Allen-Bradley Rockwell Automation 857 User Manual page 182

5-10
Measurement Functions
857-UM001A-EN-P – July 2009
Example 1 – Single phase injection
U = 100 V
N
Voltage measurement mode is "2LL+Uo".
Injection:
U = U = 100 V
a 12
U = U = 0
b 23
⎡
⎡ ⎤ −
2
U
1 1 a
=
1
⎢
⎢ ⎥
−
⎣ ⎦
U 3 ⎣
1 a
2
U = 33 %
1
U = 33 %
2
U /U = 100 %
2 1
When using a single phase test device, the relative unbalance U
will always be 100 %.
Example 2 – Two-phase injection with adjustable phase angle
U = 100 V
N
Voltage measurement mode is "2LL+Uo".
Injection:
= 100 V ∠0°
U = U
a 12
= 100/√3 V ∠ 1 50° = 57.7 V ∠ 1 50°
U = U
b 23
⎡ ⎤
⎡ ⎤ − ⎡
2
U
1 1 a
=
1
⎢ ⎥
⎢ ⎥ ⎢
−
⎣ ⎦ ⎣
U
3 ⎣ ⎦ 100
a
1
2
⎡ ⎤
∠ − °
100 / 2 3 30
= =
⎢ ⎥
∠ + °
3 ⎣ ⎦
/ 1 3 30
U = 38.5 %
1
U = 19.2 %
2
U /U = 50 %
2 1
Figure 5.4 shows a geometric solution. The input values have been
scaled with √3/100 to make the calculation easier.
⎤ ∠ ° ∠
⎡ ⎤ ⎡
100 0 100
1
=
⎥
⎢ ⎥ ⎢
∠
⎣ ⎦ ⎣
⎦ 0 3 100
∠ ° ⎡
⎤
100 0
100
=
⎢
⎥
∠ − °
⎦
/ 3 150 3 ⎣
∠ − °
⎡ ⎤
38 5 . 30
⎢ ⎥
∠ + °
⎣ ⎦
19 2 . 30
°
⎤ ⎡ ⎤
0 33
=
⎥ ⎢ ⎥
°
⎦ ⎣ ⎦
0 33
/U
2 1
⎤
∠ ° − ∠ + °
1 0 / 1 3 90
=
⎥
∠ ° − ∠ − °
⎦
1 0 / 1 3 30