Name- Abhijit Dilip Mahale

PRN: -10303320181129310018

Electrical machine II
Assignment –III
Unit 5: Fractional H P Motor
Q.1.Explain with neat sketch construction and working of single phase induction motor.
Ans:
Single phase Induction Motors:
Single-phase a.c supply is commonly used for lighting purpose in shops, offices, houses,
schools etc. Hence instead of d.c motors, the motors which work on single-phase a.c. supply
are popularly used. These a.c motors are called single-phase induction motors. A large no. of
domestic applications uses single-phase induction motors. Here we will learn how does
single phase induction motor work.

          The power rating of these motors is very small. Some of them are even fractional
horsepower motors, which are used in applications like small toys, small fans, hairdryers etc.
This article explains the construction, working principle of single-phase induction motors.
Construction of Single Phase Induction Motors:

Similar to a d.c motor, single-phase induction motor also has two main parts, one rotating and
other stationary. The stationary part in single-phase induction motors is Stator and the
rotating part is Rotor.

The stator has laminated construction, made up of stampings. The stampings are lotted on its
periphery to carry the winding called stator winding or main winding. This is excited by a
single-phase a.c supply. The laminated construction keeps iron losses to the minimum. The
stampings are made up of material from silicon steel which minimises the hysteresis loss.

          The stator winding is wound for a certain definite number of poles means when excited
by single-phase a.c supply, stator produces the magnetic field which creates the effect of the
certain definite number of poles. The number of poles for which stator winding is wound
decides the synchronous speed of the motor. The synchronous speed is denoted as Ns and it
has a fixed relation with supply frequency f and number of poles P. The relation is given by, 
 Ns = 120f/p  RPM
 The induction motor never rotates with the synchronous speed but rotates at a speed that is
slightly less than the synchronous speed. The rotor construction is of squirrel cage type. This
rotor consists of uninsulated copper or aluminium bars, placed in the slots.

            The bars are permanently shorted at both the ends with the help of conducting rings
called end rings. The entire structure looks like cage hence it is called a squirrel cage
rotor. The construction of  single-phase induction motors is shown in below figure:

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PRN: -10303320181129310018

As the bars are permanently shorted to each other, the resistance of the entire rotor is very
very small. The air gap between stator and rotor is kept uniform and as small as possible. The
main feature of this rotor is that it automatically adjusts itself for the same the number of
poles as that of the stator winding. The schematic diagram of two-pole single phase induction
motor is shown in the below figure: 

Working Principle of Single Phase Induction Motors:

       For the motoring action, there must exist two fluxes which interact with each other to
produce the torque. In d.c motors, field winding produces the main flux while d.c
supply given to armature is responsible to produce armature flux. The main flux and armature
flux interact to produce the torque.
 In the single-phase induction motor, single-phase a.c supply is given to the stator
winding. The stator winding carries an alternating current which produces the flux which is
also alternating in nature. This flux is called the main flux. This flux links with the rotor
conductors and due to transformer action e.m.f gets induced in the rotor.  The induced emf
drives current through the rotor as the rotor circuit is the closed circuit.

 This rotor current produces another flux called rotor flux required for the motoring
action. Thus second flux is produced according to the induction principle due to induced
e.m.f hence the motor is called induction motor. As against this in d.c motor a separate supply
is required to the armature to produce armature flux. This is an important difference between
d.c motor and an induction motor. 

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PRN: -10303320181129310018

Q.2. Why a single phase induction motor is not self-starting?

Ans:
According to double field revolving theory, we can resolve any alternating quantity into two
components. Each component has a magnitude equal to the half of the maximum magnitude
of the alternating quantity, and both these components rotate in the opposite direction to each
other. For example – a flux, φ can be resolved into two components

Each of these components rotates in the opposite direction i. e if one φm/2 is rotating in a
clockwise direction then the other φm / 2 rotates in an anticlockwise direction.
When we apply a single phase AC supply to the stator winding of single phase induction
motor, it produces its flux of magnitude, φm. According to the double field revolving theory,
this alternating flux, φm is divided into two components of magnitude φm/2. Each of these
components will rotate in the opposite direction, with the synchronous speed, Ns.
Let us call these two components of flux as forwarding component of flux, φf and the
backward component of flux, φb. The resultant of these two components of flux at any instant
of time gives the value of instantaneous stator flux at that particular instant.

Now at starting condition, both the forward and backward components of flux are exactly
opposite to each other. Also, both of these components of flux are equal in magnitude. So,
they cancel each other and hence the net torque experienced by the rotor at the starting
condition is zero. So, the single phase induction motors are not self-starting motors.

Q.3. Explain with neat sketch the operation of single phase induction motor on the basis
of a) Double field revolving theory and b) cross field theory.
Ans:
a) Double Revolving Field Theory in single-phase induction motors:

             According to this theory, any alternating quantity can be resolved into two rotating
components which rotate in opposite directions and each having magnitude as half of the
maximum magnitude of the alternating quantity. In case of single-phase induction motors, the
stator winding produces an alternating magnetic field having the maximum magnitude of
Φ1m.

        
         According to double-revolving field theory, consider the two components of the stator
flux, each having magnitude half of maximum magnitude of stator flux i.e. (Φ1m/2). Both
these components are rotating in opposite directions at the synchronous speed Ns which is
dependent on frequency and stator poles.

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            Let Φf is forward component rotating in anticlockwise direction while Φb is the

backward component rotating in a clockwise direction. The resultant of these two
components at any instant gives the instantaneous value of the stator flux at that instant.
So resultant of these two is the original stator flux. The below figure shows the stator flux and
its two components Φf and Φb 

 At the start, both the components are shown the opposite to each other in figure(a).
Thus the resultant ΦR = 0. This is nothing but the instantaneous value of stator flux at the
start. After 90°, as shown in figure(b), the two components are rotated in such a way that both
are pointing in the same direction. 

               Hence the resultant ΦR is the algebraic sum of the magnitudes of the two
components. So ΦR = (Φ1m/2) + (Φ1m/2) =Φ1m.This is nothing but the instantaneous value
of the stator flux at 0 = 90° as shown in figure(c). Thus continuous rotation of two
components gives the original alternating stator flux. 

      
         Both the components are rotating and hence get cut by the rotor conductors. Due to the
cutting of flux, e.m.f gets induced in the rotor which circulates the rotor current. The rotor
current produces rotor flux. This flux interacts with forwarding component Φf to produce a
torque in one particular direction say anticlockwise direction. While the rotor flux interacts
with the backward component Φb to produce a torque in the clockwise direction. So if
anticlockwise torque is positive then clockwise torque is negative.
At the start, these two torques are equal in magnitude but opposite in direction. Each
torque tries to rotate the rotor in its own direction. Thus net torque experienced by the rotor is
zero at the start. And hence the single-phase induction motors are not self-starting.  By
providing the additional flux, we can make the motor self-starting. Some of the self-starting
single phase induction motors are Capacitor Start Induction Motor, Shaded pole induction
motor, Permanent split capacitor motor.

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PRN: -10303320181129310018

b) Cross Field Theory in single phase induction motors:

           Consider a single phase induction motor with standstill rotor as shown in the below
figure. The stator winding is excited by the single phase a.c. supply. This supply produces an
alternating flux Φs which acts along the axis of the stator winding. Due to this flux, emf gets
induced in the rotor conductors due to transformer action. 

              As the rotor is closed one, this e.m.f circulates current through the rotor conductors.
The direction of the rotor current is as shown in the below figure. The direction of rotor
current is so as to oppose the cause producing it, which is stator flux Φs. 

         Now Fleming's left hand rule can be used to find the direction of the force experienced
by the rotor conductors. It can be seen that when Φs acts in upward direction and increasing
positively, the conductors on left experience force from left to right while conductors on right
experience force from right to left. Thus overall, the force experienced by the rotor is zero.
Hence no torque exists on the rotor and rotor cannot start rotating.
  We have seen that there must exist two fluxes separated by some angle so as to
produce field. According to cross field theory, the stator flux can be resolved into two
components which are mutually perpendicular. One acts along the axis of the
stator winding and other acts perpendicular to it. 
  Assume now that an initial push is given to the rotor in an anticlockwise direction. Due
to the rotation, rotor physically cuts the stator flux and dynamically emf gets induced in the
rotor. This is called speed e.m.f or rotational emf. The direction of such emf can be obtained
by Fleming's right-hand rule and this emf is in phase with the stator flux Φs.

          The direction of emf is shown in the figure below. This emf is denoted as E2N. This
emf circulates current through rotor which is I2N. This current produces its own flux called
rotor flux Φr. This axis of Φr is at 90° to the axis of stator flux hence this rotor flux it called
cross-field.

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Name- Abhijit Dilip Mahale
PRN: -10303320181129310018

Q.4. Starting from first principle develop the equivalent circuit of a single phase
induction
motor. How the performance is determined?
Ans:
Equivalent Circuit of an Induction motor enables the performance characteristics which are
evaluated for steady state conditions. An induction motor is based on the principle of
induction of voltages and currents. The voltage and current is induced in the rotor circuit
from the stator circuit for the operation. The equivalent circuit of an induction motor is
similar to that of the transformer.

1) Stator Circuit Model

The stator circuit model of an induction motor consists of a stator phase winding resistance
R1, stator phase winding leakage reactance X1 as shown in the circuit diagram below.

The no load current I0 is simulated by a pure inductive reactor X0 taking the magnetizing
component Iµ and a noninductive resistor R0 carrying the core loss current Iω. Thus,

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PRN: -10303320181129310018

The total magnetizing current I0 is considerably larger in the case of the induction motor as
compared to that of a transformer. This is because of the higher reluctance caused by the air
gap of the induction motor. As we know that, in a transformer the no load current varies from
2 to 5% of the rated current, whereas in an induction motor the no load current is about 25 to
40% of the rated current depending upon the size of the motor. The value of the magnetizing
reactance X0 is also very small in an induction motor.

2) Rotor Circuit Model

When a three phase supply is applied to the stator windings, a voltage is induced in the rotor
windings of the machine. The greater will be the relative motion of the rotor and the stator
magnetic fields, the greater will be the resulting rotor voltage. The largest relative motion
occurs at the standstill condition. This condition is also known as the locked rotor or blocked
rotor condition. If the induced rotor voltage at this condition is E20 then the induced voltage at
any slip is given by the equation shown below.

The rotor resistance is constant and is independent of the slip. The reactance of the induction
motor depends upon the inductance of the rotor and the frequency of the voltage and current
in the rotor.

If L2 is the inductance of rotor, the rotor reactance is given by the equation shown below.

But, as we know

Therefore,

Where, X20 is the standstill reactance of the rotor.

The rotor circuit is shown below.

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PRN: -10303320181129310018

The rotor impedance is given by the equation below.

The rotor current per phase is given by the equation shown below.

Here, I2 is the slip frequency current produced by a slip frequency induced voltage sE20 acting
in the rotor circuit having an impedance per phase of (R2 + jsX20).

Now, dividing the equation (5) by slip s we get the following equation.

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The R2 is a constant resistance and a variable leakage reactance sX20. Similarly, the rotor
circuit shown below has a constant leakage reactance X20 and a variable resistance R2/s.

The equation (6) above explains the secondary circuit of an imaginary transformer, with a
constant voltage ratio and with the same frequency of both sides. This imaginary stationary
rotor carries the same current as the actual rotating rotor. This makes possible to transfer the
secondary rotor impedance to the primary stator side.

3) Approximate Equivalent Circuit of an Induction Motor

The equivalent circuit is further simplified by shifting the shunt impedance branches R0 and
X0 to the input terminals as shown in the circuit diagram below.

The approximate circuit is based on the assumption that V1 = E1 = E’2. In the above circuit,
the only component that depends on the slip is the resistance. All the other quantities are
constant. The following equations can be written at any given slip s is as follows: -

Impedance beyond AA’ is given as

Putting the value of ZAA’ from the equation (7) in the equation (8) we get

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Therefore,

No load current I0 is

Total stator current is given by the equation shown below.

Total core losses are given by the equation shown below.

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PRN: -10303320181129310018

Air gap power per phase is given as

Develope
d torque is given by the equation shown below.

The above equation is the torque equation of an induction motor. The approximate equivalent
circuit model is the standard for all performance calculation of an induction motor.

Q.5. Draw a typical torque slip characteristic of single phase induction motor on the
basis of a) Double field revolving theory.
Ans:
Torque Slip Characteristics of Single-Phase Induction Motor

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Name- Abhijit Dilip Mahale
PRN: -10303320181129310018

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.

Q.6. Briefly discuss different methods of starting single phase induction motor, stating
relevant applications for each.
Ans:
Methods of Starting

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Name- Abhijit Dilip Mahale
PRN: -10303320181129310018

It is clear from previous discussion that a single phase induction motor when having only one
winding and it is not self-starting. To make it a self-starting anyone of the following can be
adopted.
 
(1) Split phase starting.
 
(2) Repulsion starting.
 
(3) Shaded pole starting.

1) SPLIT PHASE INDUCTION MOTOR

 The basic principle of operation of a split phase induction motor is similar to that of a
polyphaseinduction motor. The main difference is that the single phase motor does not
produce a rotating magnetic field but produces only a pulsating filed.
 
Hence, to produce the rotating magnetic field for self-starting, phase splitting is to be done to
make the motor to work as a two phase motor for starting.
 

Working of Split Phase Motor

 
In split phase motor two windings named as main winding and starting winding are provided.
At the time of starting, both the main and starting windings should be connected across the
supply to produce the rotating magnetic field.
 
The rotor is of a squirrel cage type and the revolving magnetic field sweeps part the
stationary rotor, inducing emf in the rotor. As the rotor bars are short-circuited, a current
flows through them producing a magnetic field.
 
This magnetic field opposes the revolving magnetic field and will combine with the main
filed to produce a revolving filed. By this action, the rotor starts revolving in the same
direction of the rotating magnetic field as in the case of a squirrel cage induction motor.
 
Hence, once the rotor starts rotating, the starting winding can be disconnected from the
supply by some mechanical means as the rotor and stator fields from a revolving magnetic
field. There are several types of split phase motors.
 
 

TYPES OF SPLIT-PHASE INDUCTION MOTORS

 
1. Resistance-start, induction-run motors

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2.Capacitor-start, induction-run motors
 
3. Capacitor-start, capacitor-run motors
 
4. Shaded pole motors.
 
 

1. RESISTANCE-START, INDUCTION-RUN MOTORS

 
As the starting torque of this type of motor is relatively small and its starting current is high,
these motors are most commonly used for rating up to 0.5 HP where the load could be started
easily. The essential parts are shown in Fig:
Main winding or running winding.
 
Auxiliary winding or starting winding
 
Squirrel cage type rotor.
 
Centrifugal switch.

CONSTRUCTION AND WORKING

 
The starting winding is designed to have a higher resistance and lower reactance than the
main winding. This is achieved by using small conductors in the auxiliary winding than in the
main winding. The main winding will have higher inductance when surrounded by more iron,
which could be made possible by placing it deeper into the stator slots, it is obvious that the
current would split as shown in Fig: (b).

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Name- Abhijit Dilip Mahale
PRN: -10303320181129310018

The starting current "I" start will lag the main supply voltage "V" line by 15 degrees and the
main winding current. "I" main lags the main voltage by about 80 degrees. Therefore, these
currents will differ in time phase and their magnetic fields will combine to produce a rotating
magnetic field.
 When the motor has come up to about 75 to 80% of synchronous speed, the starting winding
is opened by a centrifugal switch and the motor will continue to operate as a single phase
motor.
 
CHARACTERISTICS
At the point where the starting winding is disconnected, the motor develops nearly as much
torque with the main winding alone as with both windings connected. This can be observed
from, the typical torque-speed characteristics of this motor, as shown in Fig:

The direction of rotating of a split-phase motor is determined by the way the main and
auxiliary windings are connected. Hence, either by changing the main winding terminals or
by changing the starting winding terminals, the reversal of direction of rotating could be
obtained.
 
APPLICATIONS
 These motors are used for driving fans, grinders, washing machines.
 

2. CAPACITOR-START, INDUCTION-RUN MOTOR

A drive which requires a large starting torque may be fitted with a capacitor-start, induction-
run motor as it has excellence starting torque as compared to the resistance-start, induction-
run motor.
 

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CONSTRUCTION AND WORKING

 
Fig: (a) shows the schematic diagram of a capacitor-start, induction-run motor. As shown, the
main winding is directly connected across the main supply whereas the starting winding is
connected across the main supply through a capacitor and centrifugal switch.
 
Both these windings are placed in a stator slot at 90 degrees electrical apart, and a squirrel
cage type rotor is used.
 
As shown in Fig: (b), at the time of starting the current in the main winding lags the supply
voltages by 90 degrees, depending upon its inductance and resistance. On the other hand, the
current in the starting winding due to its capacitor will lead the applied voltage, by say 20
degrees.
 
Hence, the phase difference between the main and starting winding becomes near to 90
degrees. This in turn makes the line current to be more or less in phase with its applied
voltage, making the power factor to be high, thereby creating an excellent starting torque.
 
However, after attaining 75% of the rated speed, the centrifugal switch operates opening the
starting winding and the motor then operates as an induction motor, with only the main
winding connected to the supply.
 

As shown in Fig: 4.9(b), the displacement of current in the main and starting winding is about
80/90 degrees, and the power factor angle between the applied voltage and line current is
very small. This results in producing a high power factor and an excellent starting torque,
several times higher than the normal running torque as shown in Fig:

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CHARACTERISTICS
The torque-speed characteristics of this motor is shown in Fig:

In order to reverse the direction of rotation of the capacitor-start, induction-run motor, either
the starting or the main winding terminals should be changed.
 
This is due to the fact that the direction of rotation depends upon the instantaneous polarities
of the main field flux and the flux produced by the starting winding. Therefore, reversing the
polarity of one of the field will reverse the torque.
 
APPLICATIONS
 
Due to the excellent starting torque and easy direction-reversal characteristics,
Used in belted fans,
Used in blower’s dryers,
Used in washing machines,
Used in pumps and compressors.
 

3. CAPACITOR-START, CAPACITOR-RUN MOTORS

As discussed earlier, one capacitor-start, induction-run motors have excellent starting torque,
say about 300% of the full load torque and their power factor during starting in high.
 
However, their running torque is not good, and their power factor, while running is low. They
also have lesser efficiency and cannot take overloads.
 

CONSTRUCTION AND WORKING

 
The aforementioned problems are eliminated by the use of a two valve capacitor motor in
which one large capacitor of electrolytic (short duty) type is used for starting whereas a

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smaller capacitor of oil filled (continuous duty) type is used for running, by connecting them
with the starting winding as shown in Fig: A general view of such a two valve capacitor
motor is shown in Fig:

This motor also works in the same way as a capacitor-start, induction-run motor, with
exception, that the capacitor C1 is always in the circuit, altering the running performance to a
great extent.
 
The starting capacitor which is of short duty rating will be disconnected from the starting
winding with the help of a centrifugal switch, when the starting speed attains about 75% of
the rated speed.
 
CHARACTERISTICS
 
The torque-speed characteristics of this motor is shown in Fig:

This motor has the following advantages:

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•  The starting torque is 300% of the full load torque

 •  The starting current is low, say 2 to 3 times of the running current
•  Starting and running power factor are good.
 •   Highly efficient running.
 •  Extremely noiseless operation.
 • Can be loaded up to 125% of the full load capacity.
 
 APPLICATIONS
 • Used for compressors, refrigerators, air-conditioners, etc.
 •  Higher starting torque.
 •  High efficiency, higher power factor and overloading.
 •  Costlier than the capacitor-start — Induction run motors of the same capacity.
 
2) REPULSION STARTING
This type of starting need a wound rotor with brush and commutator arrangement like a dc
armature Fig 4.13(a). The starting operation is based on the principle of repulsion and hence
the name.
 CONSTRUCTION AND WORKING
Repulsion starting, though complicated in construction and higher in cost, are still used in
certain industries due to their excellent starting torque, low starting current, ability to
withstand long spell of starting currents to drive heavy loads and their easy method of
reversal of direction.
 Now there is a condition that the rotor north pole will be repelled by the main north pole and
the rotor south pole is repelled by the main south pole, so that a torque could be developed in
the rotor. Now due to the repulsion action between the stator and the rotor poles, the rotor
will start rotating in a clockwise direction. As the motor torque is due to repulsion action, this
starting method is named as repulsion starting.

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To change the direction of rotation of this motor, the brush axis needs to be shifted from the
right side as shown in Fig: (b) to the left side of the main axis in a counter clockwise
direction as shown in Fig: (b).
 CHARACTERISTICS
The torque developed in a repulsion motor will depend upon the amount of brush shaft as
shown in Fig: 4.13 (b), whereas the direction of shift decides the direction of rotation.
 
Further, the speed depends upon the amount of brush shift and the magnitude of the load also
on the relationship between the torque and brush-position angle.
 
Though the starting torque from 250 to 400% of the full load torque, the speed will be
dangerously high during light loads. This is due to the fact that the speed of the repulsion
motor start does not depend on frequency or number of poles but depends upon the repulsion
principle.
Further, there is a tendency of sparking in the brushes at heavy loads, and the PF will be poor
at low speeds. Hence the conventional repulsion motor start is not much popular.
 
 
3) SHAPED POLE STARTING
 The motor consists of a yoke to which salient poles are fitted as shown in Fig: 4.14(a) and it
has a squirrel cage type rotor.

A shaded pole made of laminated sheets has a slot cut across the lamination at about one third
the distance from the edge of the pole.
Around the smaller portion of the pole, a short-circuited copper ring is placed which is called
the shading coil, and this part of the pole is known as the shaded part of the pole. The
remaining part of the pole is called the unshaded part which is clearly shown in Fig: (b).

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Around the poles, exciting coils are placed to which an AC supply is connected. When AC
supply is effected to the exciting coil, the magnetic axis shifts from the unshaded part of the
pole to the shaded part as will be explained in details in the next paragraph. This shifting of
axis is equivalent to the physical movement of the pole.
This magnetic axis, which is moving, cuts the rotor conductors and hence, a rotational torque
is developed in the rotor.
By this torque the rotor starts rotating in the direction of the shifting of the magnetic axis that
is from the unshaded part to the shaded part.
 

THE MAGNETIC FLUX SHIFTING

As the shaded coil is of thick copper, it will have very low resistance but as it is embedded in
the iron case, it will have high inductance. When the exciting winding is connected to an AC
supply, a sine wave current passes through it.
 
Let us consider the positive half cycle of the AC current as shown in Fig:

When the current raises from "Zero" Value of point "0" to a point "a" the change in current is
very rapid (Fast). Hence, it reduces an emf in the shaded coil on the basis of Faraday's law of
electromagnetic induction.
 
The induced emf in the shaded coil produces a current which, in turn, produces a flux in
accordance with Lenz Law. This induced flux opposes the main flux in the shaded portion
and reduces the main flux in that area to a minimum value as shown in Fig:
 
This makes the magnetic axis to be in the centre of the unshaded portion as shown by the
arrow in part of Fig: On the other hand, as shown in part 2 of 3 when the current raises from
point "a" to point "b" the change in current is slow the induced emf and resulting current in
the shading coil is minimum and the main flux is able to pass through the shade portion.

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This makes the magnetic axis to be shifted to the centre of the whole pole as shown in by the
arrow in part 2 of Fig:
In the next instant, as shown in part 3 of Fig: When the current falls from "b" to "c" the
change in current is fast but the change of current is from maximum to minimum.
 
Hence a large current is induced in the shading ring which opposes the diminishing main
flux, thereby increasing the flux density in the area of the shaded part. This makes the
magnetic axis to shift to the right portion of the shaded part as shown by the arrow in part.
 
From the above explanation it is clear the magnetic axis shifts from the unshaded part to the
shaded part which is more or less a physical rotary movement of the poles.
 
Simple motors of this type cannot be reversed. Specially designed shaded pole motors have
been constructed for reversing operations. Two such types:
 
a. The double set of shading coils method
 
b. The double set of exciting winding method.
 
Shaded pole motors are built commercially in very small sizes, varying approximately from
1/250 HP to 1/6 HP. Although such motors are simple in construction and cheap, there are
certain disadvantages with these motor as stated below:
 
•  Low starting torque.
 
•  Very little overload capacity.
 
•   Low efficiency.
 

APPLICATIONS
 
• Record players
 
• Fans
 
•  Hair driers.

Q.7. Prepare a table showing the rating and applications of different types of single
phase
induction motor.
Ans:

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Type of induction motor Rating Application

Split phase induction motor 0.5-1 HP 1. These motors are used in

(Resistance-start, induction - washing machines.
run motors)
2.These are used in Air
conditioning fans.
3.Used in food mixers,
grinders, floor polishers,
blowers, centrifugal pumps,
4.These are used in small
drills, lathes, office
machinery, etc.

Capacitor start, induction- 120W – 750W 1.These motors are used for
run motor heavy loads where frequent
starts are required.
2.These motors are used for
pumps and compressors, so
these are used as a
compressor in the refrigerator
and air conditioner.
3.They are also used for
conveyors and some machine
tools.

Capacitor-start, capacitor- About 2 kilowatts for 120- 1.Two value capacitor motors
run motor volt supply are used for loads of higher
inertia that require frequent
And start.
10 kilowatts for 230-volt 2.These are used in pumping
supply equipment.
3.These are used in
refrigeration, air
compressors, etc.

Permanent split capacitor Input power P1(W)-368 1.These motors are used for
motor fans and blowers in heaters.
Output power P2(W)-124
2.It is used in air
conditioners.
3.It is used to drive
refrigerator compressors.

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4.It is also used to operate

office machinery.

Shaded pole motor 1/250 to 1/6 HP Shaded-pole motors are used

to drive devices which
require low starting torque.
These motors are very
suitable for small devices like
relays, fans of all kinds, etc.
because of their low initial
cost and easy starting.
The most common
application of these motors is
in table fans, exhaust fans,
hair dryers, fans for
refrigeration and air-
conditioning equipment,
electronic equipment, cooling
fans, etc.

Q.8. Why is the auxiliary winding in a capacitor start motor disconnected after the
motor?
has picked up speed?
Ans:
In capacitor start induction motors capacitor is connected in series with the auxiliary winding.
When speed of the motor approaches to 75 to80%of the synchronous speed the starting
winding gets disconnected due to the operation of the centrifugal switch. The capacitor
remains in the circuit only at start.

Q.9.Discuss the difference between capacitor start, capacitor start and run and
permanent split capacitor motor.
Ans:
The simplest way to explain the mechanics of a capacitor would be to compare it to a battery;
both store and release electricity. Capacitors are charged with electricity then release its
stored energy at a rate of sixty times per second in a 60 cycle alternating current system. The
sizing is critical to motor efficiency just as sizing of batteries is critical to a radio. A radio
that requires a 9V battery will not work with a 1.5V size battery. Thus, as the battery
becomes weaker the radio will not play properly. A motor that requires a 7.5 uF capacitor

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will not work with a 4.0 uF capacitor. Much the same way, a motor will not run properly with
a weak capacitor. This is not to imply bigger is better, because a capacitor that is too large
can cause energy consumption to rise. In both instances, be it too large or too small, the life
of the motor will be shortened due to overheated motor windings. Motor manufacturers spend
many hours testing motor and capacitor combinations to arrive at the most efficient
combination. There is a maximum of +10% tolerances in microfarad rating on replacement
start capacitors, but exact run capacitors must be replaced. Voltage rating must always be the
same or greater than original capacitor whether it is a start or run capacitor. Always consult
manufacturers to verify correct capacitor size for the particular application.

Two basic types are used in electric motor:

1)Run capacitors are rated in a range of 3–70 microfarad (uF). Run capacitors are also rated
by voltage classification. The voltage classifications are 370V and 440V. Capacitors with
ratings above 70 microfarad (uF) are starting capacitors. Run capacitors are designed for
continuous duty, and are energized the entire time the motor is running. Single phase electric
motors need a capacitor to energize a second phase winding. This is why sizing is so critical.
If the wrong run capacitor is installed, the motor will not have an even magnetic field. This
will cause the rotor to hesitate at those spots that are uneven. This hesitation will cause the
motor to become noisy, increase energy consumption, cause performance to drop, and cause
the motor to overheat.

Examples of our Motor Run Capacitors:

CBB65 Oil-filled Capacitors

ADP Dry-type Black Box Capacitors

CBB60B Dry-type Capacitors

Italfarad Dry-type Plastic Case Capacitors

2) Starting capacitors are housed in a black plastic case and have uF range as opposed to a
specific uF rating on run capacitors. Start capacitors (ratings of 70 microfarad or higher) have
three voltage classifications: 125V, 250V, and 330V. Examples would be a 35 uF at 370V
run capacitor and an 88–108 uF at 250V start capacitor. Start capacitors increase motor
starting torque and allow a motor to be cycled on and off rapidly. Start capacitors are

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designed for momentary use. Start capacitors stay energized long enough to rapidly bring the
motor to 3/4 of full speed and are then taken out of the circuit.

Examples of our Motor Start Capacitors:

CD60B Aluminum Electrolytic Capacitors

3) Split Capacitor (PSC) Motor

The Permanent Split Capacitor motor also has a cage rotor and the two windings named as
main and auxiliary windings similar to that of a Capacitor Start and Capacitor Start Capacitor
Run Motor. It has only one capacitor connected in series with the starting winding. The
capacitor C is permanently connected in the circuit both at the starting and the running
conditions.

is also called as a Single Value Capacitor Motor. As the capacitor is always in the circuit and
thus this type of motor does not contain any starting switch. The auxiliary winding is always
there in the circuit. Therefore, the motor operates as the balanced two-phase motor. The
motor produces a uniform torque and has noise free operation.

Q.10. Discuss the procedure to determine the parameters of equivalent circuit of a

single
phase induction motor.
Ans:
EQUVALENT CIRCUIT OF SINGLE PHASE INDUCTION MOTOR
 The equivalent circuit of single phase induction motor is shown below (Fig:)

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Name- Abhijit Dilip Mahale
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Determination of Equivalent Circuit Parameters of Single Phase Induction motor

 
It is possible to find the parameters of the equivalent circuit of the single phase induction
motor experimentally as shown in Fig.4.4. For this purpose, three tests should be conducted:
 
 1- The DC Test:
 
The DC resistance of the stator can be measured by applying DC current to the terminals of
the main winding and taking the reading of the voltage and the current (or using ohmmeter)
and determine the DC resistance as follows:

2-The Blocked Rotor Test:

 
When the rotor is locked (i.e. prevented from running), Sb = Sf = 1. The secondary
impedances become much less than the magnetizing branches and the corresponding
equivalent circuit becomes that of Fig:

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Name- Abhijit Dilip Mahale
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3-The No Load Test:

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Name- Abhijit Dilip Mahale
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When the induction motor is allowed to run freely at no load, the forward slip Sf approaches
zero and the backward slip Sb approaches 2 (Sf = s, Sb = 2-s). The secondary forward
impedance becomes very large with respect to the magnetizing branch, while the secondary
backward impedance becomes very small if compared with the magnetizing branch.
Accordingly, the equivalent circuit corresponding to these operating conditions can be
approximated by that of Fig:

Fig: (a) Approximate equivalent circuit of the single phase induction motor at no load.

The circuit in Fig: (a) can be rearranged to the equivalent circuit that is shown in Fig: (b)

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Fig: (b) Rearranged approximate equivalent circuit of the single phase induction motor at no
load

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Name- Abhijit Dilip Mahale
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Q.11.Solve typical problems to determine the torque, performance and parameters of

equivalent circuit of a single phase induction motor.
Ans:
 EXAMPLE:
1)A 220-V, 6-pole, 50-Hz, single-winding single-phase induction motor has the following
equivalent circuit parameters as referred to the stator.
R1m = 3.0 W, X1m = 5.0 W
R2 = 1.5 W, X2 = 2.0 W
Neglect the magnetizing current. When the motor runs at 97% of the synchronous
speed, compute the following:
(a) The ratio Emf /Emb
(b) The ratio Vf /Vb
(c) The ratio Tf /Tb
(d) The gross total torque.
(e) The ratios Tf /(Total torque) and Tb/(Total torque)
Ans:
Solution
a)
Slip = s = 1 – 0.97 = 0.03

Since magnetizing current is neglected, X=infinity

Emf / Emb =Zf / Zb= [(1.5/0.03)+j2 / (1.5/2-0.03) + j2]

= 23.38

b) Vf and Vb are component of stator voltage Vm i.e.

Vm = Vf + Vb
These component are defined by redrawing the circuit model in the symmetrical form of
below fig.

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For the purpose of this problem X = infinity, therefore

Impedance offered to Vf component = 1/ 2{[3 + (1.5/0.03)] + j7}

= 1 /2 (53+j7)
Impedance offered to Vb component = 1/ 2{[3 + (1.5/1.97)] + j7}

= 1/2 (3.76+j7)
Vf/ Vb= (53+j7) / (3.76+j7)
= 6.73
c) Tf/Tb= Pgf / Pgb = 2-s/s = 2-0.03 /0.03 =65.7
d) Total impedance as seen from stator terminal is

z = 1/2 [(53+j7)+(3.76+j7)]
=28.38+j7 = 29.2 Angle 13.9
Im =220/29.2 = 753A
ns = (120 × 50)/6 = 1000 rpm
ωs =(2π×1000)/60 = 104.72 rad/s
Tf = Im2 R2 / ωs 2s (i)

Tb = Im2 R2 / 2(2-s) ωs (ii)

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Name- Abhijit Dilip Mahale
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Ttotal = Tf - Tb
Ttotal = Im2 R2 / ωs 2(1/s – 1/ 2-s) (iii)
=[(7.53× 2× 1.5)/ (2×104.72)](1/0.03-1/1.97)
= 13.31Nm
e) from Eqs (i),(ii) and (iii)

Tf / Ttotal=1/ 1-(s/2-s) =1.015

Tb/ Ttotal=1 / (2-s/s) -1 =0.015

2)A test on the main winding of a 1 kW, 4-pole. 2 15 V, 50 Hz, single-phase induction
motor gave the following results:
No-load test Rotor-blocked test
V0 = 215 V VSC = 85 A
I0 = 3.9 A ISC = 9.80 A
P0 = 185 W PSC = 390 W
R1 = 1.6 W
Given:
(a) Calculate the parameters of the circuit model assuming that the magnetizing
reactance hangs at the
input terminals of the model.
(b) Determine the line current power factor, shaft torque and efficiency of the motor at
a speed of
1440 rpm
SOLUTION
(a) Parameters of the circuit model are calculated using both no-load as well as rotor-blocked
tests.
(i) No-load test: Assuming the slip to be zero, the circuit model on no-load is drawn in Fig.
10.7 with magnetizing reactance at input terminals

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Name- Abhijit Dilip Mahale
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Since the backward circuit is short-circuited for practical purposes, as X being magnetizing
reactance is much larger
X/2 = 215/3.9
=55.1 Ω
Rotational loss,
P0 = 185 W
(ii) Rotor-blocked test (s = 1): The circuit model on rotor-blocked test is shown in Fig. 10.8

390 = 85× 9.8 × cos ΦSC

or ΦSC = 62° lagging
With reference to Fig. 10.8 mm

R1+ R2 = 4.7 Ω
R1 = 1.6 Ω(given)
R2 = 3.1 Ω
Xl + X2 = 8.04 Ω
The circuit model with parameter values is drawn in Fig. 10.9.

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Name- Abhijit Dilip Mahale
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Pm = 157.1 (1– 0.04) × 5.6 = 844.6 W

Rotational loss = 185 W
Pout = 844.6 – 185 = 659.6 W
Efficiency = 659.6/985.5
= 66.9%
T(shaft) = 659.6/157.1
= 4.12 Nm

3)A 230 V, 50 Hz, 4 – pole single phase induction motor has the following equivalent
circuit impedances:
R1 = 2.2Ω, R2 = 4.5Ω, X1 = 3.1Ω, X2 = 2.6Ω, Xm = 80Ω,
Friction, windage and core loss = 40 W . For a slip of 0.03pu, calculation (a) input
current, (b) power factor, (c) developed power, (d) output power, (e) efficiency
Solution:
R2/2S = 4.5/2* 0.03 = 75 Ω
R2/2(2-S) = 4.5/2*(2 -0.03) = 1.142 Ω
X2 /2 = 2.6/2 = 1.3 Ω X
m/2 = 80/2 = 40 Ω
Zf = 16.37+j30.98
Zb= 1.07+j1.92
Z1 = R1 +X1 = 2.2 + j3.1
Zt = Z1 + Zf + Zb = 19.64 + j 35.37 = 40.457 < 60.96
a) Input current
I = V/ Zt = 230 < 0 / 40.457 < 60.96 = 5.685 < -60.69 A
b) Power factor cos
(-60.69) = 0.485 Lag
c) Developed power
Pconv = Pmech = I2 (Rf – Rb ) (1-S) = (5.685)2 (16.37 – 1.07) (1 – 0.03)
= 479.65 W
d) Output power

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Pout = Pmech - loss = 479.65 - 40 = 439.65 W

Input power = VI cos ⱷ = 230 * 5.685 * 0.485 = 634.9 W
e) Efficiency = Pout / Pin = 0.692 pu

4)A 220 V, single – phase induction motor gave the following test results:

Blocked – rotor test : 120V, 9.6A, 460W

No – load test : 220V, 4.6A, 125W

The stator winding resistance is 1.5 , and during the blocked – rotor test, the starting
winding is open. Determine the equivalent circuit parameters. Also, find the core,
fraction and windage losses.

Solution:

Blocked – rotor test

Vscr=120V, Iscr= 9.6A , Pscr=460W

Ze = =12.5Ω

Re = =4.99Ω

Xe = = = 11.46Ω

X1m= X2= Xe = *11.46=5.73Ω

R1m = 1.5Ω

Re = R1m+R2

R2 = Re-R1m = 4.99-1.5 = 3.49Ω

No load test

V0= 220V,I0=4.6V,P0=125W

cosɸ0 = 0.1235

⸫ sinɸ0= 0.9923

Z0= 47.83Ω

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⸫ X0= Z0 sinɸ0 = 47.83*0.9923 = 47.46Ω

Core,fraction and windage losses

= power input to motor at no load – no load copper loss

= P0-I^20

= 125 – (4.6)2

= 74.8W

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