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Unformatted text preview: Page 1 of 9 NORTH CAROLINA STATE UNIVERSITY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING Lecturer: John W. Gajda, PE. ECE451 Test 2 Fall 2010 NAME \SjUZMTr’O/V Select four of the five problems shown. Place an “X” next to the problem # below
that yOu are choosing NOT to work. The other four problems will be graded. Problem NOT worked
Problem No. 1 (possible 25 pts.)
Problem No. 2 (possible 25 pts.)
Problem No. 3 (possible 25 pts.)
Problem No. 4 (possible 25 pts.)
Problem No. 5 (possible 25 pts.)
TOTAL (possible 100 pts.) NOTE: THIS IS A STRICTLY CLOSED BOOK EXAM. ALL WORK MUST BE
SHOWN. DO ALL FOUR PROBLEMS. Honor pledge:
I certify that I have neither given nor received unauthorized aid while taking this test. Signature: Problem Page 1 of 9 Page 2 of 9 No. 1 (25 points)
Use the attached chart of manufacturer’s conductor data for this problem. Part 1 (13 points): Assuming a short line model, calculate all complex impedances for the short line model of a transmission line with the following parameters:
1. 795 ACSR "Drake” phase conductors 2. 10 miles long
3. conductor temperature = 50 deg C
4 Vertical construction (all three phases arranged in a vertical plane), 4’ spacing between phases A to B and phases B to C Show all work. Draw the model diagram with appropriate general impedances labels, then
calculate each label and draw a square around the answer. :E’ 35%
S u a RT «1w 5: : atﬂuﬂwmmvmmm
0 "mm”? "Wig/40‘5“ 7&3 0,1234 4%, fa’oec Eif” W
X, :gLO. m3 ﬁn (if) .— 504' 61(1/2/3 XL 3—91 3;: HM: 0.0373"
(7032.3 Page 2 of 9 Page 3 of 9 Part 2 (6 points): For a line with the following parameters: 795 ACSR “Drake” phase conductors 10 miles long
conductor temperature = 50 deg C
Horizontal construction (all three phases arranged in a horizontal plane), 40’ spacing between phases A to B and phases B to C Ir
5. Operating voltage = 765 kV (phasetophase) l_ g“ 1/ 90 90} £0 PE“E‘Jr‘ Caj;ulate3e;WARS geneiajd i332; entire [213.9 g j (50, ,_ H = 50 t/
a 65 #0 : l ass/c7 “i. “i
M «5.5,; #1 (I %}
=— 5207 9’ X/Oj Jlm; ﬁg «Ht—ﬁre}
I . . : 7ﬂ650904 _, (0 Mtg; 50 £1.36? AMA“.
(HAIfC{MC [’3— X;  £¢ /.3 AMﬂJ/L‘H'E zrﬁirvegm}(2r.m = 22.5; MVAR ] Part 3 (6 points): Due to an odd situation which comes up every once in awhile in the
transmission & distribution companies, the line above has to be temporarily used as a
distribution line. All factors from Part 2 apply, except the operating voltage is now 12.47 kV (phasetophase). Calculate the MVARs generated by the entire line. I 3 Ky Mug;
7' ’ " {2W F5347’q0141‘1: ,
.. (ii/3.496.416 ' 4E Xe . I“ ”4129 59 03¢{7AH195'
Q : {(3:53}; 9‘70; (0.397) :: i 0 0079 MVAgM 7 Page 3 of 9 Page 4 of 9 Conductor data Electrical characteristits of bare aluminum conductors steelreinforced (ACSRP' Resistance
Ac, 60 Hz Reactance per conductor 112 spacing, 60 Hz
Code word Aluminum area. Standing Layers of Outside diameter. Dc, 20°C. 20°C, Wmi 50°C, Wmi GM“ D5 0 Incucﬁve Xa, Capacltive X 0* (mil ALIS: aluminum in 071.0000 (Zimi Miami
waxwing 266.800 1871 2 0.609 0.0646 0.3488 0.3031 0.0100 0.476 0.1090
Partridge 266.800 26.77 2 0.642 0.0640 0.3452 0.3792 0.0217 0.465 0.1074
Ostrich 300.000 2677 2 0.630 0.0569 0.3070 0.3372 0.0229 0.450 0.1057
Merlin 336.400 2811 2 0.684 0.0512 0.2767 0.3037 0.0222 0.462 0.1055
Unnet 336.400 26!? 2 0.721 0.050? 0.273? 0.3006 0.0243 0.451 0.1040
Oriole 336.400 3077 2 0.741 0.0504 0.2719 0.2937 0.0255 0.445 0.1032
Chickadee 397.500 1071 2 0.743 0.0433 0.2342 0.2572 0.0241 0.452 0.1031
[his 397,500 2677 2 0.703 0.0430 0.2323 0.2551 0.0264 0.441 0.1015
Peiican 4??.000 1871 2 0.014 0.0361 0.195? 0.2148 0.0264 0.441 0.1004
ﬂicker 427.000 247'? 2 0.846 0.0359 0.1943 0.2134 0.0284 0.432 0.0992
Hawk 477,000 26!? 2 0.850 0.0357 0.1931 0.2120 0.0269 0.430 0.0003
Hen 477,000 3077 2 0.003 0.0355 0.1910 0.2107 0.0304 0.424 0.0000
Osprey 556,500 1871 2 0.079 0.0309 0.2679 0.1043 0.0204 0.432 0.0981
Parakeet 556.500 2477 2 0.914 0.0308 0.1660 0.1032 0.0306 0.423 0.0969
Dove 556.500 2677 2 0.927 0.030? 0.1663 0.1026 0.0314 0.420 0.0965
Rook 636.000 24;? 2 0.977 0.0260 0.1461 0.1603 0.0327 0.415 0.0950
Grosbeak 636.000 26(7' 2 0.900 0.0260 0.1454 0.1506 0.0335 0.412 0.0946
Drake 795,000 2677 2 1.108 0.0215 0.1172 0.1204 0.0373 0.399 0.0912
Tem 795,000 4577 3 1.063 0.0217 0.1103 0.1302 0.0352 0.406 0.0925 Page 4 of 9 Page 5 of 9 Problem No. 2 (25 points) Given the following system, find the nodal admittance matrix Ybus. Show all of your work. 1 2 3 [535: [2.7251 1'17, Q [J
‘ _ l
)5; ,94; d3? ll
6 JJ 5 1/075 Page 5 01'9 Page 6 of 9 Problem No. 3 (25 points) Given the following system, find the nodal impedance matrix 21,115. Show all of your work. I 2 3 P
J a, 0 G5. 4, O G! . ‘ 050:; JO 05 k
2 1 "”5 ’3 ._1____.zﬁ9:€éw,i” 5 12
1 36 05 €955 1 0. 95 ﬂ __l_‘i;:5 [M512 1.)
" _ _'________ —— — 1‘ —"‘"‘_“ ,J
P 16’07 M55 11qu die? l
\V I — "x I' , xi
g :72 ,, {(PZN' _ ”.051 ‘ E ..
H 1': ”Zn: “JO05.1105: 05.311? £155.," (“f14w“ M0; rc/w 7%,“
x  055 gig55?” : ‘9“); GEN“ (69 30.5 3, +56%
{2' J “05" J K1496!“ leeDace
I. x"
7353 = 4“” 1% =1” 0% 1;: .
. i ‘ \II
‘21;  J00;  Mammal EF% JO‘WS p.024 JQOM‘B 1’
" “.05 _ '
t W o . .
4.3 _ do” #W, 00011:? J JU‘OH J01” 30'052 E
11115 ' “ J . 1 .
E JQCOLlﬁ JUtOSZ J 0.090
: 'C’ .05 "  HM. TEF— _ J
E23 J ‘55 " ———————(J .5}‘("O'QS) : “10.051 W ”W” Page 7 of 9 Problem No. 4 (25 points) Use the GaussSeidel algorithm to find the bus voltages for the following perunit system
described as follows: 20 —10 —10
Fiﬁ —10 15 ~5
—10 5 15 Recall the matrix equation I = W, and this particular Ybus was built from a system that has
resistances only and no reactance components. (note: since the elements are real and not
reactive, they don't have a “j” operator (which changes sign when inverted) and therefore the signs appear to be opposite that you normally see in a Ybus.) In this simplified, noncomplex number voltage & current system, bus 1 is a “slack bus,” and
busses 2 and 3 are load busses (like “PQ” busses in a conventional power flow algorithm). Knowns: V1 is set to 1.0 per unit (should remain as such in every iteration)
I; (scheduled injection) = +1.25 (independent generator) I; (scheduled injection) = 1.0 (load) Initialize the algorithm with all bus voltages set to 1.0, slack bus current injection set to 0,
and other bus current injections set to their scheduled current injections. Use a maximum error tolerance of 2.5%, and show all work. You can use the back of the
paper if necessary. I 5 yr .20 4, V; (. rm) 4— té (—m) £51 I *r  [Al—(a) 4 Vlﬂs} .4 pg (,5) Eq 2
' V ("<9 4 V105) «L lg (is) £19 3 M“: {.0 (Jimo!) 3/; : (I‘z' M(—:’oj—V3{{“;})(7L5_
%:(I_3 — V; (‘59::"14 (”gy—IIE
‘ "l ,1 ﬁ (/1 : {ng— (new) {iifs>)(;'g:) = 1.033 V‘ "l” ’(":}g""”
i : ..  —0‘ibl(*5)  _  _ 
J1 lg; ‘11:) .)(}7 f3,_r]_i(ts;)glo7($):a(i57
 1 7* . X . .— 61. “%A\ : (.23; 63: lo qsg‘qublr O (4% MAY Ek‘m): (.25, So iﬁﬂME. Page 7 of 9 Page 8 of 9 Problem No. 5 (25 points)
(Questions (11 are worth two points; question #12 is worth 3 points) Fill in the blank or circle the correct choice (select one choice unless otherwise indicated): 1. 2. I' b l‘n‘pa‘f". Load bosses are also known as (slack I PV busses. For PV busses, many types of shunt elements can be connected, but there is one
that must be present: a. loads
@oltage regulating synchronous machine (generator, motor, condenser)
o. non—voltage regulating synchronous machine (generator, motor, condenser) d. shunt capacitor banks
Circle one shunt element you will n_ot find at a PQ bus: a. loads
mm . Ly'Joltage regulating synchronous machine (generator, motor, condenser) [1 c. nonvoltage regulating synchronous machine (generator, motor, condenser)
d. shunt capacitor banks Can load busses have connected generators? (Yes No ) 2b“, is most commonly used in (power flow algorithmsmﬂcuit algorith
Ybus is most commonly used in Q ower flow algorithms {Lisbort circuit algorithms). 1"” For the following matrix type, a “zero” in an offdiagonal element with row J
and column “k” ind' a s that there is no connection in the system between bus
“j” and bus “k": (w Zbus I both ; neither) Which matrix building al . . ' m can possibly involve use of the Kron reduction
method? (Ybus f Zbus @neither) Page 8 of 9 Page 9 of 9 Problem No. 5 (continued) 9. Which variables are "known” at the slack bus (circle all that apply, and do not
circle the unknown vari  __ ' ' *6 age magnitude vltage' angle P injected I Qinjected ) 11). Which variables are “known” at a PV bus (circle all that apply, and do not circle the .n es):
. voltage magnitude f voltage angle 6 P injected 3 Q injected ) 11. Which variables are “known" for a PQ bus (circle all that apply, and do not circle
the unknown variables)‘ ( voltage magnitude r voltage angle 12. Consider an independent generator that is connected to a given bus. Assume the
generator does not regulate voltage but simply exports power “P" at unity power
factor (zero net “Q" flow at the interconnection), operating in a power factor
control mode (constant power factor). When the generator comes online and
starts exporting at its full rating, how will the bus voltage at the generator
interconnection likely change compared to what it was before it was came on—line? The bus .c age will likely:
( drop @I stay the same ). Page 9 of 9 ...
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 Fall '11
 JohnGrainger

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