Electric Power Systems - Formula Sheet Page 2
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1
2
3Zero, positive and negative sequence fault currents (I
, I
, I
) for a fault at bus n
n-0
n-1
n-2
9
)
=
=
=
,
,
,
;
0
Three-phase fault
Q
Q
Q
−
−
−
=
1
0
2
QQ
−
1
9
=
=
=
)
,
,
,
Single line-to-ground, phase a
Q
Q
Q
−
−
−
+
+
+
0
1
2
=
=
=
=
3
QQ
QQ
QQ
)
−
−
−
0
1
2
9
)
=
−
=
=
,
,
,
;
0
Line-to-line fault, phases b and c
Q
Q
Q
−
−
−
+
+
1
2
=
=
=
0
QQ
QQ
)
−
−
1
2
9
=
)
,
(
)
Q
+
−
=
=
=
1
3
+
QQ
QQ
)
=
−
−
2
0
QQ
−
+
+
=
=
=
1
3
QQ
QQ
)
−
−
2
0
+
=
=
3
=
−
QQ
)
,
,
−
0
Q
Q
−
−
+
+
2
1
=
=
=
3
QQ
QQ
)
−
−
Double line-to-ground fault, phases b and c
2
0
=
=
−
QQ
,
,
−
2
Q
Q
−
−
+
+
=
=
=
0
1
3
QQ
QQ
)
−
−
2
0
Z
, Z
and Z
denote element (n,n) of zero, positive and negative sequence bus
nn-0
nn-1
nn-2
impedance matrix Z
.
bus
If prefault currents are neglected, bus voltages during fault at bus n,
= V
− Z
V
I
bus
F
bus
F
where I
only has one nonzero element being I
– the fault current leaving bus n.
F
n
rms short-circuit current unloaded synchronous machine
( )
1
1
1
1
1
W
7
W
7
−
−
=
−
+
−
+
,
W
(
H
H
/
"
/
’
G
G
Symmetrical (ac)
DF
J
;
;
;
;
;
"
’
’
G
G
G
G
G
( )
( )
( )
=
+
,
W
,
W
L
W
2
2
Asymmetrical (ac+dc)
UPV
DF
GF
[
]
(
( )
( )
2
W
7
J
=
+
−
=
,
W
,
W
2
,
H
,
/
$
2
"
where
"
Asymmetrical (ac+maximum dc)
UPV
DF
;
"
G
Electric Power Systems – Formula Sheet
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