0195136047.pdf

768 BASIC CONTROL SYSTEMS

Solution

(a) From Equation (16.1.42), withα=0, we get

220 =

3

√

2 V

π

or V=163 V line-to-line; Vm= 230 .5V

(b) From Equation (16.1.43), we obtain

ωm=

3 × 230. 5 ×cos 60°

π× 1. 075

−

1. 5

1. 0752

25 = 69 .9 rad/s=667 r/min

(c) From Equation (16.1.45), the normalized torque corresponding to 1.2 N·mis

Tan=

πRa

3 Vm

(

Ta

Km

)

=

π× 1. 5

3 × 230. 5

(

1. 2

1. 075

)

= 0. 0076

The straight lineTan=0.0076 is to the right of the boundary for

ψ= 1 .5 rad=tan−^1

(

ωL

Ra

)

Therefore,

La=

Ra

ω

tanψ=

1. 5

2 π× 60

tan 85.9°= 55 .5mH

The external inductance needed is 55. 5 − 30 = 25 .5 mH.

Solid-State Control of Induction Motors

For our next discussions you might find it helpful to review Section 13.2. The speed-control

methods employed in power semiconductor-controlled induction motor drives are listed here:

• Variable terminal voltage control (for either squirrel-cage or wound-rotor motors)


• Variable frequency control (for either squirrel-cage or wound-rotor motors)


• Rotor resistance control (for wound-rotor motors only)


• Injecting voltage into rotor circuit (for wound-rotor motors only).

AC VOLTAGECONTROLLERS

Common applications for these controllers are found in fan, pump, and crane drives. Figure

16.1.16 shows three-phase symmetrical ac voltage-controlled circuits for wye-connected and

delta-connected stators, in which the thyristors are fired in the sequence that they are numbered,

with a phase difference of 60°. The four-quadrant operation with plugging is obtained by the use

of the typical circuit shown in Figure 16.1.17. Closed-loop speed-control systems have also been

developed for single-quadrant and multiquadrant operation. Induction motor starters that realize

energy savings are one of the ac voltage controller applications. However, one should look into

the problems associated with harmonics.