Sel 411L - Page 117

P.3.9
Date Code 20151029 Protection Manual SEL-411L Relay
Protection Functions
87L Theory of Operation
The generalized Alpha Plane algorithm of the relay selects the angular
position of one of the equivalent currents to align this current with the zone
current that yields the highest torque when projected on the differential
current phasor. This value substitutes for a fourth equation necessary to solve
for the four unknowns.
The relay calculates the following auxiliary signals:
Equation 3.5
where k = 1...N and * stands for a complex conjugate.
The zone current I
k
that yields the highest value to R
(k)
is selected for an
angular reference of one of the two equivalent Alpha Plane currents.
Equation 3.6
Next, an auxiliary signal is calculated as follows.
Equation 3.7
And the relay calculates the following two equivalent currents.
Equation 3.8
Equation 3.9
Following calculation of the two equivalent currents as per Equation 3.8 and
Equation 3.9, the generalized Alpha Plane algorithm derives the complex ratio
of the two currents and applies this to the operating characteristic. The relay
performs these internal calculations independently for the A, B, C, Q, and G
currents.
Note that when a given line terminal is a dual-breaker connection, the remote
relays have no access to the individual phasors of the two currents, only to
their sum. This is a minor limitation to the effectiveness of the generalized
Alpha Plane algorithm; its strength results from reflecting the differential and
through currents of the zone, and these two signals are always represented
correctly at all relays of the 87L scheme.
Also note that the differential and restraining currents are inputs to the
generalized Alpha Plane calculations. We can use protective relaying concepts
to manipulate these currents arbitrarily and cause propagation into the Alpha
Plane. For example:
➤ A line charging current compensation algorithm can reduce the
amount of standing differential signal by calculating the
present charging current and subtracting it from the measured
differential current. Reduction in the differential current shifts
the operating point of the Alpha Plane toward the ideal
blocking point of 1–180°.
➤ A magnetizing inrush restraining algorithm can increase the
level of restraining signal with the harmonics of the differential
current to restrain the element under transformer inrush
conditions. Increase in the restraining current shifts the
operating point of the Alpha Plane toward the ideal blocking
point of 1–180°.
➤ An external fault detection algorithm, upon detecting an
external fault and in anticipation of possible CT saturation, can
increase the level of restraining signal with the harmonics of
R
k
Real I
k
I
DIF
*• =
 Angle I
k
=
I
X
I
DIF
1–• =
NOTE: Numerical instability may
occur for faults that result in
differential and restraint currents of
similar magnitude. To avoid this
instability, the relay forces the result
of Equation 3.8 to 00° under this
condition. For this reason, when
testing the relay under laboratory
conditions that injects the same
current in all terminals, the Alpha
Plane calculation may show a value of
00° instead of the expected value
of 10°.
I
LEQ
Im I
X

2
I
RST
Re I
X
–
2
–
2I
RST
Re I
X
–•
--------------------------------------------------------------------- jImI
X
• +



=
I
REQ
I
RST
I
LEQ
–10• =