Lecture2 BEE

7/27/2019 Lecture2 BEE

1/32

23 October 2013 L.N Tripathy 1

Principle of Operation Three phase winding in stator when

get supply produce rotating magnetic

field [or flux] of Constant magnitudebut rotating at synchronous speed

This rotating magnetic field induce emf

in rotor circuit and current start flowingin rotor circuit as rotor is shortCircuited.


2/32


C0nt.. The torque is produced on the rotor due to

interaction of two fields. As per Lenzs law ,under the influence of this

toque the rotor start rotating in samedirection to catch the rotating magnetic field.The relative speed between rotating magneticfield and the rotor is called slip speed.

Note:- The rotor rotate near synchronousspeed but can not attend the synchronousspeed. So induction motor is called

Asynchronous motor.


3/32


Slip of Induction Motor[ ] [ ]

[ ]

[ ][ ] 100

%

s

s

s

s

Synchronous speed N Rotor Speed NSlip s

Synchronous Speed NN N

sN

Slip is Always expressed as percentage


4/32


Frequency of Stator current &

Rotor current Stator current frequency is same as

supply frequency f

Rotor induced emf frequency or Rotorcurrent frequency= sf

Where

s is the slip


5/32


Rotor frequency & Production

of steady torque. At stand still rotor induce voltage frequency fr

= stator induced voltage frequency fe orsupply frequency.

When rotor rotate the relative motionbetween stator flux and rotor conductorinduces voltages of frequency fr

fr = sfe called the slip frequency in

the rotor.Note:- wound rotor [Not squirrel cage] can be

used as frequency changer.


6/32


CondAt stand still rotor frequency = stator

frequency fe [s=1]. So the field

produced by rotor current rotate assame speed as stator field and steadystarting torque is produced. It tends to

turn the rotor in the direction ofrotation of stator induced field.


7/32


Cont.. Note:- The operating speed is never

equal to synchronous speed if it equal

to synchronous speed the rotorconductor will be stationary w.r.t statorfield[ relative speed is zero] no current

will be induced in rotor and hence notorque is produced.


8/32


Cond When rotor rotate in the direction of

stator field the frequency of rotor

currents is sfe and they will produce arotating flux wave which will rotate atsns w.r.t rotor in the forward direction.

With respect to stator the speed of theflux produced by rotor current is

sns+n=sns+ns(1-s) = ns


9/32


Cond Rotor current produce an air-gap flux which

rotate at synchronous speed w.r.t stator.

So the stator field and rotor field arestationary to each other and produce thesteady torque.

Torque for any mechanical rotor speed otherthan synchronous speed is calledasynchronous torque


10/32


Power Stages of Induction

Motor Stator Input

Stator Iron & Copper loss

Rotor Input

Rotor Copper loss

Mechanical power Developed

Windage and friction loss

Rotor Output


11/32


Equivalent Circuit of Induction

Motor V1 = E2 + I1(R1+jX1) --------- (1)

V1= Stator line to neutral Voltage

E2

= Counter emf ( Line to neutral) generated byresultant air gap flux

I1 = Stator current

R1 = Stator effective resistance

X1= stator leakage reactance.

Ic= Core loss component of current

Im = Magnetizing component of current.

I=Exciting current


12/32


Stator equivalent circuit for a polyphase

induction motor.


13/32


Rotor equivalent circuit for a polyphaseinduction motor at slip frequency.

Z2s = E2s/I2s = R2 + JsX2

R2 = Reffered rotor resistancesX

2

= Reffered rotor leakagereactance at slip frequency

Z2s = Slip frequency rotorLeakage Impedance

E2s = s E2 Assuming stator

& rotor have same numberof turns per phaseI2= I2s

I2 = Load current.


14/32


Cond.. sE2/I2=Z2s=R2+jsX2

Dividing by s

Z2 = E2/I2 = R2/s + jX2

Z2 impedance of stationary rotor whichappear across the load terminal

R2/s represents the combine effect ofshaft load and rotor resistance.


15/32


Single-phase equivalent circuit for apolyphase Induction motor.


16/32


Alternative form of equivalent circuit.


17/32


Equivalent circuits with the core-lossresistance Rc neglected


18/32


Analysis of Equivalent Circuit.

2 22

2

2 2

2 222 2 2

2

2 2

( ) (2)

(3)

( )

1( )

(1 )

gap ph

rotor ph

mech gap rotor ph ph

mech ph

mech gap

rotor gap

RP n I

s

P n I RR

P P P n I n I Rs

sP n I R s

P s P

P sP

----------(4)

----------------------(5)

------------------------ (6)


19/32


Power developed Inductionmotor

2 2

2

(1 ) (7)

( ) (8)

(9)

(10)

mech m mech s mech

phgapmechmech

m s s

shaft mech rotor

shaft

shaft mech rotor

m

P T s T

R

n IPP sT

P P P

PT T T


20/32


Torque-speed Characteristic

s

ph

t

tmech

s

ph

s

gap

m

MechMech

EnK

Where

s

R

XsR

KT

jXsREI

sRInPPT

2

2

2

2

2

2

2

22

22

2

2

2

,

)/(

)/(

/


21/32


Torque-speed Characteristic


22/32


Operating mode of InductionMotor

Motoring Mode : 1s0

Generating Mode :s1


23/32


Power Stages of InductionMotor

Stator Input

Stator Iron & Copper loss

Rotor Input

Rotor Copper loss

Mechanical power Developed

Windage and friction loss

Rotor Output


24/32


Losses in induction motorLosses in 3-Phase Induction Motor

Fixed losses Variable Losses

Core loss Brush friction lossIn wound rotor

Bearing and frictionloss

Windageloss


25/32


Variable loss

Variable losses

Stator Ohmic

loss

Rotor Ohmic

loss

Brush contactLoss for slip ringmotor

Stray load

loss

Fixed loss= Power input at no load-(stator I2R loss).Fixed loss can be determined by no load test of Induction Motor.Stray load losses is difficult to determine it is assumed when efficiencyIs calculated.


26/32


Rotor current and rotor power

2 2

2 2

2 2

2 2

2

2 2

2 2

22

stand still= R

any slip per phase rotor leakage impedance = R ( )

phase rotor current at stand still =R

per phase rotor current at any slip(s) is I =R

Rotor leakageimpedance at X

At sX

Eper

X

sE

2 2

2 2( )sX


27/32


Rotor power

2

2

-1 22

2

g

2 2 2

2 22

2 2 2 2

2 2 2 2

If rotor current lag the rotor voltage an angle

Power factor = Cos ,

= tan ( )

phase power input to rotor = Air gap Power = P

/R ( ) (R / ) ( )

g

sX

R

Per

P E I Cos

R R sCossX s X


28/32


Cont..

22 2 2 2 2

2 2

2 2

22 2

2 2

2 2

2

2 2

g

2 2 2 2

2 2 2 2 2 2 2 2

2 2

2 2 2 2

/

(R / ) ( )

/

(R / ) ( )

/

P can be written as

/ /

1( )

(1 )

g

g

g

g

g

g g g

R sP E I Cos E I

s X

EP I R s

s X

P I R s

P I R s I R s I R I R

sP I R I R

s

P sP s P

Pg = (Rotor ohmic loss)+( Internal mechanical power devolved in rotor)


29/32


Cont..

Rotor Ohmic loss = s(Power input torotor)

Internal mechanical power Developedby rotor Pm =I2

2R2(1-s)/s=(1-s)Pg Pm=(1-s)(Power input to Rotor)


30/32


Starting of Induction Motor.

Direct on line starting

Stator resistor(or reactor starting)

Auto Transformer Starting

Star- Delta Starting


31/32


Direct-On- Line Starting.

2 222

2

2 2 22

2

2

2

( )1

( )

( ) ( )

( )

( )

stest st

flefl fl

fl

fl

st st

st st

fl fl

RI

T I

SRT IIs

I effective stator Turns I Effective Rotor Turns

I I Effectiverotor to stator turn ratio

I I Effective rotor to stator turn ratio


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23 October 2013 L N Tripathy 32

Cond..

2

1

1

1

1

2

est st fl

efl fl

sc

st sc

est scfl

efl fl

T Is

T I

VIZ

VOn Direct switching I I

Z

T Is

T I

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Lecture2 BEE