Pag. 65 di 152
8.5.2 Measurement Formulas:
Voltage:
N
U
1
( )
∑
−
=
=
1
0
2
1
1
1
M
n
N
N
n
U
M
U
( )
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
Phase Current:
1
I
( )
∑
−
=
=
1
0
2
1
1
1
M
n
n
I
M
I
Where:
( )
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 Powers:
1
P
( ) ( )
∑
−
=
=
1
0
1
1
1
1
M
n
N
n
I
n
U
M
P
Phase reactive Powers :
1
Q
(
) ( )
n
I
M
n
U
M
Q
M
n
N
1
1
0
1
1
4
1
∑
−
=
+
=
Phase apparent Powers:
1
S
1
1
1
I
U
S
=
Phase Power Factors:
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.
