It can be shown that the values of the matrix A, B & C coefficients (see equation 1 and equation 2)
can be pre-calculated in advance depending on the relative phase shift between the reference
winding and other power transformer windings.
Table 57 summarizes the values of the matrices for all standard phase shifts between windings.
Table 57: Matrices for differential current calculation
Matrix with Zero Sequence
Reduction set to On
Matrix with Zero Sequence Reduction set to Off
Matrix for Reference Winding
2 1 1
1
1 2 1
3
1 1 2
- -
× - -
- -
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1227 V1 EN-US (Equation 3)
1 0 0
0 1 0
0 0 1
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1228 V1 EN-US (Equation 4)
Matrix for winding with 30°
lagging
1 -1 0
1
0 1 1
3
1 0 1
× -
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1229 V1 EN-US (Equation 5)
Not applicable. Matrix on the left used.
Matrix for winding with 60°
lagging
1 2 1
1
1 1 2
3
2 1 1
-
× -
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1230 V1 EN-US (Equation 6)
0 1 0
0 0 1
1 0 0
-
-
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1231 V1 EN-US (Equation 7)
Matrix for winding with 90°
lagging
0 -1 1
1
1 0 1
3
1 1 0
× -
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1232 V1 EN-US (Equation 8)
Not applicable. Matrix on the left used.
Matrix for winding with 120°
lagging
1 1 2
1
2 1 1
3
1 2 1
- -
× - -
- -
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1233 V1 EN-US (Equation 9)
0 0 1
1 0 0
0 1 0
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1234 V1 EN-US (Equation 10)
Matrix for winding with 150°
lagging
-1 0 1
1
1 1 0
3
0 1 1
× -
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1235 V1 EN-US (Equation 11)
Not applicable. Matrix on the left used.
Matrix for winding which is in
opposite phase
2 1 1
1
1 2 1
3
1 1 2
-
× -
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1236 V1 EN-US (Equation 12)
1 0 0
0 1 0
0 0 1
-
-
-
é ù
ê ú
ê ú
ê ú
ë û
EQUATION1237 V1 EN-US (Equation 13)
Table continues on next page
Section 6 1MRK 502 066-UUS B
Differential protection
122
Technical manual
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