0195136047.pdf

818 BASIC CONTROL SYSTEMS

vp

+

−

+

−

vs

vs

Vm

Ia

−Vm

−Ia

π

π

2 π

2 π

ωt

ωt

0

0

Fundamental

component

(a) (b)

i 1

IL = Ia

D 3

D 2

D 1

M

i 1

D 4

Figure P16.1.4(a)Circuit diagram.(b)Waveforms.

R vL

+

−

ia

ic

iD 1 iL

ib

vcn

van

vbn

a

a

b

b

c

c

D 1

D 4

D 3

D 6

D 5

D 2

Figure P16.1.6

terminals. For an operating frequency of 15 Hz,

find:

(a) The maximum motoring torque as a ratio of

its value at the rated frequency.

(b) The starting torque and rotor current in terms

of their values at the rated frequency.

16.1.12Given that the motor of Problem 16.1.11 has a
full-load slip of 0.05, compute the motor speed
corresponding to rated torque and a frequency of
30 Hz.

16.1.13Consider the motor of Example 16.1.4 in the text.
Let the motor be controlled by variable frequency
at a constant flux of rated value. By using the
equivalent circuit of Figure 13.2.6,

(a) Determine the motor speed and the stator cur-

rent at one-half the rated torque and 30 Hz.

(b) Redo part (a), assuming the speed–torque

curves to be straight lines forS<Smax.

16.1.14For the static rotor resistance control considered

in the text for an induction motor drive, develop

the fundamental frequency equivalent circuit of

Figure 16.1.23.

*16.1.15Consider the induction motor drive of Example

16.1.5 in the text. Compute the motor speed cor-

responding toδ= 0 .65 and 1.5 times the rated

full-load torque.

16.1.16Let the simplified per-phase equivalent circuit of

an underexcited, cylindrical-rotor, synchronous

machine be given by a sourceVf −δin series

with an impedancejXs. LetV0° andIs −φbe