EE20A Electromechanical Energy Conversion

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Department of Electrical and Computer Engineering

• EE20A - Electromechanical Energy Conversion
• Induction Machine

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Principle of Operation

• The stator coils, when energised, create a
  rotating magnetic field.
• Rotating magnetic field cuts through the rotor
  inducing a voltage in the rotor bars.
• This voltage creates its own magnetic field in
  the rotor.
• The rotor magnetic field will attempt to line up
  with the stator magnetic field.
• The stator magnetic field is rotating, the rotor
  magnetic field trying to line up with the stator
  magnetic field causes the rotor to rotate.
• The rotor magnetic field, never catches up, but
  follows slightly behind.

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Motor Analysis

• Slip is the difference between the speed of the
  stator magnetic field and the speed of the rotor
• SLIP,S, (NS - N) / NS

• When motor is stationary, it behaves like a
  transformer
• At a given Speed, flux cutting rate is reduced gt
  thereby reducing output voltage by a factor of
  the slip.

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Analysis
Per Phase Equivalent Circuit
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Analysis
Per Phase Equivalent Circuit
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Analysis
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Power per Phase

• Total Torque
• (3Pmech_gross- PFW)/wm

• Pag I12Rr/s
• Pcu sPag
• Pmech_gross (1-s)Pag

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Power per Phase
Pag Power across the air gap
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Power per Phase
P mech_gross (1-s) Pag per phase
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Power per Phase
Pcu_losses_in_rotor Pmech_gross
Pag Pcu Pmech 1s(1-s)
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Power per Phase
Slip is variable and affects only rotor circuit
Ignoring Stator values
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Power per Phase
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Torque
Simple Algebraic manipulations yield
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Torque
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Torque
Since the above calculations was derives as power
per phase, then the total torque for all three
phases would be three times the gross mechanical
torque for each phase calculated above.
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Torque
The maximum torque is obtained when
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Torque Characteristics
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Speed-Torque characteristics
 Modifications in the design of the squirrel-cage
motors permit a certain amount of control of the
starting current and torque characteristics.
These designs have been categorised by NEMA
Standards (MG1-1.16) into four main
classifications 1. Normal-torque,
normal-starting current motors (Design A) 2.
Normal-torque, low-starting current motors
(Design B) 3. High-torque, low-starting-current,
double-wound-rotor motors (Design C) 4.
High-slip motors (Design D)
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Design A Motor

• Hp range 0.5 500 hp.
• Starting current 6 to 10 times full-load current.
  
• Good running efficiency (87 - 89).
• Good power factor (87 - 89).
• Low rated slip (3 5 ).
• Starting torque is about 150 of full load
  torque.
• Maximum torque is over 200 but less than 225 of
  full-load torque.
• Typical applications constant speed
  applications where high starting torque is
  not needed and high starting torque is tolerated.
  

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Design B Motor

• Hp range 0.5 to 500 hp
• Higher reactance than the Design A motor,
  obtained by means of deep, narrow rotor bars.
• The starting current is held to about 5 times the
  full-load current.
• This motor allows full-voltage starting.
• The starting torque, slip and efficiency are
  nearly the same as for the Design A motor.
• Power factor and maximum torque are little lower
  than class A,
• Design B is standard in 1 to 250 hp drip-proof
  motors and in totally enclosed, fan-cooled
  motors, up to approximately 100 hp.
• Typical applications constant speed
  applications where high starting torque is not
  needed and high starting torque is tolerated.
• Unsuitable for applications where there is
  a high load peak

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Design C Motor

• Hp range 3 to 200 hp
• This type of motor has a "double-layer" or double
  squirrel-cage winding.
• It combines high starting torque with low
  starting current.
• Two windings are applied to the rotor, an outer
  winding having high resistance and low reactance
  and an inner winding having low resistance and
  high reactance.
• Operation is such that the reactance of both
  windings decrease as rotor frequency decreases
  and speed increases.
• On starting a much larger induced currents flow
  in the outer winding than in the inner winding,
  because at low rotor speeds the inner-winding
  reactance is quite high.

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Design C Motor

• As the rotor speed increases, the reactance of
  the inner winding drops and combined with the low
  inner-winding resistance, permits the major
  portion of the rotor current to appear in the
  inner winding.
• Starting current about 5 times full load current.
  
• The starting torque is rather high (200 - 250).
  
• Full-load torque is the same as that for both A
  and B designs.
• The maximum torque is lower than the starting
  torque, maximum torque (180-225).
• Typical applications constant speed
  loads requiring fairly high starting torque
  and lower starting currents.

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Design D Motor

• Produces a very high starting
  torque-approximately 275 of full-load torque.
• It has low starting current,
• High slip (7-16),
• Low efficiency.
• Torque changes with load
• Typical applications- used for high
  inertia loads
• The above classification is for squirrel cage
  induction motor

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Wound Rotor

• Hp 0.5 to 5000hp
• Starting torque up to 300
• Maximum torque 225 to 275 of full load torque
• Starting current may be as low as 1.5 times
  starting current
• Slip (3 - 50)
• Power factor high
• Typical applications for high starting torque
  loads where very low starting current is required
  or where torque must be applied very gradually
  and where speed control is needed.

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Current Effects on the Motor

• Induction motor current consists of reactive
  (magnetizing) and real (torque) components.
• The current component that produces torque (does
  useful work) is almost in phase with voltage, and
  has a high power factor close to 100
• The magnetizing current would be purely
  inductive, except that the winding has some small
  resistance, and it lags the voltage by nearly
  90.
• The magnetizing current has a very low power
  factor, close to zero.
• The magnetic field is nearly constant from no
  load to full load and beyond, so the magnetizing
  portion of the total current is approximately the
  same for all loads.
• The torque current increases as the load
  increases

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Current Effects on the Motor

• At full load, the torque current is higher than
  the magnetizing current.
• For a typical motor, the power factor of the
  resulting current is between 85 and 90.
• As the load is reduced, the torque current
  decreases, but the magnetizing current remains
  about the same so the resulting current has a
  lower power factor.
• The smaller the load, the lower the load current
  and the lower the power factor. Low power factor
  at low loading occurs because the magnetizing
  remains approximately the same at no load as at
  full load

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Methods to vary speed of the Induction Motor
An induction motor is a constant-speed device.
Its speed depends on the number of poles in the
stator, assuming that the voltage and frequency
of the supply to the motor remain constant.

• One method is to change the number of poles in
  the stator, for example, reconnecting a 4-pole
  winding so that it becomes a 2-pole winding will
  double the speed. This method can give specific
  alternate speeds but not gradual speed changes.
• Another method is to vary the line voltage this
  method is not the best since torque is
  proportional to the square of the voltage, so
  reducing the line voltage rapidly reduces the
  available torque causing the motor to stall

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Methods to vary speed of the Induction Motor

• Sometimes it is desirable to have a high
  starting torque or to have a constant horsepower
  output over a given speed range. These and other
  modifications can be obtained by varying the
  ratio of voltage to frequency as required. Some
  controllers are designed to provide constant
  torque up to 60 Hz and constant hp above 60 Hz to
  provide higher speeds without overloading the
  motor.
• An excellent way to vary the speed of a
  squirrel-cage induction motor is to vary the
  frequency of the applied voltage. To maintain a
  constant torque, the ratio of voltage to
  frequency must be kept constant, so the voltage
  must be varied simultaneously with the frequency.
  Modern adjustable frequency controls perform this
  function. At constant torque, the horsepower
  output increases directly as the speed increases.

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NO LOAD TEST
Per Phase Equivalent Circuit
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NO LOAD TEST

• n - ns 0 No load Speed ? Synchronous
  Speed
• i.e. no power transfer which implies that Torque
  0
• I1 0 T 0
• Power Consumed Core Losses Friction
  Windage
• Measure Vph , IIN and Wph
• ? ? ( Infinite Impedance ) since
  I1 0

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NO LOAD TEST

• INL I0 jIm
• ? INL ? ( cos ?NL - jsin ?NL )
• cos ?NL Wph
• Vph ? INL ?
• Ro Vph
  Xm Vph
• I0
  
  Im

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Lock Rotor Test
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Lock Rotor Test

• In the Lock Rotor test, No Load Speed, n 0
• Slip, s ns 0 1,
  s 1
• ns
• Then Rr ?? Rr
• s
• Apply Voltage to Variac, VLR (10 - 25 ) Vph
• Since INLltlt I1
  Then INL ? 0
• Measure values VLR , ILR and WLR

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Lock Rotor Test

• Zeq VLR / ILR
• cos ?LR WLR
• VLR ? ILR ?
• Zeq ?Zeq ? cos ?LR - jsin ?LR
• ?Zeq ? cos ?LR - ?Zeq ? jsin
  ?LR
• Rs Rr
  Xs Xr

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Lock Rotor Test

• At Standstill Under d.c. conditions ? 0
• 
  ? X ?L
• 
  ? X 0
• R1 R2 can be measured using an ohmmeter over
  two stator windings, which gives a value of Rs
• Rr Zeq cos ?LR - Rs