## Three Phase Induction Motor

**1.Introduction**An electric motor is a device which converts an electrical energy into a

mechanical energy. The motors operating on a.c. supply are called a.c.

motor. As a.c. supply is commonly available, the a.c. motors are very

popularly used in practice. The a.c. motors are classified as three

phase induction motors, single phase induction motor, universal motors,

synchronous motors etc. The three phase induction motors are widely used

for various industrial application. The important features of three

phase induction motors are self starting, higher power factor, good

speed regulation and robust construction. This chapter explains the

construction, working principle and characteristics of three phase

induction motors as well as universal motors. The working of three phase

induction motors is based on the principle of rotating magnetic field.

Let us discuss, the production of rotating magnetic field.

__2. Rotating Magnetic field (R.M.F.)__The rotating magnetic field can be defined as the field or flux having

constant amplitude but whose axis is continuously rotating in a plane

with a certain speed. So if the arrangement is made to rotate a

permanent magnet, then the resulting field is a rotating magnetic field.

But ion this method, it is necessary to rotate a magnet physically to

produce rotating magnetic field.

But in three phase induction motors such a rotating magnetic field is

produced by supplying currents to a set of stationary windings, with the

help of three phase a.c. supply. The current carrying windings produce

the magnetic field or flux. And due to interaction of three phase fluxes

produced due to three phase supply, resultant flux has a constant

magnitude and its axis rotating in space, without physically rotating

the windings. This type of field is nothing but rotating magnetic field.

Let us study how it happens.

**2.1 Production of R.M.F.**A three phase induction motor consists of three phase winding as its

stationary part called stator. The three phase stator winding is

connected in star or delta. The three phase windings are displaced from

each other by 120^{o}. The windings are supplied by a balanced

three phase a.c. supply. This is shown in the Fig. 1. The three phase

windings are denoted as R-R’ , Y-Y’ and B-B’.

Fig. 1 Star or delta connected 3phase winding |

^{o}

electrical. Each alternating phase current produces its own flux which

is sinusoidal. So all three fluxes are sinusoidal and are separated from

each other by 120

^{o}. If the phase sequence of the windings is R-Y-B, then mathematical equations for the instantaneous values of the three fluxes ?

_{R }, ?

_{Y }and ?

_{B }can be written as,

_{R }= ?

_{m }sin(?t) = ?

_{m }sin ? ………..(1)

_{Y }= sin (?t – 120

^{o}) = ?

_{m }sin (? – 120

^{o}) …………(2)

_{B }= ?

_{m }sin (?t – 240

^{o}) = ?

_{m }sin (? – 240

^{o}) ………….(3)

_{m}. Due to phase sequence R-Y-B, flux lags behind ?

_{R }by 120

^{o}and ?

_{B }lags ?

_{Y }by 120

^{o}. So ?

_{B }ultimately lags ?

_{R }by 240

^{o}. The flux ?

_{R }is taken as reference while writing the equations.

The Fig. 2(a) shows the waveforms of three fluxes in space. The

Fig.2(b) shows the phasor diagram which clearly shows the assumed

positive directions of each flux. Assumed positive direction means

whenever the flux is positive it must be represented along the direction

shown and whenever the flux is negative it must be represented along

the opposite direction to the assumed positive direction.

_{R}, ?

_{Y }and ?

_{B }be the instantaneous values of the three fluxes. The resultant flux ?

_{T }is the phasor addition of ?

_{R}, ?

_{Y }and ?

_{B}.

_{T }at the instants 1, 2, 3 and 4 as shown in the Fig. 2(a) which represents the values of ? as 0

^{o}, 60

^{o}, 120

^{o}and 180

^{o}respectively. The phasor addition can be performed by obtaining the values of ?

_{R}, ?

_{Y }and ?

_{B }by substituting values of ? in the equation (1), (2) and (3).

Fig. 2 |

**Case 1 **: ? = 0^{o}

Substituting in the equations (1), (2) and (3) we get,

?_{R }= ?_{m } sin 0^{o} = 0

?_{Y } = ?_{m } sin(-120^{o} ) = -0.866 ?_{m }

?_{B }= ?_{m } sin (-240^{o}) = + 0.866 ?_{m }

Fig. 3(a) Vector diagram of ? = 0^{o} |

addition is shown in the Fig. 3(a). The positive values are are shown in

assumed positive directions while negative values are shown in opposite

direction to the assumed positive directions of the respective fluxes.

Refer to assumed positive directions shown in the Fig 3(b).

BD is drawn perpendicular from B on ?_{T}. It bisects ?_{T}.

**. ^{.}. **OD = DA = ?

_{T}/2

^{o}

**.**cos 30

^{.}.^{o}= OD/OB = (?

_{T}/2)/(0.866 ?

_{m })

**.**?

^{.}._{T }= 2 x 0.866 ?

_{m }x cos 30

^{o}

_{m }

_{T }is 1.5 ?

_{m }and its position is vertically upwards at ? = 0

^{o}.

**Case 2**? = 60

^{o}

_{R }= ?

_{m }sin 60

^{o }= +0.866 ?

_{m }

_{Y }= ?

_{m }sin (-60

^{o}) = -0866 ?

_{m }

_{B }= ?

_{m }sin (-180

^{o}) = 0

_{R }is positive and ?

_{Y }is negative and hence drawing in appropriate directions we get phasor diagram as shown in the Fig. 3(b).

Fig 3(b) Vector diagram of ? = 60^{o} |

_{T }= 1.5 ?

_{m }

^{o }in space, in clockwise direction, from its previous position.

**Case 3 :**? = 120

^{o}

_{R }= ?m sin 120

^{o}= +0.866 ?m

_{Y }= ?m sin 0

^{o}= 0

_{B }= ?m sin (-120

^{o}) = -0.866 ?m

_{R }is positive and ?

_{B }is negative. showing ?

_{R }and ?

_{B }in the appropriate directions, we get the phasor diagram as shown in the Fig . 3(c).

Fig. 3(c) Vector diagram of ? = 120^{o} |

_{T}, it can be provided again that,

_{T }= 1.5 ?m

_{T }is such that it has rotated further through 60

^{o }from its previous position, in clockwise direction. And from its position at ? = 0

^{o}, it has rotated through 120

^{o}in space, in clockwise direction.

**Case 4**: ? = 180

^{o}

_{R }= ?m sin (180

^{o}) = 0

_{Y }= ?m sin (60

^{o}) = +0.866 ?m

_{B }= ?m sin (-60

^{o})

Fig. 3(d) Vector diagram of ? = 180^{o} |

_{R }= 0 , ?

_{Y }is positive and ?

_{B }is negative. Drawing ?

_{Y }and ?

_{B }in the appropriate directions, we get the phasor diagram as shown in the Fig. 3(d).

_{T }= 1.5 ?m

_{T }once again remains same. But it can be seen that it has further rotated through 60

^{o}from its previous position in clockwise direction.

^{o}, the resultant ?

_{T }has also rotated through . This is applicable for the windings from the above discussion we have following conclusions :

The resultant of the three alternating fluxes, separated from each

other by , has a constant amplitude of 1.5 ?m where ?m is maximum

amplitude of an individual flux due to any phase.

**Key point**:

This shows that when a three phase stationary windings are excited by

balanced three phase a.c. supply then the resulting field produced is

rotating magnetic field. Though nothing is physically rotating, the

field produced is rotating in space having constant amplitude.

**2.2 Speed of R.M.F.**There exists a fixed relation between frequency f of a.c. supply to the

windings, the number of poles P for which winding is wound and speed N

r.p.m. of rotating magnetic field. For a standard frequency whatever

speed of R.M.F. results is called synchronous speed, in case of

induction motors. It is denoted as .

direction of the R.M.F. is always from the axis of the leading phase of

the three phase winding towards the lagging phase of the winding. In a

phase sequence of R-Y-B, phase R leads Y by 120

^{o}and Y leads B by120

^{o}.

So R.M.F. rotates from axis of R to axis of Y and then to axis of B and

so on. So its direction is clockwise as shown in the Fig. 4(a). This

direction can be reversed by interchanging any two terminals of the

three phase windings while connecting to the three phase supply. The

terminals Y and B are shown interchanged in the Fig. 4(b). In such case

the direction of R.M.F. will be anticlockwise.

As Y and B of windings are connected to B and Y from winding point of

view the phase sequence becomes R-Y-B. Thus R.M.F. axis follows the

direction from R to B to Y which is anticlockwise.

**Key point**:

Thus by interchanging any two terminals of three phase winding while

connecting it to three phase a.c. supply, direction of rotation of

R.M.F. gets reversed.

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