Induction Motor

Lecture NotesDr. UD Dwivedi

Introduction Three-phase induction motors are the most common

and frequently encountered machines in industry Simple design, Low cost and rugged, requires little or no

skilled maintenance wide range of power ratings: fractional horsepower to

10 MW

Explosion free, due to the absence of a commutator or slip-rings and brushes with their associated sparking,

Run at nearly constant speed from zero-to-full – Its speed depends on the frequency of the power

source• not easy to have variable speed control • requires a variable-frequency power-electronic drive for

optimal speed control

Construction: has two main partsStator – consisting of a steel frame that supports a hollow,

cylindrical core of stacked laminations. Slots on the internal circumference of the stator house the stator winding.

Rotor – also composed of punched laminations, with rotor slots for the rotor winding.

StatorRotor

Induction Motor: Stator Stator is made from laminated iron 3 phase windings, 120° spatially apart (star/delta) Stator winding is carried in slots around the circumference of

a cylindrical bore. There is a separate winding for each phase.

Induction Motor: Rotor1. Squirrel-cage induction motor:

2. Wound-rotor induction motor

1. Squirrel-cage induction motor most common type of IM has squirrel-cage rotor windings squirrel cage rotor consists of copper bars, bar ends are welded to copper end rings, so that all

the bars are short circuited.

2. Wound-rotor induction motor has a 3-phase winding, similar to the stator winding.

The rotor winding terminals are connected to three slip rings which turn with the rotor.

The slip rings/brushes allow external resistors to be connected in series with the winding.

The external resistors are mainly used during start-up , under normal running conditions the windings short circuited externally.

TypesThere are two-types of rotor windings:1. squirrel-cage induction motor (most common) has Squirrel-cage windings Squirrel cage rotor consists of copper bars, bar ends are welded to copper end rings, so that all the bars are

short circuited.

2. wound-rotor induction motor has a 3-phase winding, similar to the stator winding. The rotor winding terminals are connected to three slip rings which

turn with the rotor. The slip rings/brushes allow external resistors to be connected in

series with the winding. The external resistors are mainly used during start-up , under

normal running conditions the windings short circuited externally.

Rotating Magnetic Field• Balanced three phase windings, i.e.

mechanically displaced 120 degrees form each other, fed by balanced three phase source

• A rotating magnetic field with constant magnitude is produced, rotating with a speed:

Where f is the supply frequency andP is the no. of poles and Ns is called the

synchronous speed in rpm (revolutions per minute)

120S

fN rpmP

=

Synchronous speed

No. of PolesP

Syn. Speed, Ns (rpm)

2 3000

4 1500

6 1000

8 750

10 600

12 500

f = 50 Hz

120S

fN rpmP

=

Rotating Magnetic Field

Rotating Magnetic Field

Rotating Magnetic Field

Principle of operation This rotating magnetic field cuts the rotor windings and

produces an induced voltage in the rotor windings Due to the fact that the rotor windings are short circuited, for

both squirrel cage and wound-rotor, and induced current flows in the rotor windings

The rotor current produces another magnetic field A torque is produced as a result of the interaction of those

two magnetic fields

Where τind is the induced torque and BR and BS are the magnetic flux densities of the rotor and the stator respectively

ind R skB Bτ = ×

Induction motor speedCan the IM run at the synchronous speed, why?

– If rotor runs at the synchronous speed, which is the same speed of the rotating magnetic field, then the rotor will appear stationary to the rotating magnetic field and the rotating magnetic field will not cut the rotor.

So, no induced current will flow in the rotor and no rotor magnetic flux will be produced so no torque is generated and the rotor speed will fall below the synchronous speed.

Therefore, the IM will always run at a speed lower than the synchronous speed

Induction motor speed

• The difference between the motor speed and the synchronous speed is called the Slip speed

Where nslip= slip speedns= speed of the rotaing magnetic fieldnr = mechanical shaft speed of the motor

slip s rn n n= −

The Slip

Notice that : if the rotor runs at synchronous speed

s = 0

if the rotor is stationary

s = 1

Slip may be expressed as a percentage by multiplying the above eq. by 100, notice that the slip is a ratio and doesn’t have units

slips

s s

nn ns n n−= = slip ssn n×=OR

Frequency of the induced emf and current in the rotor:• The frequency of the voltage induced in the rotor is given by

Where fr = the rotor frequency (Hz)P = number of stator poles

nsl = slip speed (rpm)

120sl

rP nf ×

=

( )120

120

sr

s

P n nf

P sn sf

× −=

×= =

Or

r sω ω=And hence,

The rotor circuit:

AT the starting or when the rotor is blocked (s =1) Rotor Inducde voltage (emf) = E2

‘The largest voltage and rotor frequency are induced in the rotor’, Why?

If the rotor rotates at synchronous speed (s =0) and Rotor Inducde voltage (emf) = 0The induced voltage and frequency in the rotor will be equal to zero,

Why?

.Rotor Inducde voltage (emf) = s E2

Therefore in General, If the rotor speed is n (slip =s)

Rotor Reactance at any slip sWe know that reactance,

So, as the frequency of the induced voltage in the rotor changes, the reactance of the rotor circuit also changes

Rotor reactance at slip s can be obtained as

Where X2 is the rotor reactance at the supply frequency (stationary rotor) .

.

2X L f Lω π= =

2

2

22

r r r r

r

X L f Lsf L

sX

ω ππ

= ===

Induction Motors and Transformers• Both IM and transformer works on the principle of

induced voltage.Transformer: voltage applied to the primary windings

produce an induced voltage in the secondary windings.

Induction motor: voltage applied to the stator windings produce an induced voltage in the rotor windings.

– the primary of the transformer corresponds to the stator of the induction motor, whereas the secondary corresponds to the rotor on a per phase basis.

– The difference is that, in the case of the induction motor, the secondary windings can move .

Induction Motors and Transformers Therefore an IM is equivalent to a rotating transformer

with its secondary windings (i.e. rotor)short circuited.

Presence of air-gap: The other very important difference is that a large magnetising current is required to set up working flux in an induction motor due to presence of air-gap between stator and rotor.

so, induction motors have poor power factor.

– Also due to the rotation of the rotor (the secondary winding of the IM), the induced voltage in it does not have the same frequency of the stator (the primary) voltage

The rotor equivalent circuit: on per phase basis

Divide both the numerator and denominator by s

Stator of an IM is similar to primary of a transformer so equivalent circuit can be represented as:

Rotor equivalent circuit

E1

Stator equivalent circuit

Induction motor equivalent circuit:

The stator equivalent circuit: on per phase basis

Actual rotor resistance

Resistance equivalent to mechanical load

Performance of Induction MotorSeveral performance parameters can be obtained

using Rotor Equivalent circuit

• Torque, Power, Power losses• Speed verses Torque characteristics • Slip verses Torque characteristicsI

The rotor equivalent circuit: on per phase basis

The relation between rotor input, rotor copper loss and rotor output:

From the equivalent circuit:

Total input power to the rotor (P2) which is also the power crossing the air gap is:

Power lost in rotor winding or rotor copper loss is:

Total mechanical power output is:

2 22 23.( ) . RP I

s =

22 2 23.( ) .CuP I R=2CuP

22 2

13.( ) .msP I R

s− =

2 22 23.( ) . RP I

s =

22 2 23.( ) .CuP I R=

22 Cu mPP P= +2

2 213.( ) .m

sP I Rs− =

A Very Important relationship:22 : : (1 1 ): :mCuP ssPP ⇒ −

22

2 and, 1m

Cu PPPPs s

==−

Power relations

22

1::

: : (1 )

C muPs

P Ps−

2P

2CuP

mP1

s

1-s

Rotor input orair gap power

MechanicalPower Developed

Rotor copperLoss

Gross Torque Developed

• The gross (total) Torque developed is:Where is rotor speed.

mm

r

PTω

=

21 = .(1 ) (1 )

m m mm

r s s s

P P P PTs sω ω ω ω

= = = − −

rω

2 = mm

r s

P PTω ω

=Total rotor input power (air gap power) m

s

Tω

=

Shaft Torque = Gross Torque – Friction loss

sh m lossT T T= −

Shaft Torque Developed

2

2 2 2 22 2 2 2

2 2

3.( ) . 3. .( )

R sE RP Is sR sX

= = +

2 / .m sT P ω=

We know that rotor input power or air gap power is given as:

And Total mech. Torque, Therefore,

22

22 22 2

3 . .( )m

s

sET RR sXω

= +

Torque –Slip Characteristics:

We know that total torque developed is :

Now, Let us examine the torque verses speed characteristics for different operating conditions:

22

22 22 2

3 . .( )m

s

sET RR sXω

= +

Case 1: Motor Running near Synchronous speed (s very small)

Case 2: At Starting (s=1)

T-s curve: Case 1: Motor Running near Synchronous speed

Slip s is very small, and hence, So torque expression becomes:

Near synchronous speed: Torque increases linearly with slip. If rotor resistance is high rated torque is reduced Torque is proportional to the square of applied voltage.

2 22 2( ) .R sX>>

22

22 22 2

3 . .( )m

s

sET RR sXω

= +

22

2

3 .ms

sETRω

=

22

2

αmsETR

α denotes propotionality←

General torque expression is:

T-s curve: Case 2: At Starting

For large value of slip and At starting (s=1), So torque expression becomes:

During Starting: Starting Torque increases linearly with rotor resistance (in wound rotor

motor, higher starting torque is obtained by inserting external in rotor circuit).

If leakage reactance is high, starting torque is reduced Torque is proportional to the square of applied voltage.

22

22 22 2

3 . .( )m

s

sET RR sXω

= +

22 2

22

. αstE RT

X

α denotes propotionality←

2 22 2( ) .sX R>>

22

222

3 . .sts

ET RXω

=

General torque expression is:

Torque-Slip (Speed) Characteristics

Starting Torque

Maximum TorqueOr Breakdown Torque

Full Load Torque

Linear Torque –slip Region

Speed

.

Torque

Rated Load

Slip

Comments (Torque-speed char.)1. The induced torque is zero at synchronous speed.

Discussed earlier.2. The curve is nearly linear between no-load and full

load. In this range, the rotor resistance is muchgreater than the reactance, so the rotor current, andtorque increase linearly with the slip.

3. There is a maximum possible torque that can’t beexceeded. This torque is called breakdown torqueand is 2 to 3 times the rated full-load torque.

Comments(Torque-speed char.)4. The starting torque of the motor is slightly higher

than its full-load torque, so the motor will startcarrying any load it can supply at full load.

5. The torque of the motor for a given slip varies asthe square of the applied voltage.

6. If the rotor is driven faster than synchronous speedit will run as a generator, converting mechanicalpower to electric power.

Maximum Torque and condition for Max. Torque:• Maximum Torque (also called breakdown torque)occurs when,

Slip at Maximum Torque:

Maximum Torque Tmax:

The Value of Maximum Torque does not depend on Rotor resistance.

But slip at which it occurs depend on rotor resistance (proportional to it)

2 2.sX R=

maxT 2 2/s R X=

22

max2

3 .2s

ETXω

=

Effect of rotor resistance on torque-slip (speed) characteristic

Slips=1

Ns

(Rotor Resistances)

s=0

Speed

Effect of rotor resistance on torque-slip (speed) characteristic

Rotor Resistances

Speed

0

0Ns

Need for a starting method

A squirrel cage motor is at stationary before it is started, there rotor induced emf is very high.Therefore, if this motor is connected directly to the supply, will

take an initial starting current which is about 5 to 6 times of the full load value. Though this current decreases rapidly as the motor accelerates, it will cause harm to the motor and will affect the voltage (cause voltage dips inthe power supply) and hence the other loads.

Small motors up to the size of 5 hp are allowed to be started with direct on line (DOL) starter

Starting Method of Induction Motors

MotorThree phase supply

contactor

1. Direct on Line (DOL)

• When the rating of the motor exceed 5 hp Some starting means must be used to start the motor. A star/delta starter is normally used because it is the simpliest and cheapest type of starter.

• During starting, the stator winding is temporarily connected in star. therefore only phase voltage (1/ sqrt (3) of line voltage ) is applied to the stator. The starting current is reduced to 1/3 of the Direct on line starting current. The starting torque, which is proportional to the starting current, reduces also to 1/3 of the value at direct on line starting.

• After a period of about 5 seconds, the motor have accelerated to nearly full load speed. The stator winding is now reconnected as delta, and full line voltage is applied in each phase of the stator.

2. Star-Delta Starter

Rotor

Stator

Running Starting

DeltaStar

Switch

Supply

Schematic Diagram of a Star-Delta Starter

• Some loads are very heavy and it will take a few minutesbefore it can run to full speed, these motors have to be startedby means of transformer starter.

• The reduced voltage during starting is obtained from thedifferent tappings (40% , 60% , 75%) of an auto-transformer.

• In the running condition, full voltage is applied to the statorand the transformer is cut out of the circuit.

3. Auto-transformer Starter

Supply

Rotor

StatorWinding

Auto-transformer StarterStarting

Running

• The wound rotor (slip ring) induction motor can be started byinserting additional resistance in series with the rotor windingthrough the slip rings.

• In this way, maximun torque is obtained during starting. Theadditional resistance is cut off from the circuit as soon as the motoris started to avoid excessive power loss in the resistance.

ThreePhaseSupply

Brush

Rotor Windings Slip RingsStator Windings

Running Position

Starting PositionExternal Resistors

4. Starting of Wound Rotor Induction Motor

Extra slides

Rotating Magnetic Field• The three phases of the stator winding carry balanced alternating

sinusoidal currents • Three pulsating mmf waves are now set up in the air-gap, which have a

time phase difference of 120 degree from each other. These mmf’s are oriented in space along the magnetic axes of the phases, a,b & c,

Example

A 208-V, 10hp, four pole, 60 Hz, Y-connected induction motor has a full-load slip of 5 percent1. What is the synchronous speed of this motor?2. What is the rotor speed of this motor at rated

load?3. What is the rotor frequency of this motor at

rated load?4. What is the shaft torque of this motor at rated

load?

Solution

120 120(60) 18004s

fn rpmP

= = =

(1 )(1 0.05) 1800 1710

sn s nrpm

= −= − × =

0.05 60 3rf sf Hz= = × =

260

10 746 / 41.7 .1710 2 (1/ 60)

out outsh

m

P PT n

hp watt hp N m

ω π

π

= =

×= =

× ×