TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
D5
FltAli
D
ay
5
-
F
au
lt
A
na
l
ys
i
s
July10,2013
Prepared by: Peter Anderson
eBook for You
OUTLINE
2
OUTLINE
• Symmetrical Components
• Sequence Impedances
• Analysis of Fault Conditions
RttifFlt
•
R
epresen
t
a
ti
on o
f
F
au
lt
s
eBook for You
SYMMETRICAL COMPONENTS
SYMMETRICAL
COMPONENTS
3
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SYMMETRICAL SEQUENCE COMPONENTS
4
SYMMETRICAL
SEQUENCE
COMPONENTS
Any given set of Unbalanced Three
-
phase Vectors
Any
given
set
of
Unbalanced
Three
phase
Vectors
can be represented by the sum of three sets of
Balanced or Symmetrical vectors
AA ACB
BC
B
C
PositiveSe
q
uence Ne
g
ativeSe
q
uence
Z
eroSe
q
uence
q
g q
q
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RELATIONSHIPS BETWEEN PHASE
5
VECTORS & SEQUENCE COMPONENTS
A
Piti S
P
os
iti
ve
S
equence
1A1C1A
2
1B1A
aI=I,Ia=I,I
0
B
2
B
1
B
B
0A2A1AA
I
+
I
+
I
=
I
I+I+I=I
A
B
C
NegativeSequence
2
0C2C1CC
0
B
2
B
1
B
B
I+I+I=I
I
I
I
I
B
C
2A
2
2C2A2B2A
Ia=I,aI=I,I
2
021A
I
+
aI
+
I
a
=
I
I+I+I=I
B
C
ACB
ZeroSequence
0
A
0
C
0
A
0
B
0
A
I
=
I
,
I
=
I
,
I
02
2
1C
021B
I+Ia+aI=I
I
+
aI
+
I
a
=
I
0
A
0
C
0
A
0
B
0
A
I
I
,
I
I
,
I
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SEQUENCE IMPEDANCES
SEQUENCE
IMPEDANCES
6
eBook for You
SEQUENCE IMPEDANCES
7
SEQUENCE
IMPEDANCES
SequenceCurrents&VoltagesareIndependentofeachother
•PositiveSe
q
uenceCurrentsonl
y
p
roducePositiveSe
q
uenceVolta
g
e
q y p q g
Drops
PositiveSequenceCurrentsaredeterminedsolelybythePositive
SequenceDrivingVoltagesproducedbythePowerSources,thePositive
SequencevoltageatthePointofFaultandtheSystemPositiveSequence
Impedance
NegativeSequenceCurrentsaredeterminedsolelybytheNegative
SequencevoltageatthePointofFaultandtheSystemNegativeSequence
Impedance
Impedance
ZeroSequenceCurrentsaredeterminedsolelybytheZeroSequence
voltage at the Point of Fault and the System Zero Sequence Impedance
voltage
at
the
Point
of
Fault
and
the
System
Zero
Sequence
Impedance
eBook for You
SEQUENCE IMPEDANCES
8
SEQUENCE
IMPEDANCES
ThePositiveSequenceNetworkcontainsthePositiveSequenceDriving
Volta
g
es
p
roducedb
y
thePowerSourcesandtheS
y
stemPositive
g p y y
SequenceImpedancestothePointofFault
TheNegativeSequenceNetworkcontainstheNegativeSequence
ImpedancesfromthePowerSourcestothePointofFault(NoDriving
Voltages)
Th Z S Nt k ti th Z S Id t
Th
e
Z
ero
S
equence
N
e
t
wor
k
con
t
a
i
ns
th
e
Z
ero
S
equence
I
mpe
d
ances
t
o
thePointofFaultandanyconnectionstoEarth(NoDrivingVoltages)
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POSITIVE SEQUENCE IMPEDANCE
9
POSITIVE
SEQUENCE
IMPEDANCE
TransmissionLines
Ia
Ib
Ea
Eb
Ic
Ec
Z1=E/I
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ZERO SEQUENCE IMPEDANCE
10
ZERO
SEQUENCE
IMPEDANCE
TransmissionLines
E
I
I
E
I
Z0=E/I
eBook for You
ZERO SEQUENCE IMPEDANCE
11
ZERO
SEQUENCE
IMPEDANCE
Transformers
I
I
E
I
I
I
I
I
I
Z0=E/I
Ampere‐turnsareequalineachHVandLVWinding
eBook for You
ZERO SEQUENCE IMPEDANCE
12
ZERO
SEQUENCE
IMPEDANCE
Transformers
I
I
L
I
E
I
I
I
I
H
L
I
I
n
Z0 n
H
L
eBook for You
ZERO SEQUENCE TRANSFORMER
13
CONNECTIONS
H L
A
A
B
B
ZO
B
B
SwitchesA&BinitiallyOPEN
ForGroundedWye Winding–CLOSESwitchA
ForDeltaWinding
–
CLOSESwitchB
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ZERO SEQUENCE TRANSFORMER
14
CONNECTIONS
H
L
H
L
H
L
H
L
GroundedWye/Delta Delta/GroundedWye
H L
H L
T
Grounded
Wye
/Grounded
Wye
T
Grounded
Wye
/Grounded
Wye
/Delta
Grounded
Wye
/Grounded
Wye
Grounded
Wye
/Grounded
Wye
/Delta
eBook for You
ZERO SEQUENCE TRANSFORMER
15
CONNECTIONS
WARNINGNOTICE
0
0
H L
T
Yg Yg
HLPSSE
X
0
H‐N
N
X
0
L‐N
X0
T
N
D
T
Rg
3Rg
X0
T
‐
N
H L
3Rg X0
H‐N
N
X0
L‐N
T
X0
T‐N
CORRECTMODEL
eBook for You
ANALYSIS OF FAULT CONDITIONS
ANALYSIS
OF
FAULT
CONDITIONS
16
eBook for You
ANALYSIS OF SHORT
CIRCUIT CONDITIONS
17
ANALYSIS
OF
SHORT
-
CIRCUIT
CONDITIONS
ThreePhaseFault
0
=
I
+
I
+
I
C
B
A
V
=
V
=
V
=
V
C
B
A
0
=
I
3
+
)
a
+
a
+
1
(
I
+
)
a
+
a
+
1
(
I
0=)I+Ia+aI(+)I+aI+Ia(+)I+I+I(
0
=
I
+
I
+
I
0
2
2
2
1
02
2
1021
2
021
C
B
A
V=ZIa‐ZIa‐Ea=V
V=ZI‐ZI‐E=V
V
=
V
=
V
=
V
2
2
1
1
22
B
2211A
C
B
A
0=I,0=)a+a+1(Since
0
=
I
3
+
)
a
+
a
+
1
(
I
+
)
a
+
a
+
1
(
I
0
2
0
2
1
V3=0=V+V+V
V=ZIa‐ZIa‐aE=V
CBA
22
2
11C
2
2
1
1
B
0=V=V=V
CBA
2
2
3
3
0=I
0=V)a‐1(=ZI)1‐a(=)ZIa‐ZIa‐Ea(‐)ZI‐ZI‐E(=aV‐V
2
22
2
22
2
11
3
3
2211BA
eBook for You
ANALYSIS OF SHORT
CIRCUIT CONDITIONS
18
ANALYSIS
OF
SHORT
-
CIRCUIT
CONDITIONS
Three Phase Fault
Three
Phase
Fault
0=I,0=I,
Z
E
=I
02
1
1
E
F1
Z1
F2
Z2 F0
Z0
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ANALYSIS OF SHORT
CIRCUIT CONDITIONS
19
ANALYSIS
OF
SHORT
-
CIRCUIT
CONDITIONS
Single Phase to Ground Fault
Single
Phase
to
Ground
Fault
021
021
Z+Z+Z
E3
=I=I=I
0=I=I
0=V
CB
A
PhasetoPhaseFault
E
I
I
PhasetoPhasetoGroundFault
0
2
E
)
Z+Z
(
0=I
Z+Z
=
I
‐=
I
0
21
21
0
100221
0
2
1
EZ‐
=
I
ZZ+ZZ+ZZ
)
(
=I
2
0
100221
2
EZ‐
=I
ZZ+ZZ+ZZ
=
I
100221
0
ZZ+ZZ+ZZ
eBook for You
REPRESENTATION OF FAULTS
REPRESENTATION
OF
FAULTS
20
eBook for You
ANALYSIS OF SHORT
CIRCUIT CONDITIONS
21
ANALYSIS
OF
SHORT
-
CIRCUIT
CONDITIONS
Fault Positive Negative Zer o
3Ф
3Ф
F1
F2
F0
Ф‐E
F0F2F1
Ф‐Ф
F0F2F1
Ф‐Ф‐E
F0F2F1
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