A maior rede de estudos do Brasil

Grátis
634 pág.

## Pré-visualização | Página 35 de 50

```= 86.57 X 16.68
= 1444 w ~ 1. 94 hp •
4.4.3 STARTER
If a de motor is directly connected to a de power supply, the starting current
will be dangerously high. From Fig. 4.57a,
Vt-Ea
I.= Ra
The back emf E. ( = K.<Pwm) is zero at start. Therefore,
vt
Ialstart = Ra
(4.55)
(4.56)
......
......
.,.,. .. ,,,
:: .. ::.1
r···1
.·'"'"•1
'• ~··
:.:u··
)t-"'
-
184 chapter 4 DC Machines
+
n n
(a)
Off 5
A
F
+o-+----------1 Electromagnet
~ L
(c)
FIGURE 4.57 Development of a de motor starter.
(b)
Shunt
field
+
Since Ra is small, the starting current is very large. The starting current
can be limited to a safe value by the following methods:
1. Insert an external resistance, Rae (Fig. 4.57b), at start.
2. Use a low de terminal voltage (Vt) at start. This, of course, requires a
variable-voltage supply.
With an external resistance in the armature circuit, the armature current
as the motor speeds up is
I = _V_t_-_E_a
a Ra +Rae
(4.57)
The back emf Ea increases as the speed increases. Therefore, the external
resistance Rae can be gradually taken out as the motor speeds up without
the current exceeding a certain limit. This is done using a starter, shown in
Fig. 4.57c. At start, the handle is moved to position 1. All the resistances,
R 1 , R 2 , R 3 , and R 4 , appear in series with the armature and thereby limit the
,
DC Motors 185
starting current. As the motor speeds up, the handle is moved to positions
2, 3, 4, and finally 5. At position 5 all the resistances in the starter are taken
out of the armature circuit. The handle will be held in position 5 by the
electromagnet, which is excited by the field current 11•
EXAMPLE 4.10
A 10 kW, 100 V, 1000 rpm de machine has Ra = 0.1 nand is connected to
a 100 V de supply.
(a) Determine the starting current if no starting resistance is used in the
armature circuit.
(b) Determine the value of the starting resistance if the starting current is
limited to twice the rated current.
(c) This de machine is to be run as a motor, using a starter box. Determine
the values of resistances required in the starter box such that the
armature current Ia is constrained within 100 to 200% of its rated value
(i.e., 1 to 2 pu) during start-up.
Solution
(a)
(b)
10000
Ialrated =laO= 100 A
vt 100
Ialstart= Ra = 0. 1 = 1000A= lOJalrated= 10pu
200 = 100
0.1 +Rae
Rae= 0.4 D
(c) An arrangement of the resistances in the starter box is shown in Fig.
E4.10a, where Rael, Raez, ... represent total resistances of the box for
positions 1, 2, ... , respectively. The handle will be moved to a new
position when Ia decreases to 100 A (rated armature current). The
variation of current Ia and speed n with time is shown in Fig. E4.10b.
Rae I. From part (b)
Rael = 0.4 D
= total resistance in starter box
Rae2. At any speed,
vt = Ea + la(Ra + Rae)
i i i
fixed increases decreases
with with
speed speed
..
..
186 chapter 4 DC Machines
-Rae2 __ ,..
2
----Rae!----•
(a)
FIGURE E4.10
Ia
200 A
(b)
At t = l2 (i.e., before the handle is moved to position 2),
I.= 100A
and
= 100- 100(0.1 + 0.4)
= sov
At t = tt (i.e., after the handle is moved to position 2),
V:-E I = 200A = 1 az
or
a Ra + Rae2
200 = 100- 50
0.1 + Rae2
Rae2 = 0.15 !1
Rae3· Att = t3, I.= 100A.
Ea3 = 100- 100(0.1 + 0.15)
= 100-25
= 75V
T
At t = tj,
Ia=200A= 100-75
0.1 + Rae3
Rae3 = 0.025 !1
Rae4· At t = t4, Ia = 100 A.
At t = tt,
Ea4 = 100- 100(0.1 + 0.025)
= 87.5 v
I = 200 = 100- 87.5
a 0.1 + Rae4
Rae4 = -0.0375 !1
Speed Control 18 7
The negative value of Rae4 indicates that it is not required, that is,
Rae4 = 0. At T = tt (i.e., after the handle is moved to position 4), the
armature current without any resistance in the box will not exceed
200 A. In fact, the value of Ia when the handle is moved to position 4
at t = t4 is
I = 100-87.5 = 125A
a 0.1
Therefore, three resistances in the starter box are required. Their values
are
R 1 =Rae!- Raez = 0.4- 0.15 = 0.25 !1
Rz = Raez- Rae3 = 0.15- 0.025 = 0.125 !1
R3 = Rae3 - Rae4 = 0.025 - 0 = 0.025 !1 •
4.5 SPEED CONTROL
There are numerous applications where control of speed is required, as in
rolling mills, cranes, hoists, elevators, machine tools, and transit system
and locomotive drives. DC motors are extensively used in many of these
applications. Control of the speed of de motors below and above the base
(or rated) speed can easily be achieved. Besides, the methods of control are
simpler and less expensive than those applicable to ac motors. The technol-
ogy of speed control of de motors has evolved considerably over the past
quarter-century. In the classical method a Ward-Leonard system with rotat-
ing machines is used for speed control of de motors. Recently, solid-state
converters have been used for this purpose. In this section, various methods
of speed control of de motors are discussed.
c
,.,
!
Ill I ~I
188 chapter 4 DC Machines
4.5.1 WARD-LEONARD SYSTEM
This system was introduced in the 1890s. The system, shown in Fig. 4.58a,
uses a motor-generator (M-G) set to control the speed of the de drive motor.
The motor of the M-G set (which is usually an ac motor) runs at a constant
speed. By varying the generator field current Irg. the generator voltage V1 is
changed, which in turn changes the speed of the de drive motor. The system
is operated in two control modes.
V1 Control
In the armature voltage control mode, the motor current Irm is kept constant
at its rated value. The generator field current Irg is changed such that V1
changes from zero to its rated value. The speed will change from zero to
the base speed. The torque can be maintained constant during operation in
this range of speed, as shown in Fig. 4.58b.
Ic Control
The field current control mode is used to obtain speed above the base speed.
In this mode, the armature voltage V1 remains constant and the motor
field current Irm is decreased (field weakening) to obtain higher speeds. The
armature current can be kept constant, thereby operating the motor in a
constant-horsepower mode. The torque obviously decreases as speed in-
creases, as shown in Fig. 4.58b.
4.5.2 SOLID-STATE CONTROL
In recent years, solid-state converters have been used as a replacement for
rotating motor-generator sets to control the speed of de motors. Figure 4.59
shows the block diagram of a solid-state converter system. The converters
p
nnfm + - nbase I· •I• •I
"t control / 1 control 1-+----M-G set----+o0---Dc drive motor~
(a) (b)
FIGURE 4.58 Ward-Leonard system.
¥
I
T
Power supply
(ac or del
Solid-state
converter
(to replace
M-G set)
Signal to
control
voltage
"t
de variable
voltage
<"tl
Solid-state
field
controller
"'
Speed Control 189
FIGURE 4.59 Block diagram of solid-state control of de
motors.
used are controlled rectifiers or choppers, which are discussed in Chapter
10.
Controlled Rectifiers
If the supply is ac, controlled rectifiers can be used to convert a fixed ac
supply voltage into a variable-voltage de supply. The operation of the phase-
controlled rectifiers is described in Chapter 10.
If all the switching devices in the converter are controlled devices, such
as silicon-controlled rectifiers (SCRs), the converter is called a full converter.
If some devices are SCRs and some are diodes, the converter is called a
semiconverter. In Fig. 4.60, the firing angle a of the SCRs determines the
average value (V1) of the output voltage v1 • The control voltage Vc changes
the firing angle a and therefore changes V1 • The relationship between the
average output voltage V1 and the firing angle a is as follows.
l<P or 3<P
Control signal
to change "t
Controlled
rectifiers
FIGURE 4.60 Speed control of de motors by controlled
rectifiers.
190 chapter 4 DC Machines
Single-phase input. Assume that the de current i. is continuous. For a full
converter```