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induction motor


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Title: induction motor

Induction Motor
  • By
  • Ashvani Shukla
  • Manager(CI)

  • One of the most common electrical motor used in
    most applications which is known as induction
    motor. This motor is also called as asynchronous
    motor because it runs at a speed less than
    synchronous speed. In this, we need to define
    what is synchronous speed. Synchronous speed is
    the speed of rotation of the magnetic field in a
    rotary machine and it depends upon the frequency
    and number poles of the machine. An induction
    motor always runs at a speed less than
    synchronous speed because the rotating magnetic
    field which is produced in the stator will
    generate flux in the rotor which will make the
    rotor to rotate, but due to the lagging of flux
    current in the rotor with flux current in the
    stator, the rotor will never reach to its
    rotating magnetic field speed i.e. the
    synchronous speed. There are basically two types
    of induction motor that depend upon the input
    supply - single phase induction motor and three
    phase induction motor. Single phase induction
    motor is not a self starting motor which we will
    discuss later and three phase induction motor is
    a self-starting motor. Now in general we need to
    give two supply i.e. double excitation to make a
    machine to rotate. For example if we consider a
    DC motor, we will give one supply to the stator
    and another to the rotor through brush

  • Working Principle of Induction Motor
  • But in induction motor we give only one supply,
    so it is really interesting to know that how it
    works. It is very simple, from the name itself we
    can understand that there is induction process
    occurred. Actually when we are giving the supply
    to the stator winding, flux will generate in the
    coil due to flow of current in the coil. Now the
    rotor winding is arranged in such a way that it
    becomes short circuited in the rotor itself. The
    flux from the stator will cut the coil in the
    rotor and since the rotor coils are short
    circuited, according to Faraday's law of
    electromagnetic induction, current will start
    flowing in the coil of the rotor. When the
    current will flow, another flux will get
    generated in the rotor. Now there will be two
    flux, one is stator flux and another is rotor
    flux and the rotor flux will be lagging to the
    stator flux. Due to this, the rotor will feel a
    torque which will make the rotor to rotate in the
    direction of rotating magnetic flux. So the speed
    of the rotor will be depending upon the ac supply
    and the speed can be controlled by varying the
    input supply. This is the working principle of an
    induction motor of either type.

  • Types Induction Motor
  • Split phase induction motor
  • Capacitor start induction motor
  • Capacitor start capacitor run induction motor
  • Shaded pole induction motor
  • Squirrel cage induction motor
  • Slip ring induction motor

  • Construction of Three Phase Induction Motor
  • The three phase induction motor is the most
    widely used electrical motor. Almost 80 of the
    mechanical power used by industries is provided
    by three phase induction motors because of its
    simple and rugged construction, low cost, good
    operating characteristics, absence of commutator
    and good speed regulation. In three phase
    induction motor the power is transferred from
    stator to rotor winding through induction. The
    Induction motor is also called asynchronous motor
    as it runs at a speed other than the synchronous
  • Like any other electrical motor induction motor
    also have two main parts namely rotor and stator
  • Stator As its name indicates stator is a
    stationary part of induction motor. A stator
    winding is placed in the stator of induction
    motor and the three phase supply is given to it.
  • Rotor The rotor is a rotating part of induction
    motor. The rotor is connected to the mechanical
    load through the shaft.
  • The rotor of the three phase induction motor are
    further classified as Squirrel cage rotor,
  • Slip ring rotor or wound rotor or phase wound
  • Depending upon the type of rotor construction
    used the three phase induction motor are
    classified as Squirrel cage induction motor,
  • Slip ring induction motor or wound induction
    motor or phase wound induction motor.

  • The construction of stator for both the kinds of
    three phase induction motor remains the same and
    is discussed in brief in next paragraph. The
    other parts, which are required to complete the
    induction motor, are Shaft for transmitting the
    torque to the load. This shaft is made up of
  • Bearings for supporting the rotating shaft.
  • One of the problems with electrical motor is the
    production of heat during its rotation. In order
    to overcome this problem we need fan for cooling.
  • For receiving external electrical connection
    Terminal box is needed.
  • There is a small distance between rotor and
    stator which usually varies from 0.4 mm to 4 mm.
    Such a distance is called air gap.
  • Stator of Three Phase Induction Motor
  • The stator of the three phase induction motor
    consists of three main parts Stator frame,
  • Stator core,
  • Stator winding or field winding.
  • Stator Frame

It is the outer most part of the three phase
induction motor. Its main function is to support
the stator core and the field winding. It acts as
a covering and it provide protection and
mechanical strength to all the inner parts of the
induction motor. The frame is either made up of
die cast or fabricated steel. The frame of three
phase induction motor should be very strong and
rigid as the air gap length of three phase
induction motor is very small, otherwise rotor
will not remain concentric with stator, which
will give rise to unbalanced magnetic pull.
Stator Core The main function of the stator core
is to carry the alternating flux. In order to
reduce the eddy current loss, the stator core is
laminated. These laminated types of structure are
made up of stamping which is about 0.4 to 0.5 mm
thick. All the stamping are stamped together to
form stator core, which is then housed in stator
frame. The stamping is generally made up of
silicon steel, which helps to reduce the
hysteresis loss occurring in motor.
  • Stator Winding or Field Winding
  • The slots on the periphery of stator core of the
    three phase induction motor carries three phase
    windings. This three phase winding is supplied by
    three phase ac supply. The three phases of the
    winding are connected either in star or delta
    depending upon which type of starting method is
    used. The squirrel cage motor is mostly started
    by star delta stater and hence the stator of
    squirrel cage motor is delta connected. The slip
    ring three phase induction motor are started by
    inserting resistances so, the stator winding of
    slip ring induction motor can be connected either
    in star or delta. The winding wound on the stator
    of three phase induction motor is also called
    field winding and when this winding is excited by
    three phase ac supply it produces a rotating
    magnetic field.

  • Types of Three Phase Induction Motor
  • Squirrel cage three phase induction motor The
    rotor of the squirrel cage three phase induction
    motor is cylindrical in shape and have slots on
    its periphery. The slots are not made parallel to
    each other but are bit skewed (skewing is not
    shown in the figure of squirrel cadge rotor
    beside) as the skewing prevents magnetic locking
    of stator and rotor teeth and makes the working
    of motor more smooth and quieter. The squirrel
    cage rotor consists of aluminum, brass or copper
    bars (copper bras rotor is shown in the figure
    beside). These aluminum, brass or copper bars are
    called rotor conductors and are placed in the
    slots on the periphery of the rotor. The rotor
    conductors are permanently shorted by the copper
    or aluminum rings called the end rings. In order
    to provide mechanical strength these rotor
    conductor are braced to the end ring and hence
    form a complete closed circuit resembling like a
    cage and hence got its name as "squirrel cage
    induction motor". The squirrel cage rotor winding
    is made symmetrical. As the bars are permanently
    shorted by end rings, the rotor resistance is
    very small and it is not possible to add external
    resistance as the bars are permanently shorted.
    The absence of slip ring and brushes make the
    construction of Squirrel cage three phase
    induction motor very simple and robust and hence
    widely used three phase induction motor. These
    motors have the advantage of adapting any number
    of pole pairs. The below diagram shows squirrel
    cage induction rotor having aluminum bars short
    circuit by aluminum end rings.

  • Advantages of squirrel cage induction rotor-
  • Its construction is very simple and rugged.
  • As there are no brushes and slip ring, these
    motors requires less maintenance.
  • Applications Squirrel cage induction motor is
    used in lathes, drilling machine, fan, blower
    printing machines etc.

  • Slip ring or wound three phase induction motor
    In this type of three phase induction motor the
    rotor is wound for the same number of poles as
    that of stator but it has less number of slots
    and has less turns per phase of a heavier
    conductor. The rotor also carries star or delta
    winding similar to that of stator winding. The
    rotor consists of numbers of slots and rotor
    winding are placed inside these slots. The three
    end terminals are connected together to form star
    connection. As its name indicates three phase
    slip ring induction motor consists of slip rings
    connected on same shaft as that of rotor. The
    three ends of three phase windings are
    permanently connected to these slip rings. The
    external resistance can be easily connected
    through the brushes and slip rings and hence used
    for speed control and improving the starting
    torque of three phase induction motor. The
    brushes are used to carry current to and from the
    rotor winding. These brushes are further
    connected to three phase star connected
    resistances. At starting, the resistance are
    connected in rotor circuit and is gradually cut
    out as the rotor pick up its speed. When the
    motor is running the slip ring are shorted by
    connecting a metal collar, which connect all slip
    ring together and the brushes are also removed.
    This reduces wear and tear of the brushes. Due to
    presence of slip rings and brushes the rotor
    construction becomes somewhat complicated
    therefore it is less used as compare to squirrel
    cage induction motor.

  • Advantages of slip ring induction motor - It has
    high starting torque and low starting current.
  • Possibility of adding additional resistance to
    control speed.
  • Application
  • Slip ring induction motor are used where high
    starting torque is required i.e in hoists,
    cranes, elevator etc.

Difference between Slip Ring and Squirrel Cage
Induction Motor
Slip ring or phase wound Induction motor Squirrel cage induction motor
Construction is complicated due to presence of slip ring and brushes Construction is very simple
The rotor winding is similar to the stator winding The rotor consists of rotor bars which are permanently shorted with the help of end rings
We can easily add rotor resistance by using slip ring and brushes Since the rotor bars are permanently shorted, its not possible to add external resistance
Due to presence of external resistance high starting torque can be obtained Staring torque is low and cannot be improved
Slip ring and brushes are present Slip ring and brushes are absent
Frequent maintenance is required due to presence of brushes Less maintenance is required
The construction is complicated and the presence of brushes and slip ring makes the motor more costly The construction is simple and robust and it is cheap as compared to slip ring induction motor
This motor is rarely used only 10 industry uses slip ring induction motor Due to its simple construction and low cost. The squirrel cage induction motor is widely used
Rotor copper losses are high and hence less efficiency Less rotor copper losses and hence high efficiency
Speed control by rotor resistance method is possible Speed control by rotor resistance method is not possible
Slip ring induction motor are used where high starting torque is required i.e in hoists, cranes, elevator etc Squirrel cage induction motor is used in lathes, drilling machine, fan, blower printing machines etc
  • We had mentioned above that single phase
    induction motor is not a self starting and three
    phase induction motor is self starting. So what
    is self starting? When the machine starts running
    automatically without any external force to the
    machine, then it is called as self starting. For
    example we see that when we press the key the fan
    starts to rotate automatically, so it is self
    starting. Point to be note that fan used in home
    appliances is single phase induction motor but it
    is self starting. How? We will discuss it how.
    Why is Three Phase Induction Motor Self Starting?
  • In three phase system, there are three single
    phase line with 120 phase difference. So the
    rotating magnetic field is having the same phase
    difference which will make the rotor to move. If
    we consider three phases a, b and c, when phase a
    is magnetized, the rotor will move towards the
    phase a winding, in the next moment phase b will
    get magnetized and it will attract the rotor and
    than phase c. So the rotor will continue to

Working Principle of Three Phase Induction Motor
  • Why Single Phase Induction Motor is not Self
  • But what about single phase. It will be having
    only one phase still it makes the rotor to
    rotate, so it is quite interesting. Before that
    we need to know why single phase induction motor
    is not a self starting motor and how the problem
    is overcome. We know that the ac supply is a
    sinusoidal wave and it produces pulsating
    magnetic field in uniformly distributed stator
    winding. Since pulsating magnetic field can be
    assumed as two oppositely rotating magnetic
    fields, there will be no resultant torque
    produced at the starting and due to this the
    motor does not run. After giving the supply, if
    the rotor is made to rotate in either direction
    by external force, then the motor will start to
    run. This problem has been solved by making the
    stator winding into two winding, one is main
    winding and another is auxiliary winding and a
    capacitor is fixed in series with the auxiliary
    winding. This will make a phase difference when
    current will flow through the both coils. When
    there will be phase difference, the rotor will
    generate a starting torque and it will start to
    rotate. Practically we can see that the fan does
    not rotate when the capacitor is disconnected
    from the motor but if we rotate with hand it will
    start to rotate. So this is the reason of using
    capacitor in the single phase induction motor.
    There are several advantages of induction motor
    which makes this motor to have wider application.
    It is having good efficiency up to 97. But the
    speed of the motor varies with the load given to
    the motor which is an disadvantage of this motor.
    The direction of rotation of induction motor can
    easily be changed by changing the sequence of
    three phase supply, i.e. if RYB is in forward
    direction, the RBY will make the motor to rotate
    in reverse direction. This is in the case of
    three phase motor but in single phase motor, the
    direction can be reversed by reversing the
    capacitor terminals in the winding.

  • Working Principle of Three Phase Induction Motor
  • An electrical motor is such an electromechanical
    device which converts electrical energy into a
    mechanical energy. In case of three phase AC
    operation, most widely used motor is Three phase
    induction motor as this type of motor does not
    require any starting device or we can say they
    are self starting induction motor.
  • For better understanding the principle of three
    phase induction motor, the basic constructional
    feature of this motor must be known to us. This
    Motor consists of two major parts Stator Stator
    of three phase induction motor is made up of
    numbers of slots to construct a 3 phase winding
    circuit which is connected to 3 phase AC source.
    The three phase winding are arranged in such a
    manner in the slots that they produce a rotating
    magnetic field after AC is given to them. Rotor
    Rotor of three phase induction motor consists of
    cylindrical laminated core with parallel slots
    that can carry conductors. Conductors are heavy
    copper or aluminum bars which fits in each slots
    they are short circuited by the end rings. The
    slots are not exactly made parallel to the axis
    of the shaft but are slotted a little skewed
    because this arrangement reduces magnetic humming
    noise can avoid stalling of motor.

  • Working of Three Phase Induction Motor
  • Production of Rotating Magnetic Field
  • The stator of the motor consists of overlapping
    winding offset by an electrical angle of 120.
    When the primary winding or the stator is
    connected to a 3 phase AC source, it establishes
    a rotating magnetic field which rotates at the
    synchronous speed.
  • Secrets behind the rotation
  • According to Faradays law an emf induced in any
    circuit is due to the rate of change of magnetic
    flux linkage through the circuit. As the rotor
    winding in an induction motor are either closed
    through an external resistance or directly
    shorted by end ring, and cut the stator rotating
    magnetic field, an emf is induced in the rotor
    copper bar and due to this emf a current flows
    through the rotor conductor.
  • Here the relative velocity between the rotating
    flux and static rotor conductor is the cause of
    current generation hence as per Lenz's law the
    rotor will rotate in the same direction to reduce
    the cause i.e. the relative velocity.

  • Thus from the working principle of three phase
    induction motor it may observed that the rotor
    speed should not reach the synchronous speed
    produced by the stator. If the speeds equals,
    there would be no such relative velocity, so no
    emf induction in the rotor, no current would be
    flowing, and therefore no torque would be
    generated. Consequently the rotor can not reach
    at the synchronous speed. The difference between
    the stator (synchronous speed) and rotor speeds
    is called the slip. The rotation of the magnetic
    field in an induction motor has the advantage
    that no electrical connections need to be made to
    the rotor. Thus the three phase induction motor
    is Self-starting. Less armature reaction and
    brush sparking because of the absence of
    commutators and brushes that may cause sparks.
    Robust in construction. Economical. Easier to

  • Classification of Squirrel Cage Induction Motor.
  • NEMA in United States and IEC in Europe have
    classified the design of the squirrel cage
    induction motors based on their speed-torque
    characteristics into some classes. These classes
    are Class A, Class B, Class C, Class D, Class E
    and Class F.
  • In Class A Design
  • A normal starting torque.
  • A normal starting current.
  • Low slip.
  • In this Class, pullout torque is always of 200 to
    300 percent of the full-load torque and it occurs
    at a low slip (it is less than 20 percent).
  • For this Class, the starting torque is equal to
    rated torque for larger motors and is about 200
    percent or more of the rated torque for the
    smaller motors.

  • In Class B Design
  • Normal starting torque,
  • Lower starting current,
  • Low slip.
  • Induction Motor of this Class produces about the
    same starting torque as the class A induction
    motor and this starting torque is with about 25
    percent less current.
  • Pullout torque is always greater than or equal to
    200 percent of the rated load torque. But it is
    less than that of the class A design because it
    has increased rotor reactance.
  • Again Rotor slip is still relatively low (less
    than 5 percent) at full load.
  • Applications of Class B design are similar to
    those for design A. But design B is preferred
    more because of its lower starting-current

  • In Class C Design
  • High starting torque.
  • Low starting currents.
  • Low slip at the full load (less than 5 ).
  • Up to 250 percent of the full-load torque, the
    starting torque is in this class of design.
  • The pullout torque is lower than that for class A
    induction motors.
  • In this design the motors are built from
    double-cage rotors. They are more expensive than
    motors of Class A and B classes.
  • Class C Designs are used for high-starting-torque
    loads (loaded pumps, compressors, and conveyors).

  • In Class D Design
  • In this Design of Class motors has very high
    starting torque (275 percent or more of the rated
  • A low starting current.
  • A high slip at full load.
  • Again in this class of design the high rotor
    resistance shifts the peak torque to a very low
  • It is even possible at zero speed (100 percent
    slip) for the highest torque to occur in this
    class of design.
  • Full-load slip (It is typically 7 to 11 percent,
    but may go as high as 17 percent or more) in this
    class of design is quite high because of the high
    rotor resistance always.

  • In class E Design
  • Very Low Starting Torque.
  • Normal Starting Current.
  • Low Slip.
  • Compensator or resistance starter are used to
    control starting current.
  • In Class F Design
  • Low Starting Torque, 1.25 times of full load
    torque when full voltage is applied.
  • Low Starting Current.
  • Normal Slip.

  • Circle Diagram of Induction Motor

The CIRCLE DIAGRAM means that it is figure or
curve which is drawn has a circular shape. As we
know, the diagrammatic representation is easier
compared to theoretical and mathematical
descriptions. Actually, we do not have that much
time or patience to go through the writings so we
prefer diagrammatic representation. Also, it is
very easy to remember the things which are shown
in picture. As we know, A PICTURE IS WORTH 1000
WORDS. This also holds good here and we are to
draw circle diagram in order to compute various
parameters rather than doing it mathematically.
Importance of Circle Diagram The diagram
provides information which is not provided by an
ordinary phasor diagram. A phasor diagram gives
relation between current and voltage only at a
single circuit condition. If the condition
changes, we need to draw the phasor diagram
again. But a circle diagram may be referred to as
a phasor diagram drawn in one plane for more than
one circuit conditions. On the context of
induction motor, which is our main interest, we
can get information about its power output, power
factor, torque, slip, speed, copper loss,
efficiency etc. in a graphical or in a
diagrammatic representation.
  • Test Performed to Compute Data Required for
    Drawing Circle Diagram
  • We have to perform no load and blocked rotor test
    in an induction motor. In no load test, the
    induction motor is run at no load and by two watt
    meter method, its total power consumed is
    calculated which is composed of no load losses
    only. Slip is assumed to be zero. From here no
    load current and the angle between voltage and
    current is required for drawing circle diagram
    and calculated. The angle will be large as in the
    no load condition induction motor has high
    inductive reactance. In block rotor test, rotor
    is blocked which is analogous to short circuit
    secondary of a transformer. From this test, we
    need to calculate short circuit current and the
    lag angle between voltage and current for drawing
    circle diagram. Also, we need rotor and stator
    copper loss.

  • Procedure to Draw the Circle Diagram
  • We have to assume a suitable before drawing it.
    This assumption is done according to our

  • The no load current and the no load angle
    calculated from no load test is plotted. This is
    shown by the line OA, where O0 is the no load
    power factor angle.
  • The short circuit current and the angle obtained
    from block rotor test is plotted. This is shown
    by the line OC and the angle is shown by OB.
  • The right bisector of the line AC is drawn which
    bisects the line and it is extended to cut in the
    line AE which gives us the Centre.
  • The stator current is calculated from the
    equivalent circuit of the induction motor which
    we get from the two tests. That current is
    plotted in the circle diagram according to the
    scale with touching origin and a point in the
    circle diagram which is shown by B.
  • The line AC is called the power line. By using
    the scale for power conversion that we have taken
    in the circle diagram, we can get the output
    power if we move vertically above the line AC to
    the periphery of the circle. The output power is
    given by the line MB.
  • The total copper loss is given by the line GM.
  • For drawing the torque line, the total copper
    loss should be separated to both the rotor copper
    loss and stator copper loss. The line DE gives
    the stator copper loss and the line CD gives the
    rotor copper loss. In this way, the point E is
  • The line AD is known as torque line which gives
    the torque developed by induction motor.

  • Maximum Quantities from Circle Diagram

  • Maximum Output Power
  • When the tangent to the circle is parallel to the
    line then output power will be maximum. That
    point M is obtained by drawing a perpendicular
    line from the center to the output line and
    extending it to cut at M. Maximum Torque
  • When the tangent to the circle is parallel to the
    torque line, it gives maximum torque. This is
    obtained by drawing a line from the center in
    perpendicular to the torque line and extending it
    to cut at the circle. That point is marked as N.
    Maximum Input Power
  • It occurs when tangent to the circle is
    perpendicular to the horizontal line. The point
    is the highest point in the circle diagram and
    drawn to the center and extends into S. That
    point is marked as R. Conclusion of Circle
  • This method is based on some approximations that
    we have used in order to draw the circle diagram
    and also, there is some rounding off of the
    values as well. So there is some error in this
    method but it can give good approximate results.
    Also, this method is very much time consuming so
    it is drawn at times where the drawing of circle
    diagram is absolutely necessary. Otherwise, we go
    for mathematical formulas or equivalent circuit
    model in order to find out various parameters.

  • Torque Slip Characteristics of Induction Motor

The torque slip curve for an induction motor
gives us the information about the variation of
torque with the slip. The slip is defined as the
ratio of difference of synchronous speed to the
speed at any mechanical load to the synchronous
speed of the machine. The variation of slip can
be obtained with the variation on speed that is
when speed varies the slip will also vary and the
torque corresponding to that speed will also
vary. The curve can be described in three modes
of operation-
  • Motoring Mode In this mode of operation, supply
    is given to the stator sides and the motor always
    rotates below the synchronous speed. The
    induction motor torque varies from zero to full
    load torque as the slip varies. The slip varies
    from zero to one. It is zero at no load and one
    at standstill. From the curve it is seen that the
    torque is directly proportional to the slip. That
    is, more is the slip, more will be the torque
    produced and vice-versa. The linear relationship
    simplifies the calculation of motor parameter to
    great extent. Generating Mode In this mode of
    operation induction motor runs above the
    synchronous speed and it should be driven by a
    prime mover. The stator winding is connected to a
    three phase supply in which it supplies
    electrical energy. Actually, in this case, the
    torque and slip both are negative so the motor
    receives mechanical energy and delivers
    electrical energy. Induction motor is not much
    used as generator because it requires reactive
    power for its operation. That is, reactive power
    should be supplied from outside and if it runs
    below the synchronous speed by any means, it
    consumes electrical energy rather than giving it
    at the output. So, as far as possible, induction
    generators are generally avoided.

  • Braking Mode In the breaking mode, the two leads
    or the polarity of the supply voltage is changed
    so that the motor starts to rotate in the reverse
    direction and as a result the motor stops. This
    method of breaking is known as plugging. This
    method is used when it is required to stop the
    motor within a very short period of time. The
    kinetic energy stored in the revolving load is
    dissipated as heat. Also, motor is still
    receiving power from the stator which is also
    dissipated as heat. So as a result of which motor
    develops enormous heat energy. For this stator is
    disconnected from the supply before motor enters
    the breaking mode.
  • If load which the motor drives accelerates the
    motor in the same direction as the motor is
    rotating, the speed of the motor may increase
    more than synchronous speed. In this case, it
    acts as an induction generator which supplies
    electrical energy to the mains which tends to
    slow down the motor to its synchronous speed, in
    this case the motor stops. This type of breaking
    principle is called dynamic or regenerative

  • Torque Slip Characteristics of Single Phase
    Induction Motor

  • From the figure, we see that at a slip of unity,
    both forward and backward field develops equal
    torque but the direction of which are opposite to
    each other so the net torque produced is zero
    hence the motor fails to start. From here we can
    say that these motors are not self starting
    unlike the case of three phase induction motor.
    There must be some means to provide the starting
    torque. If by some means, we can increase the
    forward speed of the machine due to which the
    forward slip decreases the forward torque will
    increase and the reverse torque will decrease as
    a result of which motor will start.
  • From here we can conclude that for starting of
    single phase induction motor, there should be a
    production of difference of torque between the
    forward and backward field. If the forward field
    torque is larger than the backward field than the
    motor rotates in forward or anti clockwise
    direction. If the torque due to backward field is
    larger compared to other, then the motor rotates
    in backward or clockwise direction.

  • Torque Equation of Three Phase Induction Motor

The torque produced by three phase induction
motor depends upon the following three
factors Firstly the magnitude of rotor current,
secondly the flux which interact with the rotor
of three phase induction motor and is responsible
for producing emf in the rotor part of induction
motor, lastly the power factor of rotor of the
three phase induction motor. Combining all these
factors together we get the equation of torque as-
Where, T is the torque produced by induction
motor, f is flux responsible of producing induced
emf, I2 is rotor current, cos?2 is the power
factor of rotor circuit. The flux f produced by
the stator is proportional to stator emf E1. i.e
f ? E1 We know that transformation ratio K is
defined as the ratio of secondary voltage (rotor
voltage) to that of primary voltage (stator
Rotor current I2 is defined as the ratio of rotor
induced emf under running condition , sE2 to
total impedance, Z2 of rotor side,
and total impedance Z2 on rotor side is given by
  • Putting this value in above equation we get,

We know that power factor is defined as ratio of
resistance to that of impedance. The power factor
of the rotor circuit is
Putting the value of flux f, rotor current I2,
power factor cos?2 in the equation of torque we
  • Combining similar term we get,

Removing proportionality constant we get,
Where ns is synchronous speed in r. p. s, ns Ns
/ 60. So, finally the equation of torque becomes,
  • Derivation of K in torque equation. In case of
    three phase induction motor, there occur copper
    losses in rotor. These rotor copper losses are
    expressed as Pc 3I22R2 We know that rotor

Substitute this value of I2 in the equation of
rotor copper losses, Pc. So, we get
The ratio of P2 Pc Pm 1 s (1 - s) Where
P2 is the rotor input, Pc is the rotor copper
losses, Pm is the mechanical power developed.
Substitute the value of Pc in above equation we
On simplifying we get,
  • The mechanical power developed Pm T?,

Substituting the value of Pm
We know that the rotor speed N Ns(1 - s)
Substituting this value of rotor speed in above
equation we get, By calculating and substituting
the all values we get the equation.
  • Equation of Starting Torque of Three Phase
    Induction Motor
  • Starting torque is the torque produced by
    induction motor when it is started. We know that
    at start the rotor speed, N is zero.

So, the equation of starting torque is easily
obtained by simply putting the value of s 1 in
the equation of torque of the three phase
induction motor,