Single Phase Induction Motor

Introduction to Single Phase Induction Motor

 

Induction motors are the most popularly used motors among all the other electric motors in industries. They are ac fed asynchronous motors as discussed in "induction motor basics”.

 

Since the AC supply is available in three phase or single phase, induction motors are designed to operate either on three phase ac supply or single-phase ac supply. In its three-phase form means three phase induction motors, these are used in high power applications such as cranes, hoist, conveyor lines in manufacturing plants, drill machines, lathe machines etc. While in its single-phase form means single phase induction motor, these are most pronounced in low power applications such as household fans, washing machines, AC, pumps, vacuum cleaners, kitchen equipment etc.

 

 

What is a Single-Phase Induction Motor?

 

A single-phase induction motor is an induction motor designed to operate on single-phase AC supply. These motors are used in low power applications, as discussed above, and are available in fractional kilowatt ratings, hence also known as fractional kilowatt Motors. 

 

Construction of Single-Phase Induction Motor

 

Like any other electric motor, a single-phase induction motor consists of two main parts i.e. stator and rotor. The stator is the stationary part and rotor is the rotating part. 

 

The stator of the single-phase induction motor is wound by a single-phase distributed winding and the rotor used in the single-phase induction motor is essentially a squirrel cage rotor. 

 

For detailed explanation about construction of stator and rotor of induction motor refer to induction motor basics.

 

Working of Single-Phase Induction Motor

 

The basic working principle for all the induction machines is the same, that is based on Faraday's Law of Electromagnetic Induction, where the torque is developed by the interaction of stator magnetic field (produced by the given AC supply) and rotor magnetic field (produced by the current flows in the short-circuited rotor conductor).

 

In a single-phase induction motor, when single phase AC supply is applied to stator winding, it produces a sinusoidally distributed rotating magnetic field in the air gap, whose amplitude is pulsating in nature.

 

This rotating magnetic field rotates at synchronous speed in the air gap and cuts the rotor conductor which induces voltage and current in the rotor conductor. 

 

This Induced current in the rotor conductor produces its own magnetic field which interacts with the stator magnetic field, similarly to three phase induction motors. However, in the case of a single-phase AC supply, the motor fails to start on its own (as explained in double revolving field theory discussed below). 

Double Revolving Field Theory

 

According to double revolving field theory, the pulsating magnetic field produced by single phase winding contains two components of equal magnitude, rotating at synchronous speed in opposite directions: one in forward direction and the other in the backward direction.

As discussed above, when a single-phase AC supply is applied to the stator winding, it produces sinusoidally distributed MMF whose peak value pulsates with time.

 

The equation represents the sinusoidally distributed MMF in the air gap is

F = F_peak Cos θ

where, θ is the angle measured from the axis of winding.

 

Since the peak value of the MMF pulsates with time, we can express it as:

F_peak  =  F_max cos ωt

Substituting this value in the MMF equation, we get, 

 

F  =  F_max cos θ . cosωt

 

Using Trigonometric identities, this expands to:

 

F = ½ F_max cos (θ - ωt)  +  ½ F_max cos(θ + ωt)

 

By observing the above equation, we can conclude that the magnetic field produced by the single-phase winding comprises two components of equal magnitude, 

 

• One is forward magnetic field, rotates in forward direction at synchronous speed,  Ff = ½ F_max cos (θ - ωt)

 

• And the other is a backward field, rotates in backward direction at synchronous speed,  Fb = ½ F_max cos(θ + ωt)

 

Since there are two magnetic fields having the same magnitude forward magnetic field and backward magnetic field. The forward magnetic field produces forward torque which tends the rotor to rotate in forward direction similarly, backward field produces backward torque which tends the rotor to rotate in backward direction. As these torques is equal, they cancel out each other, preventing the motor from starting. That's why we say that single phase induction motors are not self-starting. 

 

However, if any external force is applied in any direction, the motor will continue to rotate in that direction. This characteristic allows a single-phase induction motor to operate in both directions.

Single Phase Induction Motor Slip

As we discussed above, the rotating magnetic field generated by single phase winding consists of two components: the forward field and the backward field.  These two fields rotate in opposite directions at synchronous speed Ns.

Now, let us say that the rotor rotates in forward field direction at a speed N. In this case the slip of the rotor with respect to the forward rotating field can be expressed as follows.

Sf (Forward Slip)  =  (Ns - N)  / Ns    =   s   (similar to the slip in three phase phase induction motor)

 

And the slip of the rotor with respect to the backward rotating field can be expressed as

Similarly, if the rotor rotates in the direction of the backward field, the slip of the rotor with respect to the backward field is s, while the slip of the rotor with respect to the forward field is (2 - s). 

 

Therefore, the rotor slip in the case of a single phase induction motor with respect to the two rotating magnetic fields are different and are given by the equation (1) and (2) above.

Torque Slip Characteristics of Single-Phase Induction Motor

As we know, the torque equation of the induction motor is (refer Torque in Three Phase Induction Motor)

Now as we at the starting of the single-phase induction motor, the speed of the rotor is zero (N = 0). So, the forward slip and the backward slip is equal to 1 (calculated from the equations (1) & (2)).

Since the forward field and backward field are the same i.e. equals to 1, it means that the two rotating magnetic fields induce equal currents in the squirrel cage rotor. Consequently, these two fields produce equal torque in opposite directions, which cancel out each other, resulting in the net starting torque being zero. Thus, we can say that the single-phase induction motors are non self starting.

 

As, sb = sf = 1, then Tf  =  Tb 

However, if the rotor is made to rotate at a speed N in any direction by any external means. Then these two slips become different (i.e. s and 2 - s). In this condition the backward slip (2 - s) is significantly greater than the forward slip s. 

Note :-  In running condition N is nearly equal to Ns and s is nearly equal to zero.

As a consequence, the backward field induces a much larger rotor current compared to standstill and has a lower power factor. Due to this large induced current, the rotor produces a stronger magnetic field which opposes the backward field significantly, resulting in the substantial reduction of the backward field.

On the other hand, the low slip forward rotating field induces smaller current of higher power factor in the rotor than at stand still. This leads to the greater enhancement in the forward flux wave.

This reduction in the backward field and strengthening of the forward field is slip dependent. As the speed of the rotor increases, the forward slip decreases and the backward slip increases, which leads to the greater reduction of the backward field and the strengthening of the forward field.  In fact, at a speed close to the synchronous speed, the forward field may be several times stronger than the backward field. As a result, there is a net running toque.

As we have discussed in the above section, there are two magnetic fields: forward magnetic field and the backward magnetic field and each of these magnetic fields generate its own torques. So, the complete torque-slip characteristics is the sum of the torque speed characteristics due to these two fields. And resultant of these two characteristics represents the final torque slip characteristics of the single-phase induction motor

Below the given figure illustrate the complete torque slip characteristics of a single-phase induction motor. 

The weakening of one field and simultaneous strengthening of the other field leads to the torque speed characteristics of a single-phase induction motor like that of a 3-phase induction motor in the speed region close to synchronous speed.  The fact of zero starting torque or non self-starting nature of single phase induction motor can be clearly seen in the resultant torque slip characteristics of single phase induction motor.