Allen-Bradley Rockwell Automation 857 User Manual page 183

Injected line-to-line voltages
Ö3
150°
U
23
Figure 5.4 – Example of symmetric component calculation using line-to-line voltages
Unscaling the geometric results gives
U = 100/√3 x 2/3 = 38.5 %
1
U = 100/√3 x 1/3 = 19.2 %
2
U /U = 1/3:2/3 = 50 %
2 1
Example 3 – Two-phase injection with adjustable phase angle
U = 100 V
N
Voltage measurement mode is "3LN".
Injection:
= 100/√3 V ∠0° = 57.7 V ∠0°
U = U
a L1
= 100/√3 V ∠ 1 20° = 57.7 V ∠ 1 20°
U = U
b L2
U = U = 0 V
c L3
This is actually identical case with example 2 because the
resulting line-to-line voltages U
U = U – U = U
23 L2 L3
example 2. The only difference is a +30° phase angle difference,
but without any absolute angle reference this phase angle
difference is not seen by the device.
⎡
⎢
⎡ ⎤ ⎡ ⎤
1 1 1
U ⎢
0
⎢ ⎥ ⎢ ⎥
1 100
⎢
=
2
U 1 a a
⎢ ⎥ ⎢ ⎥
⎢
1
3
⎢ ⎥ ⎢ ⎥
2
⎢
⎣ ⎦ ⎣ ⎦
U 1 a a
2
⎢
⎣
∠ − °
⎡ ⎤ ⎡
100 60 19
⎢ ⎥
⎢
1
= ∠ ° =
200 0
⎢ ⎥ ⎢
3 3
⎢ ⎥ ⎢
∠ °
⎣ ⎦ ⎣
100 60 19
U = 19.2 %
0
U = 38.5 %
1
U = 19.2 %
2
U /U = 50 %
2 1
2
a U
23
120°
U
12
120°
aU
U
23
23
= U – U
12 L1
= 100/√3 V∠ 1 20° are the same as in
L2
⎤
100
∠ °
0
⎥
⎡
3
100
⎥
⎢
1
⎥
∠ − ° =
120 100
⎢
⎥
3 3 3
⎢
⎥
⎣
100
0
⎥
⎦
∠ − °
⎤
2 . 60
⎥
∠ °
38 5 . 0
⎥
⎥
∠ + °
⎦
2 . 60
5-11
Measurement Functions
FortescueEx2
Positive sequence
U = 2/3
1
Ö3
U
12
2 U -a U
-a U
23 12
U
12
Negative sequence
-aU
U -aU
23
12 23
Ö3
U
12
U = 1/3
2
= 100 V ∠30° and
L2
∠ ° + ∠ − °
⎤
0 100 120
⎥
∠ ° + ∠ ° =
0 100 0
⎥
⎥
∠ ° + ∠ + °
⎦
0 100 120
857-UM001A-EN-P – July 2009
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