Master Electrical Designing

TABLE OF CONTENTS

LIST OF FIGURES........................................................................................................................ ii

LIST OF TABLES.........................................................................................................................iii

REFERENCES............................................................................................................................... iv

OBJECTIVES.................................................................................................................................. v

AC MOTOR THEORY...................................................................................................................1

Principles of Operation........................................................................................................1
Rotating Field...................................................................................................................... 1
Torque Production............................................................................................................... 5
Slip....................................................................................................................................... 5
Torque.................................................................................................................................. 7
Summary.............................................................................................................................. 8

AC MOTOR TYPES.......................................................................................................................9

Induction Motor...................................................................................................................9
Single-Phase AC Induction Motors.................................................................................. 11
Synchronous Motors..........................................................................................................12
Starting a Synchronous Motor.......................................................................................... 12
Field Excitation..................................................................................................................14
Summary............................................................................................................................ 15

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AC MOTOR THEORY

AC motors are widely used to drive machinery for a wide variety of applications.
To understand how these motors operate, a knowledge of the basic theory of
operation of AC motors is necessary.

EO 1.1 DESCRIBE how a rotating magnetic field is produced

in an AC motor.

EO 1.2 DESCRIBE how torque is produced in an AC motor.

EO 1.3 Given field speed and rotor speed, CALCULATE

percent slip in an AC motor.

EO 1.4 EXPLAIN the relationship between slip and torque in

an AC induction motor.

Principles of Operation

The principle of operation for all AC motors relies on the interaction of a revolving magnetic
field created in the stator by AC current, with an opposing magnetic field either induced on the
rotor or provided by a separate DC current source. The resulting interaction produces usable
torque, which can be coupled to desired loads throughout the facility in a convenient manner.
Prior to the discussion of specific types of AC motors, some common terms and principles must
be introduced.

Rotating Field

Before discussing how a rotating magnetic field will cause a motor rotor to turn, we must first
find out how a rotating magnetic field is produced. Figure 1 illustrates a three-phase stator to
which a three-phase AC current is supplied.

The windings are connected in wye. The two windings in each phase are wound in the same
direction. At any instant in time, the magnetic field generated by one particular phase will
depend on the current through that phase. If the current through that phase is zero, the resulting
magnetic field is zero. If the current is at a maximum value, the resulting field is at a maximum
value. Since the currents in the three windings are 120° out of phase, the magnetic fields
produced will also be 120° out of phase. The three magnetic fields will combine to produce one
field, which will act upon the rotor. In an AC induction motor, a magnetic field is induced in
the rotor opposite in polarity of the magnetic field in the stator. Therefore, as the magnetic field
rotates in the stator, the rotor also rotates to maintain its alignment with the stator’s magnetic
field. The remainder of this chapter’s discussion deals with AC induction motors.

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Figure 1 Three-Phase Stator

From one instant to the next, the magnetic fields of each phase combine to produce a magnetic
field whose position shifts through a certain angle. At the end of one cycle of alternating current,
the magnetic field will have shifted through 360°, or one revolution (Figure 2). Since the rotor
has an opposing magnetic field induced upon it, it will also rotate through one revolution.

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For purpose of explanation, rotation of the magnetic field is developed in Figure 2 by "stopping"
the field at six selected positions, or instances. These instances are marked off at 60° intervals
on the sine waves representing the current flowing in the three phases, A, B, and C. For the
following discussion, when the current flow in a phase is positive, the magnetic field willdevelop
a north pole at the poles labeled A, B, and C. When the current flow in a phase is negative, the
magnetic field will develop a north pole at the poles labeled A’, B’, and C’.

Figure 2 Rotating Magnetic Field

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At point T1, the current in phase C is at its maximum positive value. At the same instance, the
currents in phases A and B are at half of the maximum negative value. The resulting magnetic
field is established vertically downward, with the maximum field strength developed across the
C phase, between pole C (north) and pole C’ (south). This magnetic field is aided by the weaker
fields developed across phases A and B, with poles A’ and B’ being north poles and poles A and
B being south poles.

At Point T2, the current sine waves have rotated through 60 electrical degrees. At this point, the
current in phase A has increased to its maximum negative value. The current in phase B has
reversed direction and is at half of the maximum positive value. Likewise, the current in phase
C has decreased to half of the maximum positive value. The resulting magnetic field is
established downward to the left, with the maximum field strength developed across the A phase,
between poles A’ (north) and A (south). This magnetic field is aided by the weaker fields
developed across phases B and C, with poles B and C being north poles and poles B’ and C’
being south poles. Thus, it can be seen that the magnetic field within the stator of the motor has
physically rotated 60°.

At Point T3, the current sine waves have again rotated 60 electrical degrees from the previous
point for a total rotation of 120 electrical degrees. At this point, the current in phase B has
increased to its maximum positive value. The current in phase A has decreased to half of its
maximum negative value, while the current in phase C has reversed direction and is at half of
its maximum negative value also. The resulting magnetic field is established upward to the left,
with the maximum field strength developed across phase B, between poles B (north) and B’
(south). This magnetic field is aided by the weaker fields developed across phases A and C, with
poles A’ and C’ being north poles and poles A and C being south poles. Thus, it can be seen
that the magnetic field on the stator has rotated another 60° for a total rotation of 120°.

At Point T4, the current sine waves have rotated 180 electrical degrees from Point T1 so that the
relationship of the phase currents is identical to Point T1 except that the polarity has reversed.
Since phase C is again at a maximum value, the resulting magnetic field developed across phase
C will be of maximum field strength. However, with current flow reversed in phase C the
magnetic field is established vertically upward between poles C’ (north) and C (south). As can
be seen, the magnetic field has now physically rotated a total of 180° from the start.

At Point T5, phase A is at its maximum positive value, which establishes a magnetic field
upward to the right. Again, the magnetic field has physically rotated 60° from the previous point
for a total rotation of 240°. At Point T6, phase B is at its maximum negative value, which will
establish a magnetic field downward to the right. The magnetic field has again rotated 60° from
Point T5 for a total rotation of 300°.

Finally, at Point T7, the current is returned to the same polarity and values as that of Point T1.
Therefore, the magnetic field established at this instance will be identical to that established at
Point T1. From this discussion it can be seen that for one complete revolution of the electrical
sine wave (360°), the magnetic field developed in the stator of a motor has also rotated one
complete revolution (360°). Thus, you can see that by applying three-phase AC to three
windings symmetrically spaced around a stator, a rotating magnetic field is generated.

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Torque Production

When alternating current is applied

to the stator windings of an AC
induction motor, a rotating
magnetic field is developed. The
rotating magnetic field cuts the
bars of the rotor and induces a
current in them due to generator
action. The direction of this
current flow can be found using
the left-hand rule for generators.
This induced current will produce
a magnetic field, opposite in
polarity of the stator field, around
the conductors of the rotor, which
will try to line up with the
magnetic field of the stator. Since
the stator field is rotating
continuously, the rotor cannot line
up with, or lock onto, the stator
field and, therefore, must follow
behind it (Figure 3).

Figure 3 Induction Motor

Slip

It is virtually impossible for the rotor of an AC induction motor to turn at the same speed as that
of the rotating magnetic field. If the speed of the rotor were the same as that of the stator, no
relative motion between them would exist, and there would be no induced EMF in the rotor.
(Recall from earlier modules that relative motion between a conductor and a magnetic field is
needed to induce a current.) Without this induced EMF, there would be no interaction of fields
to produce motion. The rotor must, therefore, rotate at some speed less than that of the stator
if relative motion is to exist between the two.

The percentage difference between the speed of the rotor and the speed of the rotating magnetic
field is called slip. The smaller the percentage, the closer the rotor speed is to the rotating
magnetic field speed. Percent slip can be found by using Equation (12-1).

NS NR
SLIP x 100% (12-1)
NS

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where

NS = synchronous speed (rpm)

NR = rotor speed (rpm)

The speed of the rotating magnetic field or synchronous speed of a motor can be found by using
Equation (12-2).

NS 120 f
P (12-2)

where

Ns = speed of rotating field (rpm)

f = frequency of rotor current (Hz)
P = total number of poles

Example: A two pole, 60 Hz AC induction motor has a full load speed of 3554 rpm. What
is the percent slip at full load?

Solution:

Synchronous speed:

NS 120 f
P

NS 120 (60 Hz)

2

NS 3600 rpm

Slip:

NS NR
SLIP x 100%
NS

SLIP 3600 3554 rpm

x 100% 1.3%
3600 rpm

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Torque

The torque of an AC induction motor is dependent upon the strength of the interacting rotor and
stator fields and the phase relationship between them. Torque can be calculated by using
Equation (12-3).

T = K  IR cos R (12-3)

where

 = torque (lb-ft)
K = constant
 = stator magnetic flux
IR = rotor current (A)
cos R = power factor of rotor

During normal operation, K, , and cos R

are, for all intents and purposes, constant,
so that torque is directly proportional to
the rotor current. Rotor current increases
in almost direct proportion to slip. The
change in torque with respect to slip
(Figure 4) shows that, as slip increases
from zero to ~10%, the torque increases
linearly. As the load and slip are
increased beyond full-load torque, the
torque will reach a maximum value at
about 25% slip. The maximum value of
torque is called the breakdown torque of
the motor. If load is increased beyond
this point, the motor will stall and come
to a rapid stop. The typical induction
motor breakdown torque varies from 200
Figure 4 Torque vs Slip
to 300% of full load torque. Starting
torque is the value of torque at 100% slip
and is normally 150 to 200% of full-load torque. As the rotor accelerates, torque will increase
to breakdown torque and then decrease to the value required to carry the load on the motor at
a constant speed, usually between 0-10%.

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Summary

The important information covered in this chapter is summarized below.

AC Motor Theory Summary

A magnetic field is produced in an AC motor through the action of the three-

phase voltage that is applied. Each of the three phases is 120° from the other
phases. From one instant to the next, the magnetic fields combine to produce
a magnetic field whose position shifts through a certain angle. At the end of
one cycle of alternating current, the magnetic field will have shifted through
360°, or one revolution.

Torque in an AC motor is developed through interactions with the rotor and

the rotating magnetic field. The rotating magnetic field cuts the bars of the
rotor and induces a current in them due to generator action. This induced
current will produce a magnetic field around the conductors of the rotor,
which will try to line up with the magnetic field of the stator.

Slip is the percentage difference between the speed of the rotor and the speed
of the rotating magnetic field.

In an AC induction motor, as slip increases from zero to ~10%, the torque

increases linearly. As the load and slip are increased beyond full-load torque,
the torque will reach a maximum value at about 25% slip. If load is
increased beyond this point, the motor will stall and come to a rapid stop.
The typical induction motor breakdown torque varies from 200 to 300% of
full-load torque. Starting torque is the value of torque at 100% slip and is
normally 150 to 200% of full-load torque.

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AC MOTOR TYPES

Various types of AC motors are used for specific applications. By matching the
type of motor to the appropriate application, increased equipment performance
can be obtained.

EO 1.5 DESCRIBE how torque is produced in a single-phase

AC motor.

EO 1.6 EXPLAIN why an AC synchronous motor does not have

starting torque.

EO 1.7 DESCRIBE how an AC synchronous motor is started.

EO 1.8 DESCRIBE the effects of over and under-exciting an AC

synchronous motor.

EO 1.9 STATE the applications of the following types of AC

motors:
a. Induction
b. Single-phase
c. Synchronous

Induction Motor

Previous explanations of the operation of an AC motor dealt with induction motors. The
induction motor is the most commonly used AC motor in industrial applications because of its
simplicity, rugged construction, and relatively low manufacturing costs. The reason that the
induction motor has these characteristics is because the rotor is a self-contained unit, with no
external connections. This type of motor derives its name from the fact that AC currents are
induced into the rotor by a rotating magnetic field.

The induction motor rotor (Figure 5) is made of a laminated cylinder with slots in its surface.
The windings in the slots are one of two types. The most commonly used is the "squirrel-cage"
rotor. This rotor is made of heavy copper bars that are connected at each end by a metal ring
made of copper or brass. No insulation is required between the core and the bars because of the
low voltages induced into the rotor bars. The size of the air gap between the rotor bars and
stator windings necessary to obtain the maximum field strength is small.

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Figure 5 Squirrel-Cage Induction Rotor

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Figure 6 Split-Phase Motor

Single-Phase AC Induction Motors

If two stator windings of unequal impedance are spaced 90 electrical degrees apart and connected
in parallel to a single-phase source, the field produced will appear to rotate. This is called phase
splitting.

In a split-phase motor, a starting winding is utilized. This winding has a higher resistance and
lower reactance than the main winding (Figure 6). When the same voltage VT is applied to the
starting and main windings, the current in the main winding (IM) lags behind the current of the
starting winding IS (Figure 6). The angle between the two windings is enough phase difference
to provide a rotating magnetic field to produce a starting torque. When the motor reaches 70 to
80% of synchronous speed, a centrifugal switch on the motor shaft opens and disconnects the
starting winding.

Single-phase motors are used for very small commercial applications such as household
appliances and buffers.

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Figure 7 Wound Rotor

Synchronous Motors

Synchronous motors are like induction motors in that they both have stator windings that produce
a rotating magnetic field. Unlike an induction motor, the synchronous motor is excited by an
external DC source and, therefore, requires slip rings and brushes to provide current to the rotor.
In the synchronous motor, the rotor locks into step with the rotating magnetic field and rotates
at synchronous speed. If the synchronous motor is loaded to the point where the rotor is pulled
out of step with the rotating magnetic field, no torque is developed, and the motor will stop. A
synchronous motor is not a self-starting motor because torque is only developed when running
at synchronous speed; therefore, the motor needs some type of device to bring the rotor to
synchronous speed.

Synchronous motors use a wound rotor. This type of rotor contains coils of wire placed in the
rotor slots. Slip rings and brushes are used to supply current to the rotor. (Figure 7).

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Starting a Synchronous Motor

A synchronous motor may be started by a DC motor on a common shaft. When the motor is
brought to synchronous speed, AC current is applied to the stator windings. The DC motor now
acts as a DC generator and supplies DC field excitation to the rotor of the synchronous motor.
The load may now be placed on the synchronous motor. Synchronous motors are more often
started by means of a squirrel-cage winding embedded in the face of the rotor poles. The motor
is then started as an induction motor and brought to ~95% of synchronous speed, at which time
direct current is applied, and the motor begins to pull into synchronism. The torque required to
pull the motor into synchronism is called the pull-in torque.

As we already know, the synchronous motor rotor is locked into step with the rotating magnetic
field and must continue to operate at synchronous speed for all loads. During no-load conditions,
the center lines of a pole of the rotating magnetic field and the DC field pole coincide (Figure 8a).
As load is applied to the motor, there is a backward shift of the rotor pole, relative to the stator
pole (Figure 8b). There is no change in speed. The angle between the rotor and stator poles is
called the torque angle ().

Figure 8 Torque Angle

If the mechanical load on the motor is increased to the point where the rotor is pulled out of
synchronism (90o), the motor will stop. The maximum value of torque that a motor can
develop without losing synchronism is called its pull-out torque.

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Field Excitation

For a constant load, the power factor of a synchronous motor can be varied from a leading value
to a lagging value by adjusting the DC field excitation (Figure 9). Field excitation can be
adjusted so that PF = 1 (Figure 9a). With a constant load on the motor, when the field excitation
is increased, the counter EMF (VG) increases. The result is a change in phase between stator
current (I) and terminal voltage (Vt), so that the motor operates at a leading power factor (Figure
9b). Vp in Figure 9 is the voltage drop in the stator winding’s due to the impedance of the
windings and is 90o out of phase with the stator current. If we reduce field excitation, the motor
will operate at a lagging power factor (Figure 9c). Note that torque angle, , also varies as field
excitation is adjusted to change power factor.

Figure 9 Synchronous Motor Field Excitation

Synchronous motors are used to accommodate large loads and to improve the power factor of
transformers in large industrial complexes.

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Summary

The important information in this chapter is summarized below.

AC Motor Types Summary

In a split-phase motor, a starting winding is utilized. This winding has a higher

resistance and lower reactance than the main winding. When the same voltage
(VT) is applied to the starting and main windings, the current in the main
winding lags behind the current of the starting winding. The angle between the
two windings is enough phase difference to provide a rotating magnetic field to
produce a starting torque.

A synchronous motor is not a self-starting motor because torque is only

developed when running at synchronous speed.

A synchronous motor may be started by a DC motor on a common shaft or by

a squirrel-cage winding imbedded in the face of the rotor poles.

Keeping the same load, when the field excitation is increased on a synchronous
motor, the motor operates at a leading power factor. If we reduce field excitation,
the motor will operate at a lagging power factor.

The induction motor is the most commonly used AC motor in industrial

applications because of its simplicity, rugged construction, and relatively low
manufacturing costs.

Single-phase motors are used for very small commercial applications such as
household appliances and buffers.

Synchronous motors are used to accommodate large loads and to improve the
power factor of transformers in large industrial complexes.

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