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= 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, 
I.= Ra 
The back emf E. ( = K.<Pwm) is zero at start. Therefore, 
Ialstart = Ra 
.,.,. .. ,,, 
:: .. ::.1 
'• ~·· 
184 chapter 4 DC Machines 
n n 
Off 5 
+o-+----------1 Electromagnet 
~ L 
FIGURE 4.57 Development of a de motor starter. 
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 
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• 
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. 
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 __ ,.. 
200 A 
At t = l2 (i.e., before the handle is moved to position 2), 
I.= 100A 
= 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 
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 
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 
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 • 
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. 
Ill I ~I 
188 chapter 4 DC Machines 
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. 
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 
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. 
Power supply 
(ac or del 
(to replace 
M-G set) 
Signal to 
de variable 
Speed Control 189 
FIGURE 4.59 Block diagram of solid-state control of de 
used are controlled rectifiers or choppers, which are discussed in Chapter 
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 
FIGURE 4.60 Speed control of de motors by controlled 
190 chapter 4 DC Machines 
Single-phase input. Assume that the de current i. is continuous. For a full