Electrical Machines : Single & Three Phase Induction Motors

By Yash Bansal|Updated : May 19th, 2021

Electrical Machines : Single & Three Phase Induction Motors








In this article, you will find the study notes on Three Phase Induction machine and Single Phase Induction machine.

3-Phase Induction Machine

  • Basically an induction motor (IM) is a type of asynchronous AC motor where power is supplied to the rotating device by means of electromagnetic induction.
  • Technological development in the field has improved to where a 100 hp (74.6 kW) motor from 1976 takes the same volume as a 7.5 hp (5.5 kW) motor did in 1897. Currently, the most common induction motor is the cage rotor motor.
  • In an induction motor is sometimes called a rotating transformer because the stator (stationary part) is essentially the primary side of the transformer and the rotor (rotating part) is the secondary side. Induction motors are widely used, especially polyphase induction motors, which are frequently used in industrial drives.
  • Induction motors are now the preferred choice for industrial motors due to their rugged construction, absence of brushes (which are required in most DC motors) and the ability to control the speed of the motor.
  • It is a single excited AC machine. Its stator winding is directly connected to AC source, whereas its rotor winding receives its energy from f stator by means of induction (i.e., transformer action).

Type of rotors Rotor 

  • Squirrel cage rotor
  • Wound rotor

Squirrel-Cage Rotor
In the squirrel-cage rotor, the rotor winding consists of single copper or aluminium bars placed in the slots and short-circuited by end-rings on both sides of the rotor. Most of single phase induction motors have Squirrel-Cage rotor. One or 2 fans are attached to the shaft in the sides of rotor to cool the circuit.


Wound Rotor


  • In the wound rotor, an insulated 3-phase winding similar to the stator winding wound for the same number of poles as stator, is placed in the rotor slots. The ends of the star-connected rotor winding are brought to three slip rings on the shaft so that a connection can be made to it for starting or speed control. It is usually for large 3 phase induction motors.
  • Compared to squirrel cage rotors, wound rotor motors are expensive and require maintenance of the slip rings and brushes, so it is not so common in industry applications.
  • Rotor has a winding the same as stator and the end of each phase is connected to a slip ring.


An AC current is applied in the stator armature which generates a flux in the stator magnetic circuit.This flux induces an emf in the conducting bars of rotor as they are “cut” by the
flux while the magnet is being moved (E = BVL (Faraday’s Law)),A current flows in the rotor circuit due to the induced emf, which in term produces a force, (F = BIL) can be changed to the torque as the output.


  • In a 3-phase induction motor, the three-phase currents Ia, Ib and Ic, each of equal magnitude, but differing in phase by 120°. Each phase current produces a magnetic flux
    and there is physical 120 °shift between each flux.
  • The summation of the three ac fluxes results in a rotating flux, which turns with constant speed and has constant amplitude. Such a magnetic flux produced by balanced three phase currents flowing in thee-phase windings is called a rotating magnetic flux or rotating magnetic field (RMF).
  • RMF rotates with a constant speed (Synchronous Speed). Existence of a RFM is an essential condition for the operation of an induction motor. If stator is energized by an ac current, RMF is generated due to the applied current to the stator winding.
  • This flux produces magnetic field and the field revolves in the air gap between stator and rotor. So, the magnetic field induces a voltage in the short circuited bars of the rotor. This voltage drives current through the bars.
  • The interaction of the rotating flux and the rotor current generates a force that drives the motor and a torque is developed consequently. The torque is proportional with the flux density and the rotor bar current (F=BLI).
  • The motor speed is less than the synchronous speed. The direction of the rotation of the rotor is the same as the direction of the rotation of the revolving magnetic field in the air gap.



Per phase induced emf In stator winding, E1 = 4.44 Nlf1φkω1 volt

In rotor winding, E2 = 4.44 N2f2φkω2 volt

where  and  = Winding factors of stator and rotor winding

N1 = Number of turns in stator winding

N2 = Number of turns in rotor winding

f1 and f2 = Frequencies of supply in stator and rotor windings respectively.

Slip: The difference between the synchronous speed (Ns) and the actual rotor speed (Nr).


where, Ns = Synchronous speed

Nr = Rotor speed

Equivalent Circuit of an Induction Motor:

The energy is transferred from primary (stator) winding to secondary (rotor) winding entirely by induction therefore, induction motor is essentially a transformer. At standstill, the induction motor is actually a static transformer having its secondary (rotor) winding short-circuited.

Here, stator emf per phase   image005

where, N1 = Number of stator turns per phase

φ = Flux per pole

 = Stator winding factor

Rotor emf at standstill  image007

∴ image008

where, image009 = Effective stator turns per phase = image010

 image011= Effective rotor turns per phase =  image012

a = Reduction factor




sE2 = I2R2 + jI2sX2 or  image016


Rotor equivalent circuit

Rotor Torque: The torque developed by the rotor of an induction motor is directly proportional to (a) rotor current l2 (b) stator flux per pole φ and (c) power factor of the rotor circuit cos φ2

∵ T ∝ φl2 cos φ2

But E ∝ φ

T ∝ E2l2 cos φ2

or T = kE2l2 cos φ2 where k is constant.

Rotor Frequency: In rotor the frequency of current and voltage must be same as the supply frequency 

         fr = sf

       where, f = Supply frequency.


There are two important factors to be considered in starting of induction motors:

  • The starting current drawn from the supply, and
  • The starting torque. 

The starting current should be kept low to avoid overheating of motor and excessive voltage drops in the supply network. The starting torque must be about 50 to 100% more than the expected load torque to ensure that the motor runs up in a reasonably short time.

  • At synchronous speed, s = 0, and therefore , R2/s =∞⇒so I2' = 0.The stator current therefore comprises only the magnetising current i.e. I1 = Iφ and is quite therefore quite small. 
  • At low speeds, R2'/X + jX2= ∞ is small, and therefore I2' is quite high and consequently I1 is quite large.
  • Actually the typical starting currents for an induction machine are ~ 5 to 8 times the normal running current.

Hence the starting currents should be reduced. The most usual methods of starting 3-phase induction motors are:

  • Rotor resistance starting For slip-ring motors
  • For squirrel-cage motors
    (i)   Direct-on -line starting
    (ii)  Star-delta starting
    (iii) Autotransformer starting.

Rotor Resistance Starting 


  • By adding eternal resistance to the rotor circuit any starting torque up to the maximum torque can be achieved; and by gradually cutting out the resistance a high torque can be maintained throughout the starting period.
  • The added resistance also reduces the starting current, so that a starting torque in the range of 2 to 2.5 times the full load torque can be obtained at a starting current of 1 to 1.5 times the full load current.

Direct-On-Line Starting


  • This is the most simple and inexpensive method of starting a squirrel cage induction motor. The motor is switched on directly to full supply voltage. The initial starting current is large, normally about 5 to 7 times the rated current but the starting torque is likely to be 0.75 to 2 times the full load torque.
  • To avoid excessive supply voltage drops because of large starting currents the method is restricted to small motors only.
  • To decrease the starting current cage motors of medium and larger sizes are started at a reduced supply voltage.

Star-Delta starting


  • This is applicable to motors designed for delta connection in normal running conditions. Both ends of each phase of the stator winding are brought out and connected to a 3-phase change -over switch.
  • For starting, the stator windings are connected in star and when the machine is running the switch is thrown quickly to the running position, thus connecting the motor in delta for normal operation.
  • The phase voltages & the phase currents of the motor in star connection are reduced to 1/√3 of the direct -on -line values in delta. The line current is 1/3 of the value in delta.
  • A disadvantage of this method is that the starting torque (which is proportional to the square of the applied voltage) is also reduced to 1/3 of its delta value.

Auto-Transformer Starting


  • This method also reduces the initial voltage applied to the motor and therefore the starting current and torque.The motor,which can be connected permanently in delta or in star, is switched first on reduced voltage from a 3-phase tapped auto -transformer and when it has accelerated sufficiently, it is switched to the running (full voltage) position.
  • The principle is similar to star/delta starting and has similar limitations. The advantage of the method is that the current and torque can be adjusted to the required value, by taking the correct tapping on the autotransformer. This method is more expensive because of the additional autotransformer.

Starting Torque: The torque developed the motor at the instant of starting is called starting torque.


image020 or 


where, image022

Ns = Synchronous speed in RPS

E2 = Rotor emf per phase at standstill

R2 = Rotor resistance per phase

X2 = Rotor reactance per phase at standstill

  • Condition for maximum starting torque

R2 = X2

  • Starting torque, Tst ∝ (supply voltage)2

Tst ∝ V2

Torque Under Running Conditions


Key Points

  • Condition for maximum torque under running conditions R2 = sX2
  • Slip corresponding to maximum torque  s = R2/X2
  • Maximum torque 


Full Load Torque and Maximum Torque


where image027

Sf = Slip corresponding to full load torque

Note In general, image028

Starting Torque and Maximum Torque


where image030 per phase

Rotor Torque and Breakdown Torque: The rotor torque at any slip s can be expressed in .terms of the maximum torque


where, Tb = Maximum (or breakdown) torque

sb = Breakdown or pull out slip

No Load Test:

Power input = P0

No load current = I0 (average of 3 ammeter reading)

Voltage = V0 (line to line voltage)


Im = I0 sin φ0

Ic = I0 cos φ0

Ro = Vo/I &  Xo = Vo/Im


Rotation loss  image035

Note: This test gives rotational losses and X0

Blocked Rotor Test: The shaft of the motor is clamped so that it cannot move and rotor winding is short-circuited.

VBR = Stator voltage (line to line) required to circulate IBR when rotor is blocked.

IBR = Stator current (average of three ammeter reading)

PBR = Total copper loss on full load at standstill

Blocked rotor impedance  image036

Blocked rotor resistance image037

Blocked rotor reactance image038


  • image039
  • image040

Speed Control of Induction Motors: The rotor speed of an induction motor is given by

Nr = (1 – s)Ns and  Ns = 120f/P

also image042


Speed Control by Frequency Changing: The synchronous speed of an induction motor is given by


The synchronous speed and therefore, the speed of the motor can be controlled by varying the supply frequency. The emf induced it the stator of the induction motor is given by


Speed Control by Pole Changing: The number of stator poles can be changed by (a) multiple stator windings, (b) method of consequent poles and (c) Pulse-Amplitude Modulation (PAM).

  • Sometimes induction machines have a special stator winding capable of being externally connected to form two different number of pole numbers. Since the
    synchronous speed of the induction machine is given by ns = f.s/p (in rev./s).

where p is the number of pole pairs, this would correspond to changing the synchronous speed.With the slip now corresponding to the new synchronous speed, the operating speed is changed.

  • This method of speed control is a stepped variation and generally restricted to two steps. If the changes in stator winding connections are made so that the air gap flux remains constant, then at any winding connection, the same maximum torque is achievable. Such winding arrangements are therefore referred to as constant-torque connections.
  • If however such connection changes result in air gap flux changes that are inversely proportional to the synchronous speeds, then such connections are called
    constant-horsepower type.

Speed Control by Slip Changing: There are three ways of controlling slip. (i) Voltage control, (ii) Rotor-resistance control, (iii) Secondary foreign voltage control, and (iv) Speed control by cascade arrangement.

Voltage control

From the torque equation of the induction machine, we can see that the torque depends on the square of the applied voltage. The variation of speed torque curves with respect to the applied voltage is shown in figure below. These curves show that the slip at maximum torque remains same, while the value of stall torque comes down with decrease in applied voltage. The speed range for stable operation remains the same. 


  • Further, we also note that the starting torque is also lower at lower voltages. Thus,even if a given voltage level is sufficient for achieving the running torque, the machine may not start. This method of trying to control the speed is best suited for loads that require very little starting torque, but their torque requirement may increase with speed.

In this article, you will find the study notes on Electric Drives which will cover the topics such as Electric drives Principle , Electric drives D.C Machines ,4-Quadrant D.C Motor,Application of Electric Drives,Advantage of Electric drives.

Rotor Resistance Control

From the expression for the torque of the induction machine, torque is dependent on the rotor resistance. The maximum value is independent of the rotor resistance. The slip at maximum torque is dependent on the rotor resistance. Therefore, we may expect that if the rotor resistance is changed, the maximum torque point shifts to higher slip values, while retaining a constant torque. Figure below shows a family of torque-speed characteristic obtained by changing the rotor resistance. 


  • The resistors connected to the slip-ring brushes should have good power dissipation capability. Water based rheostats may be used for this. A ‘solid-state’ alternative to a rheostat is a chopper controlled resistance where the duty ratio control of of the chopper presents a variable resistance load to the rotor of the induction machine.

Principle of Operation of Single Phase Induction Motor

A single-phase induction motor is not self starting but requires some starting means.The single-phase stator winding produces a magnetic field that pulsates in strength in a sinusoidal manner. The field polarity reverses after each half cycle but the field does not rotate. Consequently, the alternating flux cannot produce rotation in a stationary squirrel-cage rotor. However, if the rotor of a single-phase motor is rotated in one direction by some mechanical means, it will continue to run in the direction of rotation. As a matter of fact, the rotor quickly accelerates until it reaches a speed slightly below the synchronous speed. Once the motor is running at this speed, it will continue to rotate even though single-phase current is flowing through the stator winding. This method of starting is generally not convenient for large motors.

The single-phase induction motor operation can be described by two methods

Cross-Field Theory


  • The principle of operation of a single-phase induction motor can be explained from the cross-field theory. As soon as the rotor begins to turn, a speed emf E is induced in the rotor conductors, as they cut the stator flux FS.
  • This voltage increases as the rotor speed increases. It causes current Ir to flow in the rotor bars facing the stator poles.
  • These currents produce an ac flux FR which act at right angle to the stator flux Fs. Equally important is the fact that FR does not reach its maximum value at the same time as FS does, in effect, FR lags almost 90o behind FS, owing to the inductance of the rotor The combined action of FS and FR produces a revolving magnetic field, similar to that in a three-phase motor.
  • The value of FR increases with increasing speed, becoming almost equal to FS at synchronous speed. The flux rotates counterclockwise in the same direction as the rotor and it rotates at synchronous speed irrespective of the actual speed of the rotor. As the motor approaches synchronous speed, FR becomes almost equal to FS and a nearly perfect revolving field is produces.

Double-Field Revolving Theory

  • When the stator winding carries a sinusoidal current which is being fed from a single-phase supply, a sinusoidal space distributed mmf, whose peak or maximum value pulsates (alternates) with time, is produced in the air gap.
  • The sinusoidal varying flux (φ) is the sum of two rotating fluxes or fields, the magnitude of which is equal to half the value of the alternating flux (φ/2), and both the fluxes rotating synchronously at the speed, in opposite directions.


  • The above figure show the resultant sum of the two rotating fluxes or fields, as the time axis (angle) is changing from θ=(0°-180°).


The above figure shows the alternating or pulsating flux (resultant) varying with time or angle.

Types of Single-Phase Motors

Single-phase motors are generally built in the fractional-horsepower range and may be classified into the following four basic types:

  • Single-phase induction motors
    (i) split-phase type (ii) capacitor start type (iii) capacitor start capacitor run type (iv) shaded-pole type
  • A.C. series motor or universal motor
  •  Repulsion motors
    (i) Repulsion-start induction-run motor (ii) Repulsion-induction motor
  •  Single Phase Synchronous motors/Reluctance Motor

Single-Phase Induction Motors

These motors are most commonly used in domestic, commercial and industrial applications such as in fans, refrigerators, mixers, vacuum cleaners, washing machines etc. These are small size motors of fractional kilowatt ratings. These motors are simpler in construction as compared to 3-phase but their analysis is more complex.

Equivalent Circuit of a Single-Phase Induction Motor

Let Rl = Resistance of the main stator winding

Xl = Leakage reactance of the main stator winding

Xm = Magnetizing reactance

R2 = Standstill rotor resistance referred to the main stator winding

X2 = standstill rotor leakage reactance referred to the main stator winding


The simplified equivalent circuit of a single-phase induction motor with only its main winding energized is shown in figure.


The current in the stator winding is:


Speed Torque Characteristic of Single Phase Induction Motor


Here we can assume that the rotor is started by spinning the rotor or by using auxiliary circuit, in say clockwise direction. The flux rotating in the clockwise direction is the forward rotating flux (φf) and that in the other direction is the backward rotating flux (φb).

  • The rotor rotates opposite to the rotation of the backward flux. If its slip with respect to forward field is s, what is the slip with respect to the backward field therefore, the slip w.r.t. the backward flux will be


Making Single-Phase Induction Motor Self-Starting

  • Since we have already know that the single-phase induction motor is not self starting and it is undesirable to resort to mechanical spinning of the shaft or pulling a belt to start it.
  • To make a single-phase induction motor self-starting, we should somehow produce a revolving stator magnetic field. This may be achieved by converting a single-phase supply into twophase supply through the use of an additional winding.
  • When the motor attains sufficient speed, the starting means (i.e., additional winding) may be removed depending upon the type of the motor.

Making Single-Phase Induction Motor Self-Starting

  • Since we have already know that the single-phase induction motor is not self-starting and it is undesirable to resort to the mechanical spinning of the shaft or pulling a belt to start it.
  • To make a single-phase induction motor self-starting, we should somehow produce a revolving stator magnetic field. This may be achieved by converting a single-phase supply into two-phase supply through the use of an additional winding.
  • When the motor attains sufficient speed, the starting means (i.e., additional winding) may be removed depending upon the type of the motor.

So as a matter of fact, single-phase induction motors are classified and named according to the method employed to make them self-starting.

  • Split-phase type 
  • Capacitor start type
  • Capacitor start capacitor run type
  • Shaded-pole type

(i) Split-Phase Type




  • The stator of a split-phase induction motor is provided with an auxiliary or starting winding S in addition to the main or running winding M.
  • The starting winding is located 90° electrical from the main winding and operates only during the brief period when the motor starts up.
  • The two windings are so resigned that the starting winding S has a high resistance and relatively small reactance while the main winding M has relatively low resistance and large reactance to be as inductance (the current delay with voltage) to make shifting current as shown in Figure.
  • Consequently, the currents flowing in the two windings have a reasonable phase difference  (25° to 30°) as shown in the pharos diagram this shifting in current its necessary for starting torque.


  • When the two stator windings are energized from a single-phase supply, the main winding carries current Im while the starting winding carries current Is.
  • Since main winding is made highly inductive while the starting winding highly resistive, the currents Im and Is have a reasonable phase angle a (25° to 30°) between them.
  • Consequently, a weak revolving field approximating to that of a 2-phase machine is produced which starts the motor.
  • When the motor reaches about 80% of synchronous speed, the centrifugal switch opens the circuit of the starting winding.
  • The motor then operates as a single-phase induction motor and continues to accelerate till it reaches the normal speed. The normal speed of the motor is below the synchronous speed and depends upon the load on the motor.

(ii) Capacitor Start Motor

The capacitor-start motor is identical to a split-phase motor except that the starting winding has as many turns as the main winding. The picture of capacitor start induction motor is shown in figure below,

Moreover, a capacitor C (3-20 µF) is connected in series with the starting winding as shown in Figure. The value of the capacitor is so chosen that IS leads Im by about 80° which is considerably greater than 25° found in the split-phase motor.




  • When the two stator windings are energized from a single-phase supply, the main winding carries current Im while the starting winding carries current IS.
  • Due to capacitance, the currents Im and Is have a reasonable phase angle an (80°) between them.
  • When starting torque is much more than that of a split-phase motor Again, the starting winding is opened by the centrifugal switch when the motor attains about 80% of synchronous speed.
  • The motor then operates as a single-phase induction motor and continues to accelerate till it reaches the normal speed.
  • Capacitor-start motors are used where high starting torque is required and where the starting period may be long e.g., to drive:

         (i) compressors (ii) large fans (iii) pumps (iv) high inertia loads The power rating of such motors lies between 120 W and 7-5 kW.

(iii) Capacitor Start-Capacitor Run  Motor

  • This motor is identical to a capacitor-start motor except that starting winding is not opened after starting so that both the windings remain connected to the supply when running as well as at starting.
  • Two designs are generally used
  1. In first it shows a picture of capacitor start capacitor run induction motor. This design eliminates the need for a centrifugal switch and at the same time improves the power factor and efficiency of the motor.
  2. In the other design, two capacitors C1 and C2 are used in the starting winding. The value of the capacitor is so chosen that Is leads Im by about 80°.



  • The smaller capacitor C1 required for optimum running conditions is permanently connected in series with the starting winding. The much larger capacitor C2 is connected in parallel with C1 for optimum starting and remains in the circuit during starting.
  • The starting capacitor C2 is disconnected when the motor approaches about 80% of synchronous speed. The motor then runs as a two-phase induction motor.


  • When the two stator windings are energized from a single-phase supply, the main winding carries current Im while the starting winding carries current Is.
  • Due to capacitance C1 the currents Im and Is have a reasonable phase angle an (80°) between them.
  • When The starting capacitor C2 is disconnected when the motor approaches about 80% of synchronous speed. The motor then runs as a two-phase induction motor.


  • The starting winding and the capacitor can be designed for perfect 2-phase operation at any load. The motor then produces a constant torque and not a pulsating torque as in other single-phase motors.
  • Because of constant torque, the motor is vibration free and can be used in: (a) hospitals (b) studios and (c) other places where silence is important.

(iv) Shaded-Pole Motor

The shaded-pole motor is very popular for ratings below 0.05 H.P. (~40 W) because of its
extremely simple construction. It has salient poles on the stator excited by single-phase supply
and a squirrel cage rotor as shown in Figure.
A portion of each pole is surrounded by a short-circuited turn of copper strip called shading



  • The reversal of the direction of rotation, where desired, can be achieved by providing two shading coils, one on each end of every pole, and by open-circuiting one set of shading coils and by short-circuiting the other set.
  • The above is true due to the fact that the shaded-pole motor is single-winding (no auxiliary winding) self-starting one, makes it less costly and results in rugged construction.
  • The motor has low efficiency and is usually available in a range of 1/300 to 1/20 kW. It is used for domestic fans, record players and tape recorders, humidifiers, slide projectors, small business machines, etc.
  • The shaded-pole principle is used in starting electric clocks and other single-phase synchronous timing motors.


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