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Unformatted text preview: EE 387 Spring 2009
Midterm Exam 1 '\
if: Last Name: 6”“ First Name: Instructions:
1. This is a closed—book, closed—note exam. There is a separate equation sheet. No other
study materials should be visible or accessible during the exam.
2. Be certain to check all parameter values that you use, as many of the values differ slightly
from the ones used in the lecture notes and/or homework assignments.
3. All phasor variables are speciﬁed in rms. Likewise, your answers for such variables should be in ms. 4. Voltage and current phasors should be reported in polar form, while complex power and
immitances should be reported in rectangular form. 5. A signiﬁcant fraction of your score for each problem will be based on the manner in
which you develop your solution. It should be logical and neat. 6. You have 90 minutes to complete the exam. 7. You must turn in all pages of the exam. Do not write below this line:
Problem 1 (20 points)
Problem 2 (20 points)
Problem 3 (20 points)
Problem 4 (20 points)
Problem 5 (20 points)
TOTAL (100 points) Consider the single—phase system
shown to the right. The value of the
source voltage is I75 = 480 V.
LoadA is 12 kW with 0.866 lagging
power factor, and Load B is 10 kVA
with 0.8 lagging power factor. The
magnitude of the reactive power
associated with capacitor C is
10 kVAR. Determine the following: a. The complex power supplied by the source, SS.
b. The current drawn by Load A, IA.
c. The impedance of an equivalent series network for Load B, 23.
A ~ f’f
/: < 2: L2 4, s ,‘L ‘
91““ ,x/ 3 v A l 5% t 1 ! (/W 1
_,..____n!
t» n» ‘a 7 «K ’ ‘t t I
l; KW A: ' )2 F {a}, *“ s M“
“x;
.e l :"\ '. _ ,'
’ .‘ DZ ” '
f w 1 ,. 1
3 re "” ‘ “ ~\ i i/ 3‘ .,_
if; ! V12. : ;
“x
.1 V / a a, w.
'“ Q “a ,l x ”7
, \ w
T Q Hi ’ W
J p k?
\l
f w < "a ff“ 1 A
$3; M JL “”3 3; v i:
w / ) V (A “319% n ‘= E» J,” 1" 2
“v i :2 ”i “VA“ ’9 ff“ “i :3 W ”ng l Consider an inductor having a core
that is constructed by stacking 25
laminations like the one shown to the
right 'The thickness of each
lamination is 1 mm, and the relative
pennabﬂﬁy of each lannnaﬁon is
1000. The winding is wound around
the center leg and has 100 turns.
Estimate the value of the
magnetizing inductance. A 5:
m if
.9 W ’i
J _.,._ Wmﬂw
\ﬁx‘ﬂ ., W ,
we? in, Q!"
m
‘u”
/\ 'f‘ x r,“ \u
m 4 l ,1 517'
.,. \Jl‘g'wi ' L/
ﬂ 2)
e U ‘ ‘
“ 77c. ' "
iywpgﬂcjp
,5. (ﬂy;
~ ‘ “r“ "\ l um"
' is» l ‘
{1&4 ”a: X 3/
st 513‘
j xv
/ ,1
L/ﬁ/g 10mm 20 mm «tun—Guy 13mm (a: Natalia“: 2. (cont) 3. The single—phase transformer in the system
shown to the right is rated at 50 kVA and
4800:240 V/V; its equivalent impedance is Z = 5 + leQ referred to the primary. The I7
1
values of the load voltage and current are
V2223010°V and [222004—36.9°A,
respectively.
a. Draw an equivalent circuit for the sourcetransformerload system with all
quantities referred to the primary winding.
b. Determine the value of I71.
Determine the transformer voltage regulation.
d. Determine the transformer efficiency. 4
" “ ‘ e «" z—B‘; “5‘5 f‘,
U“ g——W'6““W
If: G?)
\Vjt ‘ a
ft, m x x jg: /
= «  “t 2" ”L a v.
@Q Vi: w iv]; (é 4‘2;
» / / i r== /’ f” c? ‘
‘ ~v ’; tam F ' f’\/~/x/ V? f
: awe ” a;  r k h a we: < ‘
R
(My fv / ‘_
9‘“: i2" .._ : f ' 3
C 1‘ if? , l U19? 5 3 \xafﬁi ‘ hm *
V 3V “ 32x d“ ”i
v w >< C53 :71» (cont) 3. Consider the (non—standard) 3—phase
transformer shown to the right. Derive the positive—sequence voltage gain ﬂab/17W]. Assume that each of the lphase
transformers is ideal and has a secondary— to primary—tums ratio of N2 /N1. y’w‘
r; y
a t
 UM t
rye”:
s:
f“, ’\ .f‘m/
w W, ”a“? ”a
x. , \‘ j
/ at W I ,,
.o x," A 3:” Mr
V iﬁ“ ‘A “ 35W"? ‘ u “‘7 4. (com) 5. Some problems requiring short solutions: a. For voltage and current phasors I?‘ 2120410" V and I: = 101 w 20° A , determine the component of I: that is in quadrature With 17X , qu' V4... Express the form of the phase admittance matrix for t/ v
a symmetric 3phase impedance. ‘ The ac current and ﬂux linkage for a particular inductor can be expressed
i(t) = x/EI cos(a)et)
1(1) = x/EA cos(a)et) where I =10A , A =O.1V's, and we :27r60 rad/s. i. Express the induced voltage e(t) .
,/ , \\Y '9’” 1 / {I \. ’E ‘—
t . 3 w "1,“ 3A,”? ‘ ‘ "z a.“ l}
e t j W A $331 is)? "" éi/z \"L‘UC Kw ,1‘ V
ii. Calculate the peak value of energy stored in the inductor W L .
l 4 A particular transformer is designed so that the copper losses and iron losses are
equal to each other at full load and 0.7 lagging power factor. Determine the percentage change in total losses if the power factor of the load is corrected to
unity. a
,ﬁesreai w... a 10 ...
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 Spring '08
 JEFFERYMAYER

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