Electrex X3M, User Manual

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Pag. 59 di 152
8.3.2 Measurements Formulas:
Phase Voltages:
N
U
1
( )
∑
−
=
=
1
0
2
1 1
1
M
n
N N
n U
M
U
where:
( )
n U
N 1
are the samples of the star voltages;
M
is the number of samples on a period (64);
Star voltages THD
N
U
THD
1
in %
1
2
sin ) (
2
cos ) (
2
) (
100
2
1
0
1
2
1
0
1
1
0
2
1
1
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑ ∑
∑
−
=
−
=
−
=
N
n
N
N
n
N
N
n
N
U
N
n
n U
N
n
n U
N
n U
THD
N π π
Line Current (coincident with the phase current ):
1
I
( )
∑
−
=
=
1
0
2
1 1
1
M
n
n I
M
I
( )
n I
1
are the samples of the line currents.
Phase current THD:
1
I
THD
1
2
sin ) (
2
cos ) (
2
) (
100
2
1
0
1
2
1
0
1
1
0
2
1
1
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑ ∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
I
N
n
n I
N
n
n I
N
n I
THD
π π
Phase Active Power:
1
P
;
( ) ( )
∑
−
=
=
1
0
1 1 1
1
M
n
N
n I n U
M
P
Phase reactive Power:
1
Q
( ) ( )
n I M n U
M
Q
M
n
N 1
1
0
1 1
4
1
∑
−
=
+ =
Phase apparent Power:
1
S
1 1 1
I U S
=
Phase Power Factor:
1
λ
( )
1
1
1
1
Q sign
S
P
=
λ
where
sign
(
x
) is equal to 1 with
x
> 0, to -1 with
x
< 0.
Total Active Power:
Σ
P 3 *
1
P P
=
Σ
Total reactive Power:
Σ
Q
3 *
1
Q Q
=
Σ
Total apparent Power:
Σ
S
2 2
Σ Σ Σ
+ =
Q P S
Total Power Factor:
Σ
λ
1
λ λ
=
Σ
where
sign
(
x
) is equal to 1 with
x
> 0, to -1 with
x
< 0.