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7
Ground Differential Protection (87N)
Figure 7.3
Ground Differential Protection of a Delta
Winding with a Shunt Reactor
7.1
Calculated Quantities
The restraining current, I
separate amplitudes of the measured phase and
ground currents. It is a measure of the total amount of
current flowing through the transformer, regardless of
whether the currents are balanced. It is calculated
according to equation 7.1 and equation 7.2:
=
+
+
i
(
k
)
i
(
k
)
i
(
k
)
i
R
A
B
C
−
N
1
1
∑
=
−
I
(
n
)
i
(
n
k
)
R
R
N
=
k
0
where N is the number of samples taken during each
power system cycle, while i
are the sampled and normalized values of the phase
and ground currents.
The fundamental vector of the ground current, I
calculated using Fourier analysis:
−
N
1
(
)
2
∑
=
−
Re
I
(
n
)
i
(
n
G
G
N
=
k
0
92
, is the scalar sum of the
R
+
(
k
)
i
(
k
)
G
( k ), i
( k ), i
( k ), and i
A
B
C
G
G
k
π
k
)
cos(
2
)
N
(
)
=
Im
I
(
n
)
G
Two calculated current vectors,
components of the algorithm:
Both quantities are calculated using the
Fourier-analysis algorithm described in equation 7.3,
equation 7.4, and equation 7.5.
The differential current, I
amplitude of the vector-difference of the measured
ground current and the calculated zero sequence
current. By convention, any current flowing into the
protected equipment is considered to have a positive
magnitude; so I
equation:
I
OP
1.2
*
I
0
1.0
0.8
0.6
0.4
(7.1)
0.2
0.0
0
(7.2)
EXTENDED TRIP AREA
Figure 7.4
( k )
, is
(7.3)
(7.4)
−
N
1
k
2
∑
π
−
i
(
n
k
)
sin(
2
)
G
N
N
=
k
0
and
, is by definition the
D
is calculated using the following
D
CLASSICAL
TRIP AREA
3 0
6 0
9 0
1 2 0
Trip Area for I*o/Io**=1
7UT51 v3
(7.5)
, are the major
(7.6)
(7.7)
(7.8)
*
* *
=
I
/
I
1
0
0
BLOCK
AREA
1 5 0
1 8 0
ϕ
(degrees)
PRIM-2330C
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