ENERGY CONVERSION ONE (Course 25741)

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ENERGY CONVERSION ONE (Course 25741)

• CHAPTER SEVEN
• INDUCTION MOTORS

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SUMMARY

• 1. Induction Motor Construction
• 2. Basic Induction Motor Concepts
• The Development of Induced Torque in an
  Induction Motor
• The Concept of Rotor Slip
• The Electrical Frequency on the Rotor
• 3. The Equivalent Circuit of an Induction
  Motor
• The Transformer Model of an induction
  Motor
• The Rotor Circuit Model
• The Final Equivalent Circuit
• 4. Powers and Torque in Induction Motor
• Losses and Power-Flow diagram
• Power and Torque in an Induction Motor
• Separating the Rotor Copper Losses and
  the Power Converted in an
• Induction Motors Equivalent Circuit
• 5. Induction Motor Torque-Speed
  Characteristics
• Induced Torque from a Physical
  Standpoint
• The Derivation of the Induction Motor
  Induced-Torque Equation
• Comments on the Induction Motor Torque
  Speed Curve
• Maximum (Pullout) Torque in an
  Induction Motor

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SUMMARY

• 7. Starting Induction Motors
• 8. Speed Control of Induction Motor
• Induction Motor Speed Control by Pole
  Changing.
• Speed Control by Changing the Line
  Frequency.
• Speed Control by Changing the Line
  Voltage.
• Speed Control by Changing the Rotor
  Resistance.
• 9. Determining Circuit Model Parameters
• The No-Load Test
• The DC Test
• The Locked-Rotor Test
• 10. Determining Circuit model parameters
• No-load test/ DC test for stator
  resistance
• Locked-Rotor test
• 11. Induction Generator
• induction generator operating alone/
  induction
• Generator application
• Induction motor ratings

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INDUCTION MOTORSINTRODUCTION

• It was shown how amortisseur windings on a
  synchronous motor could develop a starting torque
  without necessity of supplying an external field
  current to them
• Amortisseur windings work so well that a motor
  could be built without syn. motors main dc field
  circuit
• A machine with only amortisseur winding is called
  induction machine, because the rotor voltage is
  induced in rotor windings rather than being
  physically connected by wires

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INDUCTION MOTORSINTRODUCTION

• Cutaway diagram of typical large cage rotor
  induction motor

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INDUCTION MOTORSINTRODUCTION

• Sketch of Cage Rotor

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INDUCTION MOTORSINTRODUCTION

• Typical wound rotors for induction motors, slip
  rings bars connecting rotor windings to slip
  rings can be seen

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INDUCTION MOTORSINTRODUCTION

• Cutaway of a wound-rotor induction motor
• Note brushes and slip rings are shown, also
  rotor windings skewed to eliminate slot harmonics

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INDUCTION MOTORSINTRODUCTION

• Distinguishing feature no dc field current
  required to run machine
• Although it is possible to use an induction
  machine as either motor or generator, it has many
  disadvantages as a generator so is rarely used
  as Gen.
• INDUCTION MOTOR CONSTRUCTION
• Same physical stator as syn. machine with
  different rotor construction
• There are cage rotor wound rotor

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INDUCTION MOTORSCONSTRUCTION

• A cage induction rotor consists of a series of
  conducting bars laid into slots carved in face of
  rotor shorted at either end by large shorting
  rings
• This design is referred to as a cage rotor
  because of conductors arrangement on rotor
• A wound rotor has a complete set of 3 phase
  windings that are mirror images of windings on
  stator
• The 3 phase of rotor windings are usually
  Y-connected and end of 3 rotor wires tied to slip
  rings on rotor shaft
• The rotor currents accessible at stator brushes,
  where they can be examined where extra
  resistance can be inserted into rotor circuit
• This can be used to modify torque-speed
  characteristic of motor
• Wound rotor motors more expensive, require more
  maintenance due to wear associated with brushes
  slip rings, therefore wound motor induction
  motors are rarely used

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BASIC INDUCTION MOTOR CONCEPTS

• Its operation is basically same as amortisseur
  windings on syn. motors
• Development of Induced Torque
• Again a BS is developed, which is rotating
  counter-clockwise in Figure of ? next slide
• Speed of magnetic fields rotation is
  nsync120fe/p
• voltage induced in a rotor bar
• eind(v x B).l
• vvelocity of bar relative to magnetic field
• Bmagnetic flux density vector
• l length of conductor in magnetic field

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BASIC INDUCTION MOTOR CONCEPTS

• Development of Induced Torque

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BASIC INDUCTION MOTOR CONCEPTS

• relative move of rotor w.r.t. BS result in an
  induced voltage in rotor bar
• Velocity of upper rotor bars w.r.t. BS is to
  right
• Induced voltage in upper bars is out of page,
  while induced voltage in the lower bars is into
  page
• This results in a current flow out of upper bars
  into lower bars
• Since rotor assembly is inductive, peak rotor
  current flow produces a rotor magnetic field BR

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BASIC INDUCTION MOTOR CONCEPTS

• Induced torque in machine is
• Tind kBR x BS
• resulting torque is counterclockwise rotor
  accelerates in this direction
• There is a finite upper limit on motors speed
• If induction motors rotor were turning at syn.
  Speed, then rotor bars would be stationary
  relative to BS there would be no induced
  voltage eind0 no rotor current BR0 ? Tind0
• Rotor will slow down, due to friction losses
• An induction motor can speed up to near-syn.
  Speed, however it can never reach syn. speed

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BASIC INDUCTION MOTOR CONCEPTS

• Flowchart showing induction motor operation

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BASIC INDUCTION MOTOR CONCEPTS

• Note in normal operation, both BR BS rotate
  together at syn. Speed nsync while rotor itself
  turn at a slower s peed
• Concept of Rotor Slip
• Voltage induced in rotor bar depends on relative
  speed of rotor with respect to BS
• Since behavior of induction motor depends on
  motor voltage current, it is more logical to
  talk about this relative speed
• Two terms commonly used to define relative motion
  of rotor BS , slip speed slip
• slip speed defined as difference between syn.
  Speed rotor speed nslipnsync-nm

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BASIC INDUCTION MOTOR CONCEPTS

• In which
• nslip slip speed of machine
• nsync speed of magnetic fields
• nm mechanical shaft speed of motor
• slip is relative speed expressed on a per-unit
  or percentage basis snslip/nsync (x100)
• s nsync-nm / nsync (x100)
• or in terms of angular velocity
• s ?sync-?m / ?sync (x100)

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BASIC INDUCTION MOTOR CONCEPTS

• If rotor turn at syn. speed ? s0
• while if rotor stationary ? s1
• all normal motor speeds fall somewhere between
  those 2 limits
• mechanical speed of rotor shaft can be expressed
  in terms of syn. speed slip
• nm (1-s)nsync or ?m(1-s)?sync

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BASIC INDUCTION MOTOR CONCEPTS

• Electrical Frequency on Rotor
• An induction motor works by inducing voltages in
  rotor of machine because of that sometimes
  called rotating transformer
• Like a transformer, primary (stator) induces a
  voltage in secondary (rotor) but
• Unlike a transformer, secondary frequency is
  not necessarily same as primary frequency
• If rotor of motor locked so that can not move,
  rotor will have the same frequency as stator

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BASIC INDUCTION MOTOR CONCEPTS

• on the other hand, if rotor turns at syn. Speed,
  frequency on rotor will be zero
• what will rotor frequency be for any arbitrary
  rate of rotor rotation ?
• at nm0 r/min, rotor frequency frfe Hz, and slip
  s1
• at nmnsyn fr0 and slip is s0
• with any speed in between, rotor frequency is
  directly proportional to difference between speed
  of magnetic field nsync speed of rotor nm
• Snsync-nm / nsync
  
• rotor frequency can be expressed as frs
  fe

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BASIC INDUCTION MOTOR CONCEPTS

• alternative forms of last expression
• frnsync-nm / nsync . fe
• since nsync120 fe/p ?
• fr (nsync-nm)p/(120fe) fe
• fr p/120 (nsync-nm)
• Example A 208 V, 10 hp, 4 pole, 60 Hz, Y
  connected induction motor has a full-load slip of
  5 percent
• (a) what is syn. Speed of motor?

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BASIC INDUC. MOTOR CONCEPTS.EXAMPLE

• (b) what is rotor speed of this motor at rated
  load?
• (c) what is rotor frequency of this motor at
  rated load?
• (d) what is shaft torque of this motor at rated
  load?

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BASIC INDUCTION MOTOR CONCEPTS

• SOLUTION
• (a) nsync120 fe/p120x60/41800 r/min
• (b) nm(1-s) nsync (1-0.05)(1800)1710
  r/min
• (c) frs fe 0.95 x 603 Hz
• or frp/120 (nsync-nm)4/120 (1800-1710)3
  Hz
• (d) Tload Pout/?m
• 10 x 746/1710 x 2p x 1/60 41.7 N.m
• shaft load torque in English units
  Tload5252 P/n
• where T is in lb-feet , P in hp, and nm
  r/min
• Tload5252 x 10 / (1710) 30.7 lb . ft

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EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR

• Basis of an induction motor is on induction of
  voltage current in its rotor (Transformer
  Action)
• equivalent circuit of an induction motor is very
  similar to equivalent circuit of a transformer
• induction motor is called a singly excited
  machine (opposed to doubly excited syn.
  machine)
• since power is supplied to only stator
  circuit

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EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR

• Since an induction motor does not have an
  independent field circuit, its model will not
  contain an internal voltage source such as
  internal generated voltage EA in a syn. Machine
• The equivalent circuit of induction motor can be
  derived from a knowledge of transformers and
  from what already know about variation of rotor
  frequency with speed in induction motors
• The induction motor model developed by starting
  with transformer model, and then realizing
  variable rotor frequency other induction motor
  effects

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EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR

• Transformer Model of an Induction Motor
• Per-phase equivalent circuit of an induction
  motor

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TRANSFORMER MODEL ofINDUCTION MOTOR

• As shown there is certain resistance self
  inductance in primary (stator) windings which
  must be represented in equivalent circuit of
  machine
• Stator resistance called R1 stator leakage
  reactance called X1
• These appear right at input to machine model
• Flux in machine is the integral of applied
  voltage E1
• Curve of magneto-motive force versus flux,
  (magnetization curve) compared to similar curve
  for power transformer (next slide)

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TRANSFORMER MODEL ofINDUCTION MOTOR

• Magnetization curve of induction motor

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TRANSFORMER MODEL ofINDUCTION MOTOR

• Note slope of induction motors magneto-motive
  force-flux curve is much shallower than curve of
  a good transformer
• because there is an air gap in an induction motor
  which greatly increase reluctance of flux path
  therefore reduces coupling between primary
  secondary windings
• Higher reluctance caused by air gap means a
  higher magnetizing reactance XM in equivalent
  circuit will have a much smaller value (larger
  susceptance BM) than its value in an ordinary
  transformer

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TRANSFORMER MODEL ofINDUCTION MOTOR

• Primary internal stator voltage E1 coupled to
  secondary ER by an ideal transformer with an
  effective turns ratio aeff
• Effective turns ratio aeff easy to determined for
  a wound-rotor motor
• ratio of conductors per phase on stator to
  conductors per phase on rotor, modified by any
  pitch distribution factor differences
• It is rather difficult to determine aeff clearly
  in cage of a case rotor motor because there are
  no distinct windings on cage rotor

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TRANSFORMER MODEL ofINDUCTION MOTOR

• In either case there is an effective turns ratio
  for motor
• Voltage ER produced in rotor in turn produces a
  current flow in shorted rotor (or secondary)
  circuit of machine
• Primary impedance magnetization current of
  induction motor are very similar to corresponding
  components in a transformer equivalent circuit
• Induction motor equivalent circuit differs from
  transformer equivalent circuit primarily in
  effects of varying rotor frequency on rotor
  voltage ER and secondarily in rotor resistance RR
  and jXR

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ROTOR CIRCUIT MODEL

• A voltage induced in rotor windings when 3 phase
  voltage applied to stator windings
• The greater the relative motion between rotor
  stator magnetic fields, the greater the resulting
  rotor voltage rotor frequency
• The largest relative motion occurs when rotor is
  stationary, called locked-rotor or blocked-rotor
  condition
• So largest voltage rotor frequency are induced
  in rotor at that condition (locked rotor)

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ROTOR CIRCUIT MODEL

• Smallest voltage (0 V) and frequency (0 Hz) occur
  when rotor moves at same speed as stator magnetic
  field (having no relative motion)
• magnitude frequency of induced voltage in
  rotor at any speed between these extremes is
  proportional to the slip of motor
• If magnitude of induced rotor voltage at
  locked-rotor is ER0 magnitude at any slip
• 
  ERs ER0
• frequency of induced voltage frsfe
• rotor has both resistance reactance RR a
  constant (except for ski effect) , reactance
  affected in a complicated way by slip

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ROTOR CIRCUIT MODEL

• reactance of an induction motor rotor depends on
  inductance of rotor frequency of voltage and
  current in rotor
• XR?r LR 2p fr LR (realizing frsfr) ?
  XR2psfeLRs XR0 (XR0blocked-rotor reactance)
• Resulted equivalent circuit of rotor