Chapter 9: DC Motors and Generators
Problems 9-1 to 9-12 refer to the following dc motor: Prated = 15 hp I L ,rated = 55 A
VT = 240 V nrated = 1200 r/min RA = 0.40 RS = 0.04
N F = 2700 turns per pole N SE = 27 turns per pole RF = 100 Radj = 100 to 400
R
P2.11 -Y transmission transformer
A 100-MVA 230/115-kV -Y three-phase power transformer has a per-unit resistance of
0.015 pu and a per-unit reactance of 0.06 pu. The excitation branch elements are
RC = 100 pu and X M = 20 pu .
(a) If this transformer sup
A 208-V four-pole 60-Hz Y-connected wound-rotor induction motor is rated at 30 hp. Its
equivalent circuit components are
P6.5 Induction motor equivalent circuit and power relations
1 = 0.100
1 = 0.210
mech = 500 W
2 = 0.070
2 = 0.210
misc 0
For a slip
The input power to the rotor circuit of a six-pole, 60 Hz, induction motor running at 1100
r/min is 5 kW. What is the rotor copper loss in this motor?
P6.11 Power and slip relations 1
This synchronous speed of this motor is
Solution
=
nsync
120 f se 120 (
E1.7 Lorentz force on a moving current-carrying rod
Figure 1-16:
Solution
Further: Explain qualitatively the direction of the force based on the elastic properties of
magnetic field lines. The force is due to the interaction between the field lines due to
E1.10 Linear dc machine
Figure 1-27a; bar initially at rest, switch closes at time zero:
Figure 1-27b; Fapp is externally applied force, Find is electromagnetic induced force that
balances Fapp in steady state (constant velocity):
An alternative problem f
E1.4 Constitutive relation for lossless ferromagnetic materials
Figure 1-10c:
Solution
Figure 1-10d:
Question: What value is headed for as goes to infinity? What is the slope of the B-H
curve for large H?
Further: A piecewise-linear model of the nonlinear
E1.6 Faradays Law analysis of an inductor
Figure 1-15, modified:
s
s
s
Note: The arrow associated with and the + associated with establish arbitrary reference
directions. The direction of the solid arrow associated with is also a reference direction,
but
A motors shaft is spinning at a speed of 1800 r/min. What is the shaft speed in radians per
second?
P1.1 Convert rpm to radian or cyclic frequency
Solution
1 min 2 rad
The speed = (1800 r/min )
in radians per second is = 188.5 rad/s .
What is it in cyc
E2.4 Per unit specification of a power component
The transformer is rated 20 kVA, 8000/240 V, 60 Hz. The equivalent circuit referred to the
primary (high voltage) side, determined in Example 2-.2 and summarized in Figure 2-21, is:
Solution
Figure 2-25:
The motor in Problems 6-5, 6, 7 is further investigated here. It is a 208-V four-pole 60-Hz Yconnected wound-rotor induction motor is rated at 30 hp. Its equivalent circuit
components are
P6.8 Maximum torque at start
1 = 0.100
1 = 0.210
mech = 500 W
2 =
A three-phase 60-Hz induction motor runs at 715 r/min at no load and at 670 r/min at full
load.
P6.3 Linear region of torque-speed characteristic
(a) How many poles does this motor have?
(b) What is the slip at rated load?
(c) What is the speed at one-qua
An ac machine has the rotor and stator magnetic fields shown in Figure P3-1. What is the
direction of the induced torque in the machine? Is the machine acting as a motor or
generator?
P3.8 Torque in an ac electric machine
Figure P3-1:
Since ind kB R B net
The flux density distribution over the surface of a two-pole stator of radius r and length l is
given by
P3.9 Air-gap flux density and flux
B = B M cos ( m t )
Prove that the total flux under each pole face is
= 2rlB M .
(3-37b)
The total flux under a po
A 100-MVA, 14.4-kV 0.8-PF-lagging, Y-connected synchronous generator has a negligible
armature resistance and a synchronous reactance of 1.0 per-unit. The generator is
connected in parallel with a 60-Hz, 14.4-kV infinite bus that is capable of supplying o
The motor in Problem 6-5 is further investigated here. It is a 208-V four-pole 60-Hz Yconnected wound-rotor induction motor is rated at 30 hp. Its equivalent circuit
components are
P6.6 Pullout slip and torque
1 = 0.100
1 = 0.210
mech = 500 W
2 = 0.070
A three-phase 60-Hz two-pole induction motor runs at a no-load speed of 3580 r/min and a
full-load speed of 3440 r/min. Calculate the slip and the electrical frequency of the rotor at
no-load and full-load conditions. What is the speed regulation of this
A 208-V six-pole Y-connected 25-hp design class B induction motor is tested in the
laboratory, with the following results:
P6.20 Induction motor model parameters from test data
No load:
Locked rotor:
DC test:
208 V, 24.0 A, 1400 W, 60 Hz
24.6 V, 64.5 A, 2
An induction motor is rated 460-V, -connected, two-pole, 100-hp, 60 Hz, starting code
letter F.
P6.30 Induction motor starting 2
(a) What is the maximum starting current that this machines controller must be designed
to handle?
(b) The controller is desig
A 150-MVA 15/200-kV single-phase power transformer has a per-unit resistance of 1.2
percent and a per-unit reactance of 5 percent (data taken from the transformers
nameplate). The magnetizing impedance is j80 per unit.
P2.8 Single-phase transformer equiva
A 5000-kVA 230/13.8-kV single-phase power transformer has a per-unit resistance of 1
percent and a per-unit reactance of 5 percent (data taken from the transformers
nameplate) has equivalent circuit referred to the low-voltage (secondary) side found in
pa
P5.1 Synchronous motor
A 480-V, 60 Hz, 400-hp 0.8-PF-leading eight-pole -connected synchronous motor has a
synchronous reactance of 0.6 and negligible armature resistance. Ignore its friction,
windage, and core losses for the purposes of this problem. Ass
P5.2 SM at rated load and no load
A 480-V, 60 Hz, 400-hp 0.8-PF-leading eight-pole -connected synchronous motor has a
synchronous reactance of 0.6 and negligible armature resistance (this is the motor of
Problem 5-1). The motor is operating at rated condi