Pag. 51 di 152
8.1.2 Measurement Formulas:
Phase Voltages:
N
U
1
,
N
U
2
,
N
U
3
( )
∑
−
=
=
1
0
2
1
1
1
M
n
N
N
n
U
M
U
;
( )
∑
−
=
=
1
0
2
2
2
1
M
n
N
N
n
U
M
U
;
( )
∑
−
=
=
1
0
2
3
3
1
M
n
N
N
n
U
M
U
Phase-phase Voltages:
12
U
,
23
U
,
31
U
( )
( )
[
]
∑
−
=
−
=
1
0
2
2
1
12
1
M
n
N
N
n
U
n
U
M
U
;
( )
( )
[
]
∑
−
=
−
=
1
0
2
3
2
23
1
M
n
N
N
n
U
n
U
M
U
;
( )
( )
[
]
∑
−
=
−
=
1
0
2
1
3
31
1
M
n
N
N
n
U
n
U
M
U
where:
( )
( )
( )
n
U
n
U
n
U
N
N
N
3
2
1
,
,
are the star voltage samples;
M
is the number of samples taken over a period (64);
M
Star Voltages THD
N
U
THD
1
,
N
U
THD
2
,
N
U
THD
3
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
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
2
2
1
0
2
1
0
2
2
2
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
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
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
N
n
N
U
N
n
n
U
N
n
n
U
N
n
U
THD
N
π
π
Line Currents (coincident with the phase currents):
3
2
1
,
,
I
I
I
( )
∑
−
=
=
1
0
2
1
1
1
M
n
n
I
M
I
;
( )
∑
−
=
=
1
0
2
2
2
1
M
n
n
I
M
I
;
( )
∑
−
=
=
1
0
2
3
3
1
M
n
n
I
M
I
( ) ( ) ( )
n
I
n
I
n
I
3
2
1
,
,
are the samples of the line currents.
Neutral Current
N
I
( )
( )
( )
[
]
∑
−
=
+
+
=
1
0
2
3
2
1
1
M
n
N
n
I
n
I
n
I
M
I
Phase Currents THD:
1
I
THD
,
2
I
THD
,
3
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