0195136047.pdf

PROBLEMS 819

the applied voltage at the terminals and the current

drawn by the motor, respectively.

(a) WithV ̄as reference, draw a phasor diagram

for the motor.

(b) Develop an equivalent circuit with a current

source and draw the corresponding phasor

diagram withV ̄as reference.

(c) Obtain expressions for power and torque for

parts (a) and (b).

(d) Now consider the variable-frequency opera-

tion of the synchronous motor, with the per-

unit frequencyato bef/frated. TakingV ̄fas

reference in the quadrature axis, draw the pha-

sor diagram and comment on the effect of the

variable frequency.

16.1.17Consider the motor of Example 16.1.6 in the text.

(a) Determine the armature current and power

factor at one-half the rated speed, one-half the

rated torque, and rated field current.

(b) Find the torque and field current correspond-

ing to rated armature current, 1.25 times the

rated speed, and unity power factor.

16.2.1Consider the electrical transients on a linear ba-

sis in a separately excited dc generator (whose

model is shown in Figure P16.2.1), resulting from

changes in excitation. Let the generator speed be

a constant, so that the dynamics of the mechanical

drive do not enter the problem. Obtain expressions

forEa(s)/Vf(s)andIa(s)/Vf(s), and develop the

corresponding block diagrams. LetRLandLLbe

the load resistance and load inductance, respec-

tively.

16.2.2A separately excited dc generator has the follow-

ing parameters:Rf= 100 , Lf=20 H,Ra=

0. 1 , La= 0 .1H,andKg=100 V per field

ampere at rated speed. The load connected to the

generator has a resistanceRL = 4. 5 and an

inductanceLL= 2 .2 H. Assume that the prime

mover is rotating at rated speed, the load switch

is closed, and the generator is initially unexcited.

Determine the armature current as a function of

time when a 230-V dc supply is suddenly applied

to the field winding, assuming the generator speed

to be essentially constant.

16.2.3A 5-hp, 220-V, separately excited dc motor has

the following parameters:Ra= 0. 5 , k=2H,

Rf = 220 , andLf =110 H. The armature

winding inductance is negligible. The torque re-

quired by the load is proportional to the speed,

and the combined constants of the motor armature

and the load areJ =3kg·m^2 andB = 0. 3

kg·m^2 /s. Consider the armature-controlled dc mo-

tor, whose speed is made to respond to variations

in the applied motor armature voltagevt. Let the

field current be maintained constant at 1 A.

(a) Develop a block diagram relating the motor

speed and the motor applied voltage, and find

the corresponding transfer function.

(b) Compute the steady-state speed correspond-

ing to a step-applied armature voltage of 220

V.

(c) How long does the motor take to reach 0.95

of the steady-state speed of part (b)?

(d) Determine the value of the total effective vis-

cous damping coefficient of the motor-load

configuration.

−

+

+

−

+ −

ea

vt

vf

if

Lf

Rf

La

wmTe

Ts

ia

Ra Figure P16.2.1Schematic representation

of the model of a separately excited dc motor.