Malcolm Barnes. Practical Variable Speed Drives and Power Electronics
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3-Phase AC induction motors 49
Figure 2.11:
Acceleration torque during the starting of an AC induction motor
The rate of acceleration of the drive system also depends on the moment of inertia (J) of
the rotating object. The higher the value of J, the longer it takes to increase speed.
Nm
d
d
A
t
J =
T
ω
Where J = Inertia of the drive system in kgm
2
ω = Rotational speed in radians/sec
If this formula is adjusted to convert the rotational speed from rad/sec to rev/min
Nm
d
d
60
2
A
t
n
J =
T
π
Where n = Rotational speed in rev/min
Re-arranging
T
J =
n
t
A
1
60
2
d
d
π
This is integrated with respect to speed, from starting speed (n
1
) to final speed (n
2
).
The total acceleration time t
d
is given by:
secd
1
60
2
A
d
2
1
n
T
J =
t
n
n
∫
π
If the acceleration torque were constant over the acceleration period, this formula would
simplify to:
sec
T
)
n
n
(
J =
t
A
12
d
60
2
−π
50 Practical Variable Speed Drives and Power Electronics
Inertia can be calculated using the formula:
kgm
4
2
2
D G
= J
×
Where J = Moment of inertia of the rotating in kgm
2
G = Mass in kilograms (kg)
D = Diameter of gyration in meters (m)
It is not usually necessary to calculate the value of J from first principles because this
may be obtained from the manufacturer of the motor as well as the driven machine.
2.7 AC induction generator performance
The performance of the 3-phase AC induction motor has been described for the speed
range from zero up to its rated speed at 50 Hz, where it behaves as a motor. A motor
converts electrical energy to mechanical energy. The induction motor will always run at a
speed lower than synchronous speed because, even at no-load, a small slip is required to
ensure that there is sufficient torque to overcome friction and windage losses.
If, by some external means, the rotor speed was increased to the point that there was no
slip, the induced voltage and current in the rotor fall to zero and torque output is zero.
If the rotor speed is, by some external means increased above this, the rotor will run
faster than the rotating stator field and the rotor conductors again start to cut the lines of
magnetic flux. Induced voltage reappears in the rotor, but in the opposite direction. From
Lenz’s Law, this results in currents that oppose this change and the power flows in the
opposite direction from the driven rotor to the stator. Power flows from the mechanical
prime mover, through the induction machine into the electrical supply connected to the
stator. When the speed of the machine exceeds the synchronous speed n
o
, it then operates as
an induction generator.
This situation can often occur in the case of cranes, hoists, inclined conveyors, etc,
where the load ‘over-runs’ the motor.
The torque–speed curve can be extended to cover the induction generator region as
well. The shape of the curve in the generator region is identical to the motor region
because exactly the same equivalent circuit applies. The only difference is that the slip is
negative and active power is transferred back into the mains.
Figure 2.12:
Transition from induction motor to induction generator
3-Phase AC induction motors 51
2.8 Efficiency of electric motors
The efficiency of a machine is a measure of how well it converts the input electrical
energy into mechanical output energy. It is directly related to the losses in the motor,
which depend on the design of the machine. Referring to the equivalent circuit of an
induction motor, the losses comprise the following:
• Load dependent losses
These are mainly the copper losses due to the load current flowing through the
resistance of the stator and rotor windings and shown in the equivalent circuit
as roughly I
S
2
(R
S
+ R'
R
). These losses are proportional to the square of the
stator current.
• Constant losses
These losses are mainly due to the friction, windage and iron losses and are
almost independent of load. They are represented in the equivalent circuit as
I
M
2
R
C
.
Since the constant losses are essentially independent of load, while the stator and rotor
losses depend on the square of the load current, the overall efficiency of an AC induction
motor drops significantly at low load levels, as shown in Figure 2.13.
Because of price competition, AC motor manufacturers are under pressure to
economize on the quality and quantity of materials used in the motor. Reducing the
quantity of copper increases the load dependent losses. Reducing the quantity of iron
increases iron losses. Consequently, high efficiency of motors usually cost more. On large
motors, high efficiency represents a significant saving in energy costs, which can be
offset against the higher initial cost of a more efficient motor.
For electric motors used in AC variable speed drive applications, additional harmonic
currents result in additional losses in the motor making it even more desirable to use high
efficiency motors.
Figure 2.13:
Efficiency of an AC induction motor vs load
52 Practical Variable Speed Drives and Power Electronics
2.9 Rating of AC induction motors
AC induction motors should be designed or selected to match the load requirements of
any particular application. Some mechanical loads require the motor to run continuously
at a particular load torque. Other loads may be cyclical or with numerous stops and starts.
The key consideration in matching a motor to a load is to ensure that the temperature
inside the motor windings does not rise, as a result of the load cycle, to a level that
exceeds the critical temperature. This critical temperature is that level which the stator
and rotor winding insulation can withstand without permanent damage. Insulation
damage can shorten the useful life of the motor and eventually results in electrical faults.
The temperature rise limits of insulation materials are classified by standards
organizations, such as IEC 34.1 and AS 1359.32. These standards specify the maximum
permissible temperatures that the various classes of insulation materials should be able to
withstand. A safe temperature is the sum of the maximum specified ambient temperature
and the permitted temperature rise due to the mechanical load.
For purposes of motor design, most motor specifications, such as IEC, AS/NZS, specify
a maximum ambient temperature of 40
o
C. The temperature rise of the induction machine
is the permissible increase in temperature, above this maximum ambient, to allow for the
losses in the motor when running at full load. The maximum critical temperatures for
each insulation class and the temperature rise figures, which are specified by IEC 34.1
and AS 1359.32 for rotating electrical machines, are as follows:
Insulation class E B F H
Maximum temperature 120
o
C 130
o
C 155
o
C 180
o
C
Max temperature rise 70
o
C 80
o
C 100
o
C 125
o
C
Figure 2.14:
Maximum temperature ratings for insulation materials
From these tables, note that electrical rotating machines are designed for an overall
temperature rise to a level that is below the maximum specified for the insulation
materials.
For example, using class-F insulation,
Max ambient + Max temperature rise = 40
o
C + 100
o
C = 140
o
C
which gives a thermal reserve of 15
o
C. The larger the thermal reserve, the longer the life
expectancy of the insulation material.
When operating continuously at the maximum rated temperature of its class, the life
expectancy of the insulation is about 10 years. Most motors do not operate at such
extreme conditions because an additional safety margin is usually allowed between the
calculated load torque requirements and the actual size of the motor chosen for the
application. So life expectancy of a motor, which is correctly matched to its load and with
suitable safety margins, can reasonably be taken as between 15 to 20 years.
If additional thermal reserve is required, the motor can be designed for an even lower
temperature. It is common practice for the better quality manufacturers to design their
motors for class-B temperature rise but to actually use class-F insulating materials. This
provides an extra 20
o
C thermal reserve that will extend the life expectancy to more than
3-Phase AC induction motors 53
20 years. This also means that the motor could be used at higher ambient temperatures of
up to 50
o
C or more, theoretically up to 65
o
C.
In manufacturer’s catalogues, the rating of 3-phase AC induction motors are usually
classified in terms of the following:
• Rated output power, in kW
• Rated speed, depends on the number of poles
• Rated for a continuous duty cycle S1, (see below)
• Rated at an ambient temperature not exceeding 40
o
C
• Rated at an altitude not exceeding 1000 m above sea level, which implies an
atmospheric pressure of above 1050 mbar
• Rated for a relative humidity of less than 90%
Figure 2.15:
Summary of temperature rise for classes of insulation materials according to IEC 34.1
AC induction motors often need to operate in environmental conditions where the
ambient temperature and/or the altitude exceed the basis for the standard IEC or AS
rating.
Where the ambient temperature is excessively high, temperature de-rating tables are
available from the motor manufacturers. An example of one manufacturer’s de-rating
table, for both temperature and altitude, is shown in Figure 2.16 below. As pointed out
earlier, better quality AC induction motors have a built-in thermal reserve. In some
cases, where the ambient temperature is only marginally higher than 40°C, this reserve
may be used with no additional de-rating for temperature.
In motor mounting positions that are exposed to continuous direct sunshine, motors
should be provided with a protective cover.
54 Practical Variable Speed Drives and Power Electronics
Ambient
temperature
Permissible output
% of rated output
Altitude above
Sea Level
Permissible output
% of rated output
30
o
C
40
o
C
45
o
C
50
o
C
55
o
C
60
o
C
70
o
C
107 %
100 %
96 %
92 %
87 %
82 %
65 %
1000m
1500m
2000m
2500m
3000m
3500m
4000m
100 %
96 %
92 %
88 %
84 %
80 %
76 %
Figure 2.16:
Motor de-rating for temperature and altitude
At high altitudes, where there is a reduced atmospheric pressure, the cooling of
electrical equipment is degraded by the reduced ability of the air to remove the heat from
the cooling surfaces of the motor. When the air pressure falls with increased altitude, the
density of the air falls and, consequently, its thermal capacity is reduced. In accordance
with the standards, AC induction motors are rated for altitudes up to 1000 meters above
sea-level. Rated power and torque output should be de-rated for altitudes above that.
When a motor needs to be de-rated for both temperature and altitude, the de-rating
factors given in the table above should be multiplied together. For example, for a motor
operating at above 2500 m in an ambient temperature of 50°C, the overall de-rating factor
should be (0.92 × 0.88) × 100%, or 81%.
2.10 Electric motor duty cycles
The rated output of an AC induction motor given in manufacturer’s catalogues is based
on some assumptions about the proposed application and duty cycle of the motor. It is
common practice to base the motor rating on the continuous running duty cycle S1.
When a motor is to be used for an application duty cycle other than the S1 continuous
running duty, some precautions need to be taken in selecting a motor and the standard
motors may be re-rated for the application. The duty cycles are normally calculated so
that the average load over a period of time is lower than the continuous load rating S1.
In the standards, several different duty cycles are defined. In IEC 34.1 and AS 1359.30,
eight different duty types are defined by the symbols S1 to S8 as follows:
S1: Continuous running duty
3-Phase AC induction motors 55
• Operation at constant mechanical load for a period of sufficient duration for
thermal equilibrium to be reached.
• In the absence of any indication of the rated duty type of a motor, S1
continuous running duty should be assumed.
• Designation example: S1
S2: Short-time duty
• Operation at constant load, for a period of time which is less than that
required to reach thermal equilibrium, followed by a rest and motor de-
energised period of sufficient duration for the machine to re-establish
temperatures to within 2°C of the ambient or the coolant temperature.
• The values 10 min, 30 min, 60 min and 90 min are recommended periods for
the rated duration of the duty cycle.
• Designation example: S2 – 60 min
S3: Intermittent periodic duty not affected by the starting process
• A sequence of identical duty cycles, each comprising a period of operation at
constant load and a period of rest when the motor is de-energized.
56 Practical Variable Speed Drives and Power Electronics
• The period of the duty cycle is too short for thermal equilibrium to be
reached.
• Assumed that the starting current does not significantly affect the temperature
rise.
• The duration of one duty cycle is 10 min.
• The following items should also be specified for this duty cycle
− The cyclic duration factor, which represents the percentage duration
of the loaded period as a percentage of the total cycle
− Recommended values for cyclic duration factor are 15%, 25%, 40%,
60%
• Designation example: S3 – 25%
S4: Intermittent periodic duty affected by the starting process
• A sequence of identical duty cycles, each comprising a period of significant
starting current, a period of operation at constant load and a period of rest
when the motor is de-energized.
• The period of the duty cycle is too short for thermal equilibrium to be
reached.
• Assumed that the starting current is significant.
• The motor is brought to rest by the load or by mechanical braking, where the
motor is not thermally loaded.
• The following items should also be specified for this duty cycle
− The cyclic duration factor, which represents the percentage duration
of the loaded period as a percentage of the total cycle
− The number of load cycles per hour (c/h)
− The inertia factor F
I
, which is the ratio of the total moment of inertia
to the moment of inertia of the motor rotor
− The moment of inertia of the motor rotor (J
M
)
− The average moment of resistance T
V
, during the change of speed
given with rated load torque
3-Phase AC induction motors 57
• Designation example: S4 – 25% – 120 c/h – (F
I
= 2) – (J
M
= 0.1 kgm
2
) – (T
V
=
0.5T
N
)
S5: Intermittent periodic duty affected by the starting process and
also by electric braking
• A sequence of identical duty cycles, each comprising a period of significant
starting current, a period of operation at constant load, a period of rapid
electric braking and a period of rest when the motor is de-energized.
• The period of the duty cycle is too short for thermal equilibrium to be
obtained.
• The following items should also be specified for this duty cycle
− The cyclic duration factor, which represents the duration of the loaded
period as a percentage of the total cycle
− The number of load cycles per hour (c/h)
− The inertia factor F
I
, which is the ratio of the total moment of inertia
to the moment of inertia of the motor rotor.
− The moment of inertia of the motor rotor (J
M
)
− The permissible average moment of resistance T
V
, during the change
of speed given with rated load torque.
• Designation example: S5 – 40% – 120 c/h – (F
I
= 3) – (J
M
= 1.3 kgm
2
) – (T
V
=
0.3T
N
)
58 Practical Variable Speed Drives and Power Electronics
S6: Continuous operation, periodic duty with intermittent load
• A sequence of identical duty cycles, where each cycle consists of a period at
constant load and a period of operation at no-load (no-load current only), but
with no period of de-energization.
• The period of the duty cycle is too short for thermal equilibrium to be
obtained.
• Recommended values for the cyclic duration factor are 15%, 25%, 40% and
60%.
• The duration of the duty cycle is 10 min.
• Designation example: S6 – 40%.
S7: Uninterrupted periodic duty, affected by the starting process and
also by electric braking
• A sequence of identical duty cycles, each comprising a period of starting
current, a period of operation at constant load, a period of electric braking.
• The braking method is too short for thermal equilibrium to be obtained.
• The following items should also be specified for this duty cycle
− The number of load cycles per hour (c/h)