1. Double Revolving Field Theory · 2019-07-12 · UNIT-V, SINGLE PHASE INDUCTION MOTOR By VikashTiwari Page 1 1. Double Revolving Field Theory: According to this theory, any alternating

UNIT-V, SINGLE PHASE INDUCTION MOTOR

By VikashTiwari Page 1

1. Double Revolving Field Theory:

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 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.

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

backward component rotating in clockwise direction.

The resultant of these two components at any instant gives the instantaneous

value of the stator flux at the instant. So resultant of these two is the original

stator flux.

Both the components are rotating and hence get cut by the motor conductors.

Due to cutting of flux, e.m.f. gets induced in rotor which circulates rotor current.

The rotor current produces rotor flux.

This flux interacts with forward component Φf to produce a torque in one

particular direction say anticlockwise direction. While rotor flux interacts with

backward component Φb to produce a torque in the clockwise direction. So if

anticlockwise torque is positive then clockwise torque is negative.

At start, 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 start. And hence the single phase

induction motors are not self-starting.



Torque speed characteristics:

The two oppositely directed torques and the resultant torque can be shown

effectively with the help of torque-speed characteristics. It is shown in the Fig.

It can be seen that at start N = 0 and at that point resultant torque is zero. So

single phase motors are not self-starting.

However if the rotor is given an initial rotation in any direction, the resultant

average torque increase in the direction in which rotor initially rotated and

motor starts rotating in that direction. But in practice it is not possible to give

initial torque to rotor externally hence some modifications are done in the

construction of single phase induction motors to make them self-starting.

2. Equivalent circuit of Single Phase Induction Motor:

The double revolving field theory can be effectively used to obtain the equivalent

circuit of a single phase induction motor.

Imagine the single phase induction motor is made up of one stator winding and two

imaginary rotor windings. One rotor is rotating in forward direction i.e. in the

direction of rotating magnetic field with slip s while other is rotating in backward

direction i.e. in direction of oppositely directed rotating magnetic field with slip 2 - s.

To develop the equivalent circuit, let us assume initially that the core loss is absent.

1. Without core loss

Let the stator impedance be Z Ω

Where R1 = Stator resistance & X1 = Stator reactance

Now let X2 = rotor reactance referred to stator

R2 = rotor resistance referred to stator



Where

&

As the core loss is neglected, Ro is not existing in the equivalent circuit. The xo is

half of the actual magnetising reactance of the motor

. So the

equivalent circuit referred to stator is shown in the Fig. below

Now the impedance of the forward field rotor is Zf,

*(

) +

While the impedance of the backward field rotor is Zb,

*(

) +

Under standstill condition, s = 1 and 2 - s = 1 hence,

But in the running condition, Vf becomes almost 90 to 95% of the applied

voltage.

Equivalent impedance,



Current through forward rotor referred to stator,

Current through backward rotor referred to stator,

Power input to forward field rotor,

( ) ( )

Power input to backward field rotor,

(

)

Mechanical power generated,

Net power output,

Forward torque,

( ⁄ )

Backward torque,

( ⁄ )

Net torque,

Shaft torque

( ⁄ )

2. With core loss

If the core loss is to be considered, then it is necessary to connect a resistance

in parallel with exciting branch of each rotor is half the value of actual core

loss resistance.

Equivalent impedance of exciting branch in forward rotor,



Equivalent impedance of exciting branch in backward rotor,

Now the impedance of the forward field rotor is Zf,

*( ) +

Now the impedance of the backward field rotor is Zb,

*(

) +

Thus the equivalent circuit with core loss can be shown as in the Fig. below.

3. Conducts Tests on Single Phase Induction Motor

The various tests can be performed on single phase induction motor to obtain the

equivalent circuit parameters of a single phase induction motor. The tests usually

conducted are:

1. No load test or open circuit test

2. Blocked rotor test or short circuit test

1. No load test

The test is conducted by rotating the motor without load. The input current,

voltage and power are measured by connecting the ammeter, voltmeter and

wattmeter in the circuit. These readings are denoted as Vo , Io and Wo .



The motor speed on no load is almost equal to its synchronous speed hence

for practical purposes, the slip can be assumed zero.

Hence r2/s becomes ∞ and acts as open circuit in the equivalent circuit.

Hence for forward rotor circuit, the branch r2/s + j x2 gets eliminated.

While for a backward rotor circuit, the term r2/ (2 - s) tends to r2/2. Thus xo is

much higher than the impedance r2/2 + j x2. Hence it can be assumed that no

current can flow through and that branch can be eliminated. So circuit

reduces to as shown in the Fig. below

Now the voltage across xo is VAB,

*( ) +

Thus magnetising reactance Xo can be determined.

The no load power Wo is nothing but the rotational losses.

2. Blocked Rotor Test

In balanced rotor test, the rotor is held fixed so that it will not rotate. A reduced

voltage is applied to limit the short circuit current.

The input voltage, current and power is measured by connecting voltmeter,

ammeter and wattmeter respectively. These readings are denoted as Vsc , Isc and

Wsc.

Now as rotor is blocked, the slip s = 1 hence the magnetising reactance xo is much

higher than the rotor impedance and hence it can be neglected. Thus the

equivalent circuit for blocked rotor test is as shown in the Fig. below.



√( )

( )

The stator resistance is measured by voltmeter-ammeter method, by

disconnecting the auxiliary winding and capacitors present if any. Due to skin

effect, the a.c. resistance is 1.2 to 1.5 times more than the d.c. resistance.

4. Starting Methods (Types of Single phase I.M.):

Depending upon the methods of producing rotating stator magnetic flux, the

single phase induction motors are classified as,

Split phase induction motor

Capacitor start induction motor

Capacitor start capacitor run induction motor

Shaded pole induction motor

Split Phase Induction Motor

This type of motor has single phase stator winding called main winding. In

addition to this, stator carries one more winding called auxiliary winding or

starting winding.

The auxiliary winding carries a series resistance such that its impedance is

highly resistive in nature. The main winding is inductive in nature.

Let Im = Current through main winding

and Ist = Current through auxiliary winding



As main winding is inductive, current Im lags voltage by V by a large angle Φm

while Ist is almost in phase in V as auxiliary winding is highly resistive. Thus

there exists a phase difference of α between the two currents and hence between

the two fluxes produced by the two currents.

The resultant of these two fluxes is a rotating magnetic field. Due to this, the

starting torque, which acts only in one direction, is produced.

When motor gather a speed upto 75 to 80% of the synchronous speed,

centrifugal switch gets opened mechanically and in running condition auxiliary

winding remains out of the circuit. So motor runs only stator winding.

Applications: These motors have low starting current and moderate starting

torque. These are used for easily started loads like fans, blowers, grinders,

centrifugal pumps, washing machines, oil burners, office equipments etc. These

are available in the range of 1/120 to 1/2 kW.

Capacitor Start Induction Motors

The construction of this type of motors is similar to the resistance split phase

type. The difference is that in series with the auxiliary winding the capacitor is

connected.

The capacitive circuit draws a leading current, this feature used in this type to

increase the split phase angle α between the two currents Im and Ist.

The current Im lags the voltage by angle Φm while due to capacitor the current Ist

leads the voltage by angle Φst. Hence there exists a large phase difference

between the two currents which is almost 90o, which is an ideal case.



The starting torque is proportional to 'α 'and hence such motors produce very

high starting torque .

When speed approaches to 75 to 80% of the synchronous speed, the starting

winding gets disconnected due to operation of the centrifugal switch.

Capacitor Start – Capacitor Run Induction Motors

In case of capacitor start capacitor run motor, there is no centrifugal switch and

capacitor remains permanently in the circuit. This improves the power factor.

The performance not only at start but in running condition also depends on the

capacitor C hence its value is to be designed so as to compromise between best

starting and best running condition. Hence the starting torque available in such

type of motor is about 50 to 100% of full load torque.

The direction of rotation, in both the types can be changed by interchanging the

connection of main winding or auxiliary winding. The capacitor permanently in

the circuit improves the power factor. These motors are more costly than split

phase type motors.

The capacitor value can be selected as per the requirement of starting torque, the

starting torque can be as high as 350 to 400 % of full load torque.



Applications: These motors have high starting torque and hence are used for

hard starting loads. These are used for compressors, conveyors, grinders, fans,

blowers, refrigerators, air conditions etc. These are most commonly used motors.

The capacitor start capacitor run motors are used in celling fans, blowers and

air-circulations. These motors are available upto 6 kW.

Shaded Pole Induction Motor

This type of motor consists of a squirrel cage rotor and stator consisting of

salient poles i.e. projected poles.

The poles are shaded i.e. each pole carries a copper band on one of its unequally

divided part called shading band.

The current carried by the stator winding is alternating and produces alternating

flux. Due to the transformer action, e.m.f. gets induced in the copper shading

band. This circulates current through shading band as it is short circuited,

producing its own flux.

The flux produced by shading coil lags behind the main flux by almost 90o,

therefore a rotating magnetic field is produced.

The torque speed characteristic is shown in the Fig. below.



Due to absence of centrifugal switch the construction is simple and robust but

this type of motor has a lot of limitations as :

1. The starting torque is poor.

2. The power factor is very low.

3. Due to I2R, the efficiency is very low.

4. The speed reversal is very difficult.

5. The size and power rating of these motors is very small. These motors are

usually available in a range of 1/300 to 1/20 kW.

Applications: These motors are cheap but have very low starting torque, low

power factor and low efficiency. These motors are commonly used for the small

fans, by motors, advertising displays, film projectors, record players,

gramophones, hair dryers, photo copying machines etc.

5. Repulsion Motor

Repulsion motor works on the principle of repulsion between two magnetic

fields.

The armature of the machine consists of a d.c. windings having commutator and

brushes. The brushes are short circuited by a low resistance jumper.

The stator winding is given excitation in such a way as to form the poles as

shown in the Fig. below. The brushes are aligned in the same direction of the

field axis.

The stator winding will produce alternating flux which will induce e.m.f. in the

armature conductors by transformer action. The direction of induced current

will depend on position of brushes. Because of the current flowing through the

armature, it will produce its own magnetic field. Thus equal force of repulsion

exists between like poles which will not produce any torque.



If brushes are shifted by 90o, so the conductors undergoing short circuit are also

changed. The induced emf is in the same direction as before.

Apart from the coils undergoing short circuit, the remaining armature winding

gets divided into two parallel paths. It can be seen that the induced emfs are

balanced and the resultant emf is zero. Thus no current flows through the

brushes and the resultant torque is also zero.

Now if the brushes are in the position shown in the Fig. below. In this case, the

brushes axis is not in the line of main field or at an angle of 90o to main field but

it is at an angle of α with the main field.

Again the emf will be induced in the armature conductors and there will be net

voltage across brush terminals which will produce current in the armature. Thus

the armature will also produce its own magnetic field with the poles. The north

pole formed by armature winding will be repelled by the north pole formed by

the main field winding and similarly the south pole will be repelled by south pole

formed by the main field winding and the motor runs in clockwise direction.



6. AC commutator Motor:

The commutator is a feature of d.c. motors, But a.c. motors having wound rotor

with brushes and commutator arrangements, are called commutator motors

which work on single phase a.c. supply.

The commutator arrangement present in these motors is similar to the armature

of a d.c. motor.

Single Phase A.C. Series Motor

In a normal d.c. motor if direction of both field and armature current is reversed,

the direction of torque remains unchanged. So when normal d.c. series motor is

connected to an a.c. supply, both field and armature current get reversed and

unidirectional torque gets produced in the motor.

But performance of such motor is not satisfactory due to the following reasons :

i) Armature and field winding offer high reactance to a.c. due to which operating

power factor is very low.

ii) There are tremendous eddy current losses in the yoke and field cores, which

causes overheating.

iii) The sparking at brushes is a major problem because of high voltage and

current induced in the short circuited armature coils during the commutation

period.

Some modifications are required to have the satisfactory performance of d.c.

series motor on a.c. supply. The modification are :

i) To reduce the eddy current losses, yoke and pole core construction is

laminated.

ii) The power factor can be improved by reducing the magnitudes of field and

armature reactnaces. Field reactnace can be decreased by reducing the number

of turns. But this reduces the field flux. But this reduction in flux (N α 1/Φ),

increases the speed and reduce the torque. To keep the torque same it is

necessary to increase the armature turns proportionately. This increases the

armature inductance.

Now to compensate for increased armature flux which produce armature

reaction, it is necessary to use compensating winding. The flux produced by this

winding is opposite to that produced by armature.



If such a compensating winding is connected in series with the armature as

shown in the Fig. below, the motor is said to be 'conductively compensated'.

For motors to be operated on a.c. and d.c. both, the compensation should be

conductive. If compensating winding is short circuited on its self, the motor is

said to be 'inductively compensated'.

Applications : Because of high starting torque it is used in electric traction,

hoists, locomotives etc.

Universal Motor

There are small capacity series motors which can be operated on d.c. supply or

single phase alternating supply of same voltage with same characteristics, called

universal motors.

The general construction of such motor is similar to that of a.c. series motor. It is

manufactured in two types.

i) Non compensated, low h.p

ii) Compensated type, high h.p.

Non compensated type pole has 2 poles, having entire magnetic path as

laminated. Armature is wound type similar to the normal d.c. motor. Such non

compensated construction is shown in the Fig. below.



While in compensated type, the motor has distributed field winding consisting of

main field and compensating winding. This is similar to the stator of split phase

single phase induction motor type construction. This also has a wound armature

similar to the normal d.c. motor. Fig. shows the connection diagrams for both the

types of universal motor.

Applications : The universal motors are used for domestic applications like

vacuum cleaners, food processor and mixers, hair driers, coffee grinders, electric

shavers etc. Their other applications are blowers, portable tools like drilling

machines and small drivers.

Documents

1. Double Revolving Field Theory · 2019-07-12 · UNIT-V, SINGLE PHASE INDUCTION MOTOR By VikashTiwari Page 1 1. Double Revolving Field Theory: According to this theory, any alternating