Post on 31-Jul-2022
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Example (ll)
The three-phase induction motor having star-connected rotor has an induced e.m.f. of 50 Vbetween the slip rings at standstiil on open-circuit. The rotor has a resistance and reactanceper phase of 0.5 Q and 4.5 C) respectively. Find the current per phase and the power factor atstarting when (i) the slip rings are short circuited, (ii) the slip rings are connected to a star-connected rheostat of4 C2 per phase.
4.5 st 4.5*
aR"fur 5l^p Q"tor Gl'e,istotr,k,
Example (12)
A star-connected rotor winding of three-phase .induction motor has a resistance of 0.2 Cl per
phase and standstiil reactance of 1 Cl per phasp. Find the value of external resistance per,
phase to be added to give maximum starting torque. What is the power factor of the rotor
circuit then?
Example (13)
-
A 150 kW, 3000 V, 50 Ha 6-pole, star-connected induction motor has a star-connected slip-
ring rotor with a transformation ratio of 3.6 (stator/rotor). The rotor resistance is 0.1 Q per
phase and its per phase leakage inductance is 3.61 mH. The stator impedance may be
neglected. Find the starting torque on rated voltage with short-circuited siip rings.
o'5sl
Example (14)
The rotor resistance and standstill reactance per phase of a 3-phase induction motor are 0.02
f) and 0.1 Q respectively. What should be the value of the external resistance per phase to be
inserted in the rotor circuit to give mocimum torque at starting?
Examole (15)
The rotor resistance and standstill reactance of a 3-phase induction motor are 0.2 f,l and I Qper phase. The voltage between slip rings with rotor locked and full voltage on the stator is
110 V.
(i) 'Find the starting rotor ourent/phase when the rotor slip rings are short-circuited to form
the normal running condition.
(ii) What should be the value of the external resistance per phase to be. inserted in the rotor
circuit to give maximum torque at starting? Also, find the rotor cur:ent/phase nnder this
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A 440 v, 3-phase, 50 Hz, 4-pole, Y-connected induction motor has a full-load speed of L4zsr.p.m. the rotor has an impedance of (0.4 + j 4) O and rotor/stator turns ratio is 0.8. Calculate(i)firlIJoadtorqug,(ii)rotorcr:rren!and(iii)full.loadrotorCuloss.
Example(17)
Examole (20)t
An 8-pole, 3.phase, 50 Hzinduction motor lias. a rotor resistance of 0.025 CJ/phase and a rotor
A 3-phase, 4001200 V, Y-Y connected wound-rotor induction motor has 0.06 (l rotor
resistance and 0.3 Ct standstill reactance per phase. Find the additional resistance required in
the rotor circuit to make the starting torque equal to the maximum torque.
Example (22)
An 8-pole,50Hz,3-phase slip ring motor has an effective rotor resistance of 0.07 fyphase.Its staliing speed is 630 r.p.m. How much resistance must be inserted per phase to obtain themaximum torque at starting? Ignore the magnetizing current and stator leakage impedance.
Example (23)
A 4-pole, 3-phase, 50 lll slip-ring induction motor rotates at 1440 r.p.m. with slip,ringterminals short-circuited. The rotor resistance is'0.1 C)/phase and standstill reactance/phase is
0.6 C). If an external resistance of 0.1 O/phase is added to the rotor circuit, what will be the
new full-load speed?
Example (24)
A 6-pole, 50 Hz, 3-phase induction motor has rotor resistance and reactance per phase of 0.02
Q and 0.1 O respeotively. At what speed is the torque morimum? What must be the value ofexternal rotor resistance per phase to produce two-third of the maximum torque at starting?
Examnle (2il
A 3-phase induction "motor having a 6-pole, star-cormected stator winding nrns on 240 V, SO
Hz supply. The rotor resistance and standstill reactance are 0.12 e and 0.g5 C) per phase. The
ratio of stator to rotor tums'ratio is 1,8 and full-load slip is 4Yo. Calcalate the developed
torque at full-load, madmum torque and the sRe.1d at ma:<imum torque.
Examnle (26)
T[e rotor of a 4-poie, 50 Hz, 3-phase slip-ring induction motor has a resistance of 0.25
C2/phase and runs at 1440 r.p.m. on fuIl-load. Calcuiate the extemal resistance per phase
which must be added to lower the speed to 1200 r.p.B., the torque remaining constant in both
cases.
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Strnrqtolquc curvs
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Sto,rti5 torlue
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ota
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t tE G-se, fR"t, a'rcr,J resisf* re = f?.f
< l.5oo l44o\-, \500
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Itr
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[{ = ?? f", na-X Gtlwe
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*fir iere Lr-€ 2+-( R.=1.i1aX.
S=
,r SPeeJ "* T;v1rr..'e
NJ = (\-s) AJs = (t-..?) r
rF F.r
2o - ja.
o.=
o.38
f'' LIJ
+\=o
xz
o.l
{R.X''. o.l
'- r,i r.,ii*.. ,,{
.,-\,r..
:'1,,ti_{#ffi!,1,t''
TEvqu,r€ .t
lrir
?3 fn"eJ(
z\ It
3 'Yt\./
S X.-I
o . z -of max. T3rlu*e .
$oo , (Pr".
Iil
ii
'1.Iti,$
ll,n:j:
--a
?=-7-, z.6zriP*.r
a?* * (R,--- o 'ct?- "
beC.ar.rse (o< t)
= o'o l8 -tL /Pl*J<( Kx
.,t;',
ccA
t4+ 1
\
#iTh'ii
fir
TFree Phase Induction Motors
x ( z 5)
5) = 6 Y- G.^nq J."l st t-.,r
=Y?b .. z4o\,G, = o.\Z &,
^zo.$5--ru
St-.torTZ,t s Porn-.L; -* rol.ioR"tot
)or1u€, = ?? ,ot, F*ff-L"*o(
T (rw.y. .T6tu.e )
N: r'\a.'r< Cn*
5o F\Z
. i-: ii"i&ie:ii r:.rt :;t r:
m-
S.L^Jft crv^-
*l'Rotor e.^.P. / plr*se, E.
r(-7 Ro\-, J-t rns \
\.9St-f.or Ttnrns
t+ )5nclrqn-q*i
Ns -#+ fd- Loo.J. E 1u.
3l-., = it' rrJl_L.o."t a6 Ns
SPeeol, Ns
\?o;t 5o
*'E, =
1\
S't"f,a'7 €.vn. f. ZpI.*"I svpS p).a^se u-Lf,1e,)
Sr*-too.J lts A' .
' - ::"l tt :*l ji''''l;.,llf f''l
' j:'':li::.'i'r:'l-l:,:' :'., :
F - ':' 't' ' 1'' t"'\ooo fpvn = =,
,1.PS? l''it'"-'] j
., :.,:f,,;.,
Gr" * ( Srur-roqor X. ).'t4g)
Three Phase Induction Motors
o.o4 xGqf * o \?-
ztT x ( 5l-\- 3',L(o.\z) 1 ( o.o4-* o.Bs)'
T'- = 57'+ N'nt
rtL+ 5\.P o./L -'t,la_/\ to fqgu(I
Q.'11z =
o'\?
dr. o'85
I,-
l- ='9s.3 N.nt2T\.* 5o
3
,h =pe"J .t rn^x Er1we, N,^
AJ=r tl\( r- t*) /vs t+) r(
FPn^-
z E AJr S.' * (L ,x*fo.r4*(7Zf*o.\t1o.tz)t + (o.o*x o.35f
[4e ]
Three Phase Induction Motors
E" Qe)
P= 4)Nr,.tl
- uu =
P = 5o HZ ,,
t44o f Pta+
aR, = o."5 n(,fL-,
IIt
G* = ?? "- G gr:rJe Nr*1,-u.J =
ft {te se,*te torlwe.
g
CJL'
)I
I
( sU+ ) *p, *.6, i:t-(R) ( qa} ',-:\Z *t;t
rprn : "5
rPs .,-i:1111i':r-rl:,,,..'.- I --1.,...:*
Sl^p S, =
' -.:::. ...:1_11;.ti.-.., .
\5oo - '**ot^'lt":'i':i':
^t,t
IIItlli
II
I
I
I
I
I
* $nc[fonouS SPeeJ., Ns
,,
Nr=
* Er t!.e5>
P;"rt
1 5oo
Case,
( wtor) J\ (rt" Gt-o GJ) (rK*) -*rT )15 iP \l>€+
4 + #*.,fi ( [f),/L (,fr1) ^/cu-])dei
I
L2ue) c) (R*) r !: ) -.o '>J€I
(
N? *V) a,-))
I :[5o]
Three Phase Induction Motors
s, x.R_
S, 4.
R: * (s, x.)'
sz (Q. * Q^)
Q,, * (5, (Q, -n /R^f + (s X.)'
4c r< < E.A trCueso \dr,, S.) o'd€
( ,' ""^j' sJ ) terrrrs o,t.e ngtecte.l ;:;i,,,, r,i-.--z , :'
.ip,ii.,;;, i.:1...r'i.,..
(G-*.R*fS. G.
5l?- =5r.
'r.r j:i 'ee
t:
ilI
il
#i
III
<-)
?R,e, I
= lsl/p\.^t<
r,, ;l -' 'i
:!l
!r. 1 i!
i sll