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Unbalanced Faults
• Common unbalanced faults are SLG, LL and LLG faults.
• Unbalanced faults unbalance the network, but only at
the fault location.
• This causes a coupling of the sequence networks.
• How the sequence networks are coupled depends upon
the fault type.
• We’ll derive these relationships for several common
faults.
2
Single Line-to-Ground (SLG) Faults
• With a SLG fault only one phase has non-zero fault current -- we’ll assume it is phase A.
?
0
0
fa
fb
fc
I
I
I
3
SLG
0
2 0
2
Then since
1 1 1 ?1 1
1 03 3
01
f
ff f f f a
f
I
I I I I I
I
Va = 0 for a single line to ground fault
V+ + V- +V0 = 0
With the generators normally producing balanced three-phase voltages,
which are positive sequence only, we can write
4
Example
Consider a system with sequence impedances given by
Z+ = j0.2577, Z- = j0.2085, and Z0 = j0.14; find the voltages
and currents at the fault point for a single line-to-ground fault.
Solution
The sequence networks are connected in series for a SLG fault.
The sequence currents are given by;
Therefore,
6
Double Line to Ground Fault
• Fault conditions
Ia = 0
Vb= Vc=0 0// ZZZ
VI
ZIEV
VaVVV
3
0
Z
VI
o
oo
Z
VI
9
Double line-to-ground fault
bI
cI
a
b
c
nI
0 cb VV 0aI
0
0
1
1
111
3
1
2
2
2
1
0 a
a
a
a V
aa
aa
V
V
V
aaaa VVVV3
1021
2
1
0
2
1
0
2
1
0
00
00
00
0
0
a
a
a
f
a
a
a
I
I
I
Z
Z
Z
V
V
V
V
10
Double line-to-ground fault
2
1
0
2
1
0
11
11
11
00
00
00
0
0
a
a
a
f
af
af
af
I
I
I
Z
Z
Z
V
ZIV
ZIV
ZIV
2
1
0
1
2
1
0
11
11
11
00
00
00
0
0
a
a
a
f
af
af
af
I
I
I
Z
Z
Z
V
ZIV
ZIV
ZIV
11
Double line-to-ground fault
2
1
0
2
1
0
11
11
11
100
010
001
a
a
a
af
faf
af
I
I
I
Z
Z
Z
ZIV
VZIV
ZIV
0210 aaaa IIII)( 02
021
1
ZZZZ
Z
VI
f
a
fV
-
+
1Z
2Z0Z
- -
+ +
1aI 2aI0aI
-
+
1aV2aV aoV
12
Double line-to-ground fault
Example : Find the line currents and the line-to-line voltages when a
double line-to-ground fault occurs at the terminals of the generator
described in single line-to-ground fault example. Assume that the generator
was unloaded and operating at rated voltage when the fault occurred. The
generator has positive sequence reactance of 0.25 , negative sequence
reactance of 0.35 and zero sequence reactance of 0.10 per unit. The neutral
of the generator is solidly grounded. Neglect resistance.
..05.33278.0
0.1
)10.035.0/()10.035.0(25.0
00.1
)/( 020211 upj
jjjjjj
j
ZZZZZ
EI aa
)25.0)(05.3(111021 jjZIEVVV aaaaa
..237.0763.00.1 up
..68.035.0
237.0
2
22 upj
jZ
VI aa
..37.2.010.0
237.0
0
00 upj
jZ
VI aa
13
Double line-to-ground fault
037.268.005.3021 jjjIIII aaaa
37.2)68.0)(866.05.0()05.3)(866.05.0(021
2 jjjjjIaIIaI aaab
..3.13280.4555.3230.3 0 upj
37.2)866.0)(866.05.0()05.3)(866.05.0(02
2
1 jjjjjIIaaII aaac
..7.4780.4555.3230.3 0 upj
..11.737.233 0 upjjII an
..11.7555.3230.3555.3230.3 upjjjIII cbn
..711.0237.033 1021 upVVVVV aaaaa
0 cb VV
..711.0 upVVV baab
0bcV
14
Double line-to-ground fault
..711.0 upVVV acca
Expressed in amperes and volts,
0aI
AIb
00 3.13240173.13280.4837
AIc
00 7.4740177.4780.4837
AIn
00 9059519011.7837
kVVab
0066.53
8.13711.0
0bcV
kVVca
018066.53
8.13711.0
15
Line-to-line fault
bI
cI
a
b
c
cb VV 0aI cb II
c
c
a
a
a
I
I
aa
aa
I
I
I 0
1
1
111
3
1
2
2
2
1
0
00 aI 12 aa II
c
c
a
a
a
a
V
V
V
aa
aa
V
V
V
2
2
2
1
0
1
1
111
3
1
16
Line-to-line fault
2
1
0
2
1
0
2
1
0
00
00
00
0
0
a
a
a
f
a
a
a
I
I
I
Z
Z
Z
V
V
V
V
21 aa VV
22110 ZIZIV aaf
21
1ZZ
VI
f
a
fV
-
+
1Z
2Z
- -
+ +
1aV2aV
1aI 2aI
17
Line-to-line fault
Example : Find the subtransient currents and the line-to-line voltages at the fault under
subtransient conditions when a line-to-line fault occurs at the terminals of the generator
described in the sing line-to-ground fault example. Assume that the generator is unloaded
and operating at rated terminal voltage when the fault occurs. Neglect resistance.
unitperjjj
jIa 667.1
35.025.0
00.11
unitperjII aa 667.112 00 aI
0667.1667.1021 jjIIII aaaa
)866.05.0(667.1)866.05.0(667.1021
2 jjjjIaIIaI aaab
unitperjjj 0886.2443.1833.0443.1833.0
unitperjII bc 0886.2 18
Line-to-line fault
in the sing line-to-ground fault example, base current is 837A, and so
0aI
01802416837886.2 bI
002416837886.2 cI
unitperjjVV aa 583.0)25.0)(667.1(121
00 aV (Neutral of generator grounded)
Line-to-ground voltages are
..0166.1583.0583.0 0
021 upVVVV aaaa
021
2
aaab VaVVaV
)866.05.0(583.0)866.05.0(583.0 jjVV bc
..583.0 up 19
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