0195136047.pdf

772 BASIC CONTROL SYSTEMS

For a wye-connected stator, the waveform of the phase current is shown in Figure 16.1.19, which is

also the output currentiAof the inverter. The output voltage of a six-step inverter can be controlled

by controlling either the dc input voltage or the ac output voltage with multiple inverters.

EXAMPLE 16.1.4

A 440-V, 60-Hz, six-pole, wye-connected, squirrel-cage induction motor with a full-load speed

of 1170 r/min has the following parameters per phase referred to the stator:R 1 = 0. 2 , R 2 ′=

0. 1 , Xl 1 = 0. 75 , X′l 2 = 0. 7 , andXm= 20 . (See Chapter 13, Figure 13.2.6,

for the notation.) Consider the motor to be fed by a six-step inverter, which in turn is fed by a

six-pulse, fully controlled rectifier.

(a) Let the rectifier be fed by an ac source of 440 V and 60 Hz. Find the rectifier firing angle

that will obtain rated fundamental voltage across the motor.

(b) Calculate the inverter frequency at 570 r/min and rated torque when the motor is operated

at a constant flux.

(c) Now let the drive be operated at a constantV/fratio. Compute the inverter frequency at

570 r/min and half the rated torque. Neglect the derating due to harmonics and use the

approximate equivalent circuit of Figure 13.2.6, withjXmshifted to the supply terminals.

Solution

(a) From Equation (16.1.46), the fundamental rms line voltage of a six-step inverter is

VL=

√

6

π

Vd

For a six-pulse rectifier, from Equation (16.1.42),Vd=( 3 /π )Vmcosα, whereVmis the

peak ac source line voltage. Thus,

VL=

3

√

6

π^2

Vmcosα or cosα=

VL

Vm

π^2

3

√

6

WithVL=440 V andVm= 440

√

2V,

cosα=

π^2

3

√

6

√

2

= 0. 95 or α= 18 .26°

(b) For a given torque, the motor operates at a fixed slip speed for all frequencies as long as

the flux is maintained constant. At rated torque, the slip speedNSl= 1200 − 1170 = 30

r/min. Hence, synchronous speed at 570 r/min isNS=N+NSl= 570 + 30 = 600

r/min. Therefore, the inverter frequency is (600/1200)60=30 Hz.

(c) Based on the equivalent circuit, it can be shown that the torque for a constantV/fratio is

T=

3

ωS

[

Vrated^2

(

R′ 2 /S

)

(

R 1 +R′ 2 /S

) 2

+

(

Xl 1 +X′l 2

) 2

]

Witha=f/frated,