25471 Energy Conversion 16

7/23/2019 25471 Energy Conversion 16

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ENERGY CONVERSION ONE

(Course25741)CHAPTER SEVEN

..INDUCTION MOTORS


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ROTOR CIRCUIT MODEL

The rotor urre!t "IR# ER$ %RR&'R (1)

IR#ER$ %RR&'s R* or IR#ER* $ %RR $s &' R* (2)

Note:+ro, -.st e/u.t0o! .! tre.t rotor e++ets ue to3.r0! rotor s6ee.s .use . varyingimpedance su66-0e +ro, . o!st.!t 3o-t.e soureER*

E/u03.-e!t rotor 0,6e.!e +ro, th0s 6o0!t o+ 30e8" 9R e/# RR$ s & 'R* (:) rotor e/u03.-e!t 0ru0t us0! th0s o!3e!t0o! sho8!

!e;t


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ROTOR CIRCUIT MODEL

Rotor 3o-t.e 0s ER*o!st.!t < rotor0,6e.!e 9Re/o!t.0!s e++ets o+ 3.r0! s-06


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ROTOR CIRCUIT MODEL

=-ot o+ urre!t +-o8 0! rotor +ro, e/u.t0o!s" (1)< (2)sho8! e-o8"


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>IN?L E@UIV?LENT CIRCUIT

Note".t 3er -o8 s-06s res0st03e ter, RR$sAAR* rotor res0st.!e 6reo,0!.tes < rotor urre!t 3.r0es -0!e.r- 80th s-06

.t h0h s-06s R*,uh -.rer th.! RR$s< rotor urre!t.66ro.hes ste.Bst.te 3.-ue.s s-06 eo,es 3er-.re

To e3e-o6 . s0!-e 6erB6h.se e/u03.-e!t 0ru0t +or0!ut0o! ,otorshou- re+er to rotor 6.rt o+ ,oe-o3er st.tor s0e

Rotor 0ru0t ,oe- re+erre to st.tor s0e(sho8! 0!-.st e/u03.-e!t 0ru0t o+ rotor) 0! 8h0h e++et o+ s6ee3.r0.t0o! 0s o!e!tr.te 0! 0,6e.!e ter,


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Re,0!0!"th.t 0! .! or0!.r tr.!s+or,er 3o-t.es urre!ts.! 0,6e.!es o! seo!.r s0eo+ e30e .! e re+erre to6r0,.r s0e ,e.!s o+ tur!s r.t0o o+ tr.!s+or,er

V6#Vs#. Vs

I6#Is#Is $ . 9s# .2 9s S.,e sort o+ tr.!s+or,.t0o! e,6-oe +or 0!ut0o! ,otors

rotor 0ru0t

I+ the e++et03e tur!s r.t0o o+ 0!ut0o! ,otor # .e++The tr.!s+or,e 3o-t.es .re"

E1#ER#.e++ER* .! rotor urre!t 0s " I2#IR $ .e++

?! rotor 0,6e.!e eo,e" 92#.e++2 (RR$ s &' R*)


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>IN?L E@UIV?LENT CIRCUIT I+ the +o--o80! e+0!0t0o!s e,6-oe"

R2# .e++2 RR 2#.e++2 R* the e/u03.-e!t 0ru0t o+ 0!ut0o! ,otor 0s

sho8! .s e-o8" (6erB6h.se e/u03.-e!t 0ru0t)


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Rotor res0st.!e RR< -oeBrotor re.t.!eR*.re 0++0u-t or 0,6oss0-e to eter,0!e0ret- o! .e rotors< e++et03e tur!s r.t0o .e++.-so 0++0u-t to eter,0!e +or .e rotors

+ortu!.te-.! ,.e ,e.sure,e!ts th.t0ret- 6ro30ereferred resistanceandreactance R2& X2, (though RR, XR0and aeffnot

known separately) ,e.sure,e!t o+ these 6.r.,eters o3ere

-.ter


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=OFER < TOR@UE IN INDUCTIONMOTORSBLOSSES

s0!e 0!ut0o! ,otor0s . s0!- e;0te ,.h0!e

0ts6o8er < tor/ue re-.t0o!sh06s 0s 0++ere!t +ro, s!,.h0!es

Losses & power-flow D!"r!#

the 0!6ut 0s e-etr0 6o8er .! the out6ut ,eh.!0.-6o8er (8h0-e rotor 80!0!s .re short 0ru0te) ?s sho8! 0! 6o8er +-o8 >0ure (!e;t) =0!0s 0! +or, o+

: 6h.se e-etr0 3o-t.es < urre!ts

1st -osses 0s st.tor 80!0! -osses I2 R#=SCL 2!2 Hsteres0s < E urre!ts -oss 0! st.tor =ore =o8er re,.0!e .t th0s 6o0!t tr.!s+erre to rotor

throuh .0r .6" 0s .--e .0rB.6 6o8er =?G


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=.rt o+ 6o8er tr.!s+erre to rotor -ost .s " I2R#=RCL < rest o!3erte +ro, e-etr0.- to,eh.!0.- +or, =o!3 +r0t0o! < 80!.e-osses =>


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Note"0! 6r.t0e ore -oss 0s 6.rt0.-- re-.te to st.tor.! 6.rt0.-- to rotor ho8e3er s0!e 0!ut0o! ,otoro6er.tes .t . s6ee !e.r s!hro!ous s6ee re-.t03e

,ot0o! o+ ,.!et0 +0e- o3er rotor sur+.e 0s /u0te -o8(+re/ue! o+ 0!ue 3o-t.e # s +e)< rotor ore-osses .re 3er t0!

These -osses 0! 0!ut0o! ,otor e/u03.-e!t 0ru0tre6rese!te . res0stor RC(or GC)

I+ ore -osses .re 03e! .s . !u,er ( F.tts)o+te!-u,6e 80th ,eh.!0.- -osses< sutr.te .t 6o0!t

o! 0.r., 8here ,eh.!0.- -osses .re -o.te


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The h0her the s6ee o+ .! 0!ut0o! ,otorthe h0her0ts +r0t0o! 80!.e .! str. -osses8h0-e the -o8erthe ore -ossesso,et0,es these : .teor0es o+-osses .re -u,6e toether .! .--erotational losses

S0!e o,6o!e!t -osses o+ rot.t0o!.- -ossesh.!e 0!

o66os0te 0ret0o!s 80th . h.!e 0! s6eetot.-rot.t0o!.- -osses o+ . ,otor o+te! o!s0ere o!st.!t E$AMPLE :? 4* J* HK 5* h6 : 6h.se 0!ut0o!

,otor 0s r.80! J* ? .t *5 => -.0!

The st.tor o66er -osses .re 2 F .! rotor o66er-osses .re 7** F +r0t0o! < 80!.e -osses .re J** Fore -osses 1** F .! str. -osses !e-00-e >0!"

(.) =?G () =o!3 () =out () e++00e! o+ ,otor


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=OFER < TOR@UE IN INDUCTIONMOTORSBLOSSES E?M=LE

(.) =?G#=0!B=SCL =ore=0!#: VTIL#: (4*) (J*) (*5)#424 F

=?G#424B2B1# :J F

() =o!3#=?GB=RCL#:JB7**$1***#:7 F () =out#=o!3B=>


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=OFER < TOR@UE IN INDUCTIONMOTORS

E,6-o0! the e/u03.-e!t 0ru0t 6o8er


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st.tor o66er -osses ore -osses .! rotor o66er-osses .! e +ou!

st.tor o66er -osses (: 6h.se)#=SCL# : I12 R1 ore -osses =ore # : E12 GC

=?G#=0!B=SCLB=ore o!- e-e,e!t 0! e/u t 8here .0r .6 6o8er .! eo!su,e 0s res0stor R2$s < .0r .6 6o8er .! .-soe 03e!" =?G#: I22 R2$s (1)

?tu.- res0st03e -osses 0! rotor 0ru0t" =RCL#: I22R2 (2) =o!3#=?GB =RCL#:I22R2$sB:I22R2 # :I22 R2(1$sB1)

=o!3# :I22 R2(1Bs)$s


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Note" +ro, e/u.t0o!s (1) < (2)

rotor %opper losses !r "!p power ' slp

The -o8er the s-06 the -o8er the -o8er rotor -osses ?! 0+ rotor 0s st.t0o!.r s#1 < .0r .6 6o8er 0s e!t0re-o!su,e 0! rotor th0s 0s o!s0ste!t 80th the +.t th.tout6ut 6o8er 0! th0s .se 8ou- e Kero s0!e ,#*

=out#T-o. ,#* =o!3#=?GB=RCL#=?GBs=?G#(1Bs)=?G (:) I+ +r0t0o! < 80!.e -osses .! str. -osses .re

!o8! out6ut 6o8er

=out

#=o!3

B=>


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I!ue tor/ue T0!.s " tor/ue e!er.te 0!ter!.-e-etr0 to ,eh.!0.- 6o8ero!3ers0o!

It 0++ers +ro, .3.0-.-e tor/ue .,ou!t e/u.- to+r0t0o! < 80!.e tor/ues 0! ,.h0!e

T0!#=o!3$, .-so .--ee3e-o6e tor/ue o+ ,.h0!e Sust0tut0! +or =o!3+ro, (:) < +or, (1Bs) s!

T0!# (1Bs)=?G$ %(1Bs)s!# =?G$s! (4)

So (4)e;6ress 0!ue tor/ue 0! ter,s o+ .0rB.66o8er < s! S6ee8h0h 0s o!st.!t

=?G0e-s T0!


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SEPARATION of PRCL& P%o()( (*+%to( #otor E,.%%t.

=.rt o+ 6o8er o,0! .ross .0r .6o!su,e 0!rotor o66er -osses< the other 6.rt o!3erte to,eh.!0.- 6o8er to r03e ,otor sh.+t

0t 0s 6oss0-e to se6.r.te these t8o 0++ere!t uses o+.0rB.6 6o8er< 6rese!t the, se6.r.te- 0! thee/u03.-e!t 0ru0t

E/u.t0o! (1) 0s .! e;6ress0o! +or tot.- .0rB.6 6o8er8h0-e (2) 03es .tu.- rotor -osses the 0++ere!eet8ee! these t8o 0s =o!3< ,ust e o!su,e 0! .!e/u03.-e!t res0stor

Ro!3#R2$sBR2# R2(1$sB1) #R2(1Bs)$s

=OFER < TOR@UE IN INDUCTION


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The 6erB6h.se e/u03.-e!t 0ru0t 80th rotoro66er -osses< 6o8er o!3erte to ,eh+or, se6.r.te 0!to 0st0!t e-e,e!tssho8!e-o8"



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=OFER < TOR@UE IN INDUCTIONMOTORS TOR@UE E?M=LE

. 4J* V J* HK 25 h6 4 6o-e Y o!!ete 0!ut0o!,otor h.s +o--o80! 0,6e.!es 0! $6h.se re+erreto st.tor 0ru0t"

R1#*J41 R2#*::2

1# 11*J 2# *4J4 M#2J: tot.- rot.t0o!.- -osses .re 11** F < .ssu,e to e

o!st.!t

ore -oss 0s -u,6e 0! 80th rot.t0o!.- -osses >or rotor s-06 o+ 22 P .t r.te 3o-t.e < r.te +re/ue!+0!"(.) S6ee () st.tor urre!t () => () =o!3< =out

(e) T0!< T-o. (+) E++00e!


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Tot.- 0,6e.!e " 9tot# 9st.t&9+#

# *J41&'11*J&124$X:11

# 1172 & '77 #14*7 $X::J Resu-t0! st.tor urre!t"

I1#VQ$9tot# 2*J$X* $ 14*7 $X::J #

1$XB:J ?



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() ,otor 6o8er +.tor" =>#os ::J # *:: -.0! () I!6ut 6o8er o+ ,otor"

=0!#: VTVLos Z#: ; 4J* ; 1 ; *::# 125:* F =SCL#: (1)2 (*J41)#J5 F .0rB.6 6o8er "=?G#=0!B=SCL#125:*BJ5#1145

F .! the 6o8er o!3erte 0s" =o!3#(1Bs)=?G#(1B**22)(1145) #1155 F

=out#=o!3B=rot#1155B11**#1*45 F#141 h6



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(e) 0!ue tor/ue 0s" T0!#=?G$ s!# 1145 $ 15 #J2 N, out6ut tor/ue" T-o.#=out$,#

1*45$144#5J N, (+) ,otors e++00e!"

# =out$ =0!; 1**P #1*45$125:* ; 1**P

# :7 P

INDUCTION MOTOR TOR@UE


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INDUCTION MOTOR TOR@UECH?R?CTERISTIC

Ho8 oes 0ts tor/ue h.!e .s -o. h.!es[ Ho8 ,uh tor/ue .! su66- .t st.rt0!o!0t0o!s[ho8 ,uh oes the s6ee o+0!ut0o! ,otor ro6 .s 0ts sh.+t -o.

0!re.ses[ 0t 0s !eess.r to u!erst.! the re-.t0o!sh06

.,o! ,otors tor/ue s6ee .! 6o8er

the tor/ueBs6ee h.r.ter0st0 e;.,0!e+0rst+ro, 6hs0.- 30e86o0!t o+ ,otors ,.!et0+0e-< the! . e!er.- e/u.t0o! +or tor/ue .s+u!t0o! o+ s-06 er03e



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I!ue Tor/ue +ro, . =hs0.- V0e86o0!t >0ure sho8s . .e rotor o+ .! 0!ut0o!,otor

I!0t0.-- o6er.t0! .t !o -o.


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Co!se/ue!t- E

R

0!ue 0! rotor 0s 3er s,.--.! IR8ou- e s,.-- So +re/ue! 0s 3er s,.-- re.t.!e o+ rotor 0s

!e.r- Kero .! ,.;0,u, rotor urre!t IR0s

.-,ost 0! 6h.se 80th rotor 3o-t.e ER Rotor urre!t 6roues . s,.-- R.t .! .!-e

'ust s-0ht- re.ter th.! * eh0! !et

Note:st.tor urre!t ,ust e /u0te -.re e3e! .t!o -o. s0!e 0t su66- ,ost o+ !et Th.t 0s 8h 0!ut0o! ,otors h.3e -.re !o -o.

urre!ts o,6.re to other t6es o+ ,.h0!es


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The 0!ue tor/ue 8h0h ee6s rotor ru!!0! 0s03e! "T0! # R; !et or T0!# R!ets0!\

S0!e R0s 3er s,.-- T0!.-so /u0te s,.-- e!ouh'ust to o3ero,e ,otors rot.t0o!.- -osses su66ose ,otor 0s -o.e (0! >0 ()) .s -o. 0!re.se

,otor s-06 0!re.se .! rotor s6ee +.--s S0!e rotor

s6ee ere.se ,ore re-.t03e ,ot0o! e;0st et8ee!rotor < st.tor ,.!et0 +0e-s 0! ,.h0!e Gre.ter re-.t03e ,ot0o!6roues . stro!er rotor

3o-t.e ER8h0h 0! tur! 6roues . -.rer rotor

urre!t IR



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Co!se/ue!t- R.-so 0!re.ses ho8e3er .!-e o+rotor urre!t < Rh.!es .s 8e--

S0!e rotor s-06 et -.rer rotor +re/ue! 0!re.ses+r#s+e.! rotor re.t.!e 0!re.ses( LR)

Rotor urre!t !o8 -.s +urther eh0! rotor 3o-t.e (.ssho8!) < Rsh0+t 80th urre!t

>0 sho8s ,otor o6er.t0! .t . +.0r- h0h -o. Note:.t th0s s0tu.t0o! rotor urre!t 0!re.se .! \

0!re.se I!re.se 0! Rte!s to 0!re.se tor/ue 8h0-e

0!re.se 0! \ te!s to ere.se the tor/ue (\A*) Ho8e3er s0!e the e++et o+ +0rst 0s h0her th.! the

seo! 0! o3er.-- 0!ue tor/ue 0!re.se80th -o.


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Us0!" T0!# R !ets0!\ er03e out6ut tor/ueB3ersusBs6eeh.r.ter0st0 o+ 0!ut0o! ,otor

E.h ter, 0! .o3e e/u.t0o! o!s0ere se6.r.te- to er03eo3er.-- ,.h0!e eh.30or

I!030u.- ter,s .re"1 R0ret- 6ro6ort0o!.- to urre!t +-o80! 0! rotor .s -o! .srotor 0s u!s.tur.te

Curre!t +-o8 0! rotor 0!re.ses 80th 0!re.s0! s-06 (ere.s0!s6ee) 0t 0s 6-otte

2B !et ,.!et0 +0e- 0! ,otor 0s 6ro6ort0o!.- to E1< there+ore.66ro;0,.te- o!st.!t (E1.tu.-- ere.ses 80th 0!re.s0!urre!t +-o8) th0s e++et s,.-- o,6.re to the other t8o R# os ZR =>R#os(.t.! sR*$RR) 6-ot o+ rotor => 3ersus s6ee sho8! 0! +0 () S0!e 0!ue tor/ue0s 6ro6ort0o!.-to 6rout

o+ these : ter,stor/ueBs6ee h.r.ter0st0.! e o!strute +ro, r.6h0.- ,u-t06-0.t0o!o+ : 6re30ous 6-ots >0s (.) .! sho8! 0! +0

()



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De3e-o6,e!t o+ 0!ut0o! ,otor tor/ue s6ee

De3e-o6,e!t o+ 0!ut0o! ,otor


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De3e-o6,e!t o+ 0!ut0o! ,otortor/ue s6ee


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Th0s h.r.ter0st0 ur3e .! e 030e 0!to threere0o!s

1st re0o!"0s low-slip region0! 8h0h ,otor s-060!re.ses .66ro;0,.te- -0!e.r-80th 0!re.se -o. 0s .66ro;0,.te- u!0t 8h0-e rotor urre!t 0!re.ses-0!e.r- 80th s-06

The e!t0re !or,.- ste.Bst.te o6er.t0! r.!eo+ .!0!ut0o! ,otor 0s 0!-ue 0! th0s -0!e.r -o8Bs-06 re0o!



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2!2

re0o! o! ur3e .--e moderate-slip region I!,oer.teBs-06 re0o!rotor +re/ue!0sh0her th.! e+ore< rotor re.t.!e 0s o! thes.,e orer o+ ,.!0tue .s rotor res0st.!e

B I! th0s re0o! rotor urre!t !o -o!er 0!re.ses.s r.60- .s e+ore.! the => st.rts to ro6

B 6e. tor/ue(6u--out tor/ue)o+ ,otor ours .t

6o0!t 8here +or .! 0!re,e!t.- 0!re.se 0!-o. 0!re.se 0! rotor urre!t 0s e;.t-.-.!e ere.se 0! rotor =>



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:

r2

re0o! o! ur3e 0s .--e h0hBs-06 re0o! I! h0hBs-06 re0o! 0!ue tor/ue .tu.--ere.ses 80th 0!re.se -o. s0!e the0!re.se 0! rotor urre!t 0s o,6-ete-

o3ersh.o8e ere.se 0! rotor => >or . t60.- 0!ut0o! ,otor 6u--out tor/ue 0s

2** to 25* P o+ r.te +u--B-o. tor/ue

?! st.rt0! tor/ue (.t Kero s6ee) 0s .out15*P o+ +u--B-o. tor/ue U!-0e s!hro!ous ,otor 0!ut0o! ,otor .!

st.rt 80th . +u--B-o. .tt.he to 0ts sh.+t


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INDUCTION MOTOR INDUCEDBTOR@UE E@U?TION

E/u03 0ru0t o+ 0!ut0o! ,otor < 0ts 6o8er +-o80.r., use to er03e . re-.t0o! +or 0!uetor/ue 3ersus s6ee

T0!#=o!3$, or T0!#=?G$s! L.tter use+u- s0!e s!0s o!st.!t (+or +e

25471 Energy Conversion 16

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