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9.1 OVERVIEW
Sensitivity is the key performance parameter. The applied comparator uses a simple integration method in addition to the
standard hysteresis approach, to deal with chattering of the operating signal at the boundary of operation.
b) BALANCED CASE
To understand how the voltage differential protection works, consider for simplicity the grounded bank operating equation
below.
The ungrounded case is similar except that all voltages have V
an initial capacitance of C
system phase-to-ground voltage V
Substituting these results into equation 8.9, the initial operating signal is:
The match factor setting k
Therefore, as can be seen from the previous two equations, the initial operating signal will be zero.
c) SENSITIVITY
Now consider the consequences of an element failure in the upper sub-string of leg A, making a small capacitance change
in C
. The effect on the operating signal can be calculated by taking the derivative of equation 8.12 with respect to C
1A
holding C
constant. In the general case, the derivative of the absolute value function is messy, but in our case where the
2A
initial value is zero, the derivative of the absolute function is simply the absolute value of the derivative of its argument. The
derivative is thus:
Substituting equation 8.13, we have:
9
This can be written as:
9-4
V
( )
OP A
, divided into sub-strings with initial capacitances of C
A
, then the string will form a voltage divider and the initial measured voltages are:
Spg
V
1A
V
=
2A
V
( )
OP A
=
V
Spg
=
V
Spg
is chosen as:
A
k
d
---------- - V
V
=
(
)
OP 1A
dC
A
=
V
V
=
d
1
×
---------- - V
V
------ -
=
(
)
OP 1A
Spg
dC
C
A
(
)
V
pu
=
(
)
OP 1A
C70 Capacitor Bank Protection and Control System
V
k
V
=
–
1A
A
2A
subtracted. If the initial factory balanced A-leg string has
X
and C
1A
=
V
Spg
C
A
×
--------- -
V
Spg
C
2A
V
k
V
=
–
1A
A
2A
C
A
×
--------- -
–
k
V
A
Spg
C
2A
C
A
×
×
--------- -
1 k
–
A
C
2A
C
2A
=
--------- -
A
C
A
C
⎛
⎞
d
×
A
---------- - 1 k
--------- -
–
⎝
⎠
Spg
A
dC
C
A
2A
k
×
A
–
--------- -
Spg
C
2A
k
×
A
--------- -
Spg
C
2A
dC
×
V
---------- -
or dV
=
(
)
OP 1A
Spg
C
A
(
)
×
Δ
(
)
V
pu
C
pu
Spg
A
9 THEORY OF OPERATION
, and the bank is energized with
2A
(EQ 9.10)
(EQ 9.11)
(EQ 9.12)
(EQ 9.13)
(EQ 9.14)
A
(EQ 9.15)
A
(EQ 9.16)
GE Multilin
(EQ 9.9)
,
A
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