Pag. 62 di 152
8.4.2 Measurement Formulas:
Phase-phase Voltages:
12
U
( )
∑
−
=
=
1
0
2
12
12
1
M
n
n
U
M
U
Where:
( )
n
U
12
are the samples of the chained values.
M is the number of sampling on a period (64)
Phase to phase Voltages THD
23
U
THD
in %
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
12
2
1
0
12
1
0
2
12
12
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
U
N
n
n
U
N
n
n
U
N
n
U
THD
π
π
Line Currents :
3
I
( )
∑
−
=
=
1
0
2
3
3
1
M
n
n
I
M
I
( )
n
I
1
are the samples of the line currents.
THD of the phase currents:
3
I
THD
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
3
2
1
0
3
1
0
2
3
3
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
I
N
n
n
I
N
n
n
I
N
n
I
THD
π
π
Three phase Active Power:
Σ
P
(
) ( )
3
4
1
1
1
0
23
⎥
⎦
⎤
⎢
⎣
⎡
+
=
∑
−
=
Σ
n
I
M
n
U
M
P
M
n
Three phase reactive Power:
Σ
Q
( ) ( )
3
1
1
0
1
23
⎥
⎦
⎤
⎢
⎣
⎡
=
∑
−
=
Σ
M
n
n
I
n
U
M
Q
Three phase apparent Power:
Σ
S
2
2
Σ
Σ
Σ
+
=
Q
P
S
Three phase Power Factor:
Σ
λ
( )
Σ
Σ
Σ
Σ
=
Q
sign
S
P
λ
where
sign
(
x
) is equal to 1 with
x
> 0, to -1 with
x
< 0.
