Lecture 12 EE743

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Lecture 12 - EE743
AC Machines Reluctance machines - Induction
machines
Professor Ali Keyhani
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Two-Pole reluctance machines
bs axis
?r
?r
as
as'
?r
?r
as axis
as axis
bs
bs'
as
as
Single phase
Two phase
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Two-Pole reluctance machines

• Stator windings are assumed to be sinusoidally
  distributed
• For single phase machines excited by an AC
  current source, the generated flux wave has two
  opposite rotating mmfs (These motors are used in
  clocks and some other turntables)

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Two-Pole reluctance machines

• term results in
  counterclockwise (positive) travelling wave
• term results in
  clockwise (negative) travelling wave

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Two-Pole reluctance machines

• For reluctance machine (Fig. 1),

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Two-Pole reluctance machines

• For two-phase reluctance machines (see Fig.1),
  only one constant-amplitude rotating air gap mmf
  is produced during balanced steady state
  conditions
• Two-phase reluctance machines develop a constant
  torque at synchronous speed rather than a torque
  which pulsates about an average value as is the
  case with single-phase machines

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Two-pole induction machines
bs axis
br axis
?r
ar axis
?r
?r
?r
as'
ar axis
as'
?r
?r
ar'
?s
?s
br
ar'
as axis
as axis
bs
bs'
ar
br'
ar
as
as
Single phase
Two phase
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Cutaway Views of Squirrel-cage Induction Motor
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Two-pole induction machines

• Single and two pole induction machines have
  identical equivalent orthogonal windings which
  are sinusoidally distributed (see Fig.2)
• Rotor windings are short-circuited
• Single-phase induction machines are widely used
  (washers, dryers, furnace fans, etc.)
• Recall

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Two-pole induction machines

• Term 1 positive travelling flux wave
• Term 2 negative travelling flux wave
• Recall
• Single-phase induction machines do not develop a
  starting torque. At the start ?r0, Te0, i.e at
  start the rotor cannot follow either of the
  rotating mmfs since it develops as much torque to
  go in either direction
• Single-phase induction motors have two stator
  windings with provision to switch out one of the
  windings once the rotor accelerates to between 60
  to 80 percent of synchronous speed

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Two-pole induction machines

• To provide two phase power from one phase power
  supply, a capacitor is used during the starting.

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Two-pole induction machines

• For two-phase induction machines, statormmfs
  is a positive travelling flux wave which rotates
  around the air gap at a speed of ?e (see Fig.2b)
• Machine rotor windings are short-circuited

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Two-pole induction machines

• Current flowing in the rotor windings will be due
  to induction with a frequency of ?e - ?r. The
  rotor currents, iar and ibr will produce an air
  gap mmf that travels at a speed of ?e - ?r
  relative to the rotor or ?e relative to a
  stationary observer.
• Interactions of mmfr due to rotor and mmfs due to
  stator will produce torque on the rotor.

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Three-phase induction machines
bs - axis
br - axis
as'
?r
Te
?r
bs
cs
ar - axis
ar'
br
?r
Tl
?s
cr
as - axis
cr'
br'
ar
cs'
bs'
as
cs - axis
cr - axis
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Three-phase induction machines

• Three-phase induction machines have three
  identical sinusoidally distributed stator and
  rotor windings. The magnetic axes of the windings
  are displaced 120o from each other and rotor
  windings are short-circuited (see Fig.3)

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Three-phase induction machines

• mmfs is a positive travelling flux wave which
  rotates around the air gap at a speed of ?e.
• mmfr is a positive travelling flux wave which
  rotates around the air gap at a speed of ?e-?r
  relative to the rotor.
• Interactions of mmfr due to rotor and mmfs due to
  stator will produce torque on the rotor.

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Three-phase induction machines - dq axis
bs - axis
br - axis
q - axis
?r
ar - axis
?
?
?r
?s
as - axis
d - axis
cs - axis
cr - axis