on the outer periphery, is mounted on the rotor shaft.
Four stationary optical sensorsP 1 toP 4 with the corresponding light-emitting diodes and photo
transistors are placed as shown in Figure 16.1.25. Whenever the sensor faces a slot, an output