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Page 1
Fault Analysis
Symmetrical Components
For an unbalanced 3 – phase system, the analysis is done better by means of symmetrical
components.
a0
V ? Zero sequence components
a1
V ? Positive sequence components
a2
V ? Negative sequence components
a0 a
2
a1 b
2
a2 c
V 1 1 1 V
1
V 1 V
3
V 1 V
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
??
; Where
0
j120
e ??
? ? ? ?
1
sp
V A V
?
?? ?
??
p
V = phase voltage
s
V = Symmetrical component
2
2
1 1 1
A1
1
??
??
? ? ?
??
??
??
??
Power in terms of symmetrical components
a1 a1 a2 a2 a3 a0
P 3 V I V I V I
? ? ?
?? ? ? ?
??
Remember, same transformation exist for current also.
Sequence Network
Alternators
? Positive Sequence Network
1
Z positive sequence impedance
"
1d
Z jX ?
Page 2
Fault Analysis
Symmetrical Components
For an unbalanced 3 – phase system, the analysis is done better by means of symmetrical
components.
a0
V ? Zero sequence components
a1
V ? Positive sequence components
a2
V ? Negative sequence components
a0 a
2
a1 b
2
a2 c
V 1 1 1 V
1
V 1 V
3
V 1 V
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
??
; Where
0
j120
e ??
? ? ? ?
1
sp
V A V
?
?? ?
??
p
V = phase voltage
s
V = Symmetrical component
2
2
1 1 1
A1
1
??
??
? ? ?
??
??
??
??
Power in terms of symmetrical components
a1 a1 a2 a2 a3 a0
P 3 V I V I V I
? ? ?
?? ? ? ?
??
Remember, same transformation exist for current also.
Sequence Network
Alternators
? Positive Sequence Network
1
Z positive sequence impedance
"
1d
Z jX ?
? Negative Sequence Network
a2 a2 2
V I Z ??
2
Z : Negative sequence impedance
dq
2
X " X "
Zj
2
?
??
?
??
??
? Zero Sequence Network
? ?
a0 a0 0 n
V I Z 3Z ? ? ?
0
Z = Zero sequence impedance
n
Z =Neutral impedance ( ? in case of delta)
0l
Z jX ?
l
X = leakage reactance
Transformers
? Positive Sequence Network
1
Z = Positive sequence impedance
1l
Z jX ?
? Negative Sequence Network
2
Z = Negative sequence impedance
2l
Z jX ?
? Zero sequence network
Depending upon scheme of connection, we close series or shunt connection & method
of grounding.
Page 3
Fault Analysis
Symmetrical Components
For an unbalanced 3 – phase system, the analysis is done better by means of symmetrical
components.
a0
V ? Zero sequence components
a1
V ? Positive sequence components
a2
V ? Negative sequence components
a0 a
2
a1 b
2
a2 c
V 1 1 1 V
1
V 1 V
3
V 1 V
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
??
; Where
0
j120
e ??
? ? ? ?
1
sp
V A V
?
?? ?
??
p
V = phase voltage
s
V = Symmetrical component
2
2
1 1 1
A1
1
??
??
? ? ?
??
??
??
??
Power in terms of symmetrical components
a1 a1 a2 a2 a3 a0
P 3 V I V I V I
? ? ?
?? ? ? ?
??
Remember, same transformation exist for current also.
Sequence Network
Alternators
? Positive Sequence Network
1
Z positive sequence impedance
"
1d
Z jX ?
? Negative Sequence Network
a2 a2 2
V I Z ??
2
Z : Negative sequence impedance
dq
2
X " X "
Zj
2
?
??
?
??
??
? Zero Sequence Network
? ?
a0 a0 0 n
V I Z 3Z ? ? ?
0
Z = Zero sequence impedance
n
Z =Neutral impedance ( ? in case of delta)
0l
Z jX ?
l
X = leakage reactance
Transformers
? Positive Sequence Network
1
Z = Positive sequence impedance
1l
Z jX ?
? Negative Sequence Network
2
Z = Negative sequence impedance
2l
Z jX ?
? Zero sequence network
Depending upon scheme of connection, we close series or shunt connection & method
of grounding.
Shunt connection are closed for delta connection & series connection are closed for star
connection with grounded neutral. If primary & secondary are inter changed then circuit
becomes mirror image.
? Case – 1
If neutral is grounded through an impedance
n
Z
0 T0 n
Z Z 3Z ??
? Case – 2
? Case – 3
? Case – 4
Page 4
Fault Analysis
Symmetrical Components
For an unbalanced 3 – phase system, the analysis is done better by means of symmetrical
components.
a0
V ? Zero sequence components
a1
V ? Positive sequence components
a2
V ? Negative sequence components
a0 a
2
a1 b
2
a2 c
V 1 1 1 V
1
V 1 V
3
V 1 V
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
??
; Where
0
j120
e ??
? ? ? ?
1
sp
V A V
?
?? ?
??
p
V = phase voltage
s
V = Symmetrical component
2
2
1 1 1
A1
1
??
??
? ? ?
??
??
??
??
Power in terms of symmetrical components
a1 a1 a2 a2 a3 a0
P 3 V I V I V I
? ? ?
?? ? ? ?
??
Remember, same transformation exist for current also.
Sequence Network
Alternators
? Positive Sequence Network
1
Z positive sequence impedance
"
1d
Z jX ?
? Negative Sequence Network
a2 a2 2
V I Z ??
2
Z : Negative sequence impedance
dq
2
X " X "
Zj
2
?
??
?
??
??
? Zero Sequence Network
? ?
a0 a0 0 n
V I Z 3Z ? ? ?
0
Z = Zero sequence impedance
n
Z =Neutral impedance ( ? in case of delta)
0l
Z jX ?
l
X = leakage reactance
Transformers
? Positive Sequence Network
1
Z = Positive sequence impedance
1l
Z jX ?
? Negative Sequence Network
2
Z = Negative sequence impedance
2l
Z jX ?
? Zero sequence network
Depending upon scheme of connection, we close series or shunt connection & method
of grounding.
Shunt connection are closed for delta connection & series connection are closed for star
connection with grounded neutral. If primary & secondary are inter changed then circuit
becomes mirror image.
? Case – 1
If neutral is grounded through an impedance
n
Z
0 T0 n
Z Z 3Z ??
? Case – 2
? Case – 3
? Case – 4
? Case – 5
Transmission Lines
? Positive Sequence Network
? Negative Sequence Network
? Zero Sequence Network
1 2 s m
Z Z Z Z ? ? ?
0 s m
Z Z 2Z ??
s
Z = Self impedance
m
Z = mutual impedance
Remembers, all sequence networks are always drawn in per unit & never in actual values.
Fault Analysis
The following short circuit faults are considered
1. LG (Single Line to ground fault)
2. LL (Line to line fault)
3. LLG (Line to Line to Ground fault)
4. 3-phase short circuit fault.
Page 5
Fault Analysis
Symmetrical Components
For an unbalanced 3 – phase system, the analysis is done better by means of symmetrical
components.
a0
V ? Zero sequence components
a1
V ? Positive sequence components
a2
V ? Negative sequence components
a0 a
2
a1 b
2
a2 c
V 1 1 1 V
1
V 1 V
3
V 1 V
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
??
; Where
0
j120
e ??
? ? ? ?
1
sp
V A V
?
?? ?
??
p
V = phase voltage
s
V = Symmetrical component
2
2
1 1 1
A1
1
??
??
? ? ?
??
??
??
??
Power in terms of symmetrical components
a1 a1 a2 a2 a3 a0
P 3 V I V I V I
? ? ?
?? ? ? ?
??
Remember, same transformation exist for current also.
Sequence Network
Alternators
? Positive Sequence Network
1
Z positive sequence impedance
"
1d
Z jX ?
? Negative Sequence Network
a2 a2 2
V I Z ??
2
Z : Negative sequence impedance
dq
2
X " X "
Zj
2
?
??
?
??
??
? Zero Sequence Network
? ?
a0 a0 0 n
V I Z 3Z ? ? ?
0
Z = Zero sequence impedance
n
Z =Neutral impedance ( ? in case of delta)
0l
Z jX ?
l
X = leakage reactance
Transformers
? Positive Sequence Network
1
Z = Positive sequence impedance
1l
Z jX ?
? Negative Sequence Network
2
Z = Negative sequence impedance
2l
Z jX ?
? Zero sequence network
Depending upon scheme of connection, we close series or shunt connection & method
of grounding.
Shunt connection are closed for delta connection & series connection are closed for star
connection with grounded neutral. If primary & secondary are inter changed then circuit
becomes mirror image.
? Case – 1
If neutral is grounded through an impedance
n
Z
0 T0 n
Z Z 3Z ??
? Case – 2
? Case – 3
? Case – 4
? Case – 5
Transmission Lines
? Positive Sequence Network
? Negative Sequence Network
? Zero Sequence Network
1 2 s m
Z Z Z Z ? ? ?
0 s m
Z Z 2Z ??
s
Z = Self impedance
m
Z = mutual impedance
Remembers, all sequence networks are always drawn in per unit & never in actual values.
Fault Analysis
The following short circuit faults are considered
1. LG (Single Line to ground fault)
2. LL (Line to line fault)
3. LLG (Line to Line to Ground fault)
4. 3-phase short circuit fault.
3-phase short circuit fault comes under the category of symmetrical SC fault whereas other 3
faults are called as unsymmetrical SC fault.
Order of severity
LG < LL < LLG < 3 - ? SC
But if faults occur at terminal of alternator then LG fault is most severe.
Occurrence of SC fault
LG > LL > LLG > 3 - ? SC
Transient on a Transmission line
Equivalent Circuit
? ?
t ss
i t i i ??
? ? ? ?
Rt
mm L
VV
sin e sin wt
ZZ
?
? ? ? ? ? ? ? ? ?
? ?
2
12
L
tan ; Z R L
R
?
??
??
??
?
? ? ? ? ?
Maximum momentary current
? ?
m
mm
2V
i sin
Z
? ? ? ?
If resistance is neglected,
0
90 ??
m
mm
i
2V
cos
Z
??
Short circuit model of a synchronous machine
During initial SC period for 1-2 cycles, current are induced in field & damper winding of machine
so reactance at least & called as sub transient reactance ? ?
d
X"
After initial sub-transient period, current in damper winding in reduced to zero, and this period
is called as transient period & reactance of machine is called as Transient Reactance ? ?
d
X"
Read More
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Dec 22, 2024 Last updated |
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