Schweitzer Engineering Laboratories SEL-387E - The Complete List of Compensation Matrices (M = 1 to 12)

Date Code 20080110 Protection Functions 3-15
SEL-387E Instruction Manual
The compensation matrix [CTC(12)] is similar to [CTC(0)], in that it produces no phase shift (or,
more correctly, 360 degrees of shift) in a balanced set of phasors separated by 120 degrees.
However, it removes zero-sequence components from the winding currents, as do all of the
matrices having non-zero values of
m .
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−−
−−
−−
=
211
121
112
•
3
1
12CTC
that is,
(
)
3
ICWnIBWnIAWn•2
IAWnC
−
−
+
=
(
)
3
ICWnIBWn•2IAWn
IBWnC
−
+−
=
(
)
3
ICWn•2IBWnIAWn
ICWnC
+
−−
=
We could use this type of compensation in applications having wye-connected transformer
windings (no phase shift) with wye CT connections for each winding. Using W
n CTC = 12 for
each winding removes zero-sequence components, just as connection of the CTs in delta would
do, but without producing a phase shift. (One might also use W
n CTC = 1 or 11 for this same
application, yielding compensation similar to that from connection of the CTs on both sides in
DAB or DAC.)
The Complete List of Compensation Matrices (m = 1 to 12)
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
101
110
011
•
3
1
1CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
112
211
121
•
3
1
2CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
011
101
110
•
3
1
3CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−−
−−
−−
=
121
112
211
•
3
1
4CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
110
011
101
•
3
1
5CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
211
121
112
•
3
1
6CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
=
101
110
011
•
3
1
7CTC
() []
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−−
−−
−−
=
112
211
121
•
3
1
8CTC