VAMP 259 - Symmetric Components

4.10 Symmetric components
4 Measurement functions
Technical description
194
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VM259.EN007
4.10. Symmetric components
In a three phase system, the voltage or current phasors may be
divided in symmetric components according C. L. Fortescue
(1918). The symmetric components are:
 Positive sequence 1
 Negative sequence 2
 Zero sequence 0
Symmetric components are calculated according the following
equations:































W
V
U
aa
aa
S
S
S
2
2
2
1
0
1
1
111
3
1
, where
S
0
=
zero sequence component
S
1
=
positive sequence component
S
2
=
negative sequence component
2
3
2
1
1201 ja 
, a phasor rotating constant
U
=
phasor of phase
L1
(phase current or line-to-neutral voltage)
V
=
phasor of phase
L2
W
=
phasor of phase
L3
NOTE! The zero sequence or residual measurement signals connected to the
device are U
0
and 3I
0
. However, usually the name “I
0
” is used instead of
the correct name “3I
0
”
Example 1, single phase injection
U
N
= 100 V
Injection:
U
L1
= U
L12
= 100 V
U
L2
= U
L23
= 0






































33
33
0100
0100
3
1
0
0100
1
1
3
1
2
2
1
a
a
U
U
U
1
= 33 %
U
2
= 33 %
U
2
/U
1
= 100 %
When using a single phase test device, the relative unbalance
U
2
/U
1
will always be 100 %.