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1 - principles of electrical machines and power electronics p_c_sen

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speeds. For this part, 
assume a constant rotational loss of 300 W over the speed range. 
4.25 A permanent magnet de motor drives a mechanical load requiring a constant 
torque of 25 N · m. The motor produces 10 N · m with an armature current 
of 10 A. The resistance of the armature circuit is 0.2 D. A 200 V de supply is 
applied to the armature terminals. Determine the speed of the motor. 
4.26 A de shunt motor drives an elevator load which requires a constant torque 
of 300 N · m. The motor is connected to a 600 V de supply and the motor 
rotates at 1500 rpm. The armature resistance is 0.5 D. 
(a) Determine the armature current. 
(b) If the shunt field flux is reduced by 10%, determine the armature current 
and the speed of the motor. 
4.27 A de shunt motor (50 hp, 250 V) is connected to a 230 V supply and delivers 
power to a load drawing an armature current of 200 amperes and running 
at a speed of 1200 rpm. Ra = 0.2 D. 
(a) Determine the value of the generated voltage at this load condition. 
(b) Determine the value of the load torque. The rotational losses are 500 
watts. 
(c) Determine the efficiency of the motor if the field circuit resistance is 
11s n. 
4.28 A de shunt machine (23 kW, 230 V, 1500 rpm) has Ra = 0.1 D. 
1. The de machine is connected to a 230 V supply. It runs at 1500 rpm at 
no-load and 1480 rpm at full-load armature current. 
(a) Determine the generated voltage at full load. 
(b) Determine the percentage reduction of flux in the machine due to 
armature reaction at full-load condition. 
2. The de machine now operates as a separately excited generator and the 
field current is kept the same as in part 1. It delivers full load at rated 
voltage. 
(a) Determine the generated voltage at full load. 
(b) Determine the speed at which the machine is driven. 
(c) Determine the terminal voltage if the load is thrown off. 
4.29 A de shunt machine (10 kW, 250 V, 1200 rpm) has Ra = 0.25 D. The machine 
is connected to a 250 V de supply, draws rated armature current, and rotates 
at 1200 rpm. 
(a) Determine the generated voltage, the electromagnetic power developed, 
and the torque developed. 
(b) The mechanical load on the motor shaft is thrown off, and the motor 
draws 4 A armature current. 
(i) Determine the rotational loss. 
Problems 205 
(ii) Determine speed, assuming no armature reaction. 
(iii) Determine speed, assuming 10% change in flux due to armature 
reaction, for a change of armature current from rated value to 4 A. 
4.30 A 240 V, 2 hp, 1200 rpm de shunt motor drives a load whose torque varies 
directly as the speed. The armature resistance of the motor is 0.75 !1. With 
Ir = 1 A, the motor draws a line current of 7 A and rotates at 1200 rpm. 
Assume magnetic linearity and neglect armature reaction effect. 
(a) The field current is now reduced to 0.7 A. Determine the operating speed 
of the motor. 
(h) Determine the line current, mechanical power developed, and efficiency 
for the operating condition of part (a). Neglect rotational losses. 
4.31 Repeat Problem 4.30 if the load torque is constant. Determine the torque. 
4.32 A 125 V, 5 kW, 1800 rpm de shunt motor requires only 5 volts to send full-
load current through the armature when the armature is held stationary. 
(a) Determine the armature current if full-line voltage is impressed across 
the armature at starting. 
(h) Determine the value of the external resistance needed in series with the 
armature to limit the starting current to 1.5 times the full-load current. 
(c) The motor is coupled to a mechanical load by a belt. Determine the 
generated voltage at full-load condition (V, = 125 V, n = 1800 rpm, 
I a = /a(mtcdl). If the belt breaks, determine the speed of the motor. Neglect 
rotational losses and assume 10% reduction of flux due to armature 
reaction at full load. 
4.33 A de motor is mechanically connected to a constant-torque load. When the 
armature is connected to a 120 V de supply, it draws an armature current of 
value 8 A and runs at 1800 rpm. The armature resistance is Ra = 0.08 !1. 
Accidentally, the field circuit breaks and the flux drops to the residual flux, 
which is only 5% of the original flux. 
(a) Determine the value of the armature current immediately after the field 
circuit breaks (i.e., before the speed has had time to change from 
1800 rpm). 
(h) Determine the theoretical final speed of the motor after the field cir-
cuit breaks. 
4.34 At standstill, a de series motor draws 5 amperes and develops 5 N · m torque 
when connected to a 5 V de supply. The series motor is mechanically coupled 
to a load. It draws 10 amperes when connected to a 120 V de supply and 
drives the load at 300 rpm. Assume magnetic linearity. 
(a) Determine the torque developed by the motor. 
(h) Determine the value of the external resistance required to be connected 
in series with the motor. 
4.35 A de series motor (230 V, 12 hp, 1200 rpm) is connected to a 230 V supply, 
draws a current of 40 amperes, and rotates at 1200 rpm. Ra = 0.25 !1 and 
Rs, = 0.1 n. Assume magnetic linearity. 
(a) Determine the power and torque developed by the motor. 
(h) Determine the speed, torque, and power if the motor draws 20 amperes. 
i .... , 
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206 chapter 4 DC Machines 
4.36 A 50 hp, 200 V, 1800 rpm shunt motor requires a starter box. During the 
start, the armature current is constrained within the range 200 to 400 A. The 
armature circuit resistance is 0.15 !1. Determine the required number of 
resistors and the value of each resistor in the starter box. 
4.37 The Ward-Leonard speed control system shown in Fig. 4.58a uses two identi-
cal de machines of rating 250 V, 5 kW, 1200 rpm. The armature resistance 
of each machine is 0.5 ohms. The generator is driven at a constant speed of 
1200 rpm. The magnetization characteristic of each machine at 1200 rpm is 
as follows: 
(A) 0.0 I 0.1 I 0.21 0.31 0.41 0.51 0.61 0.71 0.811.0 11.211.4 
Ea (V) 5 60 120 160 190 212 230 242 250 262 270 273 
Neglect the effect of armature reaction. 
(a) If the motor field current 11m is kept constant at 0.8 A, determine the 
maximum and minimum values of the generator field current, l 1g, re-
quired for the motor to operate in a speed range of 200 to 1200 rpm at 
full-load armature current. 
(b) The generator field current is kept at 1.0 amps and the motor field current 
is reduced to 0.2 amp. Determine the speed of the motor at full-load 
armature current. 
4.38 Repeat Example 4.11 if a single-phase semiconverter (Fig. 4.60 or Fig. 10.24a) 
is used to control the speed of the de motor. 
4.39 Repeat Example 4.12 if a three-phase semiconverter is used to control the 
speed of the de motor. 
4.40 A de series motor drives an elevator load that requires a constant torque of 
200 N · m. The de supply voltage is 400 V and the combined resistance of the 
armature and series field winding is 0.75 !1. Neglect rotational losses and 
armature reaction effect. 
(a) The speed of the elevator is controlled by a solid-state chopper. At 50% 
duty cycle (i.e., a = 0.5) of the chopper, the motor current is 40 amps. 
Determine the speed and the horsepower output of the motor and the 
efficiency of the system. 
(b) The elevator is controlled by inserting resistance in series with the arma-
ture of the series motor. For the speed of part (a), determine the values 
of the series resistance, horsepower output of the motor, and efficiency 
of the system. 
chapter five 
INDUCTION 
{ASYNCHRONOUS) 
MACHINES 
The induction machine is the most rugged and the most widely used machine 
in industry. Like the de machine discussed in the preceding chapter, the 
induction machine has a stator and a rotor mounted on bearings and sepa-
rated from the stator by an air gap. However, in the induction machine both 
stator winding and rotor winding carry alternating currents. The alternating 
current (ac) is supplied to the stator winding directly and to the rotor winding 
by induction-hence the name induction machine. 
The induction machine