The AC induction motor is a rotating electric machine designed to operate from a 3-phase source of
alternating voltage. For variable speed drives, the source is normally an inverter that uses power
switches to produce approximately sinusoidal voltages and currents of controllable magnitude and
frequency.
A cross-section of a two-pole induction motor is shown in Figure 3-1. Slots in the inner periphery of
the stator accommodate 3-phase winding a,b,c. The turns in each winding are distributed so that a
current in a stator winding produces an approximately sinusoidally-distributed flux density around the
periphery of the air gap. When three currents that are sinusoidally varying in time, but displaced in
phase by 120° from each other, flow through the three symmetrically-placed windings, a
radially-directed air gap flux density is produced that is also sinusoidally distributed around the gap
and rotates at an angular velocity equal to the angular frequency ωs of the stator currents.
The most common type of induction motor has a squirrel cage rotor in which aluminum conductors or
bars are cast into slots in the outer periphery of the rotor. These conductors or bars are shorted together
at both ends of the rotor by cast aluminum end rings, which also can be shaped to act as fans. In larger
induction motors, copper or copper-alloy bars are used to fabricate the rotor cage winding.
Figure 3-1. 3-Phase AC Induction Motor
As the sinusoidally-distributed flux density wave produced by the stator magnetizing currents sweeps
past the rotor conductors, it generates a voltage in them. The result is a sinusoidally-distributed set of
currents in the short-circuited rotor bars. Because of the low resistance of these shorted bars, only a
small relative angular velocity ωr between the angular velocity ωs of the flux wave and the mechanical
angular velocity ω of the two-pole rotor is required to produce the necessary rotor current. The relative
angular velocity ωr is called the slip velocity. The interaction of the sinusoidally-distributed air gap
flux density and induced rotor currents produces a torque on the rotor. The typical induction motor
speed-torque characteristic is shown in Figure 3-2.
Squirrel-cage AC induction motors are popular for their simple construction, low cost per horsepower
and low maintenance (they contain no brushes, as do DC motors). They are available in a wide range
of power ratings. With field-oriented vector control methods, AC induction motors can fully replace
standard DC motors, even in high-performance applications.
Mathematical Description of AC Induction Motors
There are a number of AC induction motor models. The model used for vector control design can be
obtained by utilization of the space vector theory. The 3-phase motor quantities (such as voltages,
currents, magnetic flux, etc.) are expressed in the term of complex space vectors. Such a model is valid
for any instantaneous variation of voltage and current and adequately describes the performance of the
machine under both steady-state and transient operation. Complex space vectors can be described
using only two orthogonal axes. We can look at the motor as a 2-phase machine. The utilization of the
2-phase motor model reduces the number of equations and simplifies the control design.
alternating voltage. For variable speed drives, the source is normally an inverter that uses power
switches to produce approximately sinusoidal voltages and currents of controllable magnitude and
frequency.
A cross-section of a two-pole induction motor is shown in Figure 3-1. Slots in the inner periphery of
the stator accommodate 3-phase winding a,b,c. The turns in each winding are distributed so that a
current in a stator winding produces an approximately sinusoidally-distributed flux density around the
periphery of the air gap. When three currents that are sinusoidally varying in time, but displaced in
phase by 120° from each other, flow through the three symmetrically-placed windings, a
radially-directed air gap flux density is produced that is also sinusoidally distributed around the gap
and rotates at an angular velocity equal to the angular frequency ωs of the stator currents.
The most common type of induction motor has a squirrel cage rotor in which aluminum conductors or
bars are cast into slots in the outer periphery of the rotor. These conductors or bars are shorted together
at both ends of the rotor by cast aluminum end rings, which also can be shaped to act as fans. In larger
induction motors, copper or copper-alloy bars are used to fabricate the rotor cage winding.
Figure 3-1. 3-Phase AC Induction Motor
As the sinusoidally-distributed flux density wave produced by the stator magnetizing currents sweeps
past the rotor conductors, it generates a voltage in them. The result is a sinusoidally-distributed set of
currents in the short-circuited rotor bars. Because of the low resistance of these shorted bars, only a
small relative angular velocity ωr between the angular velocity ωs of the flux wave and the mechanical
angular velocity ω of the two-pole rotor is required to produce the necessary rotor current. The relative
angular velocity ωr is called the slip velocity. The interaction of the sinusoidally-distributed air gap
flux density and induced rotor currents produces a torque on the rotor. The typical induction motor
speed-torque characteristic is shown in Figure 3-2.
and low maintenance (they contain no brushes, as do DC motors). They are available in a wide range
of power ratings. With field-oriented vector control methods, AC induction motors can fully replace
standard DC motors, even in high-performance applications.
Mathematical Description of AC Induction Motors
There are a number of AC induction motor models. The model used for vector control design can be
obtained by utilization of the space vector theory. The 3-phase motor quantities (such as voltages,
currents, magnetic flux, etc.) are expressed in the term of complex space vectors. Such a model is valid
for any instantaneous variation of voltage and current and adequately describes the performance of the
machine under both steady-state and transient operation. Complex space vectors can be described
using only two orthogonal axes. We can look at the motor as a 2-phase machine. The utilization of the
2-phase motor model reduces the number of equations and simplifies the control design.
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