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3
2
2
paIpcIpbI
pI
&&&
&
−−
=
,
3
2
saIsbI
sI
&&
&
−
=
(2)
3
2
3
pbIpaIpcI
pI
&&&
&
−−
=
,
3
3
sbIscI
sI
&&
&
−
=
(3)
where,
pcIpbIpaI
&&&
,, : Primary side terminal current of transformer
scIsbIsaI
&&&
,, : Secondary side terminal current of transformer
Further, zero-sequence current is eliminated from the relay input current (Ip∗) for the calculation
of the differential current as follows:
IpoIpa
IpcIpbIpaIpapcIpbIpaI
pI −=
++−
=
−−
=
3
)(3
3
2
1
&&&
&
IpoIpb
IpcIpbIpaIpbpaIpcIpbI
pI −=
++−
=
−−
=
3
)(3
3
2
2
&&&
&
IpoIpc
IpcIpbIpaIpapbIpaIpcI
pI −=
++−
=
−−
=
3
)(3
3
2
3
&&&
&
2.2.3.2 β-method (Traditional method) phase matching
This is a traditional method that delta current (phase-to-phase current) on the Star-winding side of
a Star/Delta transformer and phase current on the Delta-winding side of that is introduced into a
relay input for the calculation of the differential current. Traditionally, the phase matching is
realized by Delta connecting the CTs on the Star-winding side and by Star connecting the CTs on
the Delta-winding side. In GRT100, however, it is realized by software.
The followings show calculation formula and current vectors in an example of a transformer
Yd11.
Ipa
Ipb
I
I
Isc
Ip1
Is1
I
3
1
pbIpaI
pI
&&
&
−
=
,
saIsI
&&
=1
(4)
3
2
pcIpbI
pI
&&
&
−
=
,
sbIsI
&&
=2
(5)
3
3
paIpcI
pI
&&
&
−
=
,
scIsI
&&
=3
(6)