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11.7 APPENDIX VIII. DERIVATION OF PHASE FAULT DETECTION USING THE NEGATIVE SEQUENCE IMPEDANCE PLANE
Relating the symmetrical component current to the phase currents.
022
1
0212
021
IIaIaIc
IIaIaIb
IIIIa
++=
++=
++=
Equation A11.8.1
Assume I0 is zero for phase-to-phase faults. Compute the phase-to-phase currents as the difference between any two of the three phase currents in Equation A11.8.1 through Equation A11.8.4.
( ) ( )( ) ( )
2
21
212
0212
021
I3032Iab
I30360I601303Iab
Ia1Ia1Iab
,IIaIaIIIIbIaIab
-=
-+-=
-+-=
++-++=-=
Equation A11.8.2
22
2
12
Ia3j2I33032Iab
faultsABfor601II
:where
==
=
( ) ( )( ) ( ) 2212
022
10212
IaaIaaIbc
IIaIaIIaIaIcIbIbc
-+-=
++-++=-= Equation A11.8.3
( ) ( ) 221221
I3j2IIaaIbc
faultsBCforII
:where
=--=
-=
( ) 3jaa:where
2 =-
( ) ( )( ) ( )
2
21
22
1
021022
1
I3032Ica
I210360I6011503Ica
I1aI1aIca
IIIIIaIaIaIcIca
-=
+-=
-+-=
++-++=-=
Equation A11.8.4
22
12
Ia3j2I21032Ica
faultsCAfor601II
:where
==
-=
Substitute the following identities into Equation A11.8.2 through Equation A11.8.4.