E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip...

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---l E{ectricat jvt&cfrines I fftr e e -? fias e Induciion SYlotors ?art (t) mffiHs-ffi 0f 0{2045000 . 0101I04$$$$

Transcript of E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip...

Page 1: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

---l

E{ectricat jvt&cfrines

I

fftr e e -? fias e Induciion

SYlotors

?art (t)

mffiHs-ffi0f 0{2045000 . 0101I04$$$$

Page 2: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Examole (l)

A 6-pole, 3-phase indu"tion ryg!* i-u_-.,g -. 4 lq Hz supply. If it is running at 970 t'P'ffi',

findthesrip iu H ffi s- ffiExamole (2) 0t01 2015000 . $t $t 104[000

A 3-phase induction motor is wound for 4-poles and is supplied from 50 Hz system. Calculate (i)

the synchronous speed, (ii) the speed of the motor when the slip is 4Yo, and (iii) the rotor current

frequency when the motor runs at 600 r'p'm'I

Examole (3)

A 6-pole alternator is running at 1000 r.p.m. and supplies an 8-pole induction motor. Find the

actual speed of the motor if the slip is 25%'

Examole (4)

A 50 !Iz, 4-pote, 3-phase induction motor has a rotor current of frequency 2l1z' Determine (i)

the slip, and (ii) the speed of the motor'

Examole (5)

A 3-phase, 6-pole induction motor is connected to a60Hzsupply. The voltage induced in the

rotor bars is 4 v when ttre rotor i1y rt*rastill. calculate the.voltage and frequency induced in

the rotor bars at 300 r.P.m.J

Examnle (6)

A 3-phase supply, 400 V wound rotor motor has detta-connected stator-winding and star-

connected rotor-winding.'The stator has 48 tums per phase while the rotor has24 turns per

phase. Find the standstill or open-circuited voltage across the slip rings.

Example (7)

A 6-pole, 3-phase, 50 Hz induction motor is running at full-load with a slip of 4%' The rotor is

star-connected and its resistance and standstill reactanie are 0.25 Q and 1.5 Q per phase' The

Page 3: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

_\

e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming

the slip rings are short-circuited.

Examole (8)

A 4-pole, 3-phase, 50 Hz induction motor has a star-connected rotor. The rotor has a resistance

of 0.1 C) per phase and standstill reactance of 2 Q per phase. The induced e.m.f. between the slip

rings is 100 V. if the full-load speed is 1460 r.p.ffi., calculate (i) the slip, (ii) the e.m.f. induced inthe rotor in each phase, (iii) the rotor reactance per phase, (iv) the rotor current, and (v) the,rotor

power factor. Assume slip rings are short-circuited.I

Example (9)

A 150 kW, 3000 V, 50 Hz, 6-pole star-connected induction motor has a star-connected slip ring

rotoi with a transformation ratio of 3.6 (stator / rotor). The rotor resistance is 0.1 Cl per phase

and its per phase leakage inductance is 3.61 mH. The stator impedance may be neglected. Find

the starting current on rated voltage with short-circuited slip rings.

Example (10)

A 3-phase siip ring motor gives a reading of 55 V across slip rings on open circuit when at

standstill with normal stator voltage applied. The rotor is star-connected and has impedance of(0.7 +3 5) Q per phase. Find the rotor current and power factor when the machine is (i) at

standstill with slip rings joined t6"a star-conn'ected starter with a phase impedance of (4 + j 3) O,

and (ii) when running normally with a 5% slip. :i

L L \-,'^c

B. " ol

Yo.' 5

f tllTrn {5

a

smffieffi[t ottoltooo' otot2o4$ooo

tr

Page 4: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase lnduction Motors

[Tttm+ttoo'$t

&ffi*{xu46000

Ad"r^t'yrt ,duV,1'vzr)td/ ?*) -.lQy,J

-. _2c )) -.L)

.a

3/-\9 l|.w ''

-\//'-,/"'J e2 ) *':); -f

,3*-, ./- -C---..---

",-l-a Z U{ '-.1,'"'"

J t a:15- oJ--'L'

Dis oJ.!*f"3*"f7

? --'\) Ot d /'

*s7,J r{<-*-,-\*

' ( .,t.c. :1"^^t /{otor) Jl ^r'&1 rJ\ (s :,

+ - l.Lon5 Lr(lCLt o1r1

^r p-)l dlU

\ - . t*t"r q'u\ ,Pd\

tt-,tu, .{-rt ti\L\, -n't\ ^r it--r---,,-F* rg-

t$/"bt) 67l.--gt o/l n,;ff-

)D) -

-2)l

I'rl

. U tlz' 'rJ AL\--t \

Page 5: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Ttrree Fhase [nciuction lviotors

St",iorSTATOBwiNolNG

Wound r,vpe

-/"-r---/

d Wirxlho

$ Gnnect,{=-U'G.

->r--W.rV

-"r- Js U1;-C1L \-J NE yr$\ ,;-o9 q<r\-+_N t-lG! Gf

Y:!. )i &r& . u-\ rrGKl o--D <l*s+ o--.r,Jl -u.idL-.--

-/-,& ,- '94\ \ -,FL OUll o -^-sD \a.^i

tL)\'*-;)

:to.iof J\ t-!-1-, frt- (!tG"

-2sl\

2'(Mtor

--qJ ,?,U\

CIf 012045000 . 0{0{204$00$

RL.r

WounA tro<

MYo tof

Squiuel cage x

l"ll.-i

Page 6: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase induotion fulotors

: fotor JJ :4 2- 3.u,D

i') Silurr<-[ Qe t:p<Srllttr'rre ( {at14 "/*/*

W; ,Ett * ut -*;1,- -f -,\r)\ rd\ =-)\ - -

iL )

JrA-

Waund lyp"( 5t*tor) J\ g dU\rotf cs_tljl (; n-) yr; eGt_ GL-

' (Y - jt",r-) Lg* drrJ GJ(\ o--6>

(fb r-*,-gs) ,,sDtl O(Jf uGJ(l U\) i 4a;LtL d/\ ,u)-_r, Ns---d dd i;At? J{-,G- <l*:, -A

,l

( rh,eo:tot-) I-otor J\ aj\,

f?otC,15 Xgnel.ic [eU. d.ue to3- (PLose

fLt-u/ffeltU-S

;bL : 5t.J"r. J\ c-,Gf- ,f ,-4 1., ,U

mffiffi&trfr01012045000 . 01012040000

,r r l"t*__t ,Ln-

I .--. tl:. 1

.-l I s\,'-rl-r J-L

Page 7: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

_t

Three Phase lnduction Motors

'uLf f*q,4 ov,6,1^n

.o-

, in u.)t,

Sin (tot -lzo") fiffiH&IUT0l 0t 20450u0 ' 0l 0{ 2040000

CSJltJ

qtrr/Yn

)

Fs)x

€ )7

,(+4")

? - of u'.lt = 3o

r\.-F\-J

€.., x

.G-l-lJ

cOr7 = € Sin (urt + l?o")I rrr

44 -t)-- ,L. iry ,{C\9) o r>\ d*}t db\ ipfJ

( + €") cP 4'3)*\tl arPt *:ti-r;v -+)oW -u@l it-dt \;-o (r-,/p"g,r)j c_,U])

)-\ - crj.. LL)t = o :c*

=O € ,Yn I

( art = o) " G \ 0 qF"rcr (*l ",f -e

)XCSI Yrr\

i 4l

tq- )

Page 8: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

T'i"rree Phasc lnduction Motors

z[qiooo ' otrt2046000

ol'{\+)

s$ffi

tlt = 3e)'

tJJt = 9o*

+*7 L

60'

s,-

tut

rl.lt

:o-J-z

.Ca3s -S\\-. \/I -rY\

Page 9: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

- _\

Three Phase Induction Motors

rut 3o

(^)tT

t,- lr.f0'

*-*r',-

r..tt- '.;h'{t*

Y F "'t' €!ts'

. ^.1^Y..,.ftous Spee.l

ol20 )

Dt- S- tr[*o s*PPb P-yn"^g , f Az7

,G ] (? -/);\> P,;*,_

Njt [r P,ml

Qt"s .

'*\;tt

"AJr" 1^-)il+J I J

l

na "-f flof-or

t 6 t

Page 10: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Tirree Phasc lnduction Motors

C-0,, ,? -,:)1 f C 6/ d# I *\.r-, " G I C).-(4 Vru+; qf ,

C tternnte tlolhe m^l"c-,( {t"'bsis Po"

f,?,t"l,y tuy"i,c freld

d)z€,Z

9,

{z

9'.,= Gs

Gs

6trn

3o

5o

rl-sL

in niL(lJL

L

Gs

/in ,nYGs \zci +

+ ;in *t /' tz'i

5(n tZ.; ]

€r1wts+ C-rt

(9,v

--1--n Sin ult t. €_-...L

G!t)L

€,- 6in of -ts +*

-3

r{ Sin ( t-.rt + t Zd) +t-

"r -J o

Sin (,rrt - n;) J Sin 3o

.--G--1.", --sI yr\

5in

l7l

(- sin -t )

Page 11: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phasc lnduotion Motors

.l

3

^-t.\Lr \ /-'1-C, +(-\,/p1 'V

€ ,n.lI -'-.'z

a/ Cos urt- + (- Sin -t)'

O'l rinCup l,e BRHAilTfi0t 0{ 2045000 . 0t 0t 2046000"4 o@

-;,e- -=

-.^FJ\ */! ^r\,-Jt ,A, q ,\,. c)Gdt Jr,. _l

\-rl dJf J-q. St*tor Jl ui;J_

* "C 1rt1 rotnr -J I crUf- ,LA -^j(- - .-V I -";"|,ll d;\ l:-a-rzot

y^otor J\ .-,GJ-1;t u.^ ?. );; dbL_ ,f,-*i ,,_*,

dLrl, G {,artr"..,} -+ ro tof J\ a -?\-, - \ "t; - 3_d

J

Jl O Y^e:-rJL )4c1JJl '-a l--^--' -4

,G\c (rotor) Jl "'-t-!'Y.-=

()A d;\ ,, -/EJJ 4-V b/!cbt o.-D rk -o3-> tr--,-

-t

-L,l € P6to r

", )r.t

t\; tt:

d#.\

i 8l

Page 12: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

-I'hrco Phocp Inrlr rnfinn I\lntorcl lll vv r lrguv lllvuvLrv^. , ' ^-.-^ J

ffiffiffi&ffi0t 0t 2045000 . 0t 01 2046000

ROTATION OF STATOR FIELD

/t)I

,J!+ *")pJO;:r:; rot"r JI

GL roto r"G] q-; -ul)"

-t; -t -

)\ -:

Sl^p t_: Dy)l

rotor )\c)*:- e ,? Ot--o -{;i U,i.o[af J ! t]+f d ;uL=- e.rn P :3cs <J_

1ep ^a^/l e t-:J'{+t QJt-o * {-t .-- e."n.P J\ tj ,s,-,l^otor S\ t--DLi_:_ ,A. &; (\_^r_" eJLo *{

(o'l-- 3or S)'l

?J^.I.d rot,i;5 ,^ rg^J;. P,.r"t sp"*l

yD, U )* ut' ",3J -J

U !. t'' '" tl JL: ''ll \ -A--,a-

dt+1 b'bb'

SQeeA

N"

5tip A =

(R"fur SPee"J.

lel

Page 13: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase induction Motors

Q, trr Currerrt- _IZl-.n3

NS_AJD'

)?o I

,tr st"^clstt |.L

NsNN,

---_---_>.

,P.

\?O PSN. a

D,, I7?<.?D=

S = I -- P'=f

= 5o HV, N = B7o [.e.rn

N), = lzo P-

rD

-dL'<)o \}.l-Lt Ofn

\ ooo f , P.rn

E*(r ) DREATffi0t0{2045000 . 0{0{2046000

i r11 !I \!-r I

Page 14: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase lnduction Motors

f)= 4,Fx (zl

L) N5

vlz )

5 = /t'/.t

P=5o

D1zo l

NJ=

o'I

MRffi&HWfi0{0,12045000, 0,l0t2046000

L) AJs

ii) ru

iii) .P'

= ?.?

7?

J_

o-L Prn??

Sot*lion

fi) 6 =,l

o.o4

Li L )

AJs - A,

AJs

l5oo r P'r.n

Nr = I ++o f'P. rn

6oa

SF

E^ (3)

AJs =aa.)

Iooo

'7 .-)

r' P. rn l----' *)Stnnn..'t"r

1, \--' ,:- <9 i'^ai- fnOt '

i il 1

Page 15: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase Induction Motors

rl- t.Q-l,t€r^qlof

s-(P

A/ f) looer rt 6

l7o, \2e,

1?o P

5o Vz

\zo * 5o

Ito ?

[)

I t|- 4- o f 'Q.^rv-'

P

= 7 so r. P.rn

at',)oA

//N)s - ft)

2q.;

?7)

HZ /

77= 5o

c') S =

Ns* Nl

AJrN, = 731 . ?.5 r. P.nt

= 4 ) P' d7.

ia ) /\i

E^ (4)

.'=

,-)

4 "/"

- .-l^*[i ^Ns

/\r =

6,^pp! ft% F

5-+ ,."^A. rr,ot. AJs

SJ

0{012045000 . 0{0t2046000

Ns-____9

I tz 1

15oo r'P.rn

Page 16: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

\

Three Phase Induction Motors

E f F.&- 4 stP on the Rto, e."a-..r

Etondsti(l S = I P' PrIrL-7 e ,^.P. P<,r pLSe

rea1to,.6p lDen p\oSe

"t st-fr s<t P'= Er

Cr-oh.z t-otol- e.- .-F. kr pLse ,

: S X. : ro to t- reacto^( e {-&,r pL.a.s< .

J.ro Lor

I-otor

t_l-z

x;'

mffiffi&rkT0{0{2045000 . 0t0t2046000

E" (s)

l-FL-L

oo

?)

6,??

Hz) E.=4vJt_l-

o-L AJ = 3oo r?ln

\2o P

S"{*Iiw\

\ ?oof\J s (rI rr I

r, P. rn

Page 17: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

.\

Three Phase lnduction Motors

ffi| *"'i, 1j'd,,

34Sunoly .-__t-,L..\}' 4'," \,14,\

# Stfir Iwincino l

,\i'

,r"'t nt

s E,'to,l I

."'-L:---i,A{ ?to

ghori€irtUtGJRotor Winding

,f St.clstiL( ri*t^t**-\c)-lq(-..+ L ?"(,)

"t runrull

-Jt( 8r

--,.)Ns-N_

Ns

-

14

= .i> C.

= sr

= o,75

F.L-z

P'

3

A-5

\o(i

A7 Itttt'

*(P' , X, ,

* (f?., , *., ,

p<r PLr^se7,, Er)

7. , E-)

L-. tL-e :t.to-r

.,., Pgtof

5t**15 titt '|et

7), tt.uditL

R/r pL..l< rotc,1-

,t- twnNr!

(,/v\* (R,, E;)

tr+ l

s t+ "s''

Page 18: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Thnee Phasc Induction Motors

5t",^Asti I

Y-ot or G,-rre,^t [:er PV.^se . T- .

rotor P. P. (F)7

R,

--(2

,?t

6t Yu^rt,y of SLp 'S "

Yator Ctxryrev^t. , T-. =

Ibtor P,F. Co, +- =R.

1,

F. EL1

ot P,'Gt

/='t-2

--t-L2_

5E-.

E* (6)

Tlt|tr. t *.I

N.(R.tor

-Er-<

t15r

Page 19: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase lnduction Motors

a/v,

{- = \f--L

G- (oc, J'rCzU^e

P=

-tL

-:'

\-Dz

X,'

'f)-z

.a+ x;

o,o4 ,( \oca

Fo. o + r( 1.5 =

=48 fu? = 74

- I L,

) 6-^"1^f t O1r1.

t_Lz Z oo V"Li

E^ (7) DME&ffi0,1012045000 . 0{012046000

E, = 4oo

6)

o,2 5

I,.

V"(t , N,

?tr U'oe

G+B

E 1L+ v*j.t

()=

R.

S"J^Jiorn

? 3l

o,o 6

\ "tt.-rL_

f(- z

9A{

5e Hz , g = 4'/. ) Y- G".*<f-rA rotor,

Xr = 1- 5 n ./ E.r"-. = loo \J*ti',

p. P^+

cr^. fwr',nt-g G^"L+i-n

SE.

S*.

ftSl

Page 20: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase Induction Motors

G'C= o,37 t,3R,-' * X.''

E.^(s)

=+

N: 1460

L') 5 =??

l?o P

O)f 5o H? .,

X. =

,Y- G,-^ecteJ

75L,-J?_

.|-.O rn

ii ) Liil x; 2

q- aT?U)

,

G.

--a5o

AJs()

+-tt

Ns- N\ +c) "/,

n/'Ar-

ilr^tisr,lI 5oo r,p. rn

N( ? 66

Ioo.F r. s4 V.{i

: o,ot66 J( ?-

J-t'b \oy )

too V.tt

t u) f-.t )

DffiHAIUI0,l0{2045000 . 0,l012046000

a*.

l17 t

= o,o 53? _ft

Page 21: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase lnduction Motcrs

t-t--+f ts.s7 rt

: o,Bb=

ffi immffi&ffii i,totto+s000 " 01012046000

G' €. t13

& (3)

'?o = (5o

Y G*^ecteJ

Ktr-r, Y- Gr^-,."Jd- St"f.or

J-y? Lol- ) Nt

f')L, t. - 5ooo Voftt t,/-F.e

o.l JL )

P = 5o Hz

I +.7 J-t-

r- 3 J-L

V*{t

)

36) R.Nt

= 1.13

:t^trr)-

i-o \o r

JL

(-:\<(JJ

t_l-7 3, 6l .^ H , (R, , X ) o,re ,,11r?cl-'L ,

' St.^t& G-n*d, I-, :U rrf";, utltaye u'"'t[^?? ,tf t,r,-q5

iJSLJ c^rcrr^t<.[ st^p

X. -: ?rf L,

X. rulurr"A to

Q, . re [e'rreo[ t"

S"J.;,S"iorl

-f-/,t- r -- f- t [^" /

; i8 1

Page 22: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phasc lnduction Motors

f /^--r 3 oo o/-L-t -

f , rQerreA t" Y"tor =

424. r s6tt7 +

J3

r-.l l.j + t4.7'\

/^\ Jooo '' \' Er. F*73z

.,l o l

Ll t3

4-z;4 . t

+

n

E" (lo)

t-t-L_nr,L LrY\e

Z, = (t?, + i< sL ,JJ./

55

J X.

V-lt Y - G,-""cteJ rotctr )

= o,7 -{-

t ) T-, , G, €. of st.,-,Jstit[

to S to"- -' G*""'ecteo( St"^fe'r

'lt' ) S=

rpitL

"+

57.

s U4: rt13s j6ined

4+ )3 -rL

{\Rt Xs

, Co, 'fS",l^jic,rA

{;ic-=Lz = f zu^" / J3

I is I

3r I v-tI

Page 23: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase Induction Motors

i)

XzlI

Xt

, ud?, Xr- I Y- Gr^"J1t)SturJetf

r3-A- /'(-q, \Xr

I V G,.-^"ctea I

I Y'otof r

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Page 24: E{ectricat jvt&cfrines - ECED Mansoura · PDF file01-05-2014 · e.m.f. between slip rings is 100 V. find the rotor current per phase and power factor assuming the slip rings are short-circuited.

Three Phase Induction Motors

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