0195136047.pdf

776 BASIC CONTROL SYSTEMS

0 T

ωs

ωm

Trated

δ = 0

δ = 1

1 > δ 1 > δ 2 > 0

δ 2

δ 1

Natural

Figure 16.1.24Effect of static rotor resistance control on

speed–torque curves.

WithjXmshifted to the stator terminals in Figure 16.1.23 as an approximation, we get

I ̄ 2 ′=

V ̄ 1

[

R 1 +R′b+(R′a/S)

]

+j(Xl 1 +X′l 2 )

(16.1.55)

and

T=

3

ωs

(I 2 ′)^2

(

R′a

S

)

(16.1.56)

Figure 16.1.24 shows the nature of the speed–torque characteristics for different values of the

duty ratioδ.

EXAMPLE 16.1.5

A 440-V, 60-Hz, six-pole, wye-connected, wound-rotor induction motor with a full-load speed of

1170 r/min has the following per-phase parameters referred to the stator:R 1 =R 2 ′= 0. 5 , Xl 1 =

X′l 2 = 2 , Xm= 40 , and a stator-to-rotor turns ratio of 2.5.

The scheme of Figure 16.1.21 is employed for speed control withRd= 0. 02 andR= 1 .

For a speed of 1000 r/min at 1.5 times the rated torque, find the duty ratioδ, neglecting friction

and windage, and using the equivalent circuit withjXmmoved adjacent to the stator terminals.

Solution

Full-load torque without rotor resistance control is

T=

3

ωS

[

V 12 (R′ 2 /S)

(R 1 +R′ 2 /S)^2 +(Xl 1 +X′l 2 )^2

]

WithV 1 = 440 /

√

3 =254 V;ωS=125.7 rad/s, and full-load slip=( 1200 − 1170 )/ 1200 = 0 .025,

then

T=

3

125. 7

[

2542 ( 0. 5 / 0. 025 )

( 0. 5 + 0. 5 / 0. 025 )^2 + 42

]

= 70 .6N·m