P.3.8
SEL-411L Relay Protection Manual Date Code 20151029
Protection Functions
87L Theory of Operation
traditional Alpha Plane works on the zone currents and would
require each zone current to be compensated individually for
the effect of the line charging current.
➤ Ability to provide in-line transformer protection, particularly
with the advantage of harmonic restraining for the magnetizing
inrush conditions. The traditional Alpha Plane does not
recognize the concept of a restraining signal and cannot
accommodate such applications.
➤ Ability to better restrain the sequence differential elements
(87LQ and 87LG) under external faults that do not generate
any natural restraint for these elements (three-phase
symmetrical faults, for example).
In the following description of the generalized Alpha Plane algorithm, all
currents belong to the same phase of the 87LP element (A, B or C) or are the
negative-sequence (3I2) or zero-sequence (3I0) currents for the 87LQ and
87LG elements, respectively.
➤ I
1
, I
2
, … I
N
are the phasors of the individual currents of the 87L
zone (“partial differential” terms),
➤ I
1RST
, I
2RST
, … I
NRST
are the magnitudes of the currents of the
87L zone (“partial restraint” terms),
➤ I
DIF
is the phasor of the differential current,
➤ I
RST
is the magnitude of the restraining current,
➤ I
L(EQ)
is the phasor of the first equivalent current of the
generalized Alpha Plane,
➤ I
R(EQ)
is the phasor of the second equivalent current of the
generalized Alpha Plane.
The differential current is a sum of phasors of individual currents.
Equation 3.3
Such calculation occurs naturally through the concept of “partial differential”
signals, as explained in Signal Processing. Each relay adds the local currents
prior to transmission, and each relay adds quantities it receives, and the local
quantities, to obtain the true differential signal.
The relay calculates the restraining current magnitude as a sum of the
magnitudes of individual currents.
Equation 3.4
Such calculation occurs naturally through the concept of “partial restraining”
signals, as explained in Signal Processing: each relay adds the magnitudes of
the local currents prior to transmission, the received quantities, and the local
quantities, to obtain the true restraining signal.
The generalized Alpha Plane responds to the differential phasor as per
Equation 3.3 and the restraining scalar as per Equation 3.4 and calculates the
two equivalent current phasors, I
L(EQ)
and I
R(EQ)
. The algorithm selects the
two equivalent currents that yield exactly the same differential current phasor
and restraining scalar in the equivalent two-current zone as in the original
N-current zone. This means that the algorithm starts with three equations (real
and imaginary parts of the differential signal and the level of the restraining
current) to obtain the four unknowns (real and imaginary parts of the two
equivalent currents).
I
RST
I
1RST
I
2RST
... I
NRST
+++=
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