Sel 411L - Page 122

P.3.14
SEL-411L Relay Protection Manual Date Code 20151029
Protection Functions
87L Theory of Operation
When the relays calculate the differential currents, they will arrive at the
following value.
Equation 3.16
Note that the term:
Equation 3.17
represents the total line charging current the relays calculate through use of
the full line capacitance and the average terminal voltage. In the general case
of N-terminal lines (N = 2, 3, or 4), the algorithm effectively works with the
following term.
Equation 3.18
The average terminal voltage (from Equation 3.18) represents the voltage
profile better than any particular single voltage along the line length, and its
use improves the accuracy of the charging current compensation. Note that the
relays do not use their communications bandwidth to share voltages; the
effective averaging is a result of the signal processing shown in Figure 3.7.
By subtracting the total charging current from the differential signal prior to
using the generalized Alpha Plane algorithm, the relay moves the operating
point to the ideal blocking point (1–180°) when no internal fault conditions
exist. This allows more sensitive settings, particularly for the 87LP element.
Note that the method works properly not only for an already energized line,
but for energizing a line as well. Under this condition, the charging current
that the line-energizing breaker supplies becomes a non-zero restraint term
and the non-zero measured differential signal. The charging current
compensation algorithm calculates and subtracts the charging current in real
time, decreasing the compensated differential current to much lower values,
ideally zero. The generalized Alpha Plane working with a near-zero
differential term and a non-zero restraining term will yield the ideal blocking
point of 1–180°.
Equation 3.13 is a simplification for the purpose of explaining the method.
The actual implementation for a three-phase transmission line uses the matrix
approach to represent both the self- and mutual-capacitances of the line:
Equation 3.19
where we can derive the self- and mutual-components from the positive- and
zero-sequence susceptances of the line, per user settings.
Equation 3.20
Equation 3.21
The charging current compensation is beneficial for long transmission lines.
The lumped parameter model of Equation 3.13 or Equation 3.19, however,
cannot represent these lines precisely. As a result, the algorithm may over- or
under-compensate certain frequency components of the line charging current
(see Figure 3.8, for example). The mismatch between the distributed
i
DIF
i
LOC1
i
LOC2
+ i
MEASURED1
i
MEASURED2
C
LINE
d
-
•
–+==
C
LINE
d
dt
-----
v
1
v
2
+
2
-----------------
• •
C
LINE
d
dt
-----
v
1
... v
N
++
N
-----------------------------• =
i
CHARGE A
i
CHARGE B
i
CHARGE C
C
S
C
M
C
M
C
M
C
S
C
M
C
M
C
M
C
S
d
dt
-----
v
A
v
B
v
C
• =
C
S
1
3 •
------------- B
0
2B
1
+=
C
M
1
3 •
------------- B
0
B
1
–=