Unit - 4
Single-phase induction motor
Construction:
Like any other electrical motor asynchronous motor also have two main parts namely rotor and stator.
1. Stator:
As its name indicates stator is a stationary part of the induction motor. A single-phase AC supply is given to the stator of a single-phase induction motor.
2. Rotor:
The rotor is a rotating part of an induction motor. The rotor connects the mechanical load through the shaft. The rotor in the single-phase induction motor is of squirrel cage rotor type.
The construction of a single-phase induction motor is almost similar to the squirrel cage three-phase induction motor. But in the case of a single-phase induction motor, the stator has two windings instead of one three-phase winding in a three-phase induction motor.
4.1.1 Stator of Single-Phase Induction Motor
1. The stator of the single-phase induction motor has laminated stamping to reduce eddy current losses on its periphery.
2. The slots are provided on its stamping to carry stator or main winding. Stampings are made up of silicon steel to reduce the hysteresis losses.
3. When we apply a single-phase AC supply to the stator winding, the magnetic field gets produced, and the motor rotates at speed slightly less than the synchronous speed Ns. Synchronous speed Ns is given by
Where,
f = supply voltage frequency,
P = No. Of poles of the motor.
4. The construction of the stator of the single-phase induction motor is similar to that of a three-phase induction motor except there are two dissimilarities in the winding part of the single-phase induction motor.
5. Firstly, the single-phase induction motors are mostly provided with concentric coils. We can easily adjust the number of turns per coil can with the help of concentric coils. The mmf distribution is almost sinusoidal.
6. Except for the shaded pole motor, the asynchronous motor has two stator windings namely the main winding and the auxiliary winding. These two windings are placed in space quadrature to each other.
4.1.2 Rotor of Single Phase Induction Motor
1. The construction of the rotor of the single-phase induction motor is similar to the squirrel cage three-phase induction motor.
2. The rotor is cylindrical and has slots all over its periphery.
3.The slots are not made parallel to each other but are a little bit skewed as the skewing prevents magnetic locking of stator and rotor teeth and makes the working of induction motor more smooth and quieter (i.e. less noisy).
4. The squirrel cage rotor consists of aluminium, brass, or copper bars. These aluminium or copper bars are called rotor conductors and placed in the slots on the periphery of the rotor. The copper or aluminium rings permanently short the rotor conductors called the end rings.
5. To provide mechanical strength, these rotor conductors are braced to the end ring and hence form a complete closed circuit resembling a cage and hence got its name as squirrel cage induction motor.
6. As end rings permanently short the bars, the rotor electrical resistance is very small and it is not possible to add external resistance as the bars get permanently shorted. The absence of slip ring and brushes make the construction of single-phase induction motor very simple and robust.
Fig 1. Constructional features
Key takeaways:
1. The slots are provided on its stamping to carry stator or main winding. Stampings are made up of silicon steel to reduce the hysteresis losses.
2. To provide mechanical strength, these rotor conductors are braced to the end ring and hence form a complete closed circuit resembling a cage and hence got its name as squirrel cage induction motor.
1. The double-revolving field theory of a single-phase induction motor states that a pulsating magnetic field is resolved into two rotating magnetic fields.
2. They are equal in magnitude but opposite in directions. The induction motor responds to each of the magnetic fields separately.
3. The net torque in the motor is equal to the sum of the torque due to each of the two magnetic fields.
The equation for an alternating magnetic field is given as:
4. Where βmax is the maximum value of the sinusoidally distributed air-gap flux density produced by a properly distributed stator winding carrying an alternating current of the frequency ω, and α is the space displacement angle measured from the axis of the stator winding.
As we know,
)
So, the equation (1) can be written as
5. The first term of the right-hand side of the equation (2) represents the revolving field moving in the positive α direction. It is known as a Forward Rotating field. Similarly, the second term shows the revolving field moving in the negative α direction and is known as the Backward Rotating field.
6. The direction in which the single-phase motor is started initially is known as the positive direction. Both the revolving field rotates at the synchronous speed. ωs = 2πf in the opposite direction. Thus, the pulsating magnetic field is resolved into two rotating magnetic fields. Both are equal in magnitude and opposite in direction but at the same frequency.
7. At the standstill condition, the induced voltages are equal and opposite as a result; the two torques are also equal and opposite. Thus, the net torque is zero and, therefore, a single-phase induction motor has no starting torque.
Fig 2. Double revolving field theory
Key takeaways:
1. The net torque in the motor is equal to the sum of the torque due to each of the two magnetic fields.
2. At the standstill condition, the induced voltages are equal and opposite as a result; the two torques are also equal and opposite.
1. The equivalent circuit of any machine shows the various parameter of the machine such as its Ohmic losses and also other losses.
2. The losses are modeled just by inductor and resistor.
3. The copper losses have occurred in the windings so the winding resistance is taken into account. Also, the winding has inductance for which there is a voltage drop due to inductive reactance, and also a term called power factor comes into the picture. There are two types of equivalent circuits in the case of a three-phase induction motor-
Exact Equivalent Circuit
Fig 3. Equivalent Circuit
Here, R1 is the winding resistance of the stator.
X1 is the inductance of the stator winding.
Rc is the core loss component.
XM is the magnetizing reactance of the winding.
R2/s is the power of the rotor, which includes output mechanical power and copper loss of the rotor.
If we draw the circuit with referred to the stator then the circuit will look like-
Fig 4. Equivalent circuit
Here all the other parameters are the same except-
R2’ is the rotor winding resistance referred to as stator winding.
X2’ is the rotor winding inductance referred to as stator winding.
R2 (1 – s) / s is the resistance that shows the power which is converted to mechanical power output or useful power. The power dissipated in that resistor is the useful power output or shaft power.
4. The approximate equivalent circuit is drawn just to simplify our calculation by deleting one node. The shunt branch is shifted towards the primary side.
5. This has been done as the voltage drop between the stator resistance and inductance is less and there is not much difference between the supply voltage and the induced voltage.
However, this is not appropriate due to the following reasons-
1. The magnetic circuit of the induction motor has an air gap so the exciting current is larger compared to the transformer so an exact equivalent circuit should be used.
2. The rotor and stator inductance is larger in the induction motor.
3. In an induction motor, we use distributed windings.
4. This model can be used if the approximate analysis has to be done for large motors. For smaller motors, we cannot use this.
Key takeaways:
1. The winding has inductance for which there is a voltage drop due to inductive reactance and also a term called power factor comes into the picture.
2. This has been done as the voltage drop between the stator resistance and inductance is less and there is not much difference between the supply voltage and the induced voltage.
3. The magnetic circuit of the induction motor has an air gap so the exciting current is larger compared to the transformer so an exact equivalent circuit should be used.
1. A stationary pulsating magnetic field might be resolved into two rotating fields, both having equal magnitude but opposite in direction.
2. So the net torque induced is zero at standstill. Here, the forward rotation is called the rotation with slip s, and the backward rotation is given with a slip of (2 – s). The equivalent circuit is-
Fig 5. Equivalent circuit
3. In most cases the core loss component r0 is neglected as this value is quite large and does not affect much in the calculation.
4. Here, Zf shows the forward impedance and Zb shows the backward impedance.
Also, the sum of forwarding and backward slip is 2 so in case of a backward slip, it is replaced by (2 – s).
R1 = Resistance of the stator winding.
X1 = Inductive reactance of the stator winding.
Xm = Magnetising reactance.
R2’ = Rotor Reactance with referred to the stator.
X2’ = Rotor inductive reactance with referred to the stator.
Key takeaways:
1. A stationary pulsating magnetic field might be resolved into two rotating fields, both having equal magnitude but opposite in direction
2. The net torque induced is zero at a standstill
1. The Split Phase Motor is also known as a Resistance Start Motor. It has a single cage rotor, and its stator has two windings known as main winding and starting winding.
2. Both the windings are displaced 90 degrees in space. The main winding has very low resistance and a high inductive reactance whereas the starting winding has high resistance and low inductive reactance.
3. Split-Phase-Induction-Motor-resistor is connected in series with the auxiliary winding. The current in the two windings is not equal as a result the rotating field is not uniform.
4. Hence, the starting torque is small, of the order of 1.5 to 2 times of the starting running torque. At the starting of the motor both the windings are connected in parallel.
5. As soon as the motor reaches the speed of about 70 to 80 % of the synchronous speed the starting winding is disconnected automatically from the supply mains.
6. If the motors are rated about 100 Watt or more, a centrifugal switch is used to disconnect the starting winding and for the smaller rating motors relay is used for the disconnecting of the winding.
7. A relay is connected in series with the main winding. In the starting, the heavy current flows in the circuit, and the contact of the relay gets closed.
8. Thus, the starting winding is in the circuit, and as the motor attains the predetermined speed, the current in the relay starts decreasing. Therefore, the relay opens and disconnects the auxiliary winding from the supply, making the motor runs on the main winding only.
The phasor diagram of the Split Phase Induction Motor is shown below.
Fig 6. Schematic diagram and phasor diagram of split-phase induction motor
9. Split-Phase-Induction-Motor-The current in the main winding (IM) lag behind the supply voltage V almost by the 90-degree angle. The current in the auxiliary winding IA is approximately in phase with the line voltage.
10. Thus, there exists a time difference between the currents of the two windings. The time phase difference ϕ is not 90 degrees, but of the order of 30 degrees. This phase difference is enough to produce a rotating magnetic field.
Applications of Split Phase Induction Motor
This type of motors are cheap and are suitable for easily starting loads where the frequency of starting is limited. This type of motor is not used for drives that require more than 1 KW because of the low starting torque. The various applications are as follows:
1. Used in the washing machine, and air conditioning fans.
2. The motors are used in mixer grinder, floor polishers.
3. Blowers, Centrifugal pumps
4. Drilling and lathe machine.
Key takeaways:
1. As soon as the motor reaches the speed of about 70 to 80 % of the synchronous speed the starting winding is disconnected automatically from the supply mains.
2. This type of motor is not used for drives that require more than 1 KW because of the low starting torque
References:
1. A. E. Fitzgerald and C. Kingsley, "Electric Machinery”, McGraw Hill Education,2013.
2. M. G. Say, “Performance and design of AC machines”, CBS Publishers,2002.
3. P. S. Bimbhra, “Electrical Machinery”, Khanna Publishers,2011.
4. I. J. Nagrath and D. P. Kothari, “Electric Machines”, McGraw Hill Education,2010.
5. A. S. Langsdorf, “Alternating current machines”, McGraw Hill Education,1984.
6. P. C. Sen, “Principles of Electric Machines and Power Electronics”, John Wiley & Sons,2007.
