CONFIDENTIAL
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
FINAL EXAMINATION
SEMESTER I
SESSION 20rrl20r2
COURSE NAME
POLYPTIASE CIRCUIT ANALYSIS
COURSE CODE
BEF 23803
PROGRAMME
2 BEF
EXAMINATION DATE
JANUARY 2OI2
DURATION
2 HOURS 30 MINUTES
INSTRUCTION
ANSWER ALL QUESTIONS
THIS PAPER CONSISTS OF TEN (10) PAGES
CONFIDENTIAL
BEF 23803
Qr
(a)
with the aid of phasor diagram, write the phase voltage expression of three-phase
generator E*, Ebn, and E.n for ABC sequence and ACB r"q.retr"e in phasor
form.
(8 marks)
(b)
A three phase 33 kV, 50 Hz line is connected to
loads as in Figure Ql(b).Evaluate
(i)
(iD
(iii)
(iv)
(D
several balanced three phase
The real power, reactive power, apparent power and power factor of each
load,
The line current and phase current of the motor and Load 1,
Total real powel (p), reactive power (e), apparent power (S), and power
factor drawn to the loads.
If the poweT factor of the system needs to improve to 0.9g lagging, find
the required reactive power of capacitor bank should Ue i.rstafGO in
parallel with the loads,
If the capacitor bank in Q@)(iv) is delta-connected, calculate the per phase
capacitor value.
(17 marks)
Q2
(a)
A
single-phase system has two transformers Tl and T2 connected between each
other by line B. The rating of the components is:
Transformer Tl
Transformer T2
Line B
Load
(i)
(iD
(iii)
500
V/l.3 kV, 7 kVA, leakage reactance 5%o
ll20 V, 5 kVA, leakage rcactance 3yo
1.2 kV
series impedance 0.5 + j3.0 O
120 V,3.5 kVA at 0.8 power factor lagging
Compute the value of load impedance in ohms
Find the actual ohmic impedance of transformer Tl and T2 referred to
their primary and secondary sides
Express all the system impedance in per-unit values if the base voltaee and
base power at B is 1.2 kV and l0 kVA respectively.
(12 marks)
(b)
construct an impedance diagram for the one-line diagram of three-phase
transmission system in Figure e2(b) and express all the quantities in p.u. use
common base of 100 MVA and 69 kV on the generator side-. The generaior has
a
synchronous reactance of 0.18 p.u. The line length is 65 km with the reactance
of
0.5Olkm.
(13 marks)
BEF 23803
Q3
(a)
proof that the constant ABCD parameters for nominal-n circuit of medium
transmission line model as shown in Figure Q3(a) is given by,
u=('.7)
B=Z
, =r(r*q\
4)
'=('.+)
\
(10 marks)
(b)
simple three-phase power system network is shown in Figure Q3(b). By
applying Kirchoffs Current Law (KCL) to the independent nodes 1 through 4,
construct the bus admittance matrix, Y6u, for the network'
A
(15 marks)
Q4
(a) (D
Sketch the phasor diagram representation of symmetrical components for
positive sequence, negative sequence, and zero sequence. Write the
expression olpositive sequence current for each phase in phasor form.
(ii)
Obtain the symmetrical components for the following set of unbalanced
currents,
Io = l-8130' A, Ib = l'02180' A' I" = 0'8 2135" A
(9 marks)
(b)
Sketch the zero sequence equivalent impedance diagram for the oneline diagram
shown in Figure q+Ol. Then, find the total impedance for the circuit looking
from point p. fne zero sequence per-unit values for each component is depicted in
Table Q4(b).
(16 marks)
BEF 23803
FINAL EXAMINATION
PROGRAMME :2 BEF
SEMESTER/SESSION : SEMESTER V SESSION 2OIII2OI2
: POLYPHASE CIRCUIT ANALYSIS
COURSE
COURSE CODE : BEF 23803
2.5Hp
33
Three phase motor
p.f. :0.65 lagging
kV, 50Hz
line
Efficiency
:90%
200 kvA 3(D
A-connected load
p.f. = 0.8 lagging
FIGURE Ol(b)
T2
T1
A
B
C
Load
E
FIGURE O2(a)
4
BEF 23803
FINAL EXAMINATION
SEMESTER/SESSION : SEMESTER V SESSION 2OIII2OI2
COURSE
: POLYPHASE CIRCUIT ANALYSIS
PROGRAMME :2 BEF
COURSE CODE: BEF 23803
Bus
50
MVA
3
Load
MVA
69/t32kV
MVA
132/lt kv
r0%
7%
30
25
FIGURE O2(b)
Z:R+JXI
FIGURE 03 (a)
10
MVA
0.8 p.f lagging
BEF 23803
FINAL EXAMINATION
PROGRAMME :2 BEF
COURSE CODE: BEF 23803
SEMESTER/SESSION : SEMESTER V SESSION 2OII/2012
: POLYPHASE CIRCUIT ANALYSIS
COURSE
7 : jo.3
Z
: j0.08
F'IGURE O3ft)
JY^
-lf
q,.--r
rY
TL
I.2
TL2-3
^Yl
2
YI
A
FIGURE O4(b)
BEF 23803
FINAL EXAMINATION
SEMESTER/SESSION : SEMESTER Y SESSION 201I/2012
COURSE
: POLYPHASE CIRCUIT ANALYSIS
PROGRAMME :2 BEF
COURSE CODE : BEF 23803
TABLE O4(b)
ComDonents
X'(pu)
Gr
0.07
Gz
0.10
G3
0.05
Gr
0.
T1
0.10
T2
0.10
Tr
0.r2
Ta
0.1
l0
l
TL:rz
0.50
TL1-3 = TL2-3
0.80
7
BEF 23803
FINAL EXAMINATION
SEMESTER/SESSION : SEMESTER V SESSION 2011/2012
: POLYPHASE CIRCUIT ANALYSIS
COURSE
Formula
Single Phase per-unit system
'
Base current.
A=
Base impedance
-
kvA t'
base voltage, kVt"
base
-
base voltage'
vt*
base current,
A
kVlp
base MVA 16
Base power, kWlp = base kVA l/
Base power, MW 14 = base MVA l/
Base impedance =
(base voltage,
)2
Three Phase per-unit system
Base current,
A=
basekVA3,
J3 Xbasevoltage,kVtt
/1
Base impedance
=
1,
base
Base Power, kW3O = base
unit
zn"*
=per- unit
Transmission Line
% =AZn + B1R
Ir=CVp+DIR
t2
)'
MVA,
kVA3/
Base Power, MWsA = base
per-
r rr
Oasg voltag-? -kvt-t
MVA3,
rd.[ffi)'[ffi)
PROGRAMME :2 BEF
COURSE CODE: BEF 23803
BEF 23803
FINAL EXAMINATION
SEMESTER/SESSION : SEMESTER V SESSION 2OIII2OI2
: POLYPHASE CIRCUIT ANALYSIS
COURSE
: 2 BEF
COURSE CODE : BEF 23803
PROGRAMME
Zero sequence equivalent circuit of Transformer
-T-
Vs
Ir
-r
Vr
Vs
-
\i
Zg
BEF 23803
FINAL EXAMINATION
v SESSION 20t1t2ot2
:poLypHASE cIRcuIT ANALysrs
SEMESTER/SESSION : SEMESTER
couRSE
pRocRAMME : 2 BEF
couRSE coDE: BEF 23803
Zero sequence equivalent circuit of Transformer
lsFz
F-+-
Ir
Vs
+
Vr
Y
\i
H
+
Is
Ir
o-->-a
Vs
Vr
10