EE 340 - $pring '12 - Test 3

Problem 1:A 3-phase, 480 V, 50 hp, 2-pole, 60 Hz, induction motor has the following circuitparameters: R1 = 0.322O, R2 = 0.196 O, X1 = 0.675 O, X2 = 0.510 O, Xm = 12.5 O.The total rotational loss (including core loss) is 1,850 W. Under rated load condition, therotor slip is 3%. Calculate the following:

1) The stator current drawn from the sourcea)33.28A , _ , 1711,1"@- z=ra,+jx,+i{^//(Vr;x):6,:"s'< i'c) 51'17 A ,r, t/"/ n-ta ; ' )1;> E\'q"C) Cl.l/A - ,t) 'a

\> t-^ r ,/^5i.o) oo.ssn r. g4 nn'(3 i- 6q ?q ^Trra marar ^Ar^,ar

iFaa*ae z t ffiLll'1" \-i-i-",Ltr\ s.'2) The motor power factor

b) 85% lagc) 89% lagd) 92o/o lag

?F 'o (.v-e') = 64 G1

L3) The motor induced torque

a) 65 Nmffi r;-,d) 85 Nm

?: - 3T,'R ,

='- jtn7

rF "\aux /*,asxl'8)--3qr'al t t"f'.\/-- 3rrl3orIt€- lSt",

P*.urr'.

71rT4) The speed at which the maximum torque is developed

a) 2,875 rpm

-*",i faf-Gf;_,p_.'l\rin= (-S)ns=@9

V,nn = 26z.tst{eau = O.4e*<.'^:j.6?ssu

(2,

5) The maximum torque developedr-"flF;N-h

c) 223 Nm

z

^{ ?e, ( U* (r(6"1r8ltr 7 - ivr'"a\ ?92 hlm \-\

^.({ A+C."r) '-.r{ttd) 254 Nm6) The starting current of the motor.

a) 145 A

il-K,'"+i4) = o.as3 ht'"Z " h+SXt +r=+=7) The starting torque developed

a) 68 Nmb) 79 Nm

107 Nm

gu; c.

/

a) 33.28 A

b) 185A-c) 2154

c) 9?xr

",,v ky,*qL+(Jin)=)'n

Problem 2:Consider the power system below with the following equipment ratings:Generator: 30 MVA, 15 kV, x = 17o/o

Transformer T1: 30 MVA, 151138 kV, x = 104/o

TransformerT2:25 MVA, 138113.8 kV, x= 10o/o

Transformer T3: 20 MVA, 138112.5 kV, x = 10o/o

Use 30 MVA as the power base, and 15 kV as a voltage base on the generator side.

i zso Jqo.s- @

Jl Ssukrg

1) Fill in the per-unit impedance values in the per-phase equivalent circuit below.

Ao, #= 6,7Y,t s>

O "1,, CD j,usCil' o*)

CD l.tvz @ @

G),,) 'kl 6.q1) J'ra

i,Ir(-7rss)

J .rr

J b,Z3to(-) q.L*)(o

tj &'3,

+@\-.v -''T"V l*"il r

@Tr_

(-) (')

2) Derive the Y-bus matrix (7x7)

Ymr=j

:I$:F .+t0.. ....e... ...?.... ...a....

-.lgr:11 .*8.:!1 ...0.... ...o...

:.19:.lf..l.nt ...a...

.15,3.7 +fi'.33

=f:17

r.a0@-

Calculate the magnitude and phase of the current injected by bus 1 by thegenerator if the node voltages are as follows:

, ota-l ' , -- rq q1 7f l* *- to ,*tflrczq-:lr.ot6*+'l {'*) l1'q+11 + (o'9V+

...4...

A{{..}..{

...o....

...4....

.-LQt9

3)

v"al,tA'\ -u1,sl-

-vf') o.ee@-

4) Form the above result, calculate the real and reactive power (in MW and MVAR)

+rgHt'g o

supplied by the generator.

6\ rr/ ,p;* r .fe 66'8'f,-- wt#t = 1,0"-/ T'ot :

@,0'cl ,53,1

: 0 .Z+ 14.rt fl *

: ("2 * jq's')xbo =