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Date Code 20020129
Differential, Restricted Earth Fault,
3-13
Overcurrent, Voltage, and Frequency Elements
SEL-387E Instruction Manual
Setting Calculation
General Discussion of Connection Compensation
The general expression for current compensation is as follows:
( )
[
]
ß
ß
ß
à
Þ
Ï
Ï
Ï
Ð
Î
=
ß
ß
ß
à
Þ
Ï
Ï
Ï
Ð
Î
ICWn
IBWn
IAWn
•
m
CTC
ICWnC
IBWnC
IAWnC
where IAWn, etc., are the three-phase currents entering terminal “n” of the relay; IAWnC, etc.,
are the corresponding phase currents after compensation; and [CTC(m)] is the three-by-three
compensation matrix.
Setting WnCTC = m specifies which [CTC(m)] matrix the relay is to use. The setting values are
0, 1, 2, …, 11, 12. These are discrete values “m” can assume in [CTC(m)]; the values physically
represent the “m” number of increments of 30 degrees that a balanced set of currents with ABC
phase rotation will be rotated in a counterclockwise direction when multiplied by [CTC(m)]. If a
given set of such currents is multiplied by all 12 of the CTC matrices, the resulting compensated
values would seem to move completely around the circle in a counterclockwise direction,
returning to the original start position. This is the same as successively multiplying [CTC(1)]
times the original currents, then times each successive compensated result value, a total of 12
times.
If a balanced set of currents with ACB phase rotation undergoes the same exercise, the rotations
by the [CTC(m)] matrices are in the clockwise direction. This is because the compensation
matrices, when performing phasor addition or subtraction involving B or C phases, will produce
“mirror image” shifts relative to Phase A, when ACB phase rotation is used instead of ABC. In
ACB phase rotation the three phases still rotate in a counterclockwise direction, but C-phase is in
the 120-degree lagging position and B-phase leads by 120 degrees, relative to A-phase.
The discussions below assume ABC phase rotation, unless mentioned otherwise.
The “0” setting value is intended to create no changes at all in the currents and merely multiplies
them by an identity matrix. Thus, for WnCTC = 0,
( )
[
]
ß
ß
ß
à
Þ
Ï
Ï
Ï
Ð
Î
=
1
0
0
0
1
0
0
0
1
0
CTC
that is,
IAWnC = IAWn
IBWnC = IBWn
ICWnC = ICWn
The “1” setting performs a 30-degree compensation in the counterclockwise direction, as would a
delta CT connection of type DAB (30-degree leading). The name for this connection comes from
the fact that the polarity end of the A-phase CT connects to the nonpolarity end of the B-phase
CT, and so on, in forming the delta. Thus, for WnCTC = 1, the relay uses the following
[CTC(m)] matrix:
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