induction motor.pptx

8/19/2019 Induction Motor.pptx

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Induction Motor

By

Ashvani Shukla

Manager(C&I)

BGR ENERG


2/43

• INTRODUCTION

• !ne o" the #ost co##on electrical #otor used in #ost a$$licais kno%n as induction motor 'his #otor is also called asasynchronous #otor ecause it runs at a s$eed less than synchs$eed In this %e need to de*ne %hat is synchronous s$eed Sys$eed is the s$eed o" rotation o" the #agnetic *eld in a rotary #and it de$ends u$on the "re+uency and nu#er $oles o" the #ainduction motor al%ays runs at a s$eed less than synchronouecause the rotating #agnetic *eld %hich is $roduced in the stgenerate ,u- in the rotor %hich %ill #ake the rotor to rotate uthe lagging o" ,u- current in the rotor %ith ,u- current in the strotor %ill never reach to its rotating #agnetic *eld s$eed ie th

synchronous s$eed 'here are asically t%o types of inductiothat de$end u$on the in$ut su$$ly . single $hase induction #otthree $hase induction #otor Single $hase induction #otor is nstarting #otor %hich %e %ill discuss later andthree $hase induction #otor is a sel".starting #otor No% in genneed to give t%o su$$ly ie doule e-citation to #ake a #achinrotate /or e-a#$le i" %e consider a 0C #otor %e %ill give one

the stator and another to the rotor through rush arrange#ent

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• Working Principle of Induction Motor

• But in induction #otor %e give only one su$$ly so it is reallyinteresting to kno% that ho% it %orks It is very si#$le "ro# titsel" %e can understand that there is induction $rocess occu

Actually %hen %e are giving the su$$ly to the stator %indinggenerate in the coil due to ,o% o" current in the coil No% the%inding is arranged in such a %ay that it eco#es short circurotor itsel" 'he ,u- "ro# the stator %ill cut the coil in the rotosince the rotor coils are short circuited according to/araday1s la% o" electro#agnetic induction current %ill start the coil o" the rotor 2hen the current %ill ,o% another ,u- %

generated in the rotor No% there %ill e t%o ,u- one is statoanother is rotor ,u- and the rotor ,u- %ill e lagging to the s0ue to this the rotor %ill "eel a tor+ue %hich %ill #ake the rorotate in the direction o" rotating #agnetic ,u- So the s$eedrotor %ill e de$ending u$on the ac su$$ly and the s$eed cancontrolled y varying the in$ut su$$ly 'his is the working pof an induction motor o" either ty$e

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4/43

• 'y$es Induction Motor

• SING3E 45ASE IN06C'I!N M!'!R • S$lit $hase induction #otor

• Ca$acitor start induction #otor

• Ca$acitor start ca$acitor run induction #otor

• Shaded $ole induction #otor

• '5REE 45ASE IN06C'I!N M!'!R • S+uirrel cage induction #otor

• Sli$ ring induction #otor

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5/43

• Construction o" 'hree 4hase Induction Motor

• 'he three $hase induction #otor is the #ost %idely used electrical #otor o" the #echanical $o%er used y industries is $rovided ythree $hase induction #otors ecause o" its si#$le and rugged constructiogood o$erating characteristics asence o" co##utator and good s$eed rethree $hase induction #otor the $o%er is trans"erred "ro# stator to rotor %through induction 'he Induction #otor is also called asynchronous #otor

a s$eed other than the synchronous s$eed• 3ike any other electrical #otor induction #otor also have t%o #ain $arts n

and stator

• Stator: As its na#e indicates stator is a stationary $art o" induction #otor %inding is $laced in the stator o" induction #otor and the three $hase su$$to it

• Rotor: 'he rotor is a rotating $art o" induction #otor 'he rotor is connecte

#echanical load through the sha"t• 'he rotor o" the three $hase induction #otor are "urther classi*ed as S+uir

rotor

• Sli$ ring rotor or %ound rotor or $hase %ound rotor

• 0e$ending u$on the ty$e o" rotor construction used the three $hase inducare classi*ed as: S+uirrel cage induction #otor

• Sli$ ring induction #otor or %ound induction #otor or $hase %ound induct

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7/43

It is the outer most part of the three phase induction motor. Its main functio

support the stator core and the field winding. It acts as a covering and it proprotection and mechanical strength to all the inner parts of the induction moframe is either made up of die cast or fabricated steel. The frame ofthree phase induction motor should be very strong and rigid as the air gap lethree phase induction motor is very small, otherwise rotor will not remain cowith stator, which will give rise to unbalanced magnetic pull.

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8/43

Stator CoreThe main function of the stator core is to carry the alternating flux. In ord

eddy current loss, the stator core is laminated. These laminated types of made up of stamping which is about 0.4 to 0.5 mm thick. ll the stampintogether to form stator core, which is then housed in stator frame. The stgenerally made up of silicon steel, which helps to reduce the hysteresis lomotor.

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9/43

• tator Winding or "ield Winding

• 'he slots on the $eri$hery o" stator core o" the three $hase inductiocarries three $hase %indings 'his three $hase %inding is su$$lied $hase ac su$$ly 'he three $hases o" the %inding are connected eithor delta de$ending u$on %hich ty$e o" starting #ethod is used 'he cage #otor is #ostly started y star < delta stater and hence the sta

s+uirrel cage #otor is delta connected 'he sli$ ringthree $hase induction #otor are started y inserting resistances so %inding o" sli$ ring induction #otor can e connected either in star o

'he %inding %ound on the stator o" three $hase induction #otor is a*eld %inding and %hen this %inding is e-cited y three $hase ac su$$roduces a rotating #agnetic *eld

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11/43

Advantages of squirrel cage induction rotor-!.Its construction is very simple and rugged.".s there are no brushes and slip ring, these motors re#uires less maintenApplications: $#uirrel cage induction motor is used in lathes, drilling m

blower printing machines etc.

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12/43

• lip ring or wound t!ree p!ase induction motor $ In this tythree $hase induction #otor the rotor is %ound "or the sa#e nu#$oles as that o" stator ut it has less nu#er o" slots and has les$er $hase o" a heavier conductor 'he rotor also carries star or d%inding si#ilar to that o" stator %inding 'he rotor consists o" nuslots and rotor %inding are $laced inside these slots 'he three e

ter#inals are connected together to "or# star connection As itsindicates three $hase sli$ ring induction #otor consists o" sli$ riconnected on sa#e sha"t as that o" rotor 'he three ends o" thre%indings are $er#anently connected to these sli$ rings 'he e-tresistance can e easily connected through the rushes and sli$hence used "or s$eed control and i#$roving the starting tor+ue $hase induction #otor 'he rushes are used to carry current to

the rotor %inding 'hese rushes are "urther connected to three connected resistances At starting the resistance are connectedcircuit and is gradually cut out as the rotor $ick u$ its s$eed 2h#otor is running the sli$ ring are shorted y connecting a #etal%hich connect all sli$ ring together and the rushes are also re#reduces %ear and tear o" the rushes 0ue to $resence o" sli$ rinrushes the rotor construction eco#es so#e%hat co#$licated it is less used as co#$are to s+uirrel cage induction #otor

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13/43

1.Advantages of slip ring induction motor - It has high starting tor#uestarting current.".%ossibility of adding additional resistance to control speed.Application:$lip ring induction motor are used where high starting tor#ue is re#uir

hoists, cranes, elevator etc.

Difference between Slip ing and Squirrel Cage Induction !otor

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14/43

Slip ring or phase wound Induction motor Squirrel cage induction motor

&onstruction is complicated due to presence of

slip ring and brushes&onstruction is very simple

The rotor winding is similar to the stator

winding

The rotor consists of rotor bars which ar

permanently shorted with the help of en

'e can easily add rotor resistance by using slipring and brushes

$ince the rotor bars are permanently shits not possible to add external resistanc

(ue to presence of external resistance high

starting tor#ue can be obtained$taring tor#ue is low and cannot be imp

$lip ring and brushes are present $lip ring and brushes are absent

)re#uent maintenance is re#uired due to

presence of brushes*ess maintenance is re#uired

The construction is complicated and the

presence of brushes and slip ring makes the

motor more costly

The construction is simple and robust an

cheap as compared to slip ring induction

This motor is rarely used only !0 + industry

uses slip ring induction motor

(ue to its simple construction and low c

s#uirrel cage induction motor is widely u

otor copper losses are high and hence less

efficiency

*ess rotor copper losses and hence high

efficiency

$peed control by rotor resistance method is

possible

$peed control by rotor resistance metho

possible

$lip ring induction motor are used where high

starting tor#ue is re#uired i.e in hoists, cranes,elevator etc

$#uirrel cage induction motor is used in

drilling machine, fan, blower printing maetc

p g q g


15/43

• 2e had #entioned aove that single $hase induction #otsel" starting and three $hase induction #otor is sel" startin%hat is sel" starting> 2hen the #achine starts runningauto#atically %ithout any e-ternal "orce to the #achine tcalled as sel" starting /or e-a#$le %e see that %hen %e $

key the "an starts to rotate auto#atically so it is sel" startto e note that "an used in ho#e a$$liances issingle $hase induction #otor ut it is sel" starting 5o%> 2discuss it ho% W!y is T!ree P!ase Induction Motor tarting%

• In three $hase syste# there are three single $hase line %

$hase dierence So the rotating #agnetic *eld is having $hase dierence %hich %ill #ake the rotor to #ove I" %e three $hases a and c %hen $hase a is #agnetied the #ove to%ards the $hase a %inding in the ne-t #o#ent $%ill get #agnetied and it %ill attract the rotor and than $the rotor %ill continue to rotate

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Working Principle of T!ree P!ase Induction • W!y ingle P!ase Induction Motor is not elf tarting%

• But %hat aout single $hase It %ill e having only one $hase still it #akes therotate so it is +uite interesting Be"ore that %e need to kno% %hysingle $hase induction #otor is not a sel" starting #otor and ho% the $role#2e kno% that the ac su$$ly is a sinusoidal %ave and it $roduces $ulsating #auni"or#ly distriuted stator %inding Since $ulsating #agnetic *eld can e asso$$ositely rotating #agnetic *elds there %ill e no resultant tor+ue $roducedstarting and due to this the #otor does not run A"ter giving the su$$ly i" the to rotate in either direction y e-ternal "orce then the #otor %ill start to run 'has een solved y #aking the stator %inding into t%o %inding one is #ain %another is au-iliary %inding and a ca$acitor is *-ed in series %ith the au-iliary 'his %ill #ake a $hase dierence %hen current %ill ,o% through the oth coils%ill e $hase dierence the rotor %ill generate a starting tor+ue and it %ill sta4ractically %e can see that the "an does not rotate %hen the ca$acitor is discothe #otor ut i" %e rotate %ith hand it %ill start to rotate So this is the reasonca$acitor in the single $hase induction #otor 'here are several advantages oinduction #otor %hich #akes this #otor to have %ider a$$lication It is havingeDciency u$ to F9 But the s$eed o" the #otor varies %ith the load given to %hich is an disadvantage o" this #otor 'he direction o" rotation o" induction #easily e changed y changing the se+uence o" three $hase su$$ly ie i" RBdirection the RB %ill #ake the #otor to rotate in reverse direction 'his is in three $hase #otor ut in single $hase #otor the direction can e reversed ythe ca$acitor ter#inals in the %inding

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18/43

• 2orking o" 'hree 4hase Induction Motor

• 4roduction o" Rotating Magnetic /ield

• 'he stator o" the #otor consists o" overla$$ing %inding oset y a

angle o" ?@8 2hen the $ri#ary %inding or the stator is connecte$hase AC source it estalishes a rotating #agnetic *eld %hich rotsynchronous s$eed

• Secrets ehind the rotation:

• According to /aradays la% an e#" induced in any circuit is due tochange o" #agnetic ,u- linkage through the circuit As the rotor %an induction #otor are either closed through an e-ternal resistanc

directly shorted y end ring and cut the stator rotating #agnetic *e#" is induced in the rotor co$$er ar and due to this e#" a currethrough the rotor conductor

• 5ere the relative velocity et%een the rotating ,u- and static rotois the cause o" current generationJ hence as $er 3en1s la% the rorotate in the sa#e direction to reduce the cause ie the relative ve

h " h ki i i l f ! !


19/43

• 'hus "ro# the working principle of t!ree p!aseinduction motor it #ay oserved that the rotor s$should not reach the synchronous s$eed $roduced stator I" the s$eeds e+uals there %ould e no suchvelocity so no e#" induction in the rotor & no curr

%ould e ,o%ing and there"ore no tor+ue %ould egenerated Conse+uently the rotor can not reach atsynchronous s$eed 'he dierence et%een the sta(synchronous s$eed) and rotor s$eeds is called the rotation o" the #agnetic *eld in an induction #otoradvantage that no electrical connections need to

to the rotor 'hus the t!ree p!ase induction motSel".starting K 3ess ar#ature reaction and rush s$ecause o" the asence o" co##utators and rush#ay cause s$arks K Roust in construction K EconK Easier to #aintain

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20/43

•Classi*cation o" S+uirrel Cage Induction Motor

•NEMA in 6nited States and IEC in Euro$e have classi*edesign o" the s+uirrel cage induction #otors ased on s$eed.tor+ue characteristics into so#e classes 'hese are Class A Class B Class C Class 0 Class E and Clas

•In Class & Design

•A nor#al starting tor+ue

•A nor#al starting current

•3o% sli$

•In this Class $ullout tor+ue is al%ays o" @88 to H88 $er

the "ull.load tor+ue and it occurs at a lo% sli$ (it is less$ercent)

•/or this Class the starting tor+ue is e+ual to rated tor+larger #otors and is aout @88 $ercent or #ore o" the tor+ue "or the s#aller #otors

• In Class ' Design


21/43

• In Class ' Design

• Nor#al starting tor+ue

• 3o%er starting current

• 3o% sli$

• Induction Motor o" this Class $roduces aout the sa#e startas the class A induction #otor and this starting tor+ue is %it@L $ercent less current

• 4ullout tor+ue is al%ays greater than or e+ual to @88 $ercenrated load tor+ue But it is less than that o" the class A desigecause it has increased rotor reactance

• Again Rotor sli$ is still relatively lo% (less than L $ercent) at

• A$$lications o" Class B design are si#ilar to those "or designdesign B is $re"erred #ore ecause o" its lo%er starting.currre+uire#ents

In Class C Design


22/43

In Class C Design

• 5igh starting tor+ue

• 3o% starting currents

• 3o% sli$ at the "ull load (less than L 9)

•6$ to @L8 $ercent o" the "ull.load tor+ue the starting tin this class o" design

• 'he $ullout tor+ue is lo%er than that "or class A induct#otors

• In this design the #otors are uilt "ro# doule.cage ro 'hey are #ore e-$ensive than #otors o" Class A and B

• Class C 0esigns are used "or high.starting.tor+ue load$u#$s co#$ressors and conveyors)


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• In Class D Design

• In this 0esign o" Class #otors has very high startor+ue (@FL $ercent or #ore o" the rated tor+ue

• A lo% starting current

• A high sli$ at "ull load

• Again in this class o" design the high rotor resistshi"ts the $eak tor+ue to a very lo% s$eed

• It is even $ossile at ero s$eed (?88 $ercent sli

the highest tor+ue to occur in this class o" desig• /ull.load sli$ (It is ty$ically F to ?? $ercent ut #

as high as ?F $ercent or #ore) in this class o" de+uite high ecause o" the high rotor resistance a


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• In class ( Design

• ery 3o% Starting 'or+ue

• Nor#al Starting Current

•

3o% Sli$• Co#$ensator or resistance starter are used to co

starting current

• In Class " Design

• 3o% Starting 'or+ue ?@L ti#es o" "ull load tor+u

"ull voltage is a$$lied• 3o% Starting Current

• Nor#al Sli$

Ci l 0i " I d i


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Circle 0iagra# o" InductionMotor

The -&I&* (I/1 means that it is figure or curve which is drawn hasshape. s we know, the diagrammatic representation is easier comtheoretical and mathematical descriptions. ctually, we do not have that m

or patience to go through the writings so we prefer diagrammatic reprelso, it is very easy to remember the things which are shown in picture. s

- %I&T2 I$ '3T !000 '3($1. This also holds good here and we acircle diagram in order to compute various parameters rather thanmathematically.I#$ortance o" Circle 0iagra#The diagram provides information which is not provided by an ordinary phasdiagram. phasor diagram gives relation between current and voltage only single circuit condition. If the condition changes, we need to draw the phasoagain. ut a circle diagram may be referred to as a phasor diagram drawn inplane for more than one circuit conditions. 3n the context of induction motoour main interest, we can get information about its power output, power factor#ue, slip, speed, copper loss, efficiency etc. in a graphical or in a diagramrepresentation.


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• 4rocedure to 0ra% the Circle 0iagra#


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g

• 2e have to assu#e a suitale e"ore dra%ing it 'his assu#$tioaccording to our convenience

• 'he no load current and the no load angle calculated "ro# no load test


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g 'his is sho%n y the line !A %here 8 is the no load $o%er "actor ang

• 'he short circuit current and the angle otained "ro# lock rotor test i 'his is sho%n y the line !C and the angle is sho%n y B

• 'he right isector o" the line AC is dra%n %hich isects the line and it to cut in the line AE %hich gives us the Centre

•

'he stator current is calculated "ro# the e+uivalent circuit o" the induc%hich %e get "ro# the t%o tests 'hat current is $lotted in the circle diaccording to the scale %ith touching origin and a $oint in the circle diais sho%n y B

• 'he line AC is called the $o%er line By using the scale "or $o%er conv%e have taken in the circle diagra# %e can get the out$ut $o%er i" %vertically aove the line AC to the $eri$hery o" the circle 'he out$ut $given y the line MB

• 'he total co$$er loss is given y the line GM

• /or dra%ing the tor+ue line the total co$$er loss should e se$arated rotor co$$er loss and stator co$$er loss 'he line 0E gives the stator cand the line C0 gives the rotor co$$er loss In this %ay the $oint E is s

• 'he line A0 is kno%n as tor+ue line %hich gives the tor+ue develo$ed #otor

• Ma-i#u# Ouantities "ro# Circle 0iagra#


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g

• Ma)imum Output Power


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• 2hen the tangent to the circle is $arallel to the line then out$ut $e #a-i#u# 'hat $oint M is otained y dra%ing a $er$endiculathe center to the out$ut line and e-tending it to cut at M Ma)imTor#ue

• 2hen the tangent to the circle is $arallel to the tor+ue line it give

#a-i#u# tor+ue 'his is otained y dra%ing a line "ro# the cen$er$endicular to the tor+ue line and e-tending it to cut at the circ$oint is #arked as N Ma)imum Input Power

• It occurs %hen tangent to the circle is $er$endicular to the horio 'he $oint is the highest $oint in the circle diagra# and dra%n to tand e-tends into S 'hat $oint is #arked as R Conclusion o" Circle

• 'his #ethod is ased on so#e a$$ro-i#ations that %e have used

dra% the circle diagra# and also there is so#e rounding o o" th%ell So there is so#e error in this #ethod ut it can give good a$results Also this #ethod is very #uch ti#e consu#ing so it is drti#es %here the dra%ing o" circle diagra# is asolutely necessary!ther%ise %e go "or #athe#atical "or#ulas or e+uivalent circuit order to *nd out various $ara#eters

• 'or+ue Sli$ Characteristics o" Induction Motor


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'or+ue Sli$ Characteristics o" Induction MotorThe tor#ue slip curve for an induction motor gives us the information abotor#ue with the slip. The slip is defined as the ratio of difference of synchrospeed at any mechanical load to the synchronous speed of the machine. Tcan be obtained with the variation on speed that is when speed varies theand the tor#ue corresponding to that speed will also vary.

The curve can be described in three modes of operation6

• Motoring Mode In this #ode o" o$eration su$$ly is given to


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g $ $$ y gstator sides and the #otor al%ays rotates elo% the synchrons$eed 'he induction #otor tor+ue varies "ro# ero to "ull loaas the sli$ varies 'he sli$ varies "ro# ero to one It is ero aand one at standstill /ro# the curve it is seen that the tor+udirectly $ro$ortional to the sli$ 'hat is #ore is the sli$ #ore

the tor+ue $roduced and vice.versa 'he linear relationshi$ sthe calculation o" #otor $ara#eter to great e-tent *eneratIn this #ode o" o$eration induction #otor runs aove the syns$eed and it should e driven y a $ri#e #over 'he stator %connected to a three $hase su$$ly in %hich it su$$lies electrienergy Actually in this case the tor+ue and sli$ oth are negthe #otor receives #echanical energy and delivers electrical

Induction #otor is not #uch used as generator ecause it re+reactive $o%er "or its o$eration 'hat is reactive $o%er shousu$$lied "ro# outside and i" it runs elo% the synchronous s$any #eans it consu#es electrical energy rather than giving out$ut So as "ar as $ossile induction generators are generavoided

• 'raking Mode In the reaking #ode the t%o leads or th


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g go" the su$$ly voltage is changed so that the #otor starts in the reverse direction and as a result the #otor sto$s '#ethod o" reaking is kno%n as $lugging 'his #ethod is%hen it is re+uired to sto$ the #otor %ithin a very short $ti#e 'he kinetic energy stored in the revolving load is dis

as heat Also #otor is still receiving $o%er "ro# the statois also dissi$ated as heat So as a result o" %hich #otor denor#ous heat energy /or this stator is disconnected "rosu$$ly e"ore #otor enters the reaking #ode

• I" load %hich the #otor drives accelerates the #otor in thdirection as the #otor is rotating the s$eed o" the #otor

increase #ore than synchronous s$eed In this case it acinduction generator %hich su$$lies electrical energy to th%hich tends to slo% do%n the #otor to its synchronous s$this case the #otor sto$s 'his ty$e o" reaking $rinci$le dyna#ic or regenerative reaking

• 'or+ue Sli$ Characteristics o" Single 4hase Induct


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o +ue S $ C a ac e s cs o S g e ase duc

• /ro# the *gure %e see that at a sli$ o" unity oth "or%a


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g $ yack%ard *eld develo$s e+ual tor+ue ut the direction oare o$$osite to each other so the net tor+ue $roduced ishence the #otor "ails to start /ro# here %e can say tha#otors are not sel" starting unlike the case o" three $hainduction #otor 'here #ust e so#e #eans to $rovide starting tor+ue I" y so#e #eans %e can increase the "s$eed o" the #achine due to %hich the "or%ard sli$ decrthe "or%ard tor+ue %ill increase and the reverse tor+ue decrease as a result o" %hich #otor %ill start

• /ro# here %e can conclude that "or starting o" single $hinduction #otor there should e a $roduction o" dieren

tor+ue et%een the "or%ard and ack%ard *eld I" the "o*eld tor+ue is larger than the ack%ard *eld than the #rotates in "or%ard or anti clock%ise direction I" the tor+uack%ard *eld is larger co#$ared to other then the #orotates in ack%ard or clock%ise direction

'or+ue E+uation o" 'hree 4hase Induction Motor


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'or+ue E+uation o" 'hree 4hase Induction Motor

The tor#ue produced by three phase induction motor depends upon thfactors7)irstly the magnitude of rotor current, secondly the flux which interact three phase induction motor and is responsible for producing emf in the rotomotor, lastly the power factor of rotor of the three phase induction motor. &

factors together we get the e#uation of tor#ue as6

'here, T is the tor#ue produced by induction motor, 8 is flux responsible ofproducing induced emf, I" is rotor current, cos9" is the power factor of rotor

circuit. The flux 8 produced by the stator is proportional to stator emf !. i.e ! 'e know that transformation ratio : is defined as the ratio of secondary vo

;rotor voltage< to that of primary voltage ;stator voltage


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otor current I" is defined as the ratio of rotor induced emf under running conditi

impedance, =" of rotor side,

and total impedance =" on rotor side is given by

• 4utting this value in aove e+uation %e get

http://www.electrical4u.com/electric-current-and-theory-of-electricity/http://www.electrical4u.com/electric-current-and-theory-of-electricity/


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4utting this value in aove e+uation %e get

'e know that power factor is defined as ratio of resistance to that of impedan

power factor of the rotor circuit is

%utting the value of flux 8, rotor current I", power factor cos9" in the e#uat

tor#ue we get,

• Co#ining si#ilar ter# %e get

http://www.electrical4u.com/electrical-power-factor/http://www.electrical4u.com/electrical-resistance-and-laws-of-resistance/http://www.electrical4u.com/electrical-power-factor/http://www.electrical4u.com/electric-current-and-theory-of-electricity/http://www.electrical4u.com/electrical-power-factor/http://www.electrical4u.com/electrical-power-factor/http://www.electrical4u.com/electric-current-and-theory-of-electricity/http://www.electrical4u.com/electrical-power-factor/http://www.electrical4u.com/electrical-resistance-and-laws-of-resistance/http://www.electrical4u.com/electrical-power-factor/


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g g

emoving proportionality constant we get,

'here ns is synchronous speed in r. p. s, ns > ?s @ A0. $o, finally the e#uat

of tor#ue becomes,

• 0erivation o" Q in tor+ue e+uation In case o" thre


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+ +$hase induction #otor there occur co$$er lossesrotor 'hese rotor co$$er losses are e-$ressed as

HI@@R@ 2e kno% that rotor current

$ubstitute this value of I" in the e#uation of rotor copper losses, %c. $o, we

The ratio of %" 7 %c 7 %m > ! 7 s 7 ;! 6 s< 'here %" is the rotor input, %c is th

copper losses, %m is the mechanical power developed.


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$ubstitute the value of %c in above e#uation we get,

3n simplifying we get,

• 'he #echanical $o%er develo$ed 4# '


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'he #echanical $o%er develo$ed 4# '

$ubstituting the value of %m

'e know that the rotor speed ? > ?s;! 6 s< $ubstituting this value of rotor s

in above e#uation we get,y calculating and substituting the all values we get the e#uation.

• (#uation of tarting Tor#ue of T!ree P!ase


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# g #Induction Motor

• Starting tor+ue is the tor+ue $roduced yinduction #otor %hen it is started 2e kno% that

the rotor s$eed N is ero

$o, the e#uation of starting tor#ue is easily obtained by simply putting thein the e#uation of tor#ue of the three phase induction motor,
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induction motor.pptx

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