CHAPTER 11
THREE-PHASE
SYNCHRONOUS
MACHINES
11.1 Introduction
It was shown in an earlier chapter that an alternator
driven at a constant speed produces an alternating voltage
at a fixed frequency dependent on the number of poles in
the machine. A machine designed to be connected to the
supply and run at synchronous speed is referred to as a
synchronous machine. The description applies to both
motors and generators. A synchronous condenser is a
special application of a synchronous motor.
While the synchronous motor has only one generally
used name, the synchronous generator is on occasion
referred to as an alternator or as an a.c. generator. The
term alternator has been used in previous chapters and
will be used in this chapter but it should be remembered
that other terms are in use.
In general, the principles of construction and
operation are similar for both alternators and generators,
just as there were basic similarities between d.c. motors
and generators.
While alternators were once seldom seen outside
power houses and whole communities were supplied from
a central source, there is now an expanding market for
smaller sized alternators suitable for the provision of
power for portable tools. Today, with the growth in
computer control, there is a further need for standby
generating plant to ensure a continuity of supply to
prevent a loss of data from computer memories. So much
information is being stored in computers today that even
brief interruptions to the power supplies can have serious
consequences on the accuracy and extent of information
stored.
In the majority of cases, the rotor has the d.c. winding
and the stator the a.c. winding. An alternator with a
rotating a.c. winding and a stationary d.c. winding, while
suitable for smaller outputs, is not satisfactory for the
larger outputs required at power stations. With these
machines the output can be in megawatts; a value too
large to be handled with brushes and slip rings. Because
the terminal voltages range up to 33 kV, the only
satisfactory construction is to have the a.c. windings
stationary and to supply the rotor with d.c.
This arrangement has the following advantages:
l. extra winding space for the a.c. windings;
2. easier to insulate for higher voltages;
3. simple, strong rotor construction;
4. lower voltages and currents in the rotating windings;
5. the high current \Vindings have solid connections to the
"outside" circuit;
6. better suited to the higher speeds (and smaller number
of poles) of turbine drives.
11.2 Alternators
11.2.1 Stator
The stator of the three-phase synchronous machine
consists of a slotted laminated core into which the stator
winding is fitted. The stator winding consists of three
separate windings physically displaced from each other by
120° E. Each phase winding has a number of coils
connected in series to form a definite number of magnetic
poles. A four-pole machine, for example, has four groups
of coils per phase or four "pole-phase groups". The ends
of the three phase windings are connected in either star or
delta to the external circuit.
Details of phase windings for a three-phase machine
were shown in Chapter l 0 to consist of three identical
windings symmetrically distributed around the stator.
The three-phase synchronous machine has two main
windings:
1. a three-phase a.c. winding;
2. another winding carrying d.c.
11.2.2 Rotor
The alternator rotor can be of two types-low speed and
high speed.
209
210
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TR
11.2.3 Prime movers
Low speed
Most diesel engines used as prime movers for
alternators operate within the speed range of 50
r /min and this necessitates the use of rotors witl
pairs of poles.
Hydroelectric turbines have water-driven in
which operate at low speeds, consequently they all
rotors with. many poles. While the diesel-driven alt
usually has its shaft in the horizontal plat
hydroelectric unit has its shaft in the vertical plar
method of construction means that special thrust t
have to be fitted to take the end thrust of the 1
component.
Fig. 11.1 Stator for a tour-pole 415 V three-phase 350 kVA
alternator
DUNLITE GENERATING SET MANUFACTURERS
Low speed (salient pole)
This type usually consists ofa "spider" similar to that used
in d.c. machines, on which are bolted the field poles and
the field coils (see Fig. l l .2(a)). Physical constraints limit
the use of this type of rotor to low-speed machines.
High speed (cylindrical)
The cylindrical rotor was developed to meet the needs of
higher-speed prime movers. To counteract centrifugal
forces its diameter must be small in comparison to its
length (see Fig. l l.2(b)).
High speed
Turbine prime movers, whether steam or gas,
efficiently at speeds in the vicinity of 3000 r / n
alternator driven by a turbine and producing a fn
of 50 Hz at 3000 r /min must consist of only two
In Chapter 6 the relationship between
frequency and the number of poles was shown tc
~
~
By transposition
120/
n=--
p
where n = r/min
f = frequency in hertz
p = number of poles
For a large-diameter rotor of twenty-four
50 Hz
n =
120
X
50
24
= 250 r/min
For a turbine-type rotor of two poles at 50 f
n =
120
x
2
50
= 3000 r/min
(b)
Fig. 11.2 Main types of alternator rotors: (a) low speed-salient pole, (b) high speed-cylindrical
1
THREE-PHASE SYNCHRONOUS MACHINES
211
Example 11.1
At what speed would the governor of a twelve-pole dieseldriven alternator have to be set to enable a frequency of
60 Hz to be generated?
n = 120{
p
120 x 60
= 600 r/min
12
An alternator in this speed range will have a large
diameter and have a comparatively short axial length.
With turbines, the extra expense and auxiliary machinery
needed restricts their use to larger sizes. Higher outputs
mean that the length of the alternator must be increased
and the increase in length causes complications in cooling.
11.2.4 Alternator cooling
Low speed
With engine-driven or hydroelectric alternators, there is
no great difficulty in providing adequate ventilation
because of the characteristically large diameter and short
axial length. In addition to the large surface area available
for direct radiation of heat, there is a fanning action due to
the rotation of the fields; an action which can be increased
by the addition of fan blades if necessary.
When the axial length is short, the heat developed in
the imbedded windings is quickly conducted to the ends,
where the fanning action can dissipate it. As the machine
size becomes larger, it is often necessary to provide
ventilation ducts within the core to provide paths through
which cooling air can flow.
High speed
The provision of adequate cooling facilities is a problem in
high-speed machines of large capacity if the operating
temperature of the windings is to be kept within safe
limits. The surface area available for cooling in a highspeed machine is less than that in a low-speed machine of
the same capacity.
The diameter of the rotor must be small enough to
keep the surface speed down to a safe value, so for large
capacities the length of the machine must be considerable.
This long axial length causes difficulty in cooling the
central portion of the core, because the heat generated
cannot be conducted away quickly enough to limit the
temperature rise in the core to a value that will protect the
windings and the insulation.
These considerations gave rise to the necessity for
completely enclosing the alternator, and allowing the use
of forced ventilation to carry away the heat produced.
Where cooling air is used, it must be filtered to keep it
clean and sometimes washed by passing it through a spray
chamber to prevent a build-up of dust within the machine.
Washing the air has the added advantage of cooling it,
and so further reducing the temperature of the alternator
and allowing the rating of the machine to be increased.
To increase alternator ratings still more, hydrogen gas
is used instead of air because ofits greater ability to absorb
heat. The machine is completely enclosed and the
hydrogen is blown through the alternator and then ~
through a heat-exchanger before being cycled through the (" ~
alternator again. The total exclusion of air from a fully Jsealed machine is necessary to prevent an explosive 'mixture from forming.
3
These cooling methods require considerable powe 1o:::
and auxiliary equipment, so the output from th \0
alternator must be increased an appreciable amount fo \;,
the method to be economically feasible. Accordingly. it is '. "£,.
only used on very high-capacity machines.
~ ~ _,,
11.2.5 Excitation
The usual method for d.c. excitation of the rotor
\Vindings is for each machine to have its own d.c.
generator called an "exciter" (refer to Fig. 11.3). The
exciter can be belt-driven or geared down from the
synchronous machine. but the usual practice is for the
exciter to be directly coupled to the rotor shaft.
The exciter armature rotates within the influence of
the exciter field, causing a d.c. voltage to be generated in
1----------------1
Exciter
Alternator
, - - - - - - - - - --1
I
I
I
I
t
I
I
Exciter
field
I
Stator
windings
Brush
gear
and
slip
rings
Rotor
field
I
I
I
L ___________ J
L
I
I
I
I
I
I
I
I
_________________ J
Fig. 11.3 Basic alternator circuit
~
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TR
212
the armature. The exciter output is fed into the field where V, = generated voltage per phase (r.m.s.)
windings of the synchronous machine. By adjusting the
IP = flux per pole in webers
rheostat in the exciter field circuit, the strength of the
f = frequency in hertz
magnetic field in the rotor can be varied.
N = number of turns per phase
kd = a constant, dependent on winding di
With very large alternators the d.c. excitation
requirements are substantial. This means that the d.c.
ti on
kp = a constant, dependent on coil pitch
generators have to be large also; so large that they may not
be able to self-excite. Because of this, the generator may
need an exciter of its own-one that is able to self-excite Example 11.2
and provide power for the field of the main d.c. generator Calculate the line voltage of a 50 Hz star-cor
which in turn supplies the rotor field of the alternator.
alternator given the following details:
Some alternators use "brushless" excitation in which
IP = 0.67 Wb/pole
the exciter armature has been replaced by a three-phase
Kd
= 0.85
winding which rotates within the influence of a d.c.
KP
= 0.98
magnetic field, causing a three-phase voltage to be
N = 36 turns/phase
generated in the exciter. This three-phase exciter output is
fed through a full-wave bridge rectifier, mounted on the
V, = 4.44 IPJN KdKp
end of the exciter and converted to d.c.
= 4.44 x 0.67 x 50 x 36 x 0.85
The resulting d.c. is in turn fed into the rotor windings
= 4460 v
of the synchronous machine. By varying the current
through the exciter field, the rotor field is varied and so
Then V, = yJ x Vp
governs the value of the generated voltage (see Fig. 11.4).
= I. 732 x 4460
= 7725 v
11.2.6 Generated voltage
The value of the generated a.c. voltage depends on the 11.2. 7 Effect of load on alternator voltage
strength of the rotor flux and the speed at which it cuts the An alternator can be considered to consist c
windings. Because the speed must be constant (and is components in series:
linked to the frequency required), the sole remaining I. an a.c. generating source;
factor determining the value of the generated voltage is the 2. a resistor-representing iron and copper losse~
strength of the rotor flux.
3. an inductor-representing the inductance
For an alternator the generated voltage is found from:
windings and magnetic leakage.
Any load placed on the alternator must be assum
v, = 4.44 IPJNkdkp I
in series with these components as shown in Fjgu
Three-phase bridge
rectifier
Three-phase exciter
windings
+
Rotor
Stator
field
windings
Exciter
field
1.
Rotating components
.1
Fig. 11.4 Brushless excitation
213
THREE-PHASE SYNCHRONOUS MACHINES
,---- l
I
I
I
I
I
I
I
I
I
I
R
I
I
I
I Alternator
Load
z
I
I
L
I
L_
__ J
I
generated voltage v,. For a load with a lagging power
factor, however, the magnetic effect of the stator currents
opposes that of the rotor, resulting in a weakened rotor
field and reducing the output voltage further than did the
resistive load (see Fig. l l .6(b)). As before, IR is in phase
with the load current!. /Xis at 90°E to JR so placing /Z at
a different angle to the previous case. In a similar manner,
V, is equal to the phasor sum of the output voltage and /Z.
For a load with a leading power factor, the flux caused by
the stator currents assists that of the rotor resulting in an
increased output voltage (see Fig. l l.6(c)). The
characteristics of the three types of loads are shown in
Figure 11.7.
Fig. 11.5 Equivalent circuit of an alternator
11.2.8 Voltage regulation
The series impedance of the resistance and inductance
provides a drop in voltage before the generated voltage
can reach the connected load. Additionally the load
current in the a.c. windings produces
an
armature
reaction which also affects the output voltage.
With a unity power factor load the armature reaction
merely distorts the main field and the effect on voltage is
minimal, the voltage drop in the main being due to the
series impedance. Figure l I.6(a) shows that the resistive
voltage drop IR is in phase with the load current I and the
voltage drop due to the reactance IX is at 90°E to the IR
drop. These two values combine to form a voltage drop IZ
due to the impedance of the alternator windings. The
phasor sum of the output voltage and /Z gives the
v,_
IZ
: IX
v.
IR
(a) Unity power factor
An alternator is required to give a prescribed terminal
voltage at full load. The difference in output between no
load and full load is a measure of its voltage regulation.
The difference is compared to the full-load value in a
similar manner to that for d.c. machines.
.
Voltage regulat10n
= [VNLVFL VFL
X
100 ] %
Example 11.3
A three-phase star-connected alternator has an output
voltage of 3300 V at full load with unity power factor.
When the load is removed and the excitation is unchanged
the voltage rises to 3350 V. Find the percentage
regulation.
Change in voltage = 3350 - 3300 = 50 V
.
50 x 100
Regulal!on =
3300
= I.5% at unity power factor.
Note The regulation must also be referred to the load
power factor because these figures at any other
power factor would be different.
v,
IZ_./.:
_.·IX
V
-E---.--7· ·.:
JR
(b) Lagging power factor
Leading power
Output
voltage
rE=::::::::==:::~~;~-=~;
factor
Unity power
factor
Lagging power
factor
(c) Leading power factor
Fig. 11.6 Phasors for various power factor loads on an
alternator
Load current
Fig. 11.7 Effect of power factor on output voltage of an
alternator
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TRI
214
11.2.9 Alternator ratings
An alternator is rated according to three basic factors:
I. frequency;
2. voltage;
3. current.
The first fixes the speed at which the alternator must
be driven; the second states the designed output voltage;
and the third is the full-load current output. The last two
factors help establish the volt-ampere rating, usually
expressed in kV A.
The power factor of any load placed on the alternator
is beyond the control of the manufacturer and because it
could vary considerably, the alternator rating cannot be
given in kilowatts.
Example 11.4
Find the power loading in kilowatts of a three-phase, 415
V, 50 Hz alternator rated at 150 kV A at 0.8 power factor,
if the load has a power factor of:
(a) 0.8;
(b) 0.6.
Machine is rated at 150 kVA and 0.8 power factor,
then at this load:
power output = 150 x 0.8 = 120 kW
At 0.6 power factor,
power output = 150
x 0.6
= 90 kW
In both cases, the current flowing will be the full-load
current value, which should not be exceeded because of
cooling problems within the windings.
At 0.8 power factor,
P =
i.e. 120 000 =
:. I=
VJ VIA.
;j3
x 415 x Ix 0.8
V3
120000
= 208 A
x 415 x 0.8
~
Purchase price
The overall cost for smaller units may be lower,
terms of cost per kVA they are more expensb
operate at lower efficiencies. As the size of tt
increases, the cost per kV A reduces while the op1
efficiency increases.
Type of prime mover
The economy of the prime mover in terms of effi
has a bearing on its selection. This in turn is affec
the type of service it will encounter. For exarr
steam turbine has a good economy throughout its
load range. However, it is expensive, large, and n
long time to get the unit on load from cold. An i1
combustion engine has poor efficiency at light load,
much cheaper to buy initially. For some loads it is c
to buy several smaller alternators than one larg'
Problems of paralleling the units then have
considered (see sect. 11.4). The cost and availab
fuel must always be a consideration. While disti
more expensive initially, as is the diesel engine its1
fuel cost per hour is less while maintenance costs
higher than those for a petrol engine. The petrol er
cheaper to buy, the fuel is readily available, and the
suited to smaller units used purely for portable
supplies on intermittent duties. In the long term th(
engine runs better on full loads than the petrol engir
petrol engine is more tolerant of dirty fuel than th<
engine and does not need specialised skil
maintenance purposes.
Starting methods
These are governed by the intended use of the geni
unit. The quicker the changeover to auxiliary pm
more expensive is the starting method. The ct
method involves merely starting the unit manually
is realised that the main power supply has failed. f
1
This is the full-load current rating for each phase winding
of this particular alternator and it applies irrespective of
the load power factor or of the load power.
11.3 Emergency power supplies and
portable alternators
The factors affecting the buying and running of
alternators can be many and varied. They range from
buying a small portable unit at the best possible price to
careful planning for the most suitable unit for a particular
purpose. It is not enough to simply select an alternator
with respect to the load it has to supply; the choice should
be affected by many other considerations. Some of these
factors are listed below and their order of importance is
governed by the actual use intended for the alternator.
self~contained portable power supply. 7
alternator rated at 6 kVA is driven by a pet
engine. The size and weight of the unit is.
that it can be carried to any site where po·
required.
DEPT OF A'
Fig. 11.8 A
215
THREE-PHASE SYNCHRONOUS MACHINES
expensive method involves the use of a changeover
contactor which drops out when the main supply fails. In
turn this connects a starting motor to the engine and after
the alternator has got up to speed connects it to the load.
At the top end of the scale is the so-called "no-break"set.
The alternator with a heavy flywheel is run as a synchronous motor, being separated from the prime-mover
by an electrically operated clutch. When a mains failure
occurs the clutch is released connecting the alternator and
the flywheel to the engine. The engine is quickly run up to
speed and the alternator reverts to its intended purpose.
The changeover period can be short enough to ensure
continuity of operation of essential equipment. The
method is very expensive with high operating costs.
Load sizes and alternator capacities
Smaller generating plant is usually intended for standby
purposes for short periods. It usually has only one load
connected to it at a time, such as a portable tool or a small
lighting load. With middle- and larger-sized alternators
consideration has to be given to the possible connection of
intermittent larger loads, such as the starting currents of
motors. The unit then has to have the electrical capacity
and engine power to maintain both the output voltage and
frequency during these current surges to avoid interruptions to other equipment connected to the same
supply.
Operation of alternators
With the exception of some manually operated equipment, most operations today are beyond the control of the
operator. Where some degree of manipulation is available
there are two important factors that should always be
considered-voltage and frequency. In most cases the
voltage is governed by automatic voltage regulators while
the frequency is controlled by the engine governor. The
order of operation is to set the speed first, which in turn
sets the frequency, and then adjust the voltage of the unit.
To do this in the reverse order is to alter the voltage each
time the speed is altered.
11.4 Parallel operation of alternators
-synchronising
Most commercial power stations are designed to have a
number of alternators operating in parallel, supplying a
common load at constant voltage. Because alternator
efficiency is maximum near its full-load capacity, it is
more economical to have each machine delivering its
approximate rated output. During the early hours of the
morning, for example, when there is a light load, it may be
necessary to have only one machine connected to the line,
delivering its rated output. As the load varies during the
24-hour period, so the number of machines connected in
parallel is determined.
Before a three-phase alternator can be connected in
parallel with another three-phase supply, the followin2
conditions must be fulfilled:
1. The output waveform of each supply must be identical.
This is determined by the design features of the
alternators. It is standard practice to generate a
sinusoidal waveform supply.
2. The phase sequence or' rotation of each supply must be
the same and this ensures that the e.m.fs of each supply
reach their maximum values in the same sequence; for
example, R, W, B. The phase sequence is determined
by the method of connection of the alternator phase
windings to the terminals of the machine. This check is
carried out during the commissioning process after the
initial installation, or following a major maintenance
overhaul, and it is not necessary to do it each time the
machine is connected in parallel with others.
3. The alternator and supply voltages must be the same.
4. The alternator and supply voltages must also be in
phase.
5. The alternator and supply frequencies must be
identical.
The last three conditions are explained in Chapter 10.
The value of the voltages, their phase relationship and
their frequencies can be adjusted by the operator. The
Fig.11.9 An alternative form of
"no~break
unit". The unit shown
has a 1470 r.p.m. motor· driving
an alternator at all times. The
generated frequency is 49 Hz so
the unit cannot be used to supply
frequency sensitive equipment.
The photograph shows the
alternator, driving motor,
flywheel, clutch and diesel engine.
When a power failure occurs, the
flywheel keeps the alternator
rotating tor 7 seconds allowing
the diesel engine to start. The
electrically operated clutch then
connects the engine to the
alternator. The interruption of
power to the load is in the
order of 0.5 cycle.
DEPT OF AVIATION
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TRi
216
d.c.
Alternator on load
,--
Synchronising
lamps
Incoming
alternator
d.c.
--~\\-'---------+~._-----Three-phase
distributions
Fig. 11.10 "Three dark" lamp method for synchronising alternators
1111
1111
voltage of the incoming alternator is adjusted by varying
the field excitation, and the frequency is determined by the
speed of the prime mover.
To ensure that the alternator and supply voltages are
in phase with each other before connecting them in
parallel to the load, some method of indicating the phase
relationship is required. Smaller-sized alternators can be
synchronised with lamps, but for larger machines a more
exact method is required.
11.4.1 Synchronising alternators with
incandescent lamps
"Three dark" method
Voltages for synchronising purposes can be checked by
connecting a voltmeter to each machine in turn, but this
does not give any indication of polarities or phase
relationships. Incandescent lamps can be used to indicate
this and the circuit is shown in Figure 11.10.
The voltage rating of the lamps needs to be twice the
alternator phase voltage, and the simplest way to achieve
this is to connect two lamps of equal wattage in series. The
lamps can be observed as three pairs oflamps or three can
be covered, leaving only three visible (as shown in the box
in the diagram).
If the alternator is properly connected, the three lamps
should all become bright and dim simultaneously. If they
brighten and dim in sequence, it means that the phase
rotation of the alternator is opposite to that on the
distribution system, so the phase rotation of the incoming
alternator must be reversed.
The lamps flicker at a rate equal to the diffen
frequency between that of the incoming alternator'
busbars leading to the distribution system. 1
alternator frequency approaches that of the busb•
rate of flickering slows down; when the two freq1
are equal, the flickering stops. When the lamps '
(dark), the connecting switch can be closed and t
machines will remain synchronised. When all the
are dark, there is no potential across the lamps, ind
that the two voltages are in phase with each other
The disadvantage of this connection is that th<
can be dark even with a "small" voltage across ther
smaller alternators the two a.c. sources can sync!
themselves ifthe difference is not too great, but wit!
alternators the mechanical and electrical forces ere:
a phase displacement between the two sources ca1
considerable damage.
"Two bright, one dark" method
The circuit for this method is shown in Figure 11.
can be seen to be similar to that of the previous
except that the connections for two of the Ian
crossed. Again two lamps are in series and it is t
cover up three lamps, leaving only three visible (as
by the dotted lines).
To use this circuit it is essential to check thj
rotation by the "three dark" method first.
established that the phase rotation is correct i
lamps reconnected, it will be found that the lamps!
and bright in sequence. By noting the order of bri!
it becomes a reference in determining whetl
incoming alternator is fast or slow.
THREE-PHASE SYNCHRONOUS MACHINES
d.c.
Alternator on load
217
Synchronising
lamps
,--1
Incoming
alternator
d.c.
I
I
L-------~-+-----_.. Three-phase distribution system
Fig. 11.11 "Two bright, one dark" lamp method for synchronising alternators
Synchronism occurs when the lower lamp in Figure
11.11 is dark and the other two are of equal brilliance.
Then the switch can be safely closed.
The significance of the correct lamp being dark lies in
the fact that it is connected between two similar phases.
When these two phases are synchronised, the voltage
difference between them is zero. This cannot apply to the
other lamps since they are connected across dissimilar
phases.
The "two bright, one dark" method gives greater
a revolution of the flywheel but varies according to ihe
positions of the pistons. Even with a heavy flywheel, the
accuracy-both in determining the relative speeds and
variation in torque can result in changes in the induced
frequencies, as well as showing fairly accurately the
instant for synchronising.
currents to flow between alternators in parallel, resulting
11.4.2 Synchronising alternators with a
synchroscope
A synchroscope is an instrument that indicates both phase
relationships and relative speed for an incoming
alternator. There are variations between manufacturers
for the operating principles, but in general a synchroscope
consists of a two-phase stator connected to the incoming
alternator with the rotor wound with a polarising coil and
connected to the supply source. Some models use rotating
vanes with no actual electrical connection to the rotor.
The synchroscope front panel is shown in Figure 11. 12
and the connections are shown in Figure 11.13.
If there is any difference between the frequencies of the
supply and the incoming alternator, a pointer attached to
the rotor of the synchroscope will rotate at a speed
proportional to this difference. Its direction of rotation
indicates whether the incoming machine is running fast or
slow (i.e. above or below synchronous speed). At
synchronism the pointer will remain stationary, but it
must be brought to an indicated position on the scale
before the main switch of the incoming alternator is
closed.
11.5 Hunting in alternators
The driving torque of a diesel engine is not uniform during
voltage. These voltage pulses can cause circulating
Fig.11.12 Portable synchroscope contained in a polished
wooden box. At the moment of synchronisation
the pointer should be stationary over the
vertical line.
A. J. WILLIAMS
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TRI
218
d.c.
d.c.
Incoming
alternator
Alternator on load
Synchroscope
'-+---------4-+------ Three-phase distributions
Fig. 11.13 Synchroscope connection for synchronising alternators
1!11·
in mechanical oscillations. With turbines, the pulsing or polarity: one field is that of the rotating stator a
hunting is usually due to fluctuations in the governor other that of the rotor.
settings with changes in load. Remedies for hunting
involve the use of heavy flywheels and special windings in
11111
the pole faces. These windings are discussed in more detail
in the next section.
11.6 Synchronous motors
11.6.1 Construction
Stator
The stator of a synchronous motor has a three-phase
winding, as described in a previous chapter, and is of the
same type as that in an alternator.
When this winding is energised with a.c. it produces a
magnetic flux, which rotates at a speed called the
synchronous speed. It is the same speed at which the
synchronous motor would have to be driven to generate
an a.c. voltage at line frequency.
The speed can be derived from the same formula used
for alternators in section 11.2.3.
Rotor
Although of similar construction to the alternator rotor, it
is usually made with salient poles. When excited with d.c.
it produces alternate north and south magnetic poles,
which are attracted to those produced in the stator.
11.6.2 Operating principle
A synchronous motor works on the principle of magnetic
attraction between two magnetic fields of opposite
A synchronous motor has torque only at synch
speed, so special steps have to be taken to get the
up to speed and synchronised with the supply. Tl
magnetic fields are then rotating at the same spe1
lock in with each other. A later section in this c
discusses starting methods for synchronous motors
11.6.3 Effect of load on a synchronous mo
When a synchronous motor runs on no load, the I
positions of stator and rotor poles coincide as sh
Figure l l.14(a).
When a load is applied, the rotor must still cont
rotate at synchronous speed but due to the rel
action of the load, the rotor pole lags behind th<
pole. Their relative positions are displaced by the:
(called the "torque" or "load" angle), as shown in
l l.14(b). The greater the load applied, the lar:
torque angle.
The magnetic coupling between each stator an
pole distorts according to the load applied. If the I
the motor becomes excessive, the magnetic C<
breaks and the rotor slows down until it stops.
When the motor is rotating at synchronous
with a fixed d.c. excitation in the rotor windings, tt
flux cuts the stator windings, inducing a voltage
phase winding and opposing the applied voltage
law). The phase relationship between this induced
and the applied voltage depends upon the
219
THREE-PHASE SYNCHRONOUS MACHINES
Rotation of stator
Torque angle
I
\
Rotor
\.
·~
I
(a) No load
(b) Loaded
Fig. 11.14 Relative positions of stator and rotor magnetic fields in a synchronous motor
positions of each stator and rotor pole, which in turn
depend upon the load applied to the motor.
Neglecting motor losses, on no load the torque angle is
zero, and so the induced voltage V, and the applied
voltage V are equal and opposite. The resultant voltage
VR across the windings is zero, and so the current drawn
from the supply is also zero. This is illustrated by the
phasors in Figure l l .15(a).
When a light load is applied to the motor, the torque
angle a increases, and the induced voltage Vg in the stator
windings is now ( 180 - a) 0 E out of phase with the applied
voltage V, as shown in Figure l l. l 5(b ). These two
voltages combine to produce an effective voltage v.
across the stator windings, which is sufficient to draw a
current I from the supply. Because of the relatively high
inductance of the stator windings, the line current /in each
winding lags each resultant voltage v. by nearly 90°E.
This causes the line current I to lag the applied voltage
by cl>.
As the load is increased, so the torque angle is
increased. This causes an increase in the resultant voltage
VR across each stator winding, as seen in Figure l l.15(c).
Because of the increase in the value of VR• the line current
I increases, and the phase angle ¢ between the applied
voltage V and the line current I also increases.
v,
For a fixed rotor winding excitation, an increase in
load on a synchronous motor will therefore cause an
increase in current drawn from the supply.. with a poorer
power factor.
11.6.4 Effect of varying field excitation
If the load applied to a synchronous motor is constant, the
power input to the motor is also constant.
When the rotor field excitation is varied, the induced
voltage in each stator winding is also altered.
The phasor diagram in Figure l l.16(a) represents the
conditions for a given load at unity power factor. The
power input per phase is Vl1. If the rotor field excitation is
decreased, the induced voltage Ve decreases, as shown in
Figure l l. l 6(b ). This causes the line current h to lag the
applied voltage Vby <1>2. Since the load, and so the power
input, is constant, the power component of /2 must remain
the same as Ii in Figure l l.16(a). The line current Ii must
increase to accommodate the lagging power factor. A
reduction in the d .c. field excitation therefore causes an
increase in line current, and a lagging power factor.
If the d.c. excitation is increased, the induced voltage
V,increases as shown in Figure l l.16(c). The line current
h will therefore lead the applied voltage V by ci>J, and will
v
(a) No load
(b) Light load
Fig. 11.15 Effect of load on line current with constant excitation
(c) Heavier load
220
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TR,
Where large amounts of power are being dist1
and power factor correction is needed, specially d<
synchronous motors are run without any load con1
Under these circumstances the overexcited synch
motor is called a synchronous condenser.
Voltage control
v An important application is in the control of volt:
I
transmission lines. Synchronous motors are inst:::
suitable positions along the line and their exc
adjusted as desired to cause them to draw lagi
leading currents in order to raise or lower the \I
When synchronous motors are installed unde1
conditions, there is a tendency to greater stab
voltage on the transmission line.
(a) Unity power factor
I] (b) Lagging power factor
vg
I
Low-speed drives
A synchronous motor has good efficiency and
speeds its higher initial cost is adequately compens
the comparatively lower running cost. At low spe1
induction motor has a decreasing efficiency, wl
synchronous motor retains its high efficiency.
,,
v
-+-----:,
',,
'
'-
'
V
(c) Leading power factor
Fig. 11.16 The effect of varying the d.c. excitation
also be greater than Ii in Figure l l.16(a) because the
power component is the same, due to the load remaining
constant. An increase in d.c. excitation therefore causes
an increase in line current and a leading power factor.
This characteristic of the synchronous motor, where
its power factor can be altered by varying its d.c.
excitation, gives rise to its main application in industrypower factor correction.
11.6.5 Applications of synchronous motors
Power factor correctiOn
If a synchronous motor has sufficient d.c. excitation to
cause it to draw a leading current from the supply, the
effect is one of power factor correction for other loads
within an installation.
A motor running with a leading power factor is called
overexcited, and is often designed to run as a synchronous
motor driving a load and correcting overall power factor
at the same time. The driven load selected is usually one in
demand throughout the installation (e.g. air compressors,
hydraulic systems or frequency changers for portable
tools).
An added advantage can be an economical incentive
offered by supply authorities for ensuring a certain
minimum value power factor in an installation. For
example, the charge per kWh may be reduced if the power
factor does not drop below 0.75 or some similar figure.
11.6.6 Hunting in synchronous motors
A change in load on a synchronous motor causes a
in the value of the torque angle (Fig. 11.14). In!
the inertia of the rotor prevents an instant chang1
new conditions. with the result that the rotor shi
ihe point- of equilibrium and then has to correc
While the rotor and the rotating field in the stator
rotating at a synchronous average speed, the ch
load on the rotor causes this periodic swing aro
point of equilibrium. This surging or hunting ca
undesirable fluctuation in line current to the mot
The usual method for damping these surges i
damper winding, called an amortisseur wine
consists of copper bars embedded in the pole fac<
rotor and shorted out at each end (Fig. 11. I"
/Dampe•
rQ .. o
-
-
-
IT:. I
--s
.
loo o
--
-
--11 •• ·1
Fig.11.17 Salient pole with amortisseur wind
THREE-PHASE SYNCHRONOUS MACHINES
surging causes an induced voltage in the copper bars. This
results in a magnetic field being created and opposing the
221
connected to the supply. It is an expensive method.
particularly if high starting torques are required.
surging effect.
Often the shorting-out bars are extended around the Induction motor starting
rotor. resulting in a squirrel cage-type rotor winding A reduced line voltage is applied to the stator windings
about the salient poles. While damping any tendency of and the d.c. winding on the rotor is short-circuited. With
the rotor to hunt, they can also assist the motor in starting. the aid of the amortisseur winding, the complete machine
behaves as an induction motor as it accelerates up to a
11.6. 7 Starting methods for synchronous motors speed slightly below synchronism. At an appropriate time
the short is removed from the rotor winding. d.c. is
Auxiliary motors
applied
and the full line voltage applied to the stator
Some synch'ronous motors are equipped with a special
winding.
Because the speed is only slightly less than
motor designed for use during the starting period only.
synchronous
speed, the rotor field is able to lock in with
The auxiliary motor runs the synchronous motor up to
the
stator
field
and accelerate to synchronism.
speed, at which stage it is first synchronised and then
Exercises
11.1
What advantages are there in using the
rotating d.c. field-type construction for
synchronous machines?
11.2 What are the constructional differences
between low-speed and high-speed alternators?
11.3 Explain why a low-speed synchronous
machine has a large salient pole-type rotor.
11.4 What is the purpose of the "exciter"?
11.5
11.6
11. 7
How many poles must a synchronous
machine have to operate at 250 r/min and a
frequency of 50 Hz?
How does the power factor of the load affect
the output voltage of an alternator?
State five conditions that must be satisfied
before an alternator can be synchronised
with an existing supply.
11.8
What is meant by the term "phase sequence"
when applied to three-phase synchronous
alternators?
11.9 In what way does the principle of operation of
a synchronous motor differ from that of an
induction motor?
11.10 Why is a synchronous motor not selfstarting?
11.11 State two characteristics that are applicable
only to a synchronous motor.
11.12 Explain how an increase in the load applied to
a synchronous motor affects the line current
and power factor.
11.13 How can the power factor of a synchronous
motor be changed?
11.14 What are some applications for synchronous
motors?
CHAPTER12
THREE-PHASE
INDUCTION MOTOR!
12.1 Introduction
The majority of a.c. motors used in industry are of the
induction type. They are rugged and have a high degree of
reliability. A three-phase induction n1otor consists of a
laminated stator with three identical windings placed
symmetrically in slots within it. The rotor is also
laminated, and usually has single-turn conductors placed
within its slots and short-circuited at the ends. To achieve
special characteristics, conventional windings are sometimes used instead. The motor derives its name from the
fact that the currents flowing in the rotor are induced and
not drawn directly from the supply.
12.2 Construction
12.2.1 Stator
The laminated stator core is made up from sheet steel
punchings with slots on the inner surface. The windings
consist of three identical windings, laid out in the same
fashion as the alternator and synchronous motor. In
motors of higher power ratings the stator slots are of the
open type to allow the insertion of pre-shaped and
insulated coils, but in smaller sizes the slots are partially
closed to reduce the air gap as much as possible.
Fig. 12.1 The component parts of a 415 V, 3.7 kW, four-pole
three-phase induction motor. This particular
motor is of the totally enclosed type and is
intended for direct coupling to its load as shown
by the flanged construction of the endshield at
POPE ELECTRIC MOTORS
the upper left.
222
The stator core is held in the motor frame whi
serves to carry the bearings holding the rotor, to
the coils and to provide a means whereby the wholl
mounted (see Fig. 12.1 ).
The motor frame takes various forms, depen1
the conditions under which the motor will aper;
open-type frame allo\vs free ventilation to take
drip-proof frame has a closed upper half, while a
ventilation through the lower half; a totally enclm
prevents the exchange of air between the inside
outside of the frame.
12.2.2 Motor enclosures
The conditions governing the actual installatio
induction motor are normally beyond the contrc
motor manufacturer. As a result the motor is
factured in various enclosures. A motor dr
compressor for a refrigerated display cabir
example, may operate under such clean and d
ditions that the motor enclosure need only pr
mounting for the bearings and a means for fi:;.
motor in a horizontal plane. At the same time
closure provides mechanical protection against ac
spillage and enables cooling air to circulate freely·
the motor windings.
Compare this situation with a water turbin
used for irrigation purposes. In most cases the t
mounted vertically at the bore head and is g
protection from the weather. The motor neeC
totally enclosed to prevent the entry of water and
is by means of heat transfer through the motor 1
The air sealed within the motor housing is circulat
internal fan, so transferring the heat generatec
windings to the housing. This heat is then transl
the atmosphere by a second fan circulating free a
the outside of the motor housing.
For detailed information on electric motor s
reference should be made to Australian Stan1
1359 on the requirements for rotating e
machines. It is an extensive standard with many
and often calls up other standards that may be
to particular sections. Electrical rotating macl
now classified by two letters followed by four n
223
THREE-PHASE INDUCTION MOTORS
I
II \I II
II \I II
Fig. 12.2 Squirrel-cage rotor for an induction motor
POPE ELECTRIC MOTORS
111111
111111
111111
This classification number is different for such categories
as cooling, mounting and protection.
Fig. 12.3 Wound rotor for an induction motor
12.2.3 Rotor
Squirrel-cage rotor
The rotor of a three-phase motor consists of a shaft with
bearings, laminated iron core, and rotor conductors. The
most common type of construction is that with rotor bars
in the lamination slots rather than a winding. The rotor
bars, short-circuited at each end by a solid ring, are often
made of copper strip welded to copper rings, but for small
to medium size motors they may be cast in one piece out of
aluminium. Usually included in the rotor casting is a series
of vanes for creating air movement. Figure I 2.2 shows
these vanes standing out from each shorting ring. The
photograph also shows skewed conductors in the rotor.
The main purpose for slanting the conductors in the rotor
is to ensure a smooth steady acceleration during starting.
Varying the physical design features of the bars affects the
motor performance. Embedding them deeper into the
rotor, for example, increases their inductance and gives a
lower starting current but at the same time creates a lower
pull-out torque.
This type of rotor is then restricted to loads requiring
low-starting torques such as centrifugal pumps. The rotor
windings, if assembled without the laminations, resemble
a metal cage giving rise to the often-used name of
"squirrel-cage" rotors although the standards refer to
them simply as "cage" rotors.
Wound rotor
The wound rotor is fitted with insulated windings, similar
to the stator winding and having the same number of
poles. Usually the rotor winding has three phases,
connected internally in star, and terminating at three slip
rings. A typical wound rotor is shown in Figure 12.3.
The slip rings are connected by means of brushes to a
star-connected variable resistance, as in Figure 12.4. This
rotor rheostat provides the means of increasing the
resistance of the rotor circuit during starting, thereby
producing a high starting torque at a low starting current.
As the speed increases, the external resistance is gradually
reduced, lowering the rotor circuit resistance as the rotor
reactance decreases.
Under operating conditions, the variations in rotor
circuit resistance provide a means of cbntrolling the speed
of the motor-an increase in resistance produces a
reduction in speed. This also produces a loss in efficiency
due to the 12 R losses in the rheostat.
The wound-rotor motor is more expensive than the
squirrel-cage motor due to the cost of manufacture of the
wound rotor. It also has a higher starting torque and
lower starting current, but poorer running characteristics
than the squirrel-cage motor.
12.3 Operating principles
12.3.1 Rotating magnetic fields
For its operation a three-phase induction motor is
dependent on a rotating magnetic field being established
by the a.c. windings. The three separate windings are
Three-phase
supply
Stator
Rotor
Slip rings
Fig. 12.4 Circuit for a wound-rotor induction motor
Rheostat
224
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TF
A
+
A
..-
/
s,
~
/
•··
/
.. 7
..I
··.
I
..
I
I
I
\
I
·.
\,.. ,;::
/
•/
ccr
....
/
/
... ....
..
...·
(b) Three phases
(a) One phase
Fig. 12.5 Polarities and connections in a two-pole, three-phase motor
installed in the stator at 120° E intervals to each other and
provide a fixed number of poles for each phase. This is
shown diagrammatically in Figure l 2.5(a) for one phase
of a two-pole machine. Figure 12.5(b) shows the three
phases in relationship to each other giving a total of six
poles. Phase A is drawn as a solid line, phase Bas a dotted
line and phase Casa dashed line. Note that this sequence
is carried through for the explanation and applies to the
for example, alternates in direction in the diagran
not rotate in any way. lt simply varies in stren
direction in the vertical plane. Similarly a pulsatir
also established by the other two phases giving a
three magnetic fluxes which combine into one r
flux. This flux rotates at synchronous speed. At r
current waveforms, the magnetic fields and the phasors.
'•
Assun1ption
In the following explanation for the production of a
rotating field one assumption has been made as a
reference, that winding ends A, B, C when connected to a
positive source of voltage makes the adjacent iron core a
north magnetic pole. From this it will follow that the
opposite poles become south magnetic poles. These
details are also shown in Figure 12.5(a). If the current
flow is reversed then the magnetic poles are also reversed.
With the three windings connected in star by joining
ends Ai, B1, C, together, and the ends A, B and C
connected to a three-phase supply, the phase currents IA,
!Band !care 120 °E out of phase with each other. These
are shown in Figure 12.6. Because each current is
alternating, each pair of poles sets up a magnetic flux that
continually changes from one polarity to the other. Note
that although the flux set up by A phase in Figure l 2.5(b),
le
---.
\
·;
/
\
I ·..
\
\
I
I
I
I
0°
:
\
240°
120~
I
I
\ .
\
... \
I
'
2
/
3
4
.....
5
6
7
Fig. 12.6 Waveform diagram showing three-phase<
at 120° E to each other (for reference num
text)
225
THREE-PHASE INDUCTION MOTORS
<l>c
····........ . .
/
- - , - , - •-••-~- <l>R
,/
B
···...
.......... <t>
B
Flg.12.7 The resultant flux produced by currents flowing at position 1 in Figure 12.6
position I in Figure 12.6, the current IA is zero and no flux
is produced by the winding A-A1. Current Is is negative
and so will produce a south pole at Band a north pole at
B1. Current leis positive and so will produce a north pole
at C and a south pole at C1. Because currents /oand le are
equal the two magnetic fields are equal in strength. The
direction of these fields are shown in Figure 12. 7. In the
accompanying phasor diagram the addition of these two
fields is shown giving a resultant instantaneous field 4>n.
At position 2 in Figure 12.6, IA is positive, Io is still
negative while leis zero. This produces a north pole at A,
a south pole at B, and nothing at C. These are shown in
Figure 12.8 together with the phasor diagram showing the
addition of the phasors to give the resultant instantaneous
magnetic field. Since all coils have an equal number of
turns, the relative strengths of the magnetic fields can be
gauged by measuring the vertical heights of the current
waveforms at the positions indicated by the reference
number. In this instance the direction of the resultant
magnetic field has shifted 60° E clockwise from that in
position I. If drawn to scale it can also be shown that the
length of the resultant has remained constant, indicating
that the field strength has remained constant.
At position 3 (Fig. 12.6), IA is positive, producing a
north pole at A and a south pole at A,, 18 is zero, and
le is negative, producing a south pole at C and a north
pole at C 1. These fields are drawn out in Figure 12.9
together with their phasors. The resultant field has rotated
a further 60°E in a clockwise direction. (There is a 60°E
difference between all the numbered positions in Fig.
12.6.) For each of the numbered positions the resultant
field rotates a further 60°E in a clockwise direction. For
one complete cycle of current (360°E) the resultant
magnetic field rotates 360°E.
Fig. 12.8 The resultant flux produced at position 2 in
Fig. 12.9 The resultant flux produced at position 3 in
Figure 12.6
12.3.2 Rate of rotation
BycomparingFigures 12.6, 12.7, 12.8and 12.9itcanbe
seen that for the time intervals of 60° E between the
positions l, 2 and 3 the resultant field rotates an equal
Figure 12.6
226
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL Tl
.---------{_) R
amount around the stator. For a complete cycle of a.c., a
two-pole field rotates one complete revolution around the
stator. The synchronous speed of the magnetic field in
revolutions per minute can be determined from the
frequency of the supply.
~c,
Example 12.1
A two-pole machine is connected to a 50 Hz supply. Find
the speed at which the magnetic field rotates around the
stator.
50 Hz = 50 cycles per second
speed of rotation = 50 revolutions per second
= 50 x 60 revolutions per minute
= 3000 r/min.
With a four-pole machine, 360°E represents one-half of
a full revolution of the stator field, and the speed of
rotation of the field is consequently halved. Similarly, the
speed of field rotation for a six-pole machine is reduced
to one-third that of a two-pole machine. In each case
the speed is usually expressed in revolutions per minute,
whereas the frequency is in hertz (cycles per second). The
speed in revolutions per minute can be found from the
following formula:
.-------~
120{
ns1•11 = - " .
p
c
...... ow
I
I
L _ - - - - - -------0 B
(a) RWB sequence
... ·····
c
B,
' '
\Ow
\
...
:\
where
nsyn =
..................................../ bs
number of revolutions per minute
.f = frequency in Hz
p = number of poles
(b) RBW sequence
The speed n of the rotating magnetic field is called the
synchronous speed of the motor. The synchronous speeds
of common sizes of motors at a frequency of 50 Hz are
given in Table 12.1. The formula above is identical to that
shown in Chapter 6.
Table 12.1 Speed of the rotating field in an induction
motor for various number of poles
Poles
2
4
6
8
1O
12
600
500
Synchronous
speed (r/min)
3000 1500 1000 750
12.3.3 Direction of rotation and reversal
The direction of rotation of a rotating field depends on the
phase sequence of the three currents flowing through the
windings. In Figure 12.1 O(a) the three supply lines R. W
and Bare connected to terminals A, Band C of the motor.
The resultant magnetic field rotates in a clockwise
direction.
In Figure 12. 1O(b) the supply lines to phases B and C
have been changed over and. using the procedure from the
previous section. it can be shown that the rotation of the
magnetic field is reversed. That is. the direction of rotation
of the field. can be controlled by interchanging any two
supply lines to the motor. In section 12.4.1 on torque it
is shown that the rotation of a three-phase induction
111otor is in the same direction as that of the rotating field.
Fig. 12.10 Phase sequence and field rotatil
12.4 Induction and its effects
When the stator windings of a three-phase i
motor are energised from a three-phase s1
magnetic field is produced, rotating at sync
speed. This rotating magnetic field crosses the ai1
cuts the rotor conductors, inducing a voltage
(magnetic field, conductors and relative motior
the rotor circuit is complete (through end rings it
of the squirrel-cage rotor, or external resistance ii
of the wound rotor), the induced voltages ca
currents to flow in the rotor conductors.
12.4.1 Torque
Figure 12.11 (a) represents a part of the stator an
of an induction motor with the stator flux rot2
clockwise direction as indicated. When these line
cut the rotor conductors from left to right, the
movement between the stator flux and the re
ductor is from right to left. By applying Flemin
hand rule (sect. 6.1. l) the direction of inducec
flow in the conductor is towards the reader. D
comparatively high rotor currents flowing, a Jar
established around the conductor as sho\vn i
12.1 l(b). The stator and rotor fluxes react withe;
as shown in Figure 12.11 (c) to form a resultant f
resultant field tends to straighten itself out, a1
-
227
THREE-PHASE INDUCTION MOTORS
LJ
N
N
Rotor conductor
-
~
Thrust
Rotor flux
.
'
(a) Stator flux
{b) Rotor flux
(c) Resultant flux
Fig. 12.11 Production of torque in an induction motor
process causes a force to be exerted on the rotor
conductor trying to force it to the right and out of the
stator magnetic field. A similar force is exerted on all the
rotor conductors as the field rotates, and if sufficient force
is created the rotor will commence rotating in the same
direction as the rotating magnetic field. Provided it is free
to rotate the rotor will accelerate until it approaches
synchronous speed.
This rotating force, called the torque of the motor, is
the result of the interaction of the two fluxes. The stator
flux remains fairly constant, but the rotor flux varies with
the rotor current, which is determined by such factors as
the impedance, the induced voltage and the relative speed
of the rotor conductors.
12.4.2 Slip
To produce torque, there must be a rotor flux caused by
current flowing through the rotor conductors. If the rotor
could run at synchronous speed, there would be no
relative motion between the stator flux and rotor
conductors. Consequently, there would be no induced
voltage, no rotor current, no rotor flux, no torque
developed, and so the rotor would slow down. An
induction motor therefore cannot run at synchronous
speed.
With the rotor runningjust below synchronous speed,
relative motion exists and sufficient torque is developed to
keep the rotor turning. The difference between the
synchronous speed of the rotating field and the actual
speed of the rotor is calfed the slip speed. It is commonly
expressed as a percentage of the synchronous speed.
Example 12.2
Determine the slip of a four~pole induction motor running
at 1440 r/min when connected to a 50 Hz supply.
n,,. =
120{
p
slip speed
=
=
120 x 50
= 1500r/min
4
1500 - 1440 = 60 r/min
1 ~~
1500
percentage slip
=
4%
44
0x
100
The formula for determining percentage slip is:
s% =
where s%
nsyn - n
nsyn
x 100
= percentage slip
= synchronous speed
n = rotor speed
nsyn
At standstill (i.e. when starting) the slip is !00%,
whereas if the motor could run at synchronous speed, the
slip would be zero.
12.4.3 Rotor frequency
When the rotor of a two-pole motor is at standstill and the
stator is connected to a 50 Hz supply, each rotor
conductor is cut by a north pole and a south pole at a rate
of 50 times per second. At standstill, the frequency of the
rotor voltage (rotor frequency) is the same as the
frequency of the supply (stator frequency).
As the rotor speeds up to half the synchronous speed
(!500 r/min), the rotor conductors are cut by only onehalf as many north and south poles per second as at
standstill, and so the rotor frequency is one-half the
supply frequency (i.e. 25 Hz). If the rotor revolved at
synchronous speed, the rotor frequency would be zero.
The rotor frequency depends upon the differences in the
speeds of the stator flux and the rotor (i.e. the slip of the
motor), as shown in Figure 12.12.
The rotor frequency can be calculated using the
following formula:
~
~
where fr = rotor frequency in Hz
s = slip percentage
f = supply frequency in Hz
228
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL TF
Supply frequency
..................
Rotor
frequency
/Rotor
stationary
0
Slip
100°/o
Fig. 12.12 Relation between rotor frequency and slip
Example 12.3
Determine the rotor frequency of a two-pole, 50 Hz
induction motor if the rotor speed is 2850 r/min.
s =
nsyn -
n x 100
nSJ'll
3000 - 2850
3000
x 100
f,,
= 5%
s.[
=TOO
5 x 50
= loO = 2.5
Hz
As the rotor frequency varies, so does the rotor
inductive reactance, and this affects the starting and
running characteristics of the motor.
12.5 Operating characteristics
12.5.1 Squirrel-~age motors
When power is first applied to a stationary motor, the
stator windings act as transformer primary windings with
the resultant magnetic field rotating at synchronous
speed. The rotor then behaves as a shorted secondary
winding causing a high circulating current in the rotor
bars and a high starting current in the stator windings. As
the rotor accelerates in the direction of the rotating field,
the difference between its speed and the rotating m
field becomes less and the generated voltage cam
rotor circulating currents also becomes less. This
reduces the stator current.
The typical relationship between the stator
and the rotor speed is shown in Figure 12.13(
initial circulating current in the rotor is affected
frequency of the supply, the resistance of the rot
and the inductance of the rotor circuit-that is, the
limiting factor is the impedance of the rotor circu
the usual type of power transformer, the frequ
the supply is the line frequency, but in this c
frequency commences at line frequency and
decreases as the motor speed increases. As a consi
the torque created can change as the speed chan.
Figure l 2. l 3(b) for the typical relationships I
speed and torque. For small values of slip the t
assumed to be proportional to the slip. As the mo
increases the torque increases and the speed de
until the torque reaches a maximum value ca
breakdown torque. If the motor is loaded bey'
point, the torque and the speed both decrease
motor quickly comes to a standstill. An overa
for starting torque is in the region of 1.5 times t
torque, while the breakdown torque is usually abc
the rated torque. Australian Standard 1359.41
minimum requirements for these torque val·
provides a table for a range of motor sizes.
The resistance of the rotor conductors
constant at power line frequencies for all 1
purposes, while the inductive reactance decreas(
rotor speed increases. As a guide, torque re
maximum when the rotor resistance in ohms is
the rotor reactance in ohms. Since the resistance
then the breakdown torque can only be al
relationship to the motor speed by altering the inc
of the rotor. In turn this affects the starting
Australian Standard 1359.41 allows for only t•
types of rotor-normal and high torque-and a
types are necessarily by prior arrangements
1nanufacturer. For the high-torque motor the
breakdown torque remains around twice rate<
Breakdown
torque
Current ( 0/11)
Torque(%)
Locked
)._1or torque
Rated
speed
Rated torque
100
Rated current
100
0
n
(a) Current/speed curve
fl syn
0
n
{b) Torque/speed curve
Fig. 12.13 Operating characteristics tor a squirrel-cage induction motor
n,
229
THREE-PHASE INDUCTION MOTORS
300
300
Torque
%
200
Torque
%
100
Rated torque
-------------
200
r---Rated torque
100
Oc__ _ _ _ _ _ _ _
~-l-
Speed
Speed
n~yn
Fig.12.17 High resistance rotor bars
Fig. 12.14 Low starting torque rotor bars
300
Rated
speed
200
Torque
%
100
Rated torque
o~------------e~
Speed
nsyn
Fig.12.15 Standard rotor bars
300
Torque
200
%
100
_____
Rated
------.,speed
Rated torque
--------------
o~----------'+Speed
bars of greater cross-section where part is imbedded
deeper into the rotor magnetic circuit. Starting torque is
still about 150% of running torque but the starting current
is reduced to about five times the running current. It is
suitable for use with equipment of low starting inertia
such as fans, blowers and some types of machinery.
Figure 12.16 gives one example of a rotor with two sets
of rotor bars. The inner set is shown with half as many
bars as the outer set and includes an optional air gap.
Depending on performance requirements there may
be different shaped bars, no air gap or a full set of bars in
the cage. Starting torque is high-here it is 225% of rated
torque-and starting current is about five times rated
running current. Applications are air compressors,
crushers, refrigerator compressor motors or reciprocating
force pumps. A typical example of high resistance rotor
bars with low starting current requirements is shown in
Figure 12. l 7. With this construction the starting torque
can be increased to about 275% with fairly low starting
currents. It is at the expense of a lower rated speed (i.e.
increased slip). Typical uses are flywheel mounted
machinery such as presses and punches. It is excellent with
hoists where the maximum load occurs at the start of the
lift. The details above apply particularly to copper rotor
bars. If aluminium is used for the rotor bars then the
cross-sectional area of the bars must be increased to allow
for the metal's higher resistivity. The shape may also be
changed to incorporate desired starting and running
characteristics. Figure 12. l 8 shows a "tear-drop" shaped
cast aluminium bar. In practice the shape may also be
inverted to alter the characteristics to suit a particular
purpose.
nsyn
Flg.12.16 Double cage rotor tor high starting torque
while the starting torque is increased to approximately 2.5
times rated torque.
Figure 12.14 shows typically shaped rotor bars where
the starting current is about 6-7 times rated current and
the motor has a starting torque of approximately 150%
of rated running torque. Its use is restricted to very low
starting torque requirements. Figure 12.15 shows rotor
Fig. 12.18 Cast aluminium rotor bars
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL T
230
12.5.2 Wound-rotor motors
The introduction of resistance into the rotor circuit of an
induction motor produces three effects:
I. rotor current is reduced, resulting in less stator current;
2. starting torque is increased, because rotor and stator
magnetic fields are more in phase with each other;
3. slip speed is increased.
An adjustable resistor is used external to the rotor,
which is wound with comparatively low resistance
windings. The value of the external resistance can be
adjusted as required and as the motor accelerates, the
value is gradually reduced until all the resistance is out of
the rotor circuit and the motor behaves as an ordinary
induction motor.
The torque-speed characteristic of a typical threestage wound-rotor motor is shown in Figure 12.19. When
all the resistance is in the rotor circuit, the starting current
is low and the starting torque is high as shown by curve a.
If this resistance is left in, the full-load torque would occur
at approximately 25% slip, resulting in extremely poor
speed regulation.
If one stage of the resistance in the rotor circuit is
shorted out, the operating characteristics are modified as
shown by curve b.
If all the Cxternal resistance in the rotor circuit is
shorted out the operating characteristic is shown by
curve c.
d
Rated speed
r'
······ ...
Aated_!_o~~
100
The normal starting procedure is to start th
with all the resistance in the rotor circuit. As th
speeds up the resistance is reduced and tht
increases in speed, but maintains a high torque.
the starting procedure, the torque-speed curve is c
by the thicker curve d.
12.5.3 Operating parameters
By comparing Figures 12.13 and 12.19, it can be'
full-load torque occurs at a greater slip in a wow
motor than a squirrel-cage motor. This is due to 1
resistance of the windings in the wound rotor.
On no load, the stator current ofany inductic
is largely a magnetising current, with a smal
component required to supply the no-load
Accordingly, the power factor of an induction n
no load is very low. The no-load current is relatb
when compared with a transformer because of
reluctance of the magnetic circuit, due to the
between the stator and rotor.
The stator flux remains fairly constant from n
full load, and so the magnetising current is al
constant. In Figure l 2.20(a), the no-load stator c
lags the supply voltage by cf> degrees.
As a load is applied to the motor, a load cun
required to accommodate that load. This load ct
lags the supply voltage slightly, due to the effo
stator and rotor reactance. The two current corr
Io and /' 1 combine to give the total stator current
load. The phase angle decreases from cf> to q,,
power factor of the induction motor increases as
on the motor increases.
Figure 12.21 gives representative characterist
for some parameters of a three-phase induction 1
shows the speed decreasing and the slip increasi:
load on the motor is increased. It also shows
current increasing and the power factor improvi
same time .
a
___ _
12.6 Motor starting methods
0
n
Flg.12.19 Operating characteristic for a wound-rotor motor
Induction motors are subject to the same
limitations as d.c. motors. In Chapter 7 it was sh
a d.c. motor needed a series resistor to limit f
starting current and, as the motor accelera
resistance was gradually reduced until it was no
---(a) No-load conditions
(b) Loaded conditions
Fig. 12.20 Current phasors for an induction motor
THREE-PHASE INDUCTION MOTORS
100%
231
L, 0-----j
L'D-----1
Lau-----1
Fig. 12.22 Basic power circuit for primary resistance motor
st·arting
resistance, the greater is the voltage drop across each
Power output
Fig. 12.21 Typical parameters for a three-phase induction
motor showing how they alter as the load varies
circuit. Limiting the current drawn by the motor during
starting is directly applicable to both a.c. and d.c. motors,
and is achieved by reducing the voltage across the motor
windings. The only exception to this is the wound-rotor
resistor and the less the voltage at the motor. Because of
this lower voltage, the starting current is reduced. As the
rotor accelerates, the resistance is reduced in steps until
full voltage is applied across the motor terminals.
This method of starting greatly reduces the starting
torque of the motor because it is proportional to the
square of the applied voltage.
i.e.
It must be appreciated that this expression shows the
starting
torque is reduced four times if the applied voltage
motor.
is halved. Such a reduction in torque may prevent a motor
While ad .c. motor can only use series resistance, there 1
from starting against even a small load.
are alternative current-limiting methods for a.c. motors.
Advantages of current limiting
I. Less mechanical forces exerted on windings.
2. Less mechanical shock forces on motor frame, shaft
and transmission.
3. Steadier acceleration with connected loads.
4. Reduction of line voltage drop.
5. Less disturbance to the supply system.
Disadvantages of current limiting
I. Reduction in starting torque.
2. Extra cost of starting equipment.
3. Increased maintenance requirements.
4. More con1plex equipn1ent.
12,6,1 Direct-on-line starting
Cage motors may be started with the full supply voltage
connected across the stator windings. This method is
usually referred to as direct-on-line or D.O.L. starting.
The large starting current can cause excessive voltage
drop in the supply lines and disturbances to the supply
voltage. For this reason, the supply authorities usually
limit the starting current of motors. The D.0.L. method
of starting is usually restricted to smaller-sized motors.
12,6,3 Star-delta starting
Another way to reduce the starting current by reducing
the voltage applied to each winding is the star-delta
method. The motor is started in the star connection and
when it has gained sufficient speed, it is quickly changed
over to the delta connection.
The starting torque is considerably reduced with this
method, which is usually applicable to motors being
started on light loads, the main load being applied after
the motor has reached full speed and is connected in delta.
The two ends of each phase winding of the motor are
brought out to the stator terminals. During the starting
sequence in star, the voltage across each phase is 1/ V3 or
58% of the line voltage. As a result, the torque is reduced
2
to ( 1/ VJ) or 1/3 of its normal running value.
The line and phase currents in star are equal, but when
the windings are connected in delta this condition no
longer applies. The phase voltage is increased VJ times or
173% over the star connections, consequently the phase
current is increased by the same ratio. In addition the line
current is now equal to V3. Iphase, or three times the line
current value for the star connection. These values are
illustrated in Figure 12.23 for a winding impedance of
24 ohms.
12,6.2 Primary resistance starting
An effective method for reducing the starting current of an
induction motor is to add resistance in series with the
supply lines (see Fig. 12.22). The higher the value of
12.6.4 Autotransformer starting
Autotransformer starters are the most popular of any
reduced voltage type. The voltage applied across the
232
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL 1
Torque and input power
113 of "run" condition
10 A
30 A
10 Ai
Start (star-connected)
Run (delta-c
Fig. 12.23 Comparison of star and delta starting
stator windings can be reduced to a percentage of the
supply voltage by using a star-connected autotransformer.
During starting, the primary of a step-down autotransformer is connected to the supply, and the secondary
is connected to the stator windings of the induction
motor, as shown in Figure 12.24.
By providing a range of tappings in the transformer
windings (e.g. 60%, 70%and 80%), it is possible to have a
choice of voltages (and currents) for starting purposes.
When the motor is up to speed, the stator windings are
connected across the full supply voltage, and the
autotransformer is open-circuited.
The use of a transformer makes it possible to reduce
the line input current at a greater rate than that at which
the torque is reduced. Transformers are discussed in
greater detail in Chapter 15, but briefly:
input voltage x input current
= output voltage x output current
i.e.
v, x r,
=
v, x r, (neglecting all losses)
During starting, a reduced voltage ( V,) is applied to
the motor, so reducing the starting current(!,). Because of
transformer action, however, the input current (/1) is
reduced still further. It can be illustrated by the following
example.
Example 12.4
A 415 V, three-phase induction motor draws 160
connected D.O.L. If an autotransformer starter,
motor connected to the 70% tapping, is used to
motor, determine:
(a) the voltage applied to the motor during start
(b) the starting current taken by the motor;
(c) the starting current drawn from the supply.
,,
,,
V1 =
415 v
Vi
=
70°/o of V1
Fig. 12.25 Circuit diagram for example 12.·
(a) For 70% tapping:
motor voltage = 70% of input voltage
=70%of415V
= 0.7 x 415
= 290.5 v
0
Fig. 12.24 Starting connections with a three-phase, star-connected autotransformer
233
THREE-PHASE INDUCTION MOTORS
(b) For 70% tapping:
motor current = 70% of D.O.L. starting current
= 70%of 160A
= 0.7 x 160
= 112A
(c) V,J,
:. J,
V2l2
V,h = 290.5 x 112
v,
415
= 78.4 A
Fig. 12.26 Starting connections for an induction motor
Note that the motor voltage has been reduced by 70%
to 290 V. Because T o:: V2 , the torque will have been
reduced to (0.7) 2 =0.49 of the D.O.L. value. While the
motor current has only been reduced to 70%, the input
current has been reduced to 0.49 or 49% of the D.0.L.
value.
The significance of these figures can be seen when
compared to those of the same motor when the primary
resistance starting method is used.
Motor impedance between lines at standstill
v 415
z =I=
160 =
2.59 !1 (D.0.L.)
The line input current from example 12.4 is 78.4 A
(autotransformer).
For primary resistance starting with this same value of
current the applied voltage would be reduced to:
V
= !Z
= 78.4 x 2.59
=203.lV
For the same input current for both methods (78.4 A),
the relative torque values would be:
D.O.L.
415)'
( ill x 100 = !00%
autotransformer
( 2!~55 )' x
primary resistance
203
( 415· 1 )' x 100 = 24"'
70
100 = 49%
That is, for the same input current the autotransformer starter enables the motor to develop twice as
much starting torque as the primary resistance method.
With three autotransformers used as in Figure I 2.24 it
is usual, when changing over to full voltage, to opencircuit the star-point and momentarily supply the motor
through part of the transformer windings in series. These
parts of the windings are then shorted out, effectively
taking them out of the circuit. This method is called the
Korndorfer method of starting. Autotransformers are
more often used in the open-delta circuit where only two
windings are used as in Figure 12.26. It is a cheaper
method and while the circuit is unbalanced during the
starting sequence, it is balanced as soon as the motor is in
the running connection.
using an open-delta autotransformer
12.6.5 Secondary resistance starling
This method of starting can only be used with woundrotor motors. Full line voltage is applied to the stator
windings and the starting current is limited by connecting
external resistance across the rotor terminals, as shown in
Figure 12.27. As ihe motor's speed increases, the
resistance is gradually removed from the circuit until at
full speed all the resistance is shorted out.
12.6.6 Other types of motor starters
Liquid
Instead of using resistors as a form of current limiting,
one trend is to use liquid containers with two electrodes
and a chemical electrolyte. Although this is often more
compact than the resistor type there needs to be some
form of increased maintenance to check on the state of
the electrolyte. The liquid is a simple replacement for
the resistor and is often a mixture of water and salt, with
occasionally other chemicals.
Solid state
Starters with this type of construction are initially
expensive, but generally incorporate some form of
operator-adjustable starting current control. In addition,
many systems incorporate a variable frequency generator
for speed control. Most models work on a principle of
converting the alternating current to direct current and
then generating voltages and frequencies to suit. See also
sections 12.9.2 and 17.9.2.
12.7 Typical pushbutton-operated
starter circuits
12.7.1 Circuit protection
Electrical starting circuits are protected against faulty
operation with fuses, circuit breakers and contactors.
L,
0-----,'
L2
0----;
Lo
o------',
Fig. 12.27 Basic power circuit for secondary resistance
motor starting
234
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL -
Fuses
A fuse is designed to become an open circuit once a certain
value of current is exceeded. This does not mean that a
fuse will "blow" immediately its rating is reached. The fuse
element can carry small overloads for a period of time,
depending on the amount of the excess current and the
rate at which the heat being generated can be dissipated.
This characteristic makes a fuse suitable for motor
L,
L,
La
protection circuits, where the fuse must be able to handle
the starting currents.
*
Circuit breakers
Circuit breakers, on the other hand, can be designed to
operate with only small overloads and steps may have to
be taken to slow the action down and enable motors to be
started. Some circuit breakers operate on a magnetic
attraction principle, others on a thermal element; most
operate with both magnetic and thermal elements.
Contactors
Both fuses and circuit breakers are designed to protect
electrical circuits against excessive currents, but serve no
useful purpose in the event of power failures. As a means
of protection contactors are used. When a power failure
or low-voltage situation occurs the contactor drops out,
so switching the equipment off until power is restored. As
an added protection against faulty starting sequences,
most motor starters are automatic once the initial
pushbutton operation has been made.
The following examples show pushbutton-operated
circuits for each of the five means of starting three-phase
induction motors. The circuits are shown with fuse
protection and thermal overload current protection as
possibly the most common protection methods encountered. Individual manufacturers have their own
preferences for starter circuits and these may vary in detail
from one firm to another and from one model to another.
K1.1
K1.2
E
K1.3
Oil-
Power circuit
I
Control ci.
Fig. 12.28 Contactor circuit tor D.0.L. starting
L,
L,
La
12.7.2 D.O.L. contactor starter circuit (Fig. 12.28)
Circuit operation
1. Pressing the start button completes a circuit from L 3
through the normally closed stop button to coil KI,
and the overload to L2 •
2. Main contactor coil Kl then closes and applies full
line voltage directly to the motor via contactor
contacts Kl.I, Kl.2 and Kl.3.
3. Contact Kl.4 bridges out the start button contacts so
that, on the release of the start button, the contactor
remains in the operational state-Le. the control circuit
is latched in the "on" position. Pressing the stop button
disables the latching circuit and allows the main
contactor to revert to the "off" state.
K1.1
12.7.3 Primary resistance contactor starter circuit
(Fig. 12.29)
Circuit operation
1. Pressing the start button completes a circuit from L 3
through the normally closed stop button to coil KI,
and the overload to L2.
Power circuit
Control ci1
Fig. 12.29 Contactor circuit for primary resistance s
235
THREE-PHASE INDUCTION MOTORS
2. The main contactor KI operates. Contact Kl .4 closes
and bridges out the start button contacts, so that on
the release of the start button the Kl contactor circuit
remains latched.
3. Contacts Kl.I, Kl.2 and Kl.3 close, and a reduced
line voltage is applied to the motor through the
resistors in series with each line to the motor. The
starting current is limited by the resistors to a value
below that of D.O.L. starting.
4. Delayed action contact K 1.5 operates after a predeter-
mined delay and completes the circuit for coil K2. Its
operation causes contacts K2. l, K2.2 and K2.3 to
close and allow full line voltage to be applied to the
motor.
5. Pressing the stop button de-energises all coils and
allows the starter to revert to the "off' state.
2. When K2 operates, it causes the "ends" of the three
windings to be joined in "star" via contacts K2. l, K2.2
and K2.3.
3. Simultaneously, coil K3 is open-circuited by K2.5.
This is the delta connecting coil and must be isolated
when the star connection is in operation. Similarly,
when the delta connection is in operation the star
connection must be isolated, a method called
"electrical interlocking". As a precaution, the star and
delta connecting contactors are often mechanically
interlocked in addition to the electrical interlocking
provided by contacts K2.5 and K3.4.
4. When K2.4 closes, a voltage is applied to the timer
K4 and to coil Kl. This allows Kl.4 to close and
bridge the start button.
5. Contacts Kl.I, Kl.2 and Kl.3 close and apply a
voltage to the "starts" of the motor windings.
6. The voltage applied across the windings is only a
proportion of full line voltage (0.58), and starting
12.7.4 Star-delta contactor starter circuit
(Fig. 12.30)
current is reduced accordingly.
7. When the time delay period has elapsed, contact K4. l
Circuit operation
I. Pressing the start button completes a circuit from L3
opens and forces contactor K2 to disconnect the star
connection. The dropping-out action of K2 completes
through the normally closed stop button and two
normally closed contactor contacts (K4.l and K3.4)
to coil K2, and the overload contact t to L2.
the circuit of coil K3 through K2.5, and it is then
activated. This open-circuits the interlocking contact
K3.4 and also switches off the timer K4 via K3.5.
L,
L,
E
E
K3.1
I
K3.2
K3.3
I
1<1.4
K4.1
~
K3.4
K2/5
K2.5
K3.5
K3/5
Control circuit
Fig. 12.30 Con/actor circuit for star-delta starting
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL -
236
8. Contacts K3.l, K3.2 and K3.3 close and complete the
delta connection, allowing full line voltage to be
applied to the motor.
9. Pressing the stop button de-energises all coils and
allows the starter to revert to the "off' state.
12.7.5 Autotransformer contactor starter circuit
(Fig. 12.31)
Circuit operation
1. Pressing the start button completes a circuit from L3
through the normally closed stop button, a normally
closed delay contact Kl.5, electrical interlock K3.3,
coil K2, and the normally closed thermal overload
contact t to L 2.
2. When K2 is activated, it closes the contacts K2. l and
K2.2 connecting the ends of the autotransformers to
line L 2 in an open delta configuration.
3. The operation of K2 simultaneously closes contact
K2.3 and opens contact K2.4-the electrical interlock
to prevent K3 operating while K2 is active.
4. K2.3 supplies power to coil Kl, which is also activated.
Contacts Kl.I, Kl.2, Kl.3 and Kl.4 close. Full line
voltage is connected to the autotransformers and a
reduced line voltage is supplied to the motor via the
transformer tapping. Contact Kl.4 ensures that a
voltage is available to the control circuit whe
button is released.
5. The delayed opening contact Kl.5 opens afi
determined time lapse and forces K2 to op
the delta connection. Contact K2.4 then clo
and coil K3 is activated.
6. Contacts K3.l and K3.2 close, and full lin
is applied to the motor through the Kl cc
series with two lines. The electrical interloc
K3.3 opens and isolates coil K2.
7. Pressing the stop button de-energises all
allows the starter to revert to the "off'' state.
12.7.6 Secondary resistance contactor start
(Fig. 12.32)
Circuit operation
l. Pressing the start button completes a circui1
through the normally closed stop button, coi
the thermal overload contact t to L2 • Coil ~
is in parallel with coil Kl, is activated at
time as Kl but only operates after a pred<
time delay.
2. Contact K 1.4 bridges out the start button cc
that on the release of the start button the ,
remains in the operational state-Le. the cont1
is latched in the "on" position.
L,
L,
La
I
I
K1 .1
K1.2
K1.3
K3.1
IE
I
IE
I
K32
K1.4
K2.3
1
~
Power circuit
I
I
I
I
I
I
Control circuit
Fig. 12.31 Contactor circuit for autotransformer starting
237
THREE-PHASE INDUCTION MOTORS
L,
L,
L,
K1.4
E
K2.1
R
R
R
R
R
R
K1/4
Power circuit
K3.1
K4/2
Control circuit
Fig. 12.32 Contactor circuit for secondary resistance starting
3. Contacts Kl.I, Kl.2 and Kl.3 close and apply full
line voltage to the stator terminals of the motor. The
rotor has two resistors in series with each winding and,
as the ends are connected in star, current flows in the
rotor windings and the motor is able to generate torque
and commence turning.
4. After the delay time, K2 operates and closes contact
K2.l. This causes K4 to be activated along with K3,
a second time delay relay.
5. Contacts K4.l and K4.2 then close and reduce the
amount of resistance connected across the slip rings.
This action enables the motor to attain a higher speed.
6. After a further time delay, coil K3 operates and closes
contact K3.l. Coil K5 is then activated and closes
contacts K5 .I and K5 .2. This action removes the
remainder of the resistance in the rotor circuit and
the motor is in its normal running mode.
7. Pressing the stop button de-energises all coils and
allows the starter to revert to the "off' state.
12.7.7 Part winding starters
Another method of motor starting gradually gaining a
measure of acceptance is the part winding motor starting
method. As with other methods the primary intention is
to reduce starting current and/or torque of a motor. With
larger motors the initial starting torque can transmit high
and damaging shock values to transmission components,
and some type of reduced torque starting becomes
essential.
The phase windings of the stator are divided into
parallel sections each of the requisite number of poles
and each capable of withstanding full line voltage. Parts
of the stator winding are energised and as the motor gains
speed more sections of the stator winding are energised.
Normal control and power components are used to
provide the necessary switching. As much of the motor's
windings remain connected to the line in a closed
transition sequence, current surges are kept to a
minimum.
238
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL l
Table 12.2 Relative characteristics of various starting methods
Starting
Stator
method
voltage at
Starting
current
start
(
Direct-on-
line voltage
0
/o/FL)
Starting
torque
{O/o TFL}
700°/o
No. of
starting
steps
Current surge
during
transition
stages
n.a.
150o/o
line
Types of
Example loads
Genera
comme
loads
suited
light ine~ia
loads
centrifugal
fans
poor sta
torque
motorgenerator
starting
pumps; lathes
starting
greate1
load to
Primary
reduced
resistance
300o/o
40o/o
2+
no
almost no
Star-delta
200°/o
33o/o
2
yes
load
light loads
reduced
units
Autotrans-
300o/o
reduced
80o/o
2
yes
substantial hydraulic
proportion pumps;
of full load conveyors
former
Secondary line voltage
1 OOo/o
1 OOo/o
2+
no
high inertia shock loads;
presses;
loads
resistance
shears
Note: The figures quoted in this table must be considered as a general
113 full I
torque
starting
slightly
than fu
torque
rotor ref
adjuste
start (T
~uide
only. Many variables can be encountered-types an,
stators and rotors, applications, loads and starters being only some oft e factors.
L,
In Figure 12.33 each phase winding has been divided
into two sections, each section sequentially being
connected to the line voltage. Starting torque is down
to approximately 45% and starting current is about 65%
of normal D.0.L. starting. Because of current imbalance
during the starting sequence, the motors tend to be noisy
at this time, which restricts application of the methoc!
to cases in which a motor requires occasional starting
before running for long periods.
(a) Start (stage 1)
12.8 Motor output power
L,
In an induction motor, the magnetic fields of the stator
and rotor interact to cause a force to be developed on the
rotor conductors. This force, acting at a distance from the
shaft equal to the radius of the mean circle of the rotor
conductors, develops a torque or turning force at the shaft
of the motor. Torque is measured in newton-metres (Nm)
and is calculated by the product of force (newtons) and
radius (metres).
T= F.r
(b) Transition (stage 2)
L,
L,
Example 12.5
A motor exerts a force of 360 newtons at the rim of a
pulley with a diameter of 0.5 metre. Calculate the torque
developed by the motor.
T= F.r
(c) Run (stage 3)
= 360 x .Q2 = 90 Nm
2
=
L,
Fig. 12.33 Part winding starting
L,
239
THREE-PHASE INDUCTION MOTORS
Example 12.6
12.9 Speed control of induction motors
If the n1otor in example 12.5 was fitted with a 0.3 m diameter
pulley, calculate the force exerted at the rim of the pulley.
motor was shown to be:
F
= .I_
nsyn =
r
90
- 0.15
= 600N
When considering the mechanical output of the
induction motor, it is necessary to determine the power
produced.
power
= rate of doing work
= work done per second (watts)
work done = force exerted
distance
x
distance moved
= 2rr.r for 1 revolution
(where r = radius in metres)
= 2 rrr X
power
In section 12.3.2 the synchronous speed of an induction
n
for 1 second
60
(wheren = r/min)
= force x distance
2rrrn
2rrn
=FX(;0=6QXFr
But torque ( 7) = Fr
60
where n is in r/min.
Example 12.7
A 415 V, three-phase, 50 Hz, four-pole induction motor
has a full-load speed of 1440 r/min. Calculate the power
produced by the motor if it develops a torque of 100 Nm.
p = 2rr.n. T
60
2 x .,,. x 1440
60
15 079 watts
15.1 kW
p
That is, the speed depends on both the frequency and the
nu1nber of magnetic poles in the machine.
The synchronous speed is that of the rotating
magnetic field, while the actual speed must always be less
than this by the amount of slip necessary to allow the
motor to develop the required amount of torque. To
change the speed of an induction motor by an appreciable
amount, other than by loading it to alter the slip speed,
either the frequency of the supply or the number of poles
in the windings must be changed. Under normal circumstances the speed of the induction motor must then be
considered as fixed. If any application requires that the
speed be adjustable, then special and expensive
equipment must be used. (Refer to sect. 17.9.)
12.9.1 Wound-rotor motors
The degree of slip in a wound-rotor motor may be
changed comparatively easily by varying the amount of
external resistance in the rotor circuit. This provides
dubious results in that the speed changes every time the
load changes, efficiency can be as low as 40% because
2rrnT
P =--watts
i.e.
120(
of the /ZR losses in the resistors and the available torque
can be appreciably reduced. In addition, heavy-duty
resistors have to be provided owing to the fact that the
normal resistors are rated for starting purposes only (i.e.
a short duty cycle). Combinations of wound-rotor motors
connected in various ways have attempted to overcome these disadvantages-called cascading and
concatenation-but the methods tend to be cumbersome
and expensive. Special motors have been developed with
better results, but the costs are still so high that the direct
current machine becomes competitive even after allowing
for the provision of a d.c. supply.
x 100
Example 12.8
If the above motor draws 31 A from the supply, and the
power factor is 0.86, determine the efficiency of the
motor.
P;. = VJVIA.
_ output
T/ - input
= 15 079 x IOO
VJVIA.
15 079 x 100
= ,jj x 415 x 31 x 0.86
= 78.7%
12.9.2 Squirrel-cage motors
This type of motor under normal operating circumstances
is considered as a fixed speed machine with only very
small variations in speed from no load to full load.
Reducing the supply voltage has negligible effect on the
speed but reduces the amount of available torque and
eventually the machine stalls.
Special connection arrangements of the windings
1hc1nsclves allow n1otors to be connected, for example, as
either two- or four-pole motors. This only provides a step
change in speed and allows no other control. If other
speeds are required then possibly a second winding has to
be used. For example, one winding could give both two
and four poles while the second winding gives six poles. It
is however still only speed changes in three steps. While
satisfactory for some uses such as lathe work, it is not
suitable for any project such as rolling mills where
incremental changes may be required. The method of
speed change in the ratio of 2: I for single windings was
developed many years ago. More recently the advent of
240
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL T
control of the operator, and can be done man1
a control knob on the unit. The speed range ol
is from 1% to 200% of normal running speeds
and efficiency are high throughout the complete
The unit's operating principle is to convert ti
phase alternating current supply to direct current
to generate a three-phase supply at any desired f1
within the range of the equipment. The units 1
reversing facilities, and provision can be made fo
control stations. The units are available in a
sizes. The photograph of a typical unit is shown i
12.35.
12.10 Motor braking
The main power equipment in most electrical sys
rotating electrical machine. There are many app
where it is necessary to bring the machine tc
quickly, to keep a load from moving or to enable:
reversal of direction. In general there are two
braking-mechanical and electrical.
12.10.1 Mechanical braking
Mechanical brakes are mostly solenoid operated
tension holds the brakeshoes or band against ad
it operates as a stopping device as well as a parkir
This is necessary to prevent undesired movemen
..
. IJ
Fig. 12.34 A two-stage secondary resistance starter. The
direct-on-line contactor is at the top, while the
lower contactor short-circuits the rotor resistors
when operated by the timer.
pole amplitude modulation (PAM) represented an
advance on this concept in that it gave closer ratios in the
order of 6:4 and 8:6 and other similar ratios. Note
however it is still step changes and not incremental. The
PAM motor is made in all sizes and its "secret" lies in the
internal connections of the pole groups. Six leads are
brought out in a similar fashion to two-speed motor
windings. The windings are halved and each half is
connected in star across the supply lines, giving double or
parallel star for one speed, while the windings are all
connected together in series delta for the other.
could occur with a crane holding a suspended loa
power is applied to the driving motor, the soleno
activated, so releasing the brake and allowing tr
full control. Light duty brakes may adopt the di
configuration but these have limited application:
12.10.2 Electrical braking
There are two types of electrical braking and e;
also be used in conjunction with mechanical bra
Dynamic braking
In this method the motor converts its energy o
into electrical energy. For a three-phase inductic
Another recent development for speed control of
squirrel-cage motors is the electronic control unit.
Provision is usually made in the unit for adjustable rates
of current increase to control starting currents, and the
voltage supplied by the unit to the motor is stabilised.
The motor is accelerated from standstill at a
predetermined current rate.
Once running under load, the motor speed can be
varied by changing the frequency. This is usually under
Fig. 12.35 An incremental speed control unit for i
motors. It uses an electronically gener
ASI
variable frequency.
241
THREE-PHASE INDUCTION MOTORS
the most common method is to disconnect the a.c. supply
and reconnect the windings to a source of d.c., as shown
in Figure 12.36. An inspection of the circuit will show
that the main and brake contactors are electrically
interlocked with a time delay to switch the d.c. off after
a short period. Because the rotor conductors are still
rotating and the d.c. field is stationary, there is a
generated voltage and a circulating current in the rotor
bars. This creates a torque in the opposite direction to
the rotation of the n1otor, resulting in a rapid slowing
down. The rate of slowing down is fairly constant, unlike
the d.c. n1otor with dynan1ic braking, where the braking
effect din1inishes markedly as the speed reduces.
Satisfactory operation of three-phase motors on a
three-phase supply depends on several factors:
I. three equal voltages at the correct phase displace1nent.
Under normal operating conditions the phase
displacement is a function of the generating equipment
and stays relatively fixed, but the line voltages can
vary depending on the individual loads connected at
that tin1e. For balanced loads, such as three-phase
motors, unbalanced phase voltages lead to unbalanced
currents flowing in the motor windings. As a
consequence, circulating currents are set up, heating
is increased and uneven, and torque is reduced.
2. the stator windings being correctly connected in either
star or delta. Phase currents become unbalanced,
Plug braking
windings generate increased heat, and torque is greatly
reduced. Refer to section 12. l I. I for more details.
Plug braking for an induction motor is simply a matter of
reconnecting for the reverse direction of rotation while it is
still rotating in a forward direction. While the d.c. motor
needed some form of current limiting, the induction
motor does not since the current drawn is substantially the
same as the D.O.L. starting current. Once the motor has
stopped, some form of switching is needed to prevent it
accelerating up to speed in the reverse direction. This is
often achieved by a friction driven contact on the shaft of
the motor.
3. the three line voltages being connected to the 1notor
windings. When any one supply line is not able to
supply current to the winding to which it is connected,
the condition known as "single-phasing" occurs. For
further details refer to section 12.1 1.2.
4. the condition of.both windings in the 1noto1: The stator
windings connected to the supply are pron1inent and
obvious areas of concern. Noisy operation and reduced
torque of a three-phase n1otor can mean that the bars
of the rotor-the second winding-are in need of
attention. Many cages consist of aluminium cast into
shape in the laminations, and little can be done in the
way of niaintenance; many of the larger motors,
however, have prefabricated bars and rings of copper
which are welded into place. It is possible to repair
dan1age to these ite1ns, whether they are broken or
sin1ply loose in the rotor.
12.11 Abnormal operating conditions
The following applies specifically to three-phase motors.
For further information on abnormal operating
conditions applying to both single and three-phase
motors see section 13.6 in the next chapter.
L,
L,
L,
I
I
I
t-----+---+-r-.,
r;;\
~
l1> y ,
K2.1-2.3
-
+
Power circuit
j
-
I
IE
I
II~K2.4
I
K1/5
K2/4
K3/1
~-____.
Control circuit
Fig. 12.36 Braking an a.c. motor by d.c. injection
ELECTRICAL PRINCIPLES FOR THE ELECTRICAL 1
242
c
-8
c
A,
A
A
I
B
I
I
Reversed
phase
I
I
s,
I
I
(a)
(b)
Fig. 12.37 Reversal of one phase tor a star-connected motor
12.11.1 Phase reversal
Previously in this chapter the operation of the induction
motor has been based on the assumption that the motor
had three identical windings and three equal currents
flowing in them, all spaced at 120° E to each other. If one
phase is reversed, however, as shown in Figure l 2.37(a)
for a star connection, these conditions no longer hold
true. Two of the three currents that flow are at 60° E to
each other and the load system is unbalanced (Fig.
12.37(b)). The same condition applies to delta-connected
loads, and both connections were discussed in Chapter 10.
As a result of this incorrect connection, the motor
loses most ofits torque and is often unable to start against
even a light load. If able to start at all, it usually rotates
very slowly and has unequal values of current in the phase
windings. The values of current approach those drawn
during normal starting, but remain high. The motor
I
L,
usually emits a "growling" noise and has an a
vibration due to the sustained high current valt
12.11.2 Single-phasing
Single-phasing is a condition that occurs when c
a three-phase supply is open-circuited and is no
supply current to a three-phase load. The nar
used when one of the three phase windings in
open-circuited.
The condition for single-phasing in a star-(
load is shown in Figure 12.38 (a), and it can be
a break in either the line or the phase windin.
the circuit to a single current path.
Figure 12.38(b) shows an open-circuited I
delta-connected motor. There is one main cur
from L 1 to L3 through phase A and another l
L 1 to L3 through phases B and C in series. Bot!
~----
0 - - - - - - - , '1
-~----
I
....
L,0-----~
\
\
A
\
\
\
I
x
\
I
I
L20-X_]
,
'\
B
______
L2 o-x---~
......
_________
/
B
----
JL2 0---1--fY--VYl
\
I
I
-
-,I
JL,()----------J
L, ( _ } - - - - - - - - - '
--------·--/
/
(a)
(c)
(b)
Fig. 12.38 Circuit conditions causing single-phasing with
a three-phase
motor
243
THREE-PHASE INDUCTION MOTORS
are in parallel with each other, although not necessarily
connected induction motor is shown with phase C open-
than normal currents in the parts of the circuit still
operating, with values approaching starting current
values in some circumstances. It can also emit a low-
circuited. There are two current paths-L 1 through phase
A to L3 and L, through phase B to L,.
In each of the cases shown in Figure 12.38, the rotating magnetic field is either destroyed or unbalanced, and
causes unsatisfactory operation of the motor. The motor
rotates at slower speeds, if it is able to start at all, because
of a much reduced starting torque. It usually draws higher
pitched "growling" noise similar to that which occurs
during a phase reversal. If single-phasing occurs while the
motor is operating at normal speeds, the normal
humming sound often changes to a higher-pitched whine.
For any of the conditions for single-phasing outlined
above, the
ratios between line and phase values are no
longer valid.
in phase with each other. In Figure 12.38(c), a delta-
VJ
Exercises
12.1
12.2
Briefly describe how the rotating magnetic
field is produced in a three-phase motor.
(a) Define the term "synchronous speed''.
(b) Make a table showing the synchronous
speeds of two-, four-, six- and eight-pole
induction motors for frequencies of 40, 50
and 60 Hz.
12.3
Explain why an induction motor runs at less
than synchronous speed.
12.4
Explain why the power factor of an induction
motor increases with the load.
Briefly describe the construction of the
squirrel-cage and the wound-rotor.
12.5
12.6
List three methods by which the starting
current of a three-phase squirrel-cage induction motor may be reduced.
12.7
What is the disadvantage in starting a
squirrel-cage induction motor on a reduced
voltage?
12.8
What is meant by:
(a) synchronous speed of an induction
motor?
(b) actual speed?
(c) slip speed?
(d) What is the relationship between each
of these three speeds?
12.9 Sketch a typical torque/speed curve for an
induction motor having a normal squirrelcage rotor. At low values of slip, how does the
torque vary with load? What occurs when
breakdown torque is reached?
12.10 Why do squirrel-cage motors take relatively
large amounts of current when connected
D.0.L.?
12.11 Discuss speed control by a method of
changing the number of poles in a motor.
12.12 Draw a circuit diagram for a star-delta starter
using push buttons for its initiation. Discuss
the operation of the circuit and list two uses
for this type of starter.
Problems
12.13 Determine the percentage slip for the
following three-phase, 50 Hz motors:
(a) four-pole, 1420 r/min;
(b) six-pole, 960 r/min;
(c) eight-pole, 720 r/min.
12.14 A 15 kW, three-phase, 415 V, 50 Hz, four-pole
induction motor draws 190 A when started
D.O.L. in delta. Determine the starting
current using:
(a) the star-delta method;
(b) the autotransformer method (60% tapping).
12.15 At full load the efficiency of the motor in
problem 12.14 is 83%, the power factor is 0.84
and the slip is 4%. Determine:
(a) the torque developed;
(b) the current drawn.
12.16 Calculate the full-load torque of each of the
following motors:
(a) 7.5 kW, 1440 r/min;
(b) 1.5 kW, 940 r/min;
(c) 12 kW, 720 r/min;
(d) 5 kW, 1450 r/min.
12.17 On full load, a three-phase, 415 V, 50 Hz,
six-pole motor draws 19 A at a power factor of
0.85. If the torque developed is 95 Nm and the
slip is 7%, calculate the efficiency of the
motor.
12.18 A cutting tool exerts a tangential force of 400
N on a 90 mm diameter steel bar which is
rotating at 145 r/min in a lathe. The efficiency
of the lathe gear train is 62% and the threephase, 415 V motor efficiency is 81%.
Calculate the motor current if the power
factor is 0.83.
12.19 The rotor speed of a 10 kW, 415 V, threephase, four-pole motor is 1455 r/min when it
operates from a source of 50 Hz. Find:
(a) synchronous speed;
(b) slip speed;
(c) frequency of rotor currents.