Symmetric Components - Allen-Bradley Rockwell Automation 857 User Manual

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:
⎡ ⎤ ⎡ ⎤
S 1 1 1
0
⎢ ⎥ ⎢ ⎥
1
=
2
S 1 a a
⎢ ⎥ ⎢ ⎥
1
3
⎢ ⎥ ⎢ ⎥
2
⎣ ⎦ ⎣ ⎦
S 1 a a
2
S = zero sequence component
0
S = positive sequence component
1
S = negative sequence component
2
1
= ∠ ° = − +
a 1 120 j
2
U = phasor of phase L1
(phase current or line-to-neutral voltage)
V = phasor of phase L2
W = phasor of phase L3
In case the voltage measurement mode is "2LL+Uo" i.e. two line-to-
line voltages are measured, the following equation is used instead.
⎡ ⎤
⎡ ⎤ ⎡
−
2
U U
1 1 a
=
1
⎢ ⎥
⎢ ⎥ ⎢
−
⎣ ⎦ ⎣
U 3 ⎣ ⎦ U
1 a
2
U = Voltage between phases L1 and L2.
12
U = Voltage between phases L2 and L3.
23
When using line-to-line voltages, any zero sequence voltage can not
be calculated.
NOTE: The zero sequence or residual measurement signals
connected to the device are −U
"I " is used instead of the correct name "3I
0
Measurement Functions
⎡ ⎤
U
⎢ ⎥
V
, where
⎢ ⎥
⎢ ⎥
⎣ ⎦
W
3
, a phasor rotating constant
2
⎤
12
⎥
, where
⎦
23
and 3I . However, usually the name
0 0
"
0
5-9
857-UM001A-EN-P – July 2009